Econometric analysis of the real estate
market and investment
This book provides an economic and econometric analysis of real estate investment and
real estate market behaviour. The author examines fluctuations in the real estate business
to reveal the mechanisms governing the interaction between real estate and other sectors
of the economy.
Addressing new developments in financial and economic research, the workings of the
real estate market are analysed through theory and the use of econometric models, with
real cases demonstrating the applications. The methodology and theoretical developments
in the book are universal to the professions of economics, econometrics and finance, but
it is the first time that many of them have been applied to real estate research, particularly
in book-length format. The author draws upon literature of the business cycle, the
efficient market hypothesis and rational expectations, while applying and discussing
econometric methods that include those used for investigating trends and cycles,
decomposition of trends and cycles, common trends and common cycles, and univariate
and multivariate shock persistence profiles.
This book should prove to be valuable reading for financial economists and
econometricians, real estate researchers and doctoral students and researchers working in
finance with a focus on financial markets.
Peijie Wang teaches in finance and investment at UMIST and University of
Manchester. He has extensive research experience and has published widely in finance,
real estate, economics and econometrics.
Econometric analysis of the real
estate market and investment
Peijie Wang
London and New York
First published 2001 by Routledge 11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York,
NY 10001
Routledge is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2005.
“ To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of
thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.”
© 2001 Peijie Wang
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or
by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or retrieval system, without permission
in writing from the publishers.
British Library Cataloguing in Publication Data A catalogue record for this book is available from
the British Library
Library of Congress Cataloging in Publication Data Wang, Peijie, 1956– Econometric analysis of
the real estate market and investment / Peijie Wang. p. cm. Includes bibliographical references
and index. 1. Real estate investment – Great Britain – Econometric models. 2. Commercial real
estate – Great Britain – Econometric models. 3. Real estate business – Great Britain – Econometric
models. 4. Business cycles – Great Britain – Econometric models.I. Title. HD596 W36 2001
332.63′24′015195–dc21 00–47057
ISBN 0-203-16439-3 Master e-book ISBN
ISBN 0-203-25852-5 (Adobe e-Reader Format)
ISBN 0-415-24181-2 (Print Edition)
Contents
List of figures
vii
List of tables
viii
List of abbreviations and variables
Preface
PART I Preliminaries
1 Background
xi
xiii
1
2
2 Real estate and the economy: preliminary statistics
15
3 Theories of dynamics
31
PART II The dynamic behaviour of economic and financial time series
48
4 Trends, cycles and persistence
52
5 A unified representation of economic fluctuations and dynamics
64
PART III The dynamic behaviour of real estate
80
6 Recapturing market information from appraisal-based real estate indices
81
7 Real estate’s response to shocks
95
8 Price discovery and study of real estate market efficiency
116
9 Cyclical fluctuations in the real estate market
125
10 Summary
Bibliography
140
146
Index of names
159
Subject index
165
Figures
1.1 Investment in property by life assurance companies
9
1.2 Investment in property by general insurance companies
10
1.3 Investment in property by pension funds
11
1.4 Real estate by sector
12
1.5 Overall performance comparison, 1977 Quarter 2–1993
Quarter 2
13
2.1 Relevant time series variables
28-30
3.1 The development of business cycle theory
37
4.1 The effect of a shock to the stochastic trend process
55
4.2 The effect of a shock to the deterministic trend process
56
6.1 Smoothing in the appraisal-based index – original and
unsmoothed JLW quarterly indices against FTAP
90
6.2 Smoothing in the appraisal-based index – original and
unsmoothed IPD monthly indices against FTAP
91
7.1 Persistence in real estate market and other economic activities 98– levels
101
7.2 Persistence in real estate market and other economic activities 102– first difference
105
9.1 Coherence and phase – an example (GDP with lagged GDP)
136
9.2 Coherence and phase – real estate with other variables
138
Tables
1.1
UK Insurance company (long-term) asset structures
6
1.2
UK Insurance company (general) asset structures
7
1.3
UK Pension funds structures
8
1.4
Overall performance comparison: 1977 Quarter 2–1993 Quarter 13
2, quarterly data
2.1
(a)
Property’s correlations with selected economic variables: 1977 19
Quarter 2–1993 Quarter 2 JLW – first difference filter (rates of
change analysis)
2.1
(b)
Property’s correlations with selected economic variables: 1977
Quarter 2–1993 Quarter 2 JLW–Hodrick–Prescott filter
2.2
(a)
Property’s correlations with selected economic variables: 1977 21
Quarter 2–1993 Quarter 2 HPK – first difference filter (rates of
change analysis)
2.2
(b)
Property”s correlations with selected economic variables: 1977 22
Quarter 2–1993 Quarter 2 HPK–Hodrick–Prescott filter
2.3
Cointegration of real estate with selected economic variables:
1977 Quarter 2–1993 Quarter 2 JLW – Johansen procedure
23
2.4
Cointegration of real estate with selected economic variables:
1977 Quarter 2–1993 Quarter 2 JLW – ADF statistic
24
2.5
Cointegration of real estate with selected economic variables:
1977 Quarter 2–1993 Quarter 2 HPK – Johansen procedure
25
2.6
Cointegration of real estate with selected economic variables:
25
20
1977 Quarter 2–1993 Quarter 2 HPK – ADF statistic
6.1
Summary statistics – MF-Shilling method, JLW index
87
6.2
Summary statistics – MF-Shilling method, IPD index
89
6.3
Summary statistics – implied cointegration, JLW
92
6.4
Summary statistics – implied cointegration, IPD
93
6.5
Unsmoothing of the JLW index
93
6.6
Unsmoothing of the IPD index
94
7.1
Transitory components in shocks
106
7.2
Multivariate persistence Vk (with unsmoothed JLW index)
110
7.3
Multivariate persistence Vk (with original JLW index)
110
7.4
Multivariate persistence Vk (with fully-unsmoothed JLW index) 111
7.5
Summary statistics for the money growth model
112
7.6
Multivariate persistence Vk, monetary shocks decomposed
112
7.7
Multivariate persistence Vk, summary of monetary and nonmonetary shocks
113
8.1
Unit root test, Perron’s (1993) model
119
8.2
Cointegration, long-run and short-term relationship,
unsmoothed JLW and FTAP
121
8.3
Cointegration, long-run and short-term relationship, original
JLW and FTAP
122
9.1
Serial correlation in individual series
127
9.2
Feature (cycles) tests: JLW has a feature involving other
variables (with unsmoothed JLW index)
127
9.3
Feature (cycles) tests: other variables have a feature involving
JLW (with unsmoothed JLW index)
128
9.4
Feature (cycles) tests: JLW has a feature involving other
variables (with the original JLW index)
128
9.5
Feature (cycles) tests: other variables have a feature involving
JLW (with original JLW index)
129
9.6
Cointegration and common cycles
130
9.7
Common features tests – coincident common cycles using IV
method
132
9.8
Common features tests. Phase-shifting common cycles using IV 133
method (two lags)
9.9
Common features tests. Phase-shifting common cycles using IV 134
method (four lags)
Abbreviations and variables
ADF
augmented Dickey–Fuller
AIC
Akaike information criterion
AMEX
American Stock Exchange
APT
arbitrage pricing theory
ARIMA
autoregressive integrated moving
average
CAPM
capital asset pricing model
CAR
cumulative abnormal returns
CC
coincident indicator
CO
construction output on new work
CSO
Central Statistical Office
CV
coefficient of variance
DF
Dickey–Fuller
DS
difference stationary
DWG
indicator of fixed investment in
dwellings
DYMIMIC
dynamic multiple indicator, multiple
cause
ECM
error correction mechanism
EMH
efficient market hypothesis
FTA
Financial Times actuary all-share
index
FTAP
property company sector of FTA
GARCH
generalised autoregressive conditional
heteroscedaticity
GDP
gross domestic product
GLT
gilts
GMM
generalised method of moments
GNP
gross national product
HFX
Halifax Building Society house price
index
HP
Hodrick and Prescott
HPK
Hillier Parker property market return
index
IPD
Investment Property Databank
JLW
Jones Lang Wootten property total
return index
LG
lagging indicator
LL
longer leading indicator
M0
narrowly defined money
M4
broad money supply
MNG
manufacturing sector
NCREIF
National Council of Real Estate
Investment Fiduciaries
NO
construction new orders
NPT
number of property transactions
NTW
Nationwide Building Society house
price index
NYSE
New York Stock Exchange
ONS
Office for National Statistics
PDN
industrial production
REH
rational expectations hypothesis
REIT
real estate investment trust
RESA
stock under construction
RESC
change in stock under construction
RMSE
root mean squared errors
SC
Schwartz’s criterion
SL
shorter leading indicator
SUR
seemingly unrelated regression
SVC
services sector
TS
trend stationary
UER
unemployment rate
VAR
vector autoregressive
Preface
This book is on the economic and econometric analysis of real estate investment and real
estate market behaviour in the UK. Issues of fluctuations in real estate and its dynamics
are addressed and examined, to reveal the mechanisms governing the interactions
between real estate and the other sectors in the economy, and to study the ways in which
real estate influences and is influenced by the economy. The term ‘real estate’ is used
throughout the book to mean commercial real estate as in the US, or commercial property
as in the UK.
The book covers theories of economic fluctuations and dynamic analysis, econometric
approaches to investigating economic fluctuations and dynamics, and an empirical study
on fluctuations and dynamics in the real estate market and investment. Its methodology
and theoretical developments are universal to the economics profession, including
econometrics and finance. Most methods in the book are either new in general or new to
real estate research. The empirical part is the applications of the theories and econometric
methodologies.
The book addresses new developments in financial and economic research, as well as
some relevant traditional ideas in finance. The book analyses and explains how the real
estate market works with the theories and models, and demonstrates the applications with
real cases. It would also be a helpful reference book and tool, helping researchers in their
studies and projects with useful methods and procedures, together with their relevance to
real estate research.
The intended audience includes: economists and econometricians who have an interest
in real estate or who are interested in applying theories to real problems; real estate
researchers and teachers who are keen to learn the new developments in financial
econometrics and the ever-growing literature in the area; doctorate students researching
real estate; and researchers working in finance with a focus on financial markets.
It is assumed that the reader has the basic knowledge in econometrics up to univariate
and multivariate regression, ARIMA (autoregressive integrated moving average) models
and Box-Jenkins analysis, and the VAR (vector autoregression) model. In finance and
investment areas, the reader is assumed to have knowledge in fundamentals of corporate
finance, financial markets and investment. There are many excellent textbooks available,
e.g., Econometric Analysis by Greene (1993), Time Series Analysis by Hamilton (1994),
Unit Roots, Cointegration, and Structural Change by Maddala and Kim (1998), and
Introduction to Econometrics by Maddala (1992), for basic econometrics and time series
analysis. With regard to finance and investment, there are Capital Markets by Fabozzi
and Modigliani (1996), Financial Institutions and Markets by Kolb and Rodriguez
(1996), Corporate Finance by Ross, Westerfield and Jaffe (1996), Financial Theory and
Corporate Policy by Copeland and Weston (1992), Financial Management by Brigham,
Gapenski and Ehrhardt (1999), and Investments by Sharpe, Alexander and Bailey (1998).
On the other hand, the book introduces and discusses a number of econometric models
and methodologies which are currently scattered in the literature and yet to be included
and integrated in single books.
The book is divided into three parts and consists of 10 chapters. After an introduction
to the background, current research and the literature in real estate in Chapter 1, a straight
forward and descriptive statistical analysis of the real estate market and performance is
provided in Chapter 2, in relation to relevant sectors or activities in the economy. Real
estate is analysed in levels and in changes, examining both short-term and long-run
relationships. Chapter 3 discusses three related theories with common attributes of
dynamics: the efficient market hypothesis, rational expectations, and business cycle
theory. The discussion leads to empirical examinations of real estate market behaviour in
later chapters. It has been revealed that fluctuations in real estate are linked to the
economic environment in a variety of ways. This constitutes the theme and framework
for this book. It has been made clear that further scrutiny is required to gain insights into
the crucial relationships and underlying mechanism in the real estate market. This is
achieved by utilising and developing more constructive economic and econometric
models and analytical techniques pertinent to the research.
In Chapter 4, time series attributes of cycles, trends and persistence are discussed in
both univariate and multivariate circumstances. It covers decomposition of time series
into cycles and trends; the effects of shocks, e.g., transitory and permanent effects of
shocks; and monetary and real shocks. Attention has been paid to their implications.
Chapter 5 presents a framework for modelling and analysing economic fluctuations and
dynamics. It incorporates common trends and common cycles and analyses common
trends and common cycles at the same time. Phase-shifting common cycles in a nonstationary system are further explored. In these two chapters, which form Part II of the
book, econometric models and analytical approaches are presented, extended and
developed. Fluctuations and dynamic behaviour in real estate investment markets are
prominently exhibited in cycles, trends, their response to shocks and common factors
among them. Consequently, econometric modelling approaches reflecting these time
series attributes and characteristics are explored with statistical explanations and with
economic sense. This part has, in many ways, extended the current literature in the study
of economic dynamics and developed the econometric modelling framework and
strategies which will be utilised to make empirical inquiry into real estate markets.
Chapter 6 is the first step of empirical research in the book. It discusses the smoothing
issues in real estate indices and proposes two multivariate approaches to unsmoothing the
appraisal-based real estate indices. It then applies these procedures to the UK real estate
indices of LaSalle (formerly Jones Lang Wootten) and Investment Property Databank, to
be used in following chapters. Chapter 7 investigates the persistence patterns in the real
estate market, and examines the impact of shocks in other economic and financial
variables on the real estate market. In addition, the effects of monetary and non-monetary
shocks on the real estate market are also studied. In Chapter 8, the price discovery
mechanism in direct and indirect real estate investment markets is investigated. The
analysis takes into account both long-run and short-term relationships between these two
investments. Moreover, it has further examined asymmetry in indirect real estate
investment and direct real estate investment. In Chapter 9, both coincident and phaseshifting common cycles are examined in the economy involving real estate. Common
cycle analysis on its own is an extension of common trend analysis. But common cycles
differ from common trends in that the phase matters in the former, therefore analysis is
more complicated, and sometimes, rather difficult. When these attributes and trend-cycle
behaviour are investigated together in a dynamic system, as proposed in Chapter 5, the
study of this chapter is a further advancement of the previous two chapters, especially
Chapter 7. These four chapters in Part III are an empirical study of the dynamic
behaviour of real estate. Investigations are carried out on important issues pertinent to
revealing the nature and the mechanism of fluctuations and dynamic behaviour in real
estate markets, their close relation to other sectors in the economy. The book emphasises
that real estate is an integrated part of the economy and is treated and examined
accordingly throughout the research. Finally, Chapter 10 is a summary of the book.
Part I
Preliminaries
This book is on the economic and econometric analysis of commercial real estate
investment and commercial real estate market behaviour in the UK. Throughout the book,
the term ’real estate’ refers to commercial real estate as in the US and commercial
property in the UK for abbreviation.
Part I is an introduction to research in the book. It contains preliminary analysis of UK
real estate markets and discusses the research theme and framework of the book. Chapter
1 outlines the background of research in this book and the current state of research in the
area. An initial analysis of UK real estate investment and markets and real estate
performance over the last two decades is carried out to present a general picture of UK
real estate markets and the players. This, together with a literature review on the
contemporary research in the area, forms the background of research in the book, and
advocates and supports why research in this book is required.
Broad descriptive statistics are estimated and reported in Chapter 2, to gain more
intuitive understanding of the real estate market and its relationship with the other sectors
in the economy. In particular, this chapter examines the links between the real estate
market and a large number of the real sectors of the economy and financial markets, in
both the short term and the long run. Chapter 3 set out the research framework and
methodologies for the book. Three closely-related theories of dynamics, drawn from
studies of business cycle, the rational expectations hypothesis, and the efficient market
hypothesis, are discussed with specific reference to real estate.
1
Background
This book studies real estate market behaviour in the UK in an economic and
econometric analytical framework. The book will examine patterns of real estate market
fluctuations, and reveal its relationship with the economy. In particular, it will investigate
the ways in which real estate influences, and is influenced by, the other sectors of the
economy, and identify the sources and mechanism of shock transmission in the real estate
market. As part of this approach, economic and econometric models will be developed to
study real estate fluctuations and dynamics in both the short term and the long run and in
a multivariate environment. Topics including common cycles and common trends,
sources and persistence of shocks, and cointegration, error correction and market
efficiency will be covered.
Research in this book is motivated by the need for a reconsideration of real estate
market behaviour which, until recently, has generally been viewed as different and
distinctive from other financial markets. This separation has failed to develop satisfactory
explanations, and arises from a lack of economic studies on the UK real estate market
utilising modern finance and economic theory. The research will investigate real estate
market behaviour in three related areas: the efficient market hypothesis; rational
expectations; and business cycle theory. These three theories, with specific reference to
real estate market, eventually lead to Real Estate Dynamics – the theme of this book.
Real estate dynamics provides economic and econometric modelling for, and
explanations of real estate’s cyclical movement. It deals with the underlying mechanism
which, in this book, is to be theoretically derived and empirically tested.
Current research in real estate
Most real estate research has been carried out differently and distinctively, compared
with other research are as in finance or economic science in general. Research in real
estate has been largely professional. However, the last decade has witnessed the
reorientation of the study on real estate from professional towards academic and from
surveying and valuation towards finance and economics. Accompanying these trends are
the development and use of real estate performance indices in con-formity with stock
market research; the analysis of real estate market efficiency in a modern investment
analysis framework; the study of real estate market behaviour, expectations and
rationality; and the investigation of the cause and nature of the real estate cycle with
business cycle theories. The studies are sometimes sporadic but encouraging.
Econometric analysis of the real estate market and investment
3
Most studies have been documented in America. The operation and institutional
structures of the American real estate market are by no means the same as in Britain.
However, the implications and methodology of such studies should be useful elsewhere.
Reviewing literature in real estate research, Fisher and Webb (1992) have summarised
six current issues in the analysis of commercial real estate, three of them closely related
with economic and financial theories. They are:
• The macroeconomic and other factors affecting returns, which emphasises APT
(arbitrage pricing theory);
• Risk and return characteristics of commercialreal estate. Most recent studies challenge
the traditional view that real estate outperforms other financial assets. Fisher and
Webb claim this could have resulted from either the use of performance measures that
are not really comparable with other financial markets, or the use of incorrect
measures of risk; and
• Commercial market rental index. Again, one of the major difficulties with estimating
the returns on commercial real estate is the lack of transaction data. A tremendous step
towards improving the ability to monitor real estate market would be achieved by the
development of an index of effective market rental rates.
In fact, the interwoven research topics can be broadened and categorised as following:
real estate in institutional portfolios; risk, return and performance comparisons; the
derivation of transaction-driven data or indices; tests on real estate market efficiency;
behaviour of real estate market and prices; and analysis of the real estate cycle. Most of
the studies rely on a reliable measurement of real estate prices and performance.
Webb, Miles and Guilkey (1992) generate a transaction-driven commercial real estate
return series to determine whether the reliance on appraised values in the estimation of
real estate returns is the source of the reported underpricing of real estate relative to
shares, bonds and government securities when analysed in the traditional mean-variance
point of view, an equilibrium pricing model such as the CAPM (capital asset pricing
model), or a Markowitz efficient portfolio. While they find that the transaction-driven
real estate returns have greater variance than appraisal-based returns for individual
properties, most of the individual real estate risk is idiosyncratic and diversified away at
the portfolio levels, which makes them claim that real estate continues to be a dominant
asset class even when represented with transaction driven indices. In a sense, this
suggests that smoothing in real estate return indices is, in fact, not a big issue at the
portfolio level – a finding similar to Wang (1995a, 1995b) which allege that the weight of
real estate in a three asset portfolio is not sensitive to the degree of unsmoothing applied
to the appraisal based index.
Similar research is conducted by Miles et al. (1990) who inquire why commercial real
estate only makes up a relatively small percentage of most institutional portfolios, even
though the existing literature has consistently reported attractive risk-return
characteristics that would suggest much larger allocations. This discrepancy has been
explained by a perceived lack of comparability between return series calculated for real
estate and those calculated for other asset classes. They make adjustments, using sales
data from real estate that help comprise the NCREIF/FRC (National Council of Real
Estate Investment Fiduciaries/Frank Russell Company) index, to generate a ‘transactiondriven’ commercial real estate return series. They find that: risk adjusted real estate
Background
4
returns of the transactionbased series are more consistent with other asset classes than the
appraisal-based returns; real estate investment still presents an attractive diversification
opportunity for shares, bonds and government security portfolios; and real estate is not a
homogeneous asset, advising there is a need for further research on the performance of
subcategories within this broad asset class.
Liu et al. (1990) investigate the consequences of several imperfections associated with
real estate markets on pricing and optimal investor portfolios in a CAPM context. CAPM
assumptions are relaxed to recognise illiquidity and segmented market structure, and that
illiquidity reduces the extent to which investors hold real estate in their portfolios.
Chan et al. (1990) employ a multi-factor arbitrage pricing model using prespecified
macroeconomic factors to analyse monthly returns on equity REITs (real estate
investment trusts) which are not appraisal based. Their findings are, when a single factor
CAPM model is used, excess returns still seem to exist as in the case of appraisal based
returns; when a five factor APT model is utilised, the evidence of excess returns
disappears; and real estate is not seen to be a hedge against inflation.
The relationship between stock market and real estate market returns is examined by
Gyourko and Keim (1992). They analyse the risks and returns of real estate related firms
traded on NYSE (NewYork Stock Exchange) andAMEX (American Stock Exchange),
and the relation between real estate share portfolio returns and returns on a standard
appraisal-based index. It has been found that lagged values of traded real estate portfolio
returns can predict returns on the appraisal-based index after controlling for persistence in
the appraised series. The stock market reflects the information on the real estate market
that is later imbedded in infrequent real estate appraisal.
Empirical tests on real estate market efficiency can be found in Guntermann and
Norrbin (1991), who use a dynamic multiple indicator, multiple cause (DYMIMIC)
model to test market efficiency; in Case and Shiller (1989), McIntosh and Henderson
(1989), Rayburn et al. (1987), and Gau (1984), who adopt a forecasting approach; and in
Guntermann and Smith (1987) and Linneman (1986), who employ a traditional financial
analysis approach. These studies generally find some evidence of market inefficiency, but
the results are more or less mixed.
A recent study on real estate market efficiency and rational expectations is by Tegene
and Kuchler (1993). The methodology employed is cointegration tests on present value
models, as proposed by Campbell and Shiller (1987). They conduct tests for the
contribution of speculative bubbles to farmland prices. These tests are carried out under
the hypothesis that farmland investors rationally form expectations. They infer whether
farmland prices are determined by market fundamentals – discounted returns from the
highest economic land use, or whether rumours about farmland price movements are selffulfilling. They find little to reject the hypothesis that market fundamentals determine
farmland prices.
Tegene and Kuchler (1991) also use Campbell and Shiller’s present value models to
test the way in which the expectations are formed, and the implications of the present
value model. They find, combined with rational expectations, the present value
hypothesis is strongly rejected, while combined with adaptive expectations, the
hypothesis is accepted.
In the UK,Wang and Matysiak (1994) investigate the regional patterns in commercial
real estate rent fluctuations and movement. Their study confirms that there is regional
Econometric analysis of the real estate market and investment
5
segment, and London and the Southeast lead other regions in rent adjustments. Following
Wang and Matysiak (1994) and Matysiak and Wang (1995), Campeau (1994) examines
the geographical patterns and the relationships between unsecuritised real estate
investment and securitised real estate investment, by investigating the valuation process
and the data generating process underlying these investments. Barkham and Geltner
(1995), in a Granger causality framework, find a long-run price discovery mechanism to
link direct investment in real estate and investment in real estate company shares. Similar
findings have also been documented in Lizieri and Satchell (1997) and Wang et al.
(1997). In real estate index research, Blundell and Ward (1987) were the first to address
the issue of smoothing and pioneered an approach to correcting for smoothing in the
appraisal based real estate indices. Valuation accuracy is discussed in Lizieri and
Venmore-Rowland (1991, 1993), and Matysiak and Wang (1995), among others. The
diversification potentials of real estate in multi-asset portfolios are studied by MacGregor
and Nanthakumaran (1992), confirming US studies that real estate is a dominant asset
class for diversification.
It can be seen from the above review that tremendous efforts have been made in real
estate research, and significant results and findings have been achieved in recent years.
However, frontiers remain and the task is as large and hard as before. Price and return
dynamics has yet to be examined thoroughly in a rigorous economic and econometric
analytical framework. Specifically, factors which influence real estate performance and
the ways in which they influence and are influenced by real estate performance have yet
to be inspected; the mechanism of adjustments between real estate and other sectors in
the economy has yet to be probed; and the patterns of real estate in response to shocks of
a different nature have yet to be observed. This book is, therefore, a timely project in the
course of search for knowledge, understanding, and solutions.
Real estate investment and markets
Institutions
The institutions are the main investors in the real estate market with their real estate
holdings amounting to £53 billion at the end of 1993, according to Financial Statistics. It
would then be helpful to look into asset structures of the institutions, especially their real
estate holdings over time as they control a majority of total real estate investment.
Callender and Key (1996) estimate that about 45 per cent of commercial real estate in the
UK is held by ‘investors’, and roughly half of this is held by institutions. Of the
remaining 55 per cent, not all is owner-occupied In addition to direct investment in real
property, the institutions also have substantial equity holdings in real estate companies as
will be seen in the next section for real estate company analysis.
The post-war period has witnessed rapid growth of real property in the economy, in
volume as well as proportion. After the real estate boom in the 1950s and early 1960s, a
period of strong direct institutional investment ran from the mid-1960s through to 1981
when the institutions had over 20 per cent of their assets in property. This was largely
fuelled by the hypothesis that real estate was a hedge against inflation.
Background
6
Soon after the real estate mini-boom of 1979 to 1981, the institutions began to realise
then that it was difficult to engage in asset allocations when real estate was involved, due
to its illiquidity compared with other financial investment, e.g. equities, corporate bonds
and gilts. Many insurance companies and pension funds started rethinking and taking the
view that, on detailed analysis of volatility, liquidity and returns, real estate was less
attractive in the medium and longer term than equities. The fact that the institutions had
too much real estate at the wrong price resulted in the gradual reduction of their real
estate holdings since 1981, in order to have more flexibility in portfolio management and
to improve performance.
The structural change in real estate finance also contributed to the decline of
institutional investment in real estate during the 1980s. Bank lending to real estate
companies fuelled the expansion of a new generation of entrepreneurial developers and a
largely debt financed development boom took off in this period. The level of bank
lending to real estate companies rose dramatically in the second half of the 1980s, from
around £8 billion in 1986 to over £40 billion in 1991. The effect of the removal of
constraints on international investment which enabled a massive inflow of funds into UK
real estate market contributed to the reduced significance of institutional investment.
Detailed information on the asset structure of institutions is provided in Tables 1.1 to
1.3. The analysis at disaggregated level for insurance companies provides a clearer
Table 1.1 UK Insurance company (long-term) asset
structures
Year
1970
1975
1980
1985
1990
1993
Govt
securities
Equities Bonds Mortgages
Land and
property
Others
Total
3533
3202
2511
2332
1692
513
13781
26
23
18
17
12
4
100
6269
5062
2783
3016
4350
1863
23342
27
22
12
13
19
8
100
15469
16596
2061
3424
12362
3786
53746
29
31
4
6
2
7
100
32915
54673
4960
4268
20162
26
43
4
3
16
35892
100130
13306
6883
34828
16
43
6
3
15
66659
166291
28015
8071
30684
19
47
8
2
9
11189 128167
9
100
40275 232314
17
100
53763 353491
15
Sources: British Association of Insurers, Office for National Statistics: Financial Statistics
Note: First line for each year shows value (£ million, current market value, second line shows
percentage)
100
Econometric analysis of the real estate market and investment
7
Table 1.2 UK Insurance company (general) asset
structures
Year Govt securities Equities Bonds Mortgages
1970
1975
1980
1985
1990
1993
Land and Others Total
property
273
443
194
92
106
562
1671
16
27
12
6
6
34
100
1082
963
316
182
437
1566
4548
24
21
7
4
10
34
100
3279
2638
720
296
1280
29
23
6
3
11
6381
6264
1763
381
1595
31
30
9
2
8
8198
10251
3047
1854
3288
19
23
7
4
7
16942
10378
5009
1014
2059
28
17
8
2
3
3302 11516
29
100
4332 20716
21
100
17578 44216
40
100
24636 60068
41
100
Sources: British Association of Insurers, Office for National Statistics: Financial Statistics
Note: First line for each year shows value (£ million, current market value, second line shows
percentage)
picture as life and general insurance companies operate differently. Quite plausibly,
insurance companies with a long-term nature hold larger proportions of land and real
estate than their non long- term counterparts. The size of the assets of long-term
insurance companies is far larger than that of general insurance firms. Due, in part, to
legislative changes, pension funds have been growing rapidly and exceeded the insurance
funds in mid 1980s to become the largest sector in institutional investment. The
percentage of the assets allocated to real estate and land by pension funds is about twothirds of that by long-term insurance companies.
Figures 1.1 to 1.3 depict changes in institutional real estate and equity holdings over
the last two decades. The drop in real estate holdings by institutions, measured in
percentage terms, is actually attributed to the rapid growth of their investment in equities.
Not until 1990 did real estate experience decline in values, when it was most hit by the
recession. At the peak in 1980, real estate accounted for 23 per cent of the total assets
held by long-term insurance companies and valued at £12.4 billion; by the end of 1993,
the proportion of real estate dropped to 9 per cent, despite the fact that the value of real
estate has more than doubled and was worth £30.7 billion. The biggest investment made
by long-term insurance companies is in equities, which accounted for nearly half of the
total assets at the end of 1993 and has increased ten fold in value since 1980. Regarding
pension funds, the patterns were similar to that of long-term insurance companies. The
only difference is that equities had an even larger share amongst total assets. The asset
Background
8
Table 1.3 UK Pension funds structures
Year
1970
1975
1980
1985
1990
1993
Govt Equities Bonds
securities
Loans and
mortgages
Land and
Property
Property Others
unit trust
Total
1422
3886
1099
274
645
120
139
7836
18
50
14
4
8
2
2
100
2573
8207
–
249
1946
327
148
14467
18
57
–
2
14
2
1
100
12034
29375
–
271
8170
1460
1208
54712
22
54
–
1
15
3
2
100
28631
99842
2536
376
13190
2257
18
63
2
0
8
1
33414
189607
7748
258
26363
1656
11
63
3
0
9
1
37939
266480
7489
262
20240
1804
10
68
2
0
5
1
3974 157376
3
100
18580 302670
6
100
29549 390017
8
100
Sources: Office for National Statistics: Financial Statistics
Note: First line for each year shows value (£ million, current market value, second line shows
percentage)
structure of general insurance companies began to differ from that of their long-term
counterparts from the 1970. The proportion of both equities and real estate holdings
declined in the last 20 years, with real estate accounting for only 3 per cent in 1993.
Conceivably, these companies invested heavily in gilts, the bonds issued by the UK
government and are regarded to stand for riskless investment.
No comprehensive separate figures for insurance companies and pension funds’
disaggregate real estate by sector are available. Nevertheless, data and samples from real
estate research and consulting agencies could be representative. e.g., IPD (Investment
Property Databank) provide their fund structures separately for insurance companies and
pension funds. According to IPD and Figure 1.4, at the end of December of 1992, the
allocations to retail, office and industrial properties were 41 per cent, 44 per cent and 15
per cent respectively. IPD data bank comprises 157 funds at the end of 1991 with the
values of these funds amounting to over £31 billion, covering more than 17,000
individual properties. The funds in IPD’s databank make up half of the institutional real
estate holdings, and is the largest information collection on UK investment real estate,
sponsored by six major firms of chartered surveyors. Historically, the retail sector has
increased from about 30 per cent of total real estate in 1981 to over 40 per cent in 1992.
A large decline took place in the office sector, hit severely by the last recession. The
proportion of office real estate dropped from 56 per cent in 1981 to 44 per cent in 1992,
but the pre-recession figure in 1988 was still as high as 52 per cent. The portion of
Econometric analysis of the real estate market and investment
9
industrial real estate was relatively small and less than 15 per cent during all the time.
Changes in IPD’s sectoral allocation during the last recession reflect a
Figure 1.1 Investment in property by
life assurance companies.
Source: Office for National Statistics Financial Statistics
pattern consistent with changes in capital values and rental growth in all sectors.
Real estate companies
Real estate companies are one of the major players in the real estate market, may be only
second to the institutions. They are actively engaged in real estate development,
investment and trading. The activities of big companies usually cover all of these three
aspects, while the small ones are mostly involved in trading only. For example, Land
Securities, British Land and MEPC groups all have a diverse portfolio of offices,
shopping centres, out of town retail, food superstores, industrial and warehouse buildings
in the UK, invest in all kinds of commercial properties, and are additionally involved in
real estate trading and development.
According to market capitalisations the top ten real estate companies in mid 1994, in
addition to Land Securities, MEPC and British Land, were Hammerson, Slough Estate,
Capital Shop Ctrs, Great Portland, Brixton, Burford, and Bradford. These ten companies
accounted for 58 per cent of the total market capitalisations within the real estate
company sector listed on the London Stock Exchange, and they had a market share larger
than there maining 80 companies. As a result, analysis of the accounts of two or three of
these major companies is helpful in providing a general picture of their financial
structures, activities and related parties. The overall performance of the real estate
Background
10
company sector as measured in total returns on its share index (the combination of gain in
share prices and dividends) will be examined later in this section as against other
investment alternatives.
Real estate companies, as described above, develop, invest in, and deal with
Figure 1.2 Investment in property by
general insurance companies.
Source: Office for National Statistics Financial Statistics
properties. Real estate company shares are thus a surrogate for real estate (Isaac 1994).
They also provide a channel for investment in real estate for the investors who either lack
large financial resources, or management skills to invest in real estate directly. To invest
in real estate company shares allows people to ‘buy’ real estate piecemeal – some
thousand pounds against a whole real estate worth millions of pounds. In addition, real
estate company shares are, just like any other stock market investment, highly liquid, and
normally can be traded many times in a single day, in contrast with real property trading
which can take several months to complete a transaction. Due to these factors, real estate
company shares are financial vehicles providing a medium for indirect investment in real
estate. This indirect investment, while enjoying liquidity and divisibility, should reflect
the performance of the underlying real estate in some way. The value of a real estate
company’s shares bear some relationship to the value of the real estate it owns and the
income it derives from real estate operations, but the link is not so straightforward. First,
real estate company shares are stock market investment. They will fluctuate on the
market, depending on the value of real estate owned, but the stock market will also tend
to discount expected economic and financial events before they happen, while valuations
may lag the events. Therefore, real estate company shares may lead real estate in time
sequence. Expressed in econometric terms, the former may Granger-cause the latter,
Econometric analysis of the real estate market and investment
11
although the true cause and effect are more likely to be the other way round.
Nevertheless, the two sharply dissimilar types of investments inevitably exhibit
differential performance. This is particularly true in timing of returns and cash flows.
This means that the two investments have little short-term resemblance, as reported in a
number of studies. Second, real
Figure 1.3 Investment in property by
pension funds.
Source: Office for National Statistics Financial Statistics
estate companies are geared, and the effect of gearing is higher volatility in real estate
company shares. Third, dividend policy tends to induce additional volatility with regard
to uncertainty in the timing and amount of cash flows, as observed empirically. Fourth,
tax regimes also affect the profit and performance. While real estate company
shareholders are double taxed on the one hand, they do enjoy a corporate tax shield on
the other due to the leverage or gearing which is typically high in real estate companies.
The combined effects could benefit or disfavour investors, depending on the individual
companies and investor utilities.
Performance assessment
The overall performance of real estate company shares, the institutional real estate
investment, and general stock market investment is depicted in Figure 1.5. Descriptive
financial figures are reported in Table 1.4.
From Table 1.4, it can be seen that the real estate company sector share index,
represented by FTAP (Financial Times actuary all-share index’s real estate sector), has
the highest coefficient of variance (CV), a number dividing the variance by the rate of
Background
12
return, thus a rough measure of excess returns required for bearing additional risk.
Although CV is not recommended as a measure for ranking investment opportunities due
to a number of defects, it does provide a means to link return to risk or a risk adjusted
return, and it is all that is needed for the moment. Compared with the FTA all share
index, it has a lower return and higher volatility, and seems to be inferior to the general
stock market investment. The real estate investment has a much lower standard deviation,
2.71 for the JLW (Jones Lang Wootten)
Figure 1.4 Real estate by sector
Source: IPD
property index and 3.94 for the HPK (Hillier Parker) property index. However the
comparison of real estate company shares with real estate investment is not readily
applicable due to possible smoothing in the valuation- based real estate performance
index. The difference also exists between the two indices for real estate investment–the
CV of the JLW is 0.95 and that of the HPK is 1.18. The HPK index, based on
hypothetical properties, is claimed to react to market movement briskly, which is
reflected in its higher CV. Even so, according to the HPK, real estate still has a relatively
Econometric analysis of the real estate market and investment
13
low volatility, and is preferred to the investment in real estate company shares in terms of
CV, even if the FTAP figure is adjusted down for the effect of gearing. In fact, degearing
is unlikely to change much in CV, when both variance and rate of return become lower.
One of the interesting points displayed by Figure 1.5 is that real estate and real estate
company shares tend to move closely in the short to medium term. Since 1990 real estate
company shares, in line with real estate, have dropped considerably with possible over
reaction to their underlying operations, while the general stock market investment,
measured by the FTA all- share index, has kept growing. It
Figure 1.5 Overall performance
comparison, 1977 Quarter 2–1993
Quarter 2.
Sources: Jones Lang Wotton, Hillier Parker
Table 1.4 Overall performance comparison: 1977
Quarter 2–1993 Quarter 2, quarterly data
JLW
HPK
FTAP
FTA
GLT
r
2.85
3.33
3.51
4.93
3.48
σ
2.71
3.94
12.17
9.64
6.69
CV
0.95
1.18
3.46
1.95
1.92
then seems reasonable to model real estate with real estate company shares. But this
stance should only be taken with caution and more enquiries are needed to reach a
satisfactory conclusion.
Background
14
Organisation of the book
The book is organised as follows. Part 1 is the preliminaries of research of the book. It
first outlines background of research in this book and the current state of research in the
area. It is then devoted to the general discussion on real estate investment and the market,
and of descriptive statistics for real estate and the economy. These would generally
present a picture of various facets for real estate with its performance in relation to
economic fluctuations, in aggregate as well as in specific but pertinent sectors. The
purpose is to reveal that fluctuations in real estate are linked to its economic environment
in a variety of ways; and research methodologies and contents in the later parts of this
book reflect these views. These analyses, together with the review on the recent
developments in the real estate research literature, outline the issues and set the
framework for advanced studies in the subsequent parts of this book.
Part 2 will study the issue of economic fluctuations in real estate research.
Econometric models and analytical approaches will be presented, extended and
developed. To match the characteristics of real estate revealed and the views expressed in
Part 1, the methodology and approaches to studying real estate will be used to examine
real estate in an integrated economic system implied by the multivariate time series
modelling strategy. In particular, this part will study fluctuations and the dynamic
behaviour in real estate investment markets in terms of cycles, trends, their response to
shocks, and the common factors which real estate shares with other economic and
financial sectors in both the short and long run. This part attempts to advance the current
literature in the study of economic dynamics and develop the econometric modelling
framework and strategies which will be utilised to make an empirical inquiry into UK
real estate markets.
Part 3 will study the dynamic behaviour of real estate in the UK empirically. This part
will extend real estate research to such areas outlined in part I which are either new or
remain important and unsolved, and apply both existing econometric approaches and the
approaches developed in the previous chapters to the inquiries. Issues of real estate
fluctuations and dynamics in both the short term and the long run, with specific reference
to cycles, market efficiency and expectations, will be studied in detail. The last chapter
will summarise the book and highlight the findings.
2
Real estate and the economy
Preliminary statistics
In recent years, a small number of researchers have adopted regressional analysis in
levels between direct real estate investment performance and real estate company shares.
Although the results challenge the early perception or judgement that the performance of
real estate has little relationship with that of other financial market investments, and thus
cannot be explained by or predicted via the latter, the results are somewhat mixed. This
type of approach is motivated by the search for an easy way to describe and explain real
estate performance and real estate market behaviour in the absence of reliable
transaction-driven market data. However, analysis has been restricted to the stock market
arena. There are no reasons, nor evidence, to support the idea that real estate company
shares should necessarily behave similar to real estate. First, the investment undertaken
by real estate companies rather small portion of total investment in commercial real
estate. Second, real estate companies’ assets are geared which, along with company
management, accounting policies and taxation, would cause a big variation in
performance. And third, real estate investment, though a financial investment as well, is
by little means a stock market bustle; rather, it is more interacted with the economic
activities in the real sectors.
The purpose of this chapter is to provide a straightforward and descriptive statistical
analysis of real estate performance, in relation to relevant sectors or activities. The time
series data sets used are:
• House prices, drawn from the Halifax Building Society House Price Index (HFX) and
the Nationwide Building Society House Price Index (NTW);
• Indicators of fixed investment in dwellings (DWG);
• Number of property transactions (NPT);
• Construction output (CO) and new orders1 (NO), two new series standing for stock
under construction (RESA) and the change in stock under construction2 (RESC) being
created;
• The cyclical indicators including longer el ading (LL), shorter leading (SL), coincident
(CC), and lagging indicators (LG).
The graphs of these indicators (except cyclical indicatiors) are shown in Figure A2.1 in
the appendix to this chapter. It can be observed that they display similar patterns as real
estate, suggesting that there might exist some kinds of relationships between real estate
and these indicators.
There are two types of relationships, those of long-run nature and those of short term
characteristics, will be of general interest here. These two types of relationships in
economic and financial terms will be reflected and distinguished in their time series
Econometric analysis of the real estate market and investment
16
characteristics too, and the latter are employed only to serve as useful analytical tools for
the former.
Long-run characteristics in economics and finance are usually associated with nonstationarity in time series and called trends. Whereas short-term fluctuations are
stationary time series and called cycles. Economic time series can be viewed as
combinations of these components of trends and cycles. However, there are two different
kinds of trends and non-stationarity, and they behave rather differently. One view on
economic time series is that economic variables can be decomposed into a secular or
growth component and a cyclical component. The secular component is assumed not to
fluctuate much over the short term but rather move slowly and smoothly relative to the
cyclical component, and is therefore called deterministic trend. Stationarity is achieved
via detrending of time series by regression on time, with the residuals being cycles, and
the time series is accordingly a trend stationary (TS) process. The other kind of trend, in
contrast to the deterministic trend, has no tendency to return to a deterministic trend path.
Stationarity in such time series is achieved by taking difference operations, and the time
series is difference stationary (DS). Though both DS and TS time series are nonstationary prior to transformation, their behaviour is different. Consequently, the
behaviour of economic and financial activities, depending on which kind of time series
they subscribe to, differs too. Typically, a shock to a TS series would have a one-off
effect but no permanent effect on the time series; or, in other word, no permanent effect
on the economic activity levels. Whereas a shock to a DS series would permanently
change the path of the time series; or permanently move the activity to a different level,
either higher or a lower level. Details of these two types of non-stationarity will be
discussed in Chapter 3 in the section on business cycles.
Each activities behaviour is, therefore, analysed in levels and in changes, examining
both short-term and long-run relationships. In the long run, variables’ current positions
are derived either via the accumulation of past innovations,3 fea tured by difference
stationary, or from the deterministic trends over a long period, featured by trend
stationary. The tests on long-run relationships between two non-stationary series, are
referred to as cointegration analysis. With regard to the short-term behaviour, previous
studies usually restrict themselves to analyses in rates of returns or changes in prices.
This implicitly presumes a stochastic trend or random walk stance. While the line
between DS and TS is not clear cut, it is worthwhile to tackle the associations between
series in a TS manner. This is achieved via a HP filter, 4 named after Hodrick and
Prescott (1980). The conventional rate of return approach amounts to a first difference
filter which permits the least low frequency (equivalent to long cycles) components to
pass through, the linear filter permits the most, and the HP filter stands in between.
Depending on the values chosen for the parameters with a HP filter, the series after the
filtering would contain the highest frequency components plus the wanted lower
frequency components. Compared with first difference filters, HP filters retain some
medium cycles. That means the relationships between HP filtered data are concerned
with short and medium terms. In the following, the statistics from applying the HP filter
and the first difference filter for stationary series are reported, along with the analysis in
levels for non stationary series in the long run.
The compilation methodology of cyclical indicators means they are detrended and,
presumably, stationary. So the relationship between cyclical indicators and other data
Real estate and the economy
17
series associated with economic activity levels will not be considered. Only those series
showing movements around their trend values, which could either be obtained via HP
filters or by taking first differences, may have meaningful comparisons with cyclical
indicators. Cyclical indicators are the composite of several series and are compiled to
show consistent timing relationships with peaks and troughs in the growth of overall
economic activity. There are four of them in general use. A longer leading index indicates
turning points in activity about thirteen months in advance; a shorter leading index
indicates turning points about five months in advance; a coincident index generally
moves in line with the business cycles; and a lagging index displays turning points about
twelve months after they took place, and hence is completely useless operationally.
Construction is by all means relevant to real estate development. The relationships
may not be clear using conventional statistical methods and simple measures of
construction activity such as indicators for output and new orders, due to the timing
differences. There are time lags and leads in these two indicators with reference to real
estate development, which weakens a probable statistical relationship linking real estate
to either of them individually. Conceive each of the three variables adjust to the other
two’s activities, then there may exist a stronger, nevertheless, complicated relationship
among them dynamically. In this concern, two series have been created standing for the
stock of uncompleted orders and the change in stock of uncompleted orders. Two
methods are used to generate the series as follows:
(a) Cointegration regression, with the cointegration residuals in the statistical term as the
change in stock in the economic term, and the accumulation of residuals in the
statistical term as the stock the economic term; and
(b) The change in stock is the subtraction of output from new orders, then the stock is the
accumulation of the former. This method is much more straight forward to show the
economic sense of numerical operations, although it is less precise as it in fact imposes
an untested but reasonable restriction on the cointegration vector, i.e., the
cointegration vector is [1, 1].
The correlation between real estate performance and the selected economic variables is
reported with both lags and leads. For reasons explained previously, the analysis of
relationships in levels involves neither lags and leads,5 nor cyclical indicators. The
cyclical indicators are stationary by construction, so their relationship with real estate is
only examined in the difference but not in levels.
The short term
As discussed before, the short term is referred to stationary time series or processes. The
correlation statistic is usually used as an indicator about the short-term relationship
between two stationary time series. For the reason that real estate may lag or lead other
sectors, and therefore a contemporary correlation may not be sufficient to reveal the
relationship, the correlations up to four periods of lags and leads are reported in Table
2.1A and Table 2.1B.With the quarterly data used in this book, these statistics span over a
whole year period in both directions. Analysis of any longer period lags or leads seems
redundant for the short term.
Econometric analysis of the real estate market and investment
18
The correlation of up to four periods of lags and leads is reported in Tables 2.1 and 2.2.
In Table 2.1 in which real estate is represented by the JLW series, the correlation is
calculated for original and unsmoothed6 indices respectively. The figures maintain the
previous claims that real estate performance has little correlation with gilts and ordinary
shares – two financial assets often quoted for comparison. None of the correlation in lags,
leads and contemporaneous is significant at the five per cent level for both the original
and unsmoothed real estate indices. However, the shares of one particular sector, real
estate companies, have significant contemporaneous correlation with both real estate
indices, and significant correlation at one and two lags with the original real estate index,
at the five per cent level. Nonetheless, more significant correlation is to be found in the
real sectors. The first set of these is housing or residential real estate. Real estate
performance has correlation with the changes in the Halifax Building Society house price
index at the one per cent significance level all the way through three leads to four lags,
measured by the original real estate index; and the correlation is significant at the one per
cent level from lag 2 to lead 3 in means of the unsmoothed real estate index. The biggest
correlation occurs at lag 1. With regard to the Nationwide Building Society house price
index, the situation is broadly the same except that the significance level for the
unsmoothed JLW index is mostly the five per cent rather than the one per cent level; and
the contemporaneous correlation is the largest, suggesting more or less the same timing
and movement in residential and commercial real estate markets. The second set is
construction activities. The two series from the ONS (Office for National Statistics,
formerly CSO – Central Statistical Office) are construction output on new work and new
orders. A derived series through the difference operation between output and new orders
is used to represent the changes in the stock of uncompleted new orders. While real estate
performance seems to have correlation with construction output on new work at lead 2, it
lacks any correlation with construction new orders, no matter whether it is estimated with
the original or the unsmoothed real estate index. But impressively, the derived series of
the changes in the stock of uncompleted new orders has a strong relation with real estate
and the results suggest that either they move coincidentally or possibly with one period
lag in the changes in the stock of uncompleted new orders, implying the adjustment
mechanism in construction process in relation to real estate operations. Finally, real estate
is compared to aggregated economic cyclical indicators. The correlation structure
between real estate and the longer leading index indicates that real estate moves most
likely one or two period behind the longer leading index, i.e., about seven to ten months
in advance of the reference cycle. This is consistent with the results for the shorter
leading index and the real estate index, as real estate leads the shorter leading index for
one period, about eight months in advance of the reference cycle. Again, real estate leads
the coincident index for three to four periods, about ten months in advance.
The HPK index is claimed to be a market indicator. The Hillier Parker property index
represents values and rents of hypothetical properties and hence attempts to capture
current market conditions, while JLW and IPD are portfolio based indices representing
achieved values and net income. Accordingly, the HPK index seems to be able to catch
up real estate market movement, so the unsmoothing process is not required. The results
from using the Hillier Parker property index, as reported in Tables 2.2A and 2.2B, are,
however, consistent with that from the JLW series. Two of the most quoted financial
asset series – the GLT and the FTA, remain uncorrelated with the HPK. The
Real estate and the economy
19
Table2.1.A Property’s correlations with selected
economic variables: 1977 Quarter 2–193 Quarter 2
JLW – first difference filter (rates of change
analysis)
ρ4
CO
ρ3
ρ2
ρ1
ρ0
0.0 0.0 0.0 0.0 0.28 0.3 0.2 0.0 0.2 0.1
06, 13 57, 56 1,* 34 38, 87 61, 59
**
NO –0.1 –0.0 –0. 0.0 0.0 0.0 0.0 0.0 0.1 0.0
20, 59 063, 16 36, 94 72, 65 00, 75
DWG –0.0 0.1 0.1 0.25 0.0 –0.0 –0.0 –0.1 0.1 0.2
20, 26 65, 5* 98, 08 53, 54 62, 55*
NPT –0.1 –0.1 0.0 0.2 0.0 0.0 0.0 –0.0 –0.1 –0.2
62, 15 93, 52* 55, 02 02, 44 81, 53*
HFX
ρ–1
ρ–2
ρ–3
0.0 –0.1 0.1 0.1 0.1
62, 31 83, 91 37,
0.1
20,
0.1
44,
0.2
01,
0.0
75
0.0
49
0.3
88
**
0.6
20
**
0.2
62*
0.1
20,
0.1
40,
0.1
85,
0.0
64
0.0
57
0.0
63
ρ–4
0.0 0.25
38 1,*
0.2 0.1
05, 76
0.0 0.0
82, 01
0.0 –0.0
47, 78
0.2
27
0.0 –0.0
54, 89
0.1 0.1
49, 40
0.0 0.0
64, 54
0.2 0.2 0.4 0.4 0.5 0.4 0.6 0.4 0.6 0.4 0.8
0.7 0.4 0.6 0.25 0.5 0.1
78,* 44 66 62 64, 38 34 61 78, 71 11,
99, 83 46, 7* 16,** 94
,** ** ** ** ,** ** ** ** **
** ** **
NTW 0.2 0.2 0.3 0.3 0.5 0.3 0.5 0.2 0.5 0.3 0.5
0.5 0.2 0.4 0.1 0.27 –0.0
30, 19 95, 40 37 95 04, 48 76, 66 47,
49, 88 70, 92 1,* 12
** ** ,** ** **
** ** **
** * **
GLT –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.0 0.1 0.1 0.0 –0.0 0.0 0.0 0.0 0.0
79, 76 94, 18 95, 07 89, 01 10, 22 07, 67 83, 79 75, 60 86, 95
FTA –0.0 –0.1 –0.0 –0.0 –0.1 –0.1 –0.0 0.1 –0.0 –0.0 0.0 0.0 0.0 0.0 0.1 0.1 –0.0 –0.1
73, 17 88, 61 35, 10 02, 22 15, 38 49, 16 92, 05 74, 84 45, 82
FTAP 0.0 0.0 0.0 –0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.1 0.2 0.1 0.1 –0.0 0.0 –0.0
88, 81 30, 24 40, 61 68, 00 93,* 55* 13,* 73 97,* 35 38, 53 55, 35
RESC 0.2 0.2 0.31 0.2 0.3 0.2 0.4 0.3 0.5 0.2 0.5 0.2 0.4 0.2 0.4 0.2 0.33 0.1
15, 01 6,* 58* 92, 71* 88, 42 10, 96* 10, 83* 58, 18 34, 09 8,** 00
**
** ** **
**
**
**
LL –0.1 0.0 0.0 0.1 0.1 0.2 0.2 0.2 0.4 0.4 0.5 0.3 0.5 0.29 0.5 0.2 0.45 0.1
85, 55 03, 99 77, 34 91,* 55* 67, 06 52, 18* 67, 2* 33, 26 0,** 89
** ** **
**
**
SL
0.46 0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0.2 0.4 0.0 0.3 0.1 0.25 –0.0 0.1 –0.0
6,** 03* 21, 43 72, 44 97, 28 75, 50* 43, 78 60, 43 5,* 20 09, 30
** ** ** ** ** ** **
**
**
LG 0.60 0.2 0.4 0.1 0.3 0.0 0.1 –0.0 –0.0 –0.1 –0.1 –0.2 –0.2 –0.2 –0.3 –0.29 –0.43 –0.26
1,** 51* 92, 27 32, 09 61, 74 21, 81 94, 57 99,* 44 92, 4* 1,** 4*
**
**
**
CC 0.65 0.3 0.63 0.3 0.6 0.2 0.4 0.1 0.3 0.0 0.2 –0.0 0.0 –0.0 –0.0 –0.1 –0.1 –0.1
5**, 48** 8,** 15* 05, 64* 98, 42 49,** 42 02, 29 79, 57 23, 30 36, 73
**
Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively.
* significant at 5% level, ** significant at 1% level.
Left hand side for original index, right hand side for unsmoothed index.
ρ–i – property lags i periods, ρj – property leads j periods.
Econometric analysis of the real estate market and investment
20
Table 2.1.B Property’s correlations with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
JLW–Hodrick–Prescott filter
ρ4
ρ3
CO
0.069
0.162
NO
–0.267
DWG
ρ1
ρ0
ρ–1
ρ–2
0.284*
0.325**
0.314*
0.255*
0.255*
–0.160*
0.004
0.153
0.257*
0.322* 0.335** 0.355**
–0.010
0.180
0.212
0.181
0.280*
0.283*
0.245
0.217 0.263*
NPT
–0.327**
–0.163
–0.119
–0.123
–0.091
0.189
0.276*
0.306* 0.423**
HFX
–0.223
–0.005
0.209
0.419** 0.636**
0.827**
0.835**
0.667** 0.418**
NTW
0.005
0.216
0.400**
GLT
–0.289*
–0.302*
–0.277*
–0.217
–0.051
0.137
FTA
–0.135
–0.164
–0.164
–0.102
–0.045
FTAP
–0.139
–0.169
–0.081
0.058
RESC
–0.300*
–0.252*
–0.193
–0.094
LL
ρ2
0.473** 0.524** 0.500** 0.416**
ρ–3
ρ–4
0.246 0.268*
0.246
0.251*
0.013
0.216
0.239
0.261
0.011
0.049
0.041 –0.066
0.232
0.311*
0.276*
0.163
0.106
–0.001
0.092
0.131
0.167
0.129
–0.573** –0.577** –0.524** –0.446** –0.255*
–0.042
0.201 0.390** 0.514**
SL
–0.225
–0.095
0.046
0.198 0.328** 0.367** 0.427** 0.384** 0.325**
LG
0.485**
0.624**
0.675**
0.649** 0.545** 0.371**
CC
0.125
0.290*
0.434**
0.506** 0.497** 0.435** 0.359**
0.184
–0.016 –0.171
0.267*
0.173
Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively
* significant at 5% level, ** significant at 1% level.
ρ–i - property lags i periods, ρj - property leads j periods.
contemporaneous correlation with the FTAP is now more significant and the correlation
structure is more or less the same as exhibited by the JLW. The correlation with
construction output and new orders becomes even less significant, while the correlation
with the derived series RESC is again confirmed with the contemporaneous coefficient
being the largest. The fact that commercial real estate has strong correlation with
residential real estate is further proved via the use of the HPK index. The analysis of the
HPK index with cyclical indicators also suggests that real estate has an eight to ten
months lead on the reference cycle.
The above analysis has a number of implications. First, real estate is congruously
integrated into the economy and its performance is closely related to, and at least partially
explainable by, some of the economic activities. Therefore it might be possible for the
real estate profession to develop and use more plausible forecasting techniques, the
immediate effects of which would be to smooth out the seemingly damaging fluctuations
in the real estate market in the future. Second, real estate’s comovement with the
construction industry is better seen via the changes in the stock of uncompleted new
orders. It is a dynamic and joint adjustment between construction new orders and output
Real estate and the economy
21
to the overall performance in the real estate market. Thirdly, commercial and residential
properties have similar timing or the former might lag the latter for one period, possibly
due to the effect from interest rates. Finally, the necessity for unsmoothing the real estate
index has been evident through examination of the correlation structures: the original real
estate index, whenever correlated with other variables, has significant correlation at too
many leads and lags, unreasonably implying that real estate responds very reluctantly to
information disseminated in the economy and the market.
Table2.2.A Property’s correlations with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
HPK – first difference filter (rates of change
analysis)
ρ4
ρ3
ρ2
ρ1
ρ0
ρ–1
ρ–2
ρ–3
ρ–4
CO
–0.053
0.130
0.206
0.154
0.222
0.136
0.214
0.216
0.230
NO
–0.084
–0.095
0.094
–0.055
0.176
–0.000
0.198
0.149
0.129
DWG
0.029
0.007
0.072
0.058
0.203
0.146
0.115
0.173
0.154
NPT
–0.071
0.028
0.022
0.005
0.069
0.050
0.100
0.123
0.150
HFX
0.439** 0.603** 0.690** 0.730** 0.760** 0.749** 0.692**
0.615**
0.498**
NTW
0.358** 0.471** 0.582** 0.527** 0.594** 0.572** 0.556**
0.516**
0.382**
GLT
–0.177 –0.292* –0.253*
–0.161
–0.008
0.076
0.027
0.021
0.139
FTA
–0.053
–0.143
–0.092
–0.144
–0.013
0.058
0.079
0.070
0.105
FTAP
0.058
0.075
0.148
0.231 0.362**
0.253*
0.304*
0.232
0.160
RESC
0.208
0.266* 0.394** 0.399** 0.516** 0.469** 0.508**
0.425**
0.367**
0.240 0.410** 0.525** 0.557** 0.543**
0.519**
0.450**
SL
0.442** 0.545** 0.597** 0.628** 0.623** 0.497** 0.393**
0.303*
0.160
LG
0.551** 0.424**
CC
0.693** 0.672** 0.594** 0.481** 0.376**
LL
–0.079
0.094
0.285*
0.113
–0.044
–0.176 –0.279* –0.373** –0.428**
0.253*
0.129
0.003
–0.123
Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively
* significant at 5% level, ** significant at 1% level.
ρ–i – property lags i periods, ρj – property leads j periods.
The long run
When a long-run relationship exists between two or more non-stationary (more exactly
I (1)) time series, their linear combinations are stationary. Such a relationship is called
cointegration, and can be examined in several ways. Two most frequently used methods
are the Johansen procedure and Engle–Granger two-step method. While the former
directly tests for the cointegration relationship in a dynamic environment, the latter
Econometric analysis of the real estate market and investment
22
Table 2.2.B Property’s correlations with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
HPK – Hodrick – Prescott filter
ρ4
ρ3
ρ2
ρ1
ρ0
ρ–1
ρ–2
ρ–3
ρ–4
CO
–0.060
0.093
0.200
0.247
0.297*
0.305* 0.351** 0.380** 0.389**
NO
–0.263*
–0.182
–0.003
0.046
0.233
0.250* 0.376** 0.407** 0.360**
DWG
–0.048
0.073
0.201
NPT
–0.380**
–0.220
–0.120
HFX
0.092
0.353**
0.540**
0.643** 0.685** 0.678** 0.583** 0.429**
0.230
NTW
0.185
0.384**
0.526**
0.540** 0.541** 0.520** 0.437**
0.069
GLT
–0.408** –0.431** –0.361**
FTA
–0.146
–0.228
–0.245
FTAP
–0.086
–0.089
0.002
RESC
–0.264
–0.247*
–0.152
LL
0.306* 0.432** 0.406** 0.363** 0.371** 0.349**
–0.044
0.089
0.209
0.289* 0.382** 0.491**
0.285*
–0.216
0.016
0.145
0.215
0.275* 0.349**
–0.274*
–0.144
–0.049
0.036
0.093
0.147
0.169 0.335** 0.335** 0.344**
0.303*
0.228
0.185
0.177
–0.111
0.013
0.059
0.148
–0.661** –0.651** –0.595** –0.444**
–0.222
0.136
0.223 0.408** 0.541**
SL
–0.304
–0.188*
–0.058
0.106
0.295* 0.391** 0.456** 0.492** 0.469**
LG
0.544**
0.649**
0.699**
0.661** 0.558** 0.383**
0.013
–0.162
CC
0.091
0.280*
0.421**
0.495** 0.525** 0.506** 0.460** 0.394**
0.300*
0.202
Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively
* significant at 5% level, ** significant at 1% level.
ρ–i – property lags i periods, ρj – property leads j periods.
achieves the same objective in two separate but simple steps. The first step is to run a
regression of one time series on the other, then the second step tests whether the residual
is stationary with the DF (Dickey–Fuller) andADF (augmented Dickey–Fuller) statistics
(cf Dickey and Fuller 1979 and 1981). The DF and ADF tests were originally designed to
check the presence of unit roots in individual time series. When applied to two time
series, a stationary residual, or rejection of a unit root in the residual, implies a
cointegration relationship or a long-run relationship between the two time series.
The Johansen procedure (cf Johansen 1988 and Johansen and Juselius 1990) and the
ADF statistic are adopted for the analysis in levels, or the long-run relationships. Tables
2.3 to 2.6 present these results. The ADF is relatively easy to interpret for unit root tests,
so it is adopted in spite of the availability of other unit root test procedures which are
equally uncomplicated to use. The lag length is determined by the Akaike information
criterion (AIC) and the residuals are checked to be white noise using the Ljung-Box Q*
statistic. In the ADF test, all the statistics from lag 0 (the DF statistic) to lag 4 are
reported with † indicating those with optimal lag length. The reasons for presenting the
ADF statistic at all lags instead of only at the ‘optimal lag length’is that the AIC is a
rather subjective criterion to penalize a model which has too many lags. Other criteria
would give a different guideline on lag length choice. For example, another commonly
Real estate and the economy
23
used criterion, Schwarz’s criterion (SC), favours shorter lag lengths compared with the
AIC.
It should not be surprising that real estate moves in pace with construction and
housing in the long run, though such kind of inquiry has not been widely documented
previously. These findings are mainly attributable to the adoption of the new method, as
the derived series for the stock of uncompleted construction new orders has the most
significant and definitive cointegration with real estate. Both the trace value and the
maximum eigenvalue are much higher than their 95 per cent critical values, for both the
JLW and HPK indices, which are 19.169 and 18.594 for the JLW, and 25.252 and 20.247
for the HPK respectively. The evidence is further confirmed by the ADF statistic, which
is–3.597 for the JLW and –3.735 for the HPK, being significant at the 5 per cent level to
reject the null of a unit root in the residual,or no cointegration between the two series.
Regarding the long-run relationship between commercial and residential properties, the
Johansen procedure suggests that a cointegration vector does exist. From Table 2.3, it can
be seen that the JLW is cointegrated with both the HFX and NTW indices, and from
Table 2.5, the results show that the HPK is cointegrated with these two housing price
indices. However, while the ADF statistic supports the existence of a cointegration
relation between the JLW and both the HFX and the NTW,
Table 2.3 Cointegration of real estate with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
JLW – Johansen procedure
–T · ln(1 – )
–T · Σ ln(1 – )
CO
8.650
11.223
NO
10.012
12.365
14.017*
15.632**
NPT
8.847
9.262
HFX
21.935**
24.993**
NTW
13.360*
19.714**
GLT
7.710
7.758
FTA
14.204**
14.482*
FTAP
11.889
14.518*
RESA
18.594**
19.169**
DWG
max (0.95) = 14.069, max (0.90)=12.071; trace (0.95) =15.410,
*reject H0: no cointegration with 90% critical value
** reject H0: no cointegration with 95% critical value
trace
(0.90) = 13.325
it suggests that the HPK series only has cointegration relation with the HFX. Another
interesting point is that the real estate performance index does not only cointegrate with
the real estate company share index FTAP, it also does so with the all-share index FTA,
when assessed with the Johansen procedure. This would, therefore, play down the
Econometric analysis of the real estate market and investment
24
importance of studies of the price discovery between real estate and real estate company
shares as the all share index FTA appears to play the same role as the real estate company
sector index. The results for the long-run relationship between real estate and two simple
construction series are mixed. The HPK index’s cointegration with construction output is
established by applying both the Johansen procedure and the ADF statistics, but its
cointegration with construction new orders is only confirmed by the Johansen procedure.
For the JLW index, the long-run relationship with the construction output is only
confirmed by the ADF statistics. The same pattern applies to the total investment in
dwellings and the number of property transactions. To sum up, the analysis in levels
reveals additional information and presents further insights than those from the analysis
in differences. The stock under construction evidently adjusts to real estate performance,
and the two variables move together in the long run. The other construction and real
estate related variables, such as house prices,real estate transactions and the investment in
dwelling also prove relevant in the studies on real estate from the view of economic
analysis and modelling.
The long-run analysis has important implications. First of all, the relationship of real
estate with other sectors in the economy in the long run is stronger than that in the short
term. It is because that real estate investment has long-run attribute, its short-term
changes and swings are not so far as to reflect the underlying fundamentals as other
financial investments. When considered in the long run, real estate and other sectors in
the economy are likely to be driven by the same or relevant fundamentals and,
consequently, they may not move apart far away
Table 2.4 Cointegration of real estate with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
JLW – ADF statistic
DF
ADF(1)
ADF(2)
ADF(3)
ADF(4)
CO
–0.418
–2.598
–3.034*†
–2.561
–3.098*
NO
–0.867
–2.518
–3.583**†
–2.600
–3.207*
DWG
–1.197
–1.869
–1.993
–2.390
–3.122*†
NPT
–1.370
–2.071
–1.671
–2.427
–3.995**†
HFX
–2.234
–2.992*†
–2.304
–2.669
–3.305*
NTW
–1.859
–2.689†
–2.097
–2.195
–2.940*
GLT
–0.904
–1.487†
–2.034
–2.378
–2.542
FTA
–0.866
–2.577
–2.848†
–2.362
–3.001*
FTAP
–2.121
–2.338†
–2.302
–2.618
–2.451
RESA
–2.628
–3.439**
–3.597**†
–2.739
–3.533**
* reject H0: a unit root with 90% critical value, ** reject H0 with 95% critical value. (for critical
values cf Engle andYoo (1987) and Banerjee et al.(1993))
† indicates optimal lag length
Real estate and the economy
25
Table 2.5 Cointegration of real estate with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
HPK – Johansen procedure
–T · ln(1 – )
–T · Σ ln(1 – )
CO
10.044
15.245**
NO
11.634
14.013*
DWG
8.217
10.625
NPT
7.207
8.760
HFX
11.832
18.264**
NTW
13.859*
19.328**
GLT
7.258
7.333
FTA
13.822*
13.901*
FTAP
15.236**
18.923**
RESA
20.247**
25.252**
max (0.95) = 14.069, max (0.90)=12.071; trace (0.95) =15.410,
*reject H0: no cointegration with 90% critical value
** reject H0: no cointegration with 95% critical value
trace
(0.90) = 13.325
as in the short term. Second, real estate is more closely related with the real sector of the
economy than with the financial sector. Real estate is not a purely financial market
investment. It is, in the meantime, an investment in production, trading, work, and
storage spaces and capacity, so it shares similarity and possibly the same fundamentals
with the real sector more than with the financial sector of the economy. Third, among the
real sectors, construction has the strongest relationship with real estate in the long run,
especially when viewed with the stock of uncompleted construction new orders. It is, in
analogue to the shortterm analysis, the results of a dynamic and joint adjustment between
construction
Table 2.6 Cointegration of real estate with selected
economic variables: 1977 Quarter 2–1993 Quarter 2
HPK – ADF statistic
DF
ADF(1)
ADF(2)
ADF(3)
ADF(4)
CO
–0.778
–1.591
–2.148
–2.974*†
–3.291**
NO
–0.884
–1.747
–2.128
–3.056*†
–3.305**
DWG
–1.278
–1.329
–1.478
–2.303
–3.220**†
NPT
–1.081
–2.028
–2.026
–3.163*
–4.128**†
HFX
–2.514
–3.404**†
–3.146*
–2.810
–3.517**
Econometric analysis of the real estate market and investment
26
NTW
–1.833
–2.259†
–1.882
–1.834
–2.006
GLT
–1.365
–0.745†
–1.098
–1.838
–2.587
FTA
–0.774
–1.409
–2.100
–3.046*†
–3.583**
FTAP
–2.084
–2.018†
–1.961
–2.315
–2.239
RESA
–2.363
–2.286
–2.673
–3.735**†
–4.144**
* reject H0: a unit root with 90% critical value, ** reject H0 with 95% critical value.
† indicates optimal lag length
new orders and output to the overall performance in the real estate market, an sometimes
can possibly be called ‘construction reacts to property’ as in Tsolacos (1995). Finally, a
strong relationship found in the short term between commercial and residential properties
can be extended to the long run as well.
Notes
1 The difference in the coverage of value of new orders and value of output. Contractors’s
output is defined as the amount chargeable to customers for building and civil engineering
work. It includes the value of work done on their own initiative on buildings such as
dwellings or offices for eventual sale or lease, of work done by their own operatives on the
construction and maintenance of their own premises, and of goods made by the contractors
themselves and used in the work. The value of output on new work excludes repair and
maintenance. Though the output on new work and new orders have the same classification,
the site value and architects’ or consultants’ fees are excluded from the value of the order,
resulting in smaller figures for new orders than output on new work on average. Reflecting
this difference, a discount has been taken on output on new work to make the statistical data
more consistent in estimations.
2 Output and orders are regarded as construction flows; an annual figure would normally be as
big as four times of a quarterly one. Stock of uncompleted new orders would have the same
level whether the data are annual or quarterly. Usually the value of stock of uncompleted
new orders at its peak would roughly have the same magnitude as that of new orders
received in a period of twelve months, or of the output on new work. This is merely to give a
rough idea about the relative values of the two variables – it is not bound to hold by any
theoretical or practical reason.
3 Let xt and yt be two simple random walk processes, i.e. xt = xt–1 + 1,t,yt = yt–1+ 2,t then the
relation between the irrates of change, i.e., ∆xt and yt, would be that between 1,t and ∆2,t,
only relevant in the current period. If one intends to inquire into the relationships in their
levels, as xt = xt–1 + 1,t = xt–2 + 1,t + 1,t–1 = … = 1,t + 1,t–1+…+ 1,1,y1,t = y1,t–1 + 2,t = … =
2,t + 2,t–1 + … + 2,1, then all of their past innovations are involved. Thus it is termed ‘in the
long run’.
4 Hodrick–Prescott (HP) filters. The operation of the HP filters is to solve the following
optimisation problem
subject to
Real estate and the economy
27
The smaller the parameter , the smoother the trend path. When =
0, the trend path is a straight line, i.e., the zero frequency component
has been filtered out. The HP filter gradually filters out more lower
frequency components/cycles as increases. A HP filter with bigger
would trace the time series closer in the period. The selection of the
smoothing parameter is usually arbitrary. Judgement would be
made on the individual time series.
5 According to Engle and Granger (1987), if time series xt,yt and zt are all I(1) process, and if xt
is cointegrated with yt and zt respectively, then yt and zt are cointegrated as well. As an I(1)
series is cointegrated with its own lagged series with vector [1, –1], it follows that, e.g., if xt
is cointegrated with yt, then xt–1 will also be cointegrated with yt. Denoting zt = xt–1 confirms
this.
6 The unsmoothed index is derived using a procedure developed in Chapter 6.
Econometric analysis of the real estate market and investment
Appendix
Figure 2.1 Relevant time series
variables
28
Real estate and the economy
29
Econometric analysis of the real estate market and investment
30
3
Theories of dynamics
In the previous two chapters, descriptive analysis and broad statistical figures have been
provided, and the changing patterns of real estate and the role played by the institutions
and real estate companies analysed. Together with a review of the literature, it has been
revealed that the fluctuations in real estate are linked to the economic environment in a
variety of ways. Moreover, there is a need to address issues in real estate research, and in
particular, to reconsider real estate market behaviour utilising modern finance and
economic theory. The research theme of the book, as proposed, is to investigate real
estate market behaviour in three related areas: the market efficient hypothesis; rational
expectations; and business cycle theory. The three theories are closely related and have
common attributes of dynamics. This chapter, therefore, will study these theories of
dynamics and their relevance to real estate market behaviour.
Dynamic theories are drawn from studies of the business cycle, the rational
expectations hypothesis, and the efficient market hypothesis. Each of the three literatures
is comprehensive and could make a single volume in its own right. However, the purpose
here is to apply existing work to real estate research, not to develop theory. Nevertheless,
because real estate data and behaviour are unique, the results and implications of the
empirical investigations in this book may shed light on the theory, as any literature
exclusive of evidence in this important sector of the economy is incomplete. Moreover,
real estate is probably one of the most suited areas to link the three theories – for them to
be jointly and critically scrutinised in a way that has rarely been attempted before. In this
regard, there are no consensus, no ready body of techniques and approaches, hence such
an analysis is no easy task but rather a challenging one. In the following discussion, the
three theories are presented and discussed with regard to the development, econometric
testing procedures and implications and, in particular, their relevance to real estate
research.
Market efficiency
Market efficiency is always one of the central issues in financial market studies, and real
estate is no exception. A number of factors may make the real estate market appear less
efficient that other financial markets. These include high transaction costs, long lags
between deciding to take and actually completing a transaction, and illiquidity. The
situation is further complicated by the fact that there are no reliable real estate indices
available for assessing performance. Real estate indices, unlike transaction-driven indices
in financial markets, are usually appraisal or valuation based. Studying real estate market
efficiency is not only important but also difficult Therefore, the efficient market
hypothesis, models and procedures for testing the hypothesis, and the implications in the
real estate market will be addressed in the following.
Econometric analysis of the real estate market and investment
32
Definitions
The study of efficient markets is one of the single most important subjects in finance and
investment, being closely associated with expectations formation and price fluctuations.
Emerging from stock market analysis, the history of the efficient market hypothesis could
be traced back at least to the 1920s. In modern times, Fama (1970) is generally credited
as presenting a scholarly abstraction of the efficient market hypothesis (EMH).
According to his definition, there are three types of efficient market, depending on the
extent of information reflected in the market:
1. Weak form. A market is said to be weak form efficient if there is no relationship
between past price changes and future price changes, i.e., the price changes are
independent. No trading rules can be developed to make abnormal returns based on
the past history of an asset’s prices or returns.
2. Semi-strong form. Semi-strong form EMH states that no abnormal returns can be made
by developing a trading rule based on publicly available information. The semi-strong
form encompasses the weak form since past history is publicly available. Public
information also includes non market information, e.g. economic news, company
accounts, and stock splits.
3. Strong form. Strong form EMH extends the information set to including all
information, no matter whether it is public or private. No trading rules can be
developed to make abnormal returns based on all available information. Strong form
EMH implies semi-strong EMH which, in turn, implies weak form EMH.
An efficient market should not be confused with a perfect market. A market is said
perfect if the following conditions hold:
1. The market is informationally efficient, i.e., information is costless and it is received
simultaneously by all individuals;
2. The market is frictionless. There are no transactions costs or taxes, assets are perfectly
divisible and marketable. There are no regulatory constraints;
3. There is perfect competition in product and securities markets. In the product market,
all producers supply goods and services at the minimum average costs; and in the
securities market, agents are price takers.
4. All market participants are rational, maximising their expected utility.
The above assumptions set the conditions for the capital market to be allocationaly and
operationally efficient, in that prices would be set to equate the marginal rates of return
for all producers and savers. The concept of the efficient market is less restrictive.
Imperfect competition in the product market would imply capital market imperfection;
nevertheless the stock market could still determine security prices which fully reflect all
public available information and would be set to equal the present value of a stream of
expected future returns. Consequently the stock market could still be efficient in the
presence of imperfection.
A general statement of the efficient market hypothesis says that security prices fully
reflect all available information. A precondition for this strong form hypothesis is that
information and trading costs, the costs of getting prices to reflect information, are
always zero, as Grossman and Stiglitz (1980) suggest. A less restrictive but more rational
version of the efficient market hypothesis by Jensen (1978) states that prices reflect
Theories of dynamics
33
information to the point where the marginal benefits of acting on information do not
exceed the marginal costs.
There have been many difficulties and problems in testing the EMH in the 20 years
since the theory emerged. In his 1991 review of the efficient capital market literature,
Fama re-divides the work on market efficiency into three new categories. Instead of weak
form tests, which are only concerned with the forecast power of past returns, the first
category now covers the more general area of tests for return predictability, which also
includes forecasting returns with variables such as dividend yields and interest rates.
Since market efficiency would always go hand in hand with equilibrium pricing models,
the predictability also regards the cross sectional predictability of returns, i.e., tests of
asset pricing models and anomalies discovered in the tests.
For the second and third categories, Fama proposes changes in title, rather than
coverage. The semi-strong form tests are now replaced by a common title, event studies.
The strong form tests now becomes the tests for private information.
Tests of the efficient market hypothesis
Tests for return predictability (weak form hypothesis)
The basic weak form test is to examine whether the return process follows a random
walk:
Xt = c + Xt–1 + t
(3.1)
or
Rt = c +
t
(3.2)
where Xt is return, price or the index, Rt is the rate of return, c is a constant and t is the
serially uncorrelated residual. With Fama’s 1991 version of tests for the efficient market
hypothesis, the first category incorporates statistical tests of return predictability which
includes tests of independence between current and past returns, other forecasting
variables, volatility tests and seasonality in returns, along with cross sectional return
predictability. The tests for the predictability from past returns often amount to tests on
autocorrelation in the return series. Market efficiency implies the returns follow a random
walk, and residuals are white noise. Since returns are unpredictable, then the best forecast
of returns is the historical mean.
Other forecasting variables used for testing the efficient market hypothesis are
dividend yields (D/P) and the price earnings ratio (P/E). Therefore, the tests would
include the sevariables in equations (3.1) and (3.2). Research by Shiller (1984) and Fama
and French (1988) suggests that D/P explain small fractions of stock returns for horizons
up to 5 years. Campbell and Shiller (1988a) observe that P/E helps forecast returns with a
certain reliability. The predictability of share returns from D/P or P/E is not itself
evidence for or against market efficiency. In an efficient market, the predicting power of
D/P says that prices are high relative to dividends when discount rates and expected
Econometric analysis of the real estate market and investment
34
returns are low, and vice versa. On the otherhand, with the existence of irrational bubbles,
low D/P ratios signal irrationally high share prices that will move back toward
fundamental values. Initially, these variables were included in regressional equations to
reject the random walk hypothesis if they could help forecast returns. Controversially, the
test results did not necessarily rule out market efficiency. Nevertheless, analysis of this
kind helps understand market operating mechanisms.
Recent developments in one of the most prominent areas of econometrics, the time
varying volatility of financial time series, has provided a fresh tool in GARCH
(generalised autoregressive conditional heteroscedasticity) modelling (Bollerslev 1987)
for tests on volatility and seasonality. Earlier studies on volatility tested whether the
expected returns are constant or vary over time. With GARCH, various relationships
between returns and volatility can be explicitly expressed and tested, and the changing
returns over time do not necessarily mean market inefficiency as traditionally suggested,
as long as they do not help exploit excess returns. In many cases, it has been revealed that
the stock market is even more volatile than previously perceived. The variance (the
second moment) is changing over time and serially correlated even where the returns (the
first moment) are constant with white noise innovations. Seasonal patterns have also been
found to be more significant in the second moment than in the first moment. Such
evidence would lead to the rejection of the efficient market hypothesis in some of the
cases which had earlier supported it.
Cross-sectional predictability considers asset pricing models and anomalies and could
be termed as testing the efficient market hypothesis and asset pricing models
simultaneously.The most widely adopted asset pricing model,which has also been most
critically attacked, is the Sharpe–Lintner–Black (SLB) single factor model in which the
cross sectional expected returns are sufficiently explained by the market , the slope in
the simple regression of the return of an asset on that of the market portfolio.The multifactor asset pricing models of Merton and Ross are the generalisations of SLB,
recognising the limitations in the latter. The most popular approach amongst all the multifactor models is Ross’s (1976) arbitrage pricing theory (APT), which uses the statistical
technique of factor analysis to extract the common factors in returns to test whether
expected returns are explained by the cross sections of the factor loadings of asset returns
on the factors. The multifactor version of asset pricing models are, in fact, an ideal state
which can be made closer to, but never reached.On the other front of advancing asset
pricing models, consumption-based asset pricing models (Rubinstein 1976, Lucas 1978,
Breeden 1979) study an asset’s consumption which is the slope in the regression of its
returns on the growth rate of per capita consumption. The model abstracts all the
elements in hedge shifts in consumption and portfolio opportunities that can appear in
multi factor model with one factor relationship between expected returns and the
consumption . The empirical tests on the consumption based asset pricing models often
involve time series and cross section predictions. Again, the advances in statistical and
econometric techniques in last ten years,particularly the generalised method of moments
(GMM) proposed by Hansen (1982), have made significant contributions to the studies.
One of the earliest studies of this kind is Hansen and Singleton (1982), which jointly tests
the time series and cross-sectional predictions of the consumption-based model.
Theories of dynamics
35
Event studies (semi-strong form hypothesis)
This category is concerned with tests of the adjustment of prices to public
announcements. Obviously, some issues usually belonging to the semi-strong form
hypothesis have been moved to the first category by Fama’s recent reviews, making
Fama’s definitions and boundaries for the first two forms of market efficiency even more
ambiguous. However, as the title suggests, the tests mainly involve the investigation of
price movements around the time of an announcement, i.e., when information is made
public, to see when the expected price adjustment takes place, and the investigation of the
potential for above verage risk adjusted rates of return assuming an investor acquired or
disposed some set of securities after an announcement was made public. The question is
whether such an investor has enjoyed above verage risk adjusted profits compared with
those from buy-and-hold policy after transaction costs. The tests in this category are
usually to examine the abnormal returns (AR) and cumulative abnormal returns (CAR)
before and after an event occurs, and to observe the pattern:
(3.3)
(3.4)
where Rt is the true return, and
is the expected return (derived from an asset pricing
model). If the market is efficient and the price responds and adjusts to the event quickly,
only the AR immediately after the announcement or occurrence of the event would be
positive (for good news) or negative (for bad news). All other ARs should be close to
zero. The pattern of CAR, from equation (3.4), should show a sharp jump immediately
after the event, and the curve should be flat before and after the jump. A survey of
methods and models used in event studies can be found in Armitage (1995).
Various events to be studied include stock splits (Fama et al. 1969), new issues
(Ibbotson 1975, Ibbotson and Jaffe 1975, and Loughran and Ritter 1995), earnings
announcements (Ball and Brown 1968, and Bernard and Thomas 1990), announcement of
accounting changes (Kaplan and Roll 1972, and Biddle and Lindahl 1982), and
macroeconomic events (Chen 1991, and Chen et al. 1986). Some others are concerned
with anomalies and seasonality. Among them are the book value of equity (BE) to the
market value of equity (ME) ratio (Fama and French 1992), the size effect (Banz 1981,
and Dimson and Marsh 1986), price earnings ratio and returns (Ball 1978), the impact of
annual rebalancing, the January effect and other calendar effects (Ariel 1987, 1990,
Kleim 1988, Lakonishok and Smidt 1988, Reinganum 1983, and Ritter 1988). The
acceptance of market efficiency in this category would imply that asset prices move
swiftly to adjust to new information and investors cannot make abnormal returns by
acting after the announcements and the events. As with the first category of tests, the
evidence for and against the EMH is mixed. However, most studies on the EMH come
out of this category.
Econometric analysis of the real estate market and investment
36
Tests for private information (the strong form hypothesis)
The tests in this category investigate whether asset prices fully reflect all information,
public and private. The title, as well as the definition, is superfluous, as all information
other than private has been studied in the first two categories. This form of hypothesis is
extremely rigid, requiring that asset prices adjust swiftly to new public information, but
also that no groups have monopolistic access to specific information which they can
capitalise upon. This implies that all information is available to all investors at the same
time.
The tests in this category examine the performance of different groups of investors to
investigate whether any identifiable group has consistently had above average riskadjusted returns. Such results would either indicate they have monopolistic access to
important information or they consistently have the ability to act on public information
before other investors can, which would suggest the market is not adjusting asset prices
to all new information swiftly. Issues examined include insider trading (Jaffe 1974,
Finnerty 1976, and Seyhun 1986), security analysis (Black 1973, Hulbert 1990, and Liu
et al. 1990) and professional port-folio management (Jensen 1968, Grossman and Stiglitz
1980, Ippolito 1989, and Elton et al. 1993). The results from most studies are, as one can
image, mixed.
The efficient market hypothesis in a real estate context
Real estate company sector share prices, like other security prices, behave more or less in
a random walk manner, which at least supports a weak form efficient market hypothesis.
Real estate investment itself, as represented by various real estate price and performance
indices, has severe autocorrelation which means that the direct real estate investment
market is not, even at the lowest level, efficient. However due to the appraisal based
nature of most real estate price and performance indices which attributes to a large part of
autocorrelation, the predictable component may be smaller than that inferred from the
indices. But in a common sense, most practitioners and academics in real estate research
do not accept that the indices should be corrected for smoothing to the point when the
return or price becomes unpredictable. If the return or price is predictable, it may still be
difficult to exploit any regularities because of (a) high transaction costs and, (b) long lags
between deciding to act and actually completing a transaction. In such a situation, there is
no difference between acting on information and not acting on information, thus there are
no incentives for taking advantage of getting information. The other reason might be the
confidence in the accuracy of prediction which is not only measured with some statistical
criteria such as MSEs (mean squared errors) or RMSEs (root mean squared errors), but
more fundamentally, in relative magnitude with trading costs. With the same predicted
return and its standard deviation, the larger the trading costs, the fewer the actions taken
on receipt of information. The immediate consequence of fewer actions on information is
that real estate remains predictable to a certain extent. As autoregrassive and moving
average components in residuals are the major sources of fluctuation or cyclical
movement, the connection between real estate market efficiency and real estate cycle is
apparently observed in this way. With the development in real estate research, prediction
techniques and transaction procedures, the costs of information and the transaction costs
Theories of dynamics
37
would be gradually reduced, with the real estate market becoming more mature than it is
now and fluctuations being hampered out to a larger extent.
Business cycle theory (theories of output and price fluctuations)
It has been observed that real estate displays striking cyclical patterns. It may be one of
the most turbulent sectors in the economy in this sense, against some findings of
relatively low variance in its returns, which takes on the issues from a different
perspective. Cycles and poor performance were evident in the recession of the early
1990s which witnessed a much sharper downturn in real estate than in any other sectors.
With some previous research having reported and described cycles, it is now necessary to
bring real estate into a theoretical analytical framework, not only to show the
phenomenon of cycles, but to link the real estate cycle with other economic activities, and
furthermore, to reveal the underlying mechanisms
Figure 3.1 The development of
business cycle theory
governing the process of cycles. As one of the dynamic theories mentioned at the
beginning of this chapter, business cycle theory is presented and discussed in the
following.
Econometric analysis of the real estate market and investment
38
The development of the theory
Business cycles are periodic, but irregular up and down movements in economic activity,
measured by fluctuations in real GDP and other economic variables, which can be
decomposed into two elements: the trend, and the deviation from the trend. To identify
business cycles, attention has focused on deviation from the trend, since this gives a
direct measure of the uneven pace of economic activities, being separated from their
underlying trend growth path. A business cycle is identified as a sequence of four phases:
contraction, trough, expansion, and peak.
Business cycle theory has developed in three strands: Keynesian business cycle
theory, monetary business cycle (MBC) theory, and real business cycle (RBC) theory.
Figure 3.1 shows the development of business cycle theories and the links between them.
MBC and RBC are equilibrium business theories and have dominated the business cycle
literature since the 1970s. Equilibrium theories regard short-term deviation of output
from trend to be consistent with a state of equilibrium. RBC and MBC models view the
cycle as the result of propagation of a series of random shocks. The MBC theory
emphasizes the monetary aspects of shocks, while RBC theory highlights the importance
of real shocks. Within the monetary tradition, the theory differs between that of the
monetarists who consider the observed component of the monetary shocks causes the
fluctuation, and the new classical (NC) model, developed by Lucas (1975), Barro (1976)
and Sargent and Wallace (1975, 1976), argues that what matters is the unanticipated
changes in monetary growth.
As disequilibrium theory, Keynesian models treat rigidity or frictions in the economy,
such as sticky wages and prices, as the cause of disequilibrium and cycles which are
generated via mechanisms of multiplier-accelerator interaction (Haberler 1946, Hansen
1957, Fischer 1977). While Keynesian theory does not rule out real shocks as the source
of business cycle, it typically attributes cyclical deviations to aggregate demand shocks.
In the development of business cycle theory, Lucas’ monetary business cycle (MBC)
model has played an important role in reviving business cycle research in the 1970s and
marks a major changes from the Keynesian approach to business cycle modelling which
regards the cycles as an essential disequilibrium phenomenon. Subsequently, the MBC
approach has evolved into the real business cycle (RBC) which emphasizes the
importance of real shocks (Kydland and Prescott 1982). The widespread rejection of
MBC, due to its reliance on implausible claims of information deficiencies, resulted in
the proliferation of research on RBCin the 1980s. RBC theory retains the rational
expectations hypothesis (REH), but asserts that real shocks, in particular technological
shocks, are the major source of the impulses. Both MBC and RBC focus on key
intertemporal relationships. Towards the end of the 1980s, the RBC approach was
broadened to make use of dynamic recursive techniques to solve agent optimisation
problems subject to market clearing conditions, in a general model of economic growth.
The most influential early contributions to the RBC literature are those of Kydland and
Prescott (1982) and Long and Plosser (1983). They retain the MBC approach and rational
expectations hypothesis, while assuming that all information concerning the path of the
general price level is publicly and costlessly available. The signal extraction problem that
Theories of dynamics
39
is a key ingredient of the MBC models is thus discarded and, consequently, the
unanticipated temporary monetary shocks are of no importance. The rejection of MBC
models means that the RBC approach has to look at the real economy for both
disturbances and the propagation mechanism.
Kydland and Prescott’s (1982) ‘Time to build’ paper modifies the neoclassical growth
model to permit the capital utilisation rate to vary. The effect of this modification is to
increase the amplitude of the aggregate fluctuation predicted by theory as the equilibrium
response to technological shocks. The treatment of the current value of leisure and the
past history of leisure allows the intertemporal substitution of leisure and multiperiods are
required to build new capital goods. The technology parameter is subject to a stochastic
process with two components, permanent and temporary. Productivity is assumed to be
observable by agents, but it is observed with noise. Economic agents are unable to judge
whether the technology shock is permanent or temporary. The permanent component is
highly persistent, and shocks are therefore autocorrelated. When the technology
parameter grows smoothly, steady state growth prevails; but when it is stochastic, cycles
take place. Kydland and Prescott (1988) further extend the analysis to cover policy issues
and assert that public finance considerations are not the principal factor driving the cycle
and, thus, that abstracting from them at this stage is warranted. Only when we have
considerable confidence in a theory of business cycle fluctuations would the application
of public finance theory to the question of stabilisation be warranted. Such an extension
is straightforward in theory, but carrying it out will be difficult and will require ingenuity.
Long and Plosser (1983) adopt a highly restrictive formulation assuming rational
expectations, complete current information, no long-lived commodities, no frictions or
adjustment costs, no government, no money, and no serial correlation in the shocks. The
focus is on intertemporal consumer preferences and production processes. There is
persistence in the effects of changes in wealth, since they alter the demand for goods over
time. The production possibility hypothesis also allows for intra- and inter-temporal
substitutions. Business cycle equilibrium is preferred to non-business cycle alternatives
since agents are willing to take risks to achieve higher expected returns. Input output
relationships propagate the effects of output shocks both forward in time and across
sectors.
Other prominent contributions to business cycle theory can be found in Nelson and
Plosser (1982), King and Plosser (1984), Barro (1977, 1978), McCallum (1983, 1986,
1989), and King et al. (1991). Early work is mostly attributable to Fisher (1925), Frisch
(1933), Friedman (1957), and Solow (1957). On the empirical side, Eichenbaum and
Singleton (1986) investigate the postwar US business cycles via equilibrium business
cycle theories, to examine whether the empirical evidence for the US supports the view
that the business cycle is not a monetary phenomenon. Sims (1980) compares the
interwar and postwar business cycles with a time series approach. Davidson and
Mackinnon (1981, 1982) carry the studies on alternative business cycle theories through
non-nested hypothesis tests. The econometric issues in equilibrium business cycle models
are tackled by Singleton (1988), who analyses the nature and sources of secular, cyclical,
and seasonal fluctuations, the econometric implications of prefiltering to remove some of
these components from aggregate time series, and the methods for solving nonlinear,
dynamic stochastic business cycle models. Nelson and Plosser (1982) is among the first
papers to study trends and random walks in macroeconomic time series which is akin to
Econometric analysis of the real estate market and investment
40
the unit root tests applied later, and formally investigated by Perron (1988) from the then
new approach, the Dickey–Fuller procedure. Sims’s (1980, 1982, 1986) main
contributions to econometric analysis of business cycle theory are his vector
autorregressive process which has been applied to business cycle research by himself and
adopted by many researchers.
The cause of economic fluctuations
The basic model of the real business cycle is represented by the following formulation
which maximises a lifetime utility function with rational expectations
(3.5)
where 0 < < 1is the discount factor, ct+j(>= 0) is consumption in period t + j,lt+j(>=0)=l–
nt+j is leisure in period j, and nt+j is hours of work in period t+j. The expected life time
utility function, U, is the sum of all (discounted) future utility function, u, which is a
function of consumption ct+j and leisure lt+j in each period. Furthermore, U is concerned
with the optimal path of future consumption and leisure. Output is in the form of a
production function
yt = ztf (nt, kt)
(3.6)
where yt is the output, kt is the capital stock, nt is labour or hours of work as above, and zt
is the technology shock at time t, a random process with a mean value of unity. Equations
(3.5) and (3.6) are simple in appearance. However, there are very limited functional
forms for u and f so that the closed form solutions for kt, ct and nt can be derived. Several
authors, including Long and Plosser (1983), have consequently used the combination
which specifies u in a log-linear form and f as a Cobb–Douglas function
u(ct, 1–nt)= log ct + (1– ) log(1–nt)
(3.7)
(3.8)
Equilibrium requires:
yt = ct + [kt+1 – (1– )kt]
(3.9)
Assuming capital is written off within each period, i.e., = 1 in equation (3.9), from
equations (3.8) and (3.9), the following relationship is derived:
(3.10)
These specifications would lead to the explicit expressions for ct and kt+1
Theories of dynamics
41
(3.11)
(3.12)
The logarithm of kt would follow a stochastic process of the form
(3.13)
The process for kt is dynamically stable,
where
since |1 – α| < 1. log kt+1 is a first order autoregressive process if log zt is serial
uncorrelated. If the zt process is itself a first order autoregressive process of the form
log zt = ρ log zt–1 + t
(3.14)
where
t
is white noise, then log kt+1 would be a second order autoregressive process
(3.15)
The second order autoregressive process also applies to other crucial quantity variables
including log ct and log yt. Taking the logarithm of ct in (3.9) would yield
(3.16)
This simple special case of the prototype
where
RBCmodel suggests that withAR(1) technology shocks, important quantity variables
would have the time series properties of AR(2) process. Since (1–α) < 1 and ρ<1,
equations (3.15) and (3.16) are stationary. Moreover, when the roots of the above AR(2)
processes are complex numbers, which is the general case, equations (3.15) and (3.16)
are of cyclical fluctuations in nature.
Nelson and Plosser (1982) have classified the models of economic fluctuations into
two entirely different groups. These are models for deterministic trends and
modelsforrandomwalks.
Theprocessesofdeterministictrendsandrandomwalks
are
generally referred to as trend stationary and difference stationary respectively in the time
series analysis literature. These two processes behave quite differently.
The linear trend stationary (TS) model can be described as:
(3.17)
where α and are fixed parameters, and
and (L) are polynomials in L that satisfy
the conditions for stationary and invertibility. Depending on the nature of ct, the effect of
shocks would be different, but the uncertainty is bounded in any case. While
Econometric analysis of the real estate market and investment
42
autocorrelation in ct can be exploited in short-term forecasting, over long horizons the
only information about future zt is its mean (α+ t). Therefore neither current nor past
events will alter long-run expectations. The long-run forecast errors must be ct which has
finite variance with bounded uncertainty. In the simplest situation, when
the shock only lasts for one period. Then the output deviates from
trend for only one period too and reverts to trend immediately. The output is therefore
said to be trend reverting.
Turning to the difference stationary (DS) process, the consequences are quite different.
The linear DS process has the form:
(1–L)zt = + dt
(3.18)
where (1–L) is the difference operator, (L) and (L) are polynomials satisfying the
stationary and invertibility conditions. The simplest case is the random walk dt = µt.
When there is no shock, zt would grow at a constant rate as in the trend stationary case.
However a positive shock in this model will cause the output to move up by a magnitude
of that shock forever, then the output will grow at the constant rate of again but at a
higher level. This means that the random walk model is not trend reverting. In general,
when there is autocorrelation in dt, there would be a build up time for the output to transit
to the new trend.
The above analysis indicates that where the output is trend stationary, then shocks to
output will be transitory. On the other hand, when the output is a random walk or
difference stationary, the effect of shocks will be persistent. The characteristics of trend
and random walk have important implications in the tests for business cycle theories. If
fluctuations in output are mainly the results of monetary or aggregate demand shocks,
they would be transitory. Shocks of real nature, such as the adoption of a new technology,
would
have
permanent
effects
whichwillnotberevertingandwillleadtoahigherlevelofoutputforever. Sotests for trends and
random walks provide a tool for examining alternative equilibrium business cycle
models.
Tests of business cycle theory and the econometric issues in the analysis
of business cycle models
Accompanying the alternative business cycle theories is an empirical literature concerned
with tests of these models. One common method is to decompose the disturbances into
responses to demand and supply shocks in justifying the soundness of competing
theories. Blanchard (1989) studies the sources of shocks and claims that aggregate
demand shocks are dominant in the short run while supply shocks largely contributes to
long-run variation. Shapiro and Watson (1988) find that short-run variation in hours
worked is mainly due to aggregate demand shocks, while technology shocks explain most
of the variation in output. Another approach, adopted by Barro (1977), is to derive
reduced form equations from a structural model to test the correctness of the theory that
model represents. Due to the coexistence of several competing theories, nested and non
Theories of dynamics
43
nested testing procedures are often employed, as in Shapiro (1987). Recently, the vector
autoregression (VAR) approach and Granger causality tests have been extensively used
and proved powerful in business cycle studies. Singleton (1988) carries out a bivariate
VAR with average hours worked and the real wage. He finds that there is some evidence
for two way causality between wages and hours with seasonally unadjusted data. This is
important because of the considerable attention that has been focused on the response of
hours worked to wage changes. Other work can be found in Sims (1980), Stock
andWatson (1989), Blanchard andWatson (1986), and Chowdhury et al. (1994).
The relevance and implications of business cycle theory to real estate
research
Real estate may be one of the most turbulent sectors in the economy and has striking
cyclical behaviour. The turbulence can be judged by its cycles and common sense,
against some findings of relatively low variance in its returns, which may, to a certain
extent, be distorted by smoothing in real estate performance indices. These kinds of
claims seem to be contradictory to each other, but they maket he judgement from
different perspectives. The recession of the early 1990s witnessed a much sharper
downturn in real estate than in any other sectors. This behaviour covers not only the real
estate market, but also is reflected in real estate company share prices. Recently, real
estate cycles have been subject to research. Key et al. (1994), on behalf of the Royal
Institution of Chartered Surveyors, link the real estate cycle with various economic
variables in a linear regression framework. In Chapter 2 of this book, the cyclical
behaviour of real estate and the relationships between real estate and relevant economic
activities have been briefly investigated in both the short and long run, alternatively
assuming the underlying processes are trend stationary and random walks. The real estate
market is evidently not frictionless, there is apparent rigidity due to, e.g. rent review
procedures, transaction costs are relatively high, information is limited and then it is not
costless, and demand shocks are frequently observed. All of these are the sources of
fluctuations and seem to admit a trend reverting process. Thus new classical theory or
Keynesian disequilibrium theory appears to apply. On the other hand, the advance in
construction technologies and building materials has consistently been raising the
efficiency of construction work, doubtlessly the major shocks to technology. The
development has been seen as highly speculative which again produces shocks on the
supply side. In this sense, the effects of shocks will by nature be persistent, the process
would be more random walk like and may fit into a RBC framework.
Business cycle theory does provide a powerful tool for inquiry into real estate
behaviour which until now has yet to attract more attention from real estate professionals.
The real estate behaviour here is not restricted to cyclical patterns only, but may extend to
cover efficiency, expectations and bubbles in the market. On the other hand, real estate
may provide a source of shocks to business cycle theorists since this abundant material
for business cycle research has been largely overlooked.
Finally, let us consider the related term ‘real estate cycles’ in contemporary real estate
research to see to what extent business cycle theory can apply, and the different
emphasis. Real estate cycles, like other phenomenal cycles in the economy, have been
considered with rather different respects and interpretations. The common usage of the
Econometric analysis of the real estate market and investment
44
term ‘real estate cycle’ in the profession suggests a pattern of persistent rise and fall and,
consequently, implies predictability of the timing, magnitude and period of cycles.
Alternatively, there are recurrent but irregular fluctuations in real estate, which appear not
to follow predictable patterns. Gradually, a few of researchers become aware of the
problems associated with the former, and now adopt the latter description of real estate
cycles, in line with the modern business cycle theory discussed in this section. Real estate
cycles are considered as fluctuations around a deterministic or stochastic trend and,
consequently, the real estate time series data can be decomposed into trends and cycles.
Nevertheless, there are no perfect formulae or models for any real world activities and,
without exception, real estate cycles should be examined with the specific characteristics
being taken into account.
Rational expectations
Speculative cycles and bubbles, which have been suspected to exist in the real estate
market due to the erratic behaviour observed in the large swings in real estate cycles and
seemingly exploitable excess returns, are closely related to expectations and expectations
formation in the real estate market. Such issues cannot be solved without the analysis and
empirical test of a theory for expectations: the rational expectations hypothesis (REH).
The connections among the three literatures of EMH, BC and REH are clearly established
via expectations, whether they are rational or not. The formulation and tests of efficient
market hypothesis and various asset pricing models are all based on expectations
formation. So too is business cycle theory.
Expectations theory in economics could be said to date back a century. However, it
was Muth’s (1961) breakthrough paper on rational expectations and the theory of price
movements that marked the creation of rational expectations theory. In the paper, he
alleges that the REH asserts three things: information is scarce, and the economic system
generally does not waste it; the way expectations are formed depends specifically on the
structure of the relevant system describing the economy; and a ‘public prediction’will
have no substantial effect on the operation of the economic system. It does not assert that
the scratch work of entrepreneurs resembles the system of equations in any way; nor does
it state that predictions of entrepreneurs are perfect or that their expectations are all the
same. He argues that, from a purely theoretical standpoint, there are good reasons for
assuming rationality. First, it is a principle applicable to all dynamic systems.
Expectations in different markets and systems would not have to be treated in completely
different ways. Second, if expectations were not moderately rational, there would be
opportunities for people to make gains in commodity speculations, running a firm, or
selling the information to present owners. Third, rationality is an assumption that can be
modified. Systematic biases, incomplete or incorrect information, poor memory, etc. can
be examined with analytical methods based on rationality.
The formulation of rational expectations requires that the errors in expectations are on
average zero, and exhibit no patterns. This amounts to a statement that the prediction
errors should be uncorrelated with the entire information set available at the time when
the prediction is made. Otherwise, there would be some information left unused or a
systematic component which should have been corrected. By taking mathematical
Theories of dynamics
45
expectations, rational expectations are the most accurate expectations and the most
efficient method for forecasting, since rational expectations has the smallest prediction
errors, which all other expectations, e.g., adaptive expectations, cannot achieve.
Following Muth, Lucas is most closely associated with the development of rational
expectations (Lucas 1972, 1978; Lucas and Rapping 1969; and Lucas and Prescott 1971).
Lucas first applies his ideas about rational expectations to the Phillips curve. He provides
an example of an economy in which equilibrium prices and quantities exhibit what may
be the central feature of the modern business cycle: a systematic relation between the rate
of change in nominal prices and the level of real output, a variant of the Phillips curve.
This relationship is derived within a framework from which all forms of ‘money
illusion’are rigorously excluded: all prices are market clearing, all agents behave
optimally in light of their objectives and expectations, and expectations are formed
optimally. Therefore, rational expectations are the most accurate expectations with agents
making no systematic and consistent mistakes, that is, the errors of rational expectations
exhibit no patterns and are zero on average.
Barro (1976) has developed a rational expectations model with imperfect information.
Although the model is primarily used for studying monetary policy, it can be adapted and
applied widely elsewhere. Other prominent works include Sargent and Wallace (1974,
1975), Lawrence (1983), McCallum (1976, 1977, 1978, 1980), and Kydland and Prescott
(1977). The rational expectations literature is much interwoven with that of business
cycles in that the two issues can rarely be properly examined without referring to each
other. The rational expectations hypothesis is also central to market efficiency studies.
Campbell and Shiller (1987, 1988b) have developed a present value model approach to
test market efficiency and rationality which, in econometrics, amounts to testing for
cointegration between value/price and cash flows and relevant restrictions.
Tests of the rational expectations hypothesis
Direct tests of rationality
There are two forms of direct tests of rationality: a weaker test and a stronger test. The
weaker test says that the forecast errors should exhibit no patterns, and should be on
average zero, i.e.
Yt – Et–1Yt = t
(3.19)
where Et–1Yt is the expectation of Yt formed in period t–1, and t is the random forecast
error, which is uncorrelated with any information available in period t–1 or earlier.
If Et–1Yt is directly observable, then the data on Yt and Et–1Yt can be used in the
regression
Yt = α0 + α1Et–1yt + µt
(3.20)
where α0 and α1 are the parameters and µt is a random error with zero mean. The
rationality test then amounts to the acceptance of null hypothesis H0: α0 = 0 and α1 = 1.
Econometric analysis of the real estate market and investment
46
The directly observed expectations permit a stronger test of the rational expectations
hypothesis. If expectations of a variable are rational, they should be formed in accordance
with the process determining that variable and therefore they will depend on any set of
the past variables in exactly the same way as the variable itself depends on that set of the
past variables. i.e., if Yt is determined in the following way
Yt = α1Yt–1 + α2Yt–2 + 1Xt–1 + 2X–t–2 + v1t
(3.21)
and Et–1Yt is specified in exactly the same way as Yt
Et–1Yt = α1Yt–1 + α2Tt–2 + b1Xt–1 + b2Xt–2 + v2t
(3.22)
where v1t and v2t are random errors with zero mean. The null hypothesis of rationality is
then H0 : αi = ai, j = bj, for i,j = 1,2. This is equivalent to saying that the forecast error Yt
–Et–1Yt is independent of all lagged information.
Since the central point of these tests is the independence of forecast errors on past
information, then the following equality always holds
(3.23)
It follows that the variance of the actual series always exceeds the variance of the series
standing for expectations if the variance of the forecast error is bigger than zero. This
equality cannot hold if the forecast errors are correlated with the past variables or
information and the covariance is negative and bigger in amplitude than the variance of
the forecast errors.
Tests of the restrictions imposed by rational expectations
The rational expectations hypothesis can be viewed as imposing restrictions on what
should be observed. The rational expectations hypothesis implies a valid method of
incorporating additional information when estimating econometric models which involve
expectations. If the restriction imposed by rational expectations on a variable’s behaviour
is valid, then the imposition should not affect the explanative power of the model. The
usual test procedures adopted are the F-test or likelihood ratio test to see if there are any
differences between the restricted and unrestricted specifications.
Recent development in testing the rational expectations hypothesis: tests
of present value models via cointegration
This approach, by Campbell and Shiller (1987), uses cointegration techniques, is
particularly effective in financial and monetary analysis. A present value model for two
variables yt and Yt, states that Yt is a linear function of the present discounted value of
expected future yt
(3.24)
Theories of dynamics
47
Models of this form include the present value model of the share price, when Yt is the
share price and yt the dividend; the present value model of the real estate price, when Yt is
the real estate price and yt the rent. Let us construct a new variable St ≡ Yt – yt, called the
‘spread’. The rearrangement yields
(3.25)
and
(3.26)
If ∆yt is stationary, then St is stationary as well, and so is ∆Yt. The ‘rational bubble’
alternative is seen using (3.23) and (3.24). If a term bt is added to the right hand side of
(3.22), satisfying bt = Etbt+1, it appears on the right hand side of (3.23) but does not
affect equation (3.24). The term bt is explosive by construction, so causes explosive
behaviour of St and ∆Yt. One way to test for the rational bubble is therefore to test the
stationarity of St and ∆Yt.
Expectations in the real estate market
As the study of the efficient market hypothesis, and its joint test with an asset pricing
model in particular, directly involves assumptions and tests on expectations, the EMH’s
relevance in real estate research is straight forwardly translated to the analysis and test of
the rational expectations hypothesis. In the same way, the REH and the theory on
business cycle and output/price fluctuations are interwoven and play a role in the real
estate market. For a long time, speculative cycles and bubbles have been suspected to
exist in the real estate market, due to the presumably erratic behaviour observed in the
large-scale swings in real estate cycles and seemingly exploitable excess returns.
However, as observed above, price fluctuations do not necessarily mean market in
efficiency and irrationality. Research has to be carried out within an economic theory and
fitted into a testing model. Moreover, many limitations and factors have to be taken into
account, which are not attributable to human expectations. Such limitations and factors
include transaction costs, market friction, imperfect competition in the product market,
and so on, all of which complicate the analysis. In addition to these, the real estate market
suffers from imperfect information, regional segmentation, illiquidity and immobility. In
this regard, the theory on rational expectations provide us with a guideline to carry out
research in the real estate market and investment.
Part II
The dynamic behaviour of
economic and financial time
series
Background
An initial analysis of UK real estate investment and markets and real estate performance
over the last two decades was presented in Part I, together with a literature review on
contemporary research in the area. The changing patterns of real estate and the role
played by the institutions and real estate companies were analysed. It was revealed that
the fluctuations in real estate are linked to the economic environment in a variety of ways
in the short term and long run. The links examined included the cyclical behaviour of real
estate in relation to the stock market investment and the real economic sectors, as well as
the long-run relationships. In the short term, real estate’s performance was found to be
closely related to some of the economic activities, especially the real sectors of economy.
The long-run relationships were examined using the cointegration and multicointegration
techniques. Real estate was found to be an integrated part in the economy in both the
short term and the long run. Nonetheless, the results showed the link of real estate with
the real sectors in the economy in the long run is stronger relative to that obtained in the
short term.
Accordingly, it was proposed in Chapter 3 that real estate market behaviour be
investigated in the modern finance and economic research framework, and with the
theories which have common attributes of dynamics. These theories of dynamics were
drawn from studies of the business cycle, the rational expectations hypothesis, and the
efficient market hypothesis. Each of these was discussed with specific reference to real
estate. To study real estate market behaviour and real estate dynamics with these theories,
econometric models and testable procedures are to be formed in this Part. It is aimed to
address real estate in an integrated economic system implied by the multivariate time
series modelling strategy. In this regard, fluctuations and dynamic behaviour will be
investigated with attention being paid to time series attributes and characteristics, e.g.,
cycles, trends, persistence, and common factors. The models and procedures developed in
this Part will be used in the later chapters in an empirical study on the dynamic behaviour
of real estate with UK data.
The 1990s saw major re-examinations and appraisals of economic time series
behaviour. Real estate data, as a member of the family of economic variables, has largely
Part II: The dynamic behaviour of economic and financial time series
49
been omitted from this process. A study of real estate data would, then, be empirically
meaningful and might be theoretically augmenting. Prior to the 1980s, the general view
on economic time series was that economic variables could be decomposed into a secular
or growth component and a cyclical component. The secular component was assumed not
to fluctuate much over the short term, but rather move slowly and smoothly relative to the
cyclical component. This has led to detrending of time series by regression on time, with
the residuals interpreted as the cyclical component to be explained by business cycle
theory. This view has been questioned by Nelson and Plosser (1982) when they
investigate whether economic time series are better characterised as stationary
fluctuations around a deterministic trend or as non-stationary processes that have no
tendency to return to a deterministic trend path. They conclude that the time series of the
US economy used in the study are non-stationary stochastic processes with no tendency
to return to a trend line. Using an unobserved components model which decomposes
fluctuations into a secular or growth component and a cyclical component, they infer that
shocks to the former, which are associated with real disturbances, contribute substantially
to the variation in the observed series. The implications are that models focusing on
financial and monetary disturbances as a source of purely transitory fluctuations may
never be successful in explaining a large fraction of variation and that stochastic variation
due to real factors is an essential element of any model of economic fluctuations.
Since then, time series analysis has been dominated by the stochastic stationary
hypothesis and consequently the unit root test. The criteria for unit root tests are either
drawn or adapted from Fuller (1976) and Dickey and Fuller (1979, 1981). Their finding is
that the critical values for the t-statistic may not apply, as the non-stationarity of a time
series under the null causes the distribution to be non-standard. A significant step forward
in modelling non- stationary time series is, however, the so called cointegration and error
correction mechanism (ECM) analysis, popularised by Granger (1981, 1983) and Engle
and Granger (1987). For nearly a decade and until comparatively recently, in many of the
empirical studies, an orthodox and dogmatic procedure is adopted (a) to test for a unit
root in levels (with a overwhelming majority rejecting the null of no unit roots), and (b)
to construct models in both difference and level. The methodology differs from the Box–
Jenkins approach, in that the variables in levels, provided they are cointegrated, may also
be included in the models, and is claimed impressively advanced the understanding of
economic systems.
The flaws in adopting a difference stationary (DS) point of view are that thestationary
component is often overlooked, and most of the empirical research tend to do no more
than either reject or accept a unit root hypothesis from which implications are inferred.
There are other defects. In particular, no testing procedures are reliable and different
procedures often give different and controversial results. The biasedness in the estimates
of cointegration regressions has also raised concerns, even in a system of dynamic
specifications, due to serial correlation, endogeneity and outlier activity in the variables
and errors, as pointed out by Phillips and Hansen (1990), Phillips (1993) and Phillips et
al. (1994).
In business cycle research, the stationary transitory component plays an important
role, while the non-stationary permanent component should also be modelled correctly.
Simply put, the stationary component, which is featured by the cyclical fluctuations, must
be combined either with a deterministic or stochastic trend. Most studies, observing the
Econometric analysis of the real estate market and investment
50
obvious random walk and unit root processes, decompose economic time series into a
permanent non-stationary trend and a transitory cycle component. The focus is on the
relative contribution or magnitude of the two components to the fluctuations. Earlier
work can be found in Beveridge and Nelson (1981) on the measurement of the business
cycle (documented as the Beveridge– Nelson (BN) decomposition), with an improved
algorithm supplied by Newbold (1990). A nonparametric approach to persistence, i.e., the
relative contribution of permanent and transitory components, is devised by Cochrane
(1988). Campbell and Mankiw (1987a, 1987b) use both ARMA and nonparametric
techniques for the same purpose. The BN decomposition is of the unobserved
components approach, and those of Watson (1986) and Clark (1987) are in similar vein,
carrying out estimation in state space with Kalman filters, as outlined in Harvey (1985).
However, their assumptions on innovations are different. BN assume the innovations
from random walk and stationary components are perfectly correlated; while in Watson
and Clark, these are two independent processes. Watson investigates issues involved in
detrending economic time series when the trend is modelled as a stochastic process.
Unobserved components models are used, in which an observed series is additively
decomposed into its trend, a random walk with drift, and a residual which follows a
stationary stochastic process. Adopting Kalman filtering and smoothing techniques,
Clark’s inquiry is similar. Persistence can also be evaluated using frequency domain
techniques by estimating the sum of the coefficients of moving average representation of
a series. These examinations are univariate in nature. The trend and cycle studies also
involve multivariate cases. Evans and Reichlin (1992) consider the multivariate
generalisation of the BN decomposition when the information set includes other I(1) and
stationary variables. Stock and Watson’s (1988) testing for common trends falls generally
into cointegration analysis, but in particular deals with the business cycle. Vahid and
Engle (1993a) have developed a test for the existence of common cycles among
cointegrated variables.
Shocks which have long-lasting effects are usually attributed to real variables such as
technology and productivity changes; while those which have temporary effects are
assigned to monetary and financial variables. The former are also mostly on the supply
side, as interpreted by Blanchard and Quah (1989) as supply disturbances; and the latter
on the demand side are interpreted as demand disturbances. Real business cycle theory,
then, has another focus on identifying the sources of the disturbances. To categorise the
types of the disturbances, a priori restrictions can be imposed or information from other
economic variables can be exploited as in Blanchard and Quah (1989), Campbell and
Mankiw (1987b) and Evans (1989). Blanchard and Quah find that the effect of supply
disturbances on output increases steadily over time, peaking after two years and reaching
a plateau after five years. The demand effect peaks after two to four quarters, then
declines to disappear after about three to five years. The other facet for studying sources
of disturbances is that of aggregate versus sectoral shocks in business cycles, as stylised
by Long and Plosser (1983, 1987). They argue that the observed comovements do not
necessarily indicate the presence of a common or aggregate disturbance. It has been
shown that even if random productivity shocks are independent across sectors, the selfinterested responses of economic agents to productivity disturbances in real business
cycle models will cause comovement of activity measures from different sectors. Long
and Plosser’s methodology is factor analysis with a focus on identifying aggregate
Part II: The dynamic behaviour of economic and financial time series
51
against sectoral disturbances. The relative importance of the shocks in a multivariate
system can be investigated with impulse response models in VAR, or more recently as in
Ltkepohl and Reimers (1992), the impulse responses model in a cointegrated system.
The following chapters in this Part will study the outlined topics on dynamic
behaviour of economic time series. Chapter 4 first reviews the current research on cycles
and trends with some additional comments and generalisation, so that the model or
underlying idea is more appropriate to portray the phenomena and capture the
characteristics. Following a discussion on the existing univariate and multivariate
persistence literature, it then further develops an improved procedure for estimation of
multivariate persistence measures. Lastly in this chapter, sources of shocks are to be
addressed with regard to the economic feature of permanent and transitory effects, and
the time series attribute of stationarity and persistence, incorporating some thoughts
introduced earlier.
Chapter 5 studies the dynamic behaviour of time series in a systematic way, focusing
on common factors which real estate shares with the other sectors in the economy. The
framework for modelling and analysing economic fluctuations and dynamics is presented
by reviewing and extending the previous work on common trends and common cycles,
and incorporating the ideas from Chapter 4. This leads to a unified representation of
economic fluctuations and dynamics.
4
Trends, cycles and persistence
Background
In this chapter, current research on cycles, trends and persistence will be reviewed with
some additional comments and generalisation. The purpose is to make the model more
appropriate to capture the characteristics of real estate and express the underlying idea
with regard to real estate research.
It is now generally accepted that there are two types of trends: deterministic and
stochastic. The former becomes stationary after removing the deterministic trends, and
the latter is stationary after taking a difference operation. Accordingly, the former is
termed ‘trend stationary’ (TS) and the latter ‘difference stationary’ (DS). Nelson and
Plosser (1982) separate the two types of trends in an ARIMA process, and summarise
their respective behaviour. Hodrick and Prescot (1980), Harvey (1985) and Clark (1987)
also form part of the trend-cycle literature.
With regard to the analysis and decomposition of shocks, major contributions are
drawn from Blanchard and Quah (1989), King et al. (1991, known as KPSW after King,
Plosser, Stock and Watson), Campbell and Mankiw (1987a, 1987b). Their approaches to
decomposing time series differ in the use of information: one group is univariate, whereas
the other also brings in other relevant time series to help the analysis.
Campbell and Mankiw (1987a, 1987b) and Cochrane (1988) put forward the concept
of persistence in economic time series analysis. Their persistence measure is the ratio of
two variances of a time series: the variance in a longer period and a one period variance.
Their approaches are univariate and differ only in estimation procedures. The persistence
measure has been since generalised into multivariate applications, e.g., in Pesaran et al.
(1993) and Van de Gucht et al. (1996).
The rest of the chapter is organised as follows. Approaches to decomposing time
series into cycles and trends are to be examined and developed in the first section.
Following a discussion on the existing univariate and multivariate persistence literature,
the second section then further develops an improved procedure for estimation of
multivariate persistence measures. Attention will be paid to shocks and, in particular, to
sources of, and the responses of economic variables or activities, to shocks. Different
sources and effects of shocks contribute to cycles and trends, and ultimately, the dynamic
fluctuations of economic and financial time series data, in different ways and with
different implications. These will be addressed in the third section with regard to the
economic feature of permanent and transitory effects, and the time series attribute of
stationarity and persistence.
Trends, cycles and persistence
53
Properties of trends and cycles
The basic statistical issue is the appropriate representation of non stationary time series.
As noted previously, there are two fundamentally different groups of non stationary
processes as alternative hypotheses, proposed and studied by Nelson and Plosser (1982),
Harvey (1985), Clark (1987) and others. However, one group might reduce to the other,
subject to certain conditions on the residuals being met. The first group, trend stationary
(TS) processes, consists of a deterministic trend plus a stationary stochastic process. The
second group consists of those processes possessing a non-stationary stochastic trend,
with, as in the first group, a stationary stochastic cycle. These two groups of trend and
cycle processes can be unified in a single formulation, as in Harvey (1985) and Clark
(1987), as follows
Yt = Tt + Ct
(4.1)
where Yt is the logarithm of observed time series. Equation (4.1) states that the time series
is the sum of two components, a trend Tt, that can be either deterministic or stochastic,
and a stochastic cycle Ct. Both seasonality and residuals have been parts of the trend
and/or cycle; and both trend and cycle can be treated in a number of ways. In this chapter,
the cycle is modelled as
(4.2)
where
is a finite polynomial in L that satisfies the conditions of stationarity and
invertibility. The trend can be expressed as:
(4.3)
Equations (4.2) and (4.3) together make up equation (4.1). Equation (4.2) is purely a
cycle process and equation (4.3) a purely trend process. The trend here differs from that
of Harvey (1985) and Clark (1987) in that the residual in Tt equation is a general
invertible ARMA instead of a white noise process, and from that in Nelson and Plosser
(1982) where the TS and DS processes are treated separately and differently. The
removal of the restrictions on t allows for the shocks to trends to have other than a onejump-forever effect. Lippi and Reichlin’s (1994a) technical diffusion is a rather specific
restraint put on ARMA processes, derived from imposing a particular shape of the
dynamic impulse response to the permanent shock a priori. In theory, there could be
many restricted forms for (L), resulting from alternative hypotheses and leading to
varied investigating approaches and empirical implications. When
equation (4.3)
Econometric analysis of the real estate market and investment
reduces to a first difference stationary process. If both sigma
54
and (L)=1, it
the process is trend stationary.
reduces to a random walk process. Further, if
Lippi and Reichlin’s (1994a, 1994b) restriction on the shape of the shocks is an
improvement, compared with random walk shocks. However it still suffers two
disadvantages: first, that the response functions are symmetric, and second, that all
shocks to the non-stationary trend are regarded as technological shocks. The formulation
in this chapter fundamentally differs from that of Lippi and Reichlin. It is suggested that
the positive and negative shocks are asymmetric, both in the frequency of occurrences
and in the magnitudes. In reality, few, if any, negative shocks to technology would be
expected. If a negative shock is observed, it is really not technology shock but a
conventional term to capture the exogenous shock to the trend. Hence, while t is still
modelled to have a zero expected mean, its third moment, the excess skewness, would be
non-zero. The second asymmetry arises from the response functions to the shock. While
it is believed that it would take some periods to experience the full effect of a technical
shock, it should not necessarily have a symmetric diffusion process as in Lippi and
Reichlin (1994a). That is to say, the shape of the response is an empirical matter, taking
into account of the speed and processes of technology dissemination, spillover and
obsoletion.
Consider two simple cases, one with a random walk type trend with
and
(L)=1, and the other with a deterministic trend with both
and
In both
cases, t reduces to a constant . In the trend stationary process, all the uncertainties are
left to be explained by the cycle component Ct, and the variance is stationary by
definition. In the random walk process, uncertainties arise both from innovations in cycle
and trend components, and the variance from the trend itself is the accumulations of
over time which increases without bound as time evolves.
The fundamental difference between the two processes can also be revealed by
investigating the roots of the ARMA polynomials. If the TS plus cycle model is
differenced once, it would be:
(4.4)
is
being evaluated at L = 1. Equation (4.4) indicates that there exists a
where
unit root in the first difference [(1–L)]Yt. The presence of a unit root implies the first
differenced TS process is not invertible. Thus, the difference operation does not matter.
However, when there is an alternative DS process:
(4.5)
It appears that in levels there is a unit root in the AR polynomial. It then would emerge
that, if a series is generated by a TS process, it would fail to reject the hypothesis of a unit
root in the ARMA model in difference, and fail to reject the
Trends, cycles and persistence
55
Figure 4.1 The effect of a shock to the
stochastic trend process
hypothesis of a unit root in the ARMA model in levels if it is generated by a DS process.
Nevertheless, the difficulty caused by this dilemma on testing the unit root is only a past
story, due to the non-standard distribution under the null of a unit root. Over the last
decade, many procedures have been developed to deal with this kind of distribution.
However, it is still helpful to understand the two kinds of trends and their properties.
More essentially, it is crucial to understanding and interpreting economic fluctuations.
A general ARMA representation for the residual in a stochastic trend process would
let the effect of a shock reach its full magnitude over more than one period; while with a
white noise residual, i.e. where the stochastic trend is a random walk, the effect is
immediate. The shock in the cycle component Ct is different. A general ARMA
representation would imply that the reverse to trend value would take more than one
period; whereas if Ct is a white noise, the shock would have a one period effect and the
process would return to its trend value immediately. These are illustrated in Figures 4.1
and 4.2.
Persistence measurement
Since the economic series can be decomposed into a non stationary trend component and
a stationary cycle component, and the shocks to the two components are different in that
they have remarkable different effects on future trend values, it is natural to pose a
question of how persistent are the combined effects from the two shocks, i.e. their
relative importance to the fluctuations. Persistence is effectively
Econometric analysis of the real estate market and investment
56
Figure 4.2 The effect of a shock to the
deterministic trend process
described by the infinite polynomial of the Wold moving average representation of a time
series, A(L), being evaluated at L = 1
(4.6)
where
A(L)=1+a1L+A2L2+…
(4.7)
is a polynomial in the lag operator L, µt are zero mean and independent (not necessarily
iid) residuals. A(1)(= A1 + A + 2+ …) is A(L) valued at L = 1. The impact of a shock in
period t on the growth rate in period t + k is Ak. The impact of the shock on the level of
economic activities in period t + k is therefore 1 + A1 + … + Ak. The accumulated impact
of the shock on the level of the time series is the infinite sum of these moving average
coefficients A(1). The value of A(1) then serves as a measure of persistence. In a random
walk, A(1)=1, in any stationary time series, A(1)=0. For series which are neither
stationary nor a pure random walk, A(1) can take on any value greater than zero. If 0 <
A(1) < 1, series would display a mean reverting tendency. If A(1) > 1, an unanticipated
increase would be reinforced by other positive changes in the future, and the series would
continue to diverge from its pre-shock expected level.
There are two customary versions for the measurement of persistence. One is the
polynomial of the Wold moving average representation evaluated at L = 1, and its
variants, by Campbell and Mankiw (1987a, 1987b). The other is known as Cochrane’s
Trends, cycles and persistence
57
(1988) V, the ratio between the k period variance and one period variance, or the ratio
between the two autocorrelations
(4.8)
where ρj is the jth autocorrelation of ∆Yt. In a random walk, the variance of the k + 1
period difference is k + 1 times the variance of the one period difference, then the ratio V
= 1. For any stationary series, the variance of the k + 1 period difference approaches to a
value of twice the variance of one period difference. In this case, the ratio V approaches
zero when k becomes larger. The limit of the ratio of the two variances is therefore the
measure of persistence.
In theory,
. But, as one cannot effectively estimate A(1), one cannot
effectively estimate Vk via A(1) either. This is one of the reasons for having a Vk version
of persistence. To empirically obtain the persistence measurement, approaches include
ARMA, nonparametric, and unobserved components methods. The ARMA approach is to
estimate A(1) direct, where parameters are quite sensible to change with regard to
estimation. The nonparametric approach produces the measures known as
and âk , is
widely adopted and has been written as two RATS procedures by Goerlich (1994)
(4.9)
The nonparametric approximation of A(1) is
(4.10)
The choice of k, the number of autocorrelations to be included, is important. Too few
autorrelations may obscure trend reversion tendency in higher order autocorrelations.
Inclusion of too many autocorrelations may exaggerate the trend reversion, since as k
approaches the sample size T, the estimator approaches zero. Hence, though larger k
might be preferred, k must be small relative to the sample size.
The third approach to measuring persistence is to analyse the unobserved components.
It is related to the decomposition of the time series into a non stationary trend and a
stationary component discussed earlier in this section: the persistence measures are the
relative sizes of variance in the two components. There are two rather different ways of
imposing restrictions on the two components, i.e., those considering them as perfectly
correlated, and those with a view of two independent processes. To the former, the
Cochrane’s version of persistence V is equal to the ratio of the variance of the change in
the random walk component to the variance of the total change in the time series.
Campbell and Mankiw’s A(1) version is the standard deviation of the change in the
random walk component divided by the standard deviation of the series. Here V and A(1)
convey information on the relative importance or magnitudes of trend and cycle
Econometric analysis of the real estate market and investment
58
components in the economic time series. Regarding the later, the independence of the two
components suggests the persistence measure V can be written as a weighted average of
the equivalent measures for the two components. That is, V = V1+(1– V2), with V1 and
V2 being the persistence measures for the two components, and
In the case where the first component is a
random walk and the second component a stationary cycle, V1 = 1 and V2 = 0. Then the
total persistence measure is the ratio of the variance of the change in the random walk to
the variance of the change in the time series. It is indeed the share of the random walk in
a time series.
The persistence measures of V and A(1) can be generalised to a multivariate time
series, as proposed by Pesaran et al.(1993). The multivariate Vk and A(1) can then be
jointly applied to a group of variables or sectors, e.g., industrial production, construction
and services, to evaluate the cross section effects.The presentation is similar to (4.6)
(4.11)
The bar means a vector of variables or a vector of polynomials (matrix), and the scalar
variance of residuals, a covariance matrix. The vector of polynomial, is
(4.12)
Assuming there are m variables in the system, then variable vector, residual vector and
are (m×1) and the covariance matrix is of (m×m) dimension,
respectively. The covariance matrix of the random walk component in this multivariate
process is:
(4.13)
in a univariate time series. To evaluate the longwhich reduces, as before, to
run effect of shocks in sector j on the level of activity in sector i, individual elements in
VC will be selected and normalised. Pesaran et al.(1993) use the conditional variance of
∆Yj,t (the jth diagonal element of Σ) to normalise the jth column of VC. Van de Gucht et
al. (1996) use the unconditional variance of ∆Yj,t to scale the jth column of VC, arguing
that it is consistent with the univariate persistence measure proposed by Cochrane (1988).
Both regard the diagonal elements in the normalised VC as representing total persistence
in individual sectors, and off-diagonal elements as the cross effect between two sectors.
e.g. an element in the ith row and jth column is the effect on ith sector due to a shock in
the jth sector. Their normalisation uses a single variance for the normalisation of a
column and, whether conditional or unconditional, ignores the fact that the process is
multivariate. In fact, the normalisation is as simple as in univariate cases. Instead of being
scaled down by the unconditional variance, the covariance matrix of the random walk
components will be normalised by the unconditional covariance matrix. The multivariate
persistence measure is therefore:
Trends, cycles and persistence
59
(4.14)
where Σ is the unconditional covariance matrix of the time series variable in this
in a univariate
multivariate system. This persistence measure reduces to
process, the same expression as in Campbell and Mankiw (1987a, 1987b) and Cochrane’s
(1988) original idea. By considering possible effects from, and links with, other sectors,
this measurement of persistence for individual sectors are more precise, compared with
its univariate counterpart. Both Van de Gucht et al. (1996) and Pesaran et al. (1993) aim
to generalise the persistence measurement and have partly achieved this objective. To
have an accurate and exact expression of multivariate persistence, the normalisation
should be realised with matrix operations; it is not possible to achieve this with simple
division arithmetic. With this approach, the effect on sector i due to shocks in sector j is
represented by the (i,j) element in VCK, i.e. VCK(i,j), with VCK(i,i) measuring the sectorspecific persistence. Pesaran et al. (1993) use the square root of each diagonal element in
VC(Pi =(Pii)0.5) which is not the ratio between ‘the variances’ but between ‘the standard
deviations’, and is therefore not directly comparable to the univariate persistence measure
Vk. e.g., Pi = 2 would translate into Vk = 4 in a univariate estimation procedure. Another
problem is that the off- diagonal elements may be negative, and as a result, it may not be
possible to assess some of the cross sectional effects. Nevertheless, they do not
investigate the cross effects, and no obvious problems exposed with their estimation
procedures.
Both univariate and multivariate persistence measures can be viewed as an attempt to
measure the size of the random component of the process in a trendcycle decomposition
representation, such as (4.1). In fact,
V(Tt|Ωt–1)=A2(1)σµ
(4.15)
(4.16)
where
is a vector of trend component if (4.1) is generalised to a multivariate
representation. As such, multivariate persistence analysis nests almost all trendcycle
models.
Multivariate persistence analysis is more sensible in that, instead of analysing the
individual variables separately as in the univariate cases, it allows shocks to transmit
from one variable to another. Therefore, multivariate persistence analysis is able to
examine the sources of shocks and the effects of the shock in one sector on other sectors.
Compared with the VAR model, multivariate persistence is to evaluate the effect over an
infinite horizon, while a VAR model has to cut off at a certain lag length. So, multivariate
persistence takes all significant and insignificant lagged variables into account, but to
produce a much smaller number of statistics. Moreover, it is able to detect the effect of
certain kinds of shocks, e.g., a monetary shock, from that of other shocks. However, it is
not possible to specify the‘other’shocks in a model. Unless relevant assumptions have
been made and certain restrictions imposed, the objective of distinguishing demand
shocks from supply shocks cannot be achieved. This issue will be discussed in the next
Econometric analysis of the real estate market and investment
60
section. But, bear in mind, the decomposition of shocks into demand and supply or
monetary and real ones may involve variables which are not particularly helpful in most
multi-sectoral analysis. Models of this kind are not always sound in empirical
investigations, as assumptions have to be made and restrictions imposed with prior
judgement of the researcher. Consequently, their economic meaning is difficult to
explain, when many sectoral variables are included.
Sources of shocks – Supply v. demand, monetary v. non-monetary,
and sectoral v. aggregate
The analysis of sources of shocks is closely related to the persistence of the effect of a
shock to the time series. Shocks to technology and production are viewed as having
permanent and durable effects on output. Furthermore, the associated activities in which
shocks to technology and production play a role are on the supply side. Hence shocks to
supply and shocks to the long-run stochastic trend are perceived as equivalent. In other
words, the supply shock is linked to the variance of the innovation in the non-stationary
component of the time series, at least in appearance. Demand shocks, on the other hand,
due mainly to financial and consumption sectors, have only temporary effects on output.
Therefore, demand shocks correspond to the stationary and transitory component in the
time series. The aggregate shocks are featured by a common trend and the comovement,
distinguishable from those of the sectoral specific factors.
Having associated demand shocks with transitory component and supply shocks with
the permanent component of the time series, the study of sources of shocks then further
imposes a priori restrictions on the response of the time series to each of the
disturbances. Generally, there are two techniques for studying and identifying the
responses to different shocks. One is univariate based on the assumptions on the time
series in question itself. The other is multivariate, utilising, or being helped by, the
information and attributes in other time series. Blanchard and Quah (1989) use a bivariate
model, as do Campbell and Mankiw (1987b), focusing on two stationary variables, one in
difference and one in level, and two disturbances, one with permanent effect and one with
only a transitory effect. King et al. (1991)’s approach is multivariate, specifically with
three variable and six variable models. In fact they can be easily generalised to any
multivariate, or reduced to univariate cases, if one has an empirical study of his/her own
in mind. Let Yt denote an N-variable vector, all of the elements are I(1). vt is an N×1
vector of serially uncorrelated structural disturbances. However, there are only two types
of the disturbances, so the vector for disturbances is partitioned into two segments
with
representing a k×1 sub vector of the disturbances in the non-
stationary component of the time series, i.e., the supply shock, and standing for an (n–
k)×1 sub-vector of the disturbance to the stationary component, i.e., the demand shock.
The two types of disturbances are independent. By definition, ∆Yt can be expressed as
follows
(4.17)
Trends, cycles and persistence
61
with A(1) = [P0], in accordance with the partition of vt , P is an N×k non zero matrix with
which has the long-term effect, and 0 is an N×(N–k) matrix of zero with which has
only temporary but no permanent effect.
The implications of the partition of the disturbances into permanent and transitory
components and the partition of the long-run matrix A(1) into non zero and zero parts are
, the jth lag effect of
apparent. For any element in A(1), say
mth disturbance on Y1,t is a1,m(j), while its effect on the level of Y1,t is the sum of a1,m(0),
a1,m(1),…a1,m(j), as j approaches ∞ , the accumulated effect on the level of Yl,t is hence
is the prerequisite for
a1,m(1) times that disturbance. Then
the corresponding disturbance to be transitory, i.e., a1,m(1) is in the sub set of the long-run
structural matrix A(1), 0, and the disturbance in . As for those permanent disturbances
vn – t to have an effect on the level of Y1,t, their corresponding structural parameters
should fall in the non zero part of A(1), i.e.,
The structural parameters and disturbances in (4.17) are not readily identifiable, but
can be deduced from the general unrestricted Wold representation of Yt
(4.18)
The relationships between equations (4.17) and (4.18) indicate that
t
= A0vt and
The identification is to impose two sets of restrictions. One is the
cointegration restriction on the matrix of the long-run multiplier A(1) which identifies the
permanent components. The second is to impose an uncorrelation assumption on the two
sets of the innovations in the permanent and transitory components. This amounts to
identifying the dynamic response of the time series to the permanent disturbances.
While the demand/supply shock analysis provides insights into the economic
fluctuation mechanism, it has limitations in general economic studies as well as in real
estate research. First, most studies on the effects of demand and supply shocks are in the
framework of systems of equations which involve consumption, demand, production,
investment and output and some identity relationships among them; second, they also
traditionally assume that the two disturbances are uncorrelated, e.g. Blanchard and Quah
(1989) and King et al. (1991); and third, both types of disturbances have no long-run
effect on the stationary variables, e.g. the unemployment rate and the growth rate in GDP,
and only the supply disturbance has a long-run effect on the levels of variables. The first
point makes it unattractive in financial and real estate research. The second point seems
to impose untested and possibly unnecessary restrictions, and may distort the true effects.
The third point is arguably sound, but one might opt for some alternative. Nevertheless,
these assumptions are either required by model identification or based on some kind of
beliefs which may turn out to be untrue.
The multivariate measurement of persistence is not built on structural relations. In
addition, it is easy to include a specific kind of shock in persistence analysis and to
evaluate its effects, in a not too complicated VAR framework. It is most appealing in
studies such as real estate research, which involve some financial market attributes and
Econometric analysis of the real estate market and investment
62
where it is not appropriate to set up a system of structural equations for analysis. A
specific kind of shock can be added to the model, as in the following:
(4.19)
where vt represents the specific shocks whose effects are to be analysed, which can be the
demand shock, supply shock or monetary shock, depending on the way it is extracted
from another fitted equation(s); and
is a vector of polynomials of (m×1) dimensions.
By evaluating (4.19) with and without vt, one can establish whether an individual sector
is subject to the shock vt. Furthermore, in the existence of the effect of vt, the proportion
of the persistence due to vt and that of other shocks can be identified. In theory, more than
one set of shocks can be included; in which case, vt becomes an n dimension vector with
n being the number of sets of shocks, and
is (m×n). But, the estimation would be
empirically unsound as greater inaccuracy would be introduced. In addition, this
approach would lose appealing to those such as King et al. (1991) in a complicated
system, if it is to lose its advantages of no subjective assumptions and restrictions.
Nevertheless, if there are only two types of shocks, e.g., demand and supply, or monetary
and real, then getting one implies getting the other. Under such circumstances, vt can only
be one set of shocks, otherwise, (4.19) would be over-identified.
Persistence can be decomposed into a component due to the specific shock and that
due to other shocks:
(4.20)
(4.21)
The total persistence is
PT = Ps + P0
(4.22)
If the specific shock is chosen as a demand or monetary disturbance, then the underlying
assumption is that the demand/monetary shock may also have a longrun effect, as the
persistence measure is about the effect on the levels of variables. This assumption can be
empirically ruled out or ruled in which, in fact, becomes a hypothesis in this sense.
Although Blanchard and Quah (1989) arguably excluded the demand shock from having
a long-run effect, their empirical work suggests that the effect of a demand shock would
decline to disappear in about 25 quarters or 5–6 years! In such a long period, the
probability of a structural change or break would be rather high. If a structural change
does happen, it would override any supply shocks and the effects of demand and supply
shocks are almost mixed.
Comparing Blanchard and Quah, and King et al. with Campbell and Mankiw,
Cochrane, and Pesaran et al., the former is more based on economic theory and the latter
on statistical characteristics. The latter is also empirically applicable and flexible.
In this chapter, time series attributes of cycles, trends and persistence have been
discussed in both univariate and multivariate circumstances. Approaches to decomposing
Trends, cycles and persistence
63
time series into cycles and trends have been examined and developed. However, much
attention has been paid to shocks, represented by the innovations or residuals in the time
series data. This is because the effects of shocks can be rather different; some are
transitory while others are permanent. Moreover, shocks come from either the supply side
or demand side; and if the source is correctly identified, appropriate measures can then be
taken. Shocks to technology and production are supply shocks and viewed as having
permanent effects on output; whereas demand shocks are due mainly to financial and
consumption factors, and only have transitory effects on output. In time series analysis,
these two types of shocks are characterised by non-stationarity and stationarity
respectively. This leads to the analysis of sources of shocks to a related concept of
persistence, which is extended to the multivariate cases to study cross-sectional effects
and to identify the monetary shock.
Above issues of decomposition of time series data and identification of sources are
important and relevant to real estate research. Observing real estate data gives us an
impression that they appear to possess such time series attributes, as most other economic
and financial data do. Thus, empirical inquires in to real estate time series data are
required not only to describe the components, but also to examine the causes and effects.
This would have operational and policy implications in the real estate market.
This chapter has discussed a number of issues in individual aspects of time series data.
Based on and extending the analysis in this chapter, the dynamic behaviour of economic
and financial time series will be studied in Chapter 5, focusing on common factors in the
economic system with a unified representation of economic fluctuations and dynamics.
5
A unified representation of economic
fluctuations and dynamics
The comprehensive analysis of specific features in economic fluctuations and dynamics
naturally leads to the search for a unified representation accommodating all or most of
these features. This chapter is devoted to such an approach, built on and derived from the
discussion and deliberation on individual aspects and the review of current studies in the
previous chapters. The approach adopted introduces a concept of ‘phase shifting common
cycles’, in a system with and/or without non stationary components.
Phase is originally a frequency domain term. It differs from a conventional time
domain term ‘lag’, although it has analogous features with lags. Phases are also about
leads/lags, but they are considered with regard to the time series data across all frequency
components or cycles; whereas lags or lag structures are over a time horizon. The
following two points may explain why studying phases is helpful: (a) two time series
move pace with pace, even if they do not move exactly the same, provided the phase
function between them is linear; (b) the mapping relationship between phases and
leads/lags is nonlinear. These suggest that a simple linear relationship expressed in
phases is nonlinear and complicated when expressed in lags. The relationship cannot be
exhibited effectively in a complicated lag structure even with a large number of estimated
lag parameters and, therefore, may be ignored. In this sense, the study of phases provides
an effective way of investigating common factors among fluctuating time series.
The study of common cycles is simply an extension of common trend analysis.
Although the phase does not have a role in common trends or cointegration, it is critical
in common cycles. Whereas the phase has been noticed as a factor in economic research
for some time, it has played only a subordinate role, and has never been seriously studied.
The approach is, however, appealing to those economic sectors with cyclical behaviour,
including real estate.
The study of common cycles together with common trends aims to generalise the
Beveridge–Nelson trend cycle decomposition to a multivariate setting. The generalisation
of common trends is due to Stock and Watson (1988), leading to the ‘common trend
representation’, usually called the Beveridge–Nelson–Stock– Watson (BNSW)
representation. Embedded in this are the concepts of cointegra-tion and the long-run
comovements among several time series. Since then, the BNSW representation has
naturally been extended to incorporate common cycles (Engle and Kozicki 1993, Vahid
and Engle 1993a,b, and Engle and Issler 1995). The idea of common cycles and the so
called cofeature relations bears are markable similarity to that of common trends and
cointegration. Moreover, while a phase shift in one or more time series does not change
cointegration relations, it does affect the way in which cycles may be cancelled out. In
the simplest case, xt and yt have a common cycle factor such that a linear combination of
xt and yt would be a current period white noise innovation with no prediction capability,
A unified representation of economic fluctuations and dynamics
65
but xt and yt–1 (or xt–1 and yt) would have no common cycles (cf Engle and Kozicki 1993).
Instead they have phase shifting common cycles, or non-synchronous common cycles and
codependence as in Vahid and Engle (1993b). The effect of a phase shifting common
cycle would be that the combined series would have a shorter lag structure than the
individual series. The introduction of common cycles and the cofeature concept, in effect,
removes an untested restriction from the decomposition techniques of Blanchard and
Quah (1989) and King et al. (1991), again very similar to cointegration which removes
the untested restrictions (that none of the combinations of non stationary level variables
would lead to stationarity, i.e., the number of cointegration vectors is zero).
It is empirically helpful to make the use of terminology clear before proceeding, by
reviewing the developments and current status of business cycle studies. Recent
developments in business cycle studies include the decomposition of stochastic trends
and cycles (Beveridge and Nelson 1981, Blanchard and Quan 1989, and Campbell and
Mankiw 1987b) and the subsequent incorporation of common trends and structural
cointegration (Stock andWatson 1988, and King et al. 1991). In these cases, the
deterministic trends (if any) are always included. The common trend business cycle
economists have kept any deterministic trends without bringing in deterministic cycles.
The reason for this is that, in the real business cycle research literature, the so-called
cycles are the stationary residual elements after removing trends, a concept and term
specifically adopted in this kind of inquiry. Another description of cycles is as the
serially-correlated residuals which fluctuate or have cyclical movement. Most recently,
common cycles have been introduced into the literature. Non-synchronous common
cycles, as a further generalisation in business cycle research, could be viewed in another
way and be documented as phase-shifting common cycles. As in cybernetics or control
engineering, two series are synchronous even if there are lags or leads so long as they
keep the same lags or leads.
Therefore, it would be helpful to introduce a phase-shifting common cycle operator
matrix as a universal expression for common cycle relationships, with the specific case of
zero phase shift representing the coincident common cycle factor. Instead of having
cofeature vectors and codependence vectors separately, there would be the unified phaseshifting common cycle vectors which, unlike cofeature or codependence vectors, would
have phase-shifting operators, or lag/lead operators in the vectors. This means cofeature
and codependence vectors are unified under the concept of phase-shifting common cycle
vectors, with a zero phase shifting standing for the former.
The rest of the chapter is organised as follows: the first section proposes a unified
common cycle factor representation. In the second section, common cycles are analysed
together with common trends in the framework outlined earlier. The links between the
VAR, the reduced form moving average process and the structural disturbance
representation are established. Finally, a brief summary highlights the approach’s
appealing applications in real estate research, and the differences with the previous
studies in this area.
Econometric analysis of the real estate market and investment
66
Coincident and phase-shifting common cycles
This chapter first proposes a unified common cycle factor representation scheme in which
the cofeature relation or the coincident-phase common cycle factor is a special case. In
general, common cycle models (coincident-phase and phase-shifting) are expressed in the
VAR structure which is easy to implement in empirical studies. There are two ways to
demonstrate the phase shifting common cycle effect: a shorter moving average residual
structure and a shorter lag length in the resulting VAR models. The former clearly
exposes that phase-shifting is a non-linear operation in the time domain. Later, this
common cycle factor representation will be considered together with common trends to
yield the unified model.
First looking at a bivariate VAR model with p lags:
(5.1)
or
yt = A(L)yt = A1yt–1+…+Apyt–p+ t .
(5.2)
where L is the lag operator and
Three forms of common cycles are defined as follows:
Definition 5.1 if there exists a vector
such that:
(5.3)
then it is said that there are coincident common cycles in yt. It is equivalent to saying
that:
(5.4)
Definition 5.2 if there exists a vector
so that:
(5.5)
A unified representation of economic fluctuations and dynamics
67
where
is the combination of A1,…Ap (linear and non- linear), then it is
said that there are phase-shifting common cycles of order k in yt. This representation is
derived via nonlinear operations, and cannot simply be expressed as in (5.4). It will be
made clear later with the help of companion matrices.
Definition 5.3 if there exists a vector so that:
(5.6)
then there are common cycles of order k in yt. Obviously it is less restrictive than (5.4)
and is equivalent to saying:
(5.7)
The difference between Definition 2 and Definition 3 is that the former is a moving
average representation of order k, and the latter is an autoregressive representation of
order k(k < p). The latter is straightforward: the AR components of higher orders are
cancelled out; where as in the former, non-linear operations are involved. In fact, the
conditions in Definition 3 are a prerequisite for those in Definition 2.
It is apparent that the issues of common cycles are, in statistics, an overidentification
problem and amount to multi-colinearity in parameter matrices. For coincident common
cycles, there is overidentification in the original VAR system. The overidentification
happens in the moving average representation of phase-shifting common cycles after the
matrix operation and transformation, and the multi-colinearity is in its parameters of the
lagged variables, i.e., in the autoregressive part of the transformed specification. The
matrix operations, which are both linear and non-linear, lead to cancellation of the
autoregressive components and result in moving average residuals of lower order. The
common cycles of order k(k < p) are, simply, a multi-collinear relation amongst the
parameters representing the lagged variables at the order k and higher.
In the following, the vectors and matrices are extended so that the system is expressed
in the form of a first order vector autoregression or a one-step Markov transition. The
variable vector is defined as:
A is called the companion matrix or the Markov transition matrix with 2 × p columns and
2 × p rows, xt is a 2 × p dimension extended variable vector, and ωt a 2 × p dimension
extended residual vector. It is consciously designed so that the coefficients for the same
lag appear close together in the matrix. A1,…Ap, as 2 × 2 sub-matrices, form the first two
rows in the A matrix;and they are orderly positioned from the left to the right as in the plag autoregressive representation in (5.2). If the basic elements in (5.8) are expressed in
the 2 × 2 sub-matrices, then:
Econometric analysis of the real estate market and investment
68
(5.8)
A unified representation of economic fluctuations and dynamics
69
(5.9)
Now equation (5.1) and (5.2) can simply be written as:
xt=Axt–1+ωt .
(5.10)
It is of great interest to express (5.10) in the higher order autoregressive forms, if
coincident common cycles do not exist and other kinds of common cycles are to be
investigated. Via iterations, (5.10) becomes:
xt = Axt–1+ωt = A2xt–2+Aωt–1+ωt=…
=Amxt–m+Am–1ωt–m+1+…+Aωt–1 .
(5.11)
The number of iterations corresponds to the order of phase-shifting. With the help of the
Markov transition matrix or companion matrix, the following proposition is derived.
Proposition: There exist common cycles if, and only if, A does not have a full rank. If
matrix A has full rank, then according to one of the matrix operation properties, any Ak
will be of full rank as well. Subsequently, any order of phase-shifting operations will not
lead to the linear dependence in the rows, in particular, the first two rows, in Ak. This
rules out any kind of common cycles with linear dependence among the parameters.
Indeed, using the Laplace expansion, matrix A can be partitioned as:
Econometric analysis of the real estate market and investment
70
where Ap–=[A1…Ap–1] is 2×(2p–2) sub-matrix, Ap is a 2×2 sub-matrix, and I(2p–2)×(2p–2) is a
full rank identity sub-matrix. Also let Ac = [Ap– Ap]. There are two situations: (a)
Rank(Ac)=1, there is linear dependence in Ac, constituting the case of coincident common
cycles already discussed. (b) Rank(Ac)=2 (this does not rule out Rank (Ai…Ap)=1, i≥2),
but Rank (Ap)=1. In this case, there are no coincident common cycles, but possibly phaseshifting common cycles. Via phase-shifting operations, the linear row dependence may
shift leftwards until Rank
when a kth order
phase-shift common cycle structure emerges.
In addition, the following lemma holds: When the kth order phase-shifting exists in the
system,
To see how phase-shifting, developed in this chapter, works, simple examples are
illustrated in the following for A2. When there are no coincident common cycles, the first
two rows in A, i.e., [A1…Ap] are linearly independent. However, the first two rows in Ak
(k2) may have linear dependence. Applying matrix multiplication to A2 yields:
(5.12)
It is clear that the possibility of the linear row dependence lies only in the first two rows
in A2, as it has been assumed that there is no linear dependence in the first two rows in A,
now being moved to the third and fourth rows in A2. The linear dependence relations in
the first two rows are exactly the relations in equation (25) in Vahid and Engle (1993b).
However, to express them in the form of the Markov transition matrix (or the companion
matrix) and the first order VAR, as proposed in this chapter, has at least two advantages.
First, it reveals the phase-shift processes: no phase-shifts are required for coincident
common cycles, whereas phase-shifting may result in common cycles in the higher order
companion matrices of theVAR. Second, it is straight forward and extremely simple to
arrive at the linear dependence relationship which is to be investigated, especially in the
orders of higher than 1: they will always be found the first two rows of the matrix Ak.
The higher order transition matrix and its phase-shifting property can be viewed in
another way. Taking A2 for example, the sub-matrices
consist of two parts. The first part is A2, A3,…Ap. A common factor in cycles is made
possible via moving A2, A3,…Ap one phase forward and being added to
The second part is
From a system’s point
of view,
are the convolution of the system function At with At(t =
1, 2,…i,…) itself in the time domain, and the product of the system function and itself in
A unified representation of economic fluctuations and dynamics
71
a frequency domain. The following example shows how it works. Let a two variable
system evolve as follows:
y1t = 0.5y1,t–1 + 1t
t2t = 0.2y1,t–2 + 2t
it can be seen that:
y2t – 0.4y1,t–1 = 2t – 0.4
1,t–1
i.e., y2t and y1,t–1 share a common factor. However, do y1,t and y2t have a common factor?
If we only see a common factor among y1,t–1 and y2t, but not among y1,t and y2t, this
common factor may well be overlooked as people do not usually compare one series with
other lagged/lead series.
Express this example system in the form of (5.8) or (5.9)
It is clear that there is no coincident common cycle, as the first two rows share no multi
colinearity. But it is not clear whether there are any other kinds of common factors.
However, one phase-shift in the system yields:
It is easy to see that there is linear dependence in the first two rows in A2, a higher (first)
order phase-shifting common cycle by definition. In this way, we reveal that y2t and y1,t
(not only y2t and y1,t–1) share a common factor also, i.e.:
y1t = 0.25y1,t–2 + 0.5 1,t–1 + 1t
y2t = 0.2y1,t–2 + 2t
and a linear combination leading to moving average residuals exists:
y2t – 0.8y1t = 2t – 0.8 1t – 0.4 1,t–1
This simple example displays one of the advantages in the phase-shifting approach: it
views all variables in the system in the current period while there are leads/lags amongst
Econometric analysis of the real estate market and investment
72
these variables, revealing the common factors which would be difficult to find, or easily
overlooked otherwise.
Common cycles in non-stationary systems
So far, the common cycle structure and linear dependence relations have been defined
and demonstrated. To combine common cycles in a non-stationary system would mean
an inquiry into common cycles and common trends in the meantime. The prevailing
practice is to adopt the multivariate Beveridge– Nelson (1981) representation of trendcycle decomposition as in Stock and Watson (1988), which follows the Wold
representation theorem. Variables or a vector of variables are expressed as an infinite
moving average process of residuals. This kind of study is represented by Engle and
Issler (1995) (henceforth EI). King et al. (1991) use structural decomposition to classify
shocks with permanent and transitory effects; there are common trends but no common
cycles. The purpose of the studies combining common trends with common cycles is to
remove an untested restriction of no common cycles. Gallo and Kempf’s (1995) research
(henceforth GK) further incorporates the concept of structural decomposition proposed
by King et al. back to common cycles. Their analysis of common cycles is purely in the
form of moving average processes.
It is beneficial to investigate cycles and trends in a structural form. Nevertheless the
structural parameters and shocks are not readily identified, they have to be inferred from
the unrestricted Wold representation of EI. Both the structural and unrestricted
representations of common trends and common cycles are in the form of infinite moving
average processes which are sensitive in estimation. The moving average parameters
obtained, lack not only straightforward economic explanations, but also a dynamic view
of the processes of fluctuation. Vahid and Engle (1993b, henceforth VE) link the
unrestricted representation of common cycles and common trends to a finite VAR, where
common cycles are, specifically coincident (or cofeature), but not generally phaseshifting (or codependent). Therefore, to be consistent with the representation of common
cycles in this Chapter, processes with common cycles and common trends will also be
presented in this way.
The VAR process to be investigated is:
yt = A1yt–1+…+Apyt–p+ t .
(5.13)
In recognition of common trends or cointegration, its ECM form is
∆yt = –A(1)yt–1+Π1∆yt–1+…+Πp∆yt–p+ t ,
(5.14)
where a non zero rank A(1) implies cointegration or common trends, and Πi= –
(Ai+1+…+Ak),i = 1,…k–1. Again, using a Markov transition or a companion matrix, the
process can be expressed in the first order VAR with the ECM:
(5.15)
A unified representation of economic fluctuations and dynamics
73
where,
As in Johansen (1988), A(1) can be written as the product of two n×r vectors α′ when
there is cointegration relationship, and α is the cointegration vector. For common cycles
to exist, the following conditions should be met:
(5.16)
In fact, they can be expressed as linear row dependence relation in matrix consisting of
two blocks:
(5.17)
The higher order phase-shift common cycles (using an order of 1 as an example here) in
non-stationary system would be:
(5.18)
where
is the column rotation matrix of
with one rotation, i.e.the last column is
moved to the first column, the first column to the second column, and so on. It is again
the phase-shift operation when common trends are involved:
Econometric analysis of the real estate market and investment
74
(5.19)
The existence of phase-shifting common cycles requires linear row dependence in the
following matrix:
(5.20)
i.e.:
(5.21)
Equation (5.21) is further development of this study over Vahid and Engle (1993a,b). For
the conditions of phase-shifting common cycles to hold in non-stationary system, not
only the ECM term is required to be common, but also the phase-shifted ECM term.In
empirical estimation, with the instrument variable method for example, the ECM terms at
lag 1, as well as at lag 2, would enter in the system as instrument variables, as in Vahid
and Engle (1993b).
Trends and cycles can be easily separated with the help of the Beveridge– Nelson
decomposition and its multivariate generalisation of Stock and Watson (1988). Indeed,
this has become one of the major standard methodologies for business cycle studies. In
the following,the links between the finite VAR and the (infinite)moving verage of the
BNSW decomposition through the Wold representation theorem, and the structured
disturbance model of King et al., will be investigated.
First is the relationship between the unrestricted and the structural models. According
to the Wold representation theorem, any time series or time series vector can be
expressed as an infinite moving verage process:
∆yt = C(L) t,C(L) = I +C1L1+C2L2+… ,
(5.22)
C(L) can be decomposed as C(1) + (1–L)C*(L), therefore:
(5.23)
Taking the summation to get the variables in levels:
(5.24)
A unified representation of economic fluctuations and dynamics
75
Equation (5.24) is the Stock–Watson multivariate generalisation of the Beveridge–
Nelson trend- cycle decomposition and is referred as the BNSW decomposition.
Common trends or cointegration would imply
(5.25)
and common cycles require
(5.26)
where α and are cointegation vectors and cofeature vectors respectively. Therefore,
equation (5.24) can be written as the sum of two components, i.e., trends and cycles:
(5.27)
where and are N×(N–r) full column rank matrices, Ψ is N×(N–s) full column rank
matrix, and (L) is (N–s)×N full row rank matrix polynomial.
When r+s=N, the stack of α and would be an N×N full rank matrix,
and trends and cycles can be exclusively expressed in the cointegration and cofeature
vectors and their combinations:
(5.28)
Equations (5.24) to (5.28) have precisely depicted the nature of common trends and
common cycles, their decomposition and generating processes. In particular, when the
number of cointegration relations and the number of cofeature relations sum to N, the
trend and cycle components can be solely written in the cointegration and cofeature
vectors and their combinations.
After reviewing common trends, common cycles and their decomposition following
the Wold representation, it would be straightforward to establish the links between the
infinite moving averageWold representation and theVAR representation. First refer to the
common trends plus coincident common cycles model. The relations between the
parameters of the two representations exist for the common trend component as such:
Econometric analysis of the real estate market and investment
76
A(1)= α′,C(1)A(1)=0,α′C(1)=0,C(1) =0 ,
(5.29)
and for the common cycle part:
(5.30)
Regarding the common trends plus phase-shift common cycles model (using a first order
phase- shift model), there exist not only phase-shifted cycles, but also phase-shifted
trends. However, the parameters of two period lagged level variables are simply ΠA(1).
Due to the fact that A(1)= α′ is the long-run relation held for the variables in levels,
ΠA(1) will satisfy the long- run relation too. Therefore, for common trends to exist, the
relationships between the VAR and the unrestricted MA representations are:
A(1)= α′,C(1)A(1)=0,α′C(1)=0,C(1) =0 .
(5.31)
The common cycle relations would be more complicated:
(5.32)
It can be seen that
is sufficient to remove the cycle component of the error
correction residuals in a coincident common cycle system, but the condition of
cannot guarantee the cancellation of the cycle component of the error correction residuals
in a phase-shifting common cycle system, the second relation in (5.32) has imposed
another restriction on common cycles.
Second is the relationship between the VAR model and the unrestricted moving
average representation. The VAR model is easy to understand and analyse, in comparison
with the unrestricted infinite moving average model, since the lagged dependent variables
are on the right hand side. However, the VAR model cannot distinguish disturbances or
shocks with permanent effects from those with a transitory nature. King et al. (1991)
were among the first to decompose the disturbances into permanent and transitory
components in a cointegrated system. Gallo and Kempf (1995) further extend King et al.
to include common cycles, in which they have introduced structural form representation
for common cycles of order 0 (coincident common cycles, or cofeature relation in EI and
VE) and common cycles of higher order (phase-shift common cycles, or codependence
relation as in EI and VE).
The final relationship to be examined is that between the structural disturbance
representation of common trends and common cycles and the VAR model. Following
King et al, the unrestricted form and the structural form are set out as:
∆yt = C(L) t
(5.33)
and
A unified representation of economic fluctuations and dynamics
77
∆yt = Г(L) t ,
(5.34)
respectively. The restrictions are:
(5.35)
Combining (5.31) and (5.35) yields the common trend relations:
(5.36)
These relationships, together with the common cycle relationships between the VAR and
the unrestricted MA representations, constitute the structural VAR representation of
common trends and common cycles. Compared with (5.31), the first relation in (5.36) is
simply the same; in the third relation, the long-run parameter matrix C(1) of the
of the structural
unrestricted MA representation is replaced by Г(1) and
representation, based on what has been obtained in (5.35). The other two relations are
established in the same way.
This chapter has presented a framework for modelling and analysing economic
fluctuations and dynamics. By extending the previous work by Beveridge and Nelson,
Blanchard and Quah, Stock and Watson, King et al., Engle and Kozicki, Engle and Issler,
and Vahid and Engle on common trends and common cycles, the attributes of phaseshifting common cycles in a non-stationary system are further explored. First, we have
generalised the common cycle representation in terms of phase-shifting operations,
instead of having cofeature and codependence respectively. Phase-shifting has features
which describe the cyclical co-movement. For the cyclical components to co-move, they
must either have the same phase, or the differences in the phase are locked. Second, the
use of the Markov transition matrix or the companion matrix not only makes the
operation straightforward, but also reveals the way in which the phase-shifting
mechanism works. It has been made plain that the common cycles in a one step Markov
process are coincident, while the common cycles in a two or more step Markov transition
process have the phase- shifting attribute. That the Markov transition matrix or the
companion matrix is the reduced rank matrix is a prerequisite for common cycles to exist.
A reduced row rank Markov matrix corresponds readily to the existence of common
cycles without any phase-shifts. When the Markov transition matrix is not row rank
reduced, the higher order of the Markov matrix is row rank reduced if, and only if, the
Markov matrix itself is column rank reduced. Third, we present the analytical framework
in a VAR system. Gallo and Kempf’s analysis of common cycles is purely in the form of
moving average processes, and so is their link between the structural and the unrestricted
forms, though they start the cointegration analysis with a VAR model. The VAR
representation of common cycles and common trends has advantages in that it
demonstrates the dynamic processes and the propagation of cycles and trends over time
straight forwardly, and it is relatively easy to estimate. Fourth, the links between the
VAR and the structural disturbance representations are examined. Finally, compared with
Vahid and Engle (1993b) in which the higher order (higher than order of 1) phase-
Econometric analysis of the real estate market and investment
78
shifting (non-synchronous in VE) common cycles can be very complicated, our
procedure presents the higher order phase-shifting common cycles simply with a higher
power Markov matrix, showing that the phase-shifting is state-transition in terms of the
Markov transition matrix. While the coincident common cycle relations are linear, the
phase-shifting common cycle relations are non-linear displayed by the higher order
Markov transition matrices.
Part III
The dynamic behaviour of
real estate
This Part is devoted to empirical studies of the dynamic behaviour of real estate, built on
the methods and models developed in the previous parts, to investigate real estate
dynamics focusing on common trends and common cycles with reference to expectations
and market efficiency in the real estate market.
Prior to trend-cycle decomposition, it is crucial to construct are liable real estate index
as a smoothed index will obviously give a wrong message about the relative importance
of trends and cycles and persistence in real estate. Although there was a brief description
of unsmoothing in Part I, that was only enough to display the problems caused by
smoothing and to present a relatively objective performance comparison between real
estate and other asset investments. Therefore, in Chapter 6, the issue of smoothing in real
estate indices will be further analysed. The unsmoothed index will be constructed with a
new method based on cointegration and the idea of error in variable models, in addition
to those by applying the approaches proposed by Blundell and Ward (1987), Firstenberg
et al. (1988), Ross and Zisler (1991), Geltner (1991, 1993a,b) and Shilling (1993).
Chapter 7 analyses the persistence of shocks in real estate. It starts from the
measurement of Vk and A(1) in the terminology of Campbell and Mankiw (1987a,b) and
Cochrane (1988). Further, trend-cycle decomposition is carried out in both univariate and
multivariate systems with the aim of detecting and analysing the relative importance of
shocks from different sources, which cover sectoral and aggregate, monetary and nonmonetary, to real estate, and to conduct variance decomposition in the latter. The
fundamental issues of real estate market efficiency are investigated in Chapter 8, focusing
on the mechanism of price discovery in direct and indirect real estate investment markets.
The core issues of common trends and common cycles in real estate are addressed in
Chapter 9. These cover the analysis of the basic long-run relationship of real estate with
other investment assets; multivariate trend-cycle decomposition in a cointegrated system,
and joint analysis and tests of common cycles and common trends. As phases play an
important role in cycles and common cycles in the economy in general, and in real estate
in particular, analysis will involve both the special case of coincident common cycles and
the universal case of phase-shifting common cycles.
6
Recapturing market information from
appraisal-based real estate indices
The issues arising from using the appraisal-based real estate indices in measuring real
estate performance have been widely addressed in recent years, with most attention being
paid to the second moment estimation, or so called smoothing in real estate returns. The
phenomenon of smoothing was first raised by Working (1960). It arises from averaging a
time series of thinner interval to get a new one with wider time span, a process of
temporal aggregation. There might be several purposes for averaging: most of them are
not the topic of this book. Nonetheless, the desire to get more accurate or reliable data has
obviously played an important role. Naively, improvements in data accuracy and
reliability could be achieved from gathering as many observations as possible for an
estimate in one period. It can be observed that confidence in the use of a series for
research or assessment is related to the amount of data is similar to the process applying
to real estate indices and valuations. Working’s problem mainly involved the prices of
agricultural commodities which bear a lot of resemblance to real estate. The multidimension nature of agricultural commodity prices, e.g., heterogeneity in character,
distribution of geographical location, and non-negligible costs for the movement of
commodities, is distinct from the behaviour of financial asset prices.
Working’s prominent discovery was the 0.25 rule. This states that serial correlation
will be induced by averaging a random walk time series, and the upper limit of the serial
correlation is 0.25. Working’s example is clearly a moving average process though he did
not refer to this term, as one should notice that formal econometric estimation procedures
for a moving average process had yet to be developed at that time. Since then, many
studies have appeared in this area. For example, Tiao (1972) examines the asymptotic
behaviour of temporal aggregates of time series and provides the extreme values for the
first order autoregression and moving average parameters; Campos et al. (1990)
investigate the fixed n-period phase-averaging processes, and the relationship and
structure in the variance and autocorrelation of the original and phase-averaging
processes; and Abraham (1982) presents useful models for variousARIMA
(autoregressive integrated moving average) processes for aggregated series, provided that
the structures of the original ones are known. These studies give us insights to the actual
data generating processes and their properties in many compiled financial and economic
data series.
However, as pointed out by Blundell andWard (1987), smoothing in real estate
indices, represented by the first order auto regressive coefficient, is well above 0.25, the
extreme value any purely temporal aggregation may cause. The implication is that
smoothing in real estate indices and temporal aggregation, though similar, are not the
Econometric analysis of the real estate market and investment
82
same. This has prompted real estate researchers to address the smoothing problem in
relation to the specific procedure in real estate appraisal. Various work can be found in
Blundell and Ward (1987), Firstenberg et al. (1988), Ross and Zisler (1991), Quan and
Quigley (1989, 1991), Geltner (1989, 1991, 1993a), and Giaccotto and Clapp (1992). The
procedures developed by Blundell andWard (1987) (BW thereafter), Firstenberg et al.
(1988), and Ross and Zisler (1991) (FRZ thereafter) are similar and widely adopted due
to their simplicity, though there has never been a lack of criticism of the (unrealistic)
underlying assumption that real estate market returns follow a random walk, which
amounts to saying that the real estate market is efficient. Giaccotto and Clapp’s (1992)
approach is Monte Carlo simulation and a varying degree of smoothing for a variety of
appraisal rules is documented. Geltner (1989), applying the method of Dimson (1979)
and Scholes and Williams (1977) to the US real estate, presents a different way of
estimating real estate’s risk by regressing the real estate index return on contemporary as
well as lagged returns from a market portfolio. However, though the question as to how
much of the serial correlation is incurred in appraisal processes and how much is
attributable to the market series itself has been noticed for many years, it remains
unsolved and the focus for research on unsmoothing real estate indices. Recently, efforts
have been made by Geltner (1993b), and Barkham and Geltner (1993, 1995) among
others. They propose a reverse-filter approach to unsmoothing US and UK real estate
indices, and have allocated the smoothing factor to the UK and US appraisal-based real
estate indices respectively, which is reasonably closer to reality compared with the result
if the seriesis ‘fully’ corrected. Another interesting study is carried out by Shilling
(1993). He applies the error-in-variable method to correct the real estate indices’ second
moment, though the results are sensitive to the selection of other variables in the
regression.
In this chapter, two approaches to unsmoothing the appraisal-based real estate indices
are developed in the first section. The approaches are then applied to the real estate return
indices of JLW (Jones Lang Wootten) and IPD (Investment Property Databank) in the
second.
Approaches to unsmoothing valuation based real estate indices
This section develops approaches to unsmoothing the valuation-based real estate indices.
The approach is multivariate and utilises the cointegration and error-in-variable concept,
and is informationally more efficient and superior to the univariate unsmoothing
techniques. The variables involved are stock under construction (RESA) which is the
accumulation of change in stock under construction (RESC), the real estate indices (JLW
and IPD), and the return index of real estate company shares (FTAP).
The error-in-variable method is originally used by Shilling (1993) in reassessing the
true variance in real estate returns. The following analysis will first show how Shilling’s
method can be viewed within the traditional unsmoothing concept. Then it will be
extended to incorporate cointegration to produce better estimates.
The basic equation of Shilling (1993) states that changes in inventories under
construction is a linear function of the rate of return on real estate. One may regress
changes in inventories under construction on the rate of return on real estate to get the
Recapturing market information from appraisal-based real estate indices
83
coefficient, but due to the measurement error the coefficient would be biased. Applying
the errors-in-variable method can correct the bias and infer the true variance. The
procedure is as follows:
RESCt = c+ rt+ t
(6.1)
where RESCt is changes in stock under construction (or It – changes in inventories under
construction in Shilling’s), rt is the rate of return on real estate, and t is white noise
is normally observed which is not precisely rt but contains the
residuals. Instead of
measurement error, i.e., the regression is:
(6.2)
where
(6.3)
(6.4)
and c is a constant term. Equation (6.2) states that the construction process adjust to the
rate of return on real estate if the hypothesis is true, changes in stock under construction
is constant otherwise. The coefficient obtained from (6.2) is biased and equal to:
(6.5)
By applying the instrumental variable method or other methods to get the true coefficient,
the extent to which the variance has been smoothed can be inferred.
It should be noted that the above procedures, in particular, (6.3) and (6.4), suggest that
the variance of the observed index return (which is appraisal-based) is larger than that of
the true return series which is rather out of line with the empirical research prompted by
the obviously too low variance in the return on real estate indices.
In fact, in real estate appraisal, the error term (if it is explained in this way) ξtt is not
random, it is systematically related to the appraisal procedure to smooth the variation in
real estate return series. This explanation will become clear in the following and fit into
the universally accepted index formation process. As suggested by equation (6.6), when
ξtt is systematically related to
the variance of would be smaller than that of rt.
Nevertheless, the critical and unsolved problem is how to decide the value of the
smoothing factor α.
Now consider the traditional appraisal smoothing equation:
ra,t = αrt+(1–α)ra,t–1
(6.6)
Econometric analysis of the real estate market and investment
84
where ra,t is the rate of return on the smoothed index, and rt is the true rate of return.
Equation (6.6) in fact relaxes two restrictions in (6.3): the coefficient of rt is one, i.e., (1–
α)=1; and the error term is not only uncorrelated with rt , but also uncorrelated with ra,t.
The assumptions in (6.6) allow an unrestricted coefficient for rt, and the error term to be
uncorrelated with rt, but be possibly correlated with ra,t . Bringing (6.6) into (6.1) results:
(6.7)
where
(6.8)
is serially correlated as ra,t usually has atleast first order auto regressive residual.
Accordingly, the estimated coefficient would be biased because:
(6.9)
and k does not converge to because the last term in (6.10) does not approach zero or
disappear even in large sample cases, i.e., when T becomes very large. Instead, k is equal
to:
(6.10)
(6.11)
where ρ is the first order correlation in the rate of return of the appraised index and is
observable in the appraised index. Applying the instrumental variable method or using
Wald’s method of group average, an unbiased estimate of the coefficient can be obtained.
An estimate of the smoothing factor can be solved by comparing the unbiased and the
biased estimates of the coefficient, without presuming a random process in the true return
series. The instrumental variable method or Wald’s method of group average, in
conjunction with equation (6.6), would actually regress RESCt on rt/α.
Recapturing market information from appraisal-based real estate indices
85
The modification of Shilling’s method brings the actual appraisal process into account.
But is still requires an unbiased estimate of the coefficient to infer the extent to which the
variance has been smoothed, i.e., to infer a reasonable smoothing factor α. In the
following, a strategy using the concept of cointegration is applied. The approach is
simpler to use and more efficient in that more information is utilised in the estimation
procedure.
There is implied information content in the cointegration relationship which is relevant
to reveal the extent to which the appraised index has been smoothed. The cointegration
approach to unsmoothing real estate indices is also multivariate. Consider the appraisal
equation in levels:
Pa,t = αPt + (1–α)Pa,t,–1
(6.6′)
where Pt is the true return (price appreciation incorporating rent income) and Pa,t is the
appraised return. Rearrangement of (6.6) yields:
(6.12)
where ∆Pa,t = ra,t is the rate of return of the appraised index series. (6.12) can be written
as:
(6.13)
The above formulations have several empirically important implications. First, although
we are not able to observe the true return series, it is believed to be cointegrated with the
appraised index, as both series in levels are I(1) and the right hand side of (6.13) is I(0).
Second, the true return series and the appraised index are cointegrated with a
cointegration vector (1, –1). Third, the variation in the true return is larger than that in the
appraised index return revealed by (6.12). It is because that the true return in the current
period is the previous period appraised return plus a term which is proportional to but
larger than the change in the appraised return as α>0. In the case of α = 1, i.e., no
smoothing in the index, then (6.12) simply reduces to display the return evolution path.
Although there exists a cointegration relation between the true and appraised returns,
equation (6.12) or (6.13) cannot be estimated as both Pt and α are unknown. However,
according to one of the cointegration properties that if xt is cointegrated with yt, and xt is
cointegrated with zt, then yt and zt are also cointegrated, it is possible to bring in another
variable or a group of variables to infer the smoothing factor α. Suppose another series St
is I(1) in levels representing a variable which has a fundamental economic relationship
with real estate returns. Then if it is cointegrated with the real estate return index Pa,t with
a cointegration vector (1, – ), it should also be cointegrated with Pa,t–1,
St – Pa,t–1 – c = µt
(6.14)
Econometric analysis of the real estate market and investment
86
where µt is I(0) and may have serial correlation, c is the intercept. The true return series
should also be cointegrated with St, and in addition, be cointegrated with a cointegration
vector (1, – ),
St –Pt – c = vt
(6.15)
similarly, vt is I(0) and may have serial correlation, c is the intercept and the same as in
(6.14). Combining ( 6.14) and (6.15) yields:
Pt –Pa,t–1 = µt – vt
(6.16)
Recall (6.13), it is straightforward that:
(6.17)
Bringing (6.17) into (6.14):
(6.18)
When there is serial correlation in the residuals µt and vt, (6.18) can be estimated within
an ARMA framework.
In short, the cointegration approach involves two steps. First, it runs a cointegration
regression between St, a variable which is fundamentally related to real estate, and the
appraised real estate return index Pa,t–1, and get the residual. Second, it estimates the
coefficient for the change in the appraised real estate index in equation (6.18), and that
coefficient is in fact 1/α. There are two major advantages in adopting this strategy. First,
it exploits more information embedded in other variables other than itself. Second, it is
easy to carry out a cointegration analysis and there are quite a few variables to be used
for this purpose, compared with the errors-in-variable method. The use of instrumental
variable or other similar methods to correct for the biasedness in regression are sound in
theory, but, in practice, are often rough estimates and sometimes involve rather large
inaccuracies. This problem is minimal here, as the approach does not involve
transformation and proxies of the variables.
It is difficult to tell which one is empirically superior to the other of the two
multivariate approaches to unsmoothing. There is neither nesting nor an encompassing
relationship between them; and there is no criterion to examine their ex ante performance
either, as the real return series is not observable. Although the implied cointegration
method utilises the information in both levels and differences, it does not employ other
economic variables as in the errors-in-variable model, except through the cointegrating
variable, which is usually indirect real estate investment. Their application should be
complemented by prudent judgement and deliberation. In a sense, the contribution of
these models may lie mainly in that they provide a logical way of thinking and a
description of the working mechanism underlying the behaviour, relationship and
interaction of these real estate variables and other economic variables. When compared
with the univariate models, these multivariate models have obvious advantages. The
Recapturing market information from appraisal-based real estate indices
87
univariate models, no matter how they are set up and what kinds of assumptions are
made, uses the information in the appraised real estate index alone.
Evidence of smoothing in real estate indices and estimation
The estimation results from applying the methods of Shilling (1993) (modified) (MF–
Shilling thereafter) are reported in Tables 6.1 and 6.2, and those from the implied
cointegration approach are reported in Tables 6.3 and 6.4 for the JLW index and the IPD
index respectively. The smoothing factor α in the JLW index is estimated to be 0.6241
applying the implied cointegration approach and using the return on the Financial Times
real estate company shares as the cointegration variable. The smoothing factor in the IPD
index is 0.4179 using the implied cointegration approach. All of these estimates are in a
reasonable range and confirmed by the results from applying the method of MF–Shilling,
with being 0.5758 for the JLW and 0.4070 for the IPD index. α as in equations (6.6) and
(6.6′) is the proportion of the return represented by the market return, so a smaller means
more smoothing in the index. The smoothing factor is larger when compared with the
estimates in Barkham and Geltner (1993, 1995). Indeed, the smoothing factor in Barkham
and Geltner is quite close to that of fully unsmoothing: 0.3750 for the JLW and 0.2067
for the IPD index. The results of FRZ/BW which presumes that the true return follows a
random walk, conceivably, assigns a smaller to both JLW and IPD indices which is
0.2785 for the JLW and 0.1315 for the IPD. These results indicate that there is serial
correlation not only in the appraised but also in the true or market return series.
Although the objective of running the implied cointegration and the MF– Shilling
procedures is to infer the smoothing factor α, it is desirable to examine diagnostics from
the tests carried out in this study. A cointegration relation is confirmed to exist between
direct real estate investment, represented by the JLW and IPD indices, and indirect real
estate investment represented by the FTAP index. A model with an unrestricted constant
and unrestricted trend (model 5 in Johansen and Juselius 1990) gives a best fit with both
cointegration tests between JLW and FTAP and between IPD and FTAP, and the
cointegration relationship is accepted at the five per cent level based on the max test and
the trace value. It is reasonable to include a constant and trend without imposing
restrictions. Empirically, the short horizon of the data used and the volatile change in
these periods would make any restrictions (including those on the long-run relationship
and those suppress-
Table 6.1 Summary Statistics – MF–Shilling
Method, JLW Index
A: Total smoothness in index
ra,t = c+ρra,t–1+ζt
Dep variable
ra,t
ra,t
Constanta
ra,t–1
Q
0.0033
‡
0.6772
15.0889
(1.2544)
(7.2004)
(0.5181)
‡
14.2179
–
0.7215
Econometric analysis of the real estate market and investment
88
(8.2379)
(0.5091)
ra,t
Q
B: OLS regression
RESCt = c+ ra,t+ ′xt+ ′t
Dep variable
RESCt
Constanta
‡
–0.0278
‡
0.1008
14.8001
(4.3385)
(3.5645)
(0.4659)
C: Instrumental variable regression
RESCt =
Dep variable
RESCt
Constanta
‡
Q
–0.0150
‡
0.1725
18.0030
(4.5967)
(2.6047)
(0.2066)
D: Implied α
α = 1–(1–k*/k)/ρ = 1–(1–0.1008/0.1725)/0.7215 = 0.4242
MF–Shilling – modified Shilling (1993) method.
a Insignificant intercept depressed in calculating ρ.
xt – vector of other explanatory variables. Unlike the case of JLW, no other variables entering the
regression equation with statistical significance – vector of coefficients for xt. RESCt being times
0.1e–4.
Panel C: Instrumental variable regression uses FTAP as instrumental variable.
Q – Ljung-Box statistic for serial correlation, the order is selected as 1/4 of the observations used.
† significant at 5% level;‡ significant at 1% level.
ing constant or trend) less appealing. The maximum lag length is chosen to be two lags
by the Malcolm procedure (a Johansen procedure) with RATS, and the Ljung-Box Q
statistic indicates there is no serial correlation in the residuals. The diagnostic checking of
the results from the MF–Shilling method also confirms the model fits well at each step.
Table 6.5 summarises unsmoothing of the JLW index. It compares the smoothing
factor (α), the ratio of the standard deviation of the rate of return on the unsmoothed
index to that of the original index (σM/σA), and the coefficient of variance (CV) from
employing different methods. Table 6 is the summary for the unsmoothing of the IPD
index. By comparing and assessing these results, it can be judged that the ratio of the two
standard deviations (σM/σA) is about half size of the ratio from the fully smoothing
procedure.
Although only the variance of the indices is of interest, also it is helpful to point out
that the mean of the unsmoothed indices change as well, as this fact has been largely
ignored by most previous unsmoothing studies. For a stochastic process, the mean rate of
return is µ–σ2/2. So, if unsmoothing is applied to returns or value, instead of rates of
return, an increased σ will cause µ–σ2/2 to decrease. It is because the mean of returns or
value will not change in such unsmoothing processes, therefore only σ increases but µ
does not change. However, if unsmoothing is applied to rates of return,
Recapturing market information from appraisal-based real estate indices
89
Table 6.2 Summary Statistics – MF–Shilling
Method, IPD Index
A: Total smoothness in index
ra,t = c+ρra,t–1+
t
Dep variable
ra,t
Constanta
‡
0.8661
(0.1014)
ra,t
ra,t–1
Q
1.1743
0.0004
(7.7702)
(0.9472)
‡
–
0.8685
1.1532
(8.1585)
(0.9493)
ra,t
Q
B: OLS regression
RESCt = c+ ra,t+ ′xt+ ′t
Dep variable
RESCt
Constanta
‡
‡
–0.0082
0.2642
2.5370
(4.7457)
(5.1903)
(0.7709)
C: Instrumental variable regression
RESCt =
Dep Variable
Constanta
RESCt
–0.0096‡
0.4086‡
3.3217
(4.2158)
(2.6901)
(0.6505)
Q
D: Implied α
α = 1–(1–k*/k)/ρ = 1–(1–0.2642/0.4086)/0.885 = 0.5930
MF–Shilling – modified Shilling (1993) method.
a Insignificant intercept depressed in calculating ρ.
xt – vector of other explanatory variables. They are lagged dependent variable, real growth in GDP,
unemployment rate and Treasury bill yields in this case. – vector of coefficients for xt.
RESCt being times 0.1e–4.
Panel C: Instrumental variable regression uses FTAP as instrumental variable.
Q – Ljung-Box statistic for serial correlation, the order is selected as 1/4 of the observations used.
†significant at 5% level; ‡significant at 1% level.
they will not change, implying µ increases by the same amount as σ2/2 after unsmoothing.
Nonetheless, the effect is minimal even in the former case, as σ2/2 is very small relative
to µ.
To show how much smoothness has been caused in the appraisal index, the original
series, the series unsmoothed by the implied cointegration approach and the series
assuming a random walk, along with the return series of FT real estate company shares,
are graphed in Fig. 6.1 and Fig. 6.2. Fig. 6.1 is for the comparison between the JLW and
Econometric analysis of the real estate market and investment
90
FTAP quarterly indices, and Fig. 2 is for the IPD and FTAP monthly indices. It can be
seen that the appropriately unsmoothed real estate indices and the return on FT real estate
company shares have a very similar pattern. On the one hand, the rates of return on the
original indices are too smooth to be reliable. On the other hand, the rates of return on the
fully unsmoothed
Figure 6.1 Smoothing in the appraisalbased index – original and unsmoothed
JLW quarterly indices against FTAP
Recapturing market information from appraisal-based real estate indices
Figure 6.2 Smoothing in the appraisalbased index–original and unsmoothed
IPD monthly indices against FTAP
91
Econometric analysis of the real estate market and investment
92
Table 6.3 Summary statistics – implied
cointegration, JLW
A: Unit root in levels and in difference (ADF test)
.
.
Levels
.
Difference
JLW
.
–.3634
.
–3.9660†
FTAP
.
−2.1806
.
–7.0774‡
B: Implied cointegration analysis
St –Pa,t–1 = µt
max
α
trace
†
†
Q of vt
α
†
0.6241
1.0134
16.60
18.22
1.6022
13.9039
(30.1660)
.
.
(2.1306)
(0.4569)
Critical values in Johansen and Juselius (1990) and Osterwald-Lenum (1992) are used as
cointegration criterion; results from running Malcolm procedure with RATS.
The lag length in the ADF test is decided by the AIC, subject to satisfying the Ljung-Box statistic
for serial correlation.
* significant at 10% level, † significant at 5% level; ‡ significant at 1% level (with regard to unit
root tests, it is to reject the null of a unit root; with regard to cointegration tests, it is to reject the
null of no cointegration).
indices seem to be too volatile: the standard deviation of JLW would be 0.0704 while that
of FTAP is 0.1202 in the period of 1977 Quarter 2 to 1992 Quarter 4; and the standard
deviation of IPD would be 0.0539 compared with the standard deviation of 0.0809 of
FTAP in the period from 1987 Month 2 to 1992 Month 12. When financial leverage in
real estate companies is considered, which is about 0.50 (for example, equity was
£1,659.8m and debt was £2,281.1m in MEPC; and equity was £1,579.5m and debt was
£1,515.3m in the British Land Plc in 1995), the standard deviation of real estate company
returns may be even lower, though not substantially lower due to the reason that bond
volatility was not considerably lower than that of shares during this period. Therefore, a
full correction for smoothing implies higher volatility in the return in direct real estate
investment than in the return in real estate companies, which seems unlikely. Theoretical
reasoning and prudent judgement are in support of the unsmoothing procedures which
recognise both the importance of correction for smoothing and the fact that true real
estate returns do not (necessarily) follow a random walk; instead, there is serial
correlation in true real estate returns. Due to transaction costs, market segmentation, lack
of channels for swift information dissemination and other market inefficiencies and
imperfections, the response to a shock in the real estate market ought to be slower than in
other liquid financial markets and the effect would be felt for a longer period than in
other liquid financial markets. This suggests that returns on real estate are smoother than
returns on other kinds of investments in relatively liquid financial markets.
Recapturing market information from appraisal-based real estate indices
93
This chapter has proposed two multivariate approaches to unsmoothing the valuationbased real estate indices. In contrast to the univariate methods, these unsmoothing
procedures utilise information in other economic and financial variables implied by the
underlying economic relationships and the cointegration re lationships. Therefore,
smoothing due to valuation can be detected and corrected properly and efficiently, and
serial correlation in the market returns is not unrealistically removed. Applying these
procedures to the UK real estate indices of JLW and IPD, the estimates of the smoothing
factor suggest a reasonable volatility in direct real estate investment which is close to the
Table 6.4 Summary statistics – implied
cointegration, IPD
A: Unit root in levels and in difference (ADF test)
.
.
Levels
.
Difference
JLW
.
–1.0773
.
–3.7507†
FTAP
.
–1.1002
.
–6.6336‡
B: Implied cointegration analysis
St –Pa,t–1 = µt
max
α
trace
†
†
Q of vt
α
*
0.4179
0.9671
18.25
21.62
2.3930
12.0385
(243.2681)
.
.
(1.8999)
(0.7413)
Critical values in Johansen and Juselius (1990) and Osterwald-Lenum (1992) are used as
cointegration criterion; results from running Malcolm procedure with RATS.
The lag length in the ADF test is decided by the AIC, subject to satisfying the Ljung-Box statistic
for serial correlation.
* significant at 10% level, † significant at 5% level; ‡ significant at 1% level (with regard to unit
root tests, it is to reject the null of a unit root; with regard to cointegration tests, it is to reject the
null of no cointegration).
Table 6.5 Unsmoothing of the JLW index
Original
σM/σA (implied)
α (implied)
CV
FRZ/BW
BG
MF–Shilling
Implied CI
1.0000
2.4862
2.0817
1.9274
1.4848
01.0000
0.2785
0.3750
0.4242
0.6241
2.4594
6.9106
5.0816
4.5051
3.2392
FRZ/BW–Firstenberg, Ross and Zisler (1988), Ross and Zisler (1991) and Blundell and Ward
(1987); MF-Shilling-modified Shilling (1993) method; BG–estimates in Barkham and
Geltner(1993, 1995); Implied CI – implied cointegration.
CV – coefficient of variance; the CV of FTAP is 12.3039 during this period.
Econometric analysis of the real estate market and investment
94
Table 6.6 Unsmoothing of the IPD index
Original
FRZ/BW
BG
MF–Shilling
Implied CI
σM/σA (implied)
1.0000
3.7695
2.9455
1.5404
1.9457
α (implied)
1.0000
0.1315
0.2067
0.5930
0.4179
CV
4.9324
24.5986
15.0278
6.1170
7.7359
FRZ/BW–Firstenberg, Ross and Zisler (1988), Ross and Zisler (1991) and Blundell and Ward
(1987); MF-Shilling–modified Shilling (1993) method; BG–estimates in Barkham and Geltner
(1993, 1995); Implied CI – implied cointegration. CV – coefficient of variance; the real rate of
return on FTAP is negative and the nominal rate of return on FTAP is too small to get a sensible
CV during this period.
real world reality. Nevertheless, the estimated results should always be complemented by
prudent judgement, though the method is informationally superior and efficient.
It is crucial to construct are liable real estate index prior to analysing real estate’s
characteristics and relationships with other economic and financial variables. For
example, it might change persistence patterns; or change the relative importance of cycles
at different frequencies, and therefore, distort the results of common cycle analysis.
The unsmoothed JLW real estate index will be applied to each of the next three
chapters – the main empirical inquiries into real estate market behaviour and dynamics in
this book. The IPD index was examined and unsmoothed in this chapter merely as
another example to support the proposed unsmoothing procedures. It will not be used in
the following chapters as many other economic and financial data sets are much longer
than the IPD index and are available at a quarterly frequency.
7
Real estate’s response to shocks
This chapter is concerned with shock response patterns in the real estate market. It is
motivated by the need to advance our knowledge about the response of the real estate
market to shocks in the long run, and the impact of shocks in other economic and
financial variables on the volatility in real estate. This knowledge would enable us to
evaluate the effect on the real estate market when certain shocks occur or are forecast to
occur, and to take corresponding measures accordingly. While there have been several
studies on the long-run characteristics of the real estate market, they mainly used the
cointegration technique to investigate the long-run co-movement of real estate and other
economic and financial variables, and causal relations among them, for example, Lizieri
and Satchell (1997), and Wang et al. (1997). Few, if any, have ever studied the long-run
volatility and volatility patterns over a very long period, and the influence of other
economic and financial variables on the volatility in real estate market. An interesting but
different kind of study on persistence in real estate is Grenadier (1995), which examines
the prolonged cycles in real estate markets.
Traditionally, real estate returns, along with many economic and financial time series,
are considered to be stationary in their first difference (rate of return) and non-stationary
in their levels, and a shock would have a one-off effect on the rate of return but
permanent effect on the level. However, two points make further scrutiny necessary. First
is the case where a non-stationary time series is not a purely random walk: even if a time
series is non-stationary in its level, its behaviour can be quite different, depending on the
serial correlation structure. If there is positive serial correlation overall, the effect of
shocks would be compounding, whereas shocks on a mean-inverting process would have
smaller effect. Second is the case where economic and financial time series consist of
both stationary and non-stationary components. This is the view expressed by Campbell
and Mankiw (1987a,b), and Cochrane (1988). Their work challenged the prevailing
practice of modelling economic and financial time series as a unit root process which is
strictly first difference stationary which has sometimes falsely forced many researchers to
either accept or reject a unit root in the process. Therefore, the appropriate question asked
by them is not whether a time series is stationary or not. It is how big is the random walk
component in the time series, or the relative importance of permanent and transitory
components in the time series. This argument has lead to the development of an overall
persistence measure.
Nevertheless, the size of the persistence measure of one variable is not necessarily
inversely related to the transitory component of a shock. Therefore, transitory and
permanent components will be further decomposed, using the Beveridge– Nelson (1981)
trend-cycle decomposition approach. As the effect of cycles gradually diminishes and
that of the trend dominates with the time horizon, the decomposition would reveal the
transitional path towards the long-run destination.
Econometric analysis of the real estate market and investment
96
Univariate persistence
Since the persistence measurement in the sense of Campbell and Mankiw (1987a,b) and
Cochrane (1988) is for the long run, it is particularly helpful in the study with the longrun nature, such as the real estate market.
Considering smoothing in real estate indices. It would distort the observed persistence
pattern of real estate. However, persistence is a long-run measurement whereas
smoothing is mainly reflected in the first order (or at most upto fourth order for quarterly
data) autoregression. In this regard, persistence is a more sensible measure of the way in
which the real estate market responds to a shock. That is, accuracy in estimated
persistence is less affected by smoothing in the variance of real estate returns. To
demonstrate this feature empirically, the persistence measure of Vk and A(1), as described
in the section ‘Properties of trends and cycles’ in Chapter 4, is calculated for the original
appraised index series and the unsmoothed series (both with and without assuming a
random walk) and shown in Fig. 7.1. To compare relative persistence of shocks in real
estate and other economic and financial activities, Vk and A(1) are also calculated for a
list of variables which may influence and be influenced by real estate. These variables are
FTAP, FTA, CO, NO, NTW, and GLT, and the market index of real estate performance
HPK. Only one of the two major real estate indices, JLW, is used. The reason is that,
although the numbers of observations in JLW and IPD are in the same range, the JLW
quarterly index spans a longer time period and, consequently the persistence
measurement is more reliable and meaningful. It also avoids repetitions of calculation of
Vk and A(1) for the above mentioned variables against two indices.
Examining the Vk and A(1) measurement of the JLW index in Fig. 7.1, both original
and unsmoothed indices display similar patterns, though conceivably, the magnitude of
Vk and A(1) of the original index at the peak is higher than that of the unsmoothed index.
When k becomes large (that is what Vk really means), the Vk of both indices approaches
gradually to, but remains above, the random walk benchmark. As the patterns show, the
impact of a shock reaches its peak in about 10 to 11 quarters or slightly less than three
years. As long as the index is not fully unsmoothed, the patterns of Vk and A(1) are very
much the same, as shown by the graph. The Vk of the fully unsmoothed JLW index
displays the property of mean reversion and, understandably, converges to the random
walk benchmark, which may not be true due to the over correction. This becomes clear
when a comparison is made with some of the real sectors in the economy. In fact, there is
no mean reversion in the Vk of GDP and construction output; there is a tendency for mean
reversion in construction new orders but it never crossed and fell below the random walk
benchmark (except for the first few periods). The JLW index shares some similarity with
GDP in that a shock usually takes about three years to have its greatest impact. However,
the shape of Vk is much flatter in GDP than in JLW, suggesting larger sensitivity and over
reaction in the real estate market. Over reaction to a shock in construction output is longlasting: there is little sign of readjustment even after a very long period. Whereas
construction new orders are the most close to a random walk among the variables. This is
sensible, since it is easier to make adjustments to construction new orders than to output
in the construction sector in particular and to the economy in general.
The indices representing stock market investment are relatively close to a random
walk. In fact, Vk of FTA and FTAP can be regarded as random walks and A(1) is not
Real estate’s response to shocks
97
significantly different from 1, considering the wide range of standard error in Vk and A(1).
Vk of GLT is always very close to the random walk benchmark.
Interestingly, the pattern of Vk and A(1) of NTW (Nationwide Building Society House
Price Index) are remarkably similar to those of original and unsmoothed JLW, but not to
the fully unsmoothed JLW. The patterns of HPK, which is claimed to be a market index,
also bears remarkable similarity (and it speak of impact is even higher than that of the
unsmoothed JLW). These two points convince us to believe that certain degree of
unsmoothing is necessary, the choice of the smoothing factor is not too crucial, and full
unsmoothing is not desirable.
Fig. 7.2 shows the persistence patterns in the first difference, i.e., the rate of return on
investment or rate of change in economic activities. Vk almost approaches zero when k
becomes large (at around seven years), if the wide standard error has been taken into
account. This is an alternative way of observing stationarity. It is understandable that a
shock, no matter whether it is from demand or supply, should normally have no
permanent effect on the rate of return (while a supply shock may be able to increase or
decrease the level of activity permanently). Inspecting Vk in Fig. 7.2 confirms this
conclusion, at least as far as the variables used in this book are concerned. A(1)k, as it is
so designed, is always larger than Vk, and the patterns suggest there is serial correlation in
the rates of return or changes. Ironically, the HPK index, which is presumed to be a
market index, is more persistent than the original JLW index, and its relatively larger
standard error in its Vk and A(1)k implies large inaccuracy.
A more insightful evaluation of relative shocks is to generalise the persistence
measurement of Vk and A(1) to multivariate cases and jointly apply them to a group of
variables or sectors. The multivariate persistence analysis is more accurate in that it
removes the constraint preventing shocks being transmitted from one variable to another,
implicitly imposed in univariate cases. Therefore, multivariate persistence analysis can
examine the sources of shocks and the effects of a shock in one sector on other sectors.
Econometric analysis of the real estate market and investment
Figure 7.1 Persistence in real estate
market and other economic activities –
levels
98
Real estate’s response to shocks
99
Econometric analysis of the real estate market and investment
100
Real estate’s response to shocks
101
Econometric analysis of the real estate market and investment
Figure 7.2 Persistence in real estate
market and other economic activities –
first difference
102
Real estate’s response to shocks
103
Econometric analysis of the real estate market and investment
104
Real estate’s response to shocks
105
Permanent and transitory components in shocks (trends and cycles)
In the previous section, the persistence of shocks to real estate has been examined with
the univariate model. It is worthwhile pointing out that the amplitude of the persistence
measure for one variable is not inversely linked to the proportion of its transitory
components of shocks, as persistence measures are for very long periods when all the
transitory effects have disappeared. For example, if variable xt has a Vk of 1.8 and yt has a
Vk of 1.2, this does not suggest that the transitory component in xt would necessarily be
smaller than that in yt in, say, two years time. In a sense, the decomposition of shocks into
transitory and permanent parts illustrates, as the names suggest, the transitional path
leading to certain points in the level and there are many ways to reach the ‘destination’.
To return to the empirical analysis in this chapter, transitory and permanent
components are decomposed, using Beveridge–Nelson trend-cycle decomposition
approach. The algorithm is by Newbold (1990), and written as a RATS procedure by
Philip Meguire of North Carolina State University (1994). Prior to trend-cycle
decomposition, an ARIMA model is estimated for each variable. The order of the
ARIMA model is determined according to the principle of parsimony, subject to
satisfying the Ljung–Box Q statistic. The results are reported in Table 7.1 with one period
(one quarter), one year and five years’ horizons. In addition to the previously-defined
variables, PDN stands for the production sector, SVC for the services sector, and MNG
for manufacturing.
FTA and FTAP are not in the table, because they are very close to a purely random
walk and, therefore, only have trend but no cycle components. The fully unsmoothed
JLW series is excluded for the same reason.
Econometric analysis of the real estate market and investment
106
From Table 7.1 it can be observed that real estate has a rather small transitory
component in shocks, relative to the real sectors in the economy. The transitory
component only accounts for less than five per cent of total shocks after one quarter, and
it drops to about one per cent in one year. By contrast, the transitory component in
construction output shocks constitutes more than 20 per cent of the total in one quarter,
diminishing to about five per cent in one year. This reflects that
Table 7.1 Transitory component in shocks (% of
total shocks)
One period (quarter)
One year
Five years
JLWUS
4.52
1.14
0.42
JLW
2.09
0.69
0.29
HPK
0.73
0.27
0.16
CO
20.87
4.84
2.37
NO
14.87
11.85
3.72
NTW
3.01
0.65
0.06
GDP
11.77
5.88
1.29
PDN
9.54
1.83
0.33
SVC
14.67
3.45
0.73
MNG
12.28
3.38
0.75
the construction sector adjusts intentionally and frequently to accommodate the demand
and supply state and the price condition in commercial and residential real estate markets.
With regard to the economy as a whole, as represented by GDP, the transitory component
in shocks is about twelve per cent and six per cent of the total in one quarter and one year
respectively, reflecting the aggregate contribution of the production, construction,
services and other sectors. Interestingly again, the pattern of real estate’s response to
shocks is most close to that of housing, represented by NTW, though the latter is slightly
smaller. In a sense, real estate bears some characteristics pertinent to the real sectors in
the economy and some other characteristics pertinent to financial market investments,
with regard to the permanent and transitory components in shocks. Although real estate
has a similar long-run persistence pattern with the real sector of the economy, its
transitory, or cycle component, is profoundly smaller than that in the latter. Indeed, real
estate’s transitory component is as small as being negligible beyond one year’s horizon.
This means that cycles decay quickly and stochastic trends dominate. By comparison,
there is more transitory component in most economic activities.
The results appear to be surprising at first glance, as real estate is perceived to
fluctuate more noticeably. But, indeed, there is no economic rationalisation to justify
such a view. As a long-term investment and with long-term utility involving no frequent
transactions, what matters is the end of (long) period values and returns, not the values
and returns within the holding period. Relatively large transaction costs and illiquidity
Real estate’s response to shocks
107
also prevent real estate from joining those activities whose swift reaction to innovations
in the economy is essential to maximise values and returns to be realised immediately.
Consequently, real estate is not changed by these short-term innovations as much as
many other economic activities, and especially financial market activities. The test,
analysis and discussion in this section help clarify the matter.
Sources of shocks: multivariate and joint persistence with other
sectors
The univariate persistence of real estate has been examined in the first section of this
chapter. This Section extends persistence analysis to multivariate time series by applying
the multivariate model to a group of variables to evaluate cross-sectional effects where
real estate is perceived to influence and to be influenced by. Multivariate persistence
analysis is more sensible in that, instead of analysing the individual variables separately
as in the univariate case, it allows shocks to be transmitted from one variable to another.
Therefore, multivariate persistence analysis is able to examine the sources of shocks and
the effects of a shock in one sector on other sectors. Moreover, it is able to detect the
effect of certain kinds of shocks, e.g., a monetary shock, from that of other types of
shock.
The selection of the sectors to be included in multivariate persistence analysis and
shock decomposition should be linked to the nature and characteristics of the empirical
work to be carried out. A standard and simplified set-up of the system consists of output,
consumption and investment, as represented by King et al. (1991). The interpretation of
disturbances by Blanchard and Quah (1989) is influ-enced by a traditional Keynesian
view: permanent effects, which are persistent, are due to supply shocks, and transitory
effects, which are not persistent, are due to demand shocks. By applying a variant of
Fischer’s (1977) model, their empirical estimation simply involves just two
macroeconomic variables: output and the unemployment rate. Long and Plosser (1987)
and Pesaran et al. (1993) are typical studies on sectoral and aggregate levels, where
sectors can be aggregated to total output. In the case of Long and Plosser, the aggregate is
the manufacturing sector and the disaggregates are thirteen sections under manufacturing;
and Pesaran et al. covers ten sectors which comprise GNP. The aggregation relationship
between variables is:
and
where Ya is the aggregate of Yi(i = 1,…m). Liu and Mei (1994), combining Campbell and
Mankiw’s (1987a, 1987b) univariate persistence estimation method and Campbell and
Shiller’s (1987) present value model and its extensions (Campbell and Shiller 1989,
Campbell 1991), restrict their analysis to financial market activities and apply it to
indirect real estate investment represented by US REITs: there are no disaggregate and
aggregate relations. They first estimate a present value model in a VAR with returns on
stock portfolio, small stock portfolio and equity REITs portfolio, dividend yield and
Treasury bills; then calculate the persistence measure which is, in fact, univariate.
The last two types of analysis on the effects of shocks are the most practical and
appealing in this chapter. However, one should recognise that real estate is heavily
influenced by both financial market and real economic activities, and, consequently, both
kinds of variables should be present. In the UK, GDP is traditionally disaggregated into
Econometric analysis of the real estate market and investment
108
four broad categories and nine sectors. Before 1992 these were called section 1 for
‘agriculture’ to section 9 for ‘government and other services’. These sections are
classified, by the SIC (standard industrial classification) codes of 1992, as A, B
(Agriculture), C (Mining and quarrying), D (Manufacturing), E (Utilities), F
(Construction), G, H (Distribution), I (Transport and communication), J, K (Business
services, J and part of K, exactly), and L–Q (Government and other services, part of K,
L–Q). Among these sections, ‘mining and quarrying’, ‘manufacturing’, ‘utilities’ (C, D,
and E) are grouped as the ‘production’ sector; ‘business services’, and ‘government and
other services’ as the ‘services’ sector (G–Q); ‘construction’ and ‘agriculture’ stand on
their own. Among these industries, ‘construction’ is most relevant. ‘Production’ and
‘services’ will play a different role in the economy. These sectors constitute one facet of
study which is largely under-researched. There is no doubt that real estate, as an
investment, has been recognised to have links with the stock market and, to a certain
extent, with the non-commercial real estate market, i.e., the housing market. After these
considerations, the multivariate persistence model would consists of the real estate return
index, the FTSE index, the house price index, construction output, production, and
services. This group of selected variables differs from those variables used in the
univariate persistence analysis. On the one hand, some variables are certainly able to
provide useful information when evaluated individually, but are not appropriate to be
included in a simultaneous estimation system altogether.
All the economic data are quarterly from the Office for National Statistics. They are
all seasonally adjusted for consistency, as not all data are available in the form of nonseasonally adjusted. Table 7.2 presents the multivariate persistence estimates with the six
sectors represented by JLW, FTAP, NWT, CO, PDN, and SVC. The diagonal elements in
the table are sector-specific persistence measures (the diagonal elements in the VCK
matrix) which are equivalent to those depicted in the first section of this chapter, but are
more reliable. This is because, unlike the univariate persistence measure which ignores
the effects from other sectors, the multivariate persistence measure takes into account the
interactions between sectors. Furthermore, it is able to evaluate the effects on one sector
due to a shock in other sectors. The sector-specific persistence measure is close to the
univariate persistence measure estimated earlier, except that the persistence in
construction is much lower, with VCK = 2.8815 and A(1)=2.3618. In fact, the univariate
persistence estimates for construction output are too large and have no tendency to
converge to a certain point like other variables. FTAP, the stock market index, is most
close to a random walk with its A(1) being very close to unity. The two new variables,
production and services industries, do not have as large persistence measure as real
estate, housing and construction. No direct comparison with other studies is possible,
because there have been virtually no studies of persistence of shocks in the UK economy
and sectors. Nevertheless, this is not a serious concern as this book is not centred on these
sectors themselves but on their relationship with real estate. Several US studies have
reported that the services sector has a large persistence measure estimate while the
production sector has a relatively low value for persistence measurement. It is also
documented that utilities exhibit considerable persistence while manufacturing has a
rather small value, for persistence measurement. For example, Pesaran et al. (1993) have
estimated that, with the US data, VCK = 1.76 in utilities, VCK = 1.0 in durables
manufacturing and VCK = 0.64 in non-durables manufacturing, and VCK = 3.75 in
Real estate’s response to shocks
109
business services. In Table 7.2 the production sector’s VCK of 1.3348 would be an
aggregate estimate combining a higher value of persistence for utilities and lower value
of persistence for manufacturing. As the intention of this multivariate persistence analysis
is to investigate the cross-sectional effects between real estate and the broadly classified
sectors, no further disaggregation is necessary or appropriate here.
The off-diagonal elements in Table 7.2 provide information that is not found in
univariate persistence analysis. It has been revealed that shocks from the housing market
have the largest effect on the persistence in real estate, followed by the services sector
which is also quite substantial, the production sector, and construction. Shocks in the
stock market have effects on the persistence in real estate, but they are not as large as
those in the selected sectors in the economy.
Regarding the effects of the real estate market on other sectors, again, the largest
impacts seem to be felt in the housing market: so the commercial and non-commercial
real estate markets have very close links in this perspective. The effects of shocks on the
services sector are larger than those on the production sectors, as expected. A negative
figure for the effects on construction suggests, in statistical terms, the one period
covariance and the n(n→∞) period covariance have the different signs. This is only
possible in covariance but not in variance. The empirical meaning of a negative crosssectional persistence measure would be: a positive shock in real estate market which also
results in an increase in construction (i.e., a positive one period covariance is assumed)
would eventually lead to the decrease in construction output, or contraction in
construction industry, in the long run. This would have profound economic implications
if the particular construction figures had not been taken into account. When one looks at
the graph of construction output during this period, its universal application seems to be
less appealing, as construction output has consistently been declining, while almost all
other variables had upward trends.
The multivariate persistence measures are also estimated with the original JLW index
and with the fully-unsmoothed JLW index, and reported in Tables 7.3 and 7.4. It can be
seen that, with the original index, the persistence measure is too large for real estate as in
the univariate case. This large persistence in real estate also has consequence on the
estimates of persistence measure in other sectors. That is, not only the cross-sectional, but
also the sector-specific, persistence measures become larger; and the change is rather out
of line of the results for those sectors if the real estate index were not included. When the
fully-unsmoothed index is used in the model, persistence measures tend to be lower, but
the amount of deduction is very trivial, except in that of real estate itself and those where
real estate is directly involved. In fact, the persistence measures for the fully unsmoothed
JLW index is close to that of the stock market index. Through analysing these three sets
of results, it can be seen that the use of original JLW index in the model would distort
persistence measures across sectors and, therefore, should not be adopted. A fullyunsmooothed JLW index would leave the persistence measures of other sectors largely
intact, compared with the appropriately unsmoothed JLW index; but the persistence
measure for real estate itself would become, unreasonably, close to that for a random
walk. In this sense, the use of an unsmoothed index appears to be, no matter what the
underlying assumption, better than the original smoothed index. However, only the use of
appropriately unsmoothed index in the model gives sound estimates for real estate and
Econometric analysis of the real estate market and investment
110
across sectors, and renders insightful implications on the persistence patterns and
interactions between sectors in response to multi-sectoral shocks.
The reported multivariate persistence measurement estimates are derived with an
unrestricted VAR model of order 2, which effectively provides along-lag ARMA
structure (see Pesaran et al. 1993 and Van de Gucht et al. 1996). The restricted model,
which drops the regressors whose t-statistic of coefficient is less than one, was also
tested. The two sets of results are similar, so the unrestricted model is adopted for reasons
that it is easy to implement in the future and in slightly different situations. This is in
consistence with Cochrane’s (1988) recommendation of including all autocorrelation
terms even if they are insignificant. Both models were estimated with SUR (seemingly
unrelated regression), though there are no efficiency gains from using an OLS procedure
to applying SUR in the unrestricted model.
Table 7.2 Multivariate persistence VK (with
unsmoothed JLW index)
Sources of shocks
Effect on
JLW
FTAP
NTW
CON
PDN
SVC
JLW
2.6243
0.8744
2.7542
1.0119
1.0782
1.5273
FTAP
0.7962
0.8284
1.2710
0.6919
0.1238
1.0530
NTW
3.0412
1.5032
4.4957
1.3024
1.3020
2.3466
–0.3611
–0.0746
–0.9907
2.8815
0.7135
0.8976
PDN
0.4385
–0.1939
0.0468
1.5431
1.3348
0.5788
SVC
0.8457
0.6488
0.9700
1.9384
0.7768
1.5798
CO
Table 7.3 Multivariate persistence VK (with original
JLW index)
Sources of shocks
Effect on
JLW
FTAP
NTW
CON
PDN
SVC
JLW
6.2270
2.0697
5.0143
1.8930
1.6725
3.2187
FTAP
1.5452
1.1821
1.8337
0.9622
0.2591
1.5018
NTW
4.7747
2.2073
5.4450
1.9377
1.4215
3.2803
–0.1658
0.2065
–0.4443
3.0320
0.9240
1.2556
PDN
0.7190
0.1420
0.4433
1.8663
1.3368
1.0110
SVC
0.7174
1.1903
1.8178
2.3612
0.9585
2.2668
CO
Real estate’s response to shocks
111
Sources of shocks: persistence and monetary shocks
It would be of further interest to decompose shocks into monetary and non-monetary
shocks. The above tests have analysed the ‘sources’ of shocks, and the sources are
sectors. In the following, the sources are divided into monetary and non-monetary ones.
The reasons for adopting this line for analysis have been given in the section on ‘Sources
of shocks’ in Chapter 4. Monetary shocks can be derived from estimating a money supply
growth model and getting its residuals. The money supply growth model is specified as
follows:
∆Mt = α+ ∆Mt–1+ ∆SVCt–1+ UERt–1+vt
(7.1)
where Mt is money supply, SVCt is services sector output including the business sector
and the government, UERt is the unemployment rate. M0, the narrowly defined money, is
chosen as the money supply variable in this model. The reasons for using M0 instead of
M4, the broad money supply, are empirical. There is a big break in the M4 series in the
fourth quarter of 1981 caused by the switch between the old banking sector and the new
monetary sector. In July 1989, Abbey National’s conversion to a public limited company
caused minor breaks to the M0 series and major breaks in the M4 series. Although the
first breaks in the fourth quarter of 1981 were removed from the changes in M4, the
removal of the breaks in the changes in M4 resulted in as much distortion as the retaining
of the breaks in M4 levels. Besides these breaks, the M0 and M4 series have a similar
pattern. Beyond the concern in breaks, M0 is more liquid and more public sensitive in
representing demand factors, separated from supply factors or real factors. Table 7.5.
gives the summary statistics for fitting this model.
The multivariate shock persistence model has been re-estimated with the monetary
shocks, the residuals from the money supply growth model being included. All the
Table 7.4 Multivariate persistence VK (with fullyunsmoothed JLW index)
Sources of shocks
Effect on
JLW
FTAP
NTW
CON
PDN
SVC
JLW
0.7908
0.4364
1.4113
0.4351
0.5238
0.7001
FTAP
0.4334
0.7028
1.1013
0.5038
0.1091
0.8581
NTW
1.5724
1.2683
4.1899
0.8956
1.2844
1.9447
–0.0567
–0.1355
–0.9377
2.6298
0.7534
0.7752
PDN
0.2964
–0.2477
0.1098
1.3447
1.4548
0.4784
SVC
0.5081
0.4973
0.8540
1.6176
0.8244
1.3300
CO
Econometric analysis of the real estate market and investment
112
Table 7.5 Summary statistics for the money growth
model
α
M0
Q
‡
‡
0.0155
0.4551
(3.2723)
(4.1013)
0.3616
‡
†
–0.0011
19.9744
(2.4180)
(0.2753)
(2.6350)
Q – Ljung–Box statistic for serial correlation, the order is selected as 1/4 of the observations used.
p-value in brackets.
† significant at 5% level; ‡ significant at 1% level.
estimates are reported in Table 7.6, and a summary with sector-specific estimates and
the percentage of monetary and non-monetary effects is provided in Table 7.7. The first
line for each variable in Table 7.6. is the total persistence, the second line the effects of
non-monetary shocks as represented by the second term on the right hand side of
equation (4.19), and the third line the effects of monetary shocks represented by the first
term on the right hand side of equation (4.19). As above, the diagonal elements are
sector-specific persistence measurement, and off-diagonal elements the cross persistence
measurement. Overall, the persistence estimates are smaller than those in Table 7.2,
except for the construction sector. This is because of the inclusion of the monetary
shocks, which are expected to have smaller effects in the long run, in the model. In
previous estimation without an explicit monetary shock variable (or a monetary variable),
the persistence effects due to monetary shocks, are mixed with other shocks. Further,
scrutiny has found that the decrease in the persistence measure happens in those sectors
which are subject to monetary shocks to a substantial degree. e.g., housing with monetary
shocks account for 28 per cent in total persistence, services, 16 per cent, and stock market
20 per cent. Monetary shocks only account for 4 per cent of total
persistence in construction, and an even smaller figure of less than one per cent in the
production sector, so their total persistence estimates are largely unaffected. In summary,
a broadly defined production sector including construction, or the real economy, or the
supply side of economy, is not subject to monetary shocks
Table 7.6 Multivariate persistence VK, monetary
shocks decomposed
Sources of shocks
Effect on
JLW
FTAP
JLW
FTAP
NTW
CON
PDN
SVC
2.2304
0.4559
2.0688
0.6253
0.6802
0.8212
2.0389
0.3347
1.5680
0.7949
0.7011
0.7515
0.1915
0.1212
0.5008
–0.1695
–0.0208
0.0697
0.3265
0.5301
0.5480
0.4431
–0.1140
0.6191
0.3253
0.4216
0.3856
0.4922
–0.0267
0.5090
0.0012
0.1084
0.1624
–0.0492
–0.0874
0.1101
Real estate’s response to shocks
NTW
CO
113
2.2713
0.7616
3.3395
0.5288
0.7238
1.1391
1.9208
0.5440
2.4043
0.8496
0.7536
1.0188
0.3505
0.2176
0.9352
–0.3209
–0.0298
0.1204
–0.4758
–0.0522
–1.2515
3.0167
0.7594
0.9497
–0.3522
–0.0362
–1.0157
2.9111
0.7699
0.9403
–0.1236
–0.0160
0.0849
0.1057
–0.0105
0.0094
0.1860
–0.2489
–0.2548
1.4501
1.2941
0.4737
0.1776
–0.2774
–0.3397
1.4776
1.2826
0.4481
0.0083
0.0285
0.0849
–0.0275
0.0115
0.0256
0.1568
0.3699
–0.0256
1.6847
0.4481
1.2115
0.2742
0.2303
–0.0559
1.7202
0.6274
1.0124
PDN
SVC
−0.1174
0.1396
−0.0354
0.0303
−0.1794
0.1991
Table 7.7 Multivariate persistence VK, summary of
monetary and non-monetary shocks
Monetary shocks
VK
Non-monetary shocks
%
VK
.
%
Total
JLW
0.1915
8.59
2.0389
91.41
2.2304
FTAP
0.1084
20.45
0.4216
79.55
0.5301
NTW
0.9352
28.00
2.4043
72.00
3.3395
CO
0.1057
3.50
2.9111
96.50
3.0167
PDN
0.0115
0.89
1.2826
99.11
1.2941
SVC
0.1991
16.43
1.0124
83.57
1.2115
in the long run. However, the services sector, broadly defined to include housing and the
stock market, or the demand side of economy, or the consumption, is very much
influenced by monetary shocks. Commercial real estate, due to its fundamental links to
the real economy and financial markets, reasonably stands in the between with the effects
of monetary shocks being responsible for 9 per cent of total persistence measurement,
and a large part of persistence comes from non-monetary shocks caused in the real sector
in the economy.
This chapter first investigated the persistence patterns in the real estate market with the
original and unsmoothed real estate indices, and examined the impact of shocks in other
economic and financial variables on the real estate market. The shock persistence in the
real estate market was jointly evaluated with financial market investment and the real
world economic activities. In addition, the effects of monetary and non-monetary shocks
on the real estate market was also studied.
Econometric analysis of the real estate market and investment
114
In the long-run, what matters more is the persistence pattern than the autoregression at
a few lags. The latter is sometimes equivalent to smoothing, a combined effect of
appraisal procedure and market return process; and much effort has been devoted to it.
Although different unsmoothing methods have produced different estimates of smoothing
factor, and the discrepancy is sometimes large, the persistence patterns and the long-run
relationship with other economic and financial variables are not significantly changed
from applying one smoothing factor to another. This is because the smoothing factor has
the largest influence on the first few correlation coefficients alone and in the long run its
effect is minimal. Examining the univariate cases, as long as the index is not fully
unsmoothed which has been accepted by most real estate researchers, the patterns in the
JLW index are virtually the same and the persistence measurements reach their peak in
about two and a half to three years before declining. This means that the effect of positive
(negative) shocks is reinforced by other positive (negative) shocks in the first 11–12
quarters in an economics sense, and there is positive serial correlation (when more than
the first order autoregression is considered, the total effect would be of positive serial
correlation) in statistical measurements. The persistence pattern of the JLW index is very
similar to that of GDP, but the latter is flatter, suggesting larger sensitivity and overreaction in the real estate market, relative to the national economy as a whole. The
patterns in financial market investments are even flatter and any effect of shocks would
be exhausted in relatively short period and the adjustment takes place relatively quickly.
Compared with some real world economic activities which have close relationships with
real estate, e.g., construction, real estate investment is less persistent. It is reasonable as
real estate bears attributes of both construction and development and financial market
investments. As such, real estate investment should always be analysed, in relation not
only to financial markets, but also to the real economy.
Transitory and permanent components were decomposed next. Real estate was found
to have a rather small transitory component in shocks, relative to the real sectors in the
economy. The transitory component only accounts for less than five per cent of total
shocks after one quarter, and it drops to about one per cent in one year. By contrast, the
transitory component is much larger in the real sectors of the economy. In particular, the
construction sector has the largest transitory component in shocks, reflecting that the
construction sector adjusts intentionally and frequently to accommodate the demand and
supply state and the price condition in commercial and residential real estate markets. It
was also observed that commercial and residential real estate markets share much
similarity with regard to the permanent and transitory components in shocks.
In the study of sources of shocks and multivariate persistence, the sectorspecific
persistence measure is close to that of the univariate persistence, except that the
persistence in construction is much more sensible, verifying the superior of the
multivariate procedure. Moreover, the multivariate persistence analysis demonstrates the
cross-effects of shocks between real estate and other economic and financial variables. It
has been revealed that shocks from the housing market have the largest effect on the
persistence in real estate, followed by the services sector, production sector, andc
onstruction. Where as shocks in real estate company shares, i.e. the stock market
investment of real estate, have relatively small effects on the persistence in real estate.
This is one of the reasons that why real estate should be studied with the real world
economic activities, although the stock market investment of real estate has been
Real estate’s response to shocks
115
perceived as having close relationship with real estate, and has been used as a proxy to
the latter in case of lack of information or a reliable indicator for the latter.
The largest effects of shocks in the real estate market are felt on housing market, so
the commercial and residential real estate markets have very close links. The effects of
shocks on service sector are also substantial, followed by the production sector. However,
the most interesting finding is with the construction sectorwithanegativecrosspersistencemeasure. Thatis,theoneperiodcovariance and the n(n→∞) period covariance
have different signs. This suggests that a positive shock in the real estate market which
increases construction output would eventually lead to the decease in construction output,
or contraction in construction industry in the long-run. To a certain extent, the similar
phenomenon is attributed to demand uncertainty and construction lags by Grenadier
(1995).
The effects of monetary shocks were examined in the final section. Monetary shocks
appear to have most influential in housing market, stock market and the services sector,
which can be grouped into a wide sense services sector in the economy. They have the
least impact on production and construction sectors, or the supply side of the economy.
Real estate, due to its fundamental links to financial markets and the real sectors in the
economy, stands in between. Although real estate, the stock market investment of real
estate, housing and the construction sector are linked in many ways, their response to
monetary shocks are rather different, depending largely on whether they are on the
demand or supply side of the economy.
8
Price discovery and study of real estate
market efficiency
This chapter investigates the price discovery mechanism in real estate investment
markets. That is, price discovery in direct real estate investment and indirect real estate
investment in the stock market. The analysis takes into account both the long-run and
short-term relationships between these two investments and, therfefore adopts the
cointegration approach. In real estate research, there are several other reasons to use the
cointegration techniques The difficulties in compiling a reliable transaction driven real
estate index have prompted many real estate researchers to use some sort of proxies to a
real estate index. In the US, real estate investment trusts (REITs) are widely used for this
purpose. In the UK, there is no exact REIT counterpart, and the share price/ total return
index of real estate companies seems to be the only source with this merit. The US REITs
and the UK real estate company shares are indirect investment in real estate as the
investment is channelled to real estate via REITs or real estate company shares.
Obviously the investment in real estate companies is different to the direct investment in
real estate. A typical real estate company is usually geared, it has diversified activities,
and its performance may diverge from the performance of the properties it manages and
controls in the short term. Although indirect real estate investment is associated with
direct real estate investment, real estate company share prices may outperform or
underperform direct real estate investment. The ways in which the two investments are
linked are subject to empirical investigations.
The price discovery mechanism
From the market point of view, there is a price discovery mechanism between two related
markets, and price discovery takes place in the more efficient market. Regarding real
estate investment markets, the indirect real estate investment market of REITs or real
estate company shares is obviously much more efficient compared with the direct real
estate investment market. As it is fairly difficult to gather proper information in the direct
real estate investment market, the use of information in the indirect real estate investment
market via the price discovery mechanism looks necessary and prudent. Traditionally in
real estate investment research the correlation structure (contemporary and lagged)
between the returns on direct real estate and other financial and economic variables is
examined. The correlation is usually weak and the real estate return is typically lagged
for several periods, so not much information seemed utilisable from other sources,
including the indirect real estate investment market. A long-run view differs from the
correlation analysis on returns which results in information loss. Hence it would be
possible to find a stronger price discovery mechanism in the long run between the two
Price discovery and study of real estate market efficiency
117
real estate investment markets, to help analyse and predict the direct real estate
investment market.
This chapter follows the cointegration framework, and further carries out tests on
causality and price discovery in both the short and long run. Therefore the focus of
investigation is the relationship between direct real estate investment and indirect real
estate investment with specific reference to the price discovery between these two
investment markets in the sense of Granger causality. However, it should be borne in
mind that the Granger-type causality test is based on the concept of ‘predictability’ and
not on the concept of ‘cause and effect’ in an acceptable philosophical sense and thus is
more a technical treatment than a fundamental relationship. The outcome of tests should
thus be interpreted with careful empirical judgements.
While this chapter examines direct real estate investment in relation to indirect real
estate investment with FTAP being a proxy, it should be borne in mind that, the
aggregate of stock market investment represented by FTA has a cointegration
relationship with real estate return indices as well, and the relationship appears to be
stronger, as suggested by the statistics in Chapter 2. Nevertheless, it is of greater interest
to make inquiry into the links between these two real estate investments, so the focus of
this chapter is the two real estate investment markets instead of the real estate market and
the general stock market.
Prior to proceeding, it needs to be made clear what cointegration implies, since many
have used cointegration to address the market efficiency hypothesis, as well as the longrun equilibrium of two or more economic time series. For example, Granger (1986)
suggests that the prices of assets determined in an efficient market cannot be
cointegrated. However, this view has been challenged by a few of researchers, e.g.,
Dwyer and Wallace (1992) state that market efficiency does not preclude cointegration,
‘With market efficiency defined as the lack of arbitrage opportunities, there is no general
equivalence between market inefficiency and cointegration.’ They show cointegration
can be consistent with market efficiency in various contexts in which the converse has
been suggested. Although Dwyer and Wallace’s claim needs stricter scrutiny within the
general financial analysis framework by at least clearly refereeing to the risk, it does,
however, point out the danger of simply relating cointegration to market inefficiency
which so prevails in much of the recent applied literature. Sephton and Larsen (1991)
have also raised the concern in using the cointegration relationship as a criterion for
market efficiency. Here, real estate’s attributes are explored within a cointegration
framework for investigating Granger causality, price discovery and weak exogeneity
only, without referring specifically to market efficiency issues. Therefore, the
cointegration analysis is able to unveil more fundamental relationships among economic
time series and concentrate on more essential issues. Conventionally, quite a few
financial assets have positively correlated returns. However, their innovations or noise
components or some shocks, which could originate from and/or be influenced by some
common factors, will not necessarily be moving in the same direction. This may be one
of the intuitive implications behind cointegration.
As far as direct real estate investment and indirect real estate investment are
concerned, it is reasonable to term direct investment in real estate as the underlying asset
and the indirect investment in real estate (real estate company shares) as the derivative
asset. Information is usually compounded in the derivative market, serving for its own
Econometric analysis of the real estate market and investment
118
purposes and partly for expectations in the underlying market; which in this case means
price discovery comes from the indirect real estate investment market. In addition, it is
expected that price discovery comes from more liquid and efficient markets which again
supports the argument that the indirect real estate investment market, with less market
frictions, has price discovery over the direct real estate investment. However,
fundamentally, the returns on the derivative asset would not be independent of its
underlying asset, suggesting that the returns on the two series representing underlying
and derivative assets would not always diverge, at least in the long run (after considering
the risk premia), even if, in the short term, there might exist no clear relationships. This is
the rationale for assuming a cointegration framework in the investigation of real estate
investment in the two markets. The relationships between those markets under concern
will be further investigated in terms of causality. The underlying series, may or may not
induce short-term dynamic changes in other series, however in the long run there would
be disequilibrium information feedback to the underlying series. This hypothesis will be
tested.
Empirical evidence in the real estate market
A routine unit root test is carried out and the test statistics are reported in Table 8.1.
There is a regime shift around the end of 1989 and the beginning of 1990 with JLW and
FTAP all had a negative return in the second subperiod. Hence the statistics in Table 8.1
are reported for the whole period as well as for the two subperiods. Also the procedure
for checking the stationarity in the data series should consider the structural change in the
period. For this reason, Perron’s (1989, 1993) methodology is applied to the unit root test.
The break date is chosen (a) as known (observed from the data series), and (b) inferred by
the model. The lag length is determined by the Akaike information criterion (AIC). The
models are outlined as follows.
(8.1)
(8.2)
where DUt = 1,
if t > TB and 0 otherwise. D(TB)t = 1 if t = TB+1 and 0
otherwise. These two models are documented as Model (1) and Model (2) in Perron
(1993) respectively. Variable DUt represents a change in the intercept, variable
represents a change in the deterministic trend, and D(TB)t is the one time shock. The unit
root test is carried out for JLW and FTAP in level and in difference respectively. In each
of the data series, we present two sets of the testing results, one (the first line) for the
break date TB being treated as known, and the other (the second line) for TB being decided
by the model by maximising the t-statistic (absolute value) on the change in slope or
intercept and with k being decided according to the AIC. When we say the break date is
Price discovery and study of real estate market efficiency
119
Table 8.1 Unit root test, Perron’s (1993) models
TB
JLW
unsmoothed
89Q3 1
89Q3 1
JLW original
89Q4 1
89Q3 1
FTAP
89Q2 2
89Q2 2
∆JLW
unsmoothed
89Q3 6
89Q3 6
∆JLW original
89Q4 1
89Q3 1
∆FTAP
α
k
89Q2 1
89Q3 1
t (aic)
t(aic)
0.0010
–0.0998‡
0.0028
0.0240
.
(1.2043)
(–3.5453)
(0.9644)
0.0010
–0.0998‡
0.0028
0.0240
–0.4069
(1.2043)
(–3.5453)
(0.9644)
0.0010†
–0.0712‡
0.0019
0.9881
.
(2.253)
(–3.669)
(0.953)
0.0010†
–0.0712‡
0.0019
0.9881
–0.3676
(2.2787)
(–3.712)
(0.9636)
0.0086‡
–0.0259
–0.0299†
0.7413
.
(2.484)
(–0.296)
(–2.376)
0.0086‡
–0.0259
–0.0029†
0.7413
–2.181
(2.484)
(–0.296)
(–2.376)
0.0027‡
–0.0304‡
.
0.8224
(4.3729)
(1.9975)
0.0027‡
−0.0304‡
.
0.8224 –4.5205‡
(4.3729)
(1.9975)
0.0007‡
–0.0495‡
.
0.2569
(2.521)
(3.292)
0.0007‡
–0.0495‡
.
0.2569 –4.1236†
(2.621)
(−3.423)
0.0014
–0.1686‡
(0.893)
(2.801)
0.0014
–0.1686‡
(0.889)
(−2.820)
. –0.4492
–0.4069
–0.3634
–2.181
. –4.5205‡
. –3.9660†
. –7.0774‡
. –0.4492 –7.1257‡
t-statistics in brackets except for t(aic) and t (aic) which are separately listed. † significant at 5%
level, ‡ significant at 1% level.
t(aic) is the value of the t-statistic for testing α = 1 when TB is treated as known and k is chosen
according to the AIC. t (aic) is the value of the t-statistic when TB is chosen to maximize the tstatistic on the change in slope or intercept and k is decided according to the AIC; critical values are
based on Perron (1989, 1993). JLW and FTAP are reported as quarterly data starting in the second
quarter in 1977 and ending in the second quarter of 1993. IPD is monthly data from January 1987
Econometric analysis of the real estate market and investment
120
to December 1992. The reason for not reporting monthly FTAP has been explained in the text.
known, we mean the time series reached a turning point (the peak in this chapter). It is
quite interesting that, for the original JLW index, the model judges the break date was
earlier than that viewed in the graph, implying the emphasis of the model on the slowing
down of activity. Another point to mention is that, for indirect real estate investment,
although the peak of the index was the second quarter 1989, the model again chooses the
third quarter 1989 as the break date for the data in difference, the same data series are
confirmed to be I(1) series. i.e., the hypothesis of a unit root is break date as for direct
real estate investment. In general, as expected, all of the rejected in the difference but not
in the level, by examining the value of t(aic) and t (aic).
There is a deterministic trend in the JLW data series in difference, implying an
increasing (real term) return on the JLW index during that period. However, the regime
shift is only reflected in the change in intercept (a significant and negative ), not in the
change in slope ( ). Regarding the FTAP index, a deterministic trend only appears in
levels but not in the differenced series. This means there is no increasing return (real
term) on the FTAP index during the period. This is reasonable as the shares of real estate
companies are traded on a much more efficient stock market than in the direct real estate
investment market, and consistent return patterns should not exist. The regime shift is
also exhibited in FTAP from the third quarter of 1989.
It seems helpful to have conducted Perron’s unit root tests, in that not only has the
stationarity of the data in level and in difference been checked, but also the performance
of the relevant indices and structural change in those indices has been analysed.
In summary, the data series of JLW and FTAP are all confirmed to be I(1) series, i.e.
they are non stationary in level and stationary in first difference. There is a big difference
between the data series representing direct real estate investment and those for indirect
real estate investment as the former are appraisal based and smoothed.
The Johansen maximum likelihood procedure is used as it is more powerful than
Engle–Granger two-step method in estimation and, inparticular, various long-run and
short-term restrictions can be easily imposed and tested dynamically. Johansen’s model
H3 (Johansen and Juselius 1990) is used which imposes no restrictions on intercept and
assumes no trends in the model but allows for linear trends in DGP (data generating
process). This is evident in the JLW and FTAP series.
The test statistics are reported in Table 8.2 for the unsmoothed JLW with FTAP, and
in Table 8.3 for the original JLW index with FTAP. In each table, a is for the test on the
cointegration rank; b is for the test on the restrictions on α, a test for weak exogeneity of
JLW and FTAP, or the exclusion of the long-run variables in one or both equations; and c
is for the tests for the exclusion of short-term variables and all variables in these
equations. The statistics in a and b are from running Malcolm, the dynamic Johansen
approach. For simpler tests, c is based on Engle– Granger two-step static method. There
is no much difference between Table 8.2 and Table 8.3, so, only the results for the
unsmoothed JLW index and FTAP are explained and discussed. Both the max test and
trace test confirm there is only one cointegrating vector between direct real estate
investment and indirect real estate investment. The existence of cointegration reveals that
the relationships between direct and indirect real estate investments are stronger than
previously perceived. There at least exists a long-run price discovery mechanism to link
Price discovery and study of real estate market efficiency
121
the two real estate investment markets. This confirms the findings of Barkham and
Geltner (1995) using a simple Granger causality framework. However, there is
asymmetry regarding the causal relations in these two markets in the long-run, and the
price
Table 8.2 Cointegration, long-run and short-term
relationship, unsmoothed JLW and FTAP
a. ,
max
and Trace test
Number of cointegration vectors
i
–T.ln(1– )
–TΣln(1– )
max
trace(.95)
1
.24
16.46
14.07
19.14
15.41
2
.04
2.68
3.76
2.68
3.76
Critical values from Table 1 in Osterwald–Lenum (1992). Malcolm procedure reports two decimal
digital points for max test and Trace test.
b. Long-run parameters and restrictions
α
αi = 0
χ2
Sig level
JLW
1.0000
–0.1652
12.4978
0.0004
FTAP
–0.6272
0.1199
0.4144
0.5198
i = 1 for JLW and i = 2 for FTAP.
c. Long-run and short-term
lagged ∆JLWt
ECMt–1
F-stat
Sig level
F-stat
Sig level
lagged ∆FTAPt
F-stat
Sig level
All
F-stat
Sig level
JLW
16.6316
0.0002
4.3861
0.0043
2.7185
0.0407
4.2976
0.0004
FTAP
2.3181
0.1344
1.9656
0.1149
1.6464
0.1780
1.2183
0.3063
discovery is from the indirect real estate market to the direct real estate market. The
restriction on the long-run parameter α2 is valid with the test statistic being not significant
at all in Table 8.2 b, implying the long-run error correction term does not enter the FTAP
equation and does not help explain and predict the changes in the FTAP series. On the
other hand, the restriction on α1, the long-run parameter in the JLW equation, is invalid
and the test statistic is highly significant. This suggests the FTAP series causes the JLW
series in the long run. The asymmetric feature in the long-run parameters also implies the
information on the price disequilibrium between real estate and real estate company
shares has been fully utilised by stock market participants and no abnormal returns can be
made by developing a trading rule based on this information, while the cointegration
indicates the fundamental association between these two kinds of investments. Due to the
price discovery in the indirect real estate investment market which is disseminated to the
Econometric analysis of the real estate market and investment
122
direct real estate investment market, there seems to be some prediction ability of the
model regarding direct real estate investment. However, whether the direct real estate
investment market would be more efficient by utilising the long-run disequilibrium
information is a complicated empirical matter, depending on the tradeoff between the
transactions cost, the length of time taken to complete transactions, and the gain from
acting on such kind of information.
Table 8.2 c covers both the tests on the long-run and short-term parameters, with more
lagged variables in difference included (up to lag 4, which are largely individually
insignificant). Again, Granger causality from the FTAP series to JLW is evident, but that
from JLW to FTAP is rejected, in the long-run parameters alone,
Table 8.3 Cointegration, long-run and short-term
relationship, original JLW and FTAP
a. ,
max
and Trace test
Number of cointegration vectors
i
–T·ln(1– )
–TΣln(1– )
max
trace(.95)
1
.22
14.76
14.07
17.54
15.41
2
.05
2.79
3.76
2.79
3.76
Critical values from Table 1 in Osterwald–Lenum (1992). Malcolm procedure reports two decimal
digital points for max test and Trace test.
b. Long-run parameters and restrictions
α
αi = 0
χ
2
Sig level
JLW
1.0000
–0.1037
10.3524
0.0013
FTAP
–0.5762
0.1331
0.4034
0.5254
i = 1 for JLW and i = 2 for FTAP.
c. Long-run and short-term
ECMt–1
lagged ∆JLWt
F-stat
Sig level
F-stat
JLW
16.8786
0.0002
8.4220
FTAP
2.2952
0.1362
1.6038
Sig level
0.0000
0.1883
lagged ∆FTAPt
F-stat
2.5489
1.5817
Sig level
All
F-stat
Sig level
0.0512
8.8473
0.0000
0.1940
1.1656
0.3375
the short-term parameters alone, and both. These indicate that the real estate stock market
is not predictable through the differenced terms of direct and indirect real estate
investments, while the changes in direct real estate investment are correlated either with
the lagged variables in difference. Associated with long-run analysis, this implies that the
real estate stock market is more efficient, as this market is more liquid than the direct real
estate investment market. When this sub-market for real estate investment (consisting of
Price discovery and study of real estate market efficiency
123
direct and indirect real estate investments only) is considered in isolation, the results
accept the efficient market hypothesis (EMH) in the indirect real estate investment
market in both the weak and semi-strong forms, as no trading rules could be developed to
achieve abnormal returns based on its own past history of returns or public available
information (returns on real estate and the price disequilibrium between real estate and
real estate companies shares). However, in the direct real estate investment market, the
EMH is conclusively rejected.
It has now been made clear that real estate company shares dominate direct real estate
investment in the process of price formation, as we have expected given that information
usually flows from more liquid assets. The weak exogeneity of the indirect real estate
investment variables indicates the information flow is asymmetric between the direct and
indirect real estate investment markets in the long run, as the equation for indirect real
estate investment does not contain information on the long-run parameters while that for
direct real estate investment does. The fact that direct real estate investment is Granger
caused by indirect real estate investment in both the short term and long run while
indirect real estate investment is not Granger caused by direct real estate investment does
not necessarily mean that indirect real estate investment is more a ‘cause’than direct real
estate investment. Rather, the weak exogenous nature of indirect real estate investment
suggests it is not a fundamental underlying direct real estate investment. The information
flow asymmetry, however, does suggest that indirect real estate investment precedes
direct real estate investment.
In this chapter, the price discovery mechanism in real estate investment markets was
investigated. To put it more precisely, it was price discovery in direct real estate
investment and indirect real estate investment in the stock market. The analysis takes into
account both long run and short-term relationships between these two investments and,
therefore adopts the cointegration approach. It has been confirmed that there exists at
least one cointegration or long-run relationship between direct and indirect real estate
investments. Prediction can therefore be improved, according to Engle and Granger
(1987). Moreover, it has been further demonstrated that there exists asymmetry, i.e., the
Granger causality is a oneway effect from indirect real estate investment to direct real
estate investment, so that real estate company shares dominate direct real estate
investment in the process of price formation, and indirect real estate investment is the
main price discovery vehicle in real estate investment markets. These results suggest that
the rate of return on direct real estate investment can be explained not only by the past
rates of return on real estate company shares and on direct real estate investment itself,
but also by the past disequilibrium term between these two investments. As both long-run
and short-term parameters are not statistically significant for the variable representing
indirect real estate investment, i.e., real estate company shares, the indirect real estate
investment market appears informationally efficient – improvements in prediction can
only be achieved in the direct real estate investment market.
Yet, the predictability of real estate prices cannot simply be interpreted as evidence
against market efficiency. The two investment markets have to be considered together,
and no market is absolutely efficient or inefficient without taking into account of other
related markets and operations. The fact that real estate company share prices largely
follow a random walk without a predictable pattern means that nobody can persistently
earn excess returns from investing in real estate company shares. If there were clear
Econometric analysis of the real estate market and investment
124
patterns in real estate company share prices then one could exploit the patterns with some
strategies, such as selling high and buying low, in the stock market where transaction
costs are relatively low and the market is relatively liquid. The forecasted price changes
in real estate indices, and therefore, individual properties owned by one real estate
company or institution, and their impact on earning power and profit, would have been
already anticipated and incorporated in the share prices. It is also true that any trading
profit or loss from a real estate transaction is fully reflected in the swift changes in the
share prices of the company. Like in the circumstances for any other market which is
doomed to be inefficient due to the built-in characteristics, efficiency can and has to be
achieved with the help of another related market; and most players would be participating in both markets, or at least, few would isolate themselves in the former – the
relatively inefficient market alone. The practice of UK fund managers appears to
contradict this reasoning at first glance, as they rarely have large holdings in real estate
companies. However, if we recall the discussions in Chapter 2 that real estate returns are
not only cointegrated with real estate company returns represented by FTAP, but also
with returns on all shares represented by FTA. Then the statistics suggest that the
cointegration relationship appears to be stronger between real estate return indices and
the latter than that between real estate return indices and the former. Therefore, fund
managers can always invest in the stock market in which the real estate company sector is
a small part, to achieve efficiency. In fact, as our results imply, this might be a superior
way to achieve efficiency.
9
Cyclical fluctuations in the real estate
market
This chapter examines common cycles, with both coincident and phase-shifting
attributes, in the economy involving real estate. Common cycle analysis is, in a sense, an
extension of common trend analysis which has been popular in more than a decade and
proved useful in investigating the long-run relationship between economic variables.
Common cycles differ from common trends in that the phase matters in the former;
whereas there is no role for it in the latter. With common trends and cointegration
analysis, one of the properties can be stated as: if xt is cointegrated with yt, then xt is also
cointegrated with yt–1. However, this does not hold in common cycle analysis. It is
possible that xt and yt have no common cycle but xt and yt–1 share a common cycle. This
nature is important because usually economic fluctuations and movement are not in the
same phase. Without phase-shifting operators, any common fluctuations and common
cyclical movement, other than those coincident, would be left undetected, and a possible
economic relation would be overlooked. Real estate is one of the variables which have
noticeable cyclical characteristic but may not be in the same phase as the aggregate
economic fluctuations. Therefore, analysis on phase-shifting common cycles, in addition
to coincident common cycles, would have profound implications in real estate research.
In addition, as the usual time domain methods for phase-shifting relations are empirically
difficult to implement, frequency domain analysis is also employed in the chapter. In fact,
spectral analysis is particularly useful and easy to understand regarding cycles and their
phase.
Identifying coincident and phase-shifting common cycles
Tests on cycles
Prior to common feature tests, the existence of cycles should be checked. It is comparable
to the cointegration test in that one should verify the existence of a unit root in the time
series before carrying on the cointegration test. If a time series has a unit root, or
similarly has a cycle, then the time series can be described as having a feature, as in
Engle and Kozicki (1993). In addition to unit roots and cycles, other features could be
outliers, breaks, and so on. If two or more time series share a feature, then that feature
may disappear in the combined time series, and the two time series are said to have a
common feature, which is cointegration or the common trend when the feature is a unit
root and a common cycle when the feature is a cycle or serial correlation in the time
series. If one series has a feature and the other has not, then a testing procedure would put
all the weight to the series which has no feature and zero weight to the series with the
Econometric analysis of the real estate market and investment
126
feature. Therefore, the time series without a feature, which is cycles or fluctuations here,
should be ruled out from analysis.
Table 9.1 reports the statistics on the individual time series. The Ljung–Box Q statistic
for serial correlation includes lags up to 4, 8 and 16, with the last one being a quarter of
the total observations. The purpose for using several lags is partly to see whether there is
any possibility for stock market indices to have serial correlation, so they can be involved
in common cycle analysis. The answer is a clear no. For the FTA series which represents
the stock market investment in general, the significance level is 0.5131 for lag 4, 0.4349
for lag 8 and 0.4977 for lag 16. The respective numbers are 0.4977, 0.7506 and 0.5541
for the FTAP series, the index of real estate company shares, or indirect real estate
investment. Gilts is also very much a white noise, the significance level is 0.9391, 0.8617
and 0.5005 for these lags. Therefore, no information in stock market indices can be used
for common cycle analysis. This is one of the reasons that why one should rely on the
real sectors in the economy for real estate research. In a sense, the stock market is simply
too efficient to be useful for this kind of inquiry. In general, most sectors have serial
correlation. Those having highly significant serial correlation is construction, housing,
the money supply, the services sector, the coincident leading indicator and lagging
indicator of the ONS (Office for National Statistics). Aggregation seems to reduce serial
correlation (which can be regarded as to have common cycles in their component
variables). e.g., manufacturing has significant serial correlation using Q(4) and Q(8), but
total production only has marginally significant serial correlation with Q(4), the
appropriate measure Q(16) is not significant at all. The serial correlation displayed in
GDP is also rather weak. Three sets of Q statistic are provided for the JLW index, with
each for the unsmoothed, original, and fully unsmoothed series. The unsmoothed JLW
index displays a reasonable degree of serial correlation. The fully unsmoothed JLW
index, although based on the random walk assumption, still has serial correlation or
cycle, but the serial correlation is very little. In addition, its serial correlation structure is
distorted. Therefore, the fully unsmoothed JLW index is excluded from common cycle
analysis. The stock market indices simply do not have any serial correlation or cycles and
cannot be used for common cycle analysis either.
After those time series without significant serial correlation, or fluctuation, being ruled
out (also just one leading indicator is used, as the difference between leading indicators is
mainly in their phase), features and common features will be tested. Same as on the test
of cointegration and common trends where one would have difficulty to confer some
economic meanings to more than one cointegration vector, one would also possibly
encounter difficulty in explaining more than one common cycle. Therefore, the feature
test and common feature test are carried out in pairs between real estate and the other
variables. Table 9.2. is to check whether the feature, which is serial correlation with the
lagged variables in the pair which generates fluctuations, exists in real estate represented
by the unsmoothed JLW index, and Table 9.3. is for the feature in other variables. The
test results with the original JLW index are also provided as in Tables 9.4 and 9.5. There
is no need to have a test using the fully unsmoothed index as the index itself has not got a
feature. The test statistics used as criteria are F-statistic and χ2 statistic, and the lag length
is chosen as two. The contribution of any further lags in most series is found trivial, in
Cyclical fluctuations in the real estate market
127
common with other studies, e.g., Engle and Kozicki (1993) and Engle and Issler (1995).
It can be observed that the JLW series has a feature with all these series.
Table 9.1 Serial correlation in individual series
Series
Q(4)
JLW-unsmoothed
20.4372
0.0004
22.8767
0.0035
38.3555
0.0008
JLW-original
70.4336
0.0000
74.3681
0.0000
107.9479
0.0000
JLW-fully unsmoothed
5.9759
0.2010
10.2941
0.2450
15.8439
0.3925
PDN
7.5302
0.1104
9.0012
0.3422
12.1354
0.7346
CO
34.3577
0.0000
44.1157
0.0000
50.7638
0.0000
SVC
17.7542
0.0013
24.1725
0.0021
33.8870
0.0056
NWT
59.9269
0.0000
61.2236
0.0000
81.3520
0.0000
GDP
1.8768
0.7584
12.0061
0.1509
25.5425
0.0608
114.3367
0.0000
158.0207
0.0000
165.7199
0.0000
M0
60.3252
0.0000
71.9651
0.0000
87.4877
0.0000
MNG
15.1925
0.0043
16.6892
0.0335
20.5253
0.1975
FTAP
1.9614
0.7429
5.0648
0.7506
14.5999
0.5541
FTA
3.2738
0.5131
7.9852
0.4349
15.3707
0.4977
GLT
0.7954
0.9391
3.9486
0.8617
15.3311
0.5005
UER
211.6895
0.0000
290.6080
0.0000
318.3295
0.0000
CC
130.8385
0.0000
145.6726
0.0000
249.0968
0.0000
LL
96.1702
0.0000
127.4169
0.0000
233.2890
0.0000
SL
102.7752
0.0000
119.2907
0.0000
232.8703
0.0000
LG
127.2216
0.0000
144.7604
0.0000
230.8134
0.0000
RESA
sig level
Q(8)
sig level
Q(16)
sig level
Table 9.2 Feature (cycles) tests – JLW has a feature
involving other variables (with unsmoothed JLW
index)
Series
F-test
sig level
χ2 test
sig level
PDN
3.6726
0.0062
11.0799
0.0009
CO
3.1009
0.01578
9.0472
0.0026
SVC
4.1795
0.0028
12.6927
0.0004
NTW
4.5202
0.0017
13.7359
0.0002
Econometric analysis of the real estate market and investment
128
GDP
3.4765
0.0086
10.3800
0.0013
RESA
3.0061
0.0184
8.6990
0.0032
M0
2.8771
0.0227
8.2175
0.0041
MNG
2.6376
0.0334
7.2987
0.0069
UER
3.9667
0.0068
10.0212
0.0015
CC
2.4600
0.0562
5.3972
0.0202
Table 9.3 Feature (cycles) tests – other variables
have a feature involving JLW (with unsmoothed
JLW index)
Series
F-test
sig level
χ2 test
sig level
PDN
3.6726
0.0062
11.0799
0.0009
CO
3.7880
0.0052
11.4326
0.0007
SVC
4.5192
0.0016
13.7834
0.0002
NTW
13.7728
0.0000
30.9195
0.0000
GDP
0.1868
0.9663
1.0217
0.3121
RESA
55.6031
0.0000
48.6621
0.0000
M0
9.8676
0.0000
25.7435
0.0000
MNG
6.2643
0.0001
18.5098
0.0000
UER
490.8699
0.0000
58.2426
0.0000
CC
254.0238
0.0000
56.6950
0.0000
Table 9.4 Feature (cycles) tests – JLW has a feature
involving other variables (with the original JLW
index)
Series
F-test
sig level
χ2 test
sig level
PDN
11.3667
0.0000
28.0602
0.0000
CO
12.2946
0.0000
29.3434
0.0000
SVC
15.7999
0.0000
33.3834
0.0000
NTW
12.4889
0.0000
29.5992
0.0000
GDP
12.7949
0.0000
29.9935
0.0000
RESA
11.6308
0.0000
28.4363
0.0000
M0
12.9567
0.0000
30.1979
0.0000
MNG
11.2039
0.0000
27.8239
0.0000
Cyclical fluctuations in the real estate market
129
UER
14.2936
0.0000
28.4420
0.0000
CC
13.0109
0.0000
26.9294
0.0000
When the feature in other variables is considered, all but GDP has a clear feature. GDP is
still included for analysis, because it has small serial correlation up to very long lags.
When the original JLW index is applied in the analysis, the feature test statistics for the
other variables become slightly smaller but are largely unaffected, so the influence of the
original JLW series on the other is slightly smaller than that of the unsmoothed JLW
series. The feature test statistics in JLW have increased considerably due to the much
larger amount of serial correlation in the original JLW series, which reduces the relative
importance of the role of the other variables in the feature for JLW. The comparison
between the two sets of the results is interesting that large serial correlation in the JLW
series can only influence the feature in JLW itself but not in the other variables. That the
unsmoothing is sound can be viewed
Table 9.5 Feature (cycles) tests–other variables
have a feature involving JLW (with original JLW
index)
Series
F-test
sig level
χ2 test
sig level
PDN
3.4064
0.0094
10.1894
0.0014
CO
3.6614
0.0063
11.0420
0.0009
SVC
4.3976
0.0019
13.4601
0.0002
NTW
12.4577
0.0000
29.5584
0.0000
GDP
0.2493
0.9384
1.3536
0.2447
RESA
55.0949
0.0000
49.2556
0.0000
M0
11.4016
0.0000
28.3238
0.0000
5.4155
0.0004
16.4079
0.0001
UER
565.4358
0.0000
59.4209
0.0000
CC
254.5229
0.0000
57.5925
0.0000
MNG
from another point: there is increased influence of JLW on the other variables, and
increased influence of the other variables on JLW.
Unit roots and cointegration
Routine unit root test is carried out as well. The existence of a unit root in the variables in
levels can be confirmed and a unit root in the variables in the first difference can be ruled
out generally. The cointegration relation between real estate and other variables is
verified by Malcolm, a Johansen testing procedure with RATS. The results are briefly
reported in Table 9.6. Leading indicators and the unemployment rate are stationary, so
Econometric analysis of the real estate market and investment
130
they are excluded from the table. All the other variables are confirmed to have the
cointegration relationship with real estate and there is only one cointegration vector in
each pair between real estate and other variables. The selection of the cointegration
models is mainly based on visual inspection of the graphs, as Johansen and Juselius
(1992) did. In the following common cycle analysis, the error correction term is included
when there is a cointegration relation in the pair, and no error correction term otherwise.
In fact, only the analysis of real estate’s relations with the unemployment rate and the
leading indicator does not have an error correction term, as these two variables are
stationary themselves and there exists no error correction mechanism between them and
real estate. Only the unsmoothed JLW index is used in the cointegration analysis. Once a
cointegration relation is confirmed by the unsmoothed real estate index, that relation
should also exist for the original index, and vice versa. The confirmation of a
cointegration relation with these variables means that real estate shares a common trend
with them, and it is rather unusual if real estate does not move together with most
economic and financial activities in the long-run. In the following, it will be revealed that
the situation is different for cycles and common cycles.
Table 9.6 Cointegration and common cycles
One cointegration vector
max
a
PDN
b
CO
SVC
c
a
NTW
GDPd
RESA
a
M0c
d
MNG
Two cointegration vectors
trace
max
trace
15.83
23.32*
7.49
7.49
19.83†
26.54‡
6.71
6.71
16.78†
16.97†
0.19
0.19
15.70*
21.66†
e
5.96
5.96e
23.45†
32.00‡
8.55
8.55
18.42†
19.40†
0.98
0.98
15.70†
16.87†
1.17
1.17
18.03*
27.12‡
9.09
9.09
* significant at 10% level, † significant at 5% level, ‡ significant at 1% level.
a. model H5: with unrestricted constant and trend; b. model H2: with restricted constant and no
trend; c. model H3: with unrestricted constant and no trend; d. model H4: unrestricted constant and
restricted trend.
e. the statistic is significant with this model; other models reject the hypothesis of two cointegration
vectors, but marginally accept the hypothesis of one cointegration vector.
Common cycles
The results from common feature or common cycle tests are reported in Table 9.7, using
the unsmoothed JLW series to represent real estate investment. Both the existence of
coincident common cycles and one phase-shift common cycles are tested. The
instrumental variable (IV) method is used to estimate the coefficient in a relation that
(∆y1t – ∆y2t) has no cycles. This means (∆y1t – ∆y2t) is the white noise residual and has
Cyclical fluctuations in the real estate market
131
no serial correlation with lagged ∆y1t and ∆y2t, and the cointegration residual at t–1 if y1t
and y2t are cointegrated. The coefficient from direct regression of ∆y1t on ∆y2t would be
biased, as ∆y2t is correlated with the current period innovation. The instruments used are
the first and second lags of the JLW series and the other variable in the pair, plus the first
lag of the cointegration vector if there is a cointegration relation. In the case of phaseshifting common cycles, the instruments are the second and third lags of the relevant
variables, plus the second lag of the cointegration vector when the two variables in levels
are cointegrated. 2SLS (2 Stage Least Squares) is a similar method.
There are four statistics reported. , the coefficient of the other variable (∆y2t) in the
regression (the coefficient of JLW is set to one); a significant suggests a relation or
correlation, though may not necessarily a common cycle relation, exists between real
estate and ∆y2t, Both F-test and χ2 statistics are used to check the existence of common
cycles, or the cancelation of cyclical components, which is suggested by the insignificant
test statistics. The combined series is also examined against the serial correlation with the
Ljung–Box Q statistic – no correlation with the lagged variables is equivalent to no serial
correlation in the combined series itself.
First looking at the coincident common cycles. JLW’s common cycle feature is clearly
found to be with the house price represented by the NTW index, the services sector
(SVC) and the manufacturing sector (MNG), with very low insignificant levels for F, χ2
and Q, and a very significant . Real estate seems to be more cyclical, i.e., the magnitude
of its cycles are larger, than the service sector with of 2.5033. Put it another way, the
magnitude of cycles in real estate is about two and a half times that of the cycles in the
services sector. But the cyclical fluctuations in real estate are less that those in the
housing market, suggested by the coefficient of 0.7103. The magnitude is about the
same for real estate and the manufacturing sector. The existence of common cycles
between real estate and the money supply (M0) and between real estate and total
production (PDN) is marginally confirmed. In the case of total production, the Ljung–
Box Q statistic is the criterion, but recall that the PDN series is much closer to being a
white noise than the MNG series, partly due to the aggregation, this result should be
viewed with caution. With the money supply, only the F statistic marginally accepts the
existence of common cycles, and real estate is relatively less cyclical than the money
supply variable. There is no common cycle feature found between real estate and the
GDP series. This is not to rule out the cyclical co-movement of real estate with GDP
because, the aggregation in GDP has reduced or phased out the fluctuations in the GDP
index in general, and the GDP series is rather white in this given short period in
particular. In a sense, investigations at the sectoral level is helpful, not only in the sectoral
analysis itself, but also in inferring implications for some economic aggregates. Quite
beyond imagination, if not surprisingly, real estate shares no common cycles with the
construction sector, though the existence of common trends or long-run co-movement
between them is so evident. Common cycle feature remains non-existent even if stock
under construction, a derived variable which has profound long-run relationship with real
estate, is used in the test. The series of coincident leading indicator, GDP and total
production, though lack a common cycle feature with real estate, have a very clear
correlation with real estate. One should notice that, theoretically and empirically, the
conditions for common cycles are rather less possible to meet than those for common
trends or cointegration, as the former requires that the components in two series are
Econometric analysis of the real estate market and investment
132
proportional at every frequency of their cycles, whereas in the latter, merely the zero
frequency component plus some elements very close to zero frequency (in fact it is these
elements which would decide a cointegration relation, otherwise two I(1) series would
always be cointegrated). Therefore, while many economic time series variables have
common trends and are cointegrated, not so many have common cycles. Put it another
way, there are many different paths to reach a certain level of activity. Any path different
from a pure random walk path is cycles or fluctuations. So, there could be many different
cycle patterns even two time series are bound to move together in their levels.
For those sectors with which real estate has no coincident common cycles, inquiry is
made on whether there are phase-shifting common cycles. The existence of coincident
common cycles does not preclude phase-shifting common cycles, as phase-shifting
common cycles (of order one) cancel (a majority of) cyclical
Table 9.7 Common feature tests – coincident
common cycles using IV method
Series
PDN
CO
SVC
F-test
1.0038
18.5485
(0.0465)
(0.0795) (0.0339)
(0.2928)
–0.0814
3.6716 9.5803
42.8476
(0.6448)
(0.0062) (0.0020)
(0.0003)
0.7650 2.2982
15.6771
(0.5791) (0.1295)
(0.4757)
1.0086 3.0500
19.7933
(0.4217) (0.0807)
(0.1800)
2.8848 8.8887
23.8026
(0.0222) (0.0029)
(0.0939)
3.1168 4.0808
36.6884
(0.0152) (0.0434)
(0.0014)
1.9423 5.1160
29.4691
(0.1024) 0.0237)
(0.0210)
1.5394 0.2551
19.7070
(0.1931) (0.6135)
(0.2337)
3.3809 9.0456
41.9067
(0.0152) (0.0026)
(0.0004)
2.9531 4.1912
34.3338
(0.0278) (0.0406)
(0.0049)
2.5033
0.7103
(0.0001)
GDP
2.4395
(0.0087)
RESA
0.0501
(0.3460)
M0
0.7684
(0.0095)
MNG
0.9347
(0.0151)
UER
0.0010
(0.0306)
CC
Q
2.0996 4.5010
(0.0000)
NTW
χ2 test
0.0009
(0.2604)
Cyclical fluctuations in the real estate market
133
components but leaves an MA(1) in its residuals. While a test on the existence of phaseshifting common cycles is just a little bit more difficult than that on coincident common
cycles, the test on phase lead or lag is empirically ambiguous or infeasible, as there still
exists an MA(1) in the residual, and viewing a graph with the two time series involved
may be a better alternative. However, one may resort to frequency domain analysis to
deal with this problem. In fact, spectral analysis is particularly useful and easy to
understand regarding cycles and their phase.
The usual time domain results are reported in Table 9.8. It seems that there is no clear
pattern emerged. Only GDP appears to have possible common cycle components after
one phase shift suggested by the F-test and the Ljung–Box Q statistic. This possible
phase difference between real estate and GDP should also come from some of the GDP
sectors. Construction is one which still has no common cycles with real estate but
coherence has increased after one phase shift, viewed by the increased, but still
significant, test statistics. The production and services sectors may also have some phase
differences with real estate. As mentioned before, it is not easy to tell leads from lags in
these pairs, and it is possible one series has leads over the other at, say, lower frequencies
but lags at higher frequencies. With phase shift common cycles of order one, the residual
is MA(1), so longer lags in variables are also used and tested (with two lags, the
components to be excluded are lags 2 and 3, and the remaining ingredient
Table 9.8 Common feature tests. Phase-shifting
common cycles using IV method (two lags)
Series
PDN
CO
SVC
NTW
GDP
RESA
M0
MNG
F-test
χ2 test
Q
1.0717
2.2909
5.2909
16.9678
(0.0730)
(0.0586)
(0.0214)
(0.3877)
0.0069
3.3400
7.4187
40.4072
(0.9715)
(0.0107)
(0.0065)
(0.0007)
2.5538
1.0101
3.3091
15.3678
(0.0000)
(0.4210)
(0.0689)
(0.4979)
0.7768
0.7530
2.0872
19.0690
(0.0003)
(0.5876)
(0.1485)
(0.2106)
2.8607
1.7042
3.6462
21.7875
(0.0055)
(0.1497)
(0.0562)
(0.1502)
0.0492
3.1666
4.6833
35.7926
(0.3649)
(0.0142)
(0.0305)
(0.0019)
0.7827
2.5916
7.7120
29.0958
(0.0139)
(0.0360)
(0.0055)
(0.0233)
0.7922
2.0476
2.3817
21.7709
(0.0424)
(0.0868)
(0.1228)
(0.1507)
Econometric analysis of the real estate market and investment
UER
CC
134
0.0010
2.8542
7.4330
40.7596
(0.0325)
(0.0322)
(0.0064)
(0.0006)
0.0013
3.0516
4.7109
32.2767
(0.1427)
(0.0244)
(0.0300)
(0.0085)
includes innovations in current period and at lag one). According to Table 9.9, real estate
and the unemployment rate seem to have some common cycle elements with one phaseshift – the F-test statistic is not significant at five per cent level. The unemployment rate,
though regarded and should be a stationary variable, is in fact very persistent and has
some kind of upward trends, so further test, e.g., with even longer lags to accommodate
its serial correlation at higher orders, is of no much help. With regard to leading
indicators, they all have substantial higher frequency components to (more than) reflect
economic fluctuations. These higher frequency components would not be cancelled out in
most of their combinations with economic and financial time series. In this sense,
common cycle analysis in the frequency domain would be helpful and supplementary to
the analysis in the time domain.
Frequency domain analysis and presentation
The frequency domain results are better viewed with the coherence and the phase graphs.
The only research on real estate using a frequency domain method is Barras and Ferguson
(1985), which examines the spectra of real estate regarding its different cycle
components, or relative magnitude of cycles at different frequencies. This chapter further
investigates the cross-spectra of real estate with other economic
Table 9.9 Common feature tests. Phase-shifting
common cycles using IV method (four lags)
Series
PDN
CO
SVC
NTW
GDP
F-test
χ2 test
Q
0.9939
1.5126
3.9789
16.1872
(0.0753)
(0.1714)
(0.0461)
(0.4400)
0.2151
2.6923
7.1684
36.1416
(0.1783)
(0.0130)
(0.0074)
(0.0028)
2.5616
1.8927
6.0528
15.2049
(0.0000)
(0.0764)
(0.0139)
(0.5097)
0.8059
1.5290
3.0898
15.0102
(0.0005)
(0.1657)
(0.0788)
(0.4507)
2.4859
1.6058
5.5996
22.4413
(0.0002)
(0.1412)
(0.0180)
(0.1295)
Cyclical fluctuations in the real estate market
RESA
M0
MNG
UER
CC
135
0.0740
2.1578
3.9322
31.6439
(0.1657)
(0.0427)
(0.0474)
(0.0072)
0.7210
2.5962
12.1518
28.6301
(0.0335)
(0.0161)
(0.0004)
(0.0266)
0.9406
1.1166
7.5964
16.6337
(0.0135)
(0.3701)
(0.0058)
(0.4097)
0.0009
1.8123
6.6421
39.0673
(0.0396)
(0.0979)
(0.0100)
(0.0011)
0.0011
2.0460
5.3291
32.5282
(0.2201)
(0.0605)
(0.0210)
(0.0085)
activities, emphasising common cycles and their phases. The magnitude of crossspectrum
is coherence and the imaginary part is phase. Coherence is about how much in common
of two time series, and phase is about the lead/lag relations. The advantages of using
these two frequency domain statistics are obvious: they reveal and show the proportions
of common components in two time series at each frequency or each cycle, and the phase
lead/lag in the same way. In Fig. 9.1 four examples are depicted to show typical leads
ranging from one phase lead to four phaselead, using one time series (GDP indifference)
against its own lags. The lefthand side axis is for coherence and the right-hand side axis
for phase. Coherence is symmetric about the vertical axis and phase is symmetric about
the origin point, therefore only the right half of the graph is displayed. The horizontal
axis ranges from zero to πf (the other half from–πf to zero) with 2πf being one cycle (one
quarter in this case). At the half point of the horizontal axis the frequency is lower at f /2
and a complete cycle is in two quarters, at the frequency of f /4 the cycle is annual, and so
on. A value of one for coherence at a particular point means the two series are altogether
in common at that frequency or cycle, and if coherence is one over the whole spectrum
then the two series are common at all frequencies or cycles. If there is no phase lead/lag,
the line for phase would be zero over the whole range in horizontal axis. If there is a strict
one phase (period) lead at every frequency, then it would be a linear line as depicted in
Fig. 9.1 a. A value of
Econometric analysis of the real estate market and investment
136
Figure 9.1 Coherence and phase – an
example (GDP with lagged GDP)
one means 180°(π) degree lead in half cycle (as the other half is not displayed). A time
series has perfect coherence with itself so the value of coherence is one over the whole
spectrum. The phase statistic is one (180°) lead for the quarterly frequency in half
quarter, equivalent to 360° in one quarter; at the half point on the horizontal axis, the
phase is 0.5 (90°) lead for the semi-annual frequency that is also one quarter (1/4×2
quarters ×2). So, as long as the line for phase statistic is linear, every frequency
component will have the same lead; if the line is not linear, then some frequency
components would have longer or shorter leads than others, and would not be a purely,
say, one phase lead. Fig. 9.1 b is for two phase lead, its coherence is the same, the phase
is twice as big as in Fig. 9.1 a, as–1isthe same as +1 (360° +(–180° = 180°)), and the
negative part of the phase line can be continued upwards at the point (0.5f , 1). In Fig. 9.1
c, the phase is three times as big as that in Fig. 9.1 a, and in Fig. 9.1 d, four times as big.
As can be seen, the coherence becomes more distorted, as the series is not ideal (from –∞
to +∞ in time).
With these basic ideas, real estate is analysed in the frequency domain with other
economic variables regarding their common cycles and phase leads/lags. First looking at
the graph of JLW with GDP in Fig. 9.2. There is about 80 per cent coherence in most of
the cyclical components from quarterly to semi-annual cycles, but the cycles around the
annual frequency have little in common in these two series. Real estate and GDP are in
the same phase over nearly the whole spectrum except real estate lags in the annual cycle.
As the phase statistic is not on a straight line as in Fig. 9.1a, they are not purely
coincident nor phase-shift with a single order, so time domain techniques are not
effective (there would be many statistics for different leads, few of them would be
Cyclical fluctuations in the real estate market
137
statistically significant individually, while a possible joint significant statistic dose not
tell anything about which leads and the how big is the lead at each cycle). It has been
seen that the time domain analysis on common cycles between real estate and GDP
suggested that there probably exist such characteristics. The coherence of real estate with
construction is about 0.5, with no regular phase patterns, as shown in Fig. 9.2b. The
higher coherence happens with the quarterly cycle which seems to be in the same phase,
and the annual cycle with rather large leads (about three quarters to one year at this
frequency). Overall, no single order phase shift (and even two or three combinations) can
describe their phase relations, resulting a straightforward rejection of any common
features in cycles in the time domain. In fact, real estate and construction do share some
common cyclical movements or fluctuations. Real estate and housing have higher
coherence at the lower frequencies, close to 0.8 at around the bi-annual cycle, and the
value is about 0.5 at the higher frequencies around the quarterly cycle. They lack
coherence at about the annual frequency, and large phase difference also occurs at this
frequency. With the services sector, real estate has large coherence of about 0.8 at both
the higher and lower ends of frequencies and the two series are in the same phase at these
frequencies. There is a three-quarter lead or an annual lead (if one compares with Fig.
9.1b–9.1d) in the three-quarterly and annual cycles, but the value of their corresponding
coherence is relatively small. The patterns for JLW with the production and
manufacturing sectors are similar, and again, real estate and these sectors are in the same
phase at the lower and higher ends of the spectrum, and some three-quarter leads at the
annual and bi-annual frequencies. As the services and production sectors constitute a
large part of GDP, real estate’s coherence and phase relations with these sectors should
be reflected in the relations with GDP as well. In fact, a one-quarter lead in an annual
cycle is equivalent to a three-quarter lag. If housing is further considered, real estate’s
phase relations with GDP are reasonably consistent with the mixture of these sectors, and
so does the coherence. One interesting and common feature found is that real estate
seems to have large discrepancy with almost all the other sectors in the cycles with the
annual frequency, with less coherence and larger phase leads/lags.
Real estate’s coherence with the unemployment rate is found largely at quarterly or
semi-annual frequencies, beyond that, there is little in common. Real estate seems to lag
behind unemployment for about a third of a complete phase, amounting to a month with
the quarterly data; this is by no means quite accurate when the quarterly data have to be
used. A large phase difference at the semiannual cycle does not count much as the
coherence at that point is so small. With the coincident leading indicator, real estate
appears to be in the same phase, except in the very low frequency cycles (annual and
lower). But the phase lag closing to the vertical axis just accounts for a very small
portion, when the spectrum is considered to be continuous, not discrete. Since these two
series are (regarded) stationary in their original form, a big difference with all other series
emerges at the zero frequency: the coherence is about zero. In Fig. 9.2a–9.2f, the
coherence
Econometric analysis of the real estate market and investment
Figure 9.2 Coherence and phase – real
estate with other variables
138
Cyclical fluctuations in the real estate market
139
at the zero frequency (the unit root circle) is about their cointegration vector (1, ), with
being close to the coherence at the zero frequency. If coherence and phase are analysed
with the variables in levels, e.g., JLW with NTW, then the coherence is about 0.9 (the
value at the zero frequency in Fig. 9.2d) and the phase is zero over the whole horizontal
axis. This also holds when the pair is JLW and the lagged NTW, and simply means that if
one series is cointegrated with another series, then it is also cointegrated with the lagged
series. Therefore, phase does not play a role in cointegration but it matters in common
cycle analysis. This comparison may not be appropriate but does point out that
cointegration, or the verifying of a cointegration relationship, is not always necessary and
rarely reveals something, at least in many studies carried out in the last decade.
In this chapter, both coincident and phase-shifting common cycles were examined in
the economy involving real estate. Common cycle analysis on its own is an extension of
common trend analysis. But common cycles differ from common trends in that the phase
matters in the former, therefore analysis is more complicated, and sometimes, rather
difficult. When these attributes and trend-cycle behaviour are investigated together in a
dynamic system, as proposed in Chapter 5, the study of this chapter is a further
advancement of the previous two chapters, especially Chapter 7. The investigation has
been reinforced by the frequency domain analysis method, which is more effective in
presentation when phases are concerned.
It has been found that, first, real estate fits into the business cycle well and has the
long-run comovement with most parts of the economy. It is because real estate is not a
purely financial market investment. It is mainly an investment in production, trading,
work and storage spaces and capacity from the point of view of most companies or
industries. Due to the reason that amounts of available real estate cannot be increased or
reduced quickly and easily, the magnitude in real estate cycles is larger than that in the
business cycle for the economy as a whole and for some sectors. Second, it is once again
observed that commercial real estate and residential real estate have close links with
regard to common cycles. Third, real estate also has common cycles with the services
sector and manufacturing sector, but their magnitudes of cycles are of more interest.
Cycles in the real estate market are larger than those in GDP and the services sector, but
are of the same size as those in the manufacturing sector. This suggests that adjustments
in the real estate market are sluggish than those in the economy in general, and in the
services sector, the most liquid part of the economy, in particular. Fourth, the size of
cycles in real estate is smaller than that in the house price, which could be attributed to
the existence of an indirect investment market for commercial real estate which reduces
the cycles in the direct real estate investment market. These results and findings are also
confirmed by frequency domain analysis.
10
Summary
This book has examined UK real estate investment markets in an economic and
econometric analytical framework. The book starts from a descriptive analysis of UK real
estate investment markets and their performance over the last two decades. The changing
patterns of real estate was studied and the role played by the institutions and real estate
companies in the course analysed. Attention has also been paid to the relationships
between real estate and other economic and financial sectors. Preliminary but broad
statistical figures provided in Part I reveal that the fluctuations in real estate is linked to
its economic environment in a variety of ways. This suggests that, on the one hand, the
research should not restrain itself to the real estate sector only; and on the other hand, the
unique characteristics of real estate should be addressed and investigated more
effectively. It has been made clear that further scrutiny is required to gain insights into
the crucial relationships and underlying mechanism in the real estate market. This would
be achieved by utilising and developing more constructive economic and econometric
models and analytical techniques pertinent to the research. These analyses, together with
the review on the recent developments in the real estate research literature, outline the
issues and set the framework for advanced studies in the following parts of this book.
Part II studied the issues on economic fluctuations and real estate research.
Econometric models and analytical approaches are presented, extended and developed.
The underlying message is to address real estate in an integrated economic system
implied by the multivariate time series modelling strategy. Fluctuations and the dynamic
behaviour in real estate investment markets are prominently reflected in cycles, trends,
and their response to shocks; and the common factors which real estate shares with other
economic and financial sectors in both the short term and the long run. To investigate
such issues, time series attributes, characteristics and modelling were explored in the
fields of persistence in statistical measures and with economic sense and explanations,
trend-cycle decomposition and their relative contributions in responding to shocks, and
common factors among trends and cycles. This part has, in many ways, extended the
current literature in the study of economic dynamics and developed the econometric
modelling framework and strategies which will be utilised to make empirical inquiry into
UK real estate markets in the later chapters.
Part III was an empirical study on the dynamic behaviour of real estate. This part
extended real estate research to such areas outlined in part I which are either new or
remain important and unsolved, and applied both the existing econometric approaches
and the approaches developed in the previous chapters to the inquiries.
The critical issue of smoothing in the appraisal-based real estate return indices was
dealt with, and the actual smoothedness in UK real estate return indices of JLW and IPD
was decided, in Chapter 6. This issue has the highest priority, though it may not be the
most important, as any study employing these indices would be thought of as unreliable
as the indices themselves if some kind of remedy has not been taken. This chapter, unlike
Summary
141
most previous studies, exploits the information embedded in other variables which have a
fundamental economic and financial relationship with real estate. Two multivariate
approaches are developed which are informationally more efficient and, therefore,
superior to the univariate unsmoothing techniques. Applying these unsmoothing
procedures to UK real estate return indices, appropriate smoothing factor has been found
for the JLW and IPD indices, which is about 0.58 for the former and 0.41 for the latter
judged by the implied cointegration approach. These smoothing factors are then used to
correct for smoothing in the JLW and IPD indices, and the unsmoothed indices are
constructed and used in the studies in the later chapters, leading to a number of empirical
findings in the following.
Direct and indirect real estate investments share little similarity in their response to
shocks and their long-run persistence patterns. Trend-cycle behaviour of real estate
cannot be fully understood by examining its relationships with real estate company shares
alone. These findings are the results from examining real estate’s univariate attributes and
characteristics in the first two sections in Chapter 7, which are concerned with the
permanent and transitory components in shocks in real estate return series and the
patterns in their response to shocks, and their relative contributions to the total deviation
from the mean return. These attributes and characteristics are compared with those of
other economic and financial activities to reveal the difference, similarity and link
between them. It has been confirmed that, although indirect real estate investment, which
is investment in real estate company shares in the UK and REITs (Real Estate Investment
Trusts) in the US, is perceived as a proxy to direct real estate investment, they share little
similarity in their response to shocks and their long-run persistence patterns. Real estate
investment, as represented by the JLW index, has a long-run persistence pattern similar to
that in many sectors in the economy. Whereas indirect real estate investment, as
represented by the return series of FT’s real estate company sector, understandably, has
all attributes close to those for a white noise. Therefore, to examine real estate’s
relationships with real estate company shares alone is not able to show the whole picture
about real estate’s trend-cycle behaviour.
Real estate’s response to shocks is found to have a compounding attribute with the
effect being felt most momentously in about three years time, then reduces to that of a
random walk. Smoothing in the JLW index does not change the persistence pattern, but it
does change the magnitude of the persistence measure at its peak, though in a not
sensitive way. This suggests that smoothing is not a too big issue in the long run. Taking
the long-run attributes of real estate investment into account, smoothing may not be a big
issue overall which may in turn partly explain why the profession copes with these
indices well. Evidence in the residential real estate market also seems to support these
findings.
Real estate bears some characteristics pertinent to the real sectors in the economy and
some other characteristics pertinent to financial market investments, with regard to the
permanent and transitory components in shocks. Although real estate has a similar longrun persistence pattern with the real sector of the economy, its transitory, or cycle
component, is profoundly smaller than that in the latter. Instead, real estate’s transitory
component is as small as being negligible beyond one year’s horizon. This means that
cycles decay quickly and stochastic trends dominate. However, this is by no means to
suggest that real estate does not fluctuate significantly. With less transitory component, or
Econometric analysis of the real estate market and investment
142
stationary element in statistical terms, real estate investment carries high uncertainty. By
comparison, there is more transitory component in most economic activities. Regarding
real estate related sectors, residential real estate and commercial real estate again share
similarity in their trend-cycle decompositions. By contrast, construction output has
substantial cycle component, reflecting that the construction sector adjusts intentionally
and frequently to accommodate the demand and supply state and the price condition in
commercial and residential real estate markets, though not always in the right way and
right direction.
Persistence in real estate is not influenced most by shocks in the indirect real estate
investment market, as has been revealed by multivariate persistence analysis in the last
section of Chapter 7. The largest effect on the persistence in real estate is caused by
shocks from the housing market, followed by those in the services sector, production
sector and construction sector. In a word, shocks in real economic activities contribute
more to the long-run persistence in real estate than those in financial markets, even if it is
the financial market for indirect real estate investment. Reciprocally, shocks in real estate
have largest effect on the housing market, once again confirming that a close link exists
between commercial and residential real estate markets. The impact on the services,
production and construction sectors is also substantial.
Real estate has a mixed attribute in responding to monetary shocks in the longrun.
While the demand side of the economy is influenced by monetary shocks to a great
degree and the supply side of the economy is not subject to monetary shocks in the longrun, real estate is on neither side due to its fundamental links to both the real economy
and financial markets.
Real estate company shares dominate direct real estate investment in the process of
price formation and indirect real estate investment is the main price discovery vehicle in
real estate investment markets. Although direct real estate investment and indirect real
estate investment differ in many ways in their response to shocks in the long run, their
composition of trend and cycle components and their evolution paths over investment
horizon, these two investments are fundamentally linked. Moreover, their fundamental
relationship displays prominent asymmetry. The findings in Chapter 8 have revealed that
the rate of return on direct real estate investment can be explained not only by the past
rates of return on real estate company shares and on direct real estate investment itself,
but also by the past disequilibrium term between these two investments. The results of
analysis also re-affirm that the return on indirect real estate investment generally follows
a random walk, an attribute found in the previous chapter which fails to deal with some
aspects of real estate’s dynamic behaviour studied in that chapter. These results suggest
that the indirect real estate investment market is informationally efficient, whereas
prediction can be improved for returns on direct real estate investment.
However, the predictability of real estate prices can not simply be viewed as evidence
against market efficiency. The fact that real estate company share prices largely follow a
random walk without a predictable pattern means that nobody can persistently earn
excess returns from investing in real estate company shares. The forecasted price changes
in real estate indices, and therefore, individual properties owned by one real estate
company or institution, and their impact on earning power and profit, would have been
already anticipated and incorporated in the share prices. It is also true that any trading
profit or loss from a real estate transaction is fully reflected in the swift changes in the
Summary
143
share prices of the company. Due to low liquidity and long-time period to complete a
transaction, the efficiency has to be achieved with the help of an indirect real estate
investment market. Ultimately, it is shareholders, not companies, who have made gain or
loss.
Real estate fits into the business cycle well and has a long-run comovement with most
parts of the economy, as has been confirmed by the research in Chapter 9. Real estate is
not a purely financial market investment. It is mainly an investment in production,
trading, work and storage spaces and capacity from the point of view of most companies
or industries. With this nature, real estate has found its place in the economy. Due to the
reason that amounts of available real estate cannot be increased or reduced quickly and
easily, the magnitude in real estate price changes or real estate cycles is larger than that in
the business cycle for the economy as a whole and for some sectors. Real estate,
represented by the JLW index, has clearly shown to have common cycles with the
housing market. That is, price changes in real estate and housing are proportional at every
lag and at every cycle frequency, once again confirming close links between commercial
and residential real estate markets. Real estate also have common cycles with the services
sector and manufacturing sector. The magnitudes of cycles in the real estate market are
larger than those in GDP and the services sector, but are of the same size as those in the
manufacturing sector. This suggests that adjustments in the real estate market are
sluggish than those in the economy in general, and in the services sector, the most liquid
part of the economy, in particular. However, the size of cycles in real estate is smaller
than that in the house price, which could be attributed to the existence of an indirect
investment market for commercial real estate which reduces the cycles in the direct real
estate investment market. Frequency domain analysis, which emphasises similarity in
each cycle instead of each lag and deals with phase differences, also confirms the above
findings.
Studies in this book have made a number of contributions not only to real estate
research, but also to the econometric analytical methods. While each of these elements
has its own merits and makes contributions to their individual area, the research has high
integrity and a central theme. Real estate has been portrayed as an integrated part of the
economy on which all investigations have focused. With this theme this study has been
guided to reveal the mechanism governing the interactions between real estate and the
other sectors in the economy, real and financial, and to examine the ways in which real
estate influences and is influenced by the economy. To achieve the research objectives,
the econometric analytical methods of multivariate persistence, multivariate unsmoothing
procedures, and phase-shifting common cycles have been developed, and applied to the
empirical inquiry in this book.
Nevertheless, research in the book has a few limitations. By addressing these
limitations it is hoped that new directions and focuses of further research will emerge as
logical developments of this study and improvements in modelling real estate market
behaviour and fluctuations can be achieved more effectively.
From the very beginning of the book it has been stated clearly that the objectives were
to investigate real estate market behaviour and to investigate it in a framework of macro
dynamics involving business cycles, market efficiency and rational expectations. These
suggest that the study should have a macro analysis focus. While these objectives have
been duly achieved, they are limited to the macro aspects of the real estate market. In
Econometric analysis of the real estate market and investment
144
other words, this book has been entirely based on macroeconomic analysis of real estate
performance and dynamics. While it has been acknowledged that the analysis of market
microstructure and institutional behaviour helps lay down foundations for
macroeconomic analysis, a purely macro study may lose some intuition and consequently
the results may not have much practical appeal. Nevertheless, most micro and
institutional aspects of real estate performance have been considered, though not
thoroughly examined, in this book, so as not to distract attention from the macro dynamic
focus of the book. Future research may have a focus on market microstructure and other
micro aspects of real estate performance but will benefit from the results and discussions
in this book.
Analysis of the responses of real estate to various shocks in the book, although has
revealed important patterns and offered sensible explanations and insights which
challenge many of the previous misperceptions, has been built on appraisalbased real
estate indices. While the extent to which the indices have been unsmoothed does not
matter much in the long run, it may distort short-term results. Consequently, methods of
unsmoothing are crucial to the successful identification of short-term patterns in real
estate performance. Bearing this in mind, caution has been taken in developing two new
procedures of unsmoothing and comparing the results of this book with those of previous
studies. This may mitigate the problem of smoothing, but the problem may never be fully
solved as long as the indices are appraisal based. Thus the results and findings may not be
totally unassailable.
Taking regional and sectoral segmentations in real estate investment and performance
into account, investigation of real estate market efficiency at the aggregate level, as
adopted in this book, may only have offered partially blurred results. Large transaction
costs and illiquidity in the real estate market imply that there could be large discrepancies
in real estate performance across regions, while no arbitrage profits could be made in the
meantime. At the sectoral level, real estate performance is much influenced by the user
market in its own sector. Therefore, sectoral segmentations would also prevent investors
from making arbitrage profits even if real estate returns vary in different sectors. In
addition, different liquidity preferences make real estate performance and other financial
market performance not readily comparable. As mentioned above, research in this book is
based on appraisal-based real estate indices, so the degree of market inefficiency may be
affected by the unsmoothing procedure, though the qualitative rejection of market
efficiency remains the same. Future research will benefit greatly from using transactionbased real estate indices or a reliable substitute. It is perceived that much effort should be
made in this area, because almost all empirical investigations have to be built on a
reliable real estate performance data set.
Rationality in real estate markets and investment, as an important element in dynamic
analysis, is not directly tested but instead inferred in the book. This is constrained by the
concentration and focus of the book. Until now, it has only been partly studied by Tegene
and Kuchler (1993) who investigated the existence of speculative bubbles in farmland
prices, and Liu and Mei (1994) who analysed real estate risk using the present value
model. The former uses a very small sample of data and the latter tests in direct real
estate investment only, and both have investigated just one aspect of rationality. Future
research may give attention to this important issue in general and incorporate liquidity
preferences and segmentations into the analysis in particular. Combined with real estate
Summary
145
market efficiency and real estate cycles, studies of rationality in the real estate market
would doubtless provide a fuller picture of real estate market behaviour and further
advance people’s knowledge in this important area of research.
Bibliography
Abel, A.B. and Eberly, J. (1994), A unified model of investment under uncertainty, American
Economic Review, 84, 1369–1384.
Abraham, B. (1982), Temporal aggregation and time series, International Statistical Review, 50,
285–291.
Alesina, A. and Roubini, N. (1992), Political cycles in OECD economies, Review of Economic
Studies, 59, 663–688.
Alogoskoufis, G. and Smith, R. (1991), On error correction models: specification, interpretation,
estimation, Journal of Economic Surveys, 5, 97–128.
Ariel, R.A. (1987), A monthly effect in stock returns, Journal of Financial Economics , 18, 161–
174.
——(1990), High stock returns before holidays: existence and evidence on possible causes, Journal
of Finance, 45, 1611–1626.
Armitage, S. (1995), Event study methods and evidence on their performance, Journal of Economic
Surveys, 8, 25–52.
Ashenfelter, O. and Genesove, D. (1992), Testing for price anomalies in real estate auction,
American Economic Review, 82, 501–505.
Attanasio, O.P. (1991), Risk, time-varying second moments and market efficiency, Review of
Economic Studies, 58, 479–494.
Balchin, P.N., Kieve, J.L.and Bull, G.H.(1988), Urbanlandeconomicsandpublic policy (4th ed.),
Macmillan Education, Basingstoke, England.
Ball, R. (1978), Anomalies in relationships between securities’ yields and yield surrogates, Journal
of Financial Economics , 6, 103–126.
——and Brown, P. (1968), An empirical evaluation of accounting income numbers, Journal of
Accounting Research, 6, 159–178.
Banerjee, A., Dolado, J., Galbraith, J.W. and Hendry, D.F (1993), Co-integration, Errorcorrection, and the Econometric Analysis of Non-stationary Data, Oxford University Press,
Oxford, England.
Banz, R.W. (1981), The relationship between return and market value of common stocks, Journal
of Financial Economics , 9, 3–18.
Barkham, R. and Geltner, D. (1993), Price discovery in American and British property markets,
paper presented at the Real Estate Research Institute Meeting, Chicago.
——and——(1995), Price discovery inAmerican and British property markets, Journal of the
American Real Estate and Urban Economics Association, 23, 21–44.
Barras, R. (1983), A simple theoretical model of the office development cycle, Environment and
Planning A, 15, 1381–1394.
——(1987), Technical change and the urban development cycle, Urban Studies, 24, 5–30.
——(1994), Property and the economic cycle: building cycles revisited, Journal of Property
Research, 11, 183–197.
——and Ferguson, D. (1985), A spectral analysis of building cycles in Britain, Environment and
Planning A, 17, 1369–1391.
——and——(1987a), Dynamic modelling of the building cycle: 1. Theoretical framework,
Environment and Planning A, 19, 353–367.
——and——(1987b), Dynamic modelling of the building cycle: 2. Empirical results, Environment
and Planning A, 19, 493–520.
Bibliography
147
Barro, R.J. (1976), Rational expectations and the role of monetary policy, Journal of Monetary
Economics, 2, 1–32.
——(1977), Unanticipated money growth and unemployment in the United States, American
Economic Review, 67, 101–115.
——(1978), Unanticipated money, output, and the price level in the United States, Journal of
Political Economy, 86, 549–580.
——(1989), Modern Business Cycle Theory, Basil Blackwell, Oxford, England and Harvard
University Press.
Bernard, V.L. and Thomas, J.K. (1990), Post earnings announcement drift: delayed price response
or risk premium? Journal of Accounting Research, 27 (Supplement), 1–36.
Beveridge, S. and Nelson, C.R. (1981), A new approach to decomposition of economic time series
into permanent and transitory components with particular attention to measurement of the
‘business cycles’, Journal of Monetary Economics , 7, 151–174.
Biddle, G.C. and Lindahl, F.W. (1982), Stock price reactions to LIFO adoptions: the association
between excess returns and LIFO tax savings, Journal of Accounting Research, 20, 551–588.
Black, F. (1973), Yes Virginia, there is hope: tests of the value line ranking system, Financial
Analysts Journal, 29, 10–14.
Blanchard, O.J. (1989), A traditional interpretation of macroeconomic fluctuations, American
Economic Review, 79, 1146–1164.
——and Mankiw, N.W. (1988), Consumption: beyond certainty equivalence, American Economic
Review , 78 (Papers and Proceedings), 173–177.
——and Quah, D. (1989), The dynamic effects of aggregate demand and supply disturbances,
American Economic Review, 79, 655–673.
——and Watson, M.W. (1982), Bubbles, rational expectations and financial markets, in Wachtel,
P. (ed), Crises in the Economic and Financial Structure, Lexington Books, Lexington, MA.
——and——(1986), Are business cycles all alike?, in Gordon, R.J. (ed), American Economic
Review , University of Chicago Press, Chicago, IL.
Blundell, G.F. and Ward, C.W.R. (1987), Property portfolio allocation: a multi factor model, Land
Development Studies, 4, 145–156.
Bollerslev, T. (1987) A conditionally heteroskedastic time series model for speculative prices and
rates of return, Review of Economics and Statistics, 69, 542–547.
Breeden, D.T. (1979), An intertemporal asset pricing model with stochastic consumption and
investment opportunities, Journal of Financial Economics, 7, 265–296.
Broadhurst, R. (1991), Internationalising of real estate law and practice over the last ten years –
market aspects, Proceedings of the Conference of the Anglo-American Real Property Institute
1991, Dublin, Ireland.
Brown, G.R. (1991), Property Investment and the Capital Markets, Chapman & Hall, London,
England.
Callender, M. and Key, T. (1996), The total value of commercial property in the UK, paper
presented to the RICS ‘Cutting Edge’Conference, Bristol, England.
Campbell, J.Y. (1990), Measuring the persistence of expected returns, American Economic Review,
80 (Papers and Proceedings), 43–47.
——(1991), A variance decomposition for stock returns, The Economic Journal, 101, 157–179.
——(1994), Inspecting the mechanism – an analytical approach to the stochastic growth model,
Journal of Monetary Economics , 33, 463–506.
——and Mankiw, N.W. (1987a), Are output fluctuations transitory?, Quarterly Journal of
Economics, 102, 857–880.
——and——(1987b), Permanent and transitory components in macroeconomic fluctuations,
American Economic Review, 77 (Papers and Proceedings), 111–117.
——and——(1989), International evidence on the persistence of economic fluctuations, Journal of
Monetary Economics, 23, 319–333.
Bibliography
148
——and Shiller, R.J. (1987), Cointegration and tests of present value models, Journal of Political
Economy, 95, 1062–1088.
——and——(1988a), Stock prices, earnings and expected dividends, Journal of Finance, 43, 661–
676.
——and——(1988b), The dividend-price ratio and expectations of future dividends and discount
factors, Review of Financial Studies, 1, 195–228.
Campeau, F. (1994), A microstructure analysis of the information on securitised and unsecuritised
commercial real estate market, PhD Thesis, Department of Land Economy, University of
Cambridge.
Campos, J., Ericsson, N.R. and Hendry, D.F. (1990),An analogue model of phaseaverage
procedures, Journal of Econometrics, 43, 275–292.
Canova, F. and Marrinan, J. (1995), Predicting excess returns in financial markets, European
Economic Review, 39, 35–69.
Case, K.E. and Shiller, R.J. (1989), The efficiency of the market for single-family homes, American
Economic Review, 79, 125–137.
Chan, K.C., Hendershott, P.H. and Sanders, A.B. (1990), Risk and return on real estate: evidence
from equity REITs, Journal of the American Real Estate and Urban Economics Association, 18,
431–452.
Chen, N.F. (1991), Financial investment opportunities and the macroeconomy, Journal of Finance,
46, 529–554.
——, Roll, R. and Ross, S.A. (1986), Economic forces and the stock market, Journal of Business,
59, 383–403.
Chowdhury, A.R., McGibany, J.M. and Nourzad, F. (1994), Non-nested tests of three competing
theories of business cycles, Applied Economics, 26, 527–534.
Clark, P.K. (1987), The cyclical component of the U.S. economic activity, Quarterly Journal of
Economics, 102, 797–814.
Clark, T.E. (1992), Business cycle fluctuations in US regions and industries: the roles of national,
region-specific, and industry-specific shocks, ResearchWorking Paper RWP 92–05, Federal
Reserve Bank of Kansas City.
——(1993), Rents and prices of housing across areas of the US: across-section examination of the
present value model, Research Working Paper RWP 93–04, Federal Reserve Bank of Kansas
City.
——(1994),A comparison of two approaches to measuring common and idiosyncratic components
in sets of time series variables, Research Working Paper RWP 94–04, Federal Reserve Bank of
Kansas City.
Cochrane, J.H. (1988), How big is the random walk in GNP? Journal of Political Economy, 96,
893–920.
Cutler, D.M. and Kozicki, S. (1993), Testing for common features, Journal of Business and
Economic Statistics, 11, 369–395.
——, Poterba, J.M. and Summers, L.H. (1990), Speculative dynamics and the role of feedback
traders, American Economic Review , 80 (Papers and Proceedings), 63–68.
——,——and——(1991), Speculative dynamics, Review of Economic Studies, 58, 529–546.
Davidson, R. and MacKinnon, J.G. (1981), Several tests for model specification in the presence of
alternative hypotheses, Econometrica, 49, 781–793.
——and——(1982), Some non-nested hypothesis tests and the relations among them, Review of
Economic Studies, 49, 551–565.
Denton, F.T. (1971), Adjustment of monthly or quarterly series to annual totals: an approach based
on quadratic minimization, Journal of the American Statistical Association, 66, 99–102.
Dickey, D.A. and Fuller, W.A. (1979), Distribution of the estimators for autoregressive time series
with a unit root, Journal of the American Statistical Association, 74, 427–431.
——and——(1981), The likelihood ratio statistics for autoregressive time series with a unit root,
Econometrica, 49, 1057–1072.
Bibliography
149
Diebold, F.X. and Nerlove, M. (1990), Unit roots in economic time series: a selective survey, in
Fomby, T.B and Rhodes, G.F. Jr. (eds), Advances in Econometrics, vol 8: Cointegration,
Spurious Regressions, and Unit Roots, 3–69, JAT Press, Greenwich.
Dimson, E. (1979), Risk measurement when shares are subject to infrequent trading, Journal of
Financial Economics, 7, 197–226.
——and Marsh, P.R. (1983), The stability of UK risk measures and the problem of thin trading,
Journal of Finance, 38, 753–783.
——and——(1986) Event study methodologies and the size effect: the case of UK press
recommendations, Journal of Financial Economics, 17, 113–143.
DiPasquale, D. and Wheaton, W. (1996), Urban Economics and Real Estate Markets, Prentice
Hall, Englewood Cliffs, NJ.
Dobson, S.M. and Goddard, J.A. (1992), The determinants of commercial property prices and rents,
Bulletin of Economic Research, 44, 301–321.
Dolado, J.J., Jenkinson, T. and Sosvilla-Rivero, S. (1990), Cointegration and unit roots, Journal of
Economic Surveys, 4, 249–271.
Downs, A. (1991), International influences upon real estate markets, Proceedings of the Conference
of the Anglo-American Real Property Institute 1991, Dublin, Ireland.
Dwyer, G.P. Jr. and Wallace, M.S. (1992), Cointegration and market efficiency, Journal of
International Money and Finance, 11, 318–327.
Eichenbaum, M.S. and Singleton, K.J. (1986), Do equilibrium real business cycle theories explain
post-war United States business cycles? National Bureau of Economic Research Working Paper
No:1932.
Elton, E., Gruber, M., Das, S. and Hlavka, M. (1993), Efficiency with costly information: a
reinterpretation of evidence for managed portfolios, Review of Financial Studies, 6, 1–22.
Engle, E.M.R.A. (1984), A unified approach to the study of sums, products, timeaggregation and
other functions of ARMA processes, Journal of Time series Analysis, 5, 159–171.
Engle, R.F, and Granger, C.W.J. (1987), Cointegration and error correction: representation,
estimation, and testing, Econometrica, 55, 251–267.
——and Issler, J.V. (1995), Estimating common sectoral cycles, Journal of Monetary Economics,
35, 83–113.
Evans, G.W. (1989), Output and unemployment dynamics in the United States: 1950–1985,
Journal of Applied Econometrics, 4, 213–37.
——(1991), Pitfalls in testing for explosive bubbles in asset prices, American Economic Review ,
81, 922–930.
Evans, G. and Reichlin, L. (1992), Information, forecasts and measurement of the business
cycle,London School of Economics Centre for Economic Performance Discussion Paper No:
111.
——and——(1994), Information, forecasts, and measurement of the business cycle, Journal of
Monetary Economics, 33, 233–254.
Fama, E.F. (1970), Efficient capital market: are view of theory and empirical work, Journal of
Finance, 25, 383–417.
——(1991), Efficient capital markets:II, Journal of Finance, 46, 1575–1617.
——and French, K.R. (1988), Dividend yields and expected returns on stock returns, Journal of
Political Economy, 22, 3–25.
——and——(1992), The cross-section of expected stock returns, Journal of Finance, 47, 427–467.
——, Fisher, L., Jensen, M.C. and Roll, R. (1969), The adjustment of stock prices to new
information, International Economic Review, 10, 1–21.
Filardo, A.J. (1993), Business cycle phases and their transitional dynamics, Research Working
Paper RWP 93–14, Federal Reserve Bank of Kansas City.
——(1994), Business-cycle phases and their transitional dynamics, Journal of Business &
Economic Statistics, 12, 299–308.
Bibliography
150
——and Gordon, S. (1993), Business cycle durations, Research Working Paper RWP 93–11,
Federal Reserve Bank of Kansas City.
Finnerty, J.E. (1976), Insider trading and market efficiency, Journal of Finance, 31, 1141–1148.
Firstenberg, P.M., Ross, S.A. and Zisler, R.C. (1988), Real estate: the whole story, Journal of
Portfolio Management (Spring), 22–34.
Fischer, I. (1925), Our unstable dollar and the so-called business cycle, Journal of the American
Statistical Association, 20, 179–202.
Fischer, S. (1977), Long-term contracts, rational expectations, and the optimal money supply rule,
Journal of Political Economy, 85, 191–205.
Fisher, J.D. and Webb, R.B. (1992), Current issues in the analysis of commercial real estate,
Journal of the American Real Estate and Urban Economics Association, 20, 211–227.
Forni, M. and Reichlin, L. (1995), Dynamic common factors in large crosssections, CEPR
discussion paper No 1285.
Frisch, R. (1933), Propagation and impulse problems in dynamic economics, in Essays in Honour
of Gustav Cassel, George Allen, London.
Fraser, W.D. (1992), Principles of Property Investment and Pricing, Macmillan, Basingstoke,
England.
Friedman, M. (1957), A Theory of Consumption Function, Princeton University Press, Princeton.
——(1968), The role of monetary policy, American Economic Review, 58, 1–17.
——(1970), A theoretical framework for monetary analysis, Journal of Political Economy, 78,
193–238.
Froot, K.A. and Obstfeld, M. (1991), Intrinsic bubbles: the case of stock prices, American
Economic Review, 81, 1189–1214.
Fuller, W.A. (1976), Introduction to Statistical Time Series, Wiley, NewYork.
Gallo, G.M. and Kempf, H. (1995), Cointegration, codependence and economic fluctuations,
European University Institute Working Paper ECO No 95/27.
Garratt,A. and Hall, S.G. (1992), Measuring and forecasting underlying economic activity, London
Business School Centre for Economic Forecasting Discussion Paper No 18–92.
Gau, G.W. (1984), Weak form tests of the efficiency of real estate investment markets, Financial
Review, 19, 301–320.
Geltner, D.M. (1989), Estimating real estate’s systematic risk from aggregate level appraisal-based
returns, Journal of the American Real Estate and Urban Economics Association, 17, 463–481.
——(1991), Smoothing in appraisal based returns, Journal of Real Estate Finance and Economics,
4, 327–345.
——(1993a), Temporal aggregation in real estate return indices, Journal of the American Real
Estate and Urban Economics Association, 21, 141–166.
——(1993b), Estimating market values from appraised values without assuming an efficient
market, The Journal of Real Estate Research, 8, 325–345.
Geroski, P.A. and Hall, S.G. (1992), Price and quantity responses to cost and demand shocks,
London Business School Centre for Economic Forecasting Discussion Paper No 19–92.
Giaccotto, C. and Clapp, J. (1992), Appraisal based real estate returns under alternative market
regimes, Journal of the American Real Estate and Urban Economics Association, 20, 1–24.
Giliberto, S.M. (1988), A note on the use of appraisal data in indexes of performance measurement,
Journal of the American Real Estate and Urban Economics Association, 17, 77–83.
Goerlich, P. (1994), RATS procedure for the Cochrane measure of persistence, Documentation by
Estima.
Granger, C.W.J. (1981), Some properties of time series data and their use in econometric model
specification, Journal of Econometrics, 16, 121–130.
——(1983), Co-integrated variables and error-correcting models, Department of Economics
Discussion Paper No 83–13, University of California San Diego.
——(1986), Developments in the study of cointegrated variables, Oxford Bulletin of Economics
and Statistics, 48(3), 213–228.
Bibliography
151
——and Lee, T.H. (1990), Multicointegration, in Fomby, T., and Rhodes, G.F. Jr. (eds), Advances
in Econometrics, vol 8: Cointegration, Spurious Regression, and Unit Roots 77–84, JAI Press,
London
Grenadier, S.R. (1995), The persistence of real estate cycles, Journal of Real Estate Finance and
Economics, 10, 95–119.
Grossman, S.J. and Stiglitz, J.E. (1980), On the impossibility of informationally efficient markets,
American Economic Review, 70, 393–408.
Guntermann, K.L. and Smith, R.L. (1987), Derivation of cost of capital and equity rates from
market data, Journal of the American Real Estate and Urban Economics Association, 15, 98–
109.
——and Norrbin, S.C. (1991), Empirical tests of real estate market efficiency, Journal of Real
Estate Finance and Economics, 4(3), 297–313.
Gyourko, J. and Keim D.B. (1992), What does the stock market tell us about real estate returns?
Journal of the American Real Estate and Urban Economics Association, 20, 457–485.
Haberler, G. (1946), Prosperity and Depression, United Nations, NewYork.
Hansen, A.H. (1951), Business Cycles and National Income, Norton, NewYork.
Hansen, B.E. and Phillips, P.C.B. (1990), Estimation and inference in models of cointegration: a
simulation study, in Fomby, T.B. and Rhodes, G.F. Jr. (eds), Advances in Econometrics, vol 8:
Cointegration, Spurious Regressions, and Unit Roots, 225–248, JAT Press, Greenwich, CT.
Hansen, G.D. (1985), Indivisible labor and business cycle, Journal of Monetary Economics, 16,
309–327.
Hansen, L.P. (1982), Large sample properties of generalised method of moments estimators,
Econometrica, 50, 1029–1054.
——and Singleton, K.J. (1982), Generalised instrumental variables estimation in nonlinear rational
expectations models, Econometrica, 50, 1269–1286.
Hartzell, D., Hekman, J.S. and Miles, M.E. (1987), Real estate returns and inflation, Journal of the
American Real Estate and Urban Economics Association, 15, 617–637.
Harvey, A. (1985), Trends and cycles in macroeconomic time series, Journal of Business and
Economic Statistics, 3, 216–227.
Hendry, D.F. (1984), Econometric modelling of house prices in the United Kingdom, in Hendry,
D.F. and Wallis, K.F. (eds), Econometrics and Quantitative Economics, Basil Blackwell,
Oxford.
Hodrick, R.J. and Prescott, E.C. (1980), Post-war U.S. business cycles: an empirical investigation,
Working Paper, Carnegie Mellon University, Pittsburgh, PA.
Huffman, G.W. (1994),A primer on the nature of business cycles, Federal Reserve Bank of Dallas
Economic Review (first quarter), 27–41.
Hulbert, M. (1990), Proof of pudding, Forbes, December, 316.
Ibbotson, R.G. (1975), Price performance of common stock new issues, Journal of Financial
Economics, 2, 235–272.
——and Jaffe, J.F. (1975), ‘Hot issues’ markets, Journal of Finance, 30, 1027–1042.
Ingram, B.F., Kocherlakota, N.R. and Savin, N.E. (1994), Explaining business cycles – a multipleshock approach, Journal of Monetary Economics, 34, 415–428.
Ippolito, R.A. (1989), Efficiency with costly information: a study of mutual fund performance,
1965–84, Quarterly Journal of Economics, 104, 1–23.
Isaac, D. (1994), Property Finance, Macmillan, Basingstoke, England.
Jaffe, J.F. (1974), Special information and insider trading, Journal of Business, 47, 410–428.
Jensen, M.C. (1968), The performance of mutual funds in the period 1945–64, Journal of Finance,
23, 389–416.
——(1978), Some anomalous evidence regarding market efficiency, Journal of Financial
Economics, 6, 95–101.
Johansen, S. (1988), Statistical analysis of cointegration vectors, Journal of Economic Dynamics
and Control, 12, 231–254.
Bibliography
152
——and Juselius, K. (1990), Maximum likelihood estimation and inference on cointegration – with
applications to the demand for money, Oxford Bulletin of Economics and Statistics, 52, 169–
210.
——and——(1992), Testing structural hypotheses in a multivariate cointegration analysis of the
PPP and the UIP for UK, Journal of Econometrics, 53, 211–244.
Kaplan, R.S. and Roll, R. (1972), Investor evaluation of accounting information: some empirical
evidence, Journal of Business, 45, 225–257.
Karras, G. (1994), Sources of business cycles in Europe 1960–1988: evidence from France,
Germany, and the United Kingdom, European Economic Review, 38, 1763–1778.
Keogh, G. (1994), Use and investment markets in British real estate, Journal of Property Valuation
& Investment, 12, 58–74.
Key, T., MacGregor, B., Nanthakumaran, N. and Zarkesh, F. (1994), Understanding the Property
Cycle, Royal Institution of Chartered Surveyors, London.
——and Nanthakumaran, N. (1993), Economic cycles and property cycles, paper presented at
RICS Conference – ‘Property in the Overall Economy’, April, London.
Khoo, T., Hartzell, D. and Hoesli, M. (1993), An investigation of the change in real estate
investment trust Betas, Journal of the American Real Estate and Urban Economics Association,
21 107–130.
Kim, T. (1991), Modelling the behaviour of real estate, Journal of Real Estate Finance and
Economics, 4, 273–281.
King, R.G. and Plosser, C.I. (1984), Money, credit, and prices in a real business cycle, American
Economic Review , 74, 363–380.
——and Rebelo, S.T. (1993), Low frequency filtering and real business cycles, Journal of
Economic Dynamics and Control, 17, 207–231.
——, Plosser, C.I., and Rebelo, S.T. (1988), Production, growth, and business cycles: I. the basic
neoclassical model, Journal of Monetary Economics, 21, 195–232.
——,——, Stock, J.H. andWatson, M.W. (1991), Stochastic trends and economic fluctuations,
American Economic Review , 81, 819–840.
Kydland, F.E. and Prescott, E.C. (1977), Rules rather than discretion: the inconsistency of optimal
plans, Journal of Political Economy, 85, 473–491.
——and——(1982), Time to build and aggregate fluctuations, Econometrica, 50, 1345–1370.
——and——(1988), The workweek of capital and its implications, Journal of Monetary
Economics, 21, 343–360.
Kleim, D.B. (1988), Size related anomalies and stock return seasonality, Journal of Financial
Economics, 12, 13–32.
Lakonishok, J. and Smidt, S. (1988), Are seasonal anomalies real?: a ninety year perspective,
Review of Financial Studies, 1, 435–445.
Lawrence, C. (1983), Rational expectations, supply shocks and the stability of the inflation-output
tradeoff: some time series evidence for the United Kingdom, 1957–1977, Journal of Monetary
Economics, 11, 225–245.
Lee, T.H. (1992), Stock-flow relationships in US housing construction, Oxford Bulletin of
Economics and Statistics, 53, 419–430.
Leitch, G. and Tanner, J.E. (1991), Economic forecast evaluation: profits versus the conventional
error measures, American Economic Review , 81, 580–590.
Lewbel, A. (1994), Aggregation and simple dynamics, American Economic Review, 84, 905–918.
Linneman, P. (1986), An empirical test of the efficiency of the housing market, Journal of Urban
Economics, 20, 140–154.
Lippi, M. and Reichlin, L. (1993), The dynamic effects of aggregate demand and supply
disturbances: comment, American Economic Review , 83, 644–652.
——and——(1994a), Diffusion of technical changes and the decomposition of output into trend
and cycle, Review of Economic Studies, 61, 19–31.
Bibliography
153
——and——(1994b), Common and uncommon trends and cycles, European Economic Review, 38,
624–635.
Liu, C.H., Hartzell, D.J., Grissom, T.V. and Greig, W. (1990), The composition of the market
portfolio and real estate investment performance, Journal of the American Real Estate and
Urban Economics Association, 18, 49–75.
——and Mei, J. (1994), An analysis of real-estate risk using the present value model, Journal of
Real Estate Finance and Economics, 8, 5–20.
Liu, P.,Smith, S.D.andSyed, A.A.(1990),SecuritypricereactiontotheWallStreet Journal’s securities
recommendations, Journal of Financial and Quantitative Analysis, 25, 399–410.
Lizieri, C. and Satchell, S. (1997), Interaction between property and equity markets: an
investigation of linkages in the UK 1972–1992, Journal of Real Estate Finance and Economics,
15, 11–26
——and Venmore-Rowland, P. (1991), Valuation accuracy: a contribution to the debate, Journal of
Property Research, 8, 115–122.
——and——(1993), Valuations, prices and the market: a rejoinder, Journal of Property Research,
10, 77–84.
Long, J.B. and Plosser, C.I. (1983), Real business cycles, Journal of Political Economy, 91, 39–69.
——and——(1987), Sectoral vs. aggregate shocks in the business cycle, American Economic
Review, 77, 333–336.
Loughran, T. and Ritter, J.R. (1995), The new issues puzzle, Journal of Finance, 50, 23–51.
Lucas, R.E. Jr. (1972) Expectations and the neutrality of money, Journal of Economic Theory, 4,
103–124.
——(1975), An equilibrium model of the business cycle, Journal of Political Economy, 83, 1113–
1144.
——(1977), Understanding business cycles, in Stabilization of The Domestic and International
Economy, 7–29. Carnegie-Rochester Conference Series on Public Policy 1, North-Holland,
Amsterdam.
——(1978), Asse tprice si na nexchang eeconomy, Econometrica, 46, 1429–1445.
——(1987), Models of Business Cycles, Basil Blackwell, Oxford.
——and Prescott, E.C. (1971), Investment under uncertainty, Econometrica, 39, 67–90.
——and Rapping, L.A. (1969), Price expectations and the Phillips curve, American Economic
Review , 59, 342–350.
Lükepohl, H. and Reimers, H. (1992), Impulse response analysis of cointegrated systems, Journal
of Economic Dynamics and Control, 16, 53–78.
MacGregor, B.D. and Nanthakumaran, N. (1992), The allocation of property in the multi-asset
portfolio: the evidence and theory reconsidered, Journal of Property Research, 9, 55–32.
Matysiak, G. and Wang, P. (1995), Commercial property market prices and valuations: analysing
the correspondence, Journal of Property Research, 12, 181–202.
McCallum, B.T. (1976), Rational expectations and the natural rate hypothesis: some consistent
estimates, Econometrica, 44, 43–52.
——(1977), Price-level stickiness and the feasibility of monetary stabilization policy with rational
expectations, Journal of Political Economy, 85, 627–634.
——(1980), Rational expectations and macroeconomic stabilization policy: an overview, Journal
of Money, Credit and Banking, 12, 716–746.
——(1983), The role of overlapping-generations models in monetary economics, CarnegieRochester Conference Series on Public Policy, 18, 9–44.
——(1989a), Monetary Economics: Theory and policy, Macmillan, NewYork.
——(1989b), New classical macroeconomics: a sympathetic account, Scandinavian Journal of
Economics, 91, 223–252.
——(1989c), Real business cycle models, in Barro, R.J. (ed), Modern Business Cycle Theory, Basil
Blackwell, Oxford, and Harvard University Press.
Bibliography
154
McGrattan, E.R. (1994), A progress report on business cycle models, Federal Reserve Bank of
Minneapolis Quarterly Review (Fall), 2–16.
McGough, T. and Tsolacos, S. (1995), Property cycles in the UK: an empirical investigation of the
stylised facts, paper presented at the RICS ‘Cutting Edge’ Conference, Aberdeen, Scotland.
McIntosh, W. and Henderson, G.V. Jr. (1989), Efficiency of the office properties market, Journal
of Real Estate Finance and Economics, 2, 61–70.
Meguire, P. (1994), RATS procedure to compute the Beveridge–Nelson (BN) decomposition of a
time series, North Carolina University.
Miles, M., Cole, R. and Guilkey, D. (1990), A different look at commercial real estate returns,
Journal of the American Real Estate and Urban Economics Association, 18, 403–430.
Mullineux, A.W. and Dickson, D.G. (1992), Equilibrium business cycles: theory and evidence,
Journal of Economic Surveys, 6, 321–358.
Muscatelli,V.A. and Hurn, S. (1992), Cointegration and dynamic time series models, Journal of
Economic Surveys, 6, 1–43.
Muth, J.F. (1960), Optimal properties of exponentially weighted forecasts, Journal of the American
Statistical Association, 55, 299–306.
——(1961), Rational expectations and the theory of price movements, Econometrica, 29, 315–335.
Nelson,C.R. and Plosser, C.I. (1982), Trends and random walks in macroeconomic time series:
some evidence and implications, Journal of Monetary Economics, 10, 139–162.
Newbold, P. (1990), Precise and efficient computation of the Beveridge–Nelson decomposition of
economic time series, Journal of Monetary Economics, 26, 453–457.
Osborn, D.R. (1990), A survey of seasonality in UK macroeconomic variables, Discussion Papers
in Econometrics and Social Statistics, University of Manchester.
Osterwald-Lenum, M. (1992), A note with quantiles of the asymptotic distribution of the maximum
likelihood cointegration rank test statistics, Oxford Bulletin of Economics and Statistics, 54,
461–472.
Perron, P. (1988), Trends and random walks in macroeconomic time series: further evidence from a
new approach, Journal of Economic Dynamics and Control, 12, 297–332.
——(1989), The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57,
1361–1401.
——(1994), Trend, unit root and structural change in macroeconomic time series, in Rao, B.B. ed.,
Cointegration for the Applied Economist. St. Martin’s Press, NewYork and Macmillan Press,
London, 113–146.
Pesaran, M.H., Pierse, R.G. and Lee, K.C., (1993), Persistence, cointegration and aggregation: a
disaggregated analysis of output fluctuations in the US economy, Journal of Econometrics, 56,
67–88.
Phillips, P.C.B. (1993), Forward exchange market unbiasedness: the case of the Australian Dollar
since 1984, Cowles Foundation Discussion Paper No 1055.
——and Hansen, B.E. (1990), Statistical inference in instrumental variables regression with I(1)
processes, Review of Economic Studies, 57(1), 99–125.
——, McFarland, J.W. and McMahon, P.C. (1994), Robust tests of forward exchange market
efficiency with empirical evidence from the 1920s,CowlesFoundation Discussion Paper No
1080.
Prescott, E.C. (1986), Theory ahead of business-cycle measurement, Federal Reserve Bank of
Minneapolis Quarterly Review (Fall), 9–22.
Priestley, M.B. (1996), Spectral Analysis and Time Series 9th ed, Academic Press, London.
Quah, D. (1991), Price formation and the appraisal function in real estate markets, Journal of Real
Estate Finance and Economics, 4, 127–146.
——(1994), One business cycle and one trend from (many,) many disaggregates, European
Economic Review, 38, 605–613.
Bibliography
155
Quan, D.C. and Quigley, J.M. (1989), Inferring an investment return series for real estate from
observations on sales, Journal of the American Real Estate and Urban Economics Association,
17, 218–230.
——and——(1991), Price formation and the appraisal function in real estate markets, Journal of
Real Estate Finance and Economics, 4, 127–146.
Rayburn, W., Devaney, M. and Evans, R. (1987),A test of weak-form efficiency in residential real
estate returns, Journal of the American Real Estate and Urban Economics Association, 15, 220–
233.
Reinganum, M.R. (1983), The anomalous stock market behaviour of small firms in January,
Journal of Financial Economics, 12, 89–104.
Ritter, J.R. (1988), The buying and selling behaviour of individual investors at the turn of the year,
Journal of Finance, 43, 701–717.
Ross, S.A. (1976), The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13,
341–360.
——and Zisler, R.C. (1991), Risk and return in real estate, Journal of Real Estate Finance and
Economics, 4, 175–190.
Rouwenhorst, K.G. (1991), Time to build and aggregate fluctuations: a reconsideration, Journal of
Monetary Economics, 27, 241–254.
Royal Institution of Chartered Surveyors (1994), Understanding the Property Cycle, London.
Rubinstein, M. (1976), The strong case for the generalized logarithmic utility model as the premier
model of financial markets, Journal of Finance, 31, 551–571.
Sargent, T.J. (1987), Macroeconomic Theory (2nd ed), Academic Press Inc, Orlando, Florida.
——and Wallace, N. (1974), The elasticity of substitution and cyclical behavior of productivity,
wages, and labor’s share, American Economic Review, 64, 257–263.
——and——(1975), "Rational" expectations, the optimal monetary instrument, and the optimal
money supply rule, Journal of Political Economy, 83, 241–254.
——and——(1976), Rational expectations and the theory of economic policy, Journal of Monetary
Economics, 2, 169–183.
Sephton, P.S. and Larsen, H.K. (1991), Tests of exchange market efficiency: fragile evidence from
cointegration tests, Journal of International Money and Finance, 10, 561–570.
Seyhun, H.N. (1986), Insiders’ profits, costs of trading, and market efficiency, Journal of Financial
Economics, 16, 189–212.
Shapiro, M.D. (1987), Are cyclical fluctuations in productivity due more to supply shocks or
demand shocks? American Economic Review, 77, 118–124.
——and Watson, M.W. (1988), Sources of business cycle fluctuations, Yale Cowles Foundation
Discussion Paper No: 870.
Shiller, R.J. (1984), Stock prices and social dynamics, Brookings Papers on Economic Activity, 2,
457–510.
Shilling, J.D. (1993), Measurement error in FRC/NCREIF returns on real estate, Southern
Economic Journal, 60, 210–219.
Scholes, M. and Williams, J.T. (1977), Estimating betas from nonsynchronous data, Journal of
Financial Economics, 5, 309–327.
Sims, C.A. (1980), Comparison of interwar and postwar business cycles: monetarism reconsidered,
American Economic Review, 70 (Papers and Proceedings), 250–257.
——(1982), Policy analysis with econometric models, Brookings Papers on Economic Activity, 1,
107–152.
Singleton, K.J. (1988), Econometric issues in the analysis of equilibrium business cycle models,
Journal of Monetary Economics, 21, 361–386.
Smith, R. T. (1992), The cyclical behaviour of prices, Journal of Money, Credit, and Banking, 24,
413–430.
Society of Property Researchers, (1994), Property indices research report, Society of Property
Researchers Technical Paper No 1.
Bibliography
156
Solow, R. M. (1957), Technical change and the aggregate production function, Review of
Economics and Statistics, 39, 312–320.
Stock, J.H. and Watson, M.W. (1988), Testing for common trends, Journal of the American
Statistical Association, 83, 1097–1107.
——and——(1989), Interpreting the evidence on money-income causality, Journal of
Econometrics, 40, 161–81.
——and——(eds) (1994), Business Cycles, Indicators, and Forecasting, National Bureau of
Economic Research Studies on Business Cycles, vol 28, University of Chicago Press, Chicago,
Illinois.
Strum, B.J. (1991), Transformation of an American insurance company from ‘the widows and
orphans friendly society’to a large landlord/developer/investment advisor, Proceedings of the
Conference of the Anglo-American Real Property Institute 1991, Dublin, Ireland.
Tegene, A. and Kuchler, F.R. (1991), A description of farmland investor expectations, Journal of
Real Estate Finance and Economics, 4, 283–296.
——and——(1993), Evidence on the existence of speculative bubbles in farmland prices, Journal
of Real Estate Finance and Economics, 6, 223–236.
Timmermann, A. (1995), Cointegration tests of present value models with a time varying discount
factor, Journal of Applied Econometrics, 10, 17–31.
Tsolacos, S. (1995), An econometric model of retail rents in the United Kingdom, Journal of Real
Estate Research, 10, 519–529.
Vahid, F. and Engle, R.F. (1993a), Common trends and common cycles, Journal of Applied
Econometrics, 8, 341–360.
——and——(1993b), Non-synchronous common cycles, UCSD Economics Discussion Paper 93–
55.
Van de Gucht, L.M, Dekimpe, M.G. and Kwok, C.C. (1996), Persistence in foreign exchange rates,
Journal of International Money and Finance, 15, 191–220.
Wang, P. (1995a), Smoothing in property return indices and its effects on diversification and
portfolio allocation, Journal of Real Estate and Construction,5, 27–46.
——(1995b), Joint test for functional forms and heteroscedasticity with property sales and
valuation data, Applied Stochastic Models and Data Analysis, 11, 315–321.
——and Matysiak, G. (1994), How do UK regional commercial rents move?, Applied Economics
Letters, 1, 19–23.
——, Lizieri, C. and Matysiak (1994), How much should we invest in property? The 10th
American Real Estate Society Annual Meeting, Santa Barbara, California.
——,——and——(1997), Information asymmetry, long run relationship and price discovery in
property investment markets, The European Journal of Finance, 3, 261–275.
Watson, M.M. (1986), Univariate detrending methods with stochastic trends, Journal of Monetary
Economics, 18, 49–75.
——(1994), Business-cycle durations and postwar stabilization of the U.S. economy, American
Economic Review, 84, 24–46.
Webb, R. B., Miles M. and Guilkey, D. (1992),Transaction driven commercial real estate returns:
the panacea to asset allocation models? Journal of the American Real Estate and Urban
Economics Association, 20, 325–357.
West, K.D. (1987), A specification test for speculative bubbles, Quarterly Journal of Economics,
102, 553–580.
Wheaton, W.C. (1990), Vacancy, search, and prices in a housing market matching model, Journal
of Political Economy, 98, 1270–1292.
Wickens, M. (1993), Interpreting cointegrating vectors and common stochastic trends, London
Business School Centre for Economic Forecasting Discussion Paper No 14–93.
Wilson, T. (1991), Key trends in the UK economy and property markets over the past decade,
Proceedings of the Conference of the Anglo-American Real Property Institute 1991, Dublin,
Ireland.
Bibliography
157
Working, H. (1960) Note on the correlation of first differences of averages in a random chain,
Econometrica, 28, 916–918.
Zeria, J. (1994), Informational cycles, Review of Economic Studies, 61, 31–44.
Zorn, T.S. and Sackley, W.H. (1991), Buyers’ and sellers’ markets: A simple rational expectations
search model of the housing market,Journal of Real Estate Finance and Economics, 4, 315–
326.
Index of names
Abel, A.B. 149
Abraham, B. 85, 149
Alesina, A. 149
Alogoskoufis, G 149
Ariel, R.A. 38, 149
Armitage, S. 38, 149
Ashenfelter, O. 149
Attanasio, O.P. 149
Balchin, P.N. 149
Ball, R. 38, 149
Banerjee, A. 27, 149
Banz, R.W. 38, 149
Barkham, R. 6, 86, 91, 97, 124, 149
Barras, R. 137, 150
Barro, R.J. 40, 41, 42, 45, 48, 150
Bernard, V.L. 38, 150
Beveridge, S. 53, 67, 68, 75, 77, 78, 80, 100, 110, 150
Biddle, G.C. 38, 150
Black, F. 37, 38, 150
Blanchard, O.J. 45, 53, 55, 63 64, 65, 66, 68, 80, 111, 150, 151
Blundell, G.F. 6, 83, 86, 97, 151
Bollerslev, T. 36, 151
Breeden, D.T. 37, 151
Broadhurst, R. 151
Brown, G.R. 151
Brown, P. 38, 149
Bull, G.H. 149
Callender, M. 7, 151
Campbell, J.Y. 6, 36, 48, 49, 53, 55, 59, 60, 62, 63, 66, 68, 83, 99, 100, 112, 151
Campeau, F. 6, 151
Campos, J. 85, 151
Canova, F. 151
Case, K.E. 5, 151
Chan, K.C. 5, 152
Chen, N.F. 38, 152
Chowdhury, A.R. 45, 152
Clapp, J. 86, 155
Clark, P.K. 53, 55, 56, 152
Clark, T.E. 152
Cochrane, J.H. 53, 55, 60, 61, 62, 66, 83, 99, 100, 114, 152
Cole, R. 159
Index of names
160
Cutler, D.M. 152
Das, S. 153
Davidson, R. 42, 152
Dekimpe, M.G. 162
Denton, F.T. 152
Devaney, M. 160
Dickey, D.A. 25, 42, 52, 152
Dickson, D.G. 159
Diebold, F.X. 152
Dimson, E. 38, 86, 153
DiPasquale, D. 153
Dobson, S.M. 153
Dolado, J. 149, 153
Downs, A. 153
Dwyer, G.P. Jr 121, 153.
Eberly, J. 149
Eichenbaum, M.S. 42, 153
Elton, E. 53, 153
Engle, E.M.R.A. 25
Engle, R.F. 25, 27, 29, 52, 53, 68, 73, 75, 77, 80, 81, 124, 127, 129, 131, 153, 162
Ericsson, N.R. 151
Evans, G. 53, 153
Evans, R. 160
Fama, E.F. 34, 35, 36 ,37, 38, 153
Ferguson, D. 137, 150
Filardo, A.J. 154
Finnerty, J.E. 38, 154
Firstenberg, P.M. 83, 86, 97, 154
Fischer, I. 42, 154
Fischer, S. 40, 41, 112, 154
Fisher, J.D. 4, 154
Fisher, L. 154
Fomby, T.B. 152
Forni, M. 154
Fraser, W.D. 154
French, K.R. 36, 38, 153
Friedman, M. 40, 42, 154
Frisch, R. 42, 154
Froot, K.A. 154
Fuller, W.A. 25, 42, 52, 152, 154
Galbraith, J.W. 149
Gallo, G.M. 75, 79, 80, 154
Garratt, A. 154
Gau, G.W. 5, 154
Geltner, D. 6, 83, 86, 91, 97, 124, 149, 154
Genesove, D. 149
Index of names
161
Geroski, P.A. 155
Giaccotto, C. 86, 155
Giliberto, S.M. 155
Goddard, J.A. 153
Goerlich, P. 60, 155
Gordon, S. 151, 154
Granger, C.W.J. 6, 11, 25, 29, 45, 52, 121 124, 125, 127, 153, 155
Greig, W. 158
Grenadier, S.R 99, 119, 155.
Grissom, T.V. 158
Grossman, S.J. 35, 39, 155
Gruber, M. 153
Guilkey, D. 4, 159, 162
Guntermann, K.L. 5, 155
Gyourko, J. 5, 155
Haberler, G. 40, 41, 155
Hall, S.G. 154, 155
Hansen, A.H. 40, 41, 155
Hansen, B.E. 52, 155
Hansen, G.D. 156
Hansen, L.P. 37, 156
Hartzell, D. 156, 157, 158
Harvey, A. 53, 55, 56, 156
Hekman, J.S. 156
Hendershott, P.H. 152
Henderson, G.V. Jr. 159
Hendry, D.F. 149, 151, 156
Hlavka, M. 153
Hodrick, R.J. 17, 21, 22, 29, 55, 156
Hoesli, M. 157
Huffman, G.W. 156
Hulbert, M. 38, 156
Hurn, S. 159
Ibbotson, R.G 38, 156.
Ingram, B.F. 156
Ippolito, R.A. 39, 156
Isaac, D. 11, 156
Issler, J.V. 68, 75, 80, 131, 153
Jaffe, J.F. xii, 38, 156
Jenkinson, T. 153
Jensen, M.C. 35, 39, 151, 156
Johansen, S. 25, 26, 27, 76, 91, 92, 96, 97, 124, 133, 156
Juselius, K. 25, 91, 96, 97, 124, 133, 156
Kaplan, R.S. 38, 156
Karras, G. 157
Keim D.B. 5, 155
Index of names
162
Kempf, H. 75, 79, 80, 154
Keogh, G. 157
Key, T. 7, 46, 151, 157
Khoo, T. 157
Kieve, J.L. 149
Kim, T. xii, 157
King, R.G. 40, 42, 55, 63, 64, 65, 66, 68, 75, 77, 79, 80, 111, 157
Kleim, D.B. 38, 157
Kocherlakota, N.R. 156
Kozicki, S. 68, 80, 129, 131, 152
Kuchler, F.R. 6, 148, 162
Kwok, C.C. 162
Kydland, F.E. 40, 41, 42, 48, 157
Lakonishok, J. 38, 157
Larsen, H.K. 121, 161
Lawrence, C. 48, 157
Lee, K.C. 160
Lee, T.H. 155, 157
Leitch, G. 157
Lewbel, A. 157
Lindahl, F.W. 158
Linneman, P. 5, 157
Lippi, M. 56, 57, 158
Liu, C.H. 5, 38, 112, 148, 158
Liu, P. 158
Lizieri, C. 6, 99, 158
Long, J.B. 40, 41, 42, 54, 112, 158
Loughran, T. 38, 158
Lütkepohl, H. 54, 158
Lucas, R.E. Jr. 37, 40, 41, 48, 158
MacGregor, B.D. 6, 157, 158
MacKinnon, J.G. 42, 152
Mankiw, N.W. 53, 55, 59, 60, 62, 63, 66, 68, 83, 99, 100, 112, 150, 151
Marrinan, J. 1512
Marsh, P.R. 38, 153
Matysiak, G. 6, 159, 162
McCallum, B.T. 42, 159
McFarland, J.W. 160
McGibany, J.M. 152
McGough, T. 159
McGrattan, E.R. 159
McIntosh, W. 5, 159
McMahon, P.C. 160
Meguire, P. 110, 159
Mei, J. 112, 148, 158
Miles, M. 4, 5, 156, 159, 162
Mullineux, A.W. 159
Muscatelli, V.A. 159
Muth, J.F. 47, 48, 159
Index of names
163
Nanthakumaran, N. 6, 157, 158
Nelson, C.R. 42, 44, 52, 53, 55, 56, 67, 68, 75, 77, 80, 110, 150, 159
Nerlove, M. 152
Newbold, P. 53, 110, 159
Norrbin, S.C. 5, 155
Nourzad, F. 152
Obstfeld, M. 154
Osborn, D.R. 159
Osterwald-Lenum, M. 96, 97, 125, 126, 160
Perron, P. 42, 122, 123, 124, 160
Pesaran, M.H., 55, 61, 62, 66, 112, 113, 114, 160
Phillips, P.C.B. 52, 155, 160
Pierse, R.G. 160
Plosser, C.I. 40, 41, 42, 43, 44, 52, 54, 55, 56, 112, 157, 158, 159
Poterba, J.M. 152
Prescott, E.C. 17, 21, 29, 40, 41, 42, 48, 156, 157, 158, 160
Priestley, M.B. 160
Quah, D. 53, 55, 63, 64, 65, 66, 68, 80, 111, 150, 160
Quan, D.C. 68, 86, 160
Quigley, J.M. 86, 160
Rao, B.B. 160
Rapping, L.A. 48, 158
Rayburn, W. 5, 160
Rebelo, S.T. 157
Reichlin, L. 53, 56, 57, 153, 154, 158
Reimers, H. 54, 158
Reinganum, M.R. 38, 160
Rhodes, G.F. Jr. 152, 155
Ritter, J.R. 38, 158, 160
Roll, R. 38, 152, 154, 156
Ross, S.A. xii, 37, 83, 86, 97, 152, 154, 160
Roubini, N. 149
Rouwenhorst, K.G. 161
Royal Institution of Chartered Surveyors 46, 161
Rubinstein, M. 37, 161
Sackley, W.H. 163
Sanders, A.B. 152
Sargent, T.J. 40, 41, 48, 161
Satchell, S. 6, 99, 158
Savin, N.E. 156
Sephton, P.S. 121, 161
Seyhun, H.N. 38, 161
Shapiro, M.D. 45, 161
Shiller, R.J. 5, 6, 36, 48, 49, 112, 151, 161
Index of names
164
Shilling, J.D. 83, 86, 89, 91, 92, 93, 97, 161
Scholes, M. 86, 161
Sims, C.A. 42, 45, 161
Singleton, K.J. 37, 42, 45, 153, 156, 161
Smidt, S. 38, 157
Smith, R. 149
Smith, R.L. 5, 155
Smith, R. T. 161
Smith, S.D. 158
Society of Property Researchers 161
Solow, R.M. 42, 161
Sosvilla-Rivero, S. 153
Stiglitz, J.E. 35, 39, 155
Stock, J.H. 45, 53, 55, 67, 68, 75, 77, 78, 80, 157, 162
Strum, B.J. 162
Summers, L.H. 152
Syed, A.A. 158
Tanner, J.E. 157
Tegene, A. 6, 148, 162
Thomas, J.K. 3, 150
Timmermann, A. 162
Tsolacos, S. 28, 159
Vahid, F. 53, 68, 73, 75, 77, 80, 162
Van de Gucht, L.M. 61, 162
Venmore-Rowland, P. 6, 158
Wallace, M.S. 92, 121, 153
Wallace, N. 40, 41, 48, 161
Wallis, K.F. 156
Wang, P. 5, 6, 99, 159, 162
Ward, C.W.R. 6, 83, 86, 97, 151
Watson, M.M. 53, 162
Watson, M.W. 45, 53, 55, 67, 68, 75, 77, 80, 150, 157, 161, 162
Webb, R.B. 4, 154
West, K.D. 163
Wheaton, W. 153
Wheaton, W.C. 163
Wickens, M. 163
Williams, J.T. 86, 161
Wilson, T. 163
Working, H. 85, 163
Zarkesh, F. 157
Zeria, J. 163
Zisler, R.C. 83, 86, 97, 154, 160
Zorn, T.S. 163
Subject index
Akaike information criterion (AIC) 25, 122–123
American Stock Exchange (AMSE) 5
arbitrage pricing theory (APT) 4, 37
asymmetry 57, 124–127
augmented Dickey–Fuller (ADF) 25–28
autoregressive integrated moving average
(ARIMA) 55, 85, 110
autoregressive moving average (ARMA) 53, 56–58, 90, 114
Beveridge–Nelson decomposition 53, 67, 77–78, 110
Beveridge–Nelson–Stock–Watson
representation 67–68, 77–78
Box–Jenkins 52
British Association of Insurers 8
British Land 10
Business cycle theory 3, 33, 39–47;
disequilibrium see disequilibrium business cycle theory;
equilibrium see equilibrium business cycle theory;
Keynesian see Keynesian business cycle theory;
monetary see monetary business cycle theory (MBC);
new classical see new classical business cycle theory (NC);
real see real business cycle theory (RBC)
capital asset pricing model (CAPM) 4–5
Central Statistical Office (CSO) see Office for National Statistics (ONS)
change in stock under construction (RESC) 16, 20–24, 86–89, 131–138
coefficient of variance (CV) 12–14, 92, 97
coherence 138–142
coincident indicator (CC) 16, 20–24, 131–132, 136–137,
cointegration 25–28, 49, 89–91, 93, 96–96, 125–126, 133–134
common cycle 3, 54, 67–81, 129–130, 134–137;
coincident 69, 129, 134–135;
phase shifting 70, 72–77, 129, 134–135
common factor 54
common feature 129–131, 134
common trend 3, 54;
representation see Beveridge–Nelson–Stock–Watson representation
construction new order (NO) 16, 20–28, 100, 104, 108, 110
construction output on new work (CO) 16, 20–28, 100, 104, 108, 110, 113, 115–117, 131–138
cumulative abnormal return (CAR) 37–38
cycle, common see common cycle
Subject index
166
decomposition, trend-cycle see Beveridge–Nelson decomposition
Dickey–Fuller (DF) 25
difference stationary (DS) 17, 44, 52, 55–57
disequilibrium business cycle theory 40–42
DYMIMIC 5
efficient market hypothesis (EMH) 3, 33–39, 47, 126
equilibrium business cycle theory 40–42
error correction mechanism (ECM) 52, 75–77
errors-in-variable 87
feature, common see common feature
Financial Times Actuary (FTA) all share index 12–14, 20–28, 100–101, 103, 107, 121, 128, 130–
131
property sector (FTAP) 12–14, 20–28, 86, 91, 97, 100–101, 103, 107, 113, 115–117, 121–126, 128,
130–13
Frank Russell Company 5
frequency domain analysis 137–142
generalised autoregressive conditional heteroscedasticity (GARCH) 36
generalised method of moment (GMM) 37
gilts (GLT) 14, 20–28, 100–101, 105, 109
gross domestic product (GDP) 111, 118, 131–138
Halifax Building Society house price index (HFX) 16, 20–28, 100–101, 105, 109–110
Hillier Parker property market return index (HPK) 13–14, 100–101, 105, 109–110
Hodrick–Prescott (HP) filter 17–18, 29
House price index
Halifax Building Society see Halifax Building Society house price index (HFX)
Nationwide Building Society see Nationwide Building Society house price index (NTW)
indicator of fixed investment in dwellings (DWG) 16, 20–28
industrial production (PDN) 110, 115–117
instrumental variable 134
insurance company 7–11
Investment Property Databank (IPD) 9, 13, 86, 91–98, 100, 144
Johansen procedure 25, 92, 124
Jones Lang Wootten 86
Jones Lang Wootten property return index (JLW) 12–14, 19–22, 25–27, 91–98, 100–102, 106, 110,
113–118, 130–135, 144, 146
Kalman filter 53
Keynesian business cycle theory 40–42, 46
lagging indicator (LG) 16, 20–24, 131,
Land Securities 10
leading indicator:
long see long leading indicator (LL);
short see short leading indicator (SL)
Subject index
167
Ljung–Box Q* 25, 110, 134
longer leading indicator (LL) 16, 20–24, 131,
M0, 115–116, 131–138
M4, 115
manufacturing sector (MNG) 110, 131–138
market efficiency 15, 33–39
Markov transition 70–73;
matrix 71–73
Markowitz efficient portfolio 4
mean squared errors (MSEs) 39
MEPC 10
monetary business cycle theory (MBC) 40–42
monetary shock 63–66, 115–117,
National Council of Real Estate Investment Fiduciaries (NCREIF) 5
Nationwide Building Society house price index (NTW) 16, 100–101, 104, 108, 110–111, 113, 115–
117, 131–138
new classical business cycle theory (NC) 40–42
New York Stock Exchange (NYSE) 5
number of property transactions (NPT) 16, 20–21, 23–24
Office for National Statistics (ONS) 19, 130
pension funds 7–12
persistence 3;
multivariate 61–63, 111–117;
joint 111;
univariate 59–61, 100–109
present value model 49
price discovery 120, 124–127
production sector (PDN) 110, 113, 115–117
property market return index, Hillier Parker see Hillier Parker property market return index (HPK)
property return index, Jones Lang Wootten see Jones Lang Wootten property return index (JLW)
random walk 35
rational expectations hypothesis (REH) 3, 33, 47–50,
real business cycle theory (RBC) 40–42, 46
real estate investment trusts (REITs) 5, 120, 144
real shock 63–66
root mean square errors (RMSE) 39
Schwartz’s criterion (SC) 25
seemingly unrelated regression (SUR) 114
services sector (SVC) 110, 113, 115–117, 131–138
shock:
monetary see monetary shock;
real see real shock
shorter leading indicator (SL) 16, 20–24, 131,
smoothing 85–86
Subject index
spectrum 137–139
stationary:
difference see difference stationary (DS);
trend see trend stationary (TS)
stock under construction (RESA) 16, 26–28, 86
trend, common see common trend
trend stationary (TS) 17, 44, 55–57
unemployment rate (UER) 115, 131–138
unit root 123, 133
unsmoothing 86–98
V 60
VC 61–62
VCk 62, 113
Vector autoregression (VAR) 45, 54, 62, 75–81
Vk 100–101
60
26–28, 125–126, 134
26–28, 125–126, 134
168