Housing and macroeconomic cycles in the major
euro area countries
Álvarez, L.J., G. Bulligan, A. Cabrero, L. Ferrara and H. Stahl
Conference on Macroeconomics of Housing Markets
Banque de France, 3-4 December 2009
Outline
1. Motivation
2. Methodologies for cycle estimation
3. Cross country comovements
1. Correlation analysis
2. Turning points
4. Conclusions
2
Motivation
 Housing offers the best warning sign of recessions
– Leamer (2007)
 Recent sharp house price falls are having far reaching effects on real
variables
– Wealth effects on consumption
– Labour intensive sector
– Property as collateral (credit constraints)
 Housing markets are idiosyncratic (nontradability)
– Regulation
– Land availability
 Do different housing cycles within the euro area affect the degree of
cyclical comovement in the whole area?
3
The Methodology (I):The ideal band
pass filter
 We define the business cycle as the
outcome of an ideal band-pass filter
Ideal filter
Gain as a function of period
1.2
 The filter fully removes high-frequency
fluctuations (e.g. those with a period of
less than 6 quarters (1.5 years))
1
0.8
0.6
0.4
… and also long-run movements (e.g.
over 32 quarters (8 years))
0.2
57
52
47
42
37
32
27
22
17
12
7
2
0
Period
The gain function of a filter indicates the
extent to which it affects the series
GIBP
if | p |< p1
0

( p) =  1 if p1 | p |  p2

 0
if | p |> p2

A gain over 1 indicates that
those fluctuations are amplified

A gain of 1 implies no effect

A gain of 0 shows that
fluctuations are fully suppressed
4
The methodology (II): Butterworth
filters
 Widely used in engineering in their onesided form (Butterworth(1930))
Butterworth band pass filter
Gain as a function of period
Impact of changing d
 Can be seen as a generalization of the
HP filter (The HP filter is a particular lowpass Butterworth filter of the sine)
1.2
1
0.8
0.6
 Highly flexible. Can be given a modelbased interpretation
0.4
0.2
Period
Ideal
3
6
111
101
91
81
71
61
51
41
31
21
11
1
0
 Filters are very close to the ideal bandpass filter
9
(1  L2 ) d (1  F 2 ) d
BPF ( L, F ) 
(1  L2 ) d (1  F 2 ) d   (1  L  L2 ) d (1  F  F 2 ) d
– These filters are able to remove
satisfactorily short-run and medium
run fluctuations
– This the method we use
5
The Methodology (III): Alternative
estimation procedures
Epanechnikov kernel and Hodrick Prescott
Gain as a function of frequency
Butterworth and Baxter and King filters
Gain as a function of frequency
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
Ideal filter
Epanechnikov (15)
HP (1600)
Ideal filter
BK12
3.1
2.8
2.6
2.4
2.1
1.9
1.6
1.4
1.2
0.9
0.7
0.5
0.2
3.1
2.8
2.6
2.4
2.1
1.9
1.6
1.4
1.2
-0.2
0.9
-0.2
0.7
0.0
0.5
0.0
0.2
0.2
0.0
0.2
0.0
0.4
0.4
Butterworth
Hodrick- Prescott and linear kernels do not approximate well the ideal filter
Short cycles are almost fully passed through and cyclical fluctuations with long periods
are only partially removed. Linear kernels have an oscillatory gain
Baxter and King (1999) band-pass filter involves losing k observations at the end (the most
interesting period for policy-makers!) and beginning of the series. It is less satisfactory than the
Butterworth filter
6
Are there comovements in the
business cycle and housing variables ?
GDP
3
3
2
2
1
1
0
-1
-1
-2
-2
-3
0891 3891 6891 9891 2991 5991 8991 1002 4002 7002
DEGDP
FRGDP
15
H o u s e h o ld s ' in v e s t m e n t in h o u s in g
14
12
10
8
6
4
2
0
-2
-4
-6
-8
0891 3891 6891 9891 2991 5991 8991 1002 4002 7002
ESGDP
ITGDP
House prices
DEHUIN
FRHUIN
20
10
ESHUIN
ITHUIN
Real House prices
15
5
10
0
5
-5
-10
0
-15
-5
-20
0891 3891 6891 9891 2991 5991 8991 1002 4002 7002
DEHUPR
ITHUPR
ESHUPR
FRHUPR
-10
0891 3891 6891 9891 2991 5991 8991 1002 4002 7002
DERHUPR
ITRHUPR
ESRHUPR
FRRHUPR
7
Does housing lead the business
cycle?
Correlation of cyclical components with GDP cycle
MAXIMUM CORRELATION WITH GDP
1980-2008
MAXIMUM CORRELATION WITH H
IT
FR
ES
DE
AVERAGE
IT
FR
ES
0.52
0
0.74
0
0.7
-1
0.64
0
0.7
-0.3
0.55
-5
0.52
-4
0.48
6
0.56
6
0.67
-2
0.58
-2
0
Gross fixed capital formation in
Machinery and Equipment
0.64
0.68
0.64
0.73
0.7
Investment in construction
0
0.53
2
0
0.69
0
-1
0.74
-1
0
0.37
-1
-0.3
0.6
0.0
Households' investment in housing
(Volume)
0.53
0.53
0.65
0.71
0.6
0
0
-2
-2
-1.0
0.7
0.51
0.6
0.51
0.6
0.61
0.51
0.54
0
4
0.71
0
0.74
0
0.6
3
1
0.74
0
0.84
0
0.68
1
-1
0.51
-1
0.66
-2
0.62
-1
6
0.82
0
0.87
-1
0.43
0
2.5
0.7
-0.3
0.8
-0.8
0.6
0.8
-2
0.36
-7
0.41
-5
0.79
-2
5
0.35
4
0.51
4
0.62
5
-2
0.12
0
0.61
-5
0.7
-3
0.36
0.63
0.84
0.55
0.6
GDP
Households' consumption
Non residential construction
investment
Exports
Imports
Construction Value added
Employment in construction sector
(Full time equivalent + heads)
D
0
Residential
investment
leads 0
0.58
0.54
0.73
GDP in Spain
and3 Germany,
as
-5
-5
0.54
0.73
in Leamer0.44
(2007),
but not
in 0
-2
4
-3
France and
(but leading
in0
0.42 Italy 0.51
0.7
8 Vigna
4 2009) -3
Ferrara and
0
Housing starts, as in Leamer
(2007), and building permits
provide, as
earlier
0.38 expected,
0.73
0.72
-1
5
-3
warning signals
0
0
0
6
0
0
-2
1.0
Authorizations (building permits)
numbers
-
0.75
0.61
0.59
0.7
-
0.65
0.68
Housing starts (numbers)
-
-5
0.58
-4
-5
0.64
-5
-5
-
-5.0
0.6
-4.5
-
0
0.66
0
-7
0.75
-7
Industrial production index,
construction
0.71
0.74
0.69
0.53
0.7
0.28
0.59
0.54
0
Consumer prices (HICP)
0
0.34
5
0
0.57
5
-2
0.48
7
-2
0.37
4
-1.0
0.4
5.3
-4
0.41
1
4
-0.59
-2
-4
-0.56
-8
0
Residential construction deflator
(index)
0.31
0.6
0.54
0.77
0.6
0.86
0.47
0.56
6
-1
-2
3
1.5
1
8
0
-0
8
0
Cross country correlation analysis. Full
sample (1980Q1-2008Q4)
Contemporaneous average correlations between countries
1980:Q1 2008:Q4
0.0
GDP
Investment in construction
0.1
0.2
0.3
0.4
0.5
0.6
0.7
DE
0.8
0.9
1.0
DE
ES
FR
IT
ES
1.00
0.47
0.47
0.65
FR
0.47
1.00
0.66
0.58
IT
0.47
0.66
1.00
0.66
0.65
0.58
0.66
1.00
Households' investment in housing
n
Non residential construction investment
Construction Value added
Employment in construction sector
Building permits


ij
i j
n
Housing starts
House prices
Real House prices
 Cross country correlations are higher for GDP than for residential investment (trade flows)
 Cross country correlations are higher for housing investment than for non residential
investment (public and business investment in construction are hardly synchronized)
 Nominal house prices are almost orthogonal
 Moderate synchronization in real house prices mostly reflects comovements in consumer
prices
9
Which are the leading countries?
Cross correlations
GDP cyclical components
DE
DE
--ES
Lead (2)
FR
Lead (4)
IT
Contemp.
ES
Lag
--Lag
Lag
FR
Lag
Lead (1)
--Contemp.
IT
Contemp.
Lead (2)
Contemp.
---
Country in a row leads/lags country in a column
DE
ES
FR
IT
GDP Y-o-Y Growth rates
DE
ES
--Lag
Lead
--Contemp.
Lag
Contemp.
Contemp.
FR
Contemp.
Lead
--Contemp.
IT
Contemp.
Contemp.
Contemp.
---
Spanish GDP and, less clearly, French GDP lead those of the other countries
No German locomotive!
The results broadly hold with y-o-y rates
10
Lead/lag analysis cross correlations of
housing variables
In domestic housing markets, country-specific factors tend to play a
stronger role
Residential investment (Average contemp. CC: 0.29)
DE
DE
ES
FR
IT
ES
Lag
--Lead
Lag
Contemp.
FR
Lead
Lead
--Lag
Lag
IT
Contemp.
Lead
Lag
---
--Lead
Spanish residential investment
leads that of the other countries
Country in a row leads/lags country in a column
Nominal house prices (Average contemp. CC: 0.09)
DE
DE
ES
FR
IT
ES
Lead
--Lag
Lead
Contemp.
FR
Lag
Lag
--Lead
Contemp.
--Lag
IT
Contemp.
Contemp.
Lead
---
French nominal house prices tend
to lead and Spanish house prices
to lag
Real house prices (Average contemp. CC: 0.33)
DE
DE
ES
FR
IT
--Lag
Contemp.
Contemp.
ES
Lead
--Lead
Lead
FR
Contemp.
Lag
--Contemp.
IT
Contemp.
Lag
Contemp.
---
Spanish real house prices tend to
lag, but not conclusive leading in
other countries
11
Changes in synchronization since EMU
Simple measure
Contemporaneous average correlations between countries
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
GDP
Investment in construction
Households' investment in housing
Non residential construction investment
Construction Value added
Employment in construction sector
Building permits
Housing starts
House prices
Real House prices
1980:Q1 2008:Q4
1999:Q1 2008:Q4
 Comovements in GDP are considerably stronger in the EMU period (external trade)
 Comovements in residential investment and in the construction sector as a whole are
also much stronger in the EMU period
 Comovements in nominal house prices have increased, but remain low
 In contrast, real house prices comovements are even lower in the EMU period
12
Changes in synchronization since EMU
Peña and Rodríguez measure (2003)
Effective comovement
(Peña & Rodriguez 2003)
0.0
0.1 0.2
0.3
0.4
0.5 0.6
0.7
0.8 0.9
1.0
GDP
Investment in construction
Households' investment in housing
Non residential construction investment
Construction Value added
Employment in construction sector
Building permits
Housing starts
Roughly speaking,
Peña&Rodriguez measure is
similar to a multivariate R2
House prices
Real House prices
1980:Q1 2008:Q4
1999:Q1 2008:Q4
 For real variables, provides the same message than the average cross country
correlation
 Comovements in GDP are considerably stronger in the EMU period (external trade)
 Comovements in residential investment and in the construction sector as a whole
are also much stronger in the EMU period
 Comovements in nominal house prices remain low
 But real house prices comovements have increased in the EMU period
13
Turning Point (TP) Analysis
 Identification of TPs using BBQ algorithm
Peak at t:
{ y(t) > y(t-k) , y(t) > y(t+k) , k=1,…, K }
Trough at t:
{ y(t) < y(t-k) , y(t) < y(t+k) , k=1,…, K },
Alternative: use a Markov switching model
 Computation of binary variables ( Sit ) for a country i
Sit = 1 during a descending phase of the cycle
Sit = 0 during an ascending phase of the cycle
14
 Measure of synchronisation based on concordance indices (CI)
between 2 countries i and j :
T
1T

CI   S it S jt   (1  S it )(1  S jt )
T  t 1
t 1

CI=1 full synchronization; CI=0 no synchronization
 Cross-concordance indices (CCI) to take leads and lags k into
account (k = -4, -2, -1, 0, 1, 2, 4)
T
1T

CCI   Si ,t S j ,t k   (1  Si ,t )(1  S j ,t k )
T  t 1
t 1

– To assess leads and lags, we choose k that maximizes CCI
 Also a lead-lag analysis is made in case of strong cross
concordance
15
Concordance analysis of GDP:
Lead/lag assessment
DE
DE
ES
FR
IT
ES
FR
1.00
0.67
0.71
0.72
0.58
1.00
0.72
0.61
IT
0.69
0.72
1.00
0.73
0.72
0.59
0.73
1.00
 Evidence of synchronisation
among the 4 countries (CIs> 0.7)
Lead-lag analysis for GDP growth cycles. Country pairs (*)
(Average and median duration in number of quarters)
5
Average
Median
4
3
The French and Spanish cycle
tend to lead the German one
Confirms cross-correlation
analysis
2
1
0
FR vs DE
FR vs ES
FR vs IT
ES vs DE
ES vs IT
IT vs DE
(*) First country leads second country
Evidence of common behaviour in GDP cycles among the four
countries, Germany being slightly lagging (No German locomotive!)
16
Concordance indices: Household
investment
 Household investment
– Synchronisation between France and Spain (CI=0.72)
– Cross concordance between Germany and Italy (CCI=0.69), Italy lags by
2 quarters
DE
DE
ES
FR
IT
ES
1.00
0.64
0.45
0.68
FR
0.64
1.00
0.72
0.61
IT
0.62
0.72
1.00
0.58
0.69
0.68
0.59
1.00
Lead-lag analysis for residential investment cycles. Country pairs (*)
(Average and median duration in number of quarters)
3
Average
2
Housing cycles are quite
heterogeneous, especially the German
one
Median
1
0
But evidence of relationship between
France and Spain for housing activity
cycles
-1
-2
-3
FR vs DE
FR vs ES
FR vs IT
ES vs DE
ES vs IT
IT vs DE
(*) Positive(negative) value if first country leads(lags) second country
17
Household investment: House prices
 House prices
– Strong relationship between Spain and Italy (CCI=0.78), Spain is leading
(4 Q)
– Spain with Germany (CCI=0.69) and with France (CCI=0.63)
– Less evidence for other countries
DE
DE
ES
FR
IT
ES
1.00
0.58
0.46
0.47
DE
DE
ES
FR
IT
FR
0.69
1.00
0.63
0.70
ES
--Lag
Lag
Lag
IT
0.54
0.55
1.00
0.54
FR
Lead
--Lead
Lag
0.55
0.78
0.60
1.00
IT
Lead
Lag
--Lag
Lead
lead
lead
---
Less integration between countries regarding house prices
18
Conclusions
1. Country comovements are higher for GDP than for residential investment
(trade flows)
•Predominant role of local factors in housing markets
2. Comovements in the housing sector are much weaker for prices than for
real variables
3. Comovements are considerably stronger in the EMU period
4. No German locomotive!
19
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