The Interaction between the Macroeconomy and House
Price Returns
Qijia Wei and Bruce Morley*
(Department of Economics, the University of Bath, Bath, UK.)
Abstract
This study aims to assess the relationship between house price return and the
main macroeconomic variables using recent US data. A Vector Autoregression
(VAR) approach is employed and the results suggest strong correlations can be
found between the house price return and nominal interest rate.
However the
lagged effect of the interest rate cannot explain the movement in house price
returns, although the shock to the nominal interest rate has a contemporaneous
effect on the house price return and this confirms the theoretical predictions that
monetary policy affects the housing market. This indicates that monetary policy
is an efficient tool to manage the housing market in the US.
Key Words: house price, VAR, interest rate
J.E.L. E44, R30.
*Address for correspondence: Department of Economics, University of Bath, Bath, BA2 7AY, UK.
+44 1225 386497, e-mail: bm232@bath.ac.uk, Fax: +44 1225 383423.
1
Tel:
1. Introduction
Following the recent financial crisis there has been a debate over whether house
price variables should be considered by policy makers, particularly when
deciding on the optimal monetary policy. This could involve including them in a
simple Taylor rule (Filardo, 2000). There is evidence to suggest that the housing
market plays an important role in the macroeconomy and also the performance of
the economy could affect the housing market. As a result of this
inter-relationship, it is more appropriate to analyse the relationship between
housing markets and the macroeconomy in a system which can assess the
dynamic interrelationship between housing and the relevant macroeconomic
factors.
The aim of this paper is to contribute to the recent literature and discussion on
the macroeconomy and housing returns. This paper’s main contribution is
through adding the variables related to the Taylor rule to a VAR framework to
assess the dynamic relationship between them. It also adds different measures of
house prices not just the usual house price index but also house price return.
Recent studies, such as McDonald and Stokes (2011) have found that the interest
rate affects the housing market and excessively low nominal interest rates were
the main reason for the housing market crisis and subsequent financial crisis in
2008. Similarly Ferson and Harvey (1991) found that the Treasury Bill rate,
interest rate term structure, and unexpected inflation rate affected the return on
real estate.
In addition there is a substantial amount of evidence to suggest that real estate
price movements can affect the economy as a whole (Case et al, 2001). The first
channel is via the wealth effect because owning a house means that households
2
have assets in hand and can convert it into cash when necessary. Therefore, the
increased price of a house means the wealth of households is rising. Usually,
with the increase in wealth, people will be able to enjoy more consumption and
therefore the economy expands. The second channel is named the credit effect
because a house can be used as collateral when households need loans from the
banks. With the increase in house prices, the value of collateral is increasing and
people can receive more credit from financial institutions and therefore they have
more ability to consume products. The final channel, which is the most complex
is through financial derivative products, which are secured by housing assets.
These products link the mortgage market, housing market and financial market
together. Any change in house prices will affect the other two markets and
therefore create shocks to the financial system and economy. Thus, the housing
market is relevant to the central banks, where their aims are to keep the price and
economy stable.
Other studies which have used the VAR approach to assess the relationship
between the housing market and macroeconomy include Brooks and Tsolacos
(1999), who employed a vector autoregressive model to reveal the relationship
between macroeconomic and financial variables and UK property returns.
Similarly Goodhart and Hofmann (2008) examine the linkages between UK
house prices, money, credit and the macro economy. Both UK studies found
interest rates and inflation affected house prices. Other studies finding evidence
of a similar relationship include Watuwa and Scotia (2008), who concentrated on
the effects of economic and financial factors on real estate investment, choosing
property returns, the nominal interest rate, and growth rate of industrial
production, unexpected inflation, dividend yields and the interest rate spreads.
3
They also employed a VAR model to investigate the relationship between these
variables for Canada. Other countries have also been studied, such as Chang,
Chen and Leung (2011), who examined the dynamic housing returns in
Singapore again using a VAR. Iacoviello (2000) employed the VAR model to
investigate the relationship between interest rates and house price movements for
Europe. Although the studies often come to different conclusions, overall there
appears to be a reasonably close link between the housing market and wider
economy.
The remainder of this paper is organized into three parts. Firstly, the
methodology used is discussed, then secondly, the empirical section using the
VAR, Impulse response functions and variance decomposition will be carried out
and finally the conclusions will be made and policy implications discussed.
2. Methodology
The VAR model usually assumes all the variables are endogenous. According to
Sim(1980) and McNees (1986), the VAR model can give better forecasts
compared with structural simultaneous equations.
A reduced form VAR can be expressed as follows:
Yt = α0 + A1 Yt−1 + A2 Yt−2 + ⋯ + An Yt−n + ut
Where Y denotes a
vector, which includes m observed variables for
research, and the VAR systems contained n lagged variables and
noise term vector.
(1)
is
is a white
matrix. The variables on the right hand side
(RHS) are all predetermined variables and the error terms are serially
uncorrelated. And therefore, each separate equation in the system can be
4
estimated by OLS and consistent and asymptotically efficient estimators can be
obtained.
The purpose of employing the VAR model is to investigate whether the
explanatory variables have significant causal effects on the dependent variables,
and therefore the Granger causality tests can be used for this purpose. Suppose Y
is the
vector containing different variables and the lag length is 2. A
VAR (2) can be expressed as:
𝑏11
( ⋮ )=( ⋮ )+( ⋮
𝛼𝑚0
𝑌𝑚𝑡
𝑏𝑚1
𝑌1𝑡
𝛼10
𝑐11
⋯ 𝑏1𝑚
𝑌1𝑡−1
⋱
⋮ )( ⋮ ) + ( ⋮
𝑌𝑚𝑡−1
𝑐𝑚1
⋯ 𝑏𝑚𝑚
⋯
⋱
⋯
𝑐1𝑚
𝑌
⋮ ) ( 1𝑡−2
⋮ ) (2)
𝑐𝑚𝑚 𝑌𝑚𝑡−2
There are two further methods to determine the dynamic properties of the VAR,
which are the impulse response function and the variance decompositions.
Based on the VAR, we investigate the effect of monetary policy on house price
returns and also see the relationships between pre-specified macro-economic
variables and the house price return. These variables include industrial
production, the consumer price index (CPI) which is used to calculate the
inflation rate, the nominal federal funds rate, the interest rate spread, nominal
private credit, and the house price index of the US which is used to calculated
house price returns.
The industrial production index (denoted IP) is used because there is no monthly
data for GDP.
One hypothesis is that the increase in industrial production may
increase the house price return because a boom in the economy gives more
confidence to the investors.
5
The Federal funds rate (denoted I) is an indicator of US monetary policy. This
rate contains information about the economy since it reflects the central banks’
reaction to the movement of the economy and is a very important determinant of
households’ consumption and investment decisions. All other tools, such as open
market operations, setting the reserve requirement and so on, aim to vary this
rate via affecting the demand and supply of money. The increase of the federal
funds rate indicates a tight monetary policy and therefore will limit the
development of the housing market.
Inflation affects the asset markets such as stock markets and property markets
because investors will require a higher risk premium when they believe there is a
risk of future inflation. Moreover, inflation will also affect individual’s
consumption because if households expect future inflation they will increase
their current consumption. The inflation rate is calculated by the percentage
change of the CPI. In theory, no agreement has been reached on what the effect
of inflation on house price return is or other asset price returns.
The interest rate spreads (denoted SP) are measured by the difference between
the return of the 10-year Treasury Bonds and the three-month Treasury bill rate.
If the spread increases, it means that the investors are uncertain about the future
direction of the economy and therefore it signals that the risk of the economy is
increasing. According to the asset pricing model, the house price equals the
discounted expected future return. Therefore, an increase in the risk means the
interest spread will increase requiring a higher discount rate and therefore house
prices will fall. The house price return (denoted HPR) is the percentage rate of
change 1 in the house price index based on the Standard and Poor (S&P)
1
There are many other forms the house price measure can take, for instance Morley and Wei
(2012) use a variable measuring house price uncertainty, based on the conditional variance from
an EGARCH model.
6
Case-Shiller index. The reason the house price return is used rather than the price
alone, is that the return is of concern to most investors involved in the housing
market.
The Money supply (denoted M) is also included and is obtained from the St
Louis FRED database (USA, M2 stock). M2 measures the money supply in
circulation and is an indicator for forecasting inflation. Including this variable
into the VAR systems enables one to determine whether the money supply
affects the house price return. In theory, the increase in the money supply creates
more credit for the individuals because more money increases the ability of the
banks to give loans to investors, and therefore may create a rise in the housing
market.
When nominal interest rates reach approximately zero, then changes to
the money supply, such as through Quantitative Easing (QE) can be a useful tool
to stimulate the economy.
3. Results and discussion
All the data used is monthly running from 1987m01 until 2007m04 for the USA.
The first step is to check the correlations among different variables. Table 1
provides the summary statistics for the variables included in the VAR model.
Table 2 presents simple contemporaneous correlations. There is a negative
correlation between the house price returns and the nominal interest rate,
indicating that when the house price return is high, as expected the nominal
interest rate is low. This is a similar result to other empirical findings, which
show that usually when the housing market booms, monetary policy is too loose.
There is also as expected a negative correlation between house price returns and
the inflation rate, as well as house price returns and interest rate spreads
7
Table 2 also shows the pairwise correlations for variables at lag 12. The magnitude of
the correlation is not much different from those earlier in this Table. For example,
after one year, there is still a strong correlation between the industrial production and
the money supply. When creating the VAR, the Akaike information criterion (AIC)
suggests the optimal lag length is 4. This result is similar to other studies, such as
Ivanov and Kilian (2005) using monthly data and a VAR model. With four lags, there
is no residual autocorrelation in the VAR, indicating that the chosen lag length is
appropriate.
The Granger Causality tests, reported in Table 3, are joint significance tests for the
lagged explanatory variables in each equation. The results show that as expected the
interest spread, industrial production, and the interest rate ‘Granger Cause’ the money
supply. The house price returns appear not to ‘Granger Cause2’ the money supply and
vice-versa. A similar relationship is also found between the house price return and the
interest rate spread.
Therefore, in the sample period from 1987 until 2007,
movements of the house price return are not followed by movement of the money
supply or interest rate spread, and vice-versa.
House price return and industrial
production Granger cause each other, or in other words it is possible to show that an
innovation in one variable is followed by changes in the other. Also House price
returns ‘Granger cause’ inflation, however, inflation did not ‘Granger cause’ house
price returns. House price returns ‘Granger cause’ the nominal interest rate but not
vice-versa. Overall there is little evidence that the wider macroeconomy or financial
2
The Granger causality test does not necessarily suggest whether the movement of one variable can be attributed
to the changes of the other variable.
If a Granger causality test is significant, it can mean that the movement of
one variable is followed by another variable, rather than the reason for one variable’s changes being attributed to
the other variable in the Granger causality test.
8
sector, except industrial production have much causal effect on the housing market in
the USA, which reflects similar results from a UK study by Brooks and Tsolacos
(1999).
In order to investigate the dynamic relationship between house price returns and other
macroeconomic variables, the variance decomposition of the house price return has
been employed, to assess whether the innovations in house price returns can be
attributed to its own shocks or shocks to other variables. Table 4 shows the variance
decomposition of the house price return for 1, 2, 3,4,5,12,24 steps ahead and the
ordering3 for the variables is INF, LIP, HPGR, SP, I, LM2. The ordering of the
variance decomposition is based on the following economic theory, the increase of the
money supply will change the nominal interest rate, if the money demand is not
changed in the short-term and therefore the spread of the interest rate will change. The
varying of the risk premiums affects the house prices and therefore the house price
return, which finally affects the output for the economy, which can then cause the
inflation. Therefore, the ordering is shown as: INF, LIP, HPGR, SP, I, LM2.
Table 3 reports the variance decomposition for when the forecast horizon periods are
2 years. The shock to the house price return accounts for 54% of the variation in the
house price return; the shock to the interest rate spread accounts for 17.7% of the
variation in the house price return and the nominal interest rate explains 20.8% of the
variation. This suggests, shocks to the house price return, the risk of the market, and
the nominal interest rate explain more than 90% of the movement of the house price
return, indicating that these variables are good at transmitting the effects of the shocks
3
There is another view on ordering suggested by Lutkepohl(1991), which is that if the residual of the VAR is
almost independent it is not necessary to choose the ordering for the variance decomposition.
9
to the housing market. The shocks to house price return accounts for the biggest
proportion of the variation in the house price return, indicating that the house price
return series has been a useful source of information for predicting the movement of
returns in the housing market.
The impulse response functions are shown in Figure 1. The impulse responses show
similar results to those of the variance decomposition. Shocks to the money supply do
not affect the house price return, even 24 months later. The shock to inflation also
does not affect the system and the response of the house price return to the shock to
inflation is very small and converges to 0 after 20 months. The house price growth
rate did not react to the shocks to output initially until the end of the first year. After
the first year, the response increases, however the magnitude of the response is small.
When there is a shock to the interest rates spread, the house price return series reacts
and the magnitude of the response increases, showing a persistent trend because the
response of the house price returns to the shocks to the market risk do not die away,
even after 2 years. When there is a shock to the nominal interest rate, there is a
negative response in the house price return and this effect does not die away even
after 24 months, indicating that monetary policy affects the house price return
significantly and shocks to the interest rate, such as the large falls in the early 2000s
play an important role in affecting the housing market. This relationship suggests that
monetary policy before the financial crisis can be attributed to the over development
of the housing market in the U.S. The shocks to the house price return itself also has
significant effects on the house price return, and therefore we can say that the house
price return itself contains useful information for predicting future house prices.
10
4. Conclusions
This study provides a VAR framework to analyse the relationship between house
price returns and other relevant macroeconomic variables. Following the recent
financial crisis which began in the housing market, the link between the house price
return and other variables has become increasingly important. However much of the
literature suggests the relationship between the housing market and macroeconomy is
two way, facilitating the use of the VAR approach and the results suggest for many
variables the relationship with the housing market is bi-causal, although mostly from
the housing market to the macroeconomy.
The Granger Causality tests show that mainly industrial production ‘Granger Causes’
the house price return. However, variance decomposition shows that only innovations
in house price growth, spread premium and interest rates can explain the variations of
the house price return. The variance decomposition suggests that the shocks to interest
rates, spread rates and house price returns can be used to explain the shocks to the
house price return, which confirms the fact that monetary policy affects the housing
market. There is some evidence that the housing market ‘Granger causes’ the interest
rate. This suggests models to determine the appropriate interest rate as a part of the
wider monetary policy, such as the Taylor rule may benefit from the inclusion of
some measure of the housing market. Given the importance of the housing market to
the financial crisis, its inclusion in models aimed at predicting important monetary
measures, could help form the basis for more appropriate economic policies in future.
Future research needs to incorporate alternative measures of the housing market, such
as measures of housing risk.
11
References
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14
Table 1 Descriptive Statistics
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Sum Sq.
Dev.
Observations
HPGR
I
INF
SP
IP
M2
0.062533
0.076349
0.186473
-0.06535
0.063678
-0.01484
1.800547
13.91582
0.000951
14.50755
0.047809
0.0522
0.0985
0.0098
0.02179
0.098967
2.5445
2.384358
0.303559
11.0917
0.030072
0.028791
0.060999
0.010618
0.010489
0.655739
3.187577
16.96654
0.000207
6.976653
0.015611
0.01425
0.0369
-0.00739
0.012205
0.097942
1.76468
15.12239
0.00052
3.621641
82.40397
85.3454
105.207
62.7503
14.1367
-0.09286
1.400305
25.07066
0.000004
19117.72
4471.371
3963.6
7222.3
2852
1286.4
0.628819
1.986246
25.22372
0.000003
1037358
0.93668
232
0.109677
232
0.025413
232
0.034409
232
46164.49
232
3.82E+08
232
Notes: HPGR is house price return, I is the interest rate, INF is inflation, SP is the rate spread, IP is industrial
production and M2 is M2 money supply.
Table 2 Correlation coefficients
Panel A:
HPGR
INF
I
LIP
LM2
SPREAD
HPGR
Contemporaneous correlations
INF
I
LIP
LM2
SP
-0.1483
-0.2632
0.6319
0.5964
-0.1121
0.6311
-0.5321
-0.4159
-0.2298
-0.0845
-
HPGR
Correlations at lag 12
INF
I
LIP
LM2
SPREAD
-0.3653
-0.3601
0.7284
0.7027
-0.0421
0.6496
-0.5578
-0.4438
-0.2757
0.0675
-
Panel B:
HPGR
INF
I
LIP
LM2
SPREAD
-0.5024
-0.6145
-0.6517
-0.5462
-0.6962
-0.6785
15
0.9321
-0.2424
0.9271
-0.1488
Table 3 VAR Granger Causality Tests (P-values)
lags of variables
dependent
variables
LM2
HPGR
SP
LIP
INF
I
LM2
-
0.3538
0.0018*
0.0078*
0.3249
0.0084*
HPGR
0.1545
-
0.2190
0.0611***
0.5466
0.7462
SP
0.8827
0.4400
-
0.0669***
0.9574
0.0000*
LIP
0.7730
0.0884***
0.8004
-
0.2052
0.0287**
INF
0.2098
0.0971***
0.4396
0.2041
-
0.1581
I
0.4613
0.0224**
0.3099
0.0005*
0.4512
-
Notes: ***, **, * indicate significance at the 10%, 5% and 1% levels.
Table 4 Variance Decomposition of the House Price Return (Shock to HPGR)
1
2
3
4
5
12
24
INF
Explained by innovations in
LIP
HPGR
SP
I
LM2
0.2663
0.1159
0.0431
0.0778
0.1984
2.9056
3.1453
0.00004
0.1121
0.0653
0.0392
0.0587
0.3918
3.0991
0.0000
0.0813
0.0707
0.0395
0.0284
1.8912
20.8601
0.0000
0.0000
0.0141
0.0509
0.1033
0.3992
0.5045
99.7336
99.6895
99.8013
99.7887
99.5949
89.0057
54.6742
0.0000
0.001
0.0052
0.0036
0.0163
5.4062
17.7165
16
Figure 1 Impulse Response Functions
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of HPGR to INF
Response of HPGR to LIP
.02
.02
.01
.01
.00
.00
-.01
-.01
-.02
-.02
2
4
6
8
10 12 14 16 18 20 22 24
2
4
6
8
10 12 14 16 18 20 22 24
Response of HPGR to I
Response of HPGR to SP
.02
.02
.01
.01
.00
.00
-.01
-.01
-.02
-.02
2
4
6
8
2
10 12 14 16 18 20 22 24
4
6
8
10 12 14 16 18 20 22 24
Response of HPGR to LM2
Response of HPGR to HPGR
.02
.02
.01
.01
.00
.00
-.01
-.01
-.02
-.02
2
4
6
8
2
10 12 14 16 18 20 22 24
17
4
6
8
10 12 14 16 18 20 22 24