ï»¿ WPS6549
Policy Research Working Paper 6549
A Retrospective Analysis of the House Prices
Macro-Relationship in the United States
Ibrahim Ahamada
Jose Luis Diaz Sanchez
The World Bank
Development Economics Vice Presidency
Operations and Strategy Unit
July 2013
Policy Research Working Paper 6549
Abstract
This study provides empirical evidence on the a multivariate time series analysis is performed within
strengthening of the impact of house prices on the US subsamples. The paper finds a robust structural break in
macroeconomy. The stability of the house prices macro- the mid-1980s. In addition, time series analysis across
link is tested in a small-dimensional vector autoregressive segments provides evidence that the effect of house prices,
model over the last fifty years. The estimated break-points not only on private consumption, but also on economic
are used to split the sample into different segments and activity, has intensified since the mid-1980s.
This paper is a product of the Operations and Strategy Unit, Development Economics Vice Presidency. It is part of a larger
effort by the World Bank to provide open access to its research and make a contribution to development policy discussions
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may be contacted at jdiazsanchez@worldbank.org.
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A Retrospective Analysis of the House Prices
Macro-Relationship in the United Statesâˆ—
Ibrahim Ahamadaa and Jose Luis Diaz Sanchezb,c,d
a
International Monetary Fund
b
Paris School of Economics
c
University of Paris 1 Pantheon-Sorbonne
d
The World Bank
This study provides empirical evidence on the strengthening of
the impact of house prices on the US macroeconomy. The stabil-
ity of the house prices macro-link is tested in a small-dimensional
vector autoregressive model over the last ï¬?fty years. The estimated
break-points are used to split the sample into diï¬€erent segments and
a multivariate time series analysis is performed within subsamples.
The paper ï¬?nds a robust structural break in the mid-1980s. In addi-
tion, time series analysis across segments provides evidence that the
eï¬€ect of house prices, not only on private consumption, but also on
economic activity, has intensiï¬?ed since the mid-1980s.
JEL Code: C32, E20, E44, R30.
Keywords: House prices, mortgage market deregulation, vector au-
toregressive.
Sector Board: Financial Sector (FSE).
1. Introduction
A decade ago, Alan Greenspan suggested in his testimony to the Joint Economic
Committee of the US Congress (2002) that the strong appreciation of house prices
after the crash of the stock market in 2001 might have helped save the US economy
from a more serious recession, a point of view shared by most of the economists
âˆ—
The views expressed in this article are those of the authors and do not necessarily represent
those of the International Monetary Fund or the World Bank. The authors would like to
thank John Williams (editor of the International Journal of Central Banking ), two anonymous
referees, Joerg Breitung, Jean-Bernard Chatelain, Jordi Gali, Jean-Olivier Hairault, Juergen von
Hagen, Aristomene Varoudakis, seminar participants at the Eurostat 6th Colloquium on Modern
Tools for Business Cycle Analysis, the Bonn Graduate School of Economics Macro-Workshop,
the Central Bank of Peru research seminar, the PSE Macro-Workshop and the IMF Institute
research seminar for their helpful comments and suggestions. Authors e-mail: iahamada@imf.org
and jdiazsanchez@worldbank.org.
at that time. A few years later, a large crash in housing prices triggered -in
all likelihood- a ï¬?nancial and economic crisis. Inevitably, both events have con-
tributed to the consensus among economic practitioners and many researchers
that ï¬‚uctuations in housing prices are a key factor in the US business cycle.
The question of the extent to which the deep transformation of mortgage
markets in recent years has modiï¬?ed the house prices macro-relationship arose
naturally. A consensus rapidly emerged in the literature that the eï¬€ect of house
prices on the macroeconomy has intensiï¬?ed since the mid-1980s, a time when
important deregulations took place in the mortgage market along with the devel-
opment of secondary markets and the increasing role of the Government Sponsored
Enterprises (GSE) in mortgage ï¬?nancing.1
Consequentially, a persistent fall in mortgage transaction costs occurred along
with a strong relaxation of credit conditions. Homeowners were allowed to easily
extract equity from their houses and loan-to-value ratios associated with mortgage
loans rose, increasing the ability of landlords to borrow against their real estate.2
In the literature, theoretical models showing how a relaxation of credit con-
straints on the mortgage sector ampliï¬?es the eï¬€ect of housing prices on the
macroeconomy have been developed by Miles (1992), Kiyotaki and Moore (1997),
Iacoviello (2005), and Iacoviello and Neri (2010), among others. The primary
mechanism of these models is that a reduction of credit constraints allows eco-
nomic agents to increase the amount that they are able to borrow against their
home equity, and use these additional resources to ï¬?nance extra consumption and
investment. Thus, because of the multiple signs of a relaxation in credit conditions
in the US, we can expect that the impact of house prices in the macroeconomy
has become stronger over time.
The important role of housing prices in the US business cycle in recent years
does not provide suï¬ƒcient evidence to conclude that the house prices eï¬€ect in the
macroeconomy has strengthened. Indeed, one should take into consideration the
magnitude of the last boom and bust in house prices; according to the Shiller real
house prices index, the boom and bust in house prices has been the largest at least
since the end of the 19th century. Although time series and micro-econometric
evidence largely show that housing prices have a positive impact on the US econ-
omy (see for example Green 1997, Case, Shiller, and Quigley 2005, Haurin and
Rosenthal 2006, Bostic, Gabriel, and Painter 2008, and Miller, Peng, and Sklarz
2011), only a few papers provide empirical evidence on the strengthening of the
eï¬€ect of house prices on the macroeconomy over time. Muelbauer (2007), using
a structural single equation estimation, ï¬?nds that before the US credit market
liberalization in the 1980s there was no signiï¬?cant housing wealth eï¬€ect on con-
sumption, however, since then, the eï¬€ect has become positive. Altissimo et al
1
See Gerardi, Rosen, and Willen (2010) for a brief review on the modiï¬?cations of the U.S.
mortgage market in the last forty years.
2
Taking data from the Federal Home Loan Mortgage Corporation, we calculate a substantial
fall in fees and points for a regular 30-year ï¬?xed-rate mortgage. We obtain an average of 2.3
for the 1980s, 1.5 for the 1990s and 0.7 for the 2000s. Greenspan and Kennedy (2008) ï¬?nd a
sustained increase in both their gross and net equity-extraction measures (relative to disposable
income) since the beginning of the 1990s.
(2005) estimate a marginal propensity to consume (MPC) out of wealth from
aggregate US data. Their results suggest that the MPC appears not to have sta-
tistically changed since the beginning of the 1970s. They ï¬?nd, however, a big
increase in the MPC at the end of the 1960s.
In this paper, we provide empirical evidence of the strengthening of impact
of house prices on the US macro-variables. We proceed in two steps. First, we
test the stability of the house prices macro-link in the US during the last 50 years.
A recursive Vector Autoregressive (VAR) model including gross domestic product
(GDP) or private consumption, interest rates and house prices, is chosen to ac-
count for the house prices macro-relationship. The methodology developed in Qu
and Perron (2007) is applied to identify breaks in our multivariate system. In this
method, the dates and the number of breaks are entirely determined by the algo-
rithm, rather than being imposed ex-ante, like most of the methods used in the
time series literature.3 Thus, this methodology does not require to set a priori the
mid-80s -a period systematically found as a structural break in the literature on
the â€œGreat Moderationâ€?- as a unique break-point in the house prices macro-link.
Indeed, a rupture in this relationship could have occurred as early as the end of
the 1960s, when the privatization of the Federal National Mortgage Association
(â€œFannie Maeâ€?) in 1968 and the creation of the Federal Home Loan Mortgage
Corporation (â€œFreddie Macâ€?) in 1970 established the foundation of what would
become the renovated US mortgage market. A break might also be found as re-
cently as the early 2000s, where a deepening of markets for securitized contracts
and derivatives occurred and subprime mortgage loans developed at a very strong
pace. Furthermore, the method allows us to consider the fact that the reduction
in credit constraints has been a gradual process and that the modiï¬?cation in the
house prices macro-link did not occur all at once. The implication of this hypoth-
esis is that the afore proposed break-dates are not exclusive and that more than
one break could exist in the link. In the second step, we use the break-points
estimated to split the sample in diï¬€erent segments and, on each subsample, mul-
tivariate time series analysis, including impulse-responses and Granger causality
tests are performed.
Our results can be summarized as follows: the application of Qu and Perronâ€™s
methodology in a VAR with linear restrictions concludes that there are two break-
points in the house prices macro-relationship when GDP is introduced in the
VAR speciï¬?cation: one at the end of the 1960s and the second in the mid-1980s,
the latest rupture being the strongest among the two break-dates. We also ï¬?nd
that there is only one structural break in the link when private consumption is
included in the multivariate system, in the mid-1980s. Time series analysis across
subsamples ï¬?nds that the overall impact of house prices, not only on private
consumption but also on economic activity has intensiï¬?ed since the mid-1980s.
Our results give support to the hypothesis that the modiï¬?cation of the real estate
market in the mid-1980s seems to have been a key factor in the strengthening of
the eï¬€ect of house prices on the macroeconomy.4
3
Bai and Perron (1998) also develop a methodology to detect multiple breaks occurring at
unknown dates, but the method only considers the case of a single linear equation.
4
Generally, the â€œGreat Moderationâ€? literature ï¬?nds reduced responses of GDP to diï¬€erent
The paper is organized as follows. In Section 2, we present Qu and Perronâ€™s
methodology which is used to detect breaks. Section 3 applies this methodology
to a small-dimensional VAR model using US macro-data. In Section 4, we split
the initial sample into diï¬€erent segments using the identiï¬?ed break-points. We
then perform impulse-responses and Granger causality tests in each of the seg-
ments from the initial VAR model speciï¬?cation. Section 5 contains the concluding
remarks and proposes avenues of future research.
2. Testing Structural Changes in a Multivariate Model
The various methods of identifying structural changes in a single regression model
have been well-documented in the literature. However, in the multivariate case,
only few papers have dealt with structural breaks. Qu and Perron (2007) consider
issues related to estimation, inference, and computation when multiple structural
changes occur at unknown dates in a system of equations including a vector au-
toregressive model. The changes here can pertain to the regression coeï¬ƒcients
and/or the covariance matrix of the errors. This section presents a brief descrip-
tion of Qu and Perronâ€™s method before proceeding to an application in a VAR
model using US macro-data in the next section.
2.1 The Model and Estimator
In the presentation below, we consider a VAR model with three components,
yt = (y1t , y2t , y3t ) and one lag, as in our application in Section 3. This can be
extended to a general VAR model without any major diï¬ƒculties. The dates and
the number of structural changes in the parameters are unknown. We use m to
denote the total number of structural changes and T to denote the sample size.
The unknown break dates are denoted by the m vector Î“ = (T1 , ..., Tm ) and we
use the convention that T0 = 1 and Tm+1 = T . Hence there are m + 1 unknown
sub-periods, Tj âˆ’1 + 1 â‰¤ t < Tj , j = 1, ..., m + 1. The model can be written as:
yt = Ï€j 0 + Ï€j 1 ytâˆ’1 + Îµt , t = Tj âˆ’1 + 1, ..., Tj (1)
(i)
where yt = (y1t , y2t , y3t ) . In each sub-period Tj âˆ’1 + 1 â‰¤ t < Tj : Ï€j 0 = (Ï€j 0 )i=1,...,3
(kl)
is the vector of constant parameters; Ï€j 1 = (Ï€j 1 )k=1,..,3;l=1,..,3 indicates the 3X3
matrices of the VAR parameters; and Îµt is the vector of the residuals with mean O
and covariance matrix denoted by Î£j . Here we are interested in the estimation of
Î› = m, T1 , ..., Tm , Î£j =1,...,m+1 . We suppose in this paragraph that m is known,
and will discuss later the estimation of m. For the estimation of model (1) it is
convenient to re-write the model as:
yt = xt Î²j + Îµt (2)
shocks in the post mid-1980s period (see Stock and Watson 2002 for a survey), not increased
responses as in this paper. However, the papers related to that literature do not provide evidence
of a change on the eï¬€ect of house prices shocks on the economy.
where xt = (I3 âŠ— (1, y1tâˆ’1 , y2tâˆ’1 , y3tâˆ’1 )) and
(1) (11) (12) (13) (3) (31) (32) (33)
Î²j = Ï€j 0 , Ï€j 1, Ï€j 1 , Ï€j 1 , ..., Ï€j 0 , Ï€j 1, Ï€j 1 , Ï€j 1 . The estimation method we
consider is restricted quasi-maximum likelihood. Conditional on the given break
dates Î“ = (T1 , ..., Tm ), the Gaussian quasi-likelihood ratio is:
T
Î m +1 j
j =1 Î t=Tj âˆ’1 +1 f (yt |xt ; Î²j , Î£j )
LRÎ“ = 0 (3)
+1 Tj
Î m 0 +1 f
j =1 Î t=Tj
0
yt |xt ; Î²j , Î£0
j
âˆ’1
where f (yt |xt ; Î²j , Î£j )=(2Ï€ )âˆ’n/2 |Î£j |âˆ’1/2 exp âˆ’ 1
2
[yt âˆ’ xt Î²j ] Î£âˆ’ 1
j [yt âˆ’ xt Î²j ] and
n = 3 is the number of equations in the VAR model. Î“0 = (T1 0 0
, ..., Tm 0
), Î²j
0
and Î£j indicate the true unknown parameters. Qu and Perronâ€™s (2007) approach
introduces a restriction in Î² = (Î²1 , ..., Î²m+1 ) and Î£ = (Î£1 , ..., Î£m+1 ). For example,
we obtain a partial structural-change model when the restriction imposes that a
particular subset of Î²j is the same for all j . We denote by g (Î², vec(Î£)) = 0 the
form of the restrictions in Î² and (or) Î£, where g (.) is an r-dimensional vector and
r the number of restrictions. Hence the Restricted Log-Likelihood Ratio is given
by:
rlrÎ“ = log(LRÎ“ ) + Î» g (Î², vec(Î£)) (4)
and the estimates are
{T1 , ..., Tm , Î², Î£} = arg max(T1 ,...,Tm ,Î²,Î£) rlrÎ“ (5)
The maximization (5) is taken over all partitions Î“ = (T1 , ..., Tm ) such that
|Tj âˆ’ Tj âˆ’1 | â‰¥ [ÎµT ] and Tm â‰¤ [T (1 âˆ’ Îµ)], where Îµ is an arbitrarily small positive
number and [] denotes the integer part of the argument. The parameter Îµ plays
a trimming role and imposes a minimal length for each regime. One important
result is that under more general assumptions the estimates of the break dates
Î“ = (T1 , ..., Tm ) and the coeï¬ƒcients (Î², Î£) are asymptotically independent and
valid restrictions on the latter do not aï¬€ect the distribution of the former. Qu
and Perron (2007) also discuss a method based on the principle of dynamic pro-
gramming which searches for the optimal partition Î“ = (T1 , ..., Tm ), i.e. the
partition that yields the optimal value of the Log-Likelihood rlrÎ“ . They argue
that this method is eï¬ƒcient as it only requires least-squares calculations of order
O(T ) and matrix inversions of order O(n).
2.2 Selection of the Number of Breaks
To determine the number of breaks m we can appeal to the likelihood-ratio test
of no change versus some speciï¬?c number of changes, k . As proposed by Qu and
Perron (2007), this statistic can be constructed as follows:
sup LRT (k, pb , nbd , nbo , Îµ) = 2 log LT T1 , ..., Tk âˆ’ log LT
Here log LT T1 , ..., Tk is the maximum of the log-likelihood obtained with the
optimal partition {T1 , ..., Tk }, log LT the maximum of the log-likelihood under the
null hypothesis of no structural change, pb the total number of coeï¬ƒcients that
are allowed to change (not including the coeï¬ƒcients of the variance-covariance
matrix), and nbd and nbo indicate respectively the number of parameters that
are allowed to change amongst the diagonal and oï¬€-diagonal coeï¬ƒcients of the
variance-covariance matrix. As noted above, Îµ is a parameter that allows us to
impose a minimal length for each regime. The limiting distribution of sup LRT is
discussed in details by the authors, and depends on the aforementioned param-
eters. It is important to note that this testing procedure is particularly ï¬‚exible.
The test can be used with respect to many cases of structural change: (a) changes
only in the coeï¬ƒcients of the conditional mean (nbd = 0, nbo = 0); (b) changes
only in the coeï¬ƒcients of the covariance matrix of the residuals (pb = 0); and (c)
changes in all of the coeï¬ƒcients (pb = 0, nbd = 0, nbo = 0).
The test for no change versus an unknown number of breaks can also be con-
sidered given some upper bound M for k . This class of tests are called double max-
imum tests, and the statistic is deï¬?ned for some ï¬?xed weights W = {a1 , ..., aM }
as:
D max LRT (M ) = max [ak sup LRT (k, pb , nbd , nbo , Îµ)]
1â‰¤kâ‰¤M
For uniform weights, i.e. ai = 1, i = 1, ..., M., the statistic is always denoted by
U D max LRT (M ). The second test is noted by W D max LRT (M ) and applies
weights to the individuals tests such that the marginal p-values are equal across
values of m. Bai and Perron (1998) provide more discussion of this class of tests
and their critical values.
We can also consider the sequential test based on the null hypothesis of, say,
l break dates versus l + 1 breaks. The general form of this statistic is:
SEQT (l + 1|l) = max sup lrT T1 , ..., Tj âˆ’1 , Ï„, Tj , ..., Tl âˆ’ lrT T1 , ..., Tl
1â‰¤j â‰¤l+1 Ï„ Î›j,Îµ
Here lrT (.) denotes the log of the likelihood, {T1 , ..., Tl } the optimal partition if l
breaks are supposed, and Î›j,Îµ = {Ï„ ; Tj âˆ’1 +(Tj âˆ’ Tj âˆ’1 )Îµ â‰¤ Ï„ â‰¤ Tj âˆ’ (Tj âˆ’ Tj âˆ’1 )Îµ}. In
addition, the limiting distribution of the test depends on the number of coeï¬ƒcients
that are allowed to change.
In practice, the preferred strategy to determine the number of breaks is ï¬?rst
to look at the U D max LRT (M ) or W D max LRT (M ) tests to see if at least one
structural break exists. We can then decide the number of breaks based on the
SEQT (l + 1|l) statistic. We select m breaks such that the SEQT (l + 1|l) tests
are insigniï¬?cant for any l â‰¥ m. Bai and Perron (2003) conclude that this method
leads to the best results and recommend it for empirical applications. However, in
the case of a VAR with restrictions on the coeï¬ƒcients, Qu and Perron (2007) con-
sider only the SupLRT test to obtain the number and the location of the breaks.
2.3 Method of Lag Selection
The presence of structural changes in multivariate models introduces non-linearity.
As such, the usual model-selection criteria (Akaike and Bayesian information cri-
teria) are not applicable. One practical result in Qu and Perron (2007) is that
the limited distribution of the estimates of the break-points is not aï¬€ected by
the imposition of valid restrictions on the parameters. Hence, a non-linear VAR
model with a number of lags, say p, can be considered as a valid restriction of a
non-linear VAR model with p+1 lags, if the break-dates in the two models are
signiï¬?cantly unchanged. We use this result to decide on the number of lags in the
application section.5
3. House Prices Macro-Link in the US: Evidence of Instability
Under this section we apply the Qu and Perronâ€™s algorithm to the US macro-
data. We consider a VAR Model with three endogenous variables: real gross
domestic product (GDP) or real private consumption (C), real house prices (HP)
and the Fed Funds rate (I), as a proxy for the monetary policy stance. Closed
speciï¬?cations accounting for the house prices macro-relationship have been used
by Iacoviello (2005), Goodhard and Hoï¬€man (2007, 2008), Oikarine (2009), and
Calza, Monacelli, and Stracca (2013) among others.
We work with two diï¬€erent VAR speciï¬?cations, one including GDP and the
other private consumption, to examine whether the reduction in credit constraints
in the US could have modiï¬?ed only the impact of housing prices on consumption,
but not its eï¬€ect on overall economic activity.
Our data is in quarterly frequency from 1960q1 to 2009q3. GDP, private
consumption, and house prices are measured in logarithms, with the log values
detrended via the ï¬?rst-diï¬€erencing ï¬?lter.6 Private consumption and house prices
are deï¬‚ated using the consumer price index. The Fed Funds rate is the average
value in the ï¬?rst month of each quarter. The house price series comes from the
Shiller real home price index. Figure 1 shows the data series used.
3.1 Application of the Qu and Perronâ€™s Algorithm in a VAR with no Linear
. Constraints
The Qu and Perronâ€™s procedure to identify breaks is applied to the following
model:
yt =Ï€j 0 +Ï€j 1 ytâˆ’1 +Îµt
and t = Tj âˆ’1 + 1, ..., Tj , j = 1, ..., m + 1
5
An alternative method of lag selection in a non-linear VAR is proposed in Kurozumi and
Tuvaandorj (2011). The authors discuss a modiï¬?ed AIC and BIC to be used in the case of a
multivariate model with multiple structural changes.
6
We use the ï¬?rst-diï¬€erencing ï¬?lter instead of a two-sided moving average ï¬?lter (for example,
Hodrick-Prescott or Baxter-King) in order to test for Granger causality in Section 4. Indeed,
it is well known in the econometric literature that the use of a two-sided moving average ï¬?lter
biais the Granger causality test towards a false ï¬?nding of Granger causation (see for instance
Cogley 2008).
where yt = (âˆ†Xt , âˆ†HPt , âˆ†It ) and m denotes the unknown breaks. In each un-
(i)
known sub-period Tj âˆ’1 + 1 â‰¤ t < Tj : Ï€j 0 = (Ï€j 0 )i=1,...,3 is the vector of con-
(kl)
stant parameters; Ï€j 1 = (Ï€j 1 )k=1,..,3;l=1,..,3. indicates the 3X3 matrices of the
VAR parameters; and Îµt is the vector of the residuals with mean O and con-
stant covariance-matrix. Thus, we only consider the case of a structural change in
the conditional mean of the coeï¬ƒcients. X represents either GDP or private con-
sumption. âˆ† is the delta operator. All the tests are carried out by ï¬?xing m = 4
and a trimming value of Îµ = 0.02.7 We start by applying the tests considering a
lag ï¬?xed at p = 1.
Figure 1. Data Series
Let us ï¬?rst consider X=GDP. Table 1 shows the results of the W Dmax
LRT (M ) test, where the null hypothesis is rejected at the 5% level. The value of
the W D max LRT (M ) statistic is 54.13, whereas the critical value at the 5% level
is 30.62. Hence, there is at least one structural break in the VAR model. The
SEQT (l + 1|l) test allows us to reject the null hypothesis of one break against
the alternative of two breaks as Seq (2|1) = 40.84 with the 5% critical value being
32.60. The SEQT (l + 1|l) test allows us also to reject the null hypothesis of two
breaks against the alternative of three breaks as Seq (3|2) = 37.88 with the 5%
critical value being 33.96. Finally, the null hypothesis of three breaks against four
breaks is not rejected as Seq (4|3) = 0.00 where the 5% critical value is 34.89. The
performed tests thus lead us to conclude that there are three structural breaks
in the considered VAR system which includes a GDP variable: 1969q3, 1982q4
7
The parameter imposes a minimal length for each segment and the limiting distributions
of the diï¬€erent tests are aï¬€ected by this value. As a robustness exercise, we experiment with
three diï¬€erent values of : 0.015, 0.02, and 0.03. These values are considered in many empirical
papers and Monte Carlo simulations. We ï¬?nd that results do not diï¬€er statistically. Results of
this robustness exercise are not presented in the paper but are available by request.
and 1999q1. Table 2 shows the results of the SEQT (l + 1|l) test along with the
estimated break dates with their 95% conï¬?dence intervals.
Table 1. WDmax Test for up to 4 Breaks. VAR with no Linear
Restrictions
VAR with X=GDP VAR with X=C
WDmax statistic 54.13 50.75
Critical value at 5%: 30.62
Next we apply the procedure setting X=C. The W Dmax LRT (M ) statistic
allows us to reject the null hypothesis at the 5% level (Table 1). The value of
the W D max LRT (M ) statistic is 50.75, whereas the critical value at the 5%
level is 30.62. We conclude then that there is at least one structural break in
the considered VAR model. The SEQT (l + 1|l) test allows us to reject the null
hypothesis of one break against the alternative of two breaks as Seq (2|1) = 39.32
with the 5% critical value being 32.60. Moreover, SEQT (l + 1|l) also allows us
to reject the null hypothesis of two breaks against the alternative of three breaks
as Seq (3|2) = 37.88 with the 5% critical value being 33.96. Nevertheless, the null
hypothesis of three breaks against four breaks is not rejected as Seq (4|3) = 0.00
where the 5% critical value is 34.89. Thus, the performed tests allow us to conclude
that there are three structural breaks in the considered VAR speciï¬?cation which
includes a private consumption variable: 1970q2, 1985q1 and 1999q1. Table 3
shows the 95% conï¬?dence intervals for each break.
Table 2. The SEQT (l + 1|l) Test for a VAR with no Linear Restrictions
with X=GDP
Statistic Critical value Signiï¬?cant break
at 5% level
Seq( 2|1 ) 40.84 32.60 -
1969q3 (1968q1-1971q1);
Seq( 3|2 ) 37.88 33.96 1982q4 (1981q2-1984q2);
and 1999q1 (1997q1-2001q1)
Seq( 4|3 ) 0.00 34.89 -
Afterwards, we apply the tests using a VAR with a lag ï¬?xed at p = 2. The
number and location of the break-dates remain signiï¬?cantly unchanged.8 In both
cases, the VAR model with one lag can then be considered as a valid and parsi-
monious restriction of the VAR model with two lags.
3.2 Application of the Qu and Perronâ€™s Algorithm in a VAR with Linear
. Constraints
8
The test results are not reported because of space considerations but are available by request.
Table 3. The SEQT (l + 1|l) Test for a VAR with no Linear Restrictions
with X=C
Statistic Critical value Signiï¬?cant break
at 5% level
Seq( 2|1 ) 39.32 32.60 -
1970q2 (1967q4-1972q4);
Seq( 3|2 ) 38.82 33.96 1985q1 (1983q4-1986q2);
and 1999q1 (1998q2-1999q4)
Seq( 4|3 ) 0.000 34.89 -
The estimated break-dates in the ï¬?rst part of this section are submitted to a ro-
bustness exercise in this sub-section. We would like to dismiss the possibility that
the breaks found are not primarily driven by changes in the eï¬€ect of house prices
on the macroeconomy. For instance, the new monetary policy paradigm of the
Federal Reserve -nominal policy interest rates reacting more than proportionaly
to inï¬‚ation rate changes- could be the main factor causing the rupture detected in
the mid-80s. To avoid this issue, we constrain our VAR to only allow a change in
the set of parameters related directly to the impact of house prices in the macro-
variables. Thus, the Qu and Perronâ€™s algorithm is applied to the following VAR
model:
ï£±
ï£² âˆ†Xt = Î²1 + Î²2 âˆ†Xtâˆ’1 + Î²3j âˆ†HPtâˆ’1 + Î²4 Itâˆ’1 + t1
âˆ†HPt = Î²5 + Î²6 âˆ†Xtâˆ’1 + Î²7j âˆ†HPtâˆ’1 + Î²8 Itâˆ’1 + t2
âˆ†It = Î²9 + Î²10 âˆ†Xtâˆ’1 + Î²11j âˆ†HPtâˆ’1 + Î²12 Itâˆ’1 + t3
ï£³
and t = Tj âˆ’1 + 1, ..., Tj , j = 1, ..., m + 1
where m denotes the unknown breaks and t ={ t1 , t2 , t3 } is the error term with
mean 0 and constant variance-covariance matrix. Then, in the above VAR with
linear restrictions, only the parameters Î²3j , Î²7j and Î²11j are allowed to change.
As proposed by Qu and Perron (2007), the SupLRT test is performed to obtain
the number and the location of breaks in a VAR with linear constraints.
Let us consider the case of a VAR with X=GDP. The null hypothesis of
no break is tested against the previously estimated three breaks. Results (Table
4) show that the SupLRT test does not allow us to reject the null hypothesis
of no structural break against the alternative of three breaks, as the value of the
SupLRT statistic is 29.92 while the critical value at the 5% level is 33.71. Thus, we
cannot associate each of the three previously detected breaks as structural changes
in the eï¬€ect of house prices on the macroeconomy. We proceed to examine if two
of the estimated breaks are robust to the imposed restrictions. The SupLRT test
allows us to reject the null hypothesis of no structural break against the alternative
of two breaks, as the value of the SupLRT statistic is 29.54 while the critical
value at the 5% level is 28.17. The test gives us 1971q2 and 1983q1 as structural
breaks. The conï¬?dence intervals associated to these two breaks, 1968q2-1973q2
and 1980q2-1985q4, cover the ï¬?rst two break-points obtained in the no restricted
VAR (1969q3 and 1982q4). We can then conclude that only the break-dates
1969q3 and 1982q4 can be associated with a change in the impact of house prices
on the macroeconomy, when GDP is included in the VAR speciï¬?cation. In a ï¬?nal
step, we use the SupLRT test to detect the location of the strongest rupture in the
system during the considered period. To do this, we apply the SupLRT test with
the null hypothesis of no structural break against the alternative of one break.
The SupLRT test allows us to reject the null hypothesis of no structural break
against the alternative of one break, as the value of the SupLR statistic is 25.08
while the critical value at the 5% level is 21.37. The test gives us 1984q4 as a
break-point, and the conï¬?dence interval associated to this break, 1981q4-1987q4,
covers the second break-date obtained in the no restricted VAR (1982q4). Thus,
we conclude that the strongest rupture in the house prices macro-link, for the
considered VAR speciï¬?cation, occurred in the mid-1980s.
Table 4. The SupLRT Test for a VAR with Linear Restrictions with
X=GDP
Statistic Critical value Signiï¬?cant break
at 5% level
SupLRT test ( 1|0 ): 25.08 21.37 1984q4(1981q4-1987q4)
SupLRT test ( 2|0 ): 29.54 28.17 1971q2 (1968q2-1973q2);
1983q1 (1980q2-1985q4)
SupLRT test ( 3|0 ): 29.92 33.71 -
We now test the robustness of the three break-dates estimated in a VAR in-
cluding private consumption as an endogenous variable (i.e, X=C). Results (Table
5) show that the SupLRT test does not allow us to reject the null hypothesis of
no structural break against the alternative of three breaks, as the value of the
SupLRT statistic is 24.40 while the critical value at the 5% level is 33.70. The
SupLRT test also does not allow us to reject the null hypothesis of no structural
break against the alternative of two breaks, as the value of the SupLRT statistic
is 24.24 while the critical value at the 5% level is 28.17. Finally, the SupLRT test
allows us to reject the null hypothesis of no structural break against the alterna-
tive of one break. The test gives us 1984q3 as the only break in the system. The
conï¬?dence interval associated with this break -1981q1-1988q1- covers the second
break-point obtained in the non restricted VAR (1985q1). We can then conclude
that only the break-point 1985q1 can be associated to a change in the eï¬€ect of
house prices on the macroeconomy, when private consumption is included in the
VAR system.
Results in this section suggest that the housing prices impact on the selected
US macro-aggregates experienced an important rupture in the mid-1980s. Even
though the economic agents experienced a progressive relaxation on credit con-
straints specially during the last 30 years, the modiï¬?cation of the housing market
in the mid-1980s seems to have been a determining factor of the change of the
house prices macro-relationship.9
9
Our results also suggest that the break estimated in the end of the 1960s is not due to a
Table 5. The SupLRT Test for a VAR with Linear Restrictions with
X=C
Statistic Critical value Signiï¬?cant break
at 5% level
SupLRT test ( 1|0 ): 23.05 21.37 1984q3 (1981q1-1988q1)
SupLRT test ( 2|0 ): 24.24 28.17 -
SupLRT test ( 3|0 ): 24.40 33.70 -
4. Multivariate Time Series Analysis within Subsamples
In Section 3 we have shown that the impact of house prices on the macroeconomy
changed in the mid-1980s. In this section we look for time series evidence to ï¬?nd
in which direction the house prices macro-link has moved. More speciï¬?cally, we
seek evidence that the eï¬€ect of house prices on economic activity and on private
consumption has been reinforced after the break. In this aim, we split the sample
into two segments using the break-date estimated in the mid-1980s. Impulse-
responses and Granger-causality tests are performed for both subsamples. The
VAR speciï¬?cation used to identify the breaks in the previous section is also con-
sidered in each sub-period.10
4.1 Generalized Impulse-Response Functions
In order to analyze the dynamics of a VAR system, most of the empirical papers
in the literature use the â€œorthogonalisedâ€?impulse-responses where the underlying
shocks are orthogonalised using the Cholesky decomposition methodology. The
main problem with this method is that in practice, when the order of the vari-
ables in the VAR is modiï¬?ed, the responses are often signiï¬?cantly diï¬€erent. To
avoid the issue of potentially diï¬€erent results, we apply the generalized impulse
responses (GIRs) proposed by Pesaran and Shin (1998), which is invariant to the
ordering of the variables in the VAR. For each of the VAR speciï¬?cations, either
including GDP or consumption, we perform GIRs and cumulative GIRs for each
of the two sub-periods (Figure 2). Shocks represent an exogenous increase in one
percent in the house prices variable.11
change in the house prices eï¬€ect on consumption, but it would be mainly driven by changes in
the impact of house prices on investment. The increase in the competition on the secondary
market due to the creation of â€œFreddie Macâ€? (1970) could have played a role in the modiï¬?cation
of the link between housing investment and house prices, however more work would be needed
to clarify this issue.
10
In the previous section we have found that a VAR with one lag is a valid and parsimonious
restriction of a VAR with two lags. This result allows us to estimate for this section a VAR with
either one or two lags. We choose a VAR with one lag for the sake of preserving an adequate
number of degrees of freedom for the estimation.
11
Because the housing prices series has been log-tranformed and ï¬?rst-diï¬€erenciated, an in-
crease of one percent of this variable represents an increase in one percent in the growth rate of
Figure 2. Generalized Impulse-Responses
Results for a VAR with X=GDP
Shock to HP and response of GDP Cumulative impulse-responses
Results for a VAR with X=C
Shock to HP and response of C Cumulative impulse-responses
Note. The y-axis measures percent deviations from the baseline, while the x-axis represents
quarters after shock.
4.1.1 First Case: GIRs for a VAR Including GDP
First segment (1960q1-1982q4). The eï¬€ect of an increase in house prices by one
percent has an immediate negative eï¬€ect on GDP, however, it becomes positive
after one quarter, and then decreases steadily in the next quarters. The cumulative
impulse-responses for a 10 quarter horizon suggests that the accumulated eï¬€ect
of a one percent increase in housing prices on GDP after 10 quarters is around
0.5 percent for this segment.
Second segment (1983q1-2009q3). For this sub-period, we ï¬?nd a stronger ef-
fect of house prices on GDP compared to the eï¬€ect found in the ï¬?rst segment for
all the periods but one. Moreover, the cumulative impulse-responses show that
the accumulated eï¬€ect of a rise of one percent in house prices on GDP is around 1
house prices. The same is true for the responses of GDP and private consumption.
percent after 10 quarters for this sub-period, which is approximately 100 percent
stronger than the accumulated eï¬€ect estimated for the ï¬?rst segment.
4.1.2 Second Case: GIRs for a VAR Including Private Consumption
First segment (1960q1-1985q1). The eï¬€ect of a one percent increase in the house
prices variable increases private consumption by approximately 0.1 percent in
the ï¬?rst quarter. The shock appears to be absorbed rapidly, implying that a
change in housing prices has little inï¬‚uence on private consumption after two
quarters. The cumulative impulse-responses for a 10 quarter horizon suggests
that the accumulated eï¬€ect of an increase in housing prices of one percent on
consumption after 10 quarters is around 0.5 percent for this sub-period.
Second segment (1985q2-2009q3). For this segment, the rise in private con-
sumption following a house prices increase of one percent is very close in the short
run to the response estimated in the ï¬?rst sub-period. Nevertheless, the distur-
bance appears to impact consumption long after the initial impact. Moreover,
the cumulative impulse-responses show that the accumulated eï¬€ect of a rise of
one percent in house prices on private consumption is around 0.8 percent after
10 quarters for this sub-period, which is more than 50 percent stronger than the
accumulated eï¬€ect found for the ï¬?rst segment.
In sum, generalized impulse-responses show that the eï¬€ect of house prices
on the economic activity and on aggregate private consumption has substantially
increased since the mid-1980s.
4.2 Granger-Causality Test of Block Exogeneity
Under this short sub-section multivariate Granger-causality of block exogeneity
Wald tests are performed for each of the VAR speciï¬?cations, either including GDP
or private consumption, and for each sub-period (see Table 6).
Granger causality tests show that before the mid-80s, there is no unidirec-
tional Granger causality running either from house prices to GDP or consumption,
or in the opposite direction. However, a clear unidirectional Granger causality
running from house prices to the economic activity and to private consumption is
detected since the mid-1980s.
5. Conclusion
This paper provides empirical evidence on the strengthening of the impact of house
prices on the macroeconomy in the US. First, Qu and Perronâ€™s methodology is
applied to identify breaks in a VAR model. The choice of this method is guided
by its key advantages compared to the alternative methods used in the literature:
the method allows us to detect a break at unknown dates and it allows for multiple
breaks. Second, the estimated break-points are used to split the sample in diï¬€erent
segments, and the generalized impulse-responses proposed by Pesaran and Shin
(1998) as well as Granger causality tests are performed within the subsamples.
Table 6. Granger Causality Tests
Results for a VAR with X= GDP
Chi-square P-value
First segment HP GDP 0.81 0.37
(1960q1-1982q4) GDP HP 0.01 0.93
Second segment HP â‡’ GDP 10.86 0.00
(1983q1-2009q3) GDP HP 3.32 0.07
Results for a VAR with X=C
Chi-square P-value
First segment HP C 1.16 0.28
(1960q1-1985q1) C HP 1.00 0.31
Second segment HP â‡’ C 20.74 0.00
(1985q2-2009q3) C HP 0.66 0.42
Note. The null hypothesis is the non Granger causality. The â‡’ and symbols denote the
Granger causality and the non Granger causality, respectively, at 5% signiï¬?cance level.
Using macro-data from the last ï¬?fty years, this study ï¬?nds that there is a
robust structural break in the mid-1980s in the house prices eï¬€ect on the macroe-
conomy, which is obtained when either GDP or private consumption is included
in the multivariate speciï¬?cation. The paper also ï¬?nds time series evidence that
the overall impact of house prices on consumption and on economic activity has
reinforced since the mid-1980s. Results in this study support the widespread hy-
pothesis in the theoretical literature that the deep transformation in the mortgage
market during the mid-1980s is the main cause of the intensiï¬?cation of the impact
of housing prices, not only on household expenditures decisions, but also on the
economic activity as a whole.
Future research could be focused on the consequences of the Dodd-Frank Act
on credit conditions and to what extent it will aï¬€ect the house prices macro-
link. Indeed, a tightening in credit constraints could be expected following the
Title XIV of the Dodd-Frank Act -â€œMortgage Reform and Anti-Predatory Lend-
ing Actâ€?- since its main objective is the imposition of restrictions on mortgage
originators to only provide lending to borrowers who are likely to repay their loans.
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