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Business and Real-Estate Price Cycles Across the US:
Evidence from a Vector Markov-Switching Regression
Exercise
Aram Balagyozyan1,Christos Giannikos2, and Kyoko Mona3
1The University of Scranton, Scranton, PA 18510;
Email: aram.balagyozyan@scranton.edu; Phone: 570.941.5934
2Corresponding author, Baruch College, One Bernard Baruch Way, New York, NY 10010;
Email: christos.giannikos@baruch.cuny.edu; Phone: 646.312.3492
3Manhattanville College, 2900 Purchase St. Purchase, NY 10577;
Email: kyoko.mona@mville.edu; Phone: 914.323.5161
April 30, 2016
Abstract
This study examines whether house price cycles led or lagged business cycles in the
state-level US data from 1979 to 2012. We use a vector Markov-switching model to
test for various lead/lag scenarios across the US. For the majority of the US states as
well as the aggregate US, we could not reject the hypothesis that between 1979 and
2012 house prices did not lead the economy. We find that between 2002 and 2011,
house prices led the economy in 22 states and nationally. The states where prior to the
2007 recession house prices grew faster than six times the state’s population growth
rate were almost guaranteed to suffer the economic consequences of the pre-2007 house
price decline.
1
1 Introduction
The US recession of 2007 was a bitter reminder of the strong ties between real-estate markets
and the broader economy. The idea that these two sectors are closely related is not new;
scholars have been actively investigating the nature of this relationship since the eighteenth
century. Yet, there is no well-established consensus about the validity of the channels through
which real-estate markets and the economy are connected. The broad aim of this paper is
to advance our understanding of the link between these two sectors. In particular, we would
like to investigate whether there is an empirical connection between real-estate price and
business cycles. Below, we explain why a better understanding of this connection may help
to shed light on the transmission mechanism through which real-estate markets in general
affect the macro-economy.
It has generally been found that housing cycles lead economic cycles at the city, state, and
national levels.1Broadly speaking, the literature offers four explanations for this observation.
First, the housing market may be a proxy for another, more important variable that leads
economic cycles. For example, Strauss (2013) suggests that improvements in consumers’
expectations of future income may forecast improvements in both housing and the general
economy. If housing reacts to these expectations faster than the economy, then it would
predict the economy. The second explanation connects housing to the broader economy
through residential construction. When the housing market picks up, so does employment
in the construction industry. Rising incomes in the construction industry then spill over to
other industries and lead to higher GDP and employment. The third explanation operates
through the credit channel. When the housing market weakens, so does the strength of
the lenders’ balance sheets. Foreclosures and mortgage defaults undermine the financial
strength of the banking sector, causing the banks to tighten their lending standards, which
in turn weakens the consumer demand for goods and services that are financed by credit. We
suspect that the systemic impact of this channel became stronger with the securitization of
the credit market. Finally, there is the wealth effect. As real estate appreciates, homeowners
2
become wealthier. According to the life-cycle theory of consumption, they spend more and
thus increase equilibrium output and employment.
It is important to note that both, the credit and wealth effects of housing are the most
frequently quoted channels through which real-estate markets affect the economy and both
work through real-estate prices. It is declining real-estate prices that lead to mortgage
defaults, real-estate foreclosures, and diminishing household wealth. Conversely, continuous
appreciation of real-estate prices leads to fewer defaults and foreclosures and to increasing
household wealth. While these two effects are often quoted, there is no clear consensus about
their validity and magnitude. Case, Quigley, et al. (2005) studied a panel of US states and
found that the housing wealth effect is an important determinant of consumption. They
also found that the wealth effect of housing exceeds that of the stock market. Muellbauer
(2007) studied a cross-section of countries and found that the wealth and credit effects are
strong everywhere, but stronger in the US and UK. Moreover, the wealth effect in the US
became much stronger after the liberalization of financial markets. However, despite such
evidence there are good reasons to argue against this interpretation of data. If the wealth and
credit effects are truly valid and significant, then they must work through changes in real-
estate prices. But many authors find no compelling empirical evidence that real-estate prices
have a tendency of leading the broader economy. Leamer (2007), for example, shows that
while national housing indicators such as residential investment and volumes are powerful
predictors of business cycles, house prices are not. Ghent and Owyang (2010) and Strauss
(2013) reach similar conclusions for US cities and states respectively. Hence, the results
of these authors indirectly imply that the wealth and credit effects are weak and possibly
invalid.
In this paper, we use a vector Markov-switching model to investigate the coevolution of
business cycles and house price cycles in the cross-section of all US states as well as nationally.
Our findings suggest that at the national level, house prices sometimes lead and sometimes
lag business cycles. Moreover, in line with the conclusions of Ghent and Owyang (2010),
3
Leamer (2007), and Strauss (2013) we do not find any consistent relationship between state
business and house price cycles. Yet, for the overwhelming majority of US states as well
as the aggregate US, we also fail to reject the hypothesis that house prices do not lead the
economy. We find that the deterioration of state economies in late 2007 and early 2008 was
preceded by a decline in house prices in nearly half of US states. Although the national
recession of 2007 started sometime after a downturn in house prices, the housing market
recovery lagged the economic recovery by at least two years. These results imply that even
though we fail to observe any systematic patterns in which house prices lead state or national
economies, neither can we prove that they do not. Hence, the credit and wealth effects of
housing cannot be written off as non-existent or weak; they remain legitimate subjects for
further investigation. Finally, our analysis of the data from the 2000s suggest that growth of
housing prices relative to population growth can be a powerful predictor of where a downward
shift of house price growth may lead to an economic decline as well.
The remainder of the paper proceeds as follows: Section 2 describes the vector Markov-
switching model and hypothesis testing methodology. We describe our data in Section 3.
Section 4 explains the results and Section 5 concludes.
2 Model and Methodology
In examining the lead/lag relationship between two variables with structural (or regime)
shifts, one should be interested in at least three aspects of the relationship: first, whether
one variable leads the other; second, whether one variable leads the regimes of the other; and
third, whether the regimes of one variable lead the regimes of the other. Some type of Granger
causality testing may be required to investigate the first aspect.2If one is rather interested in
exploring the second aspect, then an attractive modeling choice would be a single-equation
Markov-switching model with its time-varying transition probabilities made dependent on
the suspected leading variable.3When it comes to the interplay between housing prices
4
and the economy, however, the third aspect is of particular interest. Changes in real-estate
prices are more likely to impact the economy when they are significant and persistent. As, for
example, the experience of the 2007 US recession revealed, it was a significant and relatively
persistent deterioration of real-estate prices that drove the country into a recession. We
would like to reflect on this experience and investigate whether it is the structural shifts in
the dynamics of housing prices (rather than the dynamics of housing prices itself) that tend
to lead business cycles. This particular angle of looking at the lead/lag relationship between
housing price and business cycles is new and to the best of our knowledge has not yet been
explored by the related literature.
We examine the interplay between housing price growth regimes and business cycles using
a version of the vector Markov-switching model employed by Hamilton and Lin (1996) and
Smith et al. (2000). The model allows for structural shifts in both variables and is capable
of revealing the lead and lag relationship between them. In our settings, the economy and
housing prices in a given region are assumed to evolve according to the following vector
Markov-switching model with no autoregressive dynamics:
y1t
y2t
=
φr
t
δs
t
+
εφt
εδt
(1)
The variables y1tand y2trepresent the growth rates of the economy and housing prices
respectively. The innovation terms εφt and εδt are assumed to be jointly normally distributed
with zero means and time-invariant correlation coefficient ρ. Their variance-covariance ma-
trix therefore has the following form:
Σ =
(σφ)2ρσφσδ
ρσφσδ(σδ)2
(2)
The intercept coefficients φrand δscan be interpreted as the mean growth rates of the
economy and housing prices respectively. These coefficients are assumed to be time varying
5
and subject to discrete switches between two regimes: low (l) and high (h). The superscripts
refer to the regime r, s ={l, h}. It follows that the growth rates of the economy and house
prices in the region may jointly assume four regimes:
R= 1 : {φl, δl}(3)
R= 2 : {φl, δh}
R= 3 : {φh, δl}
R= 4 : {φh, δh}
The individual and joint regimes are unobservable, but we assume that they follow a
Markov process. Under this assumption, inferences about regimes, their probabilities4, and
transition probabilities can be made using the procedures described in Hamilton (1994), Kim
and Nelson (1999), and Krolzig (1997).
Our specification of the vector Markov-switching model in (1) does not include any au-
toregressive (AR) dynamics. Since the objective of our study is to investigate the historical
dynamics of the mean growth rates of the economy and housing prices and since forecasting
these variables is not our goal, we are inclined to keep the model as parsimonious as possible.
This choice of parsimony over more sophisticated autoregressive specifications has its obvious
benefits and drawbacks. The biggest benefit of keeping the model free of AR dynamics is
that the intercept coefficients φrand δscan be easily interpreted as the mean growth rates
of the economy and housing prices respectively. Moreover, unless the AR coefficients are
significantly different from zero, the estimates of the intercept coefficients φrand δsin (1)
are nearly identical to those estimated under more sophisticated model specifications. On
the other hand, if the AR components in the correct specification are in fact significant then
by oversimplifying the model we risk to compromise the precision with which φrand δsare
estimated. Thus, by keeping the model free of AR components we gain in interpretability
of the coefficients albeit at the possible cost of losing in precision. Fortunately, the AR
6
components are unlikely to be significant, especially in the first equation of (1); Albert and
Chib (1993) and Hamilton (1989) carefully investigate the nature of business cycles in the
US using a Markov-switching model with AR(4) dynamics and both find that the autore-
gressive coefficients are not significantly different from zero. Hence, the cost of possible
underspecification in our case is unlikely to overwhelm the obvious benefit.
Shifts between different regimes are governed by a 4 ×4 transition probability matrix
that we estimate along with the other parameters of the model (1)-(3). The matrix is:
P=
p11 p21 p31 p41
p12 p22 p32 p42
p13 p23 p33 p43
p14 p24 p34 p44
(4)
where pij = Pr(Rt=j|Rt−1=i), i, j = 1...4 is the transition probability that the regime,
R, was iin the previous period and jin the subsequent period. Each column must add
to unity. Hence, when estimating the model only twelve probabilities of the matrix are
left as free parameters. A single element in each column is equal to one minus the sum of
the remaining elements in the column. Since the transition probability matrix (4) already
incorporates the temporal inter-dependency that may exist between house prices and the
economy, we assume that the transition probabilities are time invariant.5It is useful to
exhibit and discuss the transition probability matrix (4) more explicitly.
P=
P(φl
t, δl
t|φl
t−1, δl
t−1)P(φl
t, δl
t|φl
t−1, δh
t−1)P(φl
t, δl
t|φh
t−1, δl
t−1)P(φl
t, δl
t|φh
t−1, δh
t−1)
P(φl
t, δh
t|φl
t−1, δl
t−1)P(φl
t, δh
t|φl
t−1, δh
t−1)P(φl
t, δh
t|φh
t−1, δl
t−1)P(φl
t, δh
t|φh
t−1, δh
t−1)
P(φh
t, δl
t|φl
t−1, δl
t−1)P(φh
t, δl
t|φl
t−1, δh
t−1)P(φh
t, δl
t|φh
t−1, δl
t−1)P(φh
t, δl
t|φh
t−1, δh
t−1)
P(φh
t, δh
t|φl
t−1, δl
t−1)P(φh
t, δh
t|φl
t−1, δh
t−1)P(φh
t, δh
t|φh
t−1, δl
t−1)P(φh
t, δh
t|φh
t−1, δh
t−1)
(5)
In principle, the transition probabilities in (5) should describe all possible types of the joint
dynamics of the housing market and economy. A useful way of thinking of these types is
through the complete classification of the shocks that may impact both the economy and
the housing market. A careful consideration of each element of the transition probability
7
matrix allows us to define five categories of shocks. First, there may be no shocks. In
this case inertia dominates both sectors, so the regimes do not change. In this case, we
expect to estimate significant values of the probabilities on the principal diagonal of the
transition probability matrix, p11,p22,p33, and p44. Second, sterile shocks that affect one
sector but not the other. If these types of shocks are dominant, we expect to estimate
significant values of p12 ,p13,p42 , and p43. Third, systemic shocks that affect both sectors
simultaneously, although not necessarily in the same direction. If this type of shocks is
dominant, we expect to estimate significant values of probabilities along the minor diagonal
of the transition probability matrix, p14,p23,p32, and p41. Fourth, shocks that affect the
economy first, and housing prices after some delay. If this type of shocks are dominant, then
real-estate prices regimes would tend to follow business cycles. In this case, we would expect
to estimate significant values of p21 and p34 . Finally, shocks that affect housing first, and the
general economy with some delay. If this type of shocks are dominant, then business cycles
would tend to follow real-estate price regimes and we would expect to estimate significant
probabilities p24 and p31.
Hamilton (1990) suggests that the parameters in (7) as well as the transition probabilities
in (4) can be estimated using the iterative Expectations Maximization (EM) procedure,
which may offer closed form formulas for the parameters of the model. While in this paper
we rely on numerical maximization of the likelihood function, one can gain appealing intuition
about the transition probabilities by looking at their EM formulae:
bpij =PT
t=2 P{Rt=j, Rt−1=i|=T;b
λ}
PT
t=2 P{Rt−1=i|=T;b
λ}(6)
Here, =Trepresents the entire data-set and b
λis the full vector of maximum likelihood
estimates of (7). Hence, the estimated transition probability bpij is the number of times
regime iwas followed by regime j, expressed as a percentage relative to the number of times
the process was in regime i. For example, bp24 can be interpreted as the frequency that a
8
regime with robust housing price growth and a weak economy (R= 2) was followed by a
regime with robust housing price growth and a strong economy (R= 4). If this number
is insignificant, then we are likely to conclude that real-estate regimes with robust housing
price growth rarely pre-date economic recoveries. This observation would in turn imply that
the data contains little evidence to confirm the wealth and credit effects of housing.
The above interpretations imply that if housing price regimes in a region tend to lead
business cycles then we should be able to reject hypothesis A:HA
0:p24 =p31 = 0. Rejection
of this hypothesis implies that we are unable to reject the wealth and credit effects of housing.
Similarly, the rejection of hypothesis B,HB
0:p21 =p34 = 0 implies that the economy in a
given region may lead housing prices. Although the rejection of hypothesis Bdoes not lead
to any conclusions about the wealth and credit effects, it sheds light on how consistently
house prices in a particular region lead the economy. Based on all possible outcomes of
tests Aand B, we can place each state into one of four categories. These four categories
are summarized in Table 1. If for a given region both hypotheses (Aand B) are rejected
(Category 1), then we conclude that both leading relationships exist in the data, although
not at the same time. On the other hand, if we fail to reject either hypothesis (Category
4), then neither sector leads the other. For example, this may happen when housing and
business cycles coincide. Category 2 includes the states for which we reject hypothesis A
but sustain hypothesis B. In these states, economies tend to remain somewhat immune to
housing price fluctuations. Finally, for the states in Category 3 we reject hypothesis A but
sustain hypothesis B. In these states, business cycles tend to follow housing price cycles.
Note that the number of states for which we reject (or not) any of the two hypothesis can be
obtained by combining the states that fall in the two categories along the rows or columns of
Table 1. If, for example, we are interested in obtaining the states for which only hypothesis
HA
0was rejected, we can combine states that fall in Categories 1 or 2.
Using the procedures described in Hamilton (1994), Kim and Nelson (1999), and Krolzig
9
(1997), we obtain the maximum likelihood estimates of the following seven parameters:
λ={φl, φh, δl, δh, σφ, σδ, ρ}(7)
as well as the twelve transition probabilities in (4). Thus, the unrestricted model (1) has a
total of 19 free parameters. When estimating the model, we enforce the constraints φl< φh
and δl< δh. We also obtain the numerical standard errors of all estimated parameters. We
use the likelihood ratio statistic to determine the significance of transition probabilities and
test hypotheses Aand Bfor each individual US state as well as the US as a whole. Since
each test imposes two restrictions on the transition probability matrix, the likelihood ratio
statistics has a χ2distribution with two degrees of freedom. We test these hypotheses at 5%
significance level.
3 Data
In order to estimate equation (1), we rely on two monthly indicators from January 1979 to
September 2012. First, is the monthly coincident index of economic activity that proxies for
the level of economic activity, y1, in each US state and the US as a whole. This seasonally
adjusted monthly index is compiled by the Federal Reserve Bank (FRB) of Philadelphia and
available for most US states as well as the aggregate US from January 1979. It combines four
state-level economic indicators: non-agricultural payroll employment, unemployment rate,
average hours worked in manufacturing industries, and real wage and salary disbursements.
One important feature of the FRB of Philadelphia’s coincident index is that it excludes
proprietors’ income from wage and salary disbursement. The reason for this exclusion is
that in several agricultural states, farm income in some years represented more than 50% of
proprietors’ income. Since farm income has been fairly irregular and is heavily influenced by
government price support programs, it may not accurately reflect general business conditions
in the state. This feature of the coincident index, however, does not imply that it completely
10
disregards the agricultural sector. The index includes wage and salary disbursements that, in
turn, include non-proprietary income payouts in the agricultural industry. Another variable
included in the index is the state unemployment rate. Since the unemployment rate includes
those employed and seeking work in all industries, the index is unlikely to overlook any
industry in particular.6
Our second data set is the growth rate of the Freddie Mac housing price index that
reflects the average growth of real-estate prices, y2, in each state and nationally. The Freddie
Mac index includes valuation and location data, and is based on the combined portfolio of
loans that were purchased by either Freddie Mac or Fannie Mae since January 1979. The
portfolio of loans covers every state, although it reflects Freddie Mac and Fannie Mae’s
collective market coverage and thus is not random across states. Furthermore, the loans are
limited to one-family detached and town-home properties financed by first-lien conventional
and conforming loans. We seasonally adjust the housing price index using the US Census
Bureau’s X12 seasonal adjustment program.7
Since to our best knowledge this study is the first inquiry into the nature of the rela-
tionship between real-estate prices and business cycles that uses the FRB of Philadelphia’s
coincident index, we would like to elaborate on the shortcomings of this usage and also ac-
knowledge the great benefit. The biggest shortcoming of using the FRB of Philadelphia’s
coincident indices in the context of this study is that those are state- and country-level eco-
nomic indicators. Since in any given state there are likely to be several real-estate markets,
any state-level indicator will inevitably aggregate out some important idiosyncrasies that
may exist between different housing micro-markets within the same state. From this per-
spective, using city or even MSN real-estate data may be more desirable. Because of this,
previous real-estate literature has largely relied on various city- and MSA- level measures
to proxy for economic activity. Some of the the most comprehensive measures used in the
literature are GDP, personal income, and payroll employment. Unfortunately, none is com-
pletely satisfactory for business cycle analysis. Historical data on a city- and metro-level
11
GDP and income are available only at an annual frequency. This can be fairly problematic
for business cycle analysis because business cycle phases sometimes start and finish within
the same year. Six out of twenty-two US national recessions of the 20th and 21st century
were shorter than a year. It follows that city or metro GDP or income cannot be reliably
used as business cycle indicators. City or metro employment, on the other hand, is available
at a quarterly or even monthly frequency, yet it suffers from another important shortcom-
ing. It is well known that employment is a lagging indicator of business cycles with lags
historically being fairly inconsistent across cycles and geographies. Hence, the use of em-
ployment data as a coincident business cycle indicator requires very careful and specific to
each geography lag specification testing. On the other hand, the NBER defines a recession
as “a significant decline in economic activity spread across the economy, lasting more than a
few months, normally visible in real GDP, real income, employment, industrial production,
and wholesale-retail sales.”8Therefore, an appropriate measure of business cycles must rely
on a coincident indicator or a combination of a number of coincident indicators available at
a monthly or quarterly frequency. The state coincident index of the FRB of Philadelphia
meets all of these criteria. It is appropriately adjusted for the varying lead-lag structure of
the component indicators and is available at a monthly frequency.
Another somewhat less obvious justification for our reliance on state-level data is con-
nected to work-related commuter patterns in the United States. Because people often cross
neighborhood and city borders for work and other activities, city- or even MSA-level business
indicators may not fully reflect the economic conditions of the population that resides in a
given micro neighborhood. If the wealth effect is important, then higher levels of household
spending due to appreciated real estate may occur outside of the neighborhood where the
household is located. According to the Census Bureau’s American Fact Finder9, about 19.6%
of those who in 2012 lived inside the principal city of a metro area worked outside of the
principal city and 4.2% worked outside of the metro area. About 31.7% of those who lived
outside of the principal city in a metro area worked inside of the principal city and 7.9%
12
worked outside of the metro area of residence. Thus, the spillover of the wealth and credit
effects between two cities in the same state are likely to be greater than that between states.
4 Results
For each US state as well as the aggregate US, we estimate the Markov-switching vector
autoregressive model (1), test hypotheses Aand B, and based on the outcome of the tests
place each region in one of the four categories as described in Section 2. The full-sample
model estimates of the unrestricted parameters are presented in Table 3. Here as above, φl
and φhrepresent the estimates of low and high monthly percentage growth rates of state
economies while δland δhrepresent the estimates of the low and high growth rates of
state real-estate prices. The cross-state average low and high monthly growth rates of the
coincident index are estimated to be −0.25% and 0.35% respectively. On the other hand, the
cross-state average low and high growth rate of real-estate prices are estimated at −0.44%
and 0.9% respectively. Therefore, on average, state economies fluctuate much less than
housing prices. The correlation coefficient estimates between state economies and housing
prices vary between 0 and 0.68. The outcomes of the tests that are based on the entire
sample between 1979 and 2012 are presented in the first column of Table 2. For this entire
sample, we reject both hypotheses HA
0and HB
0for 40 out of 50 states. This implies that
for 80% of all US states, there is statistical evidence that housing price cycles in the region
may both lead and lag business cycles at different times. Hence, consistent with Ghent and
Owyang (2010), Leamer (2007), and Strauss (2013), we cannot establish that house prices
are reliable leading indicators of state business cycles. On the other hand, since there are no
states for which both hypotheses are sustained, we also conclude that business and housing
price cycles also do not have a consistent tendency of evolving independently. According to
the test results, North Dakota and Hawaii are the only states where house prices tend to lead
business cycles. In both states, however, the test decision seems to be dominated by a single
13
housing appreciation in the early 80s that pre-dated an economic recovery. In eight other
largely agricultural and oil-producing states, real-estate prices follow business cycles but not
the other way around. The aggregate US falls in Category 1. Thus, national real-estate price
cycles and business cycles each have some probability of leading the other. However, for the
US, the p-value of hypothesis Bis 0.008. Therefore, at the 1% significance level we reject
hypothesis Bonly marginally. This means that the data are fairly close to placing the US as
a whole (along with Hawaii and North Dakota) in the Category 3, implying that real-estate
prices lead the economy but not the other way around.
Strauss (2013) suggests that during the US recession of 2007, the worsening economy
in most US states followed a decline in building permits. We are interested in whether the
pre-recession period was also accompanied by a structural decline in house price growth.
If house prices are downward rigid, as for example Gao et al. (2009) suggest, then the
deterioration of the housing market prior to the recession of 2007 must have impacted the
economy through channels other than the wealth and credit effects. This would obviously
go against conventional wisdom. We re-estimate the model and test hypotheses Aand Bfor
the sub-sample starting in January 2002, right after the end of the national recession in 2001,
and ending in September 2012. The results of the test for this sub-sample are presented in
the second column of Table 2. Although Category 1 remains the most populous (19 states),
the number of states in which house prices lead business cycles (Category 3) increased from
2 to 10. The US as a whole remained in Category 1, but it is again a borderline case, close
to the Category 3 region in which real-estate prices lead the economy, but not the other
way around. Category 2, in which the economy leads house prices but not vice versa, now
consists of 17 mostly agricultural and oil-producing mid-western and southern states.
Being intrigued by the small number of states in Category 3 (house prices lead economies
but not vice versa), we note that our results may be influenced by the signs of housing
recovery that started appearing in early 2012, more than two years after the national recovery.
Hence, we conjecture that some states ended up in Category 1 solely on the basis of these
14
recent data, but should be in Category 3 if we focus the analysis on years prior to and during
the recession. That is, if the housing downturn in a region started before the economic
downturn and ended after the economic recovery, we are likely to conclude that house prices
both lead and lag the economy and label this region as Category 1. However, if we want to
answer the specific question of whether house prices led the economy before the recession of
2007, we should exclude the post-recession housing recovery from our sample. The bottom
panel of Figure 1 demonstrates this point for the aggregate US. This panel exhibits the
smoothed probabilities that the US real-estate prices (solid series) and economy (dashed
series) are in the low growth regime. One complete housing price cycle started and ended
before the recession, while another housing price cycle started right after the end of the
economic recession and continued through early 2012.10 Starting from around 2007, not
only one complete housing cycle preceded a downturn and recovery of the US economy, but
also the recovery of the national economy in 2009 led the 2012 housing recovery. Therefore,
because of the housing recovery in early 2012, the US fell into Category 1 rather than
Category 3. To restrict our viewpoint to the years prior to and during the recession of
2007, we consider a second, shorter sub-sample running from January 2002 to September
2011. The test results based on this sub-sample are presented in the third column of Table 2.
According to these results, between January 2002 and September 2011, house prices led state
economies but not the other way around in 21 out of 50 US states, as well as nationally.
During this period, economies in fifteen states did not follow the housing price dynamics
but rather led house prices. These results confirm our suspicion that in many US states as
well as the aggregate US, a downshift in house price growth led the most recent economic
downturn. On the other hand, there are fifteen states in which the signs of declining housing
prices appeared only after economic deterioration. Hence, if we concentrate our attention to
the period prior to and immediately after the 2007 recession, in 29 (21 + 8 in Categories 1
and 3 respectively ) out of 50 US states as well as nationally, a decline in house price growth
regime preceded the recession.
15
One question that we are interested in is whether there are any distinguishing charac-
teristics that separate the fifteen states in Category 2 (where housing prices between 2002
and 2011 declined only after the recession) from the twenty-one states in Category 3 (where
declining housing prices between 2002 and 2011 preceded the economic decline). We start
answering this question by first inquiring whether there is any connection between the test
outcomes in column 4 of Table 2 and the estimates of the model parameters (7). The pa-
rameter estimates that are based on the sub-sample between Jan-2002 and Sep-2011 are
presented in Table 4. Figure 2 exhibits the medians of the estimated parameters grouped
by the test outcome. One pattern that immediately stands out in this chart is that in the
Category 3 states, the median estimate of δh(0.78% per month) is much larger than the
combined national median (0.53% per month). On the other hand, for the states in Category
2, the median estimate of δh(0.36% per month) is much lower than the combined national
median. Before the 2007 recession, 15 out of 21 Category 3 states (or 71.4%) experienced
faster growth of housing prices than the national median.11 This number can be compared
to the Category 2 states where only 3 out of 15 (or 20%) experienced faster than national
median growth of housing prices.12 Figure 3 demonstrates this point graphically. This im-
plies that by and large the states whose economies suffered the consequences of the housing
price collapse are also the ones that in the pre-2007 recession period experienced more rapid
growth of housing prices than the national median.
If excessive housing price growth before the 2007 recession is an important characteristic
that sets apart the states where declining housing prices preceded the recession from the
states where they did not, then it is natural to ask whether there are any socioeconomic
characteristics that help understand this pre-2007 excess growth of housing prices as well
as our test outcomes? Glaeser and Gyourko (2005), for example, suggest that population
growth can be a powerful driver of real-estate prices. They propose that the supply curve
in the housing market is kinked and is relatively elastic above and highly inelastic below
construction costs. This particular feature of the housing market implies that when housing
16
prices are already above construction costs, a change in population and therefore housing
demand will lead to a comparatively mild change in housing prices. On the other hand,
when housing prices are below construction costs, a change in housing demand will result
in a significant change in housing prices. We start exploring the effect of population growth
on housing prices and our test outcomes by first obtaining annual state population data
starting from 1980 through 2012 from the FRED database of the Federal Reserve Bank
of St. Louis.13 For every state, we calculate the decennial geometric average population
growth rates since 1980. These averages are shown in Figure 4. In the 2000s, cross-states
median population growth was 0.95% per year. Figure 5 displays the average population
growth rates in the 2000s alone with geographies now being grouped by the 2002-2011 test
outcomes (again column 4 in Table 2). This figure also exhibits the optimal boundary rate of
population growth that maximizes the predicted number of geographies in Categories 2 and
3 (0.71%). We estimate this optimal classification boundary using the recursive regression-
tree classification method.14 In 13 out of 15 (or 86.7%) Category 2 states, the average annual
population growth in the 2000s was greater than or equal to 0.71%. On the other hand, out
of 21 Category 3 states only 10 (or 48%) experienced annual population growth in excess of
0.71%. This implies that the states with weak population growth were more likely to suffer
the consequences of housing price decline in the late 2000s.
The above discussion implies that both the rates of population growth in the 2000s and
housing appreciation in the mid-2000s played an important role in driving states into different
test categories. This in turn implies that the interaction between these two variables could
be even a more powerful determinant of the test outcomes. To shed light on this suspicion,
we generate a new variable that reflects the high-regime growth rate of house prices in the
expanding housing market of the 2000s relative to annual population growth in the same
period. For each state, we generate this variable by annualizing the monthly high-regime
growth of housing prices, δh, and dividing the result by the state’s (geometric) average annual
population growth in the 2000s. The bar chart in Figure 6 is a graphical representation of
17
this variable where again states are grouped by the 2002-2011 test outcome categories. The
chart again contains the optimal regression-tree classification boundary between states in
different test categories, but this time conditional on the ratio of housing price to population
growth rates. This boundary is equal to 6.034. As one can immediately observe from the
chart, all but two Category 3 states (90.0% of 21 states) exhibited housing price growth that
in the expanding housing market of the 2000s was greater than or equal to 6.034 times the
state’s population growth. On the other hand, in all but two Category 2 states (86.7%), the
growth of housing prices relative to the growth of population between Jan-2002 and Sep-2011
was less than 6.034. This implies that the states where prior to the 2007 recession house
prices appreciation was more than 6 times the state’s population growth were significantly
more likely to suffer the consequences of the housing price decline than the states where this
did not happen. The three Category 2 states in which housing price to population growth
was near or exceeded this threshold are ND, WV, and IA. We can only speculate that in
these states, the large value of this variable could be an artifact of the rational evolution
of the housing market. First of all, as Figure 4 suggests, these are the only three states in
which the rate of population growth rapidly turned around from negative or barely positive
in the 80s and 90s to tangibly positive in the 2000. At least in ND and WV, this rapid recent
population growth was driven by the innovation in oil and gas extracting technologies that
fueled rapid economic growth and led to an influx of workers to these states. The kinked
housing supply curve of Glaeser and Gyourko (2005) implies that if housing prices in these
states were already well below construction costs, even a slight increase in housing demand
might have sparked a significant increase in housing prices. These three states have suffered
declining population for two decades. Over these two decades, housing prices in these states
declined tremendously. As one can confirm from Table 3, the full-sample estimates of low-
regime growth rates of housing prices (δl) in ND and WV were the lowest across all states.
With δl=−0.66, IA is the 11th lowest state. We suspect that at the turn of century, housing
prices in these states were already well deflated. When fueled by economic growth of the
18
2000s, population in these states rapidly turned around, so did housing prices. Thus, it
appears that in these three Category 2 states, the housing price increase was driven by the
forces of supply and demand rather than an irrational bubble. Except for ND and WV (and
AK and MT in Category 4), the states in which housing prices grew during the housing
boom of the mid-2000s at an annual rate of more than six times the state population growth
rate were almost guaranteed to suffer the consequences of the collapse of the housing bubble.
Even though the results that we highlighted in this section dominate our data, they also
leave us with two important yet unanswered questions. First of all, what explains such
robust growth of housing prices relative to population growth that occurred in certain states
in the mid-2000s and what led to the eventual reversal of this variable. As Lilienfeld-Toal
and Mookherjee (2011) suggest, it is possible that lenient bankruptcy laws prior to the 2005
Bankruptcy Reform Act (BAPCPA) and their consequent tightening might have been at the
bottom of this phenomenon. Another question that we leave out from this study is what
made the economies of states such as Nevada and Arkansas be susceptible to the housing
decline around 2007? Nevada, for example, is one of the Category 3 states that was hit hard
by the collapse of housing prices. Yet, prior to the decline, house prices in this state grew
only mildly relative to population growth. It must be that some factors other than excessive
housing appreciation have been at play. As for example Lilienfeld-Toal and Mookherjee
(2011) argue, in states with the highest homestead exemptions for Chapter 7 (which were
lost as a result of the BAPCPA in 2005), house prices were more likely to stop growing as
fast as they had been between 2000-05, eventually causing housing prices to collapse around
2007. Out of the forty-three states that prior to BAPCPA had any existing homestead
exemption limit, Nevada had one of the highest limits ($350 thousand in 2005) second only
to Massachusetts ($500 thousand in 2005). Arkansas was one of the seven states that did
not have an exemption limit whatsoever. We are convinced that more rigorous analysis of
these questions is due and we leave them for the future research.
Before concluding this section, we would like to offer a final word of caution. Although we
19
found that house prices should not be dismissed as important precursors of business cycles,
we also found that taken alone they are not reliable predictors of state and national recessions
and expansions. In line with the findings of Ghent and Owyang (2010) and Strauss (2013),
our results indicate that in the long run, house prices may lead, lag, or coincide with regional
economies. Moreover, we could not find any obvious patterns with which the industrial base
in the region impacts the relationship between housing prices and the broader economy.
Thus, the interplay between housing price and business cycles is quite idiosyncratic with
respect to place and time and requires further theoretical and empirical investigation.
5 Conclusion
We investigate whether house price cycles led or lagged business cycles in the monthly, state-
level US data between 1979 to 2012. By restricting the transition probability matrix in a
vector Markov-switching model, we test for various lead/lag scenarios in every US state as
well as the aggregate US. For forty-two US states as well as the aggregate US, we could not
reject the hypothesis that between 1979 and 2012 house prices did not lead the economy.
This implies that we are also unable to dismiss the housing wealth and credit effects as
irrelevant for the US economy. In a sub-sample between 2002 and 2011, house price cycles
led regional business cycles but not vice versa in twenty-one US states and nationally. The
states with weak population growth in the 2000s were more likely to suffer the consequences
of declined house price growth in the late 2000s. Moreover, the states where prior to the
2007 recession house prices grew faster than six times the state’s population growth rate
were almost guaranteed to suffer the economic consequences of the pre-2007 housing price
decline. With these results standing out, however, the long-run relationship between housing
prices and the broader economy is driven by factors that are specific to geography and time
and requires further investigation.
20
Endnotes
1See for example Case, Glaeser, et al. (2000), Ghent and Owyang (2010), Iacoviello (2005),
Leamer (2007), and Strauss (2013).
2Granger (1969)
3See Ghent and Owyang (2010) for example.
4Smoothed, predicted, and filtered.
5As we explained at the beginning of this section, an alternative approach would be to
model the dependency between business cycles and house prices using a single-equation
Markov-switching model of the economy with time-varying transition probabilities made
dependent on lagged house price growth. While this approach would help us to investigate
whether house price growth leads business cycles it would not allow us to explore whether
house price growth regimes lead/lag business cycles.
6For more details about the data refer to Crone and Clayton-Matthews (2005).
7We utilized the Eviews (7th version) seasonal adjustment utility that is based on the U.S.
Census Bureau’s X12 seasonal adjustment program.
8US Business Cycle Expansions and Contractions, https://www.nber.org/cycles.html.
9American Community Survey (ACS,
http://factfinder2.census.gov/faces/nav/jsf/pages/searchresults.xhtml?refresh=t), Table
ID: B08016, 2012 ACS 1-year estimates.
10While the model interprets these two dips in house prices as different cycles, the second
dip can also be interpreted as a continuation of the first, with a temporary improvement in
2009.
11Those include NM, PA, WY, MA, NH, WA, DE, VA, VT, NJ, RI, CA, MD, HI, and LA.
12Those include ID, UT, and ND.
13The original source of these data is the US Department of Commerce: Census Bureau.
14We utilize the RPART recursive partitioning and classification package in R that
implements the regression-tree partitioning methodology found in Breiman et al. (1984).
21
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Acknowledgment: We would like to thank the anonymous referee for useful comments.
23
Figure 1: The top panel displays the actual (solid series) and expected (dashed series) month-over-
month growth rates of the US coincident index (CI). The middle panel displays the actual (solid
series) and expected (dashed series) month-over-month growth rates of the US house price index
(HPI). The bottom panel displays the smoothed model probabilities that the US CI (solid series)
and HPI (dashed series) are in the low-growth regime. The shaded bands are the NBER recessions.
24
Figure 2: Cross-state medians of the estimated parameters of the model broken down by the MS-
VAR test categories. The figure is based on the sample between Jan-2002 and Sep-2011.
25
Figure 3: The estimates of monthly high-regime growth of housing prices (δh) between Jan-2002
and Sep-2011 grouped by the MS-VAR test categories. The horizontal line is the cross-state median
δh= 0.53.
26
Figure 4: State average annual population growth (decennial geometric averages). The horizontal
line is the cross-state median of these statistics for the 2000s and it is equal to 0.95%.
27
Figure 5: State annual population growth in the 2000s grouped by the MS-VAR test categories
between Jan-2002 and Sep-2012.
28
Figure 6: State high-regime growth of house prices (δh) between Jan-2002 and Sep-2011 relative to
the average population growth in the 2000s. The data is grouped by the MS-VAR test categories.
29
Test A:
HA
0:p24 = 0 & p31 = 0
HA
1:p24 6= 0 & p31 6= 0
Reject Do not reject
Test B:
HB
0:p21 = 0
&p34 = 0
Reject
Category 1
Business cycles follow
housing price cycles
&
Housing price cycles
follow business cycles
Category 3
Business cycles follow
housing price cycles
&
Housing price cycles do not
follow business cycles
HB
1:p21 6= 0
&p34 6= 0
Do not
reject
Category 2
Business cycles do not
follow housing price cycles
&
Housing price cycles follow
business cycles
Category 4
Business cycles do not
follow housing price cycles
&
Housing price cycles do not
follow business cycles
Table 1: Possible test decisions based on the outcomes of hypotheses A and B.
30
Jan.1979-
Sep.2012
Jan.2002-
Sep.2012
Jan.2002-
Sep.2011
Category 1
Business cycles follow
housing price cycles
&
Housing price cycles
follow business cycles
(A:Reject, B:Reject)
AK,AL,AR,
AZ,CA,CO,
CT,DE,FL,
GA,IA,ID,
IL,IN,KY,
LA,MA,MD,
ME,MI,MN,
MO,MS,NC,
NE,NH,NJ,
NM,NV,NY,
OH,OK,
OR,PA,RI,
SD,US,VT,
WA,WI,WV
(41)
CA,CO,CT,
IL,IN,MD,
ME,MN,NH,
NY,OH,OR,
RI,US,VA,
WA,WI,WV,
WY
(19)
CO,CT,IN,
KS,ME,NY,
OH,OR
(8)
Category 2
Business cycles do not
follow housing price cycles
&
Housing price cycles
follow business cycles
(A:Do not Reject;
B:Reject)
KS,MT,SC,
TN,TX,UT,
VA,WY
(8)
AL,AR,AZ,
GA,IA,KS,
KY,MO,MT,
ND,NE,OK,
SC,SD,TN,
TX,UT
(17)
AL,AZ,GA,
IA,ID,KY,
MN,MO,ND,
NE,OK,SD,
TN,UT,WV
(15)
Category 3
Business cycles follow
housing price cycles
&
Housing price cycles
do not follow business cycles
(A:Reject;
B:Do not Reject)
HI, ND (2)
AK,DE,HI,
LA,MA,MS,
NC,NJ,NV,
PA
(10)
AR,CA,DE,
HI,IL,LA,
MA,MD,MI,
MS,NH,NJ,
NM,NV,PA,
RI,US,VA,
VT,WA,WI,
WY(22)
Category 4
Business cycles do not
follow housing price cycles
&
Housing price cycles do not
follow business cycles
(A:Do not Reject;
B:Do not Reject)
(0)
FL,ID,MI,
NM,VT
(5)
AK,FL,MT,
NC,SC,TX
(6)
Table 2: Actual test decisions based on the outcomes of hypotheses A and B.
31
φlφhδlδhσφσδρ φlφhδlδhσφσδρ
AK
AL
AR
AZ
CA
CO
CT
DE
FL
GA
HI
IA
ID
IL
IN
KS
KY
LA
MA
MD
ME
MI
MN
MO
MS
MT
−0.01
−0.24
−0.17
−0.01
−0.04
−0.18
−0.13
−0.10
−0.08
−0.03
−0.11
−0.2
−0.45
−0.26
−0.61
−0.34
−0.32
−0.56
−0.17
−0.22
−0.11
−0.82
−0.21
−0.14
−0.12
−0.31
0.96
0.29
0.3
0.51
0.33
0.38
0.32
0.41
0.38
0.44
0.32
0.25
0.47
0.31
0.33
0.27
0.30
0.18
0.36
0.33
0.53
0.40
0.28
0.30
0.31
0.27
0.06
−0.68
−0.54
−1.14
−0.25
−0.13
−0.01
−0.11
−1.30
−0.83
0.26
−0.66
−0.52
−0.72
−0.39
−0.20
−0.29
−0.27
−0.04
−0.18
−0.40
−1.68
−0.52
−0.57
0.12
−0.37
2.89
0.32
0.36
0.49
0.96
0.55
1.06
0.78
0.47
0.41
9.41
0.31
0.47
0.45
0.36
0.39
0.36
0.48
1.04
0.82
0.66
0.38
0.51
0.36
2.09
0.53
0.32
0.21
0.17
0.30
0.16
0.21
0.16
0.22
0.19
0.20
0.19
0.17
0.27
0.19
0.28
0.22
0.20
0.30
0.20
0.20
0.35
0.46
0.21
0.17
0.20
0.19
0.93
0.41
0.44
0.75
0.67
0.38
0.57
0.43
0.68
0.44
1.81
0.35
0.53
0.49
0.40
0.34
0.31
0.41
0.47
0.45
0.55
0.70
0.48
0.43
0.66
0.40
0.25
0.25
0.4
0.68
0.58
0.34
0.63
0.14
0.45
0.29
0.21
0.13
0.53
0.07
0.60
0.03
0
0.05
0.42
0
0.66
0.30
0.08
0.02
0.09
0.06
NC
ND
NE
NH
NJ
NM
NV
NY
OH
OK
OR
PA
RI
SC
SD
TN
TX
UT
VA
VT
WA
WI
WV
WY
US
−0.20
−0.18
−0.16
0.013
−0.11
−0.11
−0.27
−0.18
−0.79
−0.43
−0.51
−0.34
−0.30
−0.27
−0.16
−0.26
−0.20
−0.07
0.01
−0.09
−0.23
−0.19
−1.03
−0.91
−0.06
0.39
0.29
0.30
0.51
0.26
0.32
0.53
0.23
0.27
0.30
0.44
0.25
0.32
0.4
0.29
0.3
0.35
0.38
0.41
0.39
0.35
0.27
0.34
0.25
0.27
−0.23
−2.74
−0.06
−0.12
0.031
−0.03
−1.76
−0.01
−0.54
−0.41
−0.62
0.09
−0.10
−0.22
0.19
−0.05
−0.55
−0.11
−0.52
−0.03
−0.82
0.19
−1.78
−0.33
−0.60
0.41
0.32
0.51
0.97
1.15
0.80
0.39
1.03
0.32
0.40
0.67
0.85
1.32
0.46
1.48
0.47
0.34
0.69
0.53
0.81
0.55
3.18
0.34
0.61
0.42
0.20
0.21
0.21
0.24
0.18
0.17
0.29
0.13
0.31
0.24
0.26
0.23
0.24
0.25
0.18
0.17
0.16
0.16
0.18
0.22
0.19
0.18
0.46
0.26
0.11
0.36
0.53
0.33
0.49
0.48
0.38
0.71
0.55
0.39
0.35
0.52
0.40
0.54
0.42
0.42
0.43
0.45
0.47
0.47
0.37
0.59
0.62
0.63
0.50
0.31
0.21
0.13
0.02
0.42
0.65
0.08
0.44
0.35
0.08
0.03
0.14
0.26
0.43
0.52
0.15
0.16
0.49
0.64
0.54
0.33
0.05
0.33
0.19
0.08
0.20
Table 3: Full sample (January 1979-September 2012) estimates of the parameters in (7) for each US state and the aggregate US. Boldfaced
intercept and correlation coefficients are significant at 1 percent significance level.
32
φlφhδlδhσφσδρ φlφhδlδhσφσδρ
AK
AL
AR
AZ
CA
CO
CT
DE
FL
GA
HI
IA
ID
IL
IN
KS
KY
LA
MA
MD
ME
MI
MN
MO
MS
MT
−0.12
−0.67
−0.33
−0.42
−0.41
−0.30
−0.40
−0.60
−0.44
−0.48
−0.43
−0.28
−0.68
−0.56
−1.03
−0.66
−0.60
−2.80
−0.20
−0.47
−0.84
−1.10
−0.46
−0.63
−0.40
−0.23
0.14
0.15
0.12
0.19
0.16
0.22
0.19
0.11
0.16
0.14
0.18
0.15
0.31
0.12
0.12
0.07
0.13
0.08
0.25
0.14
0.06
0.03
0.14
0.10
0.15
0.33
−0.05
−0.52
−0.30
−1.28
−1.33
−0.98
−0.39
−0.44
−1.96
−0.98
−0.24
−0.26
−0.87
−0.60
−0.72
−0.72
−0.29
0.16
−0.32
−0.46
−0.26
−1.22
−0.74
−0.48
−0.26
−0.34
0.68
0.33
0.38
0.36
1.19
0.20
0.77
0.80
0.53
0.16
1.31
0.26
0.56
0.48
0.10
0.18
0.29
1.82
0.76
1.22
0.81
0.09
0.44
0.35
0.42
0.68
0.10
0.21
0.11
0.26
0.14
0.22
0.16
0.17
0.19
0.16
0.18
0.12
0.28
0.19
0.21
0.24
0.12
0.34
0.14
0.11
0.22
0.36
0.20
0.23
0.21
0.18
0.34
0.32
0.32
1.39
0.72
0.27
0.31
0.38
1.05
0.46
0.58
0.27
0.53
0.37
0.21
0.26
0.21
0.37
0.33
0.44
0.29
0.55
0.40
0.34
0.38
0.38
0.22
0.50
0.13
0.92
0.45
0.00
0.00
0.06
0.74
0.43
0.51
0.07
0.73
0.00
0.23
0.12
0.09
0.15
0.20
0.34
0.18
0.43
0.00
0.00
0.01
0.12
NC
ND
NE
NH
NJ
NM
NV
NY
OH
OK
OR
PA
RI
SC
SD
TN
TX
UT
VA
VT
WA
WI
WV
WY
US
−0.53
0.15
−0.38
−0.40
−0.38
−0.29
−0.25
−0.27
−0.78
−0.39
−0.94
−0.50
−0.45
−0.75
−0.28
−0.54
−0.18
−0.25
−0.19
−0.64
−0.42
−0.7
−1.05
−0.56
−0.43
0.18
0.72
0.14
0.19
0.13
0.26
0.20
0.17
0.13
0.27
0.27
0.15
0.19
0.21
0.21
0.16
0.30
0.35
0.12
0.08
0.22
0.12
0.18
0.32
0.17
−0.37
0.15
−0.37
−0.38
−0.29
−0.39
−1.70
−0.26
−0.55
−0.40
−0.86
−0.15
−0.46
−0.45
−0.28
−0.28
−0.09
−0.43
−0.43
−0.07
−0.57
−0.33
−0.38
−0.17
−0.41
0.36
0.71
0.26
0.77
1.05
0.70
0.50
0.79
0.19
0.39
0.76
0.72
1.15
0.33
0.33
0.39
0.34
0.60
0.84
0.84
0.78
0.45
0.44
0.72
0.78
0.22
0.30
0.20
0.13
0.11
0.17
0.60
0.10
0.21
0.23
0.28
0.18
0.16
0.21
0.16
0.12
0.14
0.23
0.14
0.16
0.18
0.14
0.32
0.24
0.18
0.34
0.17
0.24
0.37
0.34
0.31
1.62
0.37
0.28
0.27
0.53
0.35
0.47
0.35
0.27
0.27
0.23
0.52
0.53
0.39
0.43
0.31
0.37
0.31
0.38
0.11
0.21
0.20
0.00
0.30
0.23
0.97
0.09
0.02
0.00
0.28
0.00
0.31
0.35
0.00
0.28
0.32
0.81
0.70
0.13
0.55
0.00
0.17
0.27
0.48
Table 4: Truncated sample (January 2002-September 2011) estimates of the parameters in (7) for each US state and the aggregate US.
Boldfaced intercept and correlation coefficients are significant at 1 percent significance level.
33
