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Endogenous Price Volume Correlation in the Housing Market♦
Jim Clayton University of Cincinnati
Norman Miller
University of Cincinnati
Liang Peng∗ University of Cincinnati
P.O. Box 210195 Cincinnati, OH 45221-0195 Email: [email protected]
Phone: (513)5566829 Fax: (513)5560979
Current Draft: March, 2005
Abstract
Housing market cycles are featured by correlation of prices and trading volume, which is conventionally attributed to a causal relation between prices and volume. This paper relies on a large panel dataset of housing markets in 127 metropolitan statistic areas from 1990:1 to 2002:2, treats both the price and volume as endogenous variables in housing markets, and studies how exogenous shocks cause co-movement of the price and volume, which we call the endogenous price-volume correlation. We find that both home prices and trading volume are affected by conditions in labor markets, the mortgage market, and the stock market, and trading volume is Granger-caused by home prices. We find a statistically significant positive price-volume correlation; which, however, is mainly explained by the endogenous correlation. Surprisingly, the Granger-causality of home prices on trading volume seems to lead to a negative price-volume relation, and thus does not contribute to the positive price-volume correlation in the quarterly frequency. JEL classification: E32, G14 Key words: housing market, price volume correlation, trading volume © 2005 by Jim Clayton, Norman Miller and Liang Peng. All rights reserved. Preliminary draft, do not quote without permission.
♦ We thank seminar participants at Colorado University at Boulder for helpful comments. ∗ Contact author.
1
Endogenous Price Volume Correlation in the Housing Market
Abstract
Housing market cycles are featured by correlation of prices and trading volume, which is conventionally attributed to a causal relation between prices and volume. This paper relies on a large panel dataset of housing markets in 127 metropolitan statistic areas from 1990:1 to 2002:2, treats both the price and volume as endogenous variables in housing markets, and studies how exogenous shocks cause co-movement of the price and volume, which we call the endogenous price-volume correlation. We find that both home prices and trading volume are affected by conditions in labor markets, the mortgage market, and the stock market, and trading volume is Granger-caused by home prices. We find a statistically significant positive price-volume correlation; which, however, is mainly explained by the endogenous correlation. Surprisingly, the Granger-causality of home prices on trading volume seems to lead to a negative price-volume relation, and thus does not contribute to the positive price-volume correlation in the quarterly frequency. JEL classification: E32, G14 Key words: housing market, price volume correlation, trading volume
2
Endogenous Price Volume Correlation in the Housing Market
I. Introduction A rapid surge in home prices after 2000 has been seen across many areas in the
United States, which generates a lot of speculation that the US is in a “housing bubble”
(see, e.g., Case and Shiller (2003)). This concern is warranted by the importance of the
housing market - for example, Bertaut and Starr-McCluer (2002) show that residential
property accounted for about one quarter of aggregate household wealth in the US in the
late 1990’s, and Tracy and Schneider (2001) show that housing wealth accounts for about
two thirds of the wealth of the median US household. Despite the importance of the
housing markets and the economic and policy implications of home price changes, some
important aspects of housing markets are not well understood.
A well known puzzle in the housing market is that prices and trading volume
seem to correlate with each other - trading activity tends to be more intense (i.e., more
transactions and shorter time on the market before sale) in rising markets than in falling
markets. The positive correlation between prices and trading volume appears to be
inconsistent with standard rational expectation asset market models, in which housing
prices are present discounted value of future service stream (see e.g. Poterba (1984)). A
conventional interpretation of the correlation is that price changes cause changes in
trading volume. The causal relation is built on either equity constraints (homeowners’
equity constraints due to falling prices prevent people from moving, see e.g., Stein (1995),
Genesove and Mayer (1997), Lamont and Stein (1999), and Chan (2001)), nominal loss
aversion (homeowners are less willing to sell their homes in a falling market, see
3
Genesove and Mayer (2001), Cauley and Pavlov (2002), and Engelhardt (2003)), or
option value of homeowners (see Cauley and Pavlov (2002)).
Although the research regarding the causal relation between prices and trading
volume greatly improve our understanding of the dynamics of housing market, a few
important questions do not seem to be satisfactorily answered. First, is a positive price-
volume correlation a universal phenomenon? It is striking that there is only mixed
evidence regarding the relation between prices and trading volume, and the evidence is
from either aggregate national level data, or from small panel data (up to 22 metropolitan
areas). While a positive price-volume correlation is found by Stein (1995), Berkovec and
Goodman (1996), Andrew and Meen (2003), and Ortalo-Magné and Rady (2004b), a
negative relation is found by Follain and Velz (1995) and Hort (2000), and no significant
relation is found in commercial real estate by Leung and Feng (2005).
Second, does the causal relation between prices and trading volume necessarily
explain the contemporaneous price-volume correlation? The causal relation, though
strongly supported by empirical evidence, more naturally implies a lead-lag relation
instead of a positive correlation. While it is possible that a lead-lag relation in a high
frequency helps generate a contemporaneous correlation in a low frequency, or a
correlation in the same frequency due to possible positive autocorrelations of prices, to
date, no empirical study is conducted to assess the extent to which the causal relation
helps explain the price-volume correlation.
Third, is the price-volume correlation necessarily, or solely, due to the causal
relation between prices and trading volume? Houses are not only assets but also
consumption goods. As a result, the demand curve for housing may not be completely
4
flat, and the supply curve for housing may not be completely vertical even in the short
run (In fact, Smith (1976), Hanushek and Quigley (1980), DiPasquale and Wheaton
(1994), and Malpezzi and Maclennan (2001) among others, provide evidence of negative
price elasticity of housing demand and positive price elasticity of housing supply).
Therefore, shocks to the housing market may affect both home prices and trading volume,
and thus cause co-movement of them, which may lead to a price-volume correlation. In
fact, there is a solid theoretic foundation for the co-movement of prices and trading
volume in the housing market. For instance, Wheaton (1990) indicates that vacancy,
sales time – which usually negatively relates to turnover, and prices are jointly
determined. More theories in this line are proposed by Krainer (2001), Ortalo-Magné
and Rady (2004a), and Novy-Marx (2004). While the theories suggest that the price-
volume correlation could be a symptom of endogenous changes of prices and volume,
which we call endogenous price-volume correlation, there is no empirical study on the
endogenous price-volume correlation and the extent to which it helps explain the price-
volume correlation.1
This paper aims to shed light on these three questions. We empirically analyze
determinants of prices and trading volume in housing markets, and investigate the
existence and magnitude of the endogenous price-volume correlation, as well as to what
extent it helps explain the price-volume correlation. We build a panel VAR model from a
simple partial equilibrium of housing markets, and estimate how exogenous variables,
such as conditions in the labor market, the mortgage market, and the financial market,
and lagged endogenous variables affect both prices and volume in housing markets.
1 While there is a large literature in finance about the determinants of trading volume as well as return-volume relations in the stock market, this paper focuses on the theories that are specifically developed for housing markets and motivated by the fact that houses are both consumption goods and investments.
5
Heterogeneity of the MSA markets is controlled with fixed effects. We decompose the
changes of prices and volume respectively into three components: the causal component
(explained by lagged prices), the co-movement component (explained by exogenous
changes in the economy), and the residual (not explained by our model), and study how
each component helps explain the price volume correlation. We also use impulse
response functions to describe the dynamics of the price and trading volume after shocks.
An important merit of this paper is an unusually large panel dataset, which
comprises 127 metropolitan statistic areas (MSAs). The frequency of our data is
quarterly, and the sample period spans from 1990:1 to 2002:2. The cross-MSA variation
and the temporal variation of housing markets in our sample greatly help improve the
efficiency of estimation. The large number of MSAs covered by our data makes our
results more informative and more likely to reveal true economic relations.
This paper provides original insights into the determinants of prices and trading
volume in the housing market. We find that changes in both prices and trading volume
are significantly affected by changes in the labor market, which include changes in total
non-agricultural employment, average household income, and unemployment rate. The
housing market is also significantly affected by the level and the trend of mortgage rates.
When the mortgage rate is high and when the mortgage rate is falling, both home prices
and trading volume are low. In addition, interestingly, the stock market performance
statistically significantly affects housing prices. When the S&P500 index is high (level)
or when the stock market shows a down turn (trend), home prices tend to be low and
trading volume tend to be high. We also find strong evidence that home prices Granger-
6
cause trading volume, which corroborates the literature of the causal relation between
prices and trading volume.
We also provide novel evidence regarding the price volume correlation in the
housing market in the quarterly frequency. First, our results confirm the universal
existence of positive price-volume correlation – we find strong evidence of statistically
significant positive correlation. Furthermore, we find the positive correlation is almost
fully explained by the home prices and trading volume fitted by our panel VAR model.
In addition, we find that the causal components of the price and volume are negatively
correlated, which indicates that the Granger causality of prices on trading volume does
not appear to help explain the positive price-volume correlation. On the other hand, the
co-movement components of the price and volume are significantly positively correlated,
so exogenous economic shocks seem to explain the positive price-volume correlation
well. Overall, our empirical evidence suggests that home prices do affect (or lead)
trading volume, but the causal relation does not appear to be driving the positive price-
volume correlation, at least not in the quarterly frequency.
This paper is original in three aspects. First, it is the first study that investigates
the contemporaneous price volume correlation in the housing market using a large cross-
section time series data that comprise a large number of markets, 127 MSAs specifically,
that are arguably distinct from each other. Second, this paper is the first to empirically
study the possible endogenous price volume correlation – the co-movement of prices and
trading volume caused by exogenous economic/demographic shocks. Third, this paper is
the first to assess the extent to which the co-movement of price and volume and the price
volume causality, respectively, helps explain the price volume correlation.
7
The paper proceeds as follows. Next section presents the econometric model.
Section 3 discusses the specification of our model and the data. Empirical evidence is
presented in section 4. Section 5 concludes.
II. Econometric Model
II.1. A Housing Market with Heterogeneous Private Valuations
This section builds an econometric model from a simple partial equilibrium in the
single family home market. To simplify our analysis, we assume away heterogeneity of
houses, as well as interactions between the single family home market and markets of
other types of dwellings. To conceptualize the demand and supply in the market in time
period t , without loss of generality, we assume that at time t , every homeowner has a
private valuation for her home. When the market price is above her personal valuation,
she is better off selling her house now and joining the pool of potential buyers in next
time period. Assuming the private valuation follows a distribution with a probability
density function ( )f x , the supply given a market price p is ( )p
f x dx−∞∫ , which is
between 0 and 100%, and monotonically increases with p . On the other hand, assume
every potential buyer has a private valuation as well, and she would make a purchase if
the market price is lower than her private valuation. If buyers’ private valuations follow
a distribution with a density function ( )g x , the demand equals ( )p
g x dx+∞
∫ , which is
also between 0 and 100%, and decreases with p . We further assume that buyers and
sellers determine their private valuations at the beginning of each period; each period is
long enough for buyers and sellers to successfully find their counterparties; and the
equilibrium price is revealed at the end of each period. Note that our definitions of
8
market demand and supply are similar to those in Fisher et al. (2003) and Goetzmann and
Peng (2004).
The market clears when the demand equals the supply. The equilibrium market
price *tp is determined by ( ) ( )
*
*
p
pf x dx g x dx
+∞
−∞=∫ ∫ , and the equilibrium quantity is
naturally measured by turnover – the ratio of sold units to all units. Note that the
equilibrium market price in time period t can not shift the demand and supply at time t ,
for the equilibrium market price is realized after potential buyers and sellers determine
their private valuations, i.e. after the demand and supply curves are determined.
Nonetheless, market participants can update their private valuations at time 1t + , and
thus are free to base their updated private valuations on lagged equilibrium prices such as
*tp . Consequently, *
tp may affect future demand and supply.
We build a discrete time econometric model as follows. Let ,Di tq denote the log of
the quantity that potential buyers are willing to purchase in the market i in time period t
(measured with the turnover of housing units in the market). We assume that ,Di tq is a
function of time t , ,i tp the log of the market price, ,i tq the log of the realized quantity,
sd the dummy variable for the s th quarter ( 1,2,3,4s = ), ,Di tX a vector of exogenous
variables that affect the demand in the market, as well as lagged market prices and
turnover, which essentially characterizes the demand curve.
, 1 , , , 2 , ,1,2,3,4 1 1
k kD d p q Di t i i t s s s i t s s i t s i t i t
s s sq t p d p q Xα β β β β β ε− −
= = =
= + + + + + +∑ ∑ ∑ (1)
9
Let ,Si tq denote the log of the quantity that potential sellers are willing to sell in the market
i in time period t given the market price ,i tp . We assume that ,Si tq is determined by the
following equation, which describes the supply curve.
, 1 , , , 2 , ,1,2,3,4 1 1
k kS d p q Si t i i t s s s i t s s i t s i t i t
s s sq t p d p q X uλ γ γ γ γ γ− −
= = =
= + + + + + +∑ ∑ ∑ . (2)
Five points are worth noting in equations (1) and (2). First, we include lagged
market prices as explanatory variables, thus allow them to shift both the demand and the
supply curves, and affect the equilibrium price and trading volume. This essentially
accommodates possible causal relations between market prices and equilibrium trading
volume. Note that the causal relations can not be contemporaneous since the
contemporaneous relation between ,Di tq and ,i tp or ,
Si tq and ,i tp represents the slope of the
demand or the supply curve.
Second, we allow lagged trading volume to affect ,Di tq and ,
Si tq , which essentially
allows market participants to update their private valuations based on historical trading
volume. Including lagged trading volume also potentially accommodate the feed back
effects proposed by Novy-Marx (2004), according to whom, a demand shock may
increase the buyer to seller ratio in the market, and thus reduce the time on the market
and increase the turnover of housing units. Changes in trading volume, consequently, can
help sellers update their information set and thus change their ask prices, which shifts the
supply curve.
Third, though the model includes only contemporaneous exogenous variables,
lagged exogenous variables also affect the demand and supply through their impact on
lagged prices and turnover. The mechanism is simple. An exogenous shock first affects
10
the present demand and/or supply, and results in changes in the market price and turnover,
which help market participants update their information set and thus further affects future
demand and supply, as well as future market price and turnover. In fact, it is trivial to
change both equations (1) and (2) to such a form that the demand and supply are
functions of all historical exogenous variables. Nonetheless, lagged exogenous variables
may directly affect the demand and supply beyond through their effects on lagged prices
and volume. In our empirical analysis, we use a specification that allows for lagged
exogenous variables as a robustness check.
Fourthly, the prices in our model are nominal prices. We chose nominal prices
instead of real prices for an important theory that aims to explain the price-volume
correlation relies on nominal loss aversion of homeowners (see, e.g. Genesove and Mayer
(2001) and Engelhardt (2003)). Moreover, existing research suggests that people often
make financial decisions in nominal terms. For example, Shafir et al. (1997) argue that
money illusion is common in a wide variety of contexts. They find that a majority of
survey respondents focus on nominal instead of real gains in assessing hypothetical
gains/losses in selling a house.
Finally, our model accommodates the well known housing market heterogeneity
in two ways. First, our model uses MSA specific dummies to capture unobserved time-
invariant MSA characteristics, such as geographic attributes. Secondly, our model
includes economic variables at the MSA level, which help capture local economic
conditions. Nonetheless, our results should be interpreted with caution: the estimated
parameter may be treated as averages across the MSAs in our sample, and our analysis
can be interpreted as analysis on an average MSA. However, note that this is not
11
necessarily a problem - while possible variations across MSAs are interesting, the
theories we try to test are general and should apply to all MSAs, and thus results of an
average MSA serve our research purposes.
II.2. Econometric Setting and Research Design
It is clear that equation (1) describes the behavior of buyers and equation (2)
describes the behavior of sellers. Market equilibrium requires
, ,D Si t i tq q= , (3)
from which equilibrium prices and turnover can be solved out. Since our research goal is
to understand variations of the equilibrium market prices and trading volume instead of
how exogenous variables affect the demand and supply curves respectively, we conduct
our research using a reduced form model, which is much easier to estimate than structural
models. In the reduced form model, both the price and turnover are functions of
quarterly dummy variables, exogenous variables and lagged endogenous variables.
, , ,,
1,2,3,4 1, , ,
pki t i t si i t
s s s i t qs si t i t si i t
p pat A d B CX
q qbεε
−
= = −
= + + + +
∑ ∑ (4)
In equation (4), ,i tX is a vector of exogenous variables that affect either the demand or
the supply in the market.
Since our data include price indices (with index level normalized to be 100 in
1995:1) instead of the actual prices, we can not estimate (4) directly. Instead, we
estimate the first order difference of (4)
, , ,,
1,2,3,4 1, , ,
pki t i t si i t
s s s i t qs si t i t si i t
p paA d B C X
q qbνν
−
= = −
∆ ∆ = + + + ∆ + ∆ ∆
∑ ∑ . (5)
12
We assume the error terms have zero mean and are orthogonal to all explanatory
variables. The quarterly dummies in (5) are first order differences of the dummies in (4),
but we use the same notations to simplify the illustrations. The system in (5) is
essentially a fixed effect panel VAR model.
Based on the results of estimating the model in (5), we conduct the following
research. First, we test the null hypothesis that market prices do not Granger-cause the
equilibrium trading volume. This hypothesis essentially imposes the constraint that the
coefficients of all lagged prices are 0 in the second equation of (5), which can be easily
tested with F tests. The hypothesis is expected to be rejected should the theory by Stein
(1995) be valid.
Second, we investigate the existence and magnitude of the price-volume
correlation (or raw price-volume correlation in contrast to the endogenous price-volume
correlation). The price-volume correlation is defined as the correlation between changes
in home prices, i.e. ,i tp∆ , and changes in trading volume, i.e. ,i tq∆ . We do not use the
correlation between ,i tp and ,i tq because the prices per se have an uptrend and are not
stationary while the trading volume is bounded between 0 and 1, thus the correlation
between them in a long sample period does not seem to make much economic sense.
Third, we assess how well the fitted prices and volume in our model (explained
by both exogenous economic changes and lagged prices and volume) help explain the
price-volume correlation. We decompose ,i tp∆ and ,i tq∆ respectively into the fitted
values and residuals (unexplained by our model), and then calculate the correlation
between the fitted price and volume and the correlation between the residuals,
respectively. We compare the “fitted” correlation and the “unexplained” correlation with
13
the raw price-volume correlation. Though the comparison, it is easy to assess how well
our model captures the price-volume correlation overall.
Fourth, we analyze the degree to which the possible Granger-causality of the price
on trading volume and the co-movement of the price and volume helps explain the price-
volume correlation respectively. This time, we decompose ,i tp∆ and ,i tq∆ respectively
into three parts: the causal component (explained by lagged prices), the co-movement
component (explained by variables other than lagged prices), and the residual. The first
two components are respectively calculated using corresponding explanatory variables
and estimated coefficients, and the third part can be captured with regression residuals.
We then assess the significance and magnitude of the correlations for different
components, and investigate how well each component helps explain the raw price-
volume correlation.
Finally, we study how shocks in exogenous variables affect the dynamics of the
price and trading volume in the housing market. We construct and plot impulse response
functions to describe how the price and trading volume reacts to exogenous shocks
respectively. The impulse response functions certainly further help shed light on the
economic sources of the price-volume correlation.
III. Model Specifications and Data
III.1. Model Specifications
This section discusses our choice of exogenous variables ,i tX in the panel VAR
model. We categorize variables that may affect the demand and/or supply in the housing
market as labor market related, mortgage market related, and financial market related
14
variables. Note that in our estimation, it is the first order differences of the log values of
the variables that are used.
Changes in the labor market and local demographic conditions certainly affect
housing demand and/or supply. First, an increasing number of immigrants and the
growth of local economy and/or population may result in a growing labor market and
may increase demand for dwellings such as single family homes. Therefore, we include
the total non-agricultural employment as an exogenous variable. Second, changes in
income may increase housing demand. Consequently, we include the average household
income as another exogenous variable. Thirdly, changes in the unemployment rate imply
that the number of people who need to search for jobs in and out of a specific area is
changing, which likely affects the housing demand and supply in the area. As a result,
we include the unemployment rate as the third labor market related variable.
Mortgage markets certainly relate to the housing market and borrowing cost is
another ostensible exogenous variable that affects housing demand and supply. We
consider two variables that may be relevant. The first one is simply the mortgage rate per
se. It would be natural to conjecture that people’s home-purchase decisions are less
financially constrained if mortgage rates are low. The second one is the trend of
mortgage rates. Potential buyers have the real option to delay their home purchases until
the mortgage rate is more favorable. Consequently, when mortgage rates seem to be
falling (rising), potential buyers may choose to postpone their home purchases, and the
current housing demand may actually fall. A natural measure of the trend in quarter t is
the change of mortgage rates from quarter 1t − to quarter t . Since the autocorrelation of
the change in mortgage rate is indeed positive and fairly large (0.13), the change from
15
quarter 1t − to quarter t does help capture the trend. Note that, in our estimation, we
essentially use the first order and the second order differences of the mortgage rate,
which have different implications.
The stock market may also affect the housing market, while the effects might be
complicated and ambiguous. First, the well known wealth effect suggests that an
increase in the wealth may increase consumption, including consumption of housing.
Therefore, a booming stock market may generate a positive demand shock. Second, a
booming stock market may help mitigate the liquidity constraints of moving families, for
they have the option to use proceeds from selling stocks to help defray the down-payment.
As a result, the supply in the housing market may increase. Finally, houses may appear
to be less attractive assets when investors believe that stocks are better investments. The
competing effect may reduce housing demand. While we lack rigorous theory with
unambiguous predictions regarding the effects of the stock market, we try to use two
variables to capture the effects: the S&P 500 index level, which may proxy for the
financial wealth and/or constraints of households, and the gross return of the S&P500
index, which may proxy for the trend of the stock market. In our estimation, we
essentially use the first order and the second order differences of the S&P500 index.
III.2. Data
We hope to fit our model to high frequency data, for the causal relation between
prices and trading volume is more likely to be identified in high frequency data. The
highest frequency we are able to obtain is the quarterly frequency. Our data comprise the
following five MSA-level quarterly time series for 127 MSAs from 1990:1 to 2002:2 -
the home price index (obtained from the Office of Federal Housing Enterprise Oversight
16
(OFEHO)), turnover in the housing market, total non-agricultural employment, average
household income, and the unemployment rate (obtained from Bureau of Labor Statistics
(BLS) and/or Bureau of Census (BOC)).2 Our data also include two national level time
series in the same period: 30-year fixed rate mortgage rate (obtained from National
Association of Realtors), which is plotted in figure 3, and the S&P500 index (obtained
from CRSP). Figure 1 plots the home price indices for all 127 MSAs. It is easy to see
that the index level is normalized to 1 in 1995. Figure 2 plots the across-MSA 25%
percentile, median, and 75% of the estimated market turnover, total non-agriculture
employment, average household income, and unemployment rate, as well as the time
series of the mortgage rate and the S&P500 index (normalized to 1 at the beginning of the
sample period). Since the estimation of our model is based on the first order difference
of log values of these variables, we provide some statistics for the first order differences
in table 1, including across-MSA average of means, medians, variances if applicable,
autocorrelations, and correlations, as well as t-statistics if applicable.
We construct series of turnover in the single family housing market using data
from Bureau of Census (BOC). Two pieces of information are needed to calculate the
turnover in a given period – the number of home sales and the units of homes. Though
existing single family home sales are available in quarterly frequency, units of single
family homes are available once every ten years. Fortunately, single family housing units
are almost perfectly correlated with population across MSAs and across time. In fact,
two cross-sectional regressions of single family units on population in 1990:2 and 2000:2
respectively - when accurate housing units and population data are available from BOC -
2 We start with 315 MSAs, and then exclude MSAs with missing variables or changing definitions in the sample period, and end with 127 MSAs. The names of the 127 MSAs are in the appendix.
17
both generate R-squares around 0.99. Furthermore, a regression of the ratio of housing
units to population in 2000:2 against the same ratio in 1990:2 generates R-square of 0.98,
which seems to indicate that the housing unit-population ratio is highly stable across time.
The stable relation between the units of homes and population allows us to infer the units
of homes from population.
Specifically, for each MSA, we estimate the ratio of single family housing units to
population in a give period with a time-distance weighted average of the ratios in 1990:2
and 2000:2. For example, if the ratios are 0.2 and 0.3 in 1990:2 and 2000:2 respectively,
and the period is in the middle between 1990:2 and 2000:2, the estimated ratio is 0.25.
We then estimate the existing housing units in that period with the product of population,
which is provided (estimated) by BOC, and the estimated ratio. For instance, if the
population is 1 million and the estimated ratio is 0.25, the estimated housing units are
0.25 million. Finally, the turnover is obtained by dividing the existing single family
home sales by the estimated total single family units.
IV. Empirical Evidence
IV.1. Determinants of Prices and Trading Volume
We estimate three difference specifications of the fixed effect panel VAR model.
The first is linear and includes contemporaneous but not lagged exogenous variables,
which is the benchmark model due to its simplicity. The second includes
contemporaneous exogenous variables and their squared values to accommodate possible
non-linearity. The third includes both contemporaneous and lagged exogenous variables.
We use AIC to choose the optimal lag order for endogenous variables, which is 3 for all
specifications. We use only three quarterly dummies to avoid the multicollinearity of the
18
four dummies due to the within transformation. The model is estimated with feasible
GLS that allows for heteroskedasticity across MSAs. We calculate t-statistics using
heteroskedasticity-robust standard errors according to Kezdi (2003). Kezdi (2003) shows
that the robust standard deviations allow serial correlation and heteroskedasticity of any
kind, as well as unit roots and unequal spacing, and they have good small sample
properties except low power in very small samples.
Table 2 reports the estimation results of the first specification. The results
indicate that labor market shocks affect both prices and trading volume in housing
markets. On one hand, both the total non-agricultural employment and the average
household income positively affect both the prices and trading volume in housing
markets. The effects are statistically significant except for the effect of the employment
on trading volume. On the other hand, the unemployment rate has interesting impacts on
housing markets. Increases in the unemployment rate increase (but insignificantly) home
prices and significantly reduce trading volume. This seems to be consistent with the
spatial lock-in phenomenon (see Chan (2001), for example) – home sellers who are hurt
by the increased unemployment rate are likely to be subjected to financial constraints and
thus need to raise their ask prices, which shifts the supply curve upwards and thus causes
lower trading volume and higher transaction prices.
Table 2 confirms the importance of the mortgage market in the determination of
prices and trading volume. When the level of mortgage rate is high (low), home prices
are significantly low (high), so is trading volume. Furthermore, when the mortgage rate
demonstrate a rising (falling) trend, both home prices and trading volume increase
(decrease), which is consistent with the potential home buyers’ rational behavior. When
19
the mortgage rate is rising, potential home buyers would be better off purchasing now
and locking in the mortgage rate; while when the rate is falling, it seems rational for them
to wait and postpone their home purchases. The effects of the mortgage level and trend
are consistent with shifts of the housing demand.
It is interesting that the stock market has significant effects on the price and
turnover in the housing market. First, home prices are significantly lower and the trading
volume is (insignificantly) higher when the S&P500 index is higher, which appears to
indicate a shift of the supply curve to the right side (a decrease in the ask prices of sellers).
This finding seems consistent with Stein (1995) etc: the more financial wealth a
household has (if the household hold stocks), the less likely the household is financially
constrained and thus it sets a lower ask price. Second, home prices are significantly
higher and trading volume is (insignificantly) lower when the stock market shows an
uptrend. It is premature to make any conclusions regarding the economic mechanism;
however, we conjecture that private valuations of homeowners may be affected by their
expectation of the economy in the future. A booming stock market may create higher
housing demand in the future, and homeowners may adjust their private valuation upward
accordingly, which may shift the supply curve upwards.
Table 2 also suggests that lagged prices and trading volume significantly affect
home prices and trading volume. The first order autoregressive coefficients are
significantly negative for both prices and trading volume, so prices and volume tend to
reverse in the next quarter, which may indicate the adjustments of the housing market to
exogenous shocks. An adjustment of market supply to a demand shock appears
consistent with the feed back effects predicted by Novy-Marx (2004). The negative
20
coefficients of lagged prices and trading volume are also consistent with the overshooting
of home prices predicted by Ortalo-Magné and Rady (2004a).
To test whether prices Granger-cause trading volume, an F test is conducted and
the value of the F statistic is 3.37, and the p-value is 0.018. Therefore, the null
hypothesis that prices do not Granger-cause trading volume is rejected at 5% significant
level. This is a strong and direct evidence to support the theory by Stein (1995), and is
consistent with empirical evidence provided by Chan (2001), Engelhardt (2003),
Genesove and Mayer (1997), Genesove and Mayer (2001), etc.
Table 3 reports the results of the second specification, which accommodates
possible nonlinear relations. Compared with table 2, the main results of the linear
relations remain the same after including the squared variables. However, table 3
provides some evidence of nonlinearity - the coefficients of a few squared variables are
statistically significant. These variables include the household income, the level and
trend of the mortgage rate, mortgage rate trend, and lagged home prices and trading
volume. We test the null hypothesis that all coefficients of lagged prices and their
squared values are 0 in the equation of trading volume. The F statistic is 6.32, which is
significant at 1% level. As a result, under this specification, we still find strong evidence
that prices Granger-cause trading volume.
Table 4 reports the results of the third specification. We include lagged labor-
market related variables, but exclude lagged mortgage rates and lagged S&P500 index
levels because we already have the second order differences of the mortgage rate and the
S&P500 index level, and more lags will create perfect multicollinearity. We choose the
lag order of the exogenous variables using the general to specific approach based on
21
Likelihood Ratio tests. The optimal lag order is 5 for the total non-agriculture
employment and the average household income, 0 for the unemployment rate. While the
basic linear relations we find in table 2 still exist, it is interesting that lagged exogenous
variables have significant effects on prices and volume, which suggests that the housing
market reacts slowly to exogenous shocks. We test the Granger-causality of prices on
trading volume again. The F statistic is 3.55, and the corresponding p-value is 0.014.
Consequently, estimation of this specification still provides strong evidence of the
Granger-causality of home prices on trading volume.
Overall, we find that exogenous variables, such as employment, household
income, mortgage rate, etc, play significant roles in determining prices and trading
volume in the housing market, which supports the theories that argue for the effects of
exogenous variables as a possible explanation of the price-volume correlation. On the
other hand, our results reject the hypothesis that prices do not Granger-cause trading
volume; therefore, our results are also consistent with the lead-lag relation of price and
volume. Next, we directly analyze which line of theories, the one that relies on effects of
exogenous variables or the one that relies on the lead-lag price volume relations, better
explains the price-volume correlation in the quarterly frequency.
IV.2. Decomposing the Price-volume Correlation
We first calculate the raw price-volume correlation for each MSA using the series
of home appreciation rates and changes in trading volume. Then, based on results from
estimating the panel VAR model, we decompose the home appreciation rates and trading
volume into fitted components and residuals.
22
, , ,
, , ,
ˆˆ
i t i t i t
i t i t i t
hp hp uto to v
= +
= + (6)
We then calculate the correlation between ,ˆ i thp and ,ˆi tto , as well as the correlation
between ,i tu and ,i tv , which is the component of the price-volume correlation that can not
be explained by our model.
Panel A in table 5 reports the across-MSA averages of the raw price-volume
correlations, the “explained” correlations, and the correlations between residuals, using
results from estimating the panel VAR model in three different specifications. The table
also reports t-statistics of testing two-sided hypotheses that the correlations follow a
distribution with 0 mean. We have a few interesting findings. First, we find evidence of
the statistically significant positive price-volume correlation. The raw correlation is
0.047 (0.044 in the last two specifications, which have a sample period that is about 2
periods shorter) and significant at 1% level. Second, we find strong evidence of positive
correlations between “explained” prices and volume. The “explained” price-volume
correlations are much higher than the raw price-volume correlation. They are 0.202,
0.147, and 0.166 for the three different specifications respectively, and are all significant
at 1% level. Finally and most interestingly, the correlations between residuals are always
lower than the raw price-volume correlation, and are insignificant. Panel A seems to
indicate that our model captures the price volume correlation well.
To investigate the extent to which the price-volume correlation is caused by the
Granger causality of prices on trading volume and by the exogenous economics shocks,
we further decompose both ,i thp and ,i tto into three components
23
, , , ,
, , , ,
ˆˆ
i t i t i t i t
i t i t i t i t
hp hp hp uto to to v
= + +
= + +, (7)
where ,ˆ i thp and ,ˆi tto are the components explained by all exogenous and lagged variables
except lagged prices; ,i thp and ,i tto are the components explained by lagged prices; ,i tu
and ,i tv are regression residuals. We then calculate the correlation between ,ˆ i thp and ,ˆi tto
(the co-movement components), the correlation between ,i thp and ,i tto (the causal
components). These two types of correlations essentially constitute the explained
correlations.
Panel B of table 6 reports the “causal” and “co-movement” components of the
endogenous price-volume correlation, and the corresponding t-statistics of a two-sided
test that the correlations follow a distribution with zero mean. We have a few very
interesting findings. First, we find that the “co-movement” component of the price-
volume correlation is statistically significant at 1% level under all specifications.
Moreover, the correlation ranges from 0.249 to 0.315, which is much higher than the raw
correlation. Second, the “causal” component is statistically significant at 1% level but is
negative. The negative “causal” component of the price volume correlation seems to be
caused by the positive effect of prices on future turnover and the negative effect of prices
on future prices. Our finding may help reconcile the conventionally believed positive
price-volume correlation and the negative correlation found by Hort (2000). It is worth
noting that Hort (2000) controls for regional and time dummies, which is similar to our
controlling for specific exogenous variables in some sense.
Overall, our results provide strong evidence of the universal existence of positive
price-volume correlations in the quarterly frequency. Furthermore, the positive
24
correlation seems to be fully explained by fitted prices and volume in our model. A
surprising finding is that the positive price-volume correlation appears to be mainly
caused by co-movement of prices and volume due to exogenous shocks. Lagged prices
seem to lead to negative price-volume correlation and thus do not seem to explain the
positive price-volume correlation.
IV.3. Impulse-response Analysis
We use impulse-response functions to provide a more intuitive description of how
shocks in exogenous variables generate the co-movement of the price and turnover in the
housing market. The impulse-response functions are constructed using estimation results
of all three specifications. Since the patterns of responses are very similar in all the
specifications, we report the results for the first specification only. We build the analysis
on the level model in (4) instead of the first order difference model since the level model
seems easier to understand. As a result, the impulse responses are for the absolute price
level and turnover in the market, not their changes. Also, the benchmark case is a market
in which all exogenous variables remain unchanged, and thus the price and turnover do
not change over time.
Conventionally, the magnitude of the shock is determined as one standard
deviation of the underlying variable, which, however, does not seem to be the most
appropriate approach in our study. First, most exogenous variables in our study are not
mean-stationary; instead, they have trends and cycles. It is not clear how to define a
meaningful standard deviation for these non-stationary variables. Second, most MSAs
have experienced fairly smooth growth in the sample period. For these MSAs, the
standard deviation of the growth rate of economic variables is very small, and does not
25
appear to represent a meaningful shock. As a result, we define a shock as a 5% absolute
change in the level of the underlying variable.
We construct a conventional type of impulse response functions that are based on
one shock in one variable and no shock in others. It is worth noting that this simple
approach is often not suitable to study impulses in endogenous variables. A shock in an
endogenous variable will typically have contemporaneous effects not only on the
endogenous variable itself but also on other endogenous variables as well. Hence, it is
not appropriate to assume a shock on one endogenous variable while keeping other
endogenous variables fixed. To address this composition effect (defined by Koop et al.
(1996)), researchers often use either orthogonalized impulse responses or generalized
impulse responses. However, since we are interested in how shocks in exogenous
variables affect both the price and turnover, it appears reasonable to entertain
perturbations in an exogenous variable while assuming no extra shocks in other
exogenous or endogenous variables.
To construct the impulse response functions, we first let all contemporaneous
exogenous variables (except the one representing the source of shock), lagged
endogenous variables and intercepts be 0, and then introduce a 5% one-time shock in the
variable that represents the economic source of the shock. Since the VAR system is a log
linear system, a shock that equals log(1.05) implies that the corresponding variable has an
unexpected increase of 5%. The values of the price and trading volume over time are
then calculated by repeatedly plugging into the VAR system all estimated coefficients
and the lagged endogenous variables.
26
Figure 4 plots the dynamic responses of both the price and turnover in the housing
market to a 5% exogenous increase in the total non-agricultural employment, the average
household income, the unemployment rate, the mortgage rate, and the S&P500 index
level, respectively. We do not report the standard deviations of the responses for we are
interested in the patterns of the expected responses, not the statistical significance. The
pre-shock values of both the price and turnover are 1, which means the values are 1 time
of the values in the benchmark case. Values greater than 1 suggest positive deviations
from the benchmark level. For example, 1.02 means the variable is 2% higher than the
benchmark level.
Note that the responses to shocks in the mortgage rate and the S&P500 index
level should be interpreted with caution. Empirically, changes in the mortgage rate also
result in changes in the trend, so the aggregate effects will be more complicated than
what the impulse response functions show. However, these two functions can be
interpreted as thought experiments – suppose the effect of the trend is fixed, the impulse
response functions show the net effect of a change in the level, which is useful to know.
We observe a few interesting patterns. First, trading volume reacts much more
dramatically to exogenous shocks than prices do, which corroborates Andrew and Meen
(2003) and Hort (2000). For instance, after a 5% increase in the average household
income, trading volume increases by about 5%, while the price increases by less than 1%.
This is consistent with the conventional wisdom that, in real estate markets, changes in
trading volume more accurately represent changes in market condition than changes in
prices, see Berkovec and Goodman (1996) for instance.
27
Second, some shocks appear to generate co-movement of the price and volume,
while others seem to cause the price and volume to move to opposite directions. We call
the first type of shocks type I shocks, and the second type of shocks type II shocks. Since
the endogenous price-volume correlation is positive in our sample, it is very likely that
our sample is exposed to more type I shocks than type II shocks. However, one should
be cautious that, the price-volume correlation in a market can be negative, particularly if
type II shocks dominate type I shocks. The positive price-volume correlation might be a
small sample phenomenon in the sense that we happen to be in an economy where type I
shocks dominates in frequency and/or magnitude.
The third finding is that overshooting of the price and volume is very common.
Particularly, the overshooting of trading volume is observed in all four scenarios. This is
consistent with the theories by Novy-Marx (2004) and Ortalo-Magné and Rady (2004a),
which both imply or predict overshooting, though rely on different channels.
V. Conclusions Using an unusually large panel data set consisting of housing markets in 127
MSAs from 1990 to 2002, we study the determinants of home prices and trading volume
in the housing market. We find that the housing market is affected by shocks in the labor
market, mortgage market, and stock market. Moreover, trading volume is significantly
affected by lagged prices – Granger causality tests reject the null hypothesis that prices
do not cause trading volume.
We find a significant price-volume correlation in the quarterly frequency. In
addition, our results indicate that prices and volume tend to move together so the
endogenous price-volume correlation exists. Our model captures the price volume
28
correlation well - after controlling for the price-volume correlation explained by our
model, there is no significant price-volume correlation left. Furthermore, we find that the
Granger-causality of prices on trading volume appears to lead to negative price-volume
correlation, and thus does not help explain the price-volume correlation at all, while the
co-movement of prices and volume is significant, substantial, and positive. Using
impulse response functions, we find that trading volume reacts more dramatically to
economic shocks than home prices do. We also observe overshooting of trading volume
in the process of adjustment to shocks.
29
References Andrew, Mark and Meen, Geoffrey. "House Price Appreciation, Transactions and Structural Change in the British Housing Market: A Macroeconomic Perspective." Real Estate Economics, 2003, 31(1), pp. 99-116. Berkovec, James A. and Goodman, John L. "Turnover as a Measure of Demand for Existing Homes." Real Estate Economics, 1996, 24(4), pp. 421-40. Bertaut, Carol C. and Starr-McCluer, Martha. "Household Portfolios in the United States," L. Guiso, M. Haliassos and T. Jappelli, Household Portfolios. Cambridge: MIT Press, 2002, Case, Karl E. and Shiller, Robert J. "Is There a Bubble in the Housing Market?" Brookings Papers on Economic Activity, 2003, pp. 299-362. Cauley, Stephen Day and Pavlov, Andrey D. "Rational Delays: The Case of Real Estate." Journal of Real Estate Finance and Economics, 2002, 24, pp. 143-65. Chan, Sewin. "Spatial Lock-In: Do Falling House Prices Constrain Residential Mobility?" Journal of Urban Economics, 2001, 49, pp. 567-86. DiPasquale, Denise and Wheaton, William C. "Housing Market Dynamics and the Future of Housing Prices." Journal of Urban Economics, 1994, 35, pp. 1-27. Engelhardt, Gary V. "Nominal Loss Aversion, Housing Equity Constraints, and Household Mobility: Evidence from the United States." Journal of Urban Economics, 2003, 53, pp. 171-95. Fisher, Jeff; Gartzlaff, Dean; Geltner, David and Haurin, Donald. "Controlling for the Impact of Variable Liquidity in Commercial Real Estate Price Indices." Real Estate Economics, 2003, 31(2), pp. 269-303. Follain, James R. and Velz, Orawin T. "Incorporating the Number of Existing Home Sales into a Structural Model of the Market for Owner-Occupied Housing." Journal of Housing Economics, 1995, 4, pp. 93-117. Genesove, David and Mayer, Christopher J. "Equity and Time to Sale in the Real Estate Market." American Economic Review, 1997, 87(3), pp. 255-69. ____. "Nominal Loss Aversion and Seller Behavior: Evidence from the Housing Market." Quarterly Journal of Economics, 2001, 116, pp. 1233-60. Goetzmann, William N. and Peng, Liang. "Estimating Indices in the Presence of Seller Reservation Prices." Yale International Center for Finance Working Paper, 2004. Hanushek, Eric A. and Quigley, John M. "What Is the Price Elasticity of Housing Demand?" Review of Economics and Statistics, 1980, 62(3), pp. 449-54. Hort, Ktinka. "Prices and Turnover in the Market for Owner-Occupied Homes." Regional Science and Urban Economics, 2000, 30, pp. 99-119. Kezdi, Garbor. "Robust Standard Error Estimation in Fixed-Effects Panel Models." Budapest University Working Paper, 2003. Koop, Gary; Pesaran, Hashem M. and Potter, Simon M. "Impulse Response Analysis in Nonlinear Multivariate Models." Journal of Econometrics, 1996, 74, pp. 119-47. Krainer, John. "A Theory of Liquidity in Residential Real Estate Markets." Journal of Urban Economics, 2001, 49, pp. 32-53. Lamont, Owen and Stein, Jeremy C. "Leverage and House-Price Dynamics in Us Cities." Rand Journal of Economics, 1999, 30, pp. 498-514.
30
Leung, Charles Ka Yui and Feng, Dandan. "What Drives the Property Price-Trading Volume Correlation? Evidence from a Commercial Real Estate Market." Journal of Real Estate Finance and Economics, 2005, 31(2), pp. forthcoming. Malpezzi, Stephen and Maclennan, Duncan. "The Long-Run Price Elasticity of Supply of New Residential Construction in the United States and the United Kingdom." Journal of Housing Economics, 2001, 10(3), pp. 278-306. Novy-Marx, Robert. "The Microfoundations of Hot and Cold Markets." University of Chicago Working Paper, 2004. Ortalo-Magné, François and Rady, Sven. "Housing Market Dynamics: On the Contribution of Income Shocks and Credit Constraints." CESifo Working Paper No. 470, 2004a. ____. "Housing Transactions and Macroeconomic Fluctuations: A Case Study of England and Wales." Journal of Housing Economics, 2004b, 13, pp. 287-303. Poterba, James M. "Tax Subsidies to Owner-Occupied Housing: An Asset-Market Approach." Quarterly Journal of Economics, 1984, 99(4), pp. 729-52. Shafir, Eldar; Diamond, Peter and Tversky, Amos. "Money Illusion." Quarterly Journal of Economics, 1997, 112, pp. 341-74. Smith, Barton A. "The Supply of Urban Housing." Quarterly Journal of Economics, 1976, 90(3), pp. 389-405. Stein, Jeremy C. "Prices and Trading Volume in the Housing Market: A Model with Down-Payment Effects." Quarterly Journal of Economics, 1995, 110(2), pp. 379-406. Tracy, Joseph and Schneider, Henry. "Stocks in the Household Portfolios: A Look Back at the 1990's." Current Issues in Economics and Finance, 2001, 7(2), pp. 1-6. Wheaton, William C. "Vacancy, Search, and Prices in a Housing Market Matching Model." Journal of Political Economy, 1990, 98(6), pp. 1270-92.
31
Appendix: List of MSAs Abilene TX MSA Albuquerque NM MSA Alexandria LA MSA Albany GA MSA Amarillo TX MSA Anchorage AK MSA Asheville NC MSA Athens GA MSA Atlanta GA MSA Bakersfield CA MSA Baton Rouge LA MSA Bellingham WA MSA Benton Harbor MI MSA Billings MT MSA Binghamton NY MSA Birmingham AL MSA Bloomington IN MSA Boise City ID MSA Bismarck ND MSA Cedar Rapids IA MSA Cheyenne WY MSA Charlottesville VA MSA Charleston WV MSA Columbia MO MSA Colorado Springs CO MSA Corpus Christi TX MSA Columbia SC MSA Columbus OH MSA Daytona Beach FL MSA Decatur IL MSA Des Moines IA MSA Decatur AL MSA Dothan AL MSA Dover DE MSA Dubuque IA MSA Eau Claire WI MSA El Paso TX MSA Erie PA MSA Fayetteville NC MSA Florence SC MSA Fort Wayne IN MSA Fresno CA MSA Fort Walton Beach FL MSA Gainesville FL MSA Green Bay WI MSA Greensboro-Winston-Salem-High Point NC MSAGreenville NC MSA Houma LA MSA Honolulu HI MSA Huntsville AL MSA Indianapolis IN MSA Iowa City IA MSA Jacksonville FL MSA Jamestown NY MSA Jackson MI MSA Jackson MS MSA Joplin MO MSA Knoxville TN MSA Kokomo IN MSA Lafayette LA MSA Lancaster PA MSA Lafayette IN MSA Lake Charles LA MSA Lexington KY MSA Lima OH MSA Lincoln NE MSA Las Cruces NM MSA Lubbock TX MSA Lawrence KS MSA Lynchburg VA MSA Macon GA MSA Madison WI MSA Mansfield OH MSA Merced CA MSA Mobile AL MSA Modesto CA MSA Montgomery AL MSA Monroe LA MSA Myrtle Beach SC MSA Nashville TN MSA New Orleans LA MSA Ocala FL MSA Oklahoma City OK MSA Orlando FL MSA Owensboro KY MSA Panama City FL MSA Pensacola FL MSA Pueblo CO MSA Punta Gorda FL MSA Reading PA MSA
32
Redding CA MSA Reno NV MSA Roanoke VA MSA Rockford IL MSA Rochester MN MSA Rochester NY MSA Rocky Mount NC MSA Salinas CA MSA San Diego CA MSA San Angelo TX MSA Savannah GA MSA San Antonio TX MSA Sheboygan WI MSA Sioux Falls SD MSA South Bend IN MSA Springfield MO MSA Spokane WA MSA Springfield IL MSA St. Cloud MN MSA State College PA MSA St. Joseph MO MSA Syracuse NY MSA Tallahassee FL MSA Toledo OH MSA Topeka KS MSA Tucson AZ MSA Tulsa OK MSA Tyler TX MSA Waco TX MSA Wausau WI MSA Wichita KS MSA Wichita Falls TX MSA Wilmington NC MSA Yakima WA MSA York PA MSA Yuba City CA MSA Yuma AZ MSA
33
Table 1 Data Summary This table reports across-MSA averages of the means, medians, standard deviations for the first order differences of the log values of home price index, turnover in housing markets, total non-agricultural employment, average household income, unemployment rate, the national average 30-year fixed mortgage rate, and the S&P500 index, as well as corresponding t-statistics if applicable in Panel A. Panel B reports the 1 to 4-quarter autocorrelations and corresponding t-statistics if applicable. Panel C reports across-MSA average correlations among the variables and the corresponding t-statistics.
Home price
Turnover Employ-ment
Household income
Unemployment
Mortgage rate
SP500 return
Panel A. Mean, median, and standard deviation Mean **0.957%
[43.29] **0.514%
[9.86] **0451% [23.11]
**0.888% [78.04]
-0.047% [-0.96]
-0.876% 2.181%
Median **0.918% [38.03]
**0.527% [5.01]
**0.480% [23.71]
**0.883% [73.12]
**-0.373% [-4.06]
-1.196% 2.871%
Std. Dev. 1.347% 10.841% 0.718%
**0.945% 7.647% 5.068% 7.701%
Panel B. Autocorrelations 1 quarter **-0.142
[-5.00] **-0.331 [-29.78]
**0.239 [11.27]
**-0.066 [-3.14]
**0.255 [12.31]
0.135 -0.087
2 quarter **0.079 [4.11]
**-0.059 [-4.68]
**0.212 [12.97]
**0.230 [20.53]
**0.113 [6.94]
0.078 0.103
3 quarter **0.099 [5.69]
**0.047 [2.61]
**0.148 [10.37]
**-0.160 [-12.82]
0.007 [0.42]
-0.049 0.246
4 quarter **0.076 [4.06]
0.004 [0.18]
0.012 [0.74]
*-0.033 [-2.12]
**-0.067 [-3.90]
-0.252 0.027
Panel C. Correlations Home price
1 **0.046 [3.23]
*0.030 [1.99]
*0.026 [2.23]
**0.038 [2.60]
**-0.064 [-4.68]
**-0.072 [-6.29]
Turnover
1 **0.029 [2.39]
**0.137 [9.29]
**-0.040 [3.11]
**0.108 [9.43]
-0.014 [-1.14]
Employ-ment
1 **0.242 [16.33]
**-0.338 [-21.86]
**0.084 [7.75]
**0.110 [10.90]
Household Income
1 **-0.135 [-10.53]
**0.229 [19.67]
**-0.066 [7.44]
Unemployment
1 **-0.064 [-5.46]
**-0.122 [-10.41]
Mortgage rate
1 0.030
SP500 return
1
34
Table 2 Panel VAR Model: Specification 1 This table reports the estimation results for the following two-equation fixed effect panel VAR model
, , ,,
1,2,4 1, , ,
pki t i t si i t
s s s i t qs si t i t si i t
p paA d B C X
q qbνν
−
= = −
∆ ∆ = + + + ∆ + ∆ ∆
∑ ∑ ,
where ,i tp is the log value of the home price index level, ,i tq is the log value of market turnover, sd is a dummy variable for s th quarter, and ,i tX is a vector of exogenous variables (all in log values), which include total non-agricultural employment, average household income, unemployment rate, the 30 year fixed rate mortgage rate, the trend of the mortgage rate, the S&P500 index level, and the trend of the S$P500 index. The model is estimated with feasible GLS that allows for heteroskedasticity across MSAs. We calculate t-statistics using heteroskedasticity-robust standard errors. * denotes significance at the 5% level and ** at the 1% level. Equation 1: Home Price Equation 2: Turnover Variables Estimate t-Stat Estimate t-Stat 1st quarter dummy **0.002 3.42 **0.010 2.702nd quarter dummy -0.001 -1.22 -0.006 -1.594th quarter dummy **-0.004 -6.65 **-0.013 -3.17Total employment **0.094 3.71 0.165 0.86Household income **0.052 2.89 **0.943 6.85Unemployment rate 0.003 1.37 **-0.048 -2.71Mortgage rate level **-0.075 -16.78 **-0.272 -7.95Mortgage rate trend **0.057 16.71 **0.422 16.03S&P500 level **-0.025 -6.69 0.027 0.94S&P500 trend **0.019 7.18 -0.033 -1.64Home price lag 1 **-0.188 -14.58 **0.290 2.94Home price lag 2 **0.102 7.88 0.143 1.44Home price lag 3 **0.124 9.91 0.079 0.82Turnover lag 1 0.001 0.71 **-0.456 -34.80Turnover lag 2 0.003 1.37 **-0.269 -19.26Turnover lag 3 **0.005 2.92 **-0.104 -7.98
2R 0.12 0.24
35
Table 3 Panel VAR Model: Specification 2 This table reports the estimation results for the following two-equation fixed effect panel VAR model
, , ,,
1,2,4 1, , ,
pki t i t si i t
s s s i t qs si t i t si i t
p paA d B C X
q qbνν
−
= = −
∆ ∆ = + + + ∆ + ∆ ∆
∑ ∑ ,
where ,i tp is the log value of the home price index level, ,i tq is the log value of market turnover, sd is a dummy variable for s th quarter, and ,i tX is a vector of exogenous variables (all in log values) and the squared values of them, which include total non-agricultural employment, average household income, the unemployment rate, the 30 year fixed rate mortgage rate, the trend of the mortgage rate, the S&P500 index level, and the trend of the S&P500 index. The model is estimated with feasible GLS that allows for heteroskedasticity across MSAs. We calculate t-statistics using heteroskedasticity-robust standard errors. * denotes significance at the 5% level and ** at the 1% level. Equation 1: Home Price Equation 2: Turnover Variables Estimate t-Stat Estimate t-Stat 1st quarter dummy **0.002 4.64 0.007 1.842nd quarter dummy **-0.002 -3.03 0.002 0.474th quarter dummy **-0.004 -7.29 **-0.011 2.89Total employment **0.084 3.25 0.300 1.52Household income **0.077 3.67 **0.730 4.55Unemployment rate 0.003 1.47 **-0.048 -2.71Mortgage rate level **-0.076 -15.80 **-0.287 -7.78Mortgage rate trend **0.065 18.57 **0.384 14.33S&P500 level **-0.026 -6.79 0.040 1.35S&P500 trend **0.024 7.97 **-0.072 -3.19Sq. Total employment 1.415 1.29 -1.078 -0.12Sq. Household income *-1.081 -2.00 7.385 1.77Sq. Unemployment rate -0.005 -0.39 -0.122 -1.40Sq. Mortgage rate level **0.200 2.73 **-2.119 -3.78Sq. Mortgage rate trend **-0.301 -8.63 **1.253 4.69Sq. S&P500 level 0.048 1.46 0.374 1.49Sq. S&P500 trend -0.024 -1.48 0.140 1.14Home price lag 1 **-0.253 -15.68 **0.613 4.95Home price lag 2 **0.109 6.71 0.234 1.88Home price lag 3 **0.102 6.50 0.181 1.51Sq. Home price lag 1 **3.004 6.50 **-14.952 -4.22Sq. Home price lag 2 -0.195 -0.45 -5.604 -1.67Sq. Home price lag 3 *0.947 2.28 *-6.268 -1.97Turnover lag 1 0.003 1.65 **-0.458 -34.90Turnover lag 2 0.001 0.67 **-0.265 -18.83Turnover lag 3 *0.004 2.14 **-0.103 -7.90Sq. Turnover lag 1 **-0.020 -3.21 **-0.348 -7.13Sq. Turnover lag 2 *-0.013 -2.11 -0.049 -1.04Sq. Turnover lag 3 -0.008 -1.25 0.031 0.66
2R 0.15 0.26
36
Table 4 Panel VAR Model: Specification 3 This table reports the estimation results for the following two-equation fixed effect panel VAR model
, , ,,
1,2,4 1, , ,
pki t i t si i t
s s s i t qs si t i t si i t
p paA d B C X
q qbνν
−
= = −
∆ ∆ = + + + ∆ + ∆ ∆
∑ ∑ ,
where ,i tp is the log value of the home price index level, ,i tq is the log value of market turnover, sd is a dummy variable for s th quarter, and ,i tX is a vector of exogenous variables (all in log values), which include total non-agricultural employment (and 5 lags), average household income (and 5 lags), unemployment rate, the 30 year fixed rate mortgage rate, the trend of the mortgage rate, the S&P500 index level, and the trend of the S$P500 index. The model is estimated with feasible GLS that allows for heteroskedasticity across MSAs. We calculate t-statistics using heteroskedasticity-robust standard errors. * denotes significance at the 5% level and ** at the 1% level. Equation 1: Home Price Equation 2: Turnover Variables Estimate t-Stat Estimate t-Stat 1st quarter dummy **0.002 3.76 0.007 1.732nd quarter dummy -0.001 -0.93 -0.007 -1.784th quarter dummy **-0.004 -6.64 *-0.009 -2.08Total employment *0.063 2.31 -0.082 -0.39Household income **0.068 3.62 **1.117 7.62Unemployment rate 0.003 1.33 **-0.049 -2.72Mortgage rate level **-0.077 -16.69 **-0.291 -8.10Mortgage rate trend **0.057 16.02 **0.425 15.43S&P500 level **-0.033 -8.62 *0.068 2.29S&P500 trend **0.023 8.40 *-0.056 -2.65Total employment lag 1 **0.072 2.76 -0.241 -1.19Total employment lag 2 **0.074 2.88 0.368 1.84Total employment lag 3 *0.052 2.09 *-0.380 -1.98Total employment lag 4 **0.142 5.83 -0.323 -1.70Total employment lag 5 **0.103 4.28 **-0.606 -3.26Household income lag 1 **-0.053 -2.82 0.082 0.56Household income lag 2 *-0.044 -2.39 -0.280 -1.95Household income lag 3 *0.045 2.39 **0.379 2.59Household income lag 4 0.031 1.67 0.205 1.42Household income lag 5 -0.018 -0.95 0.243 1.70Home price lag 1 **-0.193 -14.60 **0.288 2.80Home price lag 2 **0.098 7.33 0.198 1.91Home price lag 3 **0.125 9.64 0.103 1.02Turnover lag 1 0.003 1.55 **-0.466 -34.27Turnover lag 2 0.002 1.03 **-0.259 -17.58Turnover lag 3 *0.005 2.57 **-0.106 -7.75
2R 0.15 0.25
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Table 5 Price-volume Correlations This table reports the decomposition of the price-volume correlations. “Raw” means the correlation between the raw home appreciation rates and the raw market turnover changes. Using the results of estimating the panel VAR model in different specifications, we decompose both the home appreciation rates and the market turnover (both with MSA specific across-time means subtracted) in two ways. In Panel A, we decompose them into two parts: the one explained by our panel VAR model (“Fitted”), and the regression residual (“Residual”). In Panel B, we decompose them into three parts: the one explained by lagged home appreciation rates (“Causal”), the one explained by all other explanatory variables (“Co-movement”), and the regression residual (“Residual”). The correlations are reported for each type of components. All reported values are means across MSAs, and t-statistics are also reported. * denotes significance at the 5% level and ** at the 1% level.
Panel A Specification Raw Fitted Residual
1 **0.047 [3.12]
**0.202 [16.62]
0.005 [0.35]
2 **0.047 [3.12]
**0.147 [11.93]
0.019 [1.43]
3 **0.044 [2.96]
**0.166 [12.86]
0.007 [0.55]
Panel B Specification Raw Causal Co-movement Residual
1 **0.047 [3.12]
**-0.437 [-26.52]
**0.315 [26.86]
0.005 [0.35]
2 **0.047 [3.12]
**-0.499 [-44.16]
**0.249 [21.20]
0.019 [1.43]
3 **0.044 [2.96]
**-0.324 [-23.12]
**0.251 [18.81]
0.007 [0.55]
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Figure 1 Home Price Indices This figure plots the OFEHO quarterly home price indices (nominal) for 127 MSAs in the US from 1990 to 2002. All index levels are normalized to be 100 in 1995.
39
Figure 2 Time Series of Turnover and Other Variables This figure reports the 25%, median, and 75% percentiles of the quarterly turnover in the housing market, total non-agriculture employment, average household income, and unemployment rate across 127 MSAs, as well as the national average 30 year FRM rate, and the S&P500 index (normalized to be 1 in 1990).
40
Figure 3 Responses of the Housing Market to Exogenous Shocks This figure reports the responses of home prices and market turnover (both in level) to a 5% one-period shock in the total non-agricultural employment, average household income, unemployment rate, and mortgage rate (in level). To construct the responses, we first let all contemporaneous exogenous variables (except the one representing the source of shock), lagged endogenous variables and intercepts be 0, and then introduce a 5% one-time shock in the variable that represents the economic source of the shock. The values of the price and trading volume over time are then calculated by repeatedly plugging into the VAR system all estimated coefficients and the lagged endogenous variables.
