Price-volume Correlation in the Housing Market: Causality and Co-movements (P.9)

purchases, and housing demand may decrease. A measure of the trend in quarter t is
the change of mortgage rates from quarter t – 1 to quarter t. Since the autocorrelation
of the change in mortgage rate is indeed positive and fairly large (0.13), the change
from quarter t – 1 to quarter t does help capture the trend.
In our estimation, we use the national average interest rate of 30year fixed rate
mortgages and its first order difference to capture the mortgage rate level and trend.
Since to our knowledge there is no theory that articulates the specific effects of these
two variables, the interpretation of the coefficients demands caution. Fortunately, our
tests rely on the aggregate effects for these two variables, not the specific manner in
which they affect the housing market.
The stock market may also affect the housing market, even though the effects
might be complicated and ambiguous. First, the well known wealth effect suggests
that an increase in wealth may increase consumption, including consumption of
housing. Therefore, a booming stock market may increase housing demand. 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
down payments for new homes. This might affect both the demand and the supply in
the housing market, given that many families are simultaneously buyers and sellers.
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 theories 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&P 500 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&P 500 index.
This paper compiles data from five sources. First, the U.S. Bureau of Census (BOC)
provides quarterly estimates for single family housing units for 209 MSAs in 1990:2
and for 280 MSAs in 2000:2. The difference in the number of MSAs is mainly due
to changes in MSA boundaries and the establishment of new MSAs. Second, the
Office of Federal Housing Enterprise Oversight (OFHEO) provides transactionbased
quarterly house price indices at the MSA level (using BOC 1999 MSA
definitions). Third, Moody’s provides quarterly measurements for
existing single family home sales, total nonagricultural employment, average
household income, population, single family home permits, and the unemployment
rate at the MSA level (using BOC 1999 MSA definitions). The sources for these
variables are respectively the National Association of Realtors (NAR), Bureau of
Labor Statistics (BLS), Bureau of Census, and Internal Revenue Service (IRS). IRS
records seem to be used to estimate migration between MSAs, which is then used to
estimate population. Fourth, NAR provides the time series of the national average
interest rate for 30 year fixed rate mortgages. Finally, CRSP provides the time series
of the SP500 index.
The sample period in our analysis is from 1990:2 to 2002:2, and the time
frequency is quarterly. We hope to fit our model to high frequency data, since the

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