Price-volume Correlation in the Housing Market: Causality and Co-movements (P.7)

et al. (1997) argue that money illusion is common in a wide variety of contexts.
Particularly, they find that a majority of survey respondents focus on nominal rather
than real gains in assessing hypothetical gains/losses when selling a house.
Finally, our model controls for the heterogeneity in the housing market in two
ways. First, our model includes MSA-specific dummies, which would capture all
unobserved time-invariant MSA characteristics, such as geographic attributes.
Second, our model includes economic variables at the MSA level, which help
capture local economic conditions that are time-variant. However, our results should
be interpreted with caution: the estimated parameters should be treated as averages
across the MSAs in our sample or subsamples, and our analysis can be interpreted as
analysis of an average MSA. Note that this is not necessarily a problem—the
theories we test are general and should apply to all MSAs; therefore, results from an
average MSA serve our research purposes.
Since our data include price indices (with the index level normalized to 100 for
1995:1) rather than actual prices, we can not estimate (1) directly. Instead, we
estimate the first order difference of (1)

We assume the error terms have zero means and are orthogonal to all explanatory
variables. The quarterly dummies in (2) are first-order differences of the dummies in
(1), but we use the same notations to simplify the illustrations. The system in (2) is
essentially a fixed-effect panel VAR model. In our estimation, we use the within
transformation to eliminate MSA dummies, so variables in (2) become demeaned.
Tests and Analysis
Based on the results of estimating the model in (2), we conduct the following
analysis. First, we test the null hypotheses that house prices do not Granger cause
trading volume, and trading volume does not Granger cause house prices. The null
hypothesis that house prices (trading volume) do not Granger cause trading volume
(house prices) essentially imposes the constraint that the coefficients of all lagged
prices (trading volume) are 0 in the second (first) equation of (2), which can be
easily tested with a F-test. These hypotheses are expected to be rejected if the
theories by Stein (1995) and Wheaton (1990) are valid.
Second, we investigate the existence and magnitude of the price–volume
correlation. The price–volume correlation is defined as the correlation between
changes in home prices, i.e. Δpi,t, and changes in trading volume, i.e. Δqi,t (both are
demeaned using the within transformation). We do not use the correlation between
pi,t and qi,t because prices have trends and are not stationary, while the trading
volume is bounded between 0 and 1; therefore, 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 Δpi,t and Δqi,t respectively into the
fitted values and residuals (unexplained by our model), and then calculate the

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