Price-volume Correlation in the Housing Market: Causality and Co-movements (P.22)

dramatically across markets—it is significantly positive for MSAs with high supply
elasticity, but significantly negative for MSAs with low supply elasticity. This seems
to be caused by the negative autocorrelation of turnover and different effects of
turnover on house prices in different markets: in loose (tight) markets, higher
turnover tends to reduce (increase) house prices in next quarter.
Overall, our results provide strong evidence of the existence of positive price–
volume correlations at quarterly frequency. Furthermore, the positive correlation
seems to be fully explained by fitted prices and volume in our model. A novel
finding is that the positive price–volume correlation appears to be mainly caused by
co-movements of prices and volume due to exogenous shocks. Lagged prices seem
to lead to negative price–volume correlation for all markets, and lagged trading
volume leads to positive price–volume correlation in MSAs with high supply
elasticity but negative price–volume correlation in MSAs with low supply elasticity,
and thus both lagged prices and trading volume do not seem to explain the positive
price–volume correlation well.
Impulse Response Analysis
We use impulse-response functions to provide a more intuitive description of how
shocks in exogenous variables generate the co-movements of the price and turnover
in housing markets. The impulse-response functions are constructed using estimation
results of the first specification (Table 2). We build the analysis on the level model in
(1) instead of the first-order difference model since the level model seems more
intuitive. 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 shock introduced equals 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 meanstationary;
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, standard deviations of the growth rates of economic variables are very small,
and do not appear to represent meaningful shocks. 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 often has contemporaneous effects not only on the endogenous
variable itself but also on other endogenous variables. Hence, it is inappropriate 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.

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