Price-volume Correlation in the Housing Market: Causality and Co-movements (P.23)

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 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.
Figure 5 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, and the mortgage rate,
respectively. We do not report the standard deviations of the responses since 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
times 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 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.
Note that in Fig. 5, the series that have higher absolute values of deviations from
1 in Period 1 are for turnover, while the other series are for house prices. 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 conditions than
changes in prices, (see Berkovec and Goodman 1996, for instance).
Second, some shocks appear to generate co-movements of the price and volume,
while others seem to cause the price and volume to move in opposite directions. We
call the first type of shocks Type I shocks, and the second type of shocks Type II
shocks. Since the 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 in our data might be a small sample phenomenon in the sense that we
happen to be in an economy where Type I shocks dominate in frequency and/or
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 (2007) and Ortalo-Magné and
Rady (2006), which both imply or predict overshooting, though rely on different

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