Price-volume Correlation in the Housing Market: Causality and Co-movements (P.8)

correlation between the fitted price and fitted volume and the correlation between
the residuals, respectively. We compare the “fitted” correlation and the “residual”
correlation with the raw price–volume correlation. The comparison helps us assess
how well our model captures the price–volume correlation overall.
Fourth, we analyze the degree to which the Granger causality between prices and
trading volume and the co-movements of the price and volume help explain the
price–volume correlation respectively. This time, we decompose the fitted values of
Δpi,t and Δqi,t respectively into three parts: the price-caused component (explained
by lagged prices), the trading volume-caused component (explained by lagged
trading volume) and the co-movement component (explained by other variables). We
then assess the significance and magnitude of the correlations for different
components and investigate how well each component helps explain the fitted
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 prices and trading volume react to exogenous
shocks respectively. The impulse response functions help shed light on the economic
sources of the price–volume correlation.
Model Specifications and Data
Model Specifications
This section discusses our choice of exogenous variables Xi,t 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 variables. Note that our estimation uses the demeaned first-order
differences of the log values of these variables.
Changes in the labor market and local demographic conditions likely affect
housing demand and/or supply for several reasons. First, increasing immigrants and
the growth of the local economy and/or population may increase demand for
dwellings such as single family homes. Therefore, we include the total nonagricultural
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 market conditions likely affect house prices and turnover as well, for
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 the
mortgage rate per se. It is plausible that home buyers are less financially constrained
when mortgage rates are lower. The second one is the trend in mortgage rates.
Among other possibilities, potential buyers have the real option to delay their home
purchases until mortgage rates are more favorable. Consequently, when mortgage
rates seem to be falling, potential buyers may choose to postpone their home

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