Price-volume Correlation in the Housing Market: Causality and Co-movements (P.6)

Second, this approach enables us to better understand the determination of house
prices and trading volume, and decompose prices and volume respectively into four
components: the component determined by exogenous variables; the component
determined by lagged prices; the component determined by lagged trading volume;
and the component determined by other unknown variables. This decomposition
allows us to calculate the price–volume correlation using each of the four
components of the price and volume and assess the direction and magnitude of the
correlation due to each of the components.
We now build the bivariate panel VAR model. We assume that both the
equilibrium housing price level and turnover are functions of quarterly dummy
variables, exogenous variables and lagged endogenous variables.

In Eq. 1, ds is a dummy variable for the sth quarter, which equals 1 if period t is
the sth quarter and 0 otherwise. For the ith MSA in period t, Pi,t denotes the log of
the equilibrium price, qi,t denotes the log of the turnover (measured with the ratio of
existing single family home sales to the units of existing single family homes), Xi,t is
a k by 1 vector of exogenous variables that affect either the demand or supply in the
market, epi
;t and eqi
;t are error terms. Coefficients and are scalars. As is a 2 by 1 vector.
Bs is 2 by 2 vector. C is a 2 by k vector with k being the number of exogenous
variables in Xi,t. All variables on the right side of the equation can affect either the
demand or supply in the housing market, and thus ultimately determine the
equilibrium price level and turnover. While the functional forms of the demand and
supply curves themselves are interesting, this paper focuses on the aggregate effect
of the explanatory variables because it appears sufficient to help us test the two lines
of theories regarding the price–volume correlation. It is not this paper’s research goal
to estimate the demand or supply curve of houses.
Four points are worth noting in Eq. 1. First, the equation includes lagged market
prices as explanatory variables, and thus allows them to affect the equilibrium price
and trading volume. This accommodates the causal relation from market prices to
trading volume as predicted by Stein (1995).
Second, the model allows lagged trading volume to affect both the price and
turnover, which essentially allows market participants to update their private
valuations based on historical trading volume. This enables us to test the Granger
causality from trading volume to prices, which Wheaton (1990) suggests. In
addition, this accommodates the feedback effects proposed by Novy-Marx (2007),
which suggests that a demand shock may increase the buyer-to-seller ratio in the
market, and thus reduce the time on the market and increase the turnover of housing
units. Changes in trading volume, consequently, can help sellers update their
information set and thus change their asking prices, which shifts the supply curve.
Third, the prices in our model are nominal prices. We chose nominal prices
instead of real prices because an important theory that aims to explain that the price–
volume correlation relies on nominal loss aversion of homeowners (see, e.g.
Genesove and Mayer 2001; Engelhardt 2003). Moreover, existing research suggests
that people often make financial decisions in nominal terms. For example, Shafir

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