Short-Term Buyers and Housing Market Dynamics

Abstract

This study demonstrates that taking into account heterogeneous investment horizons will improve our understanding of housing price and trading dynamics. Using an OLG (Overlapping Generations) model in which agents have heterogeneous preferences and investment horizons, with transaction costs, short term investors are more sensitive to changes in economic fundamentals and are less likely to own (and trade) in a declining market. The model predicts that the ownership composition contains information about current and future house prices and trading dynamics. Empirically, we find that home owners’ expected holding horizons co-vary negatively with house prices, and they also predict future (short term) returns.

Appendix

A Proof of Lemma 1

In the presence of private consumption benefits associated with home ownership, consumers will be indifferent between paying the market rent and live in the rental market and owning by paying the rental cost adjusted for the idiosyncratic private value. The indifference reservation price for each type of consumers then consists of a component that equals the rental cost given the consumer’s horizon. In addition, since owners are entitled to capital gains/losses associated with asset ownership, their reservation price also incorporates the expected price at time of sale given their different horizons. Therefore each short horizon buyer i and every long horizon buyer j have the following valuations,

$$ {P_{s,i,t }}={\eta_i}{r_{s,t }}+{g_{s,t }}, $$

$$ {P_{l,j,t }}={\eta_j}{r_{l,t }}+{g_{l,t }}, $$

(A1)

where r _s,t ,g _s,t , r _l,t and g _l,t are defined as in equation (1). Essentially the first term on both equations in (A1) refers to the buyer’s willingness to pay for housing consumption, after adjusting for buyer-specific private values associated with ownership. The second term in both equations of (A1) is the capital gains component that is specific to the buyer’s holding horizon, net of transaction cost.

Any potential buyer will only become owner if his/her valuation is greater than or equal to the market price P _t . That implies the individual demand for owner-occupied housing is ${I_{{{P_{s,i,t }}\geqslant {P_t}}}}$ for a short horizon buyer i, and is ${I_{{{P_{l,j,t }}\geqslant {P_t}}}}$ for a long horizon buyer j. Aggregating the individual demand leads to the following,

$$ {D_{s,t }}\left( {P_t } \right)=\mathop{\smallint}\limits_{{1-\psi}}^{{1+\psi }}{I_{{{P_{s,i,t }}\geqslant {P_t}}}}d{F_{\eta_i }}, $$

$$ {D_{l,t }}\left( {P_t } \right)=\mathop{\smallint}\limits_{{1-\psi}}^{{1+\psi }}{I_{{{P_{l,j,t }}\geqslant {P_t}}}}d{F_{\eta_j }}, $$

(A2)

Direct calculation of the conditional expectation of a uniform distribution will give the result in Equation (2). Q.E.D.

B Proof of Proposition 1

First we normalize the equilibrium price by the market rent level, i.e., define ${p_t}\equiv \frac{P_t }{R_t }$. Since ${R_{t+1 }}={R_t}{Y_t}$, we can eliminate the rent levels in the valuation equations, in which the rent growth rate will be the only state variable. With the equilibrium concept defined to be a steady-state stationary equilibrium, the equilibrium price-to-rent ratio to be solved involves two unknown values and we define them as p ^L and p ^H. Using the transition matrix of the rent growth rate, one can easily write-out the normalized valuation equations (by dividing (1) and (A1) by the rent level) as functions of λ,Y ^L, Y ^H along with other model primitives, as in (5). Scaling the price by the rent level does not change the distribution properties of the private values as well as buyers’ valuations, so the aggregate demand for each type of buyers is obtained again by calculating the conditional expectation of a uniform random variable (similar to equation (A2)), and one can easily verify the formula in (4).

The next step in solving the equilibrium is to employ the market clearing condition. Note that although the owner-occupied housing market has a fixed size Q, not all housing units are available for sale at any point in time. This is due to the fact that long horizon owners will hold the houses for two periods until the end of their life cycle. As a result, the portion of the owner-occupied housing stock that is absorbed by the long horizon buyers in the previous period will not be for sale during this period, which effectively reduces the housing supply. In the stationary equilibrium, the expected reduction in housing supply equals the probability weighted average of the long horizon’s demand during the previous period. Then the market clearing conditions as in (3) obtain and the equilibrium price (pair) is the solution to that system. Q.E.D.

Table 6 MSA level return forecasting regressions: alternative duration measure

Table 7 MSA level return forecasting regressions by using expected duration of buyers with a college degree