Academic journal article Real Estate Economics

An Anatomy of Price Dynamics in Illiquid Markets: Analysis and Evidence from Local Housing Markets

Academic journal article Real Estate Economics

An Anatomy of Price Dynamics in Illiquid Markets: Analysis and Evidence from Local Housing Markets

Article excerpt

This research analyzes the dynamic properties of the difference equation that arises when markets exhibit serial correlation and mean reversion. We identify the correlation and reversion parameters for which prices will overshoot equilibrium ("cycles") and/or diverge permanently from equilibrium. We then estimate the serial correlation and mean reversion coefficients from a large panel data set of 62 metro areas from 1979 to 1995 conditional on a set of economic variables that proxy for information costs, supply costs and expectations. Serial correlation is higher in metro areas with higher real incomes, population growth and real construction costs. Mean reversion is greater in large metro areas and faster growing cities with lower construction costs. The average fitted values for mean reversion and serial correlation lie in the convergent oscillatory region, but specific observations fall in both the damped and oscillatory regions and in both the convergent and divergent regions. Thus, the dynamic properties of housing markets are specific to the given time and location being considered.

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Numerous studies of a variety of asset markets have documented the existence of short-horizon serial correlation and long-horizon mean reversion in asset prices. Among asset markets, the most heavily researched is the equity market. For example, Fama and French (1988) and Poterba and Summers (1988), using different methodologies, find significant evidence of mean reversion at long horizons. Fama and French conclude "predictable variation is estimated to be about 40% of 3-5 year return variances for portfolios of small firms" (p. 246). (1) Time varying equilibrium expected returns and investor overreaction have been proposed as possible explanations. (2) Momentum strategies, which exploit serial correlation in asset prices, have been shown to be more profitable when information costs are high (Hong, Lim and Stein 2000).

The focus of our research is the more illiquid U.S. single-family housing market. Earlier studies have documented both serial correlation and mean reversion (Case and Shiller 1989, Abraham and Hendershott 1993, 1996, Capozza and Seguin 1996, Capozza, Mack and Mayer 1997, Malpezzi 1999, Meen 2002). One intriguing finding in these studies is that the extent of correlation or reversion varies with location. For example, Abraham and Hendershott (1996) document a significant difference in time-series properties between coastal and inland cities.

Since studies that use a wide variety of methodologies and cover many time periods, countries and asset types all find evidence of serial correlation and mean reversion, this characteristic may be a pervasive and ubiquitous feature of asset markets. Some logical questions to ask are: What variables might affect the time-series properties; why do regions react differently to economic shocks, (3) and does the same region react differently over time? Our empirical tests focus on the interaction among the serial correlation and mean reversion coefficients and economic forces.

In this research we first provide more definition to the dynamics by translating the standard empirical formulation for estimating serial correlation and mean reversion into the corresponding second-order difference equation. We then analyze the properties of the difference equation to derive the required values that produce the four major dynamic structures: damped versus cyclical and convergent versus divergent or explosive. By first defining the mathematical structure implied by the empirical estimates, we are able to give rigorous definition to terms like "overshooting" and "bubble."

In the context of the dynamics implied by the difference equation arising from this simple model, overshooting occurs when the correlation and reversion coefficient pairs assume values in the "oscillatory" region where the roots of the "characteristic" or "complementary" function of the difference equation are complex. …

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