A Dymimic Model of Housing Price Determination

This paper presents and ‘estimates a model of the resale housing market. The data are a cross-section of monthly time series obtained from the multiple-listing service for a suburb of San Diego. The model is specified and estimated as a dynamic multiple indicator multiple cause system of equations where the capitalization rate is taken to be an unobservable time series to be estimated jointly with the unknown parameters. These are estimated by maximum likelihood using an EM algorithm based upon Kalman filtering and smoothing. The specification of the model features hedonic equations for each house sale and a dynamic equation for the capitalization rate which is constrained to make the expectation of prices equal the present value of the net returns to home ownership whenever the economic variables stabilize at steady state values. Out of steady state, the capitalization rate slowly adapts to new information. The model attributes a large portion of housing price increases of the 1970’s to a fall in the capitalization rate which in turn was driven by rental inflation, tax rates and mortgage rates. Post-sample simulations indicate an initial flattening of housing inflation rates and later a fall brought on by the increase in steady state capitalization rates. In-sample simulations show that although both Proposition 13 and the inflation induced rise in the marginal income tax rates provided partial explanations for the fall in capitalization rates, the single most important factor was the acceleration in price of housing services which interacted with the tax treatment of home ownership to produce an amazing 18% average annual rate of price increase over the last seven years of the 1970’s.