Forecast Comparisons of Residential Housing Prices by Parametric and Semiparametric Regression

Abstract

The hedonic price theory involves examining how the price of a commodity varies with respect to its characteristics. Rosen (1974) presented an integrated treatment of the hedonic price theory and outlined the theory for estimation of the demand and supply functions which determine a hedonic price model. Unfortunately, economic theory has provided little guidance concerning the functional form of the dependence of price on quality. Thus, researchers have used econometric estimation techniques which allow flexible parametric functional forms such as the Box-Cox (1964) models. The objective of this paper is to examine the parsimony of the parametric and semiparametric conditional mean estimators by their out-of-sample forecast comparisons within the context of residential housing prices. In the construction of the parametric models, there are three choices: ordinary least squares (OLS hereafter) regression, Box-Cox (1964), and the Wooldridge (1992) transformations. The Box-Cox (1964) transformation is popular because of its flexibility in the model specification. The advantage of the Wooldridge transformation over the Box-Cox is that no second moment or other distributional assumptions are relied upon to obtain consistent estimates or to perform asymptotically valid inferences. We estimate all of the three parametric models and compare their out-of-sample forecasts as measured by the mean square prediction error. For all forecast horizons, the semiparametric model provides a much smaller mean square prediction error in comparison to the Box-Cox and Wooldridge transformations and the OLS regression.