A varying-coefficient approach to estimating hedonic housing prices and their quantiles

Despite the large body of literature on hedonic pricing, research continues on the development of new approaches to the estimation of hedonic relationships. Until the 1990s, virtually all published work on hedonic modeling of house prices is based on parametric models that involve assertions about the functional relations between house prices and the trait variables. During the past twenty years, non-parametric methods, which impose no parametric assumptions about the data process, have undergone significant outgrowth and are increasingly replacing parametric models for the latter's lack of flexibility. Popular non-parametric approaches include kernel, spline, locally weighted regression, and nearest neighbor, have all been successfully applied to the estimation of hedonic house price models. However, it is well-known that the rate of convergence of non-parametric estimators tends to decrease rapidly as the number of regressors grows. This is the curse of dimensionality that afflicts virtually all standard non-parametric methods, rendering these methods impotent when there is a large number of regressors in the model. This is clearly relevant to hedonic housing price modeling as many different characteristics can affect dwelling prices. One approach developed in the statistics literature that can go some way towards alleviating the curse of dimensionality is the varying-coefficient (VC) model popularised in the work of Hastie and Tibshirani (1993). The greatest appeal of the VC model is that it allows the unknown coefficients to vary as smooth functions of a small number of variables, known as effect modifiers. Estimation of the VC model thus involves only low-dimensional smoothing, as opposed to high-dimensional smoothing required for standard non-parametric procedures. Because only low-dimensional non-parametric functions are estimated, the curse of dimensionality can be circumvented even when there are many regressors. Moreover, the VC model assumes that there is a linear relationship between the dependent variable and regressors, albeit a changing one. The VC model thus has the flexibility of a non-parametric model and the easy interpretability of an ordinary linear regression. One purpose of this paper is to take steps in applying the VC model to hedonic price modeling. We also adress the question of possible heterogeneity of the marginal effects of attributes across the distribution of housing prices using the recently developed varying-coefficient quantile regression (VC-QR) technique. Our illustration takes the form of a rather limited, but very promising, application with Hong Kong data.