Hedonic price index estimation under mean‐independence of time dummies from quality characteristics

Abstract

Summary. We estimate hedonic price indices (HPI) for rental offices in Tokyo for the period 1985–1991. We take a partially linear regression (PLR) model, linear in x (year dummies) and nonparametric in z (office quality characteristics), as our main model; the usual linear model is used as well. Since x consists of year dummies, the linearity in x is not a restriction in the PLR model; the only restriction is that of no interaction between x and z. For the PLR model, the HPI are estimated -consistently with a two-stage procedure. For our data, x turns out to be (almost) mean-independent of z. This implies that least squares estimation (LSE) for models with a misspecified function for z is still consistent. The mean-independence also leads to an efficiency result that, under heteroskedasticity of unknown form, the two-stage PLR model estimator is at least as efficient as any LSE for models specifying (rightly or wrongly) the part for z. In addition to these, several interesting practical lessons are noted in doing the two-stage PLR model estimation. First, the cross validation (CV) used in the PLR model literature can fail if the mean-independence is ignored. Second, high order kernels can make the CV criterion function ill behaved. Third, product kernels work as well as spherically symmetric kernels. Fourth, nonparametric specification tests may work poorly due to a sample splitting problem with outliers in the data or due to choosing more than one bandwidth; in this regard, a test suggested by Stute (1997) and Stute et al. (1998) is recommended.