Parametric specifications for hedonic price equations are estimated using a data set from Alameda and San Francisco Counties and are compared to estimates using a nonparametric technique called locally weighted regression, LWR. LWR permits flexible estimation of the hedonic's curvature at median attributes and is less sensitive than standard regression techniques to the influence of unusual observations. The technique also avoids imposing a single functional form across time and municipalities. The LWR estimates of municipality-specific hedonics are then used to obtain implicit prices for housing attributes and to derive municipality-specific price indices. The results of extensive diagnostic checks of our technique are also reported.