Bayesian Estimation for Partially Linear Models with an Application to Household Gasoline Consumption

A partially linear model is often estimated in a two-stage procedure, which involves estimating the nonlinear component conditional on initially estimated linear coefficients. We propose a sampling procedure that aims to simultaneously estimate the linear coefficients and bandwidths involved in the Nadaraya-Watson estimator of the nonlinear component. The performance of this sampling procedure is demonstrated through Monte Carlo simulation studies. The proposed sampling algorithm is applied to partially linear models of gasoline consumption based on the US household survey data. In contrary to implausible price effect reported in the literature, we find negative price effect on household gasoline consumption.