Semiparametric Estimation of Consumer Demand Systems with Micro Data

Maximum likelihood and two‐step estimators of censored demand systems yield biased and inconsistent parameter estimates when the assumed joint distribution of disturbances is incorrect. This paper proposes a semiparametric estimator that retains the computational advantage of the two‐step approach but is immune to distributional misspecification. The key difference between the proposed estimator and the two‐step estimator is that the parameters of the binary censoring equations are estimated using a distribution‐free single‐index model. We implement the proposed estimator using household‐level data obtained from the Hainan province in China. specification test lends support to our approach.