Smoothed maximum score estimation with nonparametrically generated covariates

This paper develops a two-stage semiparametric procedure to estimate the preference parameters of a binary choice model under uncertainty. In the model, the agent's decision rule is affected by the conditional expectation. We nonparametrically estimate the conditional expectation in the first stage. Then, in the second stage, the preference parameters are estimated by the smoothed maximum score method. We establish the consistency and asymptotic distribution of the two-stage estimator. Furthermore, we also characterize the conditions under which the first-stage nonparametric estimation will not affect the asymptotic distribution of the smoothed maximum score estimator. Monte Carlo simulation results demonstrate that our proposed estimator performs well in finite samples.