  This paper develops maximum score estimation of preference parameters in the
binary choice model under uncertainty in which the decision rule is affected by
conditional expectations. The preference parameters are estimated in two
stages: we estimate conditional expectations nonparametrically in the first
stage and then the preference parameters in the second stage based on Manski
(1975, 1985)'s maximum score estimator using the choice data and first stage
estimates. The paper establishes consistency and derives rate of convergence of
the two-stage maximum score estimator. Moreover, the paper also provides
sufficient conditions under which the two-stage estimator is asymptotically
equivalent in distribution to the corresponding single-stage estimator that
assumes the first stage input is known. These results are of independent
interest for maximum score estimation with nonparametrically generated
regressors. The paper also presents some Monte Carlo simulation results for
finite-sample behavior of the two-stage estimator.
