Maximum Score Estimation of Preference Parameters for a Binary Choice Model under Uncertainty

TL;DR

This paper introduces a two-stage maximum score estimation method for binary choice models under uncertainty, accounting for nonparametric estimation of conditional expectations and establishing theoretical properties.

Contribution

It develops a novel two-stage estimation framework for preference parameters in binary choice models with uncertainty, including consistency, convergence rates, and asymptotic distribution results.

Findings

Estimator is consistent and converges at a specified rate.

Asymptotic equivalence to single-stage estimator under certain conditions.

Monte Carlo simulations demonstrate finite-sample performance.

Abstract

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.