Root-$n$ Asymptotically Normal Maximum Score Estimation

TL;DR

This paper demonstrates that using strictly concave surrogate score functions can achieve root-$n$ convergence and asymptotic normality in maximum score estimation, improving inference in binary choice models.

Contribution

It introduces conditions under which surrogate functions enable root-$n$ convergence and normality, addressing longstanding challenges in maximum score estimation.

Findings

Simulation studies confirm root-$n$ convergence.

Asymptotic normality of the estimator is validated.

Standard inference methods are shown to be valid.

Abstract

The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges at a slower-than-root-$n$ rate to a nonstandard limiting distribution. We investigate conditions under which strictly concave surrogate score functions can be employed to achieve identification through a smooth criterion function. This criterion enables root-$n$ convergence to a normal limiting distribution. While the conditions to guarantee these desired properties are nontrivial, we characterize them in terms of primitive conditions. Extensive simulation studies support, the root-$n$ convergence rate, the asymptotic normality, and the validity of the standard inference methods.