Finite Sample Inference for the Maximum Score Estimand

TL;DR

This paper introduces a finite sample inference method for the maximum score estimand in binary response models, applicable regardless of sample size or parameter identification status, using distributional properties and moment inequalities.

Contribution

It develops a novel finite sample inference approach for the maximum score estimand that is valid for any sample size and identification status, leveraging distributional properties and moment inequalities.

Findings

Method is valid for any sample size and identification status

Simulation studies support theoretical power properties

Inference relies on distributional properties of outcomes conditional on covariates

Abstract

We provide a finite sample inference method for the structural parameters of a semiparametric binary response model under a conditional median restriction originally studied by Manski (1975, 1985). Our inference method is valid for any sample size and irrespective of whether the structural parameters are point identified or partially identified, for example due to the lack of a continuously distributed covariate with large support. Our inference approach exploits distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on this size n sequence of exogenous covariates are constructed, and the test statistic is a monotone function of violations of sample moment inequalities. The critical value used for inference is provided by the appropriate quantile of a known function of n independent Rademacher random variables. We investigate power properties of the underlying test and provide simulation studies to support the theoretical findings.