Sharp and Robust Estimation of Partially Identified Discrete Response Models

TL;DR

This paper introduces a new class of estimators for partially identified discrete response models that are both sharp and robust, addressing limitations of classical estimators in discrete covariate settings.

Contribution

The paper proposes a novel estimator based on quantiles of random sets, extending to static and dynamic panel data models, improving robustness and sharpness.

Findings

Classical estimators lose sharpness and robustness in partial identification.

The proposed estimators are both sharp and robust, based on quantiles of random sets.

The approach applies to both cross-sectional and panel data models.

Abstract

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are discrete. In this paper we find that classical estimators, including the maximum score estimator, (Manski (1975)), loose their attractive statistical properties without point identification. First of all, they are not sharp with the estimator converging to an outer region of the identified set, (Komarova (2013)), and in many discrete designs it weakly converges to a random set. Second, they are not robust, with their distribution limit discontinuously changing with respect to the parameters of the model. We propose a novel class of estimators based on the concept of a quantile of a random set, which we show to be both sharp and robust. We demonstrate that our approach extends from cross-sectional settings to classical static and dynamic discrete panel data models.