Nonparametric maximum likelihood methods for binary response models with random coefficients

TL;DR

This paper introduces a new computational approach for nonparametric maximum likelihood estimation in binary response models with random coefficients, enhancing flexibility and applicability in econometric analysis.

Contribution

It presents a novel, more computationally feasible method for NPMLE in binary response models, leveraging hyperplane arrangement geometry to improve upon existing techniques.

Findings

Enhanced computational tractability of NPMLE methods

Application to real-world modal choice data in Washington DC

Comparison showing advantages over deconvolution approaches

Abstract

Single index linear models for binary response with random coefficients have been extensively employed in many econometric settings under various parametric specifications of the distribution of the random coefficients. Nonparametric maximum likelihood estimation (NPMLE) as proposed by Cosslett (1983) and Ichimura and Thompson (1998), in contrast, has received less attention in applied work due primarily to computational difficulties. We propose a new approach to computation of NPMLEs for binary response models that significantly increase their computational tractability thereby facilitating greater flexibility in applications. Our approach, which relies on recent developments involving the geometry of hyperplane arrangements, is contrasted with the recently proposed deconvolution method of Gautier and Kitamura (2013). An application to modal choice for the journey to work in the Washington DC area illustrates the methods.