The Plateau Problem in the Heteroskedastic Probit Model

TL;DR

This paper investigates why traditional local search methods struggle to reliably estimate parameters in the heteroskedastic probit model, identifying specific features of the likelihood function that cause convergence issues and proposing solutions.

Contribution

It reveals the causes of convergence failures in heteroskedastic probit parameter estimation and suggests modifications to improve the reliability of local search methods.

Findings

Local search methods often fail to converge in heteroskedastic probit models.

Features of the likelihood function contribute to convergence issues.

Proposed amendments improve estimation stability.

Abstract

In parameter determination for the heteroskedastic probit model, both in simulated data and in actual data, we observe a failure of traditional local search methods to converge consistently to a single parameter vector, in contrast to the typical situation for the regular probit model. We identify features of the heteroskedastic probit log likelihood function that we argue tend to lead to this failure, and suggest ways to amend the local search methods to remedy the problem.