Estimation for Dynamic and Static Panel Probit Models with Large Individual Effects

TL;DR

This paper introduces new estimators for dynamic probit models with large individual effects in short panel data, addressing limitations of Heckman's maximum likelihood approach, and demonstrates their advantages through theoretical analysis and simulations.

Contribution

It proposes novel estimators for the dynamic parameter in panel probit models with large, random individual effects, improving upon Heckman's method.

Findings

New estimators have better performance with large individual effects.

Theoretical properties of estimators are established.

Simulation results show advantages over existing methods.

Abstract

For discrete panel data, the dynamic relationship between successive observations is often of interest. We consider a dynamic probit model for short panel data. A problem with estimating the dynamic parameter of interest is that the model contains a large number of nuisance parameters, one for each individual. Heckman proposed to use maximum likelihood estimation of the dynamic parameter, which, however, does not perform well if the individual effects are large. We suggest new estimators for the dynamic parameter, based on the assumption that the individual parameters are random and possibly large. Theoretical properties of our estimators are derived and a simulation study shows they have some advantages compared to Heckman's estimator.