Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators

Abstract

This paper compares generalized method of moments (GMM) and simulated maximum likelihood (SML) approaches to the estimation of the panel probit model. Both techniques circumvent multiple integration of joint density functions without the need to restrict the error term variance- covariance matrix of the latent normal regression model. Particular attention is paid to a three-stage GMM estimator based on nonparametric estimation of the optimal instruments for given conditional moment functions. Monte Carlo experiments are carried out which focus on the small sample consequences of misspecification of the error term variance-covariance matrix. The correctly specified experiment reveals the asymptotic efficiency advantages of SML. The GMM estimators outperform SML in the presence of misspecification in terms of multiplicative heteroskedasticity. This holds in particular for the three-stage GMM estimator. Allowing for heteroskedasticity over time increases the robustness with respect to misspecification in terms of ultiplicative heteroskedasticity. An application to the product innovation activities of German manufacturing firms is presented.