Heckman sample-selection estimators under heteroskedasticity

Abstract

Abstract.

This article provides a practical guide for Stata users on the consequences of heteroskedasticity in sample-selection models. We review the properties of two Heckman sample-selection estimators, full-information maximum likelihood and limited-information maximum likelihood (LIML), under heteroskedasticity. In this case, full-information maximum likelihood is inconsistent, while LIML can be consistent in certain settings. For the LIML estimator under heteroskedasticity, we show that standard Stata commands are unable to produce correct standard errors and instead suggest the community-contributed command gtsheckman (Carlson 2022, Statistical Software Components S459109, Department of Economics, Boston College; 2024, Stata Journal 24: 687–710). Because heteroskedasticity affects the performance of these two estimators, we also offer guidance on how to test for heteroskedasticity and the conditions needed for the LIML estimator to be consistent. The Monte Carlo simulations illustrate that the suggested testing procedures perform well in terms of appropriate size and power.