Random Effects Probit and Logit: The Right Marginal Effects for the Right Econometric Specification

Abstract

Random effects probit and logit specifications are common when analyzing economic experiments. Stata's fitted values from these estimations, however, appear to fit data poorly compared to their pooled counterparts. This is entirely due to Stata reporting the median predictive value, when practitioners expect the mean predictive value. This propagates into marginal effects calculations, which may lead researchers to under- or over-state the economic significance of results. We demonstrate a simple procedure for calculating the correct predictive mean and mean marginal effect in Stata.

Keywords: Random effects, probit, logit, marginal effect, prediction

JEL Classification: C23, C24, C87