Value of Sample Separation Information in a Sequential Probit Model

Abstract

We illustrate the estimation and identification of multi-step sequential probit models with and without stepwise sample separation information. The likelihood functions are explicitly derived to ease experimentation with such models. We used data on health, activity limitations, demographic traits and work from the Survey of Income and Program Participation (SIPP) and exactly matched them with Social Security administrative records to showcase our theoretical points. Using a Monte Carlo simulation technique, our results suggest that the correlations in errors across equations may arise due to unobserved individual heterogeneity. Using a novel marginal likelihood approach, we also estimated the above sequential probit model without the sample separation information for the purpose of direct comparison. In terms of both in-sample and jackknife-type out-of-sample predictive analysis, the value of modelling the underlying sequential structure of the determination process in generating correct membership probabilities of belonging to a particular group is confirmed. JEL: C31, C34, C 35, I12, I18