Robust Analysis of Sample Selection Models through the R Package ssmrob

Abstract

The aim of this paper is to describe the implementation and to provide a tutorial for the R package ssmrob, which is developed for robust estimation and inference in sample selection and endogenous treatment models. The sample selectivity issue occurs in practice in various fields, when a non-random sample of a population is observed, i.e., when observations are present according to some selection rule. It is well known that the classical estimators introduced by Heckman (1979) are very sensitive to small deviations from the distributional assumptions (typically the normality assumption on the error terms). Zhelonkin, Genton, and Ronchetti (2016) investigated the robustness properties of these estimators and proposed robust alternatives to the estimator and the corresponding test. We briefly discuss the robust approach and demonstrate its performance in practice by providing several empirical examples. The package can be used both to produce a complete robust statistical analysis of these models which complements the classical one and as a set of useful tools for exploratory data analysis. Specifically, robust estimators and standard errors of the coefficients of both the selection and the regression equations are provided together with a robust test of selectivity. The package therefore provides additional useful information to practitioners in different fields of applications by enhancing their statistical analysis of these models.