Robust Analysis of Sample Selection Models through the R Package ssmrob

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

Robustness in sample selection models

The problem of non-random sample selectivity often occurs in practice in many different fields. In presence of sample selection, the data appears in the sample according to some selection rule. In these cases, the standard tools designed for complete samples, e.g. ordinary least squares, produce biased results, and hence, methods correcting this bias are needed. In his seminal work, Heckman proposed two estimators to solve this problem. These estimators became the backbone of the standard statistical analysis of sample selection models. However, these estimators are based on the assumption of normality and are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. In this thesis we develop a general framework to study the robustness properties of estimators and tests in sample selection models. We use an infinitesimal approach, which allows us to explore the robustness issues and to construct robust estimators and tests

On the Robustness of Two-Stage Estimators

The aim of this note is to provide a general framework for the analysis of the robustness properties of a broad class of two-stage models. We derive the influence function of a general two-stage M-estimator, present the general form of its asymptotic variance, and provide its interpretation. Finally, we illustrate our results in the case of the two-stage maximum likelihood estimator, two-stage least squares estimator and in the estimation of time series models. Keywords: Asymptoticvariance; Boundedinfluencefunction; M-estimator; Robustestimator; Time series; Two-stage least squares; Two-stage maximum likelihood.

Robust inference in sample selection models

The problem of non-random sample selectivity often occurs in practice in many fields. The classical estimators introduced by Heckman are the backbone of the standard statistical analysis of these models. However, these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. We develop a general framework to study the robustness properties of estimators and tests in sample selection models. We derive the influence function and the change-of-variance function of Heckman’s two-stage estimator, and we demonstrate the non-robustness of this estimator and its estimated variance to small deviations from the model assumed. We propose a procedure for robustifying the estimator, prove its asymptotic normality and give its asymptotic variance. Both cases with and without an exclusion restriction are covered. This allows us to construct a simple robust alternative to the sample selection bias test. We illustrate the use of our new methodology in an analysis of ambulatory expenditures and we compare the performance of the classical and robust methods in a Monte Carlo simulation study

Robust Estimation of Probit Models with Endogeneity

Probit models with endogenous regressors are commonly used models in economics and other social sciences. Yet, the robustness properties of parametric estimators in these models have not been formally studied. The influence functions of the endogenous probit model's classical estimators (the maximum likelihood and the two-step estimator) are derived and their non-robustness to small but harmful deviations from distributional assumptions is proven. A procedure to obtain a robust alternative estimator is proposed, its asymptotic normality is proven and its asymptotic variance is provided. A simple robust test for endogeneity is also constructed. The performance of the robust and classical estimators is compared in Monte Carlo simulations with different types of contamination scenarios. The use of the robust estimator is illustrated in several empirical applications