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Robust inference in sample selection models
Author(s) -
Zhelonkin Mikhail,
Genton Marc G.,
Ronchetti Elvezio
Publication year - 2016
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12136
Subject(s) - estimator , robustness (evolution) , mathematics , inference , sample size determination , delta method , asymptotic distribution , monte carlo method , econometrics , m estimator , normality , statistics , variance (accounting) , selection (genetic algorithm) , computer science , artificial intelligence , economics , biochemistry , chemistry , accounting , gene
Summary 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.