Heckman selection-t model: parameter estimation via the EM-algorithm

TL;DR

This paper extends the Heckman selection model by incorporating a Student's-t distribution for errors, providing a robust EM algorithm for parameter estimation, and demonstrating improved performance over the normal assumption in simulations and real data.

Contribution

It introduces a Heckman selection-t model with an efficient EM algorithm for maximum likelihood estimation, addressing non-normal error distributions.

Findings

The Heckman selection-t model is more robust than the normal model in heavy-tailed scenarios.

Simulations show the vulnerability of the normal model and the robustness of the t-model.

Real data examples demonstrate the practical usefulness of the proposed methods.

Abstract

Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, in some applications, the distribution of the error term departs significantly from normality, for instance, in the presence of heavy tails and/or atypical observation. In this paper, we explore the Heckman selection-t model where the random errors follow a bivariate Student's-t distribution. We develop an analytically tractable and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student's-t distributions. Simulations studies show the vulnerability of the Heckman selection-normal model, as well as the robustness aspects of the Heckman selection-t model. Two real examples are analyzed, illustrating the usefulness of the proposed methods. The proposed algorithms and methods are implemented in the new R package HeckmanEM.