Bayesian Robust Inference of Sample Selection Using Selection-t Models

TL;DR

This paper develops Bayesian methods for selection-t models to robustly analyze sample selection, especially when error distributions have heavy tails, improving over traditional Normal-based models.

Contribution

It introduces Bayesian procedures using data augmentation and parameter expansion for selection-t models with continuous or binary outcomes, avoiding complex likelihood calculations.

Findings

Selection models with Normal errors are vulnerable to heavy tails.

Selection models with t errors demonstrate robustness in simulations.

Real data analyses reveal heavy-tailed errors and sensitivity of selection effects to distribution assumptions.

Abstract

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton proposed a selection-t model to perform frequentist' robust analysis of sample selection. Instead of using their maximum likelihood estimates, our paper develops new Bayesian procedures for the selection-t models with either continuous or binary outcomes. By exploiting the Normal mixture representation of the t distribution, we can use data augmentation to impute the missing data, and use parameter expansion to sample the restricted covariance matrices. The Bayesian procedures only involve simple steps, without calculating analytical or numerical derivatives of the complicated log likelihood functions. Simulation studies show the vulnerability of the selection models with Normal errors, as well as the robustness of the selection models with t errors. Interestingly, we find evidence of heavy-tailedness in three real examples analyzed by previous studies, and the conclusions about the existence of selection effect are very sensitive to the distributional assumptions of the error terms.