Symmetric generalized Heckman models

TL;DR

This paper introduces a new class of symmetric generalized Heckman models that extend traditional sample selection models by incorporating symmetric distributions, allowing for more flexible modeling of censored data with correlated variables.

Contribution

It proposes a novel class of Heckman models based on symmetric distributions, adding variables to dispersion and correlation parameters, and demonstrates their effectiveness through simulations and real data analysis.

Findings

The models perform well in Monte Carlo simulations.

Application to real data illustrates improved flexibility.

Models effectively handle censored data with correlated variables.

Abstract

The sample selection bias problem arises when a variable of interest is correlated with a latent variable, and involves situations in which the response variable had part of its observations censored. Heckman (1976) proposed a sample selection model based on the bivariate normal distribution that fits both the variable of interest and the latent variable. Recently, this assumption of normality has been relaxed by more flexible models such as the Student-t distribution (Marchenko and Genton, 2012; Lachos et al., 2021). The aim of this work is to propose generalized Heckman sample selection models based on symmetric distributions (Fang et al., 1990). This is a new class of sample selection models, in which variables are added to the dispersion and correlation parameters. A Monte Carlo simulation study is performed to assess the behavior of the parameter estimation method. Two real data sets are analyzed to illustrate the proposed approach.