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Birnbaum–Saunders sample selection model

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journal contribution
posted on 2020-08-24, 07:28 authored by Fernando de Souza Bastos, Wagner Barreto-Souza

The sample selection bias problem occurs when the outcome of interest is only observed according to some selection rule, where there is a dependence structure between the outcome and the selection rule. In a pioneering work, J. Heckman proposed a sample selection model based on a bivariate normal distribution for dealing with this problem. Due to the non-robustness of the normal distribution, many alternatives have been introduced in the literature by assuming extensions of the normal distribution like the Student-t and skew-normal models. One common limitation of the existent sample selection models is that they require a transformation of the outcome of interest, which is common R+-valued, such as income and wage. With this, data are analyzed on a non-original scale which complicates the interpretation of the parameters. In this paper, we propose a sample selection model based on the bivariate Birnbaum–Saunders distribution, which has the same number of parameters that the classical Heckman model. Further, our associated outcome equation is R+-valued. We discuss estimation by maximum likelihood and present some Monte Carlo simulation studies. An empirical application to the ambulatory expenditures data from the 2001 Medical Expenditure Panel Survey is presented.


Wagner Barreto-Souza thanks the agencies CNPq-Brazil [grant number 305543/2018-0], FAPEMIG-Brazil [grant number APQ-00786-14], and KAUST Research Fund NIH 1R01EB028753-01 for the financial support.