cjas_a_1780570_sm1290.pdf (231.66 kB)

# Birnbaum–Saunders sample selection model

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.

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