No abstract

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. In other words, our model is parsimonious and does not require the transformation of positive outcomes. 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.

Many proposals have emerged as alternatives to the Heckman selection model, mainly to address the non-robustness of its normal assumption. The 2001 Medical Expenditure Panel Survey data is often used to illustrate this non-robustness of the Heckman model. In this paper, we propose a generalization of the Heckman sample selection model by allowing the sample selection bias and dispersion parameters to depend on covariates. We show that the non-robustness of the Heckman model may be due to the assumption of the constant sample selection bias parameter rather than the normality assumption. Our proposed methodology allows us to understand which covariates are important to explain the sample selection bias phenomenon rather than to only form conclusions about its presence. Further, our approach may attenuate the non-identifiability and multicollinearity problems faced by the existing sample selection models. We explore the inferential aspects of the maximum likelihood estimators (MLEs) for our proposed generalized Heckman model. More specifically, we show that this model satisfies some regularity conditions such that it ensures consistency