A Generalized Heckman Model With Varying Sample Selection Bias and Dispersion Parameters

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.