Bivariate Non-Normality in the Sample Selection Model

Since the seminal paper by [Heckman, J. J. 1974. “Shadow Prices, Market Wages, and Labor Supply.” Econometrica 42: 679–694], the sample selection model has been an essential tool for applied economists and arguably the most sensitive to sources of misspecification among the standard microeconometric models involving limited dependent variables. The need for alternative methods to get consistent estimators has led to a number of estimation proposals for the sample selection model under non-normality. There is a marked dichotomy in the literature that has developed in two conceptually different directions: the bivariate normality assumption can be either replaced, by using copulae, or relaxed/removed, relying on semi- and non-parametric estimators. This paper surveys the more recent proposals on the estimation of the sample selection model that deal with distributional misspecification giving the practitioner a unified framework of both parametric and semi/non-parametric options.