Extensive and intensive margin effects in sample selection models: racial effects on wages

In sample selection models, a treatment can influence the observed outcome in two ways: by affecting the binary selection or participation decision and by affecting the latent outcome. The former is called the ‘extensive margin effect’, and the latter is called the ‘intensive margin effect’. Despite the popularity of these effects, however, the intensive margin effect does not have the traditional causal parameter interpretation because it is conditioned on the selecting or participating decision, which is a post-treatment variable possibly affected by the treatment. The paper presents a causal framework for sample selection models and introduces various subpopulation effects. It is difficult to separate such effects in general; however, in certain popular models (nearly parametric sample selection models, semiparametric ‘independence models’, semiparametric zero-censored models and ‘polynomial approximation’ models) with linear latent equations, they are separately identified and easily estimable with probit and least squares estimators. An empirical analysis is provided to illustrate these causal effects in sample selection models.