Parametric Nonlinear Regression with Endogenous Switching

Based on the insightful work of Olsen (1980) for the linear context, a generic and unifying framework is developed that affords a simple extension of the classical method of Heckman (1974, 1976, 1978, 1979) to a broad class of nonlinear regression models involving endogenous switching and its two most common incarnations, endogenous sample selection and endogenous treatment effects. The approach should be appealing to applied researchers for three reasons. First, econometric applications involving endogenous switching abound. Secondly, the approach requires neither linearity of the regression function nor full parametric specification of the model. It can, in fact, be applied under the minimal parametric assumptions—i.e., specification of only the conditional means of the outcome and switching variables. Finally, it is amenable to relatively straightforward estimation methods. Examples of applications of the method are discussed.