Intercept Estimation in Nonlinear Sample Selection Models

Abstract

The intercept in endogenous selection models is of fundamental importance for the evaluation of average treatment effects. While various intercept estimators for additive linear selection models exist, there are currently no estimators for nonlinear selection models. This paper introduces estimators for semiparametric nonlinear selection models, where the joint distribution of the error terms remains unspecified. We consider models where the intercept and slope parameters can be separately identified. If the selection equation satisfies an index restriction, the resulting estimator is based on a least squares criterion function with a nonparametric correction term. This estimator is asymptotically normal at a univariate nonparametric rate, even in cases of irregular identification. In a second step, we relax the index restriction in the selection equation and adopt a nonparametric propensity score specification. We suggest a local nonlinear least squares estimator, which only uses observations close but not too close to the boundary. Such an estimator exhibits a slower convergence rate than the first one, but is robust against mis-specification of the propensity score. The empirical illustration studies the effect of private health insurance on health care utilization using count data. We find that our estimates of this effect differ from those of various parametric models (not) controlling for selection.