Intercept Estimation in Nonlinear Sample Selection Models
40 Pages Posted: 25 Oct 2018
Date Written: October 1, 2018
The intercept in endogenous selection models is of fundamental importance for the evaluation of average treatment effects. While various intercept estimators for linear additive selection models exist, many other data types are modeled nonlinearly. This paper introduces estimators for nonlinear selection models, where the joint distribution of the error terms remains unspecified. We first consider models where the intercept and slope parameters can be separately identified, and 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. This estimator is a local nonlinear least squares estimator, which only uses observations close to 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. Our empirical illustration studies the effect of private health insurance on health care utilization. We find that our estimates differ from those of various parametric models (not) controlling for selection.
Keywords: Count Data, Selection Bias, Irregular Identification, Trimming
JEL Classification: C14, C21, C24
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