Intercept Estimation in Nonlinear Sample Selection Models

Abstract

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which either the monotonic index restriction does not hold and/ or the set of observations with propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behaviour in a Monte Carlo study, and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.

Keywords: Irregular Identification, Selection Bias, Local Polynomial, Trimming, Count Data.

JEL Classification: C14, C21, C24