Estimating Average Treatment Effect by Nonlinear Endogenous Switching Regression With an Application in Botswana Fertility

Abstract

This study explores the Average Treatment Effects (ATE) estimator proposed by Terza (2009)’s Nonlinear Full Endogenous Treatment (NFES) model, where count dependent and binary treatment variables are present. Asymptotic distribution of ATE estimators based on NFES model is provided to show that nonlinear estimators have additional terms in asymptotic variance of which magnitudes depend on population coefficient. Due to their presence, the asymptotic variance of nonlinear estimators can be either larger or smaller than the linear counterparts depending on the values of coefficients. It turns out that the nonlinear ATE estimators are more efficient than linear estimators when the ATE conditional on covariates has small variance. An application to Botswana fertility is given.