Semiparametric instrumental variable estimation of treatment response models

This article introduces a new class of instrumental variable (IV) estimators for linear and nonlinear treatment response models with covariates. The rationale for focusing on nonlinear models is that, if the dependent variable is binary or limited, or if the effect of the treatment varies with covariates, a nonlinear model is appropriate. In the spirit of Roehrig (Econometrica 56 (1988) 433), identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest. One virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well-defined approximation to a treatment response function under functional form misspecification. In contrast to some usual IV models, heterogeneity of treatment effects is not restricted by the identification conditions. The ideas and estimators in this article are illustrated using IV to estimate the effects of 401(k) retirement programs on savings.