Semiparametric estimation of separable models with possibly limited dependent variables

Abstract

In this paper we introduce a general method for estimating semiparametrically the different components in separable models+ The family of separable models is quite popular in economic research because this structure offers clear interpretation, has straightforward economic consequences, and is often justified by theory+ This family is also of statistical interest because it allows us to estimate high-dimensional complexity semiparametrically without running into the curse of dimensionality+ We consider even the case when multiple indices appear in the objective function; thus we can estimate models that are typical in economic analysis, such as those that contain limited dependent variables+ The idea of the new method is mainly based on a generalized profile likelihood approach+ Although this requires some hypotheses on the conditional error distribution, it yields a quite general usable method with low computational costs but high accuracy even for small samples+ We give estimation procedures and provide some asymptotic theory+ Implementation is discussed; simulations and an application demonstrate its feasibility and good finite-sample behavior.