Semiparametric estimation of separable models with possibly limited dependent variables

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.