Semiparametric estimation of weak and strong separable models

In this paper we introduce a general method for estimating semiparametrically the different components in weak or strong separable models. The family of separable models is quite popular in economic theory and empirical research as this structure offers clear interpretation, has straight forward economic consequences and often is justified by theory. As will be seen in this article they are also of statistical interest since they allow to estimate semiparametrically high dimensional complexity without running in the so called curse of dimensionality. Generalized additive models and generalized partial linear models are special cases in this family of models. The idea of the new method is mainly based on a combination of local likelihood and efficient estimators in non or semiparametric models. Although this imposes some hypothesis on the error distribution this yields a very general usable method with little computational costs and high exactness even for small samples. E. g. it enables us to include models for censored and truncated variables which are quite common in quantitative economics. We give the estimation procedures and provide asymptotic theory for them. Implementation is discussed, simulations and an application demonstrate its feasibility in finite sample behavior