Joint Estimation and Bandwidth Selection in Partially Parametric Models

Abstract

We propose a single-step approach to estimating a model with both a known nonlinear parametric component and an unknown nonparametric component. We study the large sample behavior of a simultaneous optimization routine that estimates both the parameter vector of the parametric component and the bandwidth vector used to smooth the unknown function. In our application, we estimate a partially constant elasticity of substitution production function and uncover results that are relevant for policy-driven conclusions stemming from macroeconomic theory. An attempt to make the parametric component linear in parameters leads to parameter estimates that are economically infeasible, showing the need for our approach in practice.