In this paper we propose a model which includes both a known (potentially) nonlinear parametric component and an unknown nonparametric component. This approach is feasible given that we estimate the finite sample parameter vector and the bandwidths simultaneously. We show that our objective function is asymptotically equivalent to the individual objective criteria for the parametric parameter vector and the nonparametric function. In the special case where the parametric component is linear in parameters, our single-step method is asymptotically equivalent to the two-step partially linear model estimator in Robinson (1988). Monte Carlo simulations support the asymptotic developments and show impressive finite sample performance. We apply our method to the case of a partially constant elasticity of substitution production function for an unbalanced sample of 134 countries from 1955-2011 and find that the parametric parameters are relatively stable for different nonparametric control variables in the full sample. However, we find substantial parameter heterogeneity between developed and developing countries which results in important differences when estimating the elasticity of substitution.
Daniel Henderson is a professor of economics and the J. Weldon and Delores Cole Faculty Fellow at the University of Alabama and an associate expert at FWO (Research Foundation - Flanders) in Brussels, Belgium. He was formerly an associate and assistant professor of economics at the State University of New York at Binghamton. He has held visiting appointments at the Université catholique de Louvain, in Louvain-la-Neuve, Belgium (Institute of Statistics), Xiamen University (Wang Yanan Institute for Studies in Economics) in Xiamen, China and at Southern Methodist University, in Dallas, Texas (Department of Economics). He received his Ph.D. in economics from the University of California, Riverside in 2003 and his B.A. in economics from the University of California, Davis in 1998. His research focus is in applied nonparametric microeconometrics with an emphasis in the economics of education, and economic growth and development. He has also written papers examining the determinants of child health, environmental economics, and international trade. His work has been published in journals such as Computational Statistics and Data Analysis, Economic Journal, Economics of Education Review, European Economic Review, International Economic Review, Journal of Applied Econometrics, Journal of Business and Economic Statistics, Journal of Econometrics, Journal of Human Resources, Journal of the Royal Statistical Society, Oxford Bulletin of Economics and Statistics, and Review of Economics and Statistics.