Nonparametric Estimation of Regression Functions with Both Categorical and Continuous Data ∗ Jeff Racine Department of Economics, University of South Florida Tampa, FL 33620, USA Qi Li Department of Economics, Texas A&M University College Station, TX 77843, USA Abstract In this paper we propose a method for nonparametric regression which admits continuous and categorical data in a natural manner using the method of kernels. A data-driven method of bandwidth selection is proposed, and we establish the asymptotic normality of the estimator. We also establish the rate of convergence of the cross-validated smoothing parameters to their benchmark optimal smoothing parameters. Simulations suggest that the new estimator performs much better than the conventional nonparametric estimator in the presence of mixed data. An empirical application to a widely used and publicly available dynamic panel of patent data demonstrates that the out-of-sample squared prediction error of our proposed estimator is only 14% to 20% of that obtained by some popular parametric approaches which have been used to model this dataset. Keywords: Discrete variables, nonparametric smoothing, cross-validation, asymptotic normal- ity. * Li’s research is supported by the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanity Research Council of Canada, and by the Bush Program in the Economics of Public Policy. Racine would like to thank the USF Division of Sponsored Programs for their continuing support.