Nonparametric Identication and Estimation of Production Functions Using Control Function Approaches to Endogeneity

Using control function approaches to endogeneity, nonparametric identi…cation is established for production functions under weak conditions. The distribution of productivity is also recovered nonparametrically. Instead of "inverting out" the productivity shock, control functions "expect out" unobserved shocks. Controls are estimated using lagged levels of capital and labor as instruments, and the control function condition is justi…ed by a Markov property of productivity shock along with uncertainty faced by …rms. Nonparametric estimation of production functions then closely follows the identi…cation strategy without imposing extra modeling assumptions. A kernel estimator is proposed for nonparametric regressions with endogeneity. The estimator achieves the optimal uniform convergence rate if the preliminary estimators of controls converge su¢ ciently fast. The …nite sample performance is illustrated by extensive Monte-Carlo experiments. The application to the Chilean panel shows the empirical relevance. The proposed method yields reasonable estimates, and the empirical distribution of productivity is non-normal. Keywords: Production Functions, Endogeneity, Nonparametric Identi…cation, Control Function Approaches, Kernel Estimators, Optimal Uniform Convergence, Asymptotic Normality. JEL Codes: C14, C23, C51, D24. I am grateful to my advisor Quang Vuong for his invaluable guidance and encouragement. Comments from Mark Roberts, Joris Pinkse, Isabelle Perrigne and Runze Li are really appreciated. I also think Mark Roberts and James Tybout for providing the data set used in this paper. All errors are mine and comments are welcome to [email protected].