Nonparametric identification and estimation of production functions using control function approaches to endogeneity

Endogeneity and misspecification of models are two main concerns in structural estimation, which usually involves the optimal choices of economic agents with unobservable characteristics. In estimating production functions, input variables are endogenous because input decisions depend on unobservable productivity shocks. Economic theory rarely suggests functional forms for either production functions or the distribution of productivity.;Using control function approaches to endogeneity, nonparametric identification is established for production functions under weak conditions. The distribution of productivity is also recovered nonparametrically. Instead of "inverting out" productivity shocks, the control functions "smooth out" the unobserved shocks. Controls are constructed using lagged levels of inputs as instruments, and the control function condition is justified by a Markov property of productivity shocks along with interim uncertainty of productivity faced by firms.;Nonparametric estimation of production functions then closely follows the identification strategy without imposing extra modeling assumptions. A kernel estimator is proposed for nonparametric regressions with endogeneity. If the preliminary estimators of controls converge sufficiently fast, the estimator achieves the optimal rate of uniform convergence and the asymptotic variance is unaffected by preliminary estimators.;The same strategy also applies to parametric identification. When the Cobb-Douglas production function is considered, a partial linear model arises, where the parametric part represents the production function and the nonparametric part is the control function to account for the endogeneity of input variables. A density-weighted estimator is proposed for the partially linear model with constructed controls, and n -consistency is established under the given conditions.;The finite sample performances of the proposed estimators are illustrated by extensive Monte-Carlo experiments. The application to the Chilean panel shows the empirical relevance of the identification strategy and estimation procedure proposed in this thesis. The resulting estimates are reasonable and show that some parametric specifications may be restrictive.