A flexible stochastic production frontier model with panel data

We propose a flexible stochastic production frontier model with fixed effects for the panel data in which the semiparametric frontier is additive with bivariate interactions. To avoid potential misspecification and/or "wrong skew problem" due to distributional assumptions, we model the conditional mean of the inefficiency to depend on environmental variables and to be known up to a vector of parameters. We propose a difference-based estimator for parameters characterizing the conditional mean of the inefficiency term, a profile series estimator, and a kernel-based one-step backfitting estimator for the frontier to facilitate inference. We establish their asymptotic properties and show that each component in the frontier estimated by the kernel-based backfitting has the same asymptotic distribution as the one estimated with the true knowledge on the other components in the frontier (i.e., the oracle property). Through a Monte Carlo study, we demonstrate that the proposed estimators perform well in finite samples. Utilizing a panel of Chinese firm-level data in 2000-2006, we apply our method to estimate the frontier and efficiency scores and conclude that export plays a significant role in reducing the efficiency of firms.