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.