A new semiparametric stochastic frontier model: addressing inefficiency and model flexibility using panel data

Recent stochastic frontier models eschew distributional assumptions to robustify model misspecification. However, such models are potentially subject to several restrictions, particularly for identification of inefficiency mean function under general conditions. This paper proposes a new semiparametric stochastic frontier models with fixed effects to resolve all the restrictions with four new features. First, we specify a nonparametric conditional mean function of inefficiency, estimate it separately from frontier functions, and impose its non-negativity constraint. Second, we relax conventional assumption on the separability between inefficiency and frontier determinants and allow time-varying environmental variables to affect both frontier and inefficiency functions. Third, we generalize commonly used parametric frontier to a semiparametric smooth coefficient frontier, improving model flexibility and uncovering heterogeneous effects of inputs. Fourth, our model circumvents the curse of dimensionality problem by adopting single-index structures, which effectively incorporates potentially large number of frontier and inefficiency determinants to mitigate omitted variable bias. We employ a three-step nonparametric estimator and demonstrate its appealing finite-sample performance through simulations. By conducting an empirical analysis within the Italian banking sector, we demonstrate the superiority of our model compared to existing ones.