Semi-parametric modelling of inefficiencies in stochastic frontier analysis

We propose a novel penalized splines method to estimate a stochastic frontier model in which the frontier is linear and the inefficiency has a single index structure with unknown link function and a linear index. The approach is more flexible than the traditional methodology requiring a parametric link function and, at the same time, it does not incur the curse of dimensionality as a fully non-parametric approach. The procedure can be easily implemented using existing software. We give conditions for the model to be identified and provide some asymptotic results. We also use Monte Carlo simulations to show that the approach works well in finite samples in many situations when compared to the well specified maximum likelihood estimator. An application to the residential energy demand of US states is considered. In this case, the penalized splines approach estimates inefficiency functions that deviate substantially from those resulting from parametric maximum likelihood methods previously implemented.