Goodness-of-fit in Optimizing Models of Production: A Generalization with a Bayesian Perspective

We propose a very general approach for modeling production technologies that allows for modeling both inefficiency and noise that are specific for each input and each output. The approach is based on amalgamating ideas from nonparametric activity analysis models for production and consumption theory with stochastic frontier models. We do this by effectively re-interpreting the activity analysis models as simultaneous equations models in Bayesian compression and artificial neural networks frameworks. We make minimal assumption about noise in the data and we allow for flexible approximations to input- and output-specific slacks. We use compression to solve the problem of an exceeding number of parameters in general production technologies and we also incorporate environmental variables in the estimation. We present Monte Carlo simulation results and empirical illustration and comparison of this approach for US banking data.