Abstract
We use the concept of coarsened posteriors to provide robust Bayesian inference via coarsening in order to robustify posteriors arising from stochastic frontier models. These posteriors arise from tempered versions of the likelihood when at most a pre-specified amount of data is used, and are robust to changes in the model. Specifically, we examine robustness to changes in the distribution of the composed error in the stochastic frontier model (SFM). Moreover, coarsening is a form of regularization, reduces overfitting and makes inferences less sensitive to model choice. The new techniques are illustrated using artificial data as well as in a substantive application to large U.S. banks.
Highlights
The stochastic frontier model (SFM) is a standard tool in the estimation of efficiency from observed data
Bayesian analysis of SFM is widely used due to the convenience allowed by Markov Chain Monte Carlo in dealing with latent inefficiencies that are present in the model, under alternative distributional assumptions
Feng et al (2019) proposed a semiparametric model for stochastic frontier models, the one-sided error term is approximated by a log-transformed Rosenblatt-Parzen kernel density estimator
Summary
The stochastic frontier model (SFM) is a standard tool in the estimation of efficiency from observed data. Feng et al (2019) proposed a semiparametric model for stochastic frontier models, the one-sided error term is approximated by a log-transformed Rosenblatt-Parzen kernel density estimator. Standard inference in stochastic frontier models does not take into account outliers but, perhaps more importantly, deviations of the assumed distributions of two-sided and one-sided error terms from their actual counterparts. Rather than conditioning on the observed data assumed to be generated by the model, we condition on the event that the model generates data that are distributionally close to the observed data This technique allows examining robustness to changes in the distribution of the composed error in SFM.
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