Bayesian Inference For Normal-Reciprocal Gamma Stochastic Frontier Model

The stochastic frontier model is widely used to estimate the product efficiency. If we know the factors of inefficiency, we can set goals to promote and provide strategies to save energies and reduce wastes. So to analyse the model is useful.The stochastic frontier model is modified to allow the inefficiency term to follow a reciprocal Gamma distribution. Bayesian inference for the parameter of the normal-reciprocal Gamma stochastic frontier model is employed by using Gibbs sampling. For each model parameter, the posterior distribution is derived. A simulation study is con-ducted for small and medium sized samples. Prior sensitivity analysis is also conducted. The real electric power company generation data is analysed by this model. Some native ports data are collected,we use this model to analyse the efficiency of native ports.The simulation study shows that the Bayesian estimate is very close to its true value even for small and medium sized samples. Prior sensitivity analysis illustrates that the means of the posterior distributions of all parameters are relatively robust. The real electric power company generation data analysis evidence that the normal-reciprocal gamma stochastic frontier model is superior to the other stochastic frontier models for that it has a larger share of frontier variance to overall variance.In discussing the Gibbs sampling strategy, for the sampling efficiency of using stan-dard distribution as control function is very low in accept-reject sampling, so we construct a new distribution density as the control function. We first sample from the constructed distribution density by synthetic method, and finally realize the sampling by accept-reject sampling. This method can greatly improve the computational efficiency of Bayesian in-ference for the normal-reciprocal Gamma stochastic frontier model.