Bayesian Inference For The Dynamic Heteroscedasticity Stochastic Frontier Model

The stochastic frontier model is often used to measure the productive efficiency of single or multiple units. By analyzing the productive efficiency, the problems existed in the production can be found and solved. The stochastic frontier model plays an important role in productive analysis.If heterogeneity of the "inefficiency" term being disregarded, it will result in the incorrect estimate of this term in the stochastic frontier model. By combining the influence from characteristic differences of individuals with the time-varying property of variance, a dynamic heteroscedasticity stochastic frontier model is proposed. By the Gibbs sampling, the methodology for Bayesian analysis of the dynamic heterogeneity stochastic frontier model is given. For each model parameter, the prior distribution is specified and the posterior distribution is derived. The specific strategies of Gibbs sampling are discussed. A simulation study shows that under the criterion of minimizing the posterior mean square error, the value of parameter estimate is very close to the true value, in spite of the small and medium sized samples. Finally, the model is used to analyze the efficiency of the electric power company and the listed port and shipping companies based on the real data,From the Bayesian analysis based on the real generation data of the electric power company, it is evidenced that the variance of the "inefficiency"term is time-varying, and the inefficiency term is effected by the customer density. The model is used to analyze the operating efficiency of the listed port, and shipping companies, it is revealed that the variance of the "inefficiency" term depends heavily on the preceding variance and square of error.For the parameters in the inefficiency, the posterior distributions are not the standard distributions, and the acceptance efficiency of random walk M-H algorithm and Griddy Gibbs sampling is very low in the hierarchical models. The proposal distributions are based on an approximated GARCH model. A new ARMA model is constructed by means of the conditional variance equation. Finally, the parameter sampling is realized by the Metropolis-Hastings sampling. This method can greatly improve the sampling efficiency.