Stochastic Frontier Models With Random Coefficients

Production Function is an important idea in Economy Mathematics and Quantity Economics. It is a technology relationship which indicates the maximum production under certain technologies with a group of production requisites. Usually we call a production function a production frontier or frontier production function if it answers for the definition accurately, which different from the average production function based on conditional regression statistics. Production frontier contacts with the technical inefficiency, and it is also tallies with the boundary of possible production set. Production frontier is an important tool in measuring the efficiency of production. With the knowledge of the inefficient root and degree in production actions, one can bring forward advance countermeasures and aims, and with a result of saving energies and reducing waste, asd it is also the counterpart of cost frontier function, so it is meaningful to study the frontier.The main methods in studying the production frontier is parametric method and the non-parametric method. The main content of this dissertation is as follows:(1) Based on the rational analysis of production set and production function, the author analyses and summarizes the non-parametric method of studying the production frontier-Data Envelopment Analysis(DEA), and points out its finity.(2) The so called parametric method of studying the production frontier including positive frontier and stochastic frontier models. Analyze and summarize the methods of positive models. Based on the rational analysis of production action, for the difficulties of estimation with double error components, taking Cobb-Douglas production function as an example, the author adopts maximum likelihood estimation to construct the solving model of the stochastic frontier models with management components distributes according to truncated normal distribution, half normal distribution, exponential distribution and gamma distribution. Under the assumption of coefficients distributed according to multiply normal distributions, the solving models of stochastic frontier models with random coefficients are constructed by adopting maximum likelihood estimation.(3) Following standard practice in Bayesian analysis of stochastic frontiers, we treat the management components as parameters, based on one method of MCMC -Gibbs sampling, under the assumption of different distributions of management components, and infer the Bayesian estimation of common stochastic frontiermodels and the stochastic frontiers with random coefficients. Also we provide the Bayesian estimation of stochastic frontier models with coefficients distributes according to special multiply normal. Measurement method of inefficiency also is inferred and proved.(4) Demonstrations show maximum likelihood estimation is a wonderful way to decompose the errors in stochastic frontier models. The difference between the common stochastic frontier models and the stochastic frontier models with random coefficients is compared and analyzed and the limitation of common stochastic frontier models is pointed out.