Parameters Solution Methods And Application Research Of Stochastic Frontier Models For Panel Data

Stochastic Frontier Analysis(SFA)is an important method of measuring technical efficiency and calculating total factor productivity.This method was proposed by Aigner et al.(1977),Meeusen and Broeck(1977)and Battese and Corra(1977),and has been widely used in empirical research for more than 40 years.In practical application,scholars also improve the model from several aspects.Pitt and Lee(1981)and Schmidt and Sickles(1984)were the first to combine the quantitative analysis method of panel data with the stochastic frontier model and established the stochastic frontier model of panel data.This model relaxes the assumptions of the stochastic frontier model and estimates process that no longer relies on error distribution assumptions while allowing error term and the correlation between variables.The details nature of the panel data of stochastic frontier model also makes the measurement of technical efficiency become more robust.In recent years,with the rise of regional economics and new economic geography,scholars in the field of economics pay more and more attention to the spatial information contained in the sample data.A large number of empirical studies have shown that economic variables often include spatial correlation and spatial heterogeneity.If the spatial interaction is neglected in the efficiency research,the deviation of efficiency measurement may be caused.Druska and Horrace(2004)who first applied the method of spatial econometrics to the analysis framework of stochastic frontier model started the research of spatial stochastic frontier model.Compared with the traditional stochastic frontier model of sectional data or panel data,the spatial stochastic frontier model can accurately describe the spatial relationship between individuals.If spatial spillover effect exists between production units,the overflow will influence technical efficiency estimation,and then it will be more accurate to use the stochastic frontier model for efficiency calculation(Druska and Horrace,2004).According to the basic paradigm of the spatial stochastic frontier defined by Pavlyuk(2012),the form of spatial stochastic frontier model mainly includes spatial lag stochastic frontier model(SARSF),spatial autoregressive moving average model(SARARSF)and general spatial stochastic frontier model.Panel spatial stochastic frontier model is not limited to the above paradigm;its form is more flexible and complex.A few papers discussed the construction of stochastic frontier model of panel space and its statistical inference method,but the model forms studied are all static panel spatial stochastic frontier model(such as Druska and Horrace,2004;Jiaxin Lin,2014)with no cases of time lag of individual production units.For model estimation method,most studies using the stochastic frontier model commonly used the maximum likelihood(ML)estimation method,but the likelihood function is too complex and it is difficult to obtain the analytical solutions.In addition,the maximum likelihood estimation is not the most effective way to solve the endogeneity of the model(Kelejian and Prucha,1999).Further studies are needed for the stochastic frontier model of spatial panel data in the aspects of model construction,estimation methods and properties of estimators.The following problems are studied in this dissertation:the likelihood estimation of static panel spatial stochastic frontier model,the construction of the dynamic panel spatial stochastic frontier model and its estimation,the estimation method of the technical efficiency time-varying panel spatial stochastic frontier model.What's more,the new estimation method is applied to the empirical analysis.This dissertation is organized as follows:The first chapter introduces the research background,significance,main research content and the innovation.In the second chapter,the research status of the stochastic frontier model,spatial econometrics and spatial stochastic frontier model are summarized with the summaries of the research results of panel spatial stochastic frontier model and research to be done.On this basis,the research direction of this dissertation is determined.In the third chapter,the basic theory of stochastic frontier model,spatial econometrics and spatial stochastic frontier model are introduced,so are the main model form and estimation process.Based on the research of static panel spatial stochastic frontier model,the fourth chapter explores a new method for the numerical solution of the model likelihood function considering of the calculation complexity problems of the model in maximum likelihood estimation.Monte Carlo simulation is carried out for the solution process,and the estimation results of several sample sizes are compared.Static panel spatial stochastic frontier model is used to analyze the change of agricultural technology efficiency in various regions of China.The fifth chapter constructs the dynamic panel spatial stochastic frontier model to solve the problems of endogenous model,combined with the existing several estimation methods,design a new estimation process and prove the statistical properties of the estimator obtained,using the Monte Carlo simulation to estimate the amount of test bias degree and effectiveness.In chapter 6,on the basis of static and dynamic panel spatial stochastic frontier model,the estimation method of panel spatial stochastic frontier model with time-varying technical efficiency is explored,and the statistical property of the estimation is proved.The calculation method of the technical efficiency in the case of time-invarying and time-varying is proposed.The technical efficiency of time-varying panel space stochastic frontier model is used to estimate the technical efficiency of China's strategic emerging industries and total factor productivity.In addition,the characteristics of efficiency of China's regional strategic emerging industries and the exogenous factors are analyzed.The innovation of research work includes:first,this dissertation puts forward a solving method of maximum likelihood estimate of the static panel spatial stochastic frontier model-SQP optimizing method to solve the existing problems in the process.SQP optimizing method uses the sequential quadratic programming method to re-identify model likelihood function.The likelihood equation solving process can be converted to SQP solving process.Then code is written in Matlab to estimate the parameter.Compared with previous studies,the method has the advantage of simple algorithm implementation process.Besides,Monte Carlo simulation results show that the numerical solution of this method is with smaller errors and good finite sample properties.Second,a dynamic panel spatial stochastic frontier model is constructed to supplement the existing panel spatial stochastic frontier model.According to the characteristics of the model,tool variables are selected.Combined with Jacobs et al.(2009)and Kapoor et al.(2007),it proposes the generalized moment method,builds the moment conditions and puts forward the generalized method of moments estimation of dynamic panel spatial stochastic frontier model.The proof on the consistency of the estimator is carried out,too.The advantage of this approach is as follows:the structural parameters of estimator analytical solution can be obtained,the Monte Carlo simulation results show that the estimation of all parameters bias degree is low,and the finite sample properties is good.Third,generalized moment estimation method is proposed for the technical efficiency of time-varying panel spatial stochastic frontier model.Through the analysis of covariance structure model,the construction of time-varying factor matrix and transformation matrix method is first used to eliminate time-varying inefficiency.Other error term parameters are estimated using generalized method of moments.Combining JLMS method to compute the efficiency of the inefficiency of variance,the proof on the consistency of the estimator is carried out at the same time.This method can effectively solve the parameter estimation problem of panel spatial stochastic frontier model with time-varying technical efficiency.This dissertation makes beneficial supplement in the model building,parameter estimation and statistical validation of existing panel spatial stochastic frontier model and the theory,but there are still many improvements.The dynamic panel spatial stochastic frontier model is in the form of complexity.The estimation process also needs to be further simplified to make it be more suitable for empirical research.