A Comparative Study Of DEA-Bootstrap Methods For Technical Efficiency Estimation

Technical efficiency estimation^[1]was first proposed by Farrell in 1957.At present,domestic and foreign researches on technical efficiency estimation are mainly divided into two methods.One is a non-parametric estimation method:using DEA(Data Envelopment Analysis)model estimation technical efficiency,the other is the parameter estimation method SFA(Stochastic Frontier Analysis^[2])and COLS(Corrected Ordinary Least Squares,modified least squares).DEA was proposed by Charnes^[3]and others in 1978,using mathematical programming and related data to determine the relatively production frontier of decision units.It is a method that uses linear programming to construct nonparametric piecewise surfaces(technical frontiers)of observation data,and then calculates the efficiency by the relative distance between different decision units and the frontier.The advantage of DEA method is that it does not need to determine the form of production function in advance and do not need to consider the dimensions of input and output.However,the technical efficiency measured by the DEA method has disadvantages that cannot be statistically judged whether it is a significant,and shortcomings that have a large impact on outliers and extreme values.Simar and Wilson^[17]first proposed the use of Bootstrap and The possibility of combining DEA introduced the Bootstrap method.It makes up for the disadvantage of not being able to make statistical inferences.In the third chapter,this paper mainly introduces some statistical model related theories combining Bootstrap and DEA,as well as some asymptotic and estimation consistency conclusions.Three commonly used methods:Sub-Sampling,Simar-Wilson,Smooth method.In order to find out which method is better,Chapter 4 of this article uses Monte Carlo data to simulate the production situation,and uses the determined Cobb Douglas production function to simulate the input-output data set in the production process,According to the Farrell efficiency definition,we can define a the form of the determined production function,so we can calculate the true technical efficiency.Here we use the more common Douglas production function to perform data simulation on different function forms.The choice of parametercan determine increasing returns to scale,Constant returns to scale,decreasing returns to scale,etc.For the invalid term function simulation of different technical factors.This article considers the situation of single input and single output and the situation of multiple inputs and multiple outputs.Among them,multiple inputs and multiple outputs are taken as examples of dual inputs and dual outputs.It is found that as the input-output dimension increases,the estimation accuracy of each method decreases,and the sub-Sample receiving dimension changes much more than the other two methods.In the case of single output and single input,the estimation effect of the Sub-Sample and Simar-Wilson methods is similar and better than the Smooth method.For the case of dual output and double inputs,the estimation effect of the Simar-Wilson and Smooth methods is similar and significantly better than that of the Sub-Sampling method is good.Which method is better for different perturbations and different returns of scale?A detailed summary is given in Chapter 4,The comprehensive evaluation selects the better prediction effect as the Simar-Wilson method.In the empirical evidence in Chapter 5,we use this method to estimate the technical efficiency values of the telecommunications industry in 42 countries,and analyze the data of China's communications industry.From 2000 to 2007,the technological efficiency value of China's communications industry continued to increase.From 2004 to 2007,the technological efficiency value of China's communica--tions industry was very close to the technological frontier,and then from 2007 to2014,the technological efficiency value has been declining status.In addition,this paper also analyzes the problems of input redundancy and insufficient output.It is found that labor redundancy has always existed in the input,but there is no capital redundancy.In the output,insufficient patent output occurred from 2000 to 2008,and then did not appear.Never appeared.