导　　师： 龙志和

学科专业： 020204

授予学位： 博士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 随机前沿模型作为效率测算的计量经济参数方法的代表，最初由Aigner、Lovell/&Schmidt，Meeusen/&Van den Broeck和Battese/&Corra三组研究人员于1977年同时提出，并很快发展成为经济计量领域的一个重要分支，为经济和管理等学科测算诸如工业、农业和金融银行业等领域的效率和生产率的研究提供新的研究视角和分析工具。经过三十多年的发展，一系列关于随机前沿模型设定和参数估计及技术效率推断的理论创新成果不断涌现。在常用的经典随机前沿模型中，一般假设不同经济个体之间具有独立性，然而，在技术扩散过程中，空间交互效应在经济个体之间扮演着重要的角色，它们之间彼此独立的假设明显与现实经济状况不相符。空间经济学、区域经济学和新经济地理等学科的研究均指出，地理接近性是产生外部性和一系列相邻效应的关键因素。任何一个经济个体都不可能独立存在，它总是与相邻的其它经济个体存在着各式各样的联系。 近年来，空间经济学的理论和实证研究日益受到学术界的广泛关注，空间关系成为现代经济模型的一个重要组成部分，而空间计量经济学将空间效应引入经典计量模型和统计方法中，为处理经济管理活动中的空间交互效应和空间结构等问题提供新的理论框架和分析方法。如果经济个体（或地区）之间存在空间交互效应和空间外部性，随机前沿模型中没引入空间计量经济分析可能会产生模型设定偏误，从而导致参数估计和技术效率推断有偏，而以此为基础的全要素生产率研究也可能会出现误差。而国内外现有的将空间效应引入随机前沿模型分析框架的相关研究相对较少，仍在空间模型设定、面板模型设定和技术无效率项分布等方面存在一些不足和局限性。 本文在前人研究的基础上，进一步将空间计量经济学的理论与方法融入随机前沿分析框架中，结合两者的特点，同时考虑空间滞后因变量和空间误差自相关，分别基于正态-半正态、正态-指数分布和正态-截尾正态三种不同的概率分布假设，完善和补充已有的横截面和面板模型，提出异方差模型，对所构建的模型进行参数估计、LR检验和技术效率推断；其次，在考虑空间相关性的情形下，围绕生产前沿法和广义Malmquist生产率参数分解法展开全要素生产率变化估计及其分解的研究；最后，将空间随机前沿模型应用于测算中国工业部门的技术效率，实证考察引入空间效应给随机前沿模型分析框架的参数估计及技术效率推断所带来的影响。主要研究内容和研究结论如下： 1、基于横截面数据，将空间效应引入随机前沿模型的分析框架，同时考虑空间滞后因变量和空间误差自相关，构建正态-半正态、正态-指数分布和正态-截尾正态分布形式的横截面空间随机前沿模型。采用极大似然法估计相应模型的参数，为避免最优化过程直接涉及矩阵平方根的计算从而导致算法不稳定，进一步推导等价的对数似然函数；随后针对空间系数和技术无效率项进行五项LR检验；最后利用JLMS方法推断技术无效率项的点估计值，进而得到每个生产单位的技术效率估计。尽管同为单参数分布，但正态-指数模型的对数似然函数比正态-半正态模型的要简单，这将为其实证应用提供易操作性。另外，正态-截尾正态模型嵌套正态-半正态模型，前者为技术效率估计提供一种更加一般化的模式，但复杂度更大。 2、结合空间面板计量经济模型和经典面板随机前沿模型的特点，构建四种形式的面板空间随机前沿模型，分别为：Anselin SAR形式、KKP SAR形式、SMA形式、SEC形式，并将这四种形式统一表达在同一个模型框架中。随后基于正态-半正态、正态-指数、正态-截尾正态的概率分布假设，对模型参数进行极大似然估计；针对空间系数和技术无效率项进行五项LR检验；并利用JLMS方法推断技术效率的估计值。为了减少最优化过程的不稳定性和降低计算的复杂度，对对数似然函数中NT NT阶矩阵的逆矩阵和行列式计算进行降维处理，即转化为N N阶矩阵的逆矩阵和行列式计算。在此基础上，进一步放松技术效率非时变的假设，构建技术效率时变的面板空间随机前沿模型，且不赋予技术无效率项任何函数约束形式，并采用模拟极大似然法对时变面板空间模型进行参数估计。 3、在分别考虑随机干扰项、技术无效率项和两者存在异方差的情形下，构建正态-半正态、正态-指数分布和正态-截尾正态分布形式的异方差空间随机前沿模型。首先考察忽略异方差性所产生的后果，当随机干扰项或技术无效率项存在异方差时，斜率系数向量的估计值均是无偏的，截距项向量的估计值却均是下偏的，但前者可通过已知的技术无效率项标准差来修正偏误，这与经典随机前沿模型的情况类似；对技术效率估计值均造成一定的影响，但由于空间效应的存在，不同于经典模型，其作用方向有待进一步确认，估计值下偏或上偏将取决于具体的实证数据。针对各种设定形式的异方差模型，采用极大似然法进行参数估计，进而推断其技术效率。 4、基于时变的面板空间随机前沿模型，围绕生产前沿法和广义Malmquist生产率参数分解法分别展开全要素生产率增长估计及其分解的研究。重新构建空间随机前沿模型分析框架下的生产前沿法，将全要素生产率分解为技术进步变化、技术效率变化、配置效率部分和规模经济效应部分，这四个分解因素的表达式均体现了空间滞后因变量的直接影响，而空间误差自相关通过参数估计和技术效率推断对全要素生产率产生间接影响。将距离函数的空间滞后项引入具有产出导向型的超越对数形式距离函数中，重构考虑空间效应的广义Malmquist生产率指数，利用其将全要素生产率分解成技术进步变化、技术效率变化和规模经济效应，其中空间效应以技术效率变化的空间溢出效应形式存在，而技术进步变化部分和规模经济效应部分并没有受到空间效应的直接影响。 5、将空间随机前沿模型的分析框架应用于测算中国工业产业的技术效率。无论基于何种分布假设，空间随机前沿模型和经典模型均显示中国工业产业技术无效性的存在，与随机干扰项相比，其估计值是高度显著的。空间相关性在参数估计方面也无法证伪，空间系数（至少是空间误差自相关系数）是正的且显著，而在三种计量经济模型设定中，空间随机前沿模型估计在对数似然函数估计值方面一直表现最优，说明我国工业产业的发展呈现出很强的空间相关性，这种空间效应对工业产业发展存在正向影响。从技术效率估计的视角来看，空间随机前沿模型均在一定程度上改进经典模型的推断结果，其中基于正态-指数分布空间模型的技术效率空间分布更为符合理论预期。 Stochastic frontier model as a representative of econometric parametric methods formeasuring efficiency, initially proposed by Aigner et al./(1977/), Meeusen and Van denBroeck /(1977/) and Battese and Corra/(1977/) almost at the same time, then quickly developedinto an important branch in the field of econometrics, and provided a new researchperspective and analysis tools for economic and management subjects to measure efficiencyand productivity of industrial, agricultural and financial banking sectors and other areas.Through more than thirty years of development, a series of theoretical innovations on modelspecification, parameter estimation and technical efficiency inference of stochastic frontiermodel have emerged. In classical stochastic frontier model, generally assume that differenteconomic agents are independent of each other. However, in the process of technologydiffusion, spatial interaction effect plays an important role, and the assumption ofindependence is not consistent with economic reality. Spatial economics, regional economicsand new economic geography have pointed out that geographical proximity is a key factor ofexternalities and a series of neighborhood effects. Any economic agent could not existindependently, there are always various forms of contacts between one and its neighbors. In recent years, the theoretical and empirical studies of spatial economics haveincreasingly received extensive attention, and spatial relationship has become an importantpart of modern economic model. Spatial econometrics introduces spatial effect into classicaleconometric models and statistical methods, and provides a new theoretical framework andanalysis methods to deal with spatial interaction effect and spatial structure in economy andmanagement. If there are spatial interaction effect and externalities between economic agents,not to introduce spatial econometric analysis into stochastic frontier model may producemodel specification errors and lead to parameter estimation and technical efficiency inferencebiased, then on this basis, the research on total factor productivity may also be biased.However, the number of related researches on spatial stochastic frontier model is relativelysmall, and there are still some issues, such as spatial model specification, panel data modeland so on, deserving to be studied further. On the basis of previous studies, this paper introduces spatial econometric theory and method into stochastic frontier analysis framework further. Firstly, combining thecharacteristics of both, we consider spatial lag dependent variable and spatial errorautocorrelation at the same time. Then based on normal-half normal, normal-exponential andnormal-truncated normal distribution assumptions respectively, we improve and complementthe existing cross-section and panel models, and propose several kinds of heteroscedasticmodels, then derive parameter estimation, LR test and technical efficiency of the abovemodels. Secondly, under the situation of considering spatial correlation, we use productionfrontier approach and generalized Malmquist productivity parametric decomposition approachrespectively to estimate total factor productivity change and its decomposition. Finally, weapply spatial stochastic frontier model to measure technical efficiency of China’s industrialsector, empirically investigate spatial effect how to influence parameter estimation andtechnical efficiency inference. The main research contents and conclusions are as follows: 1. Based on cross-sectional data, normal-half normal, normal-exponential and normal-truncated normal types of spatial stochastic frontier model are proposed. We adopt maximumlikelihood method to estimate the parameters of the corresponding models, and to avoidcalculating square root of a matrix that may lead to instability in optimization process,equivalent of log-likelihood functions are derived. Then likelihood ratio /(LR/) statistic is usedto test spatial coefficient and technical inefficiency. Finally, JLMS method is applied toinference point estimates of technical inefficiency, which are used to estimate each productionunit’s technical efficiency. Although as a single parameter distribution, the log-likelihoodfunction of normal-exponential model is simpler than the one of normal-half normal model,this will provide practicality for empirical application. In addition, the normal-truncatednormal model nests the normal-half normal model, the former provides a more generalizedway to estimate technical efficiency, but is more complex. 2. Combining the characteristics of spatial econometric model and classical stochasticfrontier model, we build four types of spatial panel stochastic frontier model, respectively:Anselin SAR model, KPP SAR model, SMA model and SEC model. They are integrated intoone model framework in a unified manner. Then based on normal-half normal, normal-exponential and normal-truncated normal distribution assumptions, maximum likelihoodestimations, LR tests and technical efficiency inferences of the corresponding models are derived. In order to reduce the instability and complexity of the optimization process, we turnthe calculation of inverse and determinant of a NT NTorder matrix to that of a N Norder matrix. On this basis, the assumption of time-invariant technical efficiency is relaxed,and we further construct spatial panel stochastic frontier model with time-varying technicalefficiency, which does not follow any function form constraint. Then we adopt simulatedmaximum likelihood method to estimate the time-varying spatial panel model. 3. Considering heteroscedasticity in either of random disturbance and technicalinefficiency or both of them respectively, normal-half normal, normal-exponential and normal-truncated normal types of heteroscedastic spatial stochastic frontier model are proposed. Westudy the consequences of heteroscedasticity problems. Heteroscedasticity in either of randomdisturbance and technical inefficiency or both of them generates unbiased estimates of theslope coefficient vector and a downward-biased estimate of the intercept, exactly as in theclassical stochastic frontier model. However the bias in the estimated intercept can becorrected once the standard deviation of technical inefficiency is known. All kinds ofheteroscedastic model produce biased estimates of technical efficiency, unlike classical model,the bias downward or upward will depend on concrete empirical data. Then, we use maximumlikelihood method for parameter estimation of the above models, and finish the estimates oftechnical efficiency. 4. Based on the time-varying spatial panel stochastic frontier model, we use productionfrontier approach and generalized Malmquist productivity parametric decomposition approachrespectively to estimate total factor productivity change and its decomposition. The formerdecomposes total factor productivity change into a technical change component, a technicalefficiency change component, an allocative inefficiency component and a scale component.All the four components reflect the direct influence of spatial lag dependent variable and theindirect influence of spatial error autocorrelation. The later introduce the spatial lag term intothe output-oriented translog distant function, reconstruct generalized Malmquist productivityindex with spatial effect. Then it is used to decompose total factor productivity change into atechnical change component, a technical efficiency change component and a scale component.Spatial effect influences the technical efficiency change component directly, but the other twocomponents do not reflect the direct impact of spatial effect. 5. The spatial stochastic frontier analysis framework is applied to measure the technicalefficiency of China’s industrial sector. Regardless of which kind of distribution assumption,both of the spatial and classical models show that there is technical inefficiency in China’sindustrial sector. Compared with random disturbance, the estimates of technical inefficiencyare highly significant. Spatial correlation in terms of parameter estimation is also cannot befalsified, while spatial coefficients /(at least spatial error autocorrelation coefficient/) arepositive and significant. In each of the three econometric model specifications, spatialstochastic frontier model performs best in terms of log-likelihood, which indicates that thedevelopment of our country’s industrial sector presents a strong spatial correlation that haspositive impacts. From the perspective of technical efficiency estimation, spatial modelsimprove the inference results of classical models, among them, the spatial distribution oftechnical efficiency based on normal-exponential spatial model is more conform to thetheoretical expectation.

关 键 词： 随机前沿模型 空间计量 极大似然估计 技术效率 全要素生产率

分 类 号： [F224]

领　　域： [经济管理]