Research On The Estimation Of Spatial Stochastic Frontier Model And Technical Efficiency And Productivity

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.