C-D生产函数参数估计的分位数回归方法研究
|
摘要
目前国内外对于生产函数模型的研究还是较为齐全的,主要是应用生产函数对经济增长中的各投入要素来进行实证分析,并且近年来分析的内容也在不断加深和丰富,制度因素、产业结构因素、人力资源因素等等都已经纳入了实证分析之中。对于生产函数模型参数的估计方法上,目前主要以经典的最小二乘法为主,采用分位数回归方法对生产函数模型参数进行估计的研究较少,并且也只是停留在实证分析层面上
本论文针对上述问题,以两个解释变量的柯布-道格拉斯生产函数(C-D生产函数)模型为例,对截面数据生产函数模型与面板数据生产函数模型参数估计进行分位数回归方法的研究,在分析学者相关研究成果的基础上,通过理论方法分析和蒙特卡罗模拟方法,分别提出面板数据生产函数模型与截面数据生产函数模型的分位数回归方法,并与经典的最小二乘等回归方法进行比较研究,为广大学者进行有关生产函数模型参数估计问题的研究提供借鉴的方法和思路,为柯布-道格拉斯生产函数(C-D生产函数)模型的参数估计方法提供参考。
同时对基于2007年北京市截面数据和中国大陆各省市(1978-2008年)的面板数据的生产函数模型进行实证研究,通过分位数回归方法,反映出各要素对北京市及中国经济增长影响效应的整体分布特征,便于政府对经济增长的整体把握,为政府决策提供有关依据。
本研究的意义主要在于以下几点：一是对生产函数模型参数估计采用分位数回归方法,弥补了最小二乘法对于生产函数模型参数估计的不足；二是从不同的角度(如截面数据、面板数据)对生产函数模型进行分位数回归研究；三是对基于北京市截面数据与中国面板数据的生产函数进行实证分析,通过分位数回归方法,反映出各要素对北京市及中国经济增长影响效应的整体分布特征,得出有关结论并提供政策建议。
At present the research of production function model is quite complete. This model is mainly applied for empirical analysis of input factors in the economic growth. The content is becoming more deepened and enrich, which included institutional factors, industry structure factors, human resource factors. Least square method is the major estimation method about production function model parameter. The quantile regression is used less and just stay in the level of empirical analysis. In this thesis, the Cobb-Douglas production function (CD production function) model with two explanatory variables is used as an example to do quantile regression method research of cross-sectional data and panel data production function model parameters estimated. On the basis of the results of the analysis of scholars, quantile regression method of cross-sectional data and panel data production function model is proposed respectively through theoretical methods and Monte Carlo simulation. A comparative method is also applied with the classical least squares regression method. The purpose of this thesis is to supply methods for parameter estimation problems of production function model. References are also provided for parameter estimation process of C-D production function.
Meanwhile an empirical study has been researched of production function model based on cross-sectional data of Beijing in2007and panel data of Chinese mainlan provinces from1978to2008. The overal distribution characteristics of the economic growth of Beijing and China can be reflected through the quantile regression method, which can be used by the government for understanding the overall growth and appropriate decision.
The meaning of the research is listed as following. Firstly, quantile regression method makes up the shortage of least square method about estimation parameter of production function model. Next, different angles, such as cross-sectional data panel data quantile regression can be used for quantile regression research. Last but not the least, empirical analysis based on the Beijing cross-sectional data and panel data analysis reflecting the various elements of Beijing and Chinese economic growth, and relevant conclusions and policy recommendations through quantile regression.
本论文针对上述问题,以两个解释变量的柯布-道格拉斯生产函数(C-D生产函数)模型为例,对截面数据生产函数模型与面板数据生产函数模型参数估计进行分位数回归方法的研究,在分析学者相关研究成果的基础上,通过理论方法分析和蒙特卡罗模拟方法,分别提出面板数据生产函数模型与截面数据生产函数模型的分位数回归方法,并与经典的最小二乘等回归方法进行比较研究,为广大学者进行有关生产函数模型参数估计问题的研究提供借鉴的方法和思路,为柯布-道格拉斯生产函数(C-D生产函数)模型的参数估计方法提供参考。
同时对基于2007年北京市截面数据和中国大陆各省市(1978-2008年)的面板数据的生产函数模型进行实证研究,通过分位数回归方法,反映出各要素对北京市及中国经济增长影响效应的整体分布特征,便于政府对经济增长的整体把握,为政府决策提供有关依据。
本研究的意义主要在于以下几点：一是对生产函数模型参数估计采用分位数回归方法,弥补了最小二乘法对于生产函数模型参数估计的不足；二是从不同的角度(如截面数据、面板数据)对生产函数模型进行分位数回归研究；三是对基于北京市截面数据与中国面板数据的生产函数进行实证分析,通过分位数回归方法,反映出各要素对北京市及中国经济增长影响效应的整体分布特征,得出有关结论并提供政策建议。
At present the research of production function model is quite complete. This model is mainly applied for empirical analysis of input factors in the economic growth. The content is becoming more deepened and enrich, which included institutional factors, industry structure factors, human resource factors. Least square method is the major estimation method about production function model parameter. The quantile regression is used less and just stay in the level of empirical analysis. In this thesis, the Cobb-Douglas production function (CD production function) model with two explanatory variables is used as an example to do quantile regression method research of cross-sectional data and panel data production function model parameters estimated. On the basis of the results of the analysis of scholars, quantile regression method of cross-sectional data and panel data production function model is proposed respectively through theoretical methods and Monte Carlo simulation. A comparative method is also applied with the classical least squares regression method. The purpose of this thesis is to supply methods for parameter estimation problems of production function model. References are also provided for parameter estimation process of C-D production function.
Meanwhile an empirical study has been researched of production function model based on cross-sectional data of Beijing in2007and panel data of Chinese mainlan provinces from1978to2008. The overal distribution characteristics of the economic growth of Beijing and China can be reflected through the quantile regression method, which can be used by the government for understanding the overall growth and appropriate decision.
The meaning of the research is listed as following. Firstly, quantile regression method makes up the shortage of least square method about estimation parameter of production function model. Next, different angles, such as cross-sectional data panel data quantile regression can be used for quantile regression research. Last but not the least, empirical analysis based on the Beijing cross-sectional data and panel data analysis reflecting the various elements of Beijing and Chinese economic growth, and relevant conclusions and policy recommendations through quantile regression.
引文
[1]Koenker R, Bassett G. The Asymptotic Distribution of the Least Absolute Error Estimator. Journal of the Ameriean Statistical Associatton,1978a,73:618-622
[2]Koenker R., Bassett G. Regression Quantiles. Econometrica,1978b,46:33-50
[3]Moshe Buchinsky, Jinyong Hahn. An alternative estimator for the censored quantile regression model. Econometrica,1998,66(3):653-671
[4]E. Grifell-Tatje, C. A. K. Lovell. A Note on the Malmquist Productivity Index [J].Economics Letters,1995,47:169-175
[5]Horowitz, Joel. Lee, Sokbae.NonPararnetric Estimation of an Additive Quantile Regression Model. Journal of the American Statistical Association,2005,10:1238-1249
[6]J. Jondrow, C. A. K. Lovell, I.S.Materov and P. Schmidt. On Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model [J]. Journal of Econometrics,1982,19:233-238
[7]S. C. Ahn, H. R. Moon. On Large-N and Large-T Properties of Panel Data Estimators and the Housman Test. Mimeo. University of Southern California,2001
[8]Mogrens Dilling-Hansen, Erik Strjer Madsen and Valdemar Smith. Efficiency, R&D and Ownership-Some Empirical Evidence [J]. International Journal of Production Economics,2003,83:85-94
[9]M. M. Pitt, LF. Lee. Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry [J]. Journal of Development Economics,1981, (9):43-64.
[10]W. Meeusen, van deni Broeck. Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error [J]. International Economic Review,1977,18:435-444
[11]J.Felipe and H. Carsten. Why Do Aggregate Productions Work Fisher's Stimulations, Shaikh's Identity, and Some New Results [J]. International Review of Applied Economics,2001,15(3):261-285
[12]G. E. Battese, T. J. Coelli. Frontier Production Functions, Technical Efficiency and Panel Data:With Application to Paddy Farmers in India [J]. Journal of Productivity Analysis,1992, (3):153-169
[13]S.C. Kumbhakar. Estimation and Decomposition of Productivity Change When Production is Not Efficient:A Panel Data Approach [J]. Economic Review,2000,19:425-460
[14]C. Cornwell, P. Schmidt and R. C. Sickes. Production Frontiers With Cross-sectional and Time-series Variation in Efficiency Levels [J]. Journal of Econometrics,1990,46: 185-200
[15]Robert F. Engle,Jeffey R Ruessll. Antoregressive conditional duration:A new model for irregularly Spaced transaction. Econometrica,1998,66(5):1127-1162
[16]Jiannan wu, Stuart Bretschneider and Fredrick Marc Aurele. Estimating Models of Extreme Behavior:A Monte Carlo ComParison between SWAT and Quantile Regression. Chinese Public AdIninistration,2002,2:1100-1111
[17]W. H. Masanjala and C. Papageorgiou. The Solow Model with CES Technology: Nonlinearities and Parameter Heterogeneity [J]. Journal of Applied Econometrics, 2004,19:171-201
[18]R. M. Z. Luis, A. V.-C. Juan. The Use of Parametric and Non-Parametric Frontier Methods to Measure the Productive Efficiency in the Industrial Sector:A Comparative Study [J]. International Journal of Production Economics,2001,69:265-275.
[19]KoenkerR. BassettG.Robest tests for heteroskedasticity based on regression quantiles. Eeonometrica,1982,50:43-61
[20]Alan E Gelfand Athanasios Kottas, Steven MacEachern.Bayesian NonParametrie Spatial Modeling With Dirichlet Process Mixing. Journal of the American Statistical Association,2005,100 (471):1021-1035
[21]P. Schmidt, R. C. Sickes. Production Frontiers and Panel Data [J]. Journal of Business and Economic Statistics,1984, (2):367-374
[22]D. J. Aigner, C. A. K. Lovell and P. Schmidt Formulation and Estimation of Stochastic Frontier Production Function Models [J]. Journal of Econometrics,1977, (6):21-37
[23]Y. H. Lee, P. Schmidt. A Production Frontier Model with Flexible Temporal Variation in Technical Inefficiency.In Fried, H.O., C. A. K. Lovell, and S. S. Schmidt(Eds)[M].The Measurement of productive Efficiency:Techniques and Applications, Oxford University Press, New York,1993,237-255
[24]Gaofeng Han, Kaliappa Kalirajan, Nivrikar Singh. Productivity and Economic Growth in East Asia:Innovation, Efficiency and Accumulation [J]. Japan and the World Economy.2002,14:401-424
[25]Landajo. Manuel, De Andres. Javier, Lorca. Pedro. Measuring firm performance by using linear and non-Parametric quantile regressions Journal of the Royal Statistical Society:Series C (Applied Statistics),2008,57(2):227-250
[26]Fama E, French K. The cross-section of expected stock return. Journal of Finance,1992,2:427-464
[27]W. H. Greene. A Gamma-distributed Stochastic Frontier Model [J]. Journal of Econometrics,1990,46:141-164
[28]Whittaker, Whitehead. Disposition Dockets:Judge Owens. Journal Record,1988, 10:121-125
[29]D. W. Caves, L. R. Christensen and W. E. Diewert. The Economic Theory of Index Numbers and the Measurement of Input,Output and Productivity[J]. Econometrica,1982,50: 1393-1414
[30]C. Fernandez, G. Koop, M. Steel. A Bayesian Analysis of Multiple-output Production Frontier[J]. Journal of Econometrics,2000,98:47-79
[31]Mo-Yin S. Tam,Gilbert W.,Bassettjr. University freshmen admission index:quantile method. Statistical Research,2004,2:50-55
[32]Moshe Buchinsky. Changes In The U.S. Wage Structure 1963-1987:Application of quantile Regression. Econometrical,1994,62 (2):405-458
[33]R. Fare, S. Grosskopf, M. Norris and Z. Zhang. Productivity Growth, Technical Progress, and Efficiency Changes in Industrialized Countries [J]. American Economic Review,1994,86:66-83
[34]H. J.Gathon, P. Pestieau. Decomposition Efficiency into its Managerial and Regulatory Components:The Case of European Railways [J]. European Journal of Operational Research,1995,80:500-507
[35]Moshe Buchinskv. The Dynamics of Changes in the Female Wage Distribution in the USA:A Quantile Regression Approach. Journal of Applied Econometrics,1998b,13:1-30
[36]Mueller Richard E..Public and Private-Sector Wage Differentials in Canada Revisited. Industrial Relations,2000,39(3):375-400
[37]R M. Solow. Technical Change and the Aggregate Production Function [J]. The Review of Economics and Statistics,1957,37:312-320
[38]A. Charnes, W. W. Cooper and E.Rhodes. Evaluating Program and Managerial Efficiency:An Application of Data Envelopment Analysis to Program Follow Through [J]. Management Science,1981,27(6):668-69
[39]T. J. Coelli, D. S. P. Rao and GE. Battese. An Introduction To Efficiency And Productivity Analysis [J]. Kluwer Academic Pblishers,1998:133-181
[40]BeumJo Park. An outlier robust GARCH model and forecasting volatility of exchange rate returns.Journal of Forecasting,2002,21(5):381-390
[41]Eide, Eric R., Mark H. Showalter. Factors affecting the transmission of earnings across generations:a quantile regression approaeh. Journal of Human Resources, 1999,34 (2):253-254
[42]P. Wilson, D. Hadley and C. Asby. The Influence of Management Characteristics on the Technical Efficiency of Wheat Farmers in Eastern England [J]. Agricultural Economics,2001,24:329-338
[43]CINCERA, MICHELE. Firms'productivity growth and R&D spillovers:an analysis of alternative technological proximity measures [J]. Economics of Innovation & New Technology,2005,14:657-682.
[44]D. J. Aigner, S. F. Chu. On Estimate the Industry Production Function [J]. American Economic Review,1968,58:826-836
[45]Yao Chen. A Non-radial Malmquist Productivity Index with an Illustrative Application to Chinese Major Industries [J]. International Journal of Production Economics,2003,83:27-35
[46]M. J. Farrell. The Measurement of Productive Efficiency [J]. Journal of the Royal Statistical Society,1957,120:253-290
[47]Stephane Mussard and Nicolas Peypoch. On Multi-decomposition of the Aggregate Luenberger Productivity Index [J]. Applied Economics Letters,2006,13:113-116
[48]Jehle Geoffrey A Philip J Reny. Advanced Microeconomic Theory,2nd [M]. Pearson Education North Asia Limited and Shanghai University of Finance And Economics Press 2001
[49]P. Schmidt. On the Statistical Estimation of Parametric Frontier Production Functions [J]. Review of Economics and Statistics,1976,58:238-239
[50]PINA ALVARO MANUEL, ST. AUBYN, MIGUEL. Comparing macroeconomic returns on human and public capital:An empirical analysis of the Portuguese case (1960-2001) [J]. Journal of Policy Modeling,2005,27:585-598.
[51]M. M. Stephen, P. U. Mulkti. Total Factor Productivity and the Convergence Hypothesis [J].Journal of Macroeconomics,2002,24:267-286
[52]J. Ondrich, J. Ruggiero. Efficiency Measurement in the Stochastic Frontier Model [J]. European Journal of Operational Research,2001,129:434-442
[53]Varian, Hal R. Microeconomic Analysis [M]. Economy Science Press,1997.
[54]Wooldridge, Jeffrey M. Introductory econometrics [M]. A Modern Approach,2000.
[55]Stock James H, Mark W Watson. Introduction to econometrics [J]. Pearson Education, Inc.2003.
[56]G. E. Battese, T. J. Coelli. Prediction of Firmed-Level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data [J]. Journal of Econometrics,1988,38:387-399
[57]Wooldridge Jeffrey M. Econometric analysis of cross section and panel data [J]. Massachusetts Institute of Technology,2002.
[58]Ruud Paul A. An introduction to classical econometric theory [M]. Oxford University Press,2000
[59]S. C. Kumbhakar. Factor Productivity and Technical Change [J]. Applied Economics Letters,2003,10:291-297
[60]GRILICHES ZVI. Research expenditures, education, and the aggregate agricultural production function [J]. American Economic Review,1964,54:961-974.
[61]FELDSTEIN M S. Specification of the labour input in the aggregate production function [J]. Review of Economic Studies,1967,34:375-386.
[62]HUANG YUKON. Allocation efficiency in a developing agricultural economy in Malaya [J].American Journal of Agricultural Economics,1971,53:514-516.
[63]BAIRAM ERKIN I, McRAE SHAUN D. Testing the convergence hypothesis:a new approach [J]. Economics Letters,1999,64:351-355.
[64]S. C. Kumbhakar. Production Frontiers, Panel Data and Time-Varying Technical Inefficiency [J]. Journal of Econometrics,1990,46:201-211
[65]CHOW GREGORY, AN-LOH LIN. Accounting for economic growth in Taiwan and mainland China:a comparative analysis [J].Journal of Comparative Economics,2002,30: 507-530.
[66]B. Gong, R. Stickles. Finite Sample Evidence on the performance of Stochastic Frontiers and Data Envelopment Analysis Using Panel Data [J]. Journal of Econometrics,1992,51:259-284
[67]冯英浚,李成红.二次相对效益——衡量企业经济效益的一种新指标.[J].中国软科学,1995,(7)：31-37
[68]冯英浚,康梅,任柏明.描述不同行业投入产出差异的一种技术系数[M].系统工程理论与实践,2004,(6)：41-45
[69]马小朋.中国经济增长的收敛性分析.[J].上海经济研究.2005,(3)：14-18
[70]樊潇彦.中国工业资本收益率的测算与地区、行业结构分析.[J].世界经济,2004,(5)：48-57
[71]李育安.分位数回归及应用简介.[J].统计与信息论坛,2006,5(3)：35-38
[72]叶裕民.全国及各省区市全要素生产率的计算和分析.[J].经济学家,2002,(3)：115-121
[73]钟学义,陈平.技术,技术进步,技术经济学和数量经济学之诠释.[J].数量经济,技术经济研究,2006,23(3)：156-160
[74]吴耀华.回归分位数过程的收敛性.[J].数学年刊,1992,5,13A：622-632
[75]徐涛.引进FDI与中国技术进步.[J].世界经济,2003,(10)：22-27
[76]刘瑞涛,蒋建成.价值风险的非参数估计方法.[J].应用概率统计,2002,2：208-213
[77]郑承利,陈灯塔.中国股市截面收益率再研究：分位数回归方法.[J].南方经济,2006,1：61-71
[78]黄先海,刘毅群.物化性技术进步与我国工业经济增长.[J].数量经济技术经济研究.2006,23(4)：52-60
[79]徐小飞,龚德恩.中国地区经济科技进步贡献比较研究.数量经济学前沿,社会科学文献出版社,2001：132-137
[80]马晓强,丁小浩.我国城镇居民个人教育投资风险的实证研究.[J].教育研究,2005,4：25-31
[81]黎波,迟巍,余秋梅一种新的收入差距研究的计量方法基于分布函数的半参数化估计.[J].数量经济技术经济研究,2007,8：119-129
[82]荀鹏程,顾坚,顾海雁等.中位数回归模型及自回归模型在北京市SARS发病预测中的应用.[J].中国卫生统计,2004,8(4)：219-221
[83]季萃,陈峰,吴先萍.用百分位数回归制订正常人群血压参考值的研究.[J].数理医药学杂志,1999,12(4)：307-308
[84]岳昌君,刘燕萍.教育对不同群体收入的影响.[J].北大教育经济研究,2006,6(2)：85-92
[85]尚磊,徐勇勇,江逊等.陕西省27200名0-18岁健康儿童体质指数参考曲线.[J].中国临床康复,2003,7(18)：2576-2578
[86]冯英浚,王大伟,丁文柯,任柏明.绩效管理与管理有效性.[J].中国软科学,2003,(4)：132-136
[87]朱平芳,朱先智.企业创新人力投入强度规模效应的分位点回归研究.[J].数量经济技术经济研究,2007,24(3)：69-80
[88]葛玉红.工资分布的性别差异：分位数分解方法.[J].上海经济研究2007,4：22-30
[89]涂涛涛,张建华.外商直接投资与技术外溢效应—基于分位数回归法.[J].南方经济,2007.7：37-46
[90]李晓华.工资不平等的上升：结构效应与价格效应.中国人口科学.[J].2007,1：36-43
[91]吴建南,马伟.估计极端行为模型：分位数回归方法及其实现与应用.[J].数理统计与管理,2006,5：526-543
[92]彭国甫.基于DEA模型的地方政府公共事业管理有效性评价[J].中国软科学,2005,(8)：128-133
[93]徐铮,张润清等.1990-2004年我国经济增长因素实证分析.[J].市场经纬.2007, 4：45-46
[94]许家云,刘琳.不同生产函数条件下的中国经济研究.[J].工会论坛.2010,5：54-85
[95]张建玲,王国顺.考虑能源投入的生产函数模型及实证.[J].统计观察.2007,20：81-82
[96]陈建宝等.基于分位数回归的中国居民收人和消费的实证分析.[J].统计与信息论坛.2009.7：44-50
[97]韩立岩,王哲兵.我国实体经济资本配置效率与行业差异.[J].经济研究,2005,(1)：77-84
[98]胡永宏,贺思辉.综合评价方法[M].科学出版社,2000：39-52
[99]金相郁.区域经济增长收敛的分析方法.[J].数量经济技术经济研究.2006,23(3)：102-110
[100]石金涛,王莉.管理技能的因子分析及其对绩效影响的实证研究[J].管理工程学报,2004,18(1)：76-80
[101]冯英浚,高欣,魏松贤.生产有效性与管理有效性.[J].管理工程学报,2001,(3)：27-29
[102]王君,樊治平.组织知识管理绩效的一种综合评价方法[M].管理工程学报,2004,18(2)：44～47
[2]Koenker R., Bassett G. Regression Quantiles. Econometrica,1978b,46:33-50
[3]Moshe Buchinsky, Jinyong Hahn. An alternative estimator for the censored quantile regression model. Econometrica,1998,66(3):653-671
[4]E. Grifell-Tatje, C. A. K. Lovell. A Note on the Malmquist Productivity Index [J].Economics Letters,1995,47:169-175
[5]Horowitz, Joel. Lee, Sokbae.NonPararnetric Estimation of an Additive Quantile Regression Model. Journal of the American Statistical Association,2005,10:1238-1249
[6]J. Jondrow, C. A. K. Lovell, I.S.Materov and P. Schmidt. On Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model [J]. Journal of Econometrics,1982,19:233-238
[7]S. C. Ahn, H. R. Moon. On Large-N and Large-T Properties of Panel Data Estimators and the Housman Test. Mimeo. University of Southern California,2001
[8]Mogrens Dilling-Hansen, Erik Strjer Madsen and Valdemar Smith. Efficiency, R&D and Ownership-Some Empirical Evidence [J]. International Journal of Production Economics,2003,83:85-94
[9]M. M. Pitt, LF. Lee. Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry [J]. Journal of Development Economics,1981, (9):43-64.
[10]W. Meeusen, van deni Broeck. Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error [J]. International Economic Review,1977,18:435-444
[11]J.Felipe and H. Carsten. Why Do Aggregate Productions Work Fisher's Stimulations, Shaikh's Identity, and Some New Results [J]. International Review of Applied Economics,2001,15(3):261-285
[12]G. E. Battese, T. J. Coelli. Frontier Production Functions, Technical Efficiency and Panel Data:With Application to Paddy Farmers in India [J]. Journal of Productivity Analysis,1992, (3):153-169
[13]S.C. Kumbhakar. Estimation and Decomposition of Productivity Change When Production is Not Efficient:A Panel Data Approach [J]. Economic Review,2000,19:425-460
[14]C. Cornwell, P. Schmidt and R. C. Sickes. Production Frontiers With Cross-sectional and Time-series Variation in Efficiency Levels [J]. Journal of Econometrics,1990,46: 185-200
[15]Robert F. Engle,Jeffey R Ruessll. Antoregressive conditional duration:A new model for irregularly Spaced transaction. Econometrica,1998,66(5):1127-1162
[16]Jiannan wu, Stuart Bretschneider and Fredrick Marc Aurele. Estimating Models of Extreme Behavior:A Monte Carlo ComParison between SWAT and Quantile Regression. Chinese Public AdIninistration,2002,2:1100-1111
[17]W. H. Masanjala and C. Papageorgiou. The Solow Model with CES Technology: Nonlinearities and Parameter Heterogeneity [J]. Journal of Applied Econometrics, 2004,19:171-201
[18]R. M. Z. Luis, A. V.-C. Juan. The Use of Parametric and Non-Parametric Frontier Methods to Measure the Productive Efficiency in the Industrial Sector:A Comparative Study [J]. International Journal of Production Economics,2001,69:265-275.
[19]KoenkerR. BassettG.Robest tests for heteroskedasticity based on regression quantiles. Eeonometrica,1982,50:43-61
[20]Alan E Gelfand Athanasios Kottas, Steven MacEachern.Bayesian NonParametrie Spatial Modeling With Dirichlet Process Mixing. Journal of the American Statistical Association,2005,100 (471):1021-1035
[21]P. Schmidt, R. C. Sickes. Production Frontiers and Panel Data [J]. Journal of Business and Economic Statistics,1984, (2):367-374
[22]D. J. Aigner, C. A. K. Lovell and P. Schmidt Formulation and Estimation of Stochastic Frontier Production Function Models [J]. Journal of Econometrics,1977, (6):21-37
[23]Y. H. Lee, P. Schmidt. A Production Frontier Model with Flexible Temporal Variation in Technical Inefficiency.In Fried, H.O., C. A. K. Lovell, and S. S. Schmidt(Eds)[M].The Measurement of productive Efficiency:Techniques and Applications, Oxford University Press, New York,1993,237-255
[24]Gaofeng Han, Kaliappa Kalirajan, Nivrikar Singh. Productivity and Economic Growth in East Asia:Innovation, Efficiency and Accumulation [J]. Japan and the World Economy.2002,14:401-424
[25]Landajo. Manuel, De Andres. Javier, Lorca. Pedro. Measuring firm performance by using linear and non-Parametric quantile regressions Journal of the Royal Statistical Society:Series C (Applied Statistics),2008,57(2):227-250
[26]Fama E, French K. The cross-section of expected stock return. Journal of Finance,1992,2:427-464
[27]W. H. Greene. A Gamma-distributed Stochastic Frontier Model [J]. Journal of Econometrics,1990,46:141-164
[28]Whittaker, Whitehead. Disposition Dockets:Judge Owens. Journal Record,1988, 10:121-125
[29]D. W. Caves, L. R. Christensen and W. E. Diewert. The Economic Theory of Index Numbers and the Measurement of Input,Output and Productivity[J]. Econometrica,1982,50: 1393-1414
[30]C. Fernandez, G. Koop, M. Steel. A Bayesian Analysis of Multiple-output Production Frontier[J]. Journal of Econometrics,2000,98:47-79
[31]Mo-Yin S. Tam,Gilbert W.,Bassettjr. University freshmen admission index:quantile method. Statistical Research,2004,2:50-55
[32]Moshe Buchinsky. Changes In The U.S. Wage Structure 1963-1987:Application of quantile Regression. Econometrical,1994,62 (2):405-458
[33]R. Fare, S. Grosskopf, M. Norris and Z. Zhang. Productivity Growth, Technical Progress, and Efficiency Changes in Industrialized Countries [J]. American Economic Review,1994,86:66-83
[34]H. J.Gathon, P. Pestieau. Decomposition Efficiency into its Managerial and Regulatory Components:The Case of European Railways [J]. European Journal of Operational Research,1995,80:500-507
[35]Moshe Buchinskv. The Dynamics of Changes in the Female Wage Distribution in the USA:A Quantile Regression Approach. Journal of Applied Econometrics,1998b,13:1-30
[36]Mueller Richard E..Public and Private-Sector Wage Differentials in Canada Revisited. Industrial Relations,2000,39(3):375-400
[37]R M. Solow. Technical Change and the Aggregate Production Function [J]. The Review of Economics and Statistics,1957,37:312-320
[38]A. Charnes, W. W. Cooper and E.Rhodes. Evaluating Program and Managerial Efficiency:An Application of Data Envelopment Analysis to Program Follow Through [J]. Management Science,1981,27(6):668-69
[39]T. J. Coelli, D. S. P. Rao and GE. Battese. An Introduction To Efficiency And Productivity Analysis [J]. Kluwer Academic Pblishers,1998:133-181
[40]BeumJo Park. An outlier robust GARCH model and forecasting volatility of exchange rate returns.Journal of Forecasting,2002,21(5):381-390
[41]Eide, Eric R., Mark H. Showalter. Factors affecting the transmission of earnings across generations:a quantile regression approaeh. Journal of Human Resources, 1999,34 (2):253-254
[42]P. Wilson, D. Hadley and C. Asby. The Influence of Management Characteristics on the Technical Efficiency of Wheat Farmers in Eastern England [J]. Agricultural Economics,2001,24:329-338
[43]CINCERA, MICHELE. Firms'productivity growth and R&D spillovers:an analysis of alternative technological proximity measures [J]. Economics of Innovation & New Technology,2005,14:657-682.
[44]D. J. Aigner, S. F. Chu. On Estimate the Industry Production Function [J]. American Economic Review,1968,58:826-836
[45]Yao Chen. A Non-radial Malmquist Productivity Index with an Illustrative Application to Chinese Major Industries [J]. International Journal of Production Economics,2003,83:27-35
[46]M. J. Farrell. The Measurement of Productive Efficiency [J]. Journal of the Royal Statistical Society,1957,120:253-290
[47]Stephane Mussard and Nicolas Peypoch. On Multi-decomposition of the Aggregate Luenberger Productivity Index [J]. Applied Economics Letters,2006,13:113-116
[48]Jehle Geoffrey A Philip J Reny. Advanced Microeconomic Theory,2nd [M]. Pearson Education North Asia Limited and Shanghai University of Finance And Economics Press 2001
[49]P. Schmidt. On the Statistical Estimation of Parametric Frontier Production Functions [J]. Review of Economics and Statistics,1976,58:238-239
[50]PINA ALVARO MANUEL, ST. AUBYN, MIGUEL. Comparing macroeconomic returns on human and public capital:An empirical analysis of the Portuguese case (1960-2001) [J]. Journal of Policy Modeling,2005,27:585-598.
[51]M. M. Stephen, P. U. Mulkti. Total Factor Productivity and the Convergence Hypothesis [J].Journal of Macroeconomics,2002,24:267-286
[52]J. Ondrich, J. Ruggiero. Efficiency Measurement in the Stochastic Frontier Model [J]. European Journal of Operational Research,2001,129:434-442
[53]Varian, Hal R. Microeconomic Analysis [M]. Economy Science Press,1997.
[54]Wooldridge, Jeffrey M. Introductory econometrics [M]. A Modern Approach,2000.
[55]Stock James H, Mark W Watson. Introduction to econometrics [J]. Pearson Education, Inc.2003.
[56]G. E. Battese, T. J. Coelli. Prediction of Firmed-Level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data [J]. Journal of Econometrics,1988,38:387-399
[57]Wooldridge Jeffrey M. Econometric analysis of cross section and panel data [J]. Massachusetts Institute of Technology,2002.
[58]Ruud Paul A. An introduction to classical econometric theory [M]. Oxford University Press,2000
[59]S. C. Kumbhakar. Factor Productivity and Technical Change [J]. Applied Economics Letters,2003,10:291-297
[60]GRILICHES ZVI. Research expenditures, education, and the aggregate agricultural production function [J]. American Economic Review,1964,54:961-974.
[61]FELDSTEIN M S. Specification of the labour input in the aggregate production function [J]. Review of Economic Studies,1967,34:375-386.
[62]HUANG YUKON. Allocation efficiency in a developing agricultural economy in Malaya [J].American Journal of Agricultural Economics,1971,53:514-516.
[63]BAIRAM ERKIN I, McRAE SHAUN D. Testing the convergence hypothesis:a new approach [J]. Economics Letters,1999,64:351-355.
[64]S. C. Kumbhakar. Production Frontiers, Panel Data and Time-Varying Technical Inefficiency [J]. Journal of Econometrics,1990,46:201-211
[65]CHOW GREGORY, AN-LOH LIN. Accounting for economic growth in Taiwan and mainland China:a comparative analysis [J].Journal of Comparative Economics,2002,30: 507-530.
[66]B. Gong, R. Stickles. Finite Sample Evidence on the performance of Stochastic Frontiers and Data Envelopment Analysis Using Panel Data [J]. Journal of Econometrics,1992,51:259-284
[67]冯英浚,李成红.二次相对效益——衡量企业经济效益的一种新指标.[J].中国软科学,1995,(7)：31-37
[68]冯英浚,康梅,任柏明.描述不同行业投入产出差异的一种技术系数[M].系统工程理论与实践,2004,(6)：41-45
[69]马小朋.中国经济增长的收敛性分析.[J].上海经济研究.2005,(3)：14-18
[70]樊潇彦.中国工业资本收益率的测算与地区、行业结构分析.[J].世界经济,2004,(5)：48-57
[71]李育安.分位数回归及应用简介.[J].统计与信息论坛,2006,5(3)：35-38
[72]叶裕民.全国及各省区市全要素生产率的计算和分析.[J].经济学家,2002,(3)：115-121
[73]钟学义,陈平.技术,技术进步,技术经济学和数量经济学之诠释.[J].数量经济,技术经济研究,2006,23(3)：156-160
[74]吴耀华.回归分位数过程的收敛性.[J].数学年刊,1992,5,13A：622-632
[75]徐涛.引进FDI与中国技术进步.[J].世界经济,2003,(10)：22-27
[76]刘瑞涛,蒋建成.价值风险的非参数估计方法.[J].应用概率统计,2002,2：208-213
[77]郑承利,陈灯塔.中国股市截面收益率再研究：分位数回归方法.[J].南方经济,2006,1：61-71
[78]黄先海,刘毅群.物化性技术进步与我国工业经济增长.[J].数量经济技术经济研究.2006,23(4)：52-60
[79]徐小飞,龚德恩.中国地区经济科技进步贡献比较研究.数量经济学前沿,社会科学文献出版社,2001：132-137
[80]马晓强,丁小浩.我国城镇居民个人教育投资风险的实证研究.[J].教育研究,2005,4：25-31
[81]黎波,迟巍,余秋梅一种新的收入差距研究的计量方法基于分布函数的半参数化估计.[J].数量经济技术经济研究,2007,8：119-129
[82]荀鹏程,顾坚,顾海雁等.中位数回归模型及自回归模型在北京市SARS发病预测中的应用.[J].中国卫生统计,2004,8(4)：219-221
[83]季萃,陈峰,吴先萍.用百分位数回归制订正常人群血压参考值的研究.[J].数理医药学杂志,1999,12(4)：307-308
[84]岳昌君,刘燕萍.教育对不同群体收入的影响.[J].北大教育经济研究,2006,6(2)：85-92
[85]尚磊,徐勇勇,江逊等.陕西省27200名0-18岁健康儿童体质指数参考曲线.[J].中国临床康复,2003,7(18)：2576-2578
[86]冯英浚,王大伟,丁文柯,任柏明.绩效管理与管理有效性.[J].中国软科学,2003,(4)：132-136
[87]朱平芳,朱先智.企业创新人力投入强度规模效应的分位点回归研究.[J].数量经济技术经济研究,2007,24(3)：69-80
[88]葛玉红.工资分布的性别差异：分位数分解方法.[J].上海经济研究2007,4：22-30
[89]涂涛涛,张建华.外商直接投资与技术外溢效应—基于分位数回归法.[J].南方经济,2007.7：37-46
[90]李晓华.工资不平等的上升：结构效应与价格效应.中国人口科学.[J].2007,1：36-43
[91]吴建南,马伟.估计极端行为模型：分位数回归方法及其实现与应用.[J].数理统计与管理,2006,5：526-543
[92]彭国甫.基于DEA模型的地方政府公共事业管理有效性评价[J].中国软科学,2005,(8)：128-133
[93]徐铮,张润清等.1990-2004年我国经济增长因素实证分析.[J].市场经纬.2007, 4：45-46
[94]许家云,刘琳.不同生产函数条件下的中国经济研究.[J].工会论坛.2010,5：54-85
[95]张建玲,王国顺.考虑能源投入的生产函数模型及实证.[J].统计观察.2007,20：81-82
[96]陈建宝等.基于分位数回归的中国居民收人和消费的实证分析.[J].统计与信息论坛.2009.7：44-50
[97]韩立岩,王哲兵.我国实体经济资本配置效率与行业差异.[J].经济研究,2005,(1)：77-84
[98]胡永宏,贺思辉.综合评价方法[M].科学出版社,2000：39-52
[99]金相郁.区域经济增长收敛的分析方法.[J].数量经济技术经济研究.2006,23(3)：102-110
[100]石金涛,王莉.管理技能的因子分析及其对绩效影响的实证研究[J].管理工程学报,2004,18(1)：76-80
[101]冯英浚,高欣,魏松贤.生产有效性与管理有效性.[J].管理工程学报,2001,(3)：27-29
[102]王君,樊治平.组织知识管理绩效的一种综合评价方法[M].管理工程学报,2004,18(2)：44～47