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随机边界模型 Stochastic Frontier Models

随机边界模型 Stochastic Frontier Models. 连玉君 中山大学 岭南学院 arlionn@163.com 2013 年 12 月 9 日 New Course : http://baoming.pinggu.org/Default.aspx?id=93. 提纲. SFA 简介 截面 SFA 模型 面板 SFA 模型 双边 SFA 模型. I. SFA 简介. SFA 的模型设定思想. SFA 图示. y 1. Source: Porcelli(2009). 实证分析中的模型设定. Q: 两个干扰项如何处理？.

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随机边界模型 Stochastic Frontier Models

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  1. 随机边界模型Stochastic Frontier Models 连玉君 中山大学 岭南学院 arlionn@163.com 2013年12月9日 New Course: http://baoming.pinggu.org/Default.aspx?id=93

  2. 提纲 • SFA 简介 • 截面SFA模型 • 面板SFA模型 • 双边SFA模型

  3. I. SFA 简介

  4. SFA 的模型设定思想

  5. SFA 图示 y1 Source: Porcelli(2009)

  6. 实证分析中的模型设定 Q: 两个干扰项如何处理？ Note: 假设 v, u不相关，且二者与 x也不相关

  7. 正态分布和半正态分布的密度函数图

  8. 指数分布的密度函数图

  9. 半正态分布和指数分布对比

  10. 效率的估计 • Jondrow, Lovell, Materov and Schmidt (1982)，JLMS82 • Battese and Coelli (1988)，BC88

  11. II. 面板随机边界模型Panel SFA • Review: linear FEv.s. RE) • FE (Fixed Effect Model) • RE (Random Effect Model) • Pooled OLS

  12. II. 面板随机边界模型Panel SFA • 可能的通用模型： ai : 公司个体效应, N-1 个公司虚拟变量; i : 不随时间变化的常规干扰项; vit: 随时间变化的常规干扰项; +i : 不随时间变化的无效率项 (persistent component) u+it: 随时间变化的无效率项 (transient component)

  13. Panel SFA: Pooled SFA model

  14. Panel SFA:随机效应模型(RE-SFA)效率不随时间变化 • Pitt and Lee (1981), PL81

  15. Panel SFA:固定效应模型(FE-SFA) 效率不随时间变化 • Schmidt and Sickles (1984), SS84 • TE的估计

  16. Panel SFA: 效率时变模型 • Cornwell, Schmidt and Sickles (1990), CSS90 • Lee and Schmidt (1993), LS93

  17. Panel SFA: 效率时变模型 • Battese and Coelli(1992), BC92, 应用非常广泛

  18. Panel SFA: True FE SFA • Greene难题 (Greene Problem) • True-Model: • Estimate-Model: • Implications: • TE 的估计值将是有偏的 • 把那些个体异质性(公司文化, CEO特征等)影响产出的因素都归为“无效率项”了

  19. Panel SFA: True FE SFA • Greene(2005), TFE • 估计方法: 蛮力法 (brute force approach) • 直接估 N个公司虚拟变量和 k个 参数即可 • 需要采用一些特殊的数值计算技巧

  20. Panel SFA: True RE SFA • Greene(2005), TRE • 估计方法: MLE • 相对于传统的线性 RE 模型，只是增加了一个参数而已

  21. Panel SFA: Generalized TRE SFA • Tsionas and Kumbhakar (2013), G-TRE • 对比: TRE

  22. Panel SFA: Scaling-TFE SFA • Wang and Ho (2010), Scaling-TFE • git：scaling function, 是公司特征变量(zit)的函数 • git：可以使非效率具有异质性； • git：缩放性质使得我们可以用FD或组内去心去除个体效应 i

  23. Panel SFA: dynamicSFA • Ahn and Sickles (2000), Dynamic-SFA • i ：用于衡量第 i 家公司对非效率项的调整能力(speed) • i 越大，表明公司克服其非效率行为的能力越强

  24. 异质性 SFA: HeterogeneousSFA • 基本思想

  25. 异质性 SFA: HeterogeneousSFA • 模型设定思想 • 异方差的设定(不确定性) • 均值的设定(无效率水平)

  26. 双边随机边界模型: two-tierSFA • 基本思想

  27. 双边随机边界模型: two-tierSFA • 模型设定 • 效率的估计

  28. Thanks New Course: http://baoming.pinggu.org/Default.aspx?id=93

  29. References 1 • Aigner, D., C. Lovell, P. Schmidt, 1977, Formulation and estimation of stochastic frontier production function models, Journal of Econometrics, 6 (1): 21-37. • Arellano, M., S. Bond, 1991, Some tests of specification for panel data: Monte carlo evidence and an application to employment equations, Review of Economic Studies, 58 (2): 277-297. • Arellano, M., O. Bover, 1995, Another look at the instrumental variable estimation of error-components models, Journal of Econometrics, 68 (1): 29-51. • Battese, G., T. Coelli, 1992, Frontier production functions, technical efficiency and panel data: With application to paddy farmers in india, Journal of Productivity Analysis, 3 (1): 153-169. • Battese, G. E., T. J. Coelli, 1988, Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data, Journal of Econometrics, 38 (3): 387-399. • Battese, G. E., T. J. Coelli, 1995, A model for technical inefficiency effects in a stochastic frontier production function for panel data, Empirical Economics, 20 (2): 325-332. • Belotti, F., S. Daidone, G. Ilardi, V. Atella, 2013, Stochastic frontier analysis using stata, Stata Journal: forthcoming. • Chang, S. K., Y. Y. Chen, H. J. Wang, 2012, A bayesian estimator for stochastic frontier models with errors in variables, Journal of Productivity Analysis, 38 (1): 1-9. • Chen, N.-K., Y.-Y. Chen, H.-J. Wang, 2011, Asset prices and capital investment–a panel stochastic frontier approach, Working Paper.

  30. References 2 • Coelli, T., D. Prasada Rao, G. E. Battese. An introduction to efficiency and productivity analysis[M]. Boston: Kluwer Academic Publishers 1998. • Colombi, R., G. Martini, G. Vittadini, 2011, A stochastic frontier model with short-run and long-run inefficiency, Working Paper, Department of Economics and Technology Management, Universita di Bergamo, Italy. • Emvalomatis, G., 2012, Adjustment and unobserved heterogeneity in dynamic stochastic frontier models, Journal of Productivity Analysis, 37 (1): 7-16. • Feng, G., A. Serletis, 2009, Efficiency and productivity of the us banking industry, 1998–2005: Evidence from the fourier cost function satisfying global regularity conditions, Journal of Applied Econometrics, 24 (1): 105-138. • Fried, H. O., C. Lovell, S. S. Schmidt. 2008, Efficiency and productivity[C], in H. O. Fried, C. Lovell,S. S. Schmidt eds, The measurement of productive efficiency and productivity change (Oxford University Press, New York) 3-92. • Greene, W., 2005a, Fixed and random effects in stochastic frontier models, Journal of Productivity Analysis, 23 (1): 7-32. • Greene, W., 2005b, Reconsidering heterogeneity in panel data estimators of the stochastic frontier model, Journal of Econometrics, 126 (2): 269-303. • Greene, W., 2008, The econometric approach to efficiency analysis, The Measurement of Productive Efficiency and Productivity Change, 1 (5): 92-251.

  31. References 3 • Habib, M., A. Ljungqvist, 2005, Firm value and managerial incentives: A stochastic frontier approach, Journal of Business, 78 (6): 2053-2094. • Hadri, K., 1999, Estimation of a doubly heteroscedastic stochastic frontier cost function, Journal of Business & Economic Statistics, 17 (3): 359-363. • Huang, C. J., J.-T. Liu, 1994, Estimation of a non-neutral stochastic frontier production function, Journal of Productivity Analysis, 5 (2): 171-180. • Jondrow, J., K. Lovell, I. Materov, P. Schmidt, 1982, On the estimation of technical inefficiency in the stochastic frontier production function model, Journal of Econometrics, 19 (2-3): 233-238. • Koutsomanoli-Filippaki, A., E. C. Mamatzakis, 2010, Estimating the speed of adjustment of european banking efficiency under a quadratic loss function, Economic Modelling, 27 (1): 1-11. • Kumbhakar, S., F. Christopher, 2009, The effects of bargaining on market outcomes: Evidence from buyer and seller specific estimates, Journal of Productivity Analysis, 31 (1): 1-14. • Kumbhakar, S., G. Lien, J. B. Hardaker, 2012a, Technical efficiency in competing panel data models: A study of norwegian grain farming, Journal of Productivity Analysis: 1-17.

  32. References 4 • Kumbhakar, S., C. Lovell. Stochastic frontier analysis[M]. Cambridge: Cambridge University Press, 2000. • Kumbhakar, S., R. Ortega-Argilés, L. Potters, M. Vivarelli,P. Voigt, 2012b, Corporate r&d and firm efficiency: Evidence from europe’s top r&d investors, Journal of Productivity Analysis, 37 (2): 125-140. • Kumbhakar, S. C., 1990, Production frontiers, panel data, and time-varying technical inefficiency, Journal of Econometrics, 46 (1): 201-211. • Kumbhakar, S. C., S. Ghosh, J. T. McGuckin, 1991, A generalized production frontier approach for estimating determinants of inefficiency in us dairy farms, Journal of Business & Economic Statistics, 9 (3): 279-286. • Kumbhakar, S. C., C. F. Parmeter, E. G. Tsionas, 2013, A zero inefficiency stochastic frontier model, Journal of Econometrics, 172 (1): 66-76. • Kumbhakar, S. C., E. G. Tsionas, 2011, Some recent developments in efficiency measurement in stochastic frontier models, Journal of Probability and Statistics, 2011: forthcoming. • Lai, H.-p., C. J. Huang, 2011, Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions, Journal of Productivity Analysis: 1-14.

  33. References 5 • Lee, Y. H., P. Schmidt. 1993, A production frontier model with flexible temporal variation in technical efficiency[C], in H. Fried, C. Lovell,S. Schmidt eds, The measurement of productive efficiency: Techniques and applications (Oxford University Press, Oxford, UK) 237-255. • Lian, Y., C.-F. Chung, 2008, Are chinese listed firms over-investing?, SSRN working paper, Available at SSRN: http://ssrn.com/abstract=1296462. • Meeusen, W., J. Van den Broeck, 1977, Efficiency estimation from cobb-douglas production functions with composed error, International Economic Review, 18 (2): 435-444. • Peyrache, A., A. N. Rambaldi, 2012, A state-space stochastic frontier panel data model, working Paper. • Pitt, M. M., L.-F. Lee, 1981, The measurement and sources of technical inefficiency in the indonesian weaving industry, Journal of Development Economics, 9 (1): 43-64. • Tsionas, E. G., S. C. Kumbhakar, 2013, Firm-heterogeneity, persistent and transient technical inefficiency:A generalized true random effects model, Journal of Applied Econometrics: forthcoming.

  34. References 6 • Wang, E. C., 2007, R&d efficiency and economic performance: A cross-country analysis using the stochastic frontier approach, Journal of Policy Modeling, 29 (2): 345-360. • Wang, H., 2003, A stochastic frontier analysis of financing constraints on investment: The case of financial liberalization in taiwan, Journal of Business and Economic Statistics, 21 (3): 406-419. • Wang, H. J., C. W. Ho, 2010, Estimating fixed-effect panel stochastic frontier models by model transformation, Journal of Econometrics, 157 (2): 286-296. • Yélou, C., B. Larue, K. C. Tran, 2010, Threshold effects in panel data stochastic frontier models of dairy production in canada, Economic Modelling, 27 (3): 641-647. • 白俊红, 江可申, 李婧, 2009, 应用随机前沿模型评测中国区域研发创新效率, 管理世界, (10): 51-61. • 林伯强, 杜克锐, 2013, 要素市场扭曲对能源效率的影响, 经济研究, (9): 125-136. • 刘海洋, 逯宇铎, 陈德湖, 2013, 中国国有企业的国际议价能力估算, 统计研究, (5): 47-53. • 卢洪友, 连玉君, 卢盛峰, 2011, 中国医疗服务市场中的信息不对称程度测算, 经济研究, (4): 94-106.

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