It is proved that,firstly, the input possibility set spanned by samples (DMUs in terms of DEA) can be divided into areas of increasing return to scale (IRS), constant return to scale (CRS) and decreasing return to scale (DRS); secondly, C-D production function is quasi-concave, and non-concave on the area of IRS. The concept of IRS frontier of a production possibility set is proposed. Based on the division of input possibility set and the position of the production function surface, BCC frontier and the IRS frontier, a method to estimate production function is proposed. According to the method, production function is divided into a non-concave segments on area of IRS and a concave segment on area of non-IRS, and the estimation is processed in following steps. First, dividing the input possibility set into IRS area and non-IRS area; second, forming IRS frontier on IRS area and BCC frontier on non-IRS area, respectively; third, estimating parameters of each segment with corresponding frontier by a linear programming model, respectively. The validity of the estimation method is verified through an instance.
DONG Jin-quan, QIU Cheng-cheng, MA Zhan-xin, LIU Jun-hua, ZHENG Zhi-hua
. Estimation of Quasi-concave Production Function Based on the Division of Input Possibility Set[J]. Chinese Journal of Management Science, 2015
, 23(3)
: 32
-41
.
DOI: 10.16381/j.cnki.issn1003-207x.2015.03.004
[1] Aigner D J, Chu S F. On estimating the industry production function[J]. American Economic Review, 1968, 58(4):826-839.
[2] Zhao N, Tang Huanwen, Luo Xiaona. Research on non-linear input-output model based on production function theory and a new method to update IO coefficients matrix[J]. Applied Mathematics and Computation, 2006, 181(1):478-486.
[3] 哈尔,范里安.微观经济学:现代观点(第六版) [M].上海:上海人民出版社,2006.
[4] 魏权龄,胡显佑,肖志杰. DEA方法与前沿生产函数[J].经济数学,1988,5(5): 1-13.
[5] 杨锋,梁樑,凌六一,等.供应链前沿生产函数的DEA估计研究[J].中国管理科学, 2008,16(5): 90-95.
[6] Deprins D, Simar L, Tulkens H. Measuring labour efficiency in post offices[M]//Tulkens H,Chander P. The performance of public enterprises. Amsterdam: North -Holland, 1984:243-267.
[7] 吴文江,吴文辉.在用DEA的基础上确定生产函数的方法[J].武汉工业大学学报, 1997, 19(3):154-155.
[8] 程大友.基于DEA模型估计前沿生产函数的探讨[J].技术经济与管理研究, 2004,(4): 51-52.
[9] 马赞甫,刘妍珺. 基于DEA的生产函数估计[J].管理学报,2010, 7(8): 1237-1241.
[10] 魏权龄.数据包络分析[M].北京:科学出版社,2004.
[11] Yu Gang, Wei Quanling, Patrick Brockett, et al. Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model [J]. European Journal of Operational Research, 1996, 95(3): 491-510.
[12] 蒋中一.数理经济学的基本方法[M].北京:北京大学出版社,2006.
[13] 王祖祥.经济理论中C-D函数的有关性质[J].数量经济技术经济研究, 2000, 17(6): 63-65.
[14] Dekker D, Post T. A quasi-concave DEA model with an application for bank branch performance evaluation [J]. European Journal of Operational Research, 2001,132(2): 296-311.
[15] Post T. Transconcave data envelopment analysis [J]. European Journal of Operational Research, 2001, 132(2): 326-339.
[16] 王晓红,王雪峰,翟爱梅,等.具有边际报酬递增特性的数据包络分析模型[J].上海交通大学大学学报,2005, 39(3): 484-487.
[17] 王晓红,王雪峰,翟爱梅,等.具有边际报酬递增特性的DEA模型求解方法[J].哈尔滨工业大学学报,2004, 36(10): 1297-1300.
[18] 邱兆祥,张爱武.基于FDH方法的中国商业银行X-效率研究[J].金融研究, 2009,(11): 91-102.
[19] 赵历男,赵亚男.技术进步与规模报酬的测量模型与实证分析[J].数量经济技术经济研究,1994,(8):43-47.
[20] 申树斌,纪凤兰.夏少刚.规模报酬的数学表述方法研究[J].东北财经大学学报,2005,(3):73-76.
[21] 周长春.规模报酬变动的衡量指标[J].统计与决策,2007,(19):70-71
[22] Banker R D. Estimating most productive scale size using data envelopment analysis[J]. European Journal of Operational Research, 1984,17(1): 35-44.
[23] Fare R, Grosskopf S. A nonparametric cost approach to scale efficiency [J].The Scandinavian Journal of Economics, 1985, 87(4):594-604.
[24] 魏权龄,马赞甫,阎洪.DEA的交形式生产可能集及其应用[J].数学的实践与认识,2007, 37(4): 62-69.
[25] Wei Quanling, Yu Gang, Lu Jianshou. The necessary and sufficient conditions for returns to scale properties in generalized data envelopment analysis model [J]. Science in China (Series E), 2002, 45(5): 503-515.
[26] 谢守祥,慕晶敏. 基于时间参数DEA的江苏省工业生产函数测算[J].决策参考, 2007, (19): 52-56.
[27] 孙莹,鲍新中,刘小军.基于生产函数和数据包络方法的企业规模效益分析[J].产业经济研究,2011,(1):56-63.
