本文提出了规模报酬递增生产前沿面的概念并证明了以下两个结论:(1)基于样本数据的DEA生产投入集可划分为规模报酬递增、不变和递减区域;(2)C-D生产函数是拟凹函数,且在规模报酬递增区域非凹,在规模递减区域严格凹。基于上述结论及对生产函数曲面,BCC生产前沿面,规模报酬递增生产前沿面的相互关系的分析,提出了一种生产函数分区域估计方法:在对样本数据(决策单元)依据规模报酬增减性进行分类的基础上进行投入可能集的分划,进而在规模报酬递减(不变)和递增区域上分别通过决策单元的BCC弱有效投影和规模报酬递增弱有效投影估计生产函数。文末,通过实例验证了估计方法的有效性。
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.
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