基于利润函数框架的行业要素产出弹性与技术效率测度

Industrial Factor Output Elasticity and Technical Efficiency Measurement Based on Profit Function Framework

传统的宏观生产研究存在两大问题,一是普遍采用地区(省际)视角,不能准确反映宏观生产的技术结构,二是基于总量生产函数框架无法单独考察价格因素对生产的影响。文章在利润函数的基础上,重新构建宏观生产分析框架,利用Hotelling引理和欧拉定理,推导出宏观有约束的利润函数,从行业视角估计了宏观生产的利润前沿,并采用Farrell-Debreu径向度量法测度各个行业的技术效率。结果表明:劳动价格、资本价格和劳动投入数量对利润富有弹性,其值为正且依次递减;资本投入数量对利润接近单位弹性,但其值为负,这说明我国单位资本产出率在逐年降低。从行业来看,房地产业、批发零售业等行业技术效率较低,制造业、服务业等行业技术效率较高,经济发展战略中应予以充分重视。

There are two major problems in traditional macro productivity research.One is that the regional(provincial)perspective cannot accurately reflect the technical structure of macro production,and the other is that the impact of price factors on production cannot be investigated based on the total production function framework.Based on the profit function,this paper reconstructs a macro production analysis framework,then uses the Hotelling lemma and Euler’s theorem to derive the macro constrained profit function and estimate the macro profit frontier from the industry perspective,and finally measures the various industries’technical efficiency by using the Farrell-Debreu radial metric.The conclusions of the analysis are shown as follows:Labor price,capital price and labor input are elastic to profit,and the value is positive and decreasing in turn.The amount of capital input is close to unit elasticity for profit,but its value is negative,which indicates that China’s unit capital output rate is reducing year by year.From the perspective of industry,the level of technical efficiency in the real estate industry,wholesale and retail industry is relatively lower,and the technical efficiency of manufacturing and service industries is relatively higher,which should be given full attention in the economic development strategy.