基于投入距离函数的单要素技术效率测量方法研究

Measuring Input-specific Technical Efficiency Based on Input Distance Function

在生产中,由于企业并未掌握关于生产技术的完全信息,因此可能导致不同生产要素具有不同的技术效率水平。而传统的"径向"技术效率测量方法并不能识别生产要素之间的技术效率差异。为解决这一问题,现有的文献中分别提出了基于利润函数和方向距离函数的测量方法。但利润函数的估计需要用到难以收集的价格数据;估计方向距离函数需要事先设定投入要素缩减的方向,而这一方向对于研究者是未知的。基于投入距离函数,本文构建了一个新的可以测量单要素技术效率的框架,且无需价格数据和事先设定"方向"。文章采用贝叶斯方法分两步估计该模型:首先得到模型参数的估计值;其次在模型参数估计值给定的基础上再估计单个要素的技术效率水平。蒙特卡洛模拟分析发现,与直接估计各要素的技术效率的方法相比,这种"两步法"可以更快的实现马尔科夫蒙特卡洛(MCMC)过程的收敛,并能够较为精确的估计各要素的技术效率水平。之后将该方法应用于北京大学企业社会责任调查的数据,估计了资本和劳动力的技术效率水平。结果显示,企业在利用资本中几乎不存在技术效率损失,并且企业间的资本技术效率水平无明显差异。企业技术效率损失主要来自于劳动力利用不足,且企业间劳动力技术效率水平差异较大。平均而言,劳动力的技术效率水平为77%,即在保持产出和资本投入不变的情况下,可以使劳动力的投入下降23%。这个例子表明,本文提出的方法可以识别生产中导致技术效率损失的主要原因,从而有助于找到提升生产效率的解决方案。

Due to incomplete information about production technology,firms may use some inputs more efficiently than others,which makes the radial technical efficiency measurement inappropriate.Different approaches have been proposed to reconcile the non-radial nature of technical efficiency and the measurement methodologies.The revenue function based approach proposed by Kumbhakar and Lai(2016)can be applied to measure output-specific technical efficiency.With minor modification,the framework proposed by Kumbhakar and Lai(2016)can be extended to profit function to measure input-specific technical efficiency(ISTE).This approach has limitation in empirical research in that reliable data on input and output prices are not always available.The directional distance function approach can also be used to measure ISTE(Färe and Primont,1995).However,it requires to specify the"directions"toward which inputs can be contracted before data analysis was applied,yet this kind of information is unavailable a priori.Aparicio et al.(2017)proposed a method to measure ISTE based on the principle of least action and the corresponding DEA method was developed to estimate ISTE.It is well known that DEA method is vulnerable to extreme values and it is difficult to distinguish if the distinction between technical efficiency of each input is real or just due to statistical noise.In this paper a new method is proposed to measure input-specific technical efficiency(ISTE)based on input distance function which requires no price information and no need to specify the"direction"a priori.Let x_(j) denote the quantity of input j(j=1,…,K)used in production,y denote output.Let TE_(j)=exp(-η_(j));(0<η_(j)<∞)represents technical efficiency level of input j.Therefore,x_(j)^(0)=x_(j)·TE_(j) gives optimal level of input j while keeping the quantity of output y unchanged.Let X^(0)=(x_(1)^(0),…,x_(K)^(0))be the optimal input vector.Apparent for input distance function we can get:D(Y,X^(0))=sup_(λ){λ:(X^(0)/λ,Y)∈T}=1(1)Suppose Cobb-Douglas function can be used to approximate the distance function,from(1)we get:0=α_(0)+∑_(j=1)^(K)α_(j)ln(x_(j)⋅TE_(j))+∑_(m=1)^(M)β_(m)lny_(m)(2)where α and β are unknown parameters.By using the homogenous condition of input distance function,we get the estimable form as follows:−lnx_(k)=α_(0)+∑_(j=1)^(K−1)α_(j)ln(xj/x_(K))+∑_(m=1)^(M)β_(m)lny_(m)+ε−∑_(j=1)^(K)α_(j)η_(j)(3)whereεis the stochastic error term.In estimation,a two steps procedure is developed in the context of Bayesian econometrics:in the first step,the parameters of input distance function are estimated consistently;then in the second step,technical efficiency of each inputs are estimated based on the given estimated parameters.Monte Carlo simulation shows that this"two steps"approach can generate much faster convergence in Markov Chain Monte Carlo(MCMC)inference and accurate estimation of ISTE compare to direct Bayesian estimation of ISTE model(3).Then this method is applied to the data of Industrial Enterprise Survey by Peking University to evaluate the ISTE of labor and capital.This survey covers the period of 2000 to 2005.However,it is an unbalanced panel data set.Output is measured by revenue of each firm.To alleviate the fluctuation of revenue caused by output price change,the average revenue of each firm in this period is used as a measure of output value.Finally a cross sectional data with 1178 firms are gotten from 36 different industries.The results show that,firms are using capital efficiently and indifferently.While technical efficiency of labor is relatively low and disperse among firms in the sample.On average,technical efficiency of labor is 77%,in other words,labor can be saved by 23% while keeping output and capital use unchanged.The illustration shows that the approach developed in this study can identify the major sources of technical inefficiency,therefore can facilitate to develop strategies to improve efficiency in production.