与理论相一致的全要素生产率增长率测算

Measuring Total Factor Productivity Growth with Theoretical Consistency

全要素生产率(TFP)增长率的测算和分解是基于生产理论的,这要求所估计的生产函数与生产理论的要求相一致。对现有实证研究的分析发现对生产函数的估计存在违背生产理论的可能性,表现为投入要素边际产量为负,以及投入要素之间边际技术替代率非递减等情况。这导致TFP增长率测算结果在理论上是不一致的。因此,需要在估计生产函数时对参数的取值范围施加适当的约束,以保证得到符合生产理论的估计结果。基于MCMC算法可以直接对随机采样的取值范围施加限制,即仅以一定的概率接受符合生产理论要求的参数取值,因此本文采用贝叶斯MCMC方法估计生产函数并测算TFP的增长率。本文将该方法应用于小麦生产,以展示对生产函数参数取值范围施加理论约束会在多大程度上影响TFP的测算结果。结果显示,当对参数取值范围不加限制时,所估计的参数不能使所有的样本点同时满足生产函数的单调性和拟凹性。在施加了单调性和拟凹性的约束条件后,参数估计的HPD区间缩小,显示参数估计精度提高。同时,与有约束模型相比,无约束模型倾向于高估TFP的增长率,平均高估的程度达到167.6%。分解结果显示,技术进步率测算的偏误是导致无约束模型TFP增长率测算偏误的主要原因。这可能是由于技术进步率的测算公式中包含了生产函数模型的参数,因此受参数取值范围变化的影响较大。技术效率的测算主要受到其分布形式设定和分布参数的影响,而这些方面受生产理论的直接影响较小。

Measurement of total factor productivity(TFP)is constructed based on production theory,so the estimated production function should be consistent with production theory.Review of existing empirical studies have shown that the estimated production function is conflicting with production theory and may produce theoretically biased TFP measurement.For instance,one may encounter with negative marginal product of factors or non-decreasing marginal rate of technical substitution between factors.As a consequence,it is necessary to restrict the domain of parameter space of the estimated production function,in order to get results in line with production theory.In MCMC algorithm one can simply impose restrictions on estimated parameters by only accepting satisfied random draws with certain probability.Hence,we use Bayesian method to estimate production function and then measure TFP growth.In this paper we employ the Bayesian method to wheat production of China to demonstrate how the theoretical constraints on functional parameters would affect the estimation of TFP.The results have shown that,without imposing proper constraints in estimation,the estimate wheat production function fail to satisfy the conditions of monotonicity and quasi-concavity.After the monotonic and quasi-concave constraints were imposed,the HPD interval of estimated parameters was narrowed,which indicates improved estimating precision.Meanwhile,unconstraint model tends to overestimate TFP growth by 167.6%on average compare to constraint model.By decomposing TFP growth of wheat production to its components we found that misgauge of technical progress is the main cause of this measurement bias.The reason could be that the technical progress was constructed based on the estimated parameters of production function,so it is sensitive to the change of parameters values of production function.While the measurement of technical efficiency mainly depends on the assumption of its density function and the corresponding parameters,which only link to the impact of theoretical constraints in the estimation indirectly.