资本服务加总度量与Divisia指数

Aggregation of Capital Services and the Divisia Index

有关总量生产函数的批评很多,最直接的批评来自于从微观生产函数到总量生产函数的可加总条件不满足。本文采用几何直观的方法显示了资本加总条件的含义,明确了不满足严格的可加总条件并不必然使得总量生产函数失去意义,不满足条件只不过使得"硬性"加总后的总量生产函数出现一定程度的模糊性,而这种模糊性无论如何都会存在,其来源远远不止加总条件的不满足。在此基础上,本文阐述了Hicks加总、函数可分性加总等各种加总方法的内在逻辑联系,并通过几何方法显示了在满足可准确加总条件时,Divisia指数是一种比定基指数更为优越的方法。

There are many critical articles about the aggregate production function,of which the most important is the stringent Leontiff condition on aggregation problem.In this article,we show in a geometric way that it does not mean we can not use this sort of aggregate production function when the Leontiff condition is violated.If this condition is not satisfied,the aggregate production function will lose some accuracy,but there are many other factors which can lead to this problem.Relatively,the Leontiff condition is not very important in practice and we suggest use Divisia index can be a more appropriate method in aggregation of capital services.