On testing separability restrictions with flexible functional forms
On testing separability restrictions with flexible functional forms
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用灵活的函数形式测试可分离性限制
DOI：
10.1016/0304-4076(77)90024-0
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发表时间：
1977
期刊：
影响因子：
--
通讯作者：
R. Russell
中科院分区：
文献类型：
--
作者：
C. Blackorby;D. Primont;R. Russell
在本文中，我们研究了对跨日志和其他三种灵活形式施加可分离性的含义。我们的结果表明，弱可分离性的伯恩特-克里斯滕森“非线性”检验不仅适用于弱可分离性，而且还对所有当前已知的“灵活”函数形式的宏观和微观函数施加了限制性结构。例如，使用 translog 作为精确形式来测试弱可分离性实际上相当于使用柯布-道格拉斯聚合函数来测试强（可加性）可分离性和拟似弱可分离性的混合体。我们的结果表明，这些“灵活”的功能形式是“可分离性不灵活的”。也就是说，它们无法为给定点的任何邻域中的任意弱可分离函数提供二阶近似。
In this paper, we examine the implications of imposing separability on the translog and three other flexible forms. Our results imply that the Berndt-Christensen ‘nonlinear’ test for weak separability tests not only for weak separability, but also imposes a restrictive structure on the macro and micro functions for all currently known ‘flexible’ functional forms. For example, testing for weak separability using the translog as an exact form is in fact equivalent to testing for a hybrid of strong (additive) separability and homothetic weak separability with Cobb-Douglas aggregator functions. Our results show that these ‘flexible’ functional forms are ‘separability-inflexible’. That is, they are not capable of providing a second-order approximation to an arbitrary weakly separable function in any neighbourhood of a given point.