Imposing Linear Homogeneity on Box–Tidwell Flexible Functional Forms
考察两种Box-Tidwell成本函数形式，发现若因变量为成本对数，函数在全局和局部均违反要素价格齐次性；若成本经Box-Cox变换，全局齐次性需高度限制性参数约束，局部齐次性仅在近似基点满足。
We consider two forms of the Box–Tidwell cost function, which uses the increasingly popular Box–Cox metric. If the dependent variable is the logarithm of cost, the function violates the regularity condition of homogeneity in factor prices, globally and locally. If cost is transformed by the Box–Cox metric, global homogeneity requires highly restrictive parameter constraints such that the model is no longer flexible, and local homogeneity is satisfied at only the base point of approximation. We demonstrate that normalizing the first model by the deleted factor price alters the model so that estimates are no longer invariant.