Symmetry Constraints and Variable Returns to Scale in Logit Models
针对线性Logit成本份额模型的两个问题：对称性仅适用于一组成本份额，以及成本函数积分无法解析求解，提出了迭代非线性估计和数值近似方法，并讨论了模型性质。
This article addresses two problems with earlier applications of the linear logit model of cost shares. The first problem is that symmetry holds only for one set of cost shares. In this article, an iterative, nonlinear estimation procedure is used to impose symmetry for all predicted shares. The second problem is that analytical expressions for the integrals of log-linear cost shares cannot be derived analytically, although they exist, given the continuity of the logit share equations. This article proposes a procedure for approximating the underlying cost function by using the share predictions as stochastic, numerical approximations of these integrals. The model has constant but unequal elasticities of substitution. This feature does not contradict the Uzawa impossibility theorem, which holds for integrable functions, because the logit model is essentially a numerical approximation of the constant elasticity of substitution model. Another interesting property is that the concavity conditions are relatively stable functions of the cost shares, which remain positive given the logistic form.