Imposing Theoretical Regularity on Flexible Functional Forms
比较了三种在灵活函数形式上施加理论正则性的方法（Cholesky分解重新参数化、约束优化和贝叶斯方法），应用于超越对数成本与份额方程系统，发现全局凹性会夸大弹性估计并排除投入互补性，而约束优化和贝叶斯方法在局部或逐点凹性下能保证与新古典微观经济理论一致的推断。
In this paper we build on work by Gallant and Golub (1984 Gallant , A. R. , Golub , G. ( 1984 ). Imposing curvature restrictions on flexible functional forms . Journal of Econometrics 26 : 295 – 321 .[Crossref], [Web of Science ®] , [Google Scholar]), Diewert and Wales (1987 Diewert , W. E. , Wales , T. J. ( 1987 ). Flexible functional forms and global curvature conditions . Econometrica 55 : 43 – 68 .[Crossref], [Web of Science ®] , [Google Scholar]), and Barnett (2002 Barnett , W. A. ( 2002 ). Tastes and technology: Curvature is not sufficient for regularity . Journal of Econometrics 108 : 199 – 202 .[Crossref], [Web of Science ®] , [Google Scholar]) and provide a comparison among three different methods of imposing theoretical regularity on flexible functional forms—reparameterization using Cholesky factorization, constrained optimization, and Bayesian methodology. We apply the methodology to a translog cost and share equation system and make a distinction between local, regional, pointwise, and global regularity. We find that the imposition of curvature at a single point does not always assure regularity. We also find that the imposition of global concavity (at all possible, positive input prices), irrespective of the method used, exaggerates the elasticity estimates and rules out the possibility of a complementarity relationship among the inputs. Finally, we find that constrained optimization and the Bayesian methodology with regional (over a neighborhood of data points in the sample) or pointwise (at every data point in the sample) concavity imposed can guarantee inference consistent with neoclassical microeconomic theory, without compromising much of the flexibility of the functional form.