Imposing Theoretical Regularity on Flexible Functional Forms

In this paper we build on work by Gallant and Golub (1984), Diewert and Wales (1987), and Barnett (2002) 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.