Smooth approximations to monotone concave functions in production analysis: An alternative to nonparametric concave least squares

Estimation of banking efficiency and productivity is essential for regulatory purposes and for testing various theories in the context of banking such as the quiet life hypothesis, the bad management hypothesis etc. In such studies it is, therefore, important to place as few restrictions as possible on the functional forms subject to global satisfaction of the theoretical properties relating to monotonicity and concavity. In this paper, we propose an alternative to nonparametric segmented concave least squares. We use a differentiable approximation to an arbitrary functional form based on smoothly mixing Cobb-Douglas anchor functions over the data space. Estimation is based on Bayesian techniques organized around Markov Chain Monte Carlo. The approximation properties of the new functional form are investigated in a Monte Carlo experiment where the true functional form is a Symmetric Generalized McFadden. The new techniques are applied to a large U.S banking data set as well as a global banking data set.