Journal of Productivity Analysis, 8, 239–246 (1997) c  1997 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. On the Consistency of Maximum Likelihood Estimation of Monotone and Concave Production Frontiers BHARAT SARATH Stern School, New York University, 311, Tisch Hall, 40 West Fourth Street, New York, NY 10012 AJAY MAINDIRATTA Stern School, New York University, 315, Tisch Hall, 40 West Fourth Street, New York, NY 10012 Abstract Banker and Maindiratta (1992) provides a method for the estimation of a stochastic pro- duction frontier from the class of all monotone and concave functions. A key aspect of their procedure is that the arguments in the log-likelihood function are the fitted frontier outputs themselves rather than the parameters of some assumed parametric functional form. Estimation from the desired class of functions is ensured by constraining the fitted points to lie on some monotone and concave surface via a set of inequality restrictions. In this paper, we establish that this procedure yields consistent estimates of the fitted outputs and the composed error density function parameters. Keywords: DEA, stochastic production frontiers, consistent estimator Introduction Stochastic frontier estimation, introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977), accommodates both one-sided inefficiency and “con- ventional” two-sided disturbances in a composed error specification and yields consistent estimators. However, it is limited by the assumed parametric functional form for the frontier. Data Envelopment Analysis (DEA), on the other hand, imposes only the regularity condi- tions of monotonicity and concavity arising from economic theory and avoids restrictive parametric functional forms. Banker (1993) established consistency of the DEA frontier estimators for the setting in which the error consists solely of an inefficiency term. In a recent paper, Fan, Li and Weersink (1996) develop an alternative method for estimating a composed error model with an unspecified functional form for the production frontier. The distribution for the error term is assumed to be of a known parametric form. Pseudo- likelihood estimators for the parameters of the error term are constructed based on a kernel estimation of the conditional mean function. The method yields consistent estimates of the frontier outputs and the error distribution parameters. However, there is no guarantee that the fitted frontier will satisfy the regularity conditions of monotonicity and concavity.