Estimating Nonparametric Conditional Frontiers and Efficiencies: A New Approach

In production theory, conditional frontiers and conditional efficiency measures are flexible and appealing tools to investigate the role of environmental variables on the production process. Direct approaches estimate non-parametrically conditional distribution functions requiring smoothing techniques and the use of bandwidths. Traditional methods for selecting bandwidths provide bandwidths with order that may not be optimal when estimating the boundary of the distribution function. In this paper we suggest an approach that avoids this problem, by eliminating in a first step, with flexible control functions, the influence of the environmental factors on the inputs and the outputs. By doing this we produce “pure” inputs and outputs which allow to estimate a “pure” measure of efficiency, more reliable for ranking the firms, since the influence of the external factors have been eliminated. We are also able to recover the frontier and efficiencies in original units. This can be viewed as an extension of location-scale models for whitening the variables, avoiding often inappropriate restrictions. We describe the method, its statistical properties and we show in some Monte-Carlo simulations, how our new method dominates both the traditional direct and the location-scale approaches. We illustrate the usefulness of the approach with a real data set on banks.