Estimating nonparametric conditional frontiers and efficiencies: a new approach

SummaryIn production theory, conditional frontiers and conditional efficiency measures are flexible and appealing tools to investigate the role of environmental variables in 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 of orders that may not be optimal for 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 environmental factors on the inputs and the outputs. We thereby produce ‘pure’ inputs and outputs that make it possible to estimate a ‘pure’ measure of efficiency, which is more reliable for ranking the firms because the influence of external factors has been eliminated. We are also able to recover the frontier and efficiencies in the 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 and its statistical properties, and we show through 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.