Estimating Nonparametric Conditional Frontiers and Efficiencies: A New Approach

In production theory, conditional frontiers and conditional efficiency measures are a flexible and appealing approach to consider the role of environmental variables on the production process. Direct approaches estimate non-parametrically conditional distribution functions requiring smoothing techniques and the use of selected bandwidths. The statistical literature produces way to derive bandwidths of optimal order, by using e.g. least-squares-cross-validation techniques. However, it has been shown that the resulting order may not be optimal when estimating the boundary of the distribution function. As a consequence the direct approaches may suffer from some statistical instability. In this paper we suggest a full nonparametric approach which avoids the problem of estimating these bandwidths, by eliminating in a first step 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. This can be viewed as an extension of the use of location-scale models (implying some semi-parametric structure) to full nonparametric models, based on nonseparable, nonparametric models. We are also able to recover the frontier and efficiencies in original units. We describe the method, its statistical properties and we show in some Monte-Carlo simulations, how our new method dominates the traditional direct approach.