Bias in Transport Efficiency Estimates Caused by Misspecified DEA Models

Abstract

This paper examines transport modes that have employed Data Envelopment Analysis (DEA). It ascertains whether key DEA specifications necessary for estimating valid efficiency scores are present, the impact on the scores when they are not, and methods for correcting the errors. One critical specification is that for the sample data being used, each output must have been produced by various proportions of the inputs, with the substitutions between each pair of inputs shown on an isoquant. And, for the sample data, each input must have produced various proportions of the outputs, with the transformations between each pair of outputs shown on a production frontier. It is essential that these specifications are met by the data sample being used. DEA estimates input weights based solely on the Marginal Rate of Substitutions (MRS) between inputs on the sample data’s efficient frontier (isoquant). And DEA estimates output weights based solely on the Marginal Rate of Transformations (MRT) between outputs on the sample data’s production frontier. If there are no substitutions or transformations for the sample at hand, then there are no valid MRSs and MRTs, so DEA will utilize false weights and thereby produce false efficiency scores. In this paper, we analyze inputs and outputs that have often been used in DEA articles involving airline, urban transit, and freight rail data. Our data samples show that input substitution and output transformation are often not present. And, for our sample data, these misspecifications result in badly biased estimates of both technical efficiencies and second-stage regression parameters. We suggest methods for identifying and correcting for these specification errors, so future transportation DEA articles can avoid these problems.

Keywords: Data Envelopment Analysis, DEA, Specification errors, Efficiency, Transport, Transportation, Transit, Airlines, Trains