Comparing Input- and Output-Oriented Measures of Technical Efficiency to Determine Local Returns to Scale in DEA Models

This paper shows how one can infer the nature of local returns to scale at the input- or output-oriented efficient projection of a technically inefficient input-output bundle, when the input- and output-oriented measures of efficiency differ.

The Directional Distance Function and Measurement of Super-Efficiency: An Application to Airlines Data

Lovell and Rouse (LR) have recently proposed a modification of the standard DEA model that overcomes the infeasibility problem often encountered in computing super-efficiency. In the LR procedure one appropriately scales up the observed input vector (scale down the output vector) of the relevant super-efficient firm thereby usually creating its inefficient surrogate. An alternative procedure proposed in this paper uses the directional distance function introduced by Chambers, Chung, and Färe and the resulting Nerlove-Luenberger (NL) measure of super-efficiency. The fact that the directional distance function combines features of both an input-oriented and an output-oriented model, generally leads to a more complete ranking of the observations than either of the oriented models. An added advantage of this approach is that the NL super-efficiency measure is unique and does not depend on any arbitrary choice of a scaling parameter. A data set on international airlines from Coelli, Perelman, and Griffel-Tatje (2002) is utilized in an illustrative empirical application.

Shadow Profit Maximization and a Generalized Measure of Inefficiency

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.