Calculating scale elasticity in DEA models

Abstract

In the data envelopment analysis (DEA) efficiency literature, qualitative characterizations of returns to scale (increasing, constant, or decreasing) are most common. In economics it is standard to use the scale elasticity as a quantification of scale properties for a production function representing efficient operations. Our contributions are to review DEA practices, apply the concept of scale elasticity from economic multi-output production theory to DEA piecewise linear frontier production functions, and develop formulas for scale elasticity for radial projections of inefficient observations in the relative interior of fully dimensional facets. The formulas are applied to both constructed and real data and show the differences between scale elasticities for the two valid projections (input and output orientations). Instead of getting qualitative measures of returns to scale only as was done earlier in the DEA literature, we now get a quantitative range of scale elasticity values providing more information to policy-makers.

Keywords:

• scale elasticity
• returns to scale
• DEA
• farrell efficiency measures

Acknowledgements

This paper was written as part of the Norwegian Research Council program Efficiency in the Public Sector at the Frisch Centre, University of Oslo. It was finished while the first author was a visiting fellow at ICER, Turin Autumn 2001/Spring 2002. Additional support from the following sources is gratefully acknowledged: The Bank of Sweden Tercentenary Foundation, HSFR, Jan Wallander's Research Foundation; and Göteborg School of Economics Foundation. We are indebted to Anders Hjalmarsson for carrying out all programming and calculations, and to Vladimir Krivonozhko and Ole Olesen for valuable comments.