Aggregation of Scale Elasticities Across Firms

Fare, Rolf and Zelenyuk, Valentin (2004): Aggregation of Scale Elasticities Across Firms.

Abstract

In this paper we propose new aggregate or ‘group’ primal and dual scale elasticity measures of an economic system (e.g., industry consisting of several firms, etc.). The main contribution of the paper is that we show under what assumptions a formal relationship between these new aggregate scale elasticity measures and the individual scale elasticities can be established. The derivations are based on the principles of economic optimization, and in particular on the duality theory of Shephard (1953) and the aggregation theory of Koopmans (1957).

• Item Type: MPRA Paper
• Language: English
• Keywords: Scale Elasticity, Aggregation, Duality
• Subjects: D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity

References

Efron, B. (1979) “Bootstrap methods: another look at the jackknife,” Annals of Statistics 7, 1-26.

Färe, R., S. Grosskopf and V. Zelenyuk (2004) “Aggregation of Cost Efficiency Indicators and Indexes Across Firms,” Academia Economic Papers 32:2, 395-411.

Färe, R. and D. Primont (1995) Multi-Output Production and Duality: Theory and Applications, Kluwer Academic Publishers, Boston.

Färe, R. and V. Zelenyuk (2003) "On Aggregate Farrell Efficiency Scores," European Journal of Operations Research 146:3, 615-620.

Färe, R. and V. Zelenyuk (2007) “Extending Färe and Zelenyuk,” European Journal of Operational Research 179:2, 594-595.

Koopmans, T.C. (1957) Three Essays on the State of Economic Analysis, McGraw-Hill, New York.

Kuosmanen, T., L. Cherchye, and T. Sipiläinen (2006) “The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility Across Firms,” European Journal of Operational Research 170:3, 735-757.

Li, S.-K., Ng, Y.-C., (1995) “Measuring the Productive Efficiency of a Group of Firms,” International Advances in Economic Research 1:4 377-390.

Nesterenko, V. and V. Zelenyuk (2007) “Measuring Potential Gains from Reallocation of Resources,” Journal of Productivity Analysis 28:1, 107-116.

Shephard (1970) Theory of Cost and Production Functions, Princeton: Princeton University Press.

Simar and Zelenyuk (2007) “Statistical Inference for Aggregates of Farrell-type Efficiencies,” Journal of Applied Econometrics 22:7, 1367-1394.

Zelenyuk, V. (2006) “On Aggregation of Malmquist Productivity Indexes,” European Journal of Operational Research 174:2, 1076-1086.

Zelenyuk, V. (2010) "Aggregation of Economic Growth Rates and of its Sources," CEPA Working Papers Series WP032010, School of Economics, University of Queensland, Australia (forthcoming in European Journal of Operational Research).