Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity
This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost functions without maintaining convexity. Specifically, we introduce returns to scale assumptions into an existing non-convex technology and, dual to these various technologies, define non-convex cost functions. These non-convex cost functions are never lower than their convex counterparts. Both non-convex technologies and cost functions (total, ray-average and marginal) are characterised by simple, closed form expressions. Furthermore, a local duality result is established between a local cost function and the input distance function. Finally, nonparametric goodness-of-fit tests for the convexity axiom are developed. This is a first step towards making convexity a statistically testable hypothesis.
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- Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
- H. Alan Love, 1999. "Conflicts between Theory and Practice in Production Economics," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(3), pages 696-702.
- Coelli, T J, 1996. "Measurement of Total Factor Productivity Growth and Biases in Technological Change in Western Australian Agriculture," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 77-91, Jan.-Feb..
- Ramey, Valerie A, 1991. "Nonconvex Costs and the Behavior of Inventories," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 306-334, April.
- Jean-Paul Chavas & Thomas L. Cox, 1995. "On Nonparametric Supply Response Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(1), pages 80-92.
- Peter Bogetoft & Joseph M. Tama & Jørgen Tind, 2000. "Convex Input and Output Projections of Nonconvex Production Possibility Sets," Management Science, INFORMS, vol. 46(6), pages 858-869, June.
- Bauer, Paul W. & Berger, Allen N. & Ferrier, Gary D. & Humphrey, David B., 1998.
"Consistency Conditions for Regulatory Analysis of Financial Institutions: A Comparison of Frontier Efficiency Methods,"
Journal of Economics and Business,
Elsevier, vol. 50(2), pages 85-114, March.
- Paul W. Bauer & Allen N. Berger & Gary D. Ferrier & David B. Humphrey, 1997. "Consistency conditions for regulatory analysis of financial institutions: a comparison of frontier efficiency methods," Finance and Economics Discussion Series 1997-50, Board of Governors of the Federal Reserve System (U.S.).
- Paul W. Bauer & Allen N. Berger & Gary D. Ferrier & David B. Humphrey, 1997. "Consistency conditions for regulatory analysis of financial institutions: a comparison of frontier efficiency methods," Financial Services working paper 97-02, Federal Reserve Bank of Cleveland.
- Grosskopf, S, 1986. "The Role of the Reference Technology in Measuring Productive Efficiency," Economic Journal, Royal Economic Society, vol. 96(382), pages 499-513, June.
- Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
- Simar, Leopold & Wilson, Paul W., 2002. "Non-parametric tests of returns to scale," European Journal of Operational Research, Elsevier, vol. 139(1), pages 115-132, May.
- Léopold Simar & Paul Wilson, 2000.
"Statistical Inference in Nonparametric Frontier Models: The State of the Art,"
Journal of Productivity Analysis,
Springer, vol. 13(1), pages 49-78, January.
- Simar, L. & Wilson, P.W., 1999. "Statistical Inference in Nonparametric Frontier Models: the State of the Art," Papers 9904, Catholique de Louvain - Institut de statistique.
- Brown, Donald J., 1991. "Equilibrium analysis with non-convex technologies," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 36, pages 1963-1995 Elsevier.
- George J. Hall, 1997.
"Non-Convex Costs and Capital Utilization: A Study of Production Scheduling at Automobile Assembly Plants,"
Cowles Foundation Discussion Papers
1169, Cowles Foundation for Research in Economics, Yale University.
- Hall, George J., 2000. "Non-convex costs and capital utilization: A study of production scheduling at automobile assembly plants," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 681-716, June.
- R. Färe & S. Grosskopf & D. Njinkeu, 1988. "Note---On Piecewise Reference Technologies," Management Science, INFORMS, vol. 34(12), pages 1507-1511, December.
- Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
- M. J. Farrell, 1959. "The Convexity Assumption in the Theory of Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 67, pages 377-377.
- Jean-Paul Chavas & Thomas L. Cox, 1988. "A Nonparametric Analysis of Agricultural Technology," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 70(2), pages 303-310.
- J. Cummins & Hongmin Zi, 1998.
"Comparison of Frontier Efficiency Methods: An Application to the U.S. Life Insurance Industry,"
Journal of Productivity Analysis,
Springer, vol. 10(2), pages 131-152, October.
- J. David Cummins & Hongmin Zi, 1997. "Comparison of Frontier Efficiency Methods: An Application to the U.S. Life Insurance Industry," Center for Financial Institutions Working Papers 97-03, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Appelbaum, Elie, 1978. "Testing neoclassical production theory," Journal of Econometrics, Elsevier, vol. 7(1), pages 87-102, February.
- Seitz, Wesley D, 1971. "Productive Efficiency in the Steam-Electric Generating Industry," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 878-886, July-Aug..
- Wibe, Soren A, 1984. "Engineering Production Functions: A Survey," Economica, London School of Economics and Political Science, vol. 51(204), pages 401-411, November.
- Fare, Rolf & Li, Sung Ko, 1998. "Inner and outer approximations of technology: a data envelopment analysis approach," European Journal of Operational Research, Elsevier, vol. 105(3), pages 622-625, March.
- Førsund, Finn R. & Hjalmarsson, Lennart, 1978.
"Generalized Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants,"
Working Paper Series
17, Research Institute of Industrial Economics.
- Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
- R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
- Fare, Rolf & Grosskopf, Shawna & Lovell, C A Knox, 1983. " The Structure of Technical Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 85(2), pages 181-190.
- Jean-Paul Chavas & Thomas L. Cox, 1999.
"A Generalized Distance Function and the Analysis of Production Efficiency,"
Wisconsin-Madison Agricultural and Applied Economics Staff Papers
422, Wisconsin-Madison Agricultural and Applied Economics Department.
- Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, Southern Economic Association, vol. 66(2), pages 294-318, October.
- Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
- Fare, Rolf & Grosskopf, Shawna, 1995. "Nonparametric tests of regularity, Farrell efficiency, and goodness-of-fit," Journal of Econometrics, Elsevier, vol. 69(2), pages 415-425, October.
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