Reliability of the Translog Cost Function : Some Theory & an Application to the Demand of Energy in French Manufacturing

Baccar, Sourour (1995): Reliability of the Translog Cost Function : Some Theory & an Application to the Demand of Energy in French Manufacturing.

Abstract

We investigate the behavior of three versions of the translog cost function : the standard Log-quadratic version and two nonlinear versions with exponential and linear technical progress biases, respectively. Their performances are assessed according to three criteria: (i)on theoretical ground,(ii) on their ability to provide plausible estimates of economic and technological characteristics, and finally, (iii) on their reliability of fit for input shares, input-output ratios and unit cost. The most important result is that the standard form exhibits some weakness in fitting. We show via a series of experiments that those imprecisions are due to a lack of flexibility of the Log-quadratic form. Therefore, our results suggest that caveats should be attached to several previous studies, and care must be taken by future researchers who use such models.

• Item Type: MPRA Paper
• Language: English
• Keywords: translog cost function, reliability of fit, flexibility, energy demand, technical change modelling.
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C54 - Quantitative Policy Modeling; L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights

References

Baccar, S. (1995): ``Coût d´usage du capital et Fonction de Coût : la Marge de Liberté dans la Modélisation Laisse t-elle des Résultats Robustes?," Centre de Recherche en Economie et Statistique Seminar.

Barnett, W.A. (1983): ``New Indices of Money Supply and the Flexible Laurent Demand\- System," Journal of Business and Economic Statistics, 1, 7--23.

Barnett, W.A. (1983):``Definitions of `Second Order Approximation' and of `Flexible Functional Forms'," Economics Letters, 12, 31--35.

Barnett, W.A. (1985):``The Minflex Laurent Translog Flexible Functional Form'," {\em Journal of Econometrics}, 30, 33--44.

Barnett, W.A., and A.B. Jonas (1983):``The Muntz-Szatz Demand System," Economics Letters, 11, 337--342.

Barnett, W.A., and Y.W. Lee (1985): ``The Global Properties of the Minflex Laurent, Generalized Leontief, and Translog Functional Forms," Econometrica, 53, 1421--1437.

Barnett, W.A., Y.W. Lee, and M.D. Wolfe (1985): ``The Three Dimentional Global Properties of the Minflex Laurent, Generalized Leontief, and Translog Functional Forms," Journal of Econometrics, 30, 3--31.

Berndt, E.R., and M.S. Khaled (1979): Parametric Productivity Measurement and Choice Among Flexible Functional Forms,"Journal of Political Economy, 87, 1220--1245.

Berndt, E.R., and D.O. Wood} (1975): ``Technology Prices and the Derived Demands of Energy," Review of Economics and Statistics, 57, 259--268.

Brown, R.S. and L.R. Christensen (1981) : ``Estimating of Elasticities of Substitution in a Model of Partial Static Equilibrium : An Application to U.S. Agriculture, 1947 to 1974'', in Modeling and Measuring Natural Resource Substitution, ed. by Berndt, E.R. and B.C. Fields. Combridge, MA : M.I.T. Press, pp. 219--268.

Caves, D.W., and L.R. Christensen (1980): ``Global Properties of Flexible Functional Forms," American Economic Review, 70, 322--332.

Christensen, L.R., D.W. Jorgenson, and L.J. Lau} (1971): ``Conjugate Duality and the Trancendental Logarithmic Production Function," Econometrica, 39, 255--256.

Christensen, L.R., D.W. Jorgenson, and L.J. Lau (1973): ``Transcendental Logarithmic Production Frontiers," Review of Economics and Statistics, 55, 28--45.

Diewert, W.E. (1971): ``An Application of the Shephard Duality Theorem : A Generalized Leontief Production Function," Journal of Political Economy, 79, 481--507.

Diewert, W.E. (1974): ``Application of Duality Theory," in Frontier of Quantitative Economics , Vol II, ed. by M.D. Intriligator and D.A. Kendrick. Amesterdam~: North-Holland, pp. 106--171.

Diewert, W.E. (1982): ``Duality Approaches to Microeconomics Theory, " in Handbook of Mathematical Economics , Vol II, ed. by K.G. Arrow and M.D. Intriligator. Amesterdam : North-Holland, pp. 535--599.

Diewert, W.E., M.A. Avriel, and I. Zang (1981) : ``Nine Kinds of Quasi-concavity and Concavity," Journal of Economic Theory, 25, 397--420.

Diewert, W.E., and T.J. Wales (1987): ``Flexible Functional Forms and Global Curvature Conditions," Econometrica, 55, 43--68.

Diewert, W.E., and T.J. Wales (1988): ``A Normalized Quadratic Semi-flexible Functional Form," Journal of Econometric}, 37, 327--342.

Fuss, M.A., D.L. McFadden} (1978):``Production Economics : A Dual Approach to Theory and Applications," Amesterdam : North-Holland.

Gallant, R. A. (1981): `` On the Biais in Flexible Functional Forms and an Essantially Unbiased Form : The Fourrier Functional Form," Journal of Econometrics, 15, 211--245.

Gallant, A.R., and E.H. Golub (1984): ``Imposing Curvature Restrictions on Flexible Functional Forms," Journal of Econometrics, 26, 295--321.

Gourieroux, C., A. Holly, and A. Monfort (1982): ``Likelihood Ratios Test, Wald Test, and Kun-Tucker Test in linear Models with Inequality Constraints on the Regression Parameters," Econometrica, 50, 63--80.

Guilkey, D.K., and C.A.K. Lovell (1980) : ``On the Flexibility of the Translog Approximation," International Economic Review, 21, 137--147.

Guilkey, D.K., C.A.K. Lovell, and R.C. Sickles (1983) : ``A Comparison of the Performances of Three Flexible Functional Forms," International Economic Review, 24, 591--616.

Lau, L.J.} (1974): ``Applications of Dality Theory : a Comments," in Frontiers of Quantitative Economics}, Vol II, ed. by M.D. Intriligator and D.A. Kendrick. Amesterdam~: North-Holland, pp. 176--199.

McFadden, D.L.} (1978): ``The General Linear Profit Function," in Production Economics : A Dual Approach to Theory and Applications, Vol I, ed. by M. Fuss and D. McFadden. Amesterdam : North-Holland, pp. 269--286.

Ohta, M. (1974)}: ``A Note on the Duality Between Production and Cost Function : Rate of Returns to Scale and Rate of Technical Progress," Economic Studies Quarterly, 25, 63--65.

Rockafellar, R. T.} (1970): Convex Analysis. Princeton~: Princeton University Press.

Shephard, R. W. (1953)}: Cost and Production functions. Princeton : Princeton University Press.

Shephard, R. W. (1970): Theory of Cost and Production functions. Princeton :Princeton University Press.

Uzawa, H. (1962)}: ``Production Function with Constant Elasticities of Substitution," Review of Economic Studies, 29, 291--299.

Wales, T.J. (1977): ``On the Flexibility of Flexible Functional Forms," Journal of Econometrics, 5, 183--193.