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Aggregation and Aggregation Biases in Production Functions: A Panel Data Analysis of Translog Models

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Abstract

An applied econometric study of aggregation, based on an unbalanced panel data set for manu-facturing plants is presented. Panel data are informative in examining aggregation of variables, parameters, and relationships empirically since they (i) allow estimation at both the micro and the macro level, and (ii) enable comparison of the time series properties of the exactly aggre- gated micro relationships with those obtained by performing aggregation by analogy. Numerical aggregation of Translog production functions for three manufacturing industries is considered. We show, under linear aggregation of inputs and output, that departures between geometric and arithmetic means of the inputs and correlation between the log-inputs, both their levels and time paths, contribute substantially to aggregation biases in the output volume and instability of the derived input and scale elasticities. Hence, the existence and stability of an approximate "macro Translog production function" over time can be questioned.

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  • Erik Biørn & Terje Skjerpen, 2002. "Aggregation and Aggregation Biases in Production Functions: A Panel Data Analysis of Translog Models," Discussion Papers 317, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:317
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    1. Erik Biørn & Kjersti-Gro Lindquist & Terje Skjerpen, 2002. "Heterogeneity in Returns to Scale: A Random Coefficient Analysis with Unbalanced Panel Data," Journal of Productivity Analysis, Springer, vol. 18(1), pages 39-57, July.
    2. Klette, Tor Jakob & Griliches, Zvi, 1996. "The Inconsistency of Common Scale Estimators When Output Prices Are Unobserved and Endogenous," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 343-361, July-Aug..
    3. Erik Biorn & Kjerti-Gro Lindquist & Terje Skjerpen, 2003. "Random Coefficients in Unbalanced Panels: An Application on Data from Chemical Plants," Annals of Economics and Statistics, GENES, issue 69, pages 55-83.
    4. Bertrand Koebel, 1998. "Tests of Representative Firm Models: Results for German Manufacturing Industries," Journal of Productivity Analysis, Springer, pages 251-270.
    5. Hildenbrand, Werner, 1981. "Short-Run Production Functions Based on Microdata," Econometrica, Econometric Society, vol. 49(5), pages 1095-1125, September.
    6. Hildenbrand, W. & Kneip, A., 1999. "Demand aggregation under structural stability," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 81-109, February.
    7. Muysken, Joan, 1983. "The distribution approach to the aggregation of putty-clay production functions," European Economic Review, Elsevier, vol. 22(3), pages 351-362.
    8. Lau, Lawrence J., 1982. "A note on the fundamental theorem of exact aggregation," Economics Letters, Elsevier, vol. 9(2), pages 119-126.
    9. Erik Biørn & Kjersti-Gro Lindquist & Terje Skjerpen, 2000. "Micro Data On Capital Inputs: Attempts to Reconcile Stock and Flow Information," Discussion Papers 268, Statistics Norway, Research Department.
    10. Stoker, Thomas M, 1993. "Empirical Approaches to the Problem of Aggregation Over Individuals," Journal of Economic Literature, American Economic Association, pages 1827-1874.
    11. Hildenbrand, Werner, 1998. "How relevant are specifications of behavioral relations on the micro-level for modelling the time path of population aggregates?," European Economic Review, Elsevier, vol. 42(3-5), pages 437-458, May.
    12. Arthur Lewbel, 1992. "Aggregation with Log-Linear Models," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 635-642.
    13. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Oxford University Press, vol. 42(4), pages 525-543.
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    Cited by:

    1. Erik Biørn & Terje Skjerpen & Knut Reidar Wangen, 2003. "Parametric Aggregation of Random Coefficient Cobb-Douglas Production Functions: Evidence from Manufacturing Industries," Discussion Papers 342, Statistics Norway, Research Department.
    2. Biorn, Erik & Skjerpen, Terje, 2004. "Aggregation biases in production functions: a panel data analysis of Translog models," Research in Economics, Elsevier, pages 31-57.
    3. Biørn, Erik & Skjerpen, Terje & Wangen, Knut Reidar, 2004. "Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?," Memorandum 22/2004, Oslo University, Department of Economics.

    More about this item

    Keywords

    Aggregation. Panel Data. Translog. Scale elasticity. Input distribution.;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L60 - Industrial Organization - - Industry Studies: Manufacturing - - - General

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