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Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?

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Author Info

  • Biørn, Erik

    ()
    (Dept. of Economics, University of Oslo)

  • Skjerpen, Terje

    ()
    (Statistics Norway, Research Department)

  • Wangen, Knut Reidar

    ()
    (Statistics Norway, Research Department)

Abstract

Parametric aggregation of heterogeneous micro production technologies is discussed. A four-factor Cobb-Douglas function with normally distributed firm specific coefficients and with log-normal inputs (which agrees well with the available data) is speciffied. Since, if the number of micro units is large enough, aggregates expressed as arithmetic means can be associated with expectations, we consider conditions ensuring an approximate relation of Cobb-Douglas form to exist between expected output and expected inputs. Similar relations in higher-order moments are also derived. It is shown how the aggregate input elasticities depend on the coefficient heterogeneity and the co-variance matrix of the log-input vector and hence vary over time. An implementation based on firm panel data for two manufacturing industries gives estimates of industry level input elasticities and decomposition for expected output. Finally, aggregation errors which emerge when the correct aggregate elasticities are replaced by the expected micro elasticities, are explored.

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File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2004/Memo-22-2004.pdf
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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 22/2004.

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Length: 31 pages
Date of creation: 28 Oct 2004
Date of revision:
Handle: RePEc:hhs:osloec:2004_022

Contact details of provider:
Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
Email:
Web page: http://www.oekonomi.uio.no/indexe.html
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Related research

Keywords: Productivity.; Panel; Data.; Random; coe±cients.; Log-normal; distribution.; Aggregate; production; function;

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References

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  1. Klette, T.J., 1992. "The Inconsistency of Common Scale Estimators when Output Prices are unobserved and Endogenous," Harvard Institute of Economic Research Working Papers 1586, Harvard - Institute of Economic Research.
  2. 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.
  3. Stoker, Thomas M, 1993. "Empirical Approaches to the Problem of Aggregation Over Individuals," Journal of Economic Literature, American Economic Association, vol. 31(4), pages 1827-74, December.
  4. Biorn, Erik, 2004. "Regression systems for unbalanced panel data: a stepwise maximum likelihood procedure," Journal of Econometrics, Elsevier, vol. 122(2), pages 281-291, October.
  5. Erik Biørn & Kjersti-Gro Lindquist & Terje Skjerpen, 2000. "Micro Data On Capital Inputs: Attempts to Reconcile Stock and Flow Information," Discussion Papers 268, Research Department of Statistics Norway.
  6. Jesus Felipe & Franklin M. Fisher, 2003. "Aggregation in Production Functions: What Applied Economists should Know," Metroeconomica, Wiley Blackwell, vol. 54(2-3), pages 208-262, 05.
  7. Erik Biørn & Terje Skjerpen, 2002. "Aggregation and Aggregation Biases in Production Functions: A Panel Data Analysis of Translog Models," Discussion Papers 317, Research Department of Statistics Norway.
  8. Erik Biørn & Terje Skjerpen & Knut Reidar Wangen, 2003. "Parametric Aggregation of Random Coefficient Cobb-Douglas Production Functions: Evidence from Manufacturing Industries," Discussion Papers 342, Research Department of Statistics Norway.
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Cited by:
  1. Markus Eberhardt & Francis Teal, . "Aggregation versus Heterogeneity in Cross-Country Growth Empirics," Discussion Papers 11/08, University of Nottingham, CREDIT.

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