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

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  • Erik Biørn
  • Terje Skjerpen

    ()
    (Statistics Norway)

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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Bibliographic Info

Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 317.

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Date of creation: Apr 2002
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Handle: RePEc:ssb:dispap:317

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

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References

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  1. Hildenbrand, W. & Kneip, A., 1999. "Demand aggregation under structural stability," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 81-109, February.
  2. Erik Biørn & Kjersti-Gro Lindquist & Terje Skjerpen, 2000. "Micro Data On Capital Inputs: Attempts to Reconcile Stock and Flow Information," Discussion Papers, Research Department of Statistics Norway 268, Research Department of Statistics Norway.
  3. 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.
  4. Tor Jakob Klette & Zvi Griliches, 1994. "The Inconsistency of Common Scales Estimators when Output Prices are Unobserved and Endogenous," Discussion Papers, Research Department of Statistics Norway 127, Research Department of Statistics Norway.
  5. Hildenbrand, Werner, 1981. "Short-Run Production Functions Based on Microdata," Econometrica, Econometric Society, Econometric Society, vol. 49(5), pages 1095-1125, September.
  6. 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.
  7. Koebel, Bertrand M., 1996. "Tests of representative firm models: results for German manufacturing industries," ZEW Discussion Papers 96-16, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  8. Lewbel, Arthur, 1992. "Aggregation with Log-Linear Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 59(3), pages 635-42, July.
  9. Muysken, Joan, 1983. "The distribution approach to the aggregation of putty-clay production functions," European Economic Review, Elsevier, vol. 22(3), pages 351-362.
  10. 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.
  11. Lau, Lawrence J., 1982. "A note on the fundamental theorem of exact aggregation," Economics Letters, Elsevier, vol. 9(2), pages 119-126.
  12. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 42(4), pages 525-43, October.
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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, Research Department of Statistics Norway 342, Research Department of Statistics Norway.
  2. 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.
  3. Biorn, Erik & Skjerpen, Terje, 2004. "Aggregation biases in production functions: a panel data analysis of Translog models," Research in Economics, Elsevier, vol. 58(1), pages 31-57, March.

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