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

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Erik Biørn and Terje Skjerpen () (Statistics Norway)

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

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Find related papers by JEL classification:
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
D21 - Microeconomics - - Production and Organizations - - - Firm Behavior
E23 - Macroeconomics and Monetary Economics - - Macroeconomics: 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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hildenbrand, Werner, 1981. "Short-Run Production Functions Based on Microdata," Econometrica, Econometric Society, vol. 49(5), pages 1095-1125, September. [Downloadable!] (restricted)
  2. Erik Biørn, Kjersti-Gro Lindquist and Terje Skjerpen, . "Micro Data On Capital Inputs: Attempts to Reconcile Stock and Flow Information," Discussion Papers 268, Research Department of Statistics Norway. [Downloadable!]
  3. Lewbel, Arthur, 1992. "Aggregation with Log-Linear Models," Review of Economic Studies, Blackwell Publishing, vol. 59(3), pages 635-42, July. [Downloadable!] (restricted)
  4. Hildenbrand, W. & Kneip, A., 1999. "Demand aggregation under structural stability," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 81-109, February. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Erik Biørn, Kjersti-Gro Lindquist and Terje Skjerpen, 2000. "Heterogeneity in Returns to Scale: A Random Coefficient Analysis with Unbalanced Panel Data," Discussion Papers 292, Research Department of Statistics Norway. [Downloadable!]
  7. Nicole Fortin, 1991. "Fonctions de production et biais d'agrégation," Annales d'Economie et de Statistique, ADRES, issue 20-21, pages 04, Octobre-m. [Downloadable!]
  8. 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 343-61, July-Aug.. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
  10. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Blackwell Publishing, vol. 42(4), pages 525-43, October. [Downloadable!] (restricted)
  11. Lau, Lawrence J., 1982. "A note on the fundamental theorem of exact aggregation," Economics Letters, Elsevier, vol. 9(2), pages 119-126. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. Erik Biørn, Terje Skjerpen and 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. [Downloadable!]
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