IDEAS home Printed from https://ideas.repec.org/p/ssb/dispap/317.html

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

Author

Listed:

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://www.ssb.no/a/publikasjoner/pdf/DP/dp317.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. repec:adr:anecst:y:2003:i:69:p:03 is not listed on IDEAS
    3. Joan MUYSKEN, 1987. "The distribution approach to the aggregation of production functions," Discussion Papers (REL - Recherches Economiques de Louvain) 1987034, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. 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.
    5. Bertrand Koebel, 1998. "Tests of Representative Firm Models: Results for German Manufacturing Industries," Journal of Productivity Analysis, Springer, vol. 10(3), pages 251-270, November.
    6. Hildenbrand, Werner, 1981. "Short-Run Production Functions Based on Microdata," Econometrica, Econometric Society, vol. 49(5), pages 1095-1125, September.
    7. Hildenbrand, W. & Kneip, A., 1999. "Demand aggregation under structural stability," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 81-109, February.
    8. Muysken, Joan, 1983. "The distribution approach to the aggregation of putty-clay production functions," European Economic Review, Elsevier, vol. 22(3), pages 351-362.
    9. Lau, Lawrence J., 1982. "A note on the fundamental theorem of exact aggregation," Economics Letters, Elsevier, vol. 9(2), pages 119-126.
    10. 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.
    11. Stoker, Thomas M, 1993. "Empirical Approaches to the Problem of Aggregation Over Individuals," Journal of Economic Literature, American Economic Association, vol. 31(4), pages 1827-1874, December.
    12. 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..
    13. 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.
    14. Arthur Lewbel, 1992. "Aggregation with Log-Linear Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 635-642.
    15. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 525-543.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Erik Biørn & Terje Skjerpen & Knut R. Wangen, 2006. "Can Random Coefficient Cobb Douglas Production Functions be Aggregated to Similar Macro Functions?," Contributions to Economic Analysis, in: Panel Data Econometrics Theoretical Contributions and Empirical Applications, pages 229-258, Emerald Group Publishing Limited.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Erik Biørn & Terje Skjerpen & Knut R. Wangen, 2006. "Can Random Coefficient Cobb Douglas Production Functions be Aggregated to Similar Macro Functions?," Contributions to Economic Analysis, in: Panel Data Econometrics Theoretical Contributions and Empirical Applications, pages 229-258, Emerald Group Publishing Limited.
    3. Hildenbrand, Werner & Kneip, Alois, 2005. "Aggregate behavior and microdata," Games and Economic Behavior, Elsevier, vol. 50(1), pages 3-27, January.
    4. Arthur Lewbel, 2025. "Direct utility functions for rank two and quadratic logarithmic continuous demand systems," Journal of Productivity Analysis, Springer, vol. 63(3), pages 285-290, June.
    5. 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.
    6. van Garderen, Kees Jan & Lee, Kevin & Pesaran, M. Hashem, 2000. "Cross-sectional aggregation of non-linear models," Journal of Econometrics, Elsevier, vol. 95(2), pages 285-331, April.
    7. Laisney, François, 1991. "Mikroökonometrische Untersuchung von Aggregationsproblemen: Eine partielle Übersicht," ZEW Discussion Papers 91-03, ZEW - Leibniz Centre for European Economic Research.
    8. Cranfield, J. A. L. & Preckel, Paul V. & Eales, James S. & Hertel, Thomas W., 2004. "Simultaneous estimation of an implicit directly additive demand system and the distribution of expenditure--an application of maximum entropy," Economic Modelling, Elsevier, vol. 21(2), pages 361-385, March.
    9. Frank Denton & Dean Mountain, 2004. "Aggregation effects on price and expenditure elasticities in a quadratic almost ideal demand system," Canadian Journal of Economics, Canadian Economics Association, vol. 37(3), pages 613-628, August.
    10. Erik Biørn & Terje Hagen & Tor Iversen & Jon Magnussen, 2010. "How different are hospitals’ responses to a financial reform? The impact on efficiency of activity-based financing," Health Care Management Science, Springer, vol. 13(1), pages 1-16, March.
    11. Zizhuo Wang & Chaolin Yang & Hongsong Yuan & Yaowu Zhang, 2021. "Aggregation Bias in Estimating Log‐Log Demand Function," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 3906-3922, November.
    12. Stoker, Thomas M., 1982. "Completeness, distribution restrictions and the form of aggregate functions," Working papers 1345-82., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    13. Pedro H. Albuquerque, 2003. "A practical log-linear aggregation method with examples: heterogeneous income growth in the USA," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 665-678.
    14. Chambers, Robert G. & Pope, Rulon D., 1995. "Inequality Measures and Intergrable Demand Systems," Working Papers 197829, University of Maryland, Department of Agricultural and Resource Economics.
    15. Kesavan, Thulasiram, 1988. "Monte Carlo experiments of market demand theory," ISU General Staff Papers 198801010800009854, Iowa State University, Department of Economics.
    16. Hiroshi Fujiki & Cheng Hsiao, 2008. "Aggregate and Household Demand for Money: Evidence from the Public Opinion Survey on Household Financial Assets and Liabilities," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 26, pages 159-194, December.
    17. Jean Imbs & Eric Jondeau & Florian Pelgrin, 2006. "Aggregating Phillips curves," 2006 Meeting Papers 640, Society for Economic Dynamics.
    18. Biorn, Erik & Hagen, Terje P. & Iversen, Tor & Magnussen, Jon, 2006. "Heterogeneity in Hospitals' Responses to a Financial Reform: A Random Coefficient Analysis of The Impact of Activity-Based Financing on Efficiency," MPRA Paper 8169, University Library of Munich, Germany.
    19. Chambers, Robert G. & Pope, Rulon D., 1996. "Aggregable price-taking firms," European Economic Review, Elsevier, vol. 40(2), pages 417-428, February.
    20. Denton, Frank T. & Mountain, Dean C., 2001. "Income distribution and aggregation/disaggregation biases in the measurement of consumer demand elasticities," Economics Letters, Elsevier, vol. 73(1), pages 21-28, October.

    More about this item

    Keywords

    ;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ssb:dispap:317. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: L Maasø (email available below). General contact details of provider: https://edirc.repec.org/data/ssbgvno.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.