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Heterogeneity in Returns to Scale: A Random Coefficient Analysis with Unbalanced Panel Data

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This paper analyses the importance of scale economies by means of unbalanced plant-level panel data from three Norwegian manufacturing industries. Focus is on heterogeneous technologies, and unlike most previous work on micro data, the model description includes heterogeneity in both the scale properties (the slope coefficients) and the intercept term, represented by random coefficients in the production function. Three (nested) functional forms are investigated: the Translog, an extended Cobb-Douglas, and the strict Cobb-Douglas. Although constant or weakly increasing returns to scale is found for the average plant, the results reveal considerable variation across plants. Variations in both input and scale elasticities are to a larger extent due to randomness of the production function parameters than to systematic differences in the input mix.

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  • Erik Biørn & Kjersti-Gro Lindquist & Terje Skjerpen, 2000. "Heterogeneity in Returns to Scale: A Random Coefficient Analysis with Unbalanced Panel Data," Discussion Papers 292, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:292
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    1. 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.
    2. Wan, Guang H & Griffiths, William E & Anderson, Jock R, 1992. "Using Panel Data to Estimate Risk Effects in Seemingly Unrelated Production Functions," Empirical Economics, Springer, vol. 17(1), pages 35-49.
    3. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
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    5. Hsiao, Cheng, 1975. "Some Estimation Methods for a Random Coefficient Model," Econometrica, Econometric Society, vol. 43(2), pages 305-325, March.
    6. 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.
    7. Matyas, Laszlo & Lovrics, Laszlo, 1991. "Missing observations and panel data : A Monte-Carlo analysis," Economics Letters, Elsevier, vol. 37(1), pages 39-44, September.
    8. Baltagi, Badi H. & Chang, Young-Jae, 1994. "Incomplete panels : A comparative study of alternative estimators for the unbalanced one-way error component regression model," Journal of Econometrics, Elsevier, vol. 62(2), pages 67-89, June.
    9. ZELLNER, Arnold & KMENTA, Jan & DREZE, Jacques H., 1966. "Specification and estimation of Cobb-Douglas production function models," LIDAM Reprints CORE 12, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Mundlak, Yair, 1996. "Production Function Estimation: Reviving the Primal," Econometrica, Econometric Society, vol. 64(2), pages 431-438, March.
    11. Badi H. Baltagi & Seuck H. Song & Byoung C. Jung, 2002. "A comparative study of alternative estimators for the unbalanced two-way error component regression model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 480-493, June.
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    Cited by:

    1. Héctor Salgado Banda & Lorenzo Bernal Verdugo, 2011. "Multifactor productivity and its determinants: an empirical analysis for Mexican manufacturing," Journal of Productivity Analysis, Springer, vol. 36(3), pages 293-308, December.
    2. Hailu, Getu & Goddard, Ellen W. & Jeffrey, Scott R., 2005. "Measuring Efficiency in Fruit and Vegetable Marketing Co-operatives with Heterogeneous Technologies in Canada," 2005 Annual meeting, July 24-27, Providence, RI 19507, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    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.
    4. 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.
    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. Kjersti-Gro Lindquist, 2002. "The Effect of New Technology in Payment Services on Banks' Intermediation," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B3-2, International Conferences on Panel Data.
    7. Yuriy Gorodnichenko, 2007. "Using Firm Optimization to Evaluate and Estimate Returns to Scale," NBER Working Papers 13666, National Bureau of Economic Research, Inc.
    8. 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.
    9. Jiahang He & Toshiyuki Yamamoto & Tomio Miwa & Takayuki Morikawa, 2020. "Hazard Duration Model with Panel Data for Daily Car Travel Distance: A Toyota City Case Study," Sustainability, MDPI, vol. 12(16), pages 1-13, August.
    10. 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.
    11. Hossein Karimi Hosnijeh & Robabeh Jaberi, 2009. "The Impacts of Technical Changes on Banking Economic Indices, Case Study of Iran," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 14(2), pages 97-111, fall.
    12. Erik Biørn, 2014. "Estimating SUR system with random coefficients: the unbalanced panel data case," Empirical Economics, Springer, vol. 47(2), pages 451-468, September.
    13. 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.

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    More about this item

    Keywords

    Panel Data. Economies of Scale. Heterogeneity. Random Coefficients;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L61 - Industrial Organization - - Industry Studies: Manufacturing - - - Metals and Metal Products; Cement; Glass; Ceramics
    • L65 - Industrial Organization - - Industry Studies: Manufacturing - - - Chemicals; Rubber; Drugs; Biotechnology; Plastics
    • L73 - Industrial Organization - - Industry Studies: Primary Products and Construction - - - Forest Products

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