Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?
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.
|Date of creation:||28 Oct 2004|
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- 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.
- 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.
- 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.
- 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..
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- Tor Jakob Klette & Zvi Griliches, 1992. "The Inconsistency of Common Scale Estimators When Output Prices Are Unobserved and Engogenous," NBER Working Papers 4026, National Bureau of Economic Research, Inc.
- Tor Jakob Klette & Zvi Griliches, 1994. "The Inconsistency of Common Scales Estimators when Output Prices are Unobserved and Endogenous," Discussion Papers 127, Statistics Norway, Research Department.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)