Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?

Erik Biorn, Terje Skjerpen and Knut Wangen

No 22/2004, Memorandum from Oslo University, Department of Economics

Abstract: 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.

Keywords: Productivity.; Panel; Data.; Random; coe±cients.; Log-normal; distribution.; Aggregate; production; function (search for similar items in EconPapers)
JEL-codes: C23 C43 D21 L11 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2004-10-28
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Chapter: Can Random Coefficient Cobb Douglas Production Functions be Aggregated to Similar Macro Functions? (2006)
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