Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?
AbstractParametric 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.
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Bibliographic InfoPaper provided by Oslo University, Department of Economics in its series Memorandum with number 22/2004.
Length: 31 pages
Date of creation: 28 Oct 2004
Date of revision:
Contact details of provider:
Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
Web page: http://www.oekonomi.uio.no/indexe.html
More information through EDIRC
Productivity.; Panel; Data.; Random; coe±cients.; Log-normal; distribution.; Aggregate; production; function;
Find related papers by 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
- L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
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