Scandinavian Working Papers in Economics
Memorandum,
Oslo University, Department of Economics
No 22/2004: Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?
Erik Biørn (), Terje Skjerpen () and Knut Reidar Wangen ()
Additional contact information
Erik Biørn: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Terje Skjerpen: Statistics Norway, Research Department, Postal: P.O.B 8131 Dep, NO-0033 Oslo
Knut Reidar Wangen: Statistics Norway, Research Department, Postal: P.O.B 8131 Dep, NO-0033 Oslo
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
31 pages, October 28, 2004
Full text files
Memo-22-2004.pdf
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