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Title:Can random coefficient Cobb-Douglas production functions be aggregated to similar macro functions? PDF Logo
Authors:Biørn, Erik
Skjerpen, Terje
Wangen, Knut R.
Issue Date:2004
Series/Report no.:Memorandum, Department of Economics, University of Oslo 2004,22
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.
Subjects:Productivity
Panel
Data
Random
coefficients
Log-normal
distribution
Aggregate
production
function
JEL:C23
C43
D21
L11
Document Type:Working Paper
Appears in Collections:Memorandum, Department of Economics, University of Oslo

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