摘要：Parametric aggregation of heterogeneous micro production technologies is
discussed. A four-factor Cobb-Douglas function with normally distributed ¯rm speci¯c
coe±cients and with log-normal inputs (which agrees well with the available data) is
speci¯ed. 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 coe±cient heterogeneity and the co-
variance matrix of the log-input vector and hence vary over time. An implementation
based on ¯rm 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.
关键词：Productivity. Panel Data. Random coe±cients. Log-normal distribution.
Aggregate production function.
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