2 Application: Input
elasticities in manufacturing
We next present a simple interpretation of (1) with a single regressor (K = 1), to
be used as basis for our empirical applications. The data are from eight successive
annual Norwegian manufacturing censuses for the years 1983 - 1990 (T = 8),
collected by Statistics Norway, for four two-digit sectors, comprising 1647 firms
(plants): Manufacture of Textiles (ISIC 32) (N = 215), Manufacture of Wood and
Wood Products (ISIC 33) (N = 603), Manufacture of Paper and Paper Products
(ISIC 34) (N = 600), and Manufacture of Chemicals (ISIC 35) (N = 229). The
data base specifies labour, capital, and materials (including energy) inputs, but for
our illustrative purposes and in order not to inflate our tables of results, we confine
attention on the two latter. This pair of inputs is interesting since capital raises
much heavier measurement problems than materials, although both inputs and the
output contain potential measurement errors, both in the strict and wide sense.
Our measure of capital input is based on deflated fire insurance values, which is
a wealth related measure and hence contain potential errors as indicators of the
productive capacity of the capital.
Let us, with reference to production theory, describe two alternative interpreta-
tions of the model (1) - (5). We do not go deeply into the problems of theory-data
confrontation and refer to Stigum (1995) for a thorough discussion.
The first and simplest interpretation is to assume a technology with one output
X*t and one input Y*t, i.e., either capital or materials, both latent. Firm specific
differences in technology are represented by the factor eφi , indicating firm i’s de-
parture from the technology of the average firm (characterized by φi = 0). We
specify the technology as
(6) x; = eφ F ( K ) = A ( K )μ,
where A is a positive constant, μ is the scale elasticity for this one factor Cobb-
Douglas technology, and E(φi) = 0. We can allow for an unspecified period specific