The model is applied to the metal product sector concerning the Italian main
macroregions (i.e. North, Center and South) over the years 1980-89. The complete data
set concerns 20 Italian regions and is representative of a standard situation in (Italian)
regional economics, since regional time series are usually extremely short. Labor
comprehends both employed and self-employed workers, whose wage is assumed to be
equal within each region. Capital stock data are not available for the eighties at the
regional level, therefore it as been computed as a residual from constant price valued
added minus constant wage payroll. Even if the residual approach to build the data set is
very questionable, stocks and relative price are consistent with national patterns and
other regional information such as regional investment.7 Moreover I utilize an enlarged
definition of capital as it can include factors that are not compatible with the
neoclassical theory outlined above, such as market power. These caveats should be kept
in mind when reviewing regional elasticitities.
The first step of our analysis is to adopt a prior. I embrace both a diffuse
(noninformative) prior and a proper one. A Jeffrey’s prior can be used if we claim not to
have any a priori knowledge about parameters and has been frequently addressed as a
reductive attempt to be more "objective". A proper prior can be easily derived from
national data for the previous decade. Moreover we can also assume that the error
variances are different in the two sets (Zellner 1971, Drèze 1977) and obtain a poly t 2-0
model or we can accommodate degrees of freedom to obtain very flat prior
distributions8. Posterior moments are provided in Table 1 with moments for the proper
prior. As obvious there is a greater precision with the informative prior.
7 The value-added approach to estimate cost of capital (Cost of capital = value added - payroll) was
criticized since it includes more than cost of reproducible capital, as working capital, land and so on. It
was suggested (see also Christensen and Jorgenson (1969), Berndt and Wood (1975)) that a service price
approach is better suited since it allows to directly figure out the cost of reproducible capital alone. This
can explain the large difference in U.S. manufactoring elasticities in earlier studies, that “could in part be
traceable to the fact that two quite different types of capital inputs are involved and these two form of
capital, physical capital and working capital, behave in quite different ways" (Field and Grebenstein
(1979: p. 207). However lack of data on regional physical capital and the extreme unreliability of the
procedure adopted to construct rental price series for the Italian regions had forced to follow the value
added approach
8 In this analysis degrees of freedom are equal to 6, allowing for quite smooth distributions, but these can
be decreased further, since only second order moments are required to have well defined prior
distributions. For sake of simplicity I have implemented the most straightforward statistical model, but the
bayesian approach is flexible enough to allow any modification about prior beliefs with a larger
computational cost.