A Bayesian approach to analyze regional elasticities

lower than 1/3, the translog model still produces a reasonable approximation to the
unknown cost function in North. However it will be interesting to compare the behavior
of this functional flexible form with different ones (such as Generalized Leontief, Box-
Cox or Minflex Laurent) in further studies.

5. Conclusions

In this paper I have reviewed the well known approach to analyze production
technologies with dual flexible cost function. In this study I have chosen the standard
generalized translog cost function that had widespread applications in the empirical
literature. This has been applied to the metal product sector of the main macro region in
Italy (North, Center and South).

Since elasticity distributions are not known and approximate variances are often
completely unreliable I have adopted a bayesian approach that can provide a sound
analysis, even with a very small sample (10 observations), providing a proper prior. As I
deal with Italian regional cost function, the informative prior has been naturally formed
with national data from the previous decade. As a point of reference I have adopted a
diffuse prior to compare both results. The bayesian approach has been performed in two
steps. First I derive posterior distribution with homogeneity and symmetry that cab be
derive in a straightforward way in our natural conjugate framework. Then I have
adopted a Monte Carlo Composition method to approximate them through an i.i.d.
empirical sample from the joint distribution over parameter and predictive. Only the
replications that satisfy all the neoclassical properties are accepted and also used to
derive the posterior odds ratios concerning concavity and monotonicity. Empirical
results are roughly in line with previous findings and as expected. This is true if we
adopt a proper prior, as, with a diffuse one, even if translog parameters are significant,
elasticities display unplausible values. Moreover concavity is not acceptable in all the
regions. Even with a proper prior, neoclassical theory deteriorates in South and can be
hardly accepted.¹⁰ In any case price and substitution elasticities between capital and
labor are very low but not far away from previous findings.

¹⁰ Fiorito (1990) estimates a labor market model in the same macroregions and find unsound results in
South, while Prosperetti and Varetto (1991) found larger inefficiencies in South suggesting that
neoclassical models could be at stakes in this region.

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