A Bayesian approach to analyze regional elasticities

differentiate patterns. This task cannot be accomplish with the standard approach since
"the fundamental difficulty for classical inference is that it deduces what should be
observed as the sample increases if the model is correctly specified. By contrast, the
objective of the investigator is to modify his view of the world conditional on a given
data set, and prior information which includes the specification of the model" (Geweke
1988 p. 161).

The paper is organized as follows. In section 2, I briefly review the well known
translog cost function. In section 3 I outline the standard bayesian approach for the
general linear model with exchangeable observations. Regular regional elasticity
distributions are analyzed with a Monte Carlo Composition method that can be used to
determine the posterior probability of inequality constraints (monotonicity and
concavity). Empirical results for the Italian macro regions are presented in section 4.
Finally conclusions and directions for future research are discussed in the last section.

2. A generalized translog cost function

Consider a standard generalized transcendental logarithmic (translog):

1          1^NN

lnC(p,q,t)=α₀+α_Ylnq++γ_YY(lnq)² + ∑∑γ_ij ln p_iln p_j+

2                   ²'=¹'=1                                  (2.1)

N                         ₁N

+∑γ_Yi ln q ln p_i +δ_T t+δ_TT t² +δ_TY t ln q+∑δ_Ti t ln p_i

i=1                                          ²                                        i=1

where q is total output, p a vector of non-negative prices and t is a time index. Cost
shares are provided by Shepard Lemma:

y_i=α_i+∑^N γ_ijlnp_j+γ_Yi lnY+δ_Ti t i = 1,...,N         (2.2)

i =1

It is known that a well behaved cost function and its share systems must satisfy several
properties. Linear homogeneity in p can be globally imposed assuming:

∑αi=1; ∑γij=∑γij=∑γYi=∑δTi =0 .                 (2.3)

i     i    ji    i

while symmetry of the cross price demand responses is satisfied if γ_ij = γ _ji for all i,j.
If the translog is conceived as a Taylor approximation to a generic cost function in t=0,
p_i=q=1 for all i, by Young theorem, symmetry is a maintained hypothesis. Otherwise
(2.2) is an exact cost function whose properties can be tested or assumed (Jorgenson

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