A Bayesian approach to analyze regional elasticities

Fig. B Technical change South

As we can see from Table 1 posterior expected values and standard errors with
inequality constraints are very different with a diffuse prior. However in both cases it’s
evident that technical change has been labor saving (and capital using) in the eighties,
since only a negligible part of the distribution with a diffuse prior covers positive
values, even if our prior is mostly positive. The standard approach that estimate with
maximum likelihood methods neglecting to impose concavity can be very misleading
since a 95% Highest Posterior Density cover a large region that is not consistent with
neoclassical theory.

Now let’s consider more useful quantities as substitution and price elasticities.
As a point of reference I choose the last year of the data set (1989). Results are reported
in Table 2-4 and densities for price elasticities are plotted in Fig. C - E⁹, while
substitution elasticities are presented in Fig. F - H. We know that conditional on actual
shares elasticities are distributed as univariate t Student. Therefore we can provide exact
first moments that are shown in the following table:

⁹ Recall that ε = ε and ε = ε .
KK KL LL LK

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