A Bayesian approach to analyze regional elasticities

general we have two choices. First we can claim to know to have no information, but
neoclassical properties. In this case our prior is a Jeffrey’s non informative or diffuse
prior that satisfies neoclassical constraints. As we see below, in our standard linear
regression model, this is to assume:

f (β,σ)- I(^β^

where I(β, ^~y) is an indicator function equal to one when neoclassical constraints are
satisfied and zero otherwise.

The second possibility is to form a proper prior that expresses our a priori
knowledge about the phenomenon under investigation. I claim that any empirical
analysis in regional science can be cast with a proper prior since we always have data at
the national lavel. Therefore we can elicit a convenient prior derived from national data
for the same parameters in which we are interested. Formally in the general linear model
we can consider:

f (β, σ) ∞ I (β, ~) f_N (β / σ) f₁G

where prior distributions are simply formed using the same model with previous or
contemporaneous national data. However this procedure is not completely automatic,
since we can always monitor these distributions in a appropriate way. If for instance the
regional data belong to an “important” region, whose share is relevant, we can give a lot
of weight to this prior. On the other hand for marginal regions we can choose to make
this prior distribution more diffuse simply controlling some a priori distribution
parameters. Therefore this approach is flexible enough to suit regional science
practitioners without resorting to complex and demanding aggregation theories.

Finally I would like to stress that bayesian econometrics appear to be the only
feasible solution if we consider the huge variety of phenomena in regional science, as it
doesn’t pretend to discover the “true” model or the “true” data generating process.
Perhaps in regional science we are more interested to study interregional differences and
explain for instance why certain regions grow and others don’t. When we compare
regions we are better off if we specify a general common model within which we can

¹ Classical refrence are Zellner (1971), Press (1972), Box and Tsiao (1973) while updated text are
O’Hagan (1995), Bernardo and Smith (1994).

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