1134 The Methods of Growth Econometrics
Dissatisfaction with extreme bounds analysis and its close relatives has led some
authors to advocate more systematic methods for model selection. Hendry and
Krolzig (2004) and Hoover and Perez (2004) both employ the general-to-specific
modeling methodologies associated with the research program of David Hendry,
in order to select one version of (24.13) out of the model space. Essentially, these
papers use algorithms which select a particular regression model from a space of
possible models, through comparisons based on a set of statistical tests. The attrac-
tiveness of this approach is closely linked to that of the broader Hendry research
program (see Hendry, 1995). We do not provide an extended evaluation here, but
note that relying solely on model selection procedures does not possess a clear
decision-theoretic justification, which makes it harder to evaluate the output of
the procedure in terms of the objectives of a researcher. That said, automated pro-
cedures have the important virtue that they can identify sets of models that are
well supported by the available data, and may be especially useful as a preliminary
step in model-building.
In our judgment, the most promising approach to model uncertainty is the use of
model averaging in the Bayesian tradition, and especially the methods developed
by Adrian Raftery and co-authors (for example, Raftery, Madigan and Hoeting,
1997). Versions of these methods have been applied to growth data in Brock
and Durlauf (2001a), Brocket al. (2003), Ciccone and Jarocinski (2007), Durlauf,
Kourtellos and Tan (2008), Fernandez, Ley and Steel (2001a), Masanjala and Papa-
georgiou (2005) and Sala-i-Martin, Doppelhofer and Miller (2004), among others.
The basic idea is to treat the identity of the “true” growth model as an unobservable
variable about which the researcher is inevitably uncertain.^8 In order to account
for this, each elementmin the model spaceMis associated with a posterior model
probabilityμ(m|D). By Bayes’ rule,
μ(m|D)∝μ(D|m)μ(m), (24.18)whereμ(D|m)is the likelihood of the data given the model andμ(m)is the prior
model probability. These model probabilities are used to eliminate the dependence
of parameter analysis on a specific model. For frequentist estimates, averaging is
done across the model-specific estimatesψˆmto produce an estimateψˆvia:
ψˆ=∑mψˆmμ(m|D), (24.19)whereas, in the Bayesian context, the dependence of the posterior probability mea-
sure of the parameter of interest,μ(ψ|D,m), on the model choice is eliminated
via standard conditional probability arguments, that is:
μ(ψ|D)=∑m∈Mμ(ψ|D,m)μ(m|D). (24.20)Brocket al.(2003) argue that the strategy of constructing posterior probabilities
that are not model-dependent is especially appropriate when the objective of the
statistical exercise is to evaluate alternative policy questions, such as whether to