Paul Johnson, Steven Durlauf and Jonathan Temple 1131with important implications for econometric practice. Observe that in each case,
while the associated analyses are often motivated by formal theories, operationally
they represent efforts to develop statistical growth models that are consistent with
particular specification tests.
24.4.1 Specifying explanatory variables in growth regressions
The first point to emphasize is the sheer number of growth determinants that have
been proposed; the number of potential growth determinants now approaches the
number of countries available. The table in Appendix B of Durlaufet al. (2005) lists
many of them, with references to studies that represent either the first use of the
variable or an especially well-known use of the variable. That table contains 145
different regressors, the vast majority of which have been found to be significant
at conventional levels in at least one study. One reason why so many alternative
variables have been identified is due to questions of measurement. For example,
even given a specific claim that political freedom might affect growth, there could
be many ways to measure such freedoms. But even taking this into account, the
multiplicity of possible theories is striking. Durlaufet al. organize the empirical
literature into 43 distinct growth “theories” (that is, conceptually distinct growth
determinants) and it would not be difficult to add further examples.
Moreover, this list does not consider interactions between variables or nonlinear
transformations of variables, even though both are often used. The range of possi-
bilities hints at one of the fundamental problems with empirical growth research:
a lack of consensus on which growth determinants ought to be included in a sta-
tistical model. In this section, we discuss attempts to address this question and to
limit the degree of arbitrariness otherwise present.
To fix ideas, letSidenote the set of regressors always included by the researcher
whileRidenotes the set of additional candidate regressors, so that:
γi=ψSi+πRi+εi, (24.13)is the putative growth regression. The inclusion of a variable inSdoes not mean
the researcher is certain that it influences growth, only that it is to be included in
all models considered. If one takes the regressors that compriseRas fixed, then
statements about elements ofψare straightforward. A frequentist approach to
inference will compute an estimate of the parameterψwith an associated distribu-
tion that depends on the data-generating process (DGP). Bayesians would compute
a posterior probability density ofψgiven the researcher’s prior, the data, and the
assumption that the linear model is correctly specified. Designating the available
data asDand a particular model asm, this posterior may be written asμ(ψ|D,m).
While extant growth theories can be used to identify candidates forR, the funda-
mental problem in developing statistical statements about eitherψˆorμ(ψ|D,m)
is that there do not exist good theoretical reasons to favour one particular model
and exclude others. As Brock and Durlauf (2001a) point out, growth theories are
typically “open-ended” in the sense that different theories are often compatible
with one another, rather than mutually exclusive. For example, a theory that insti-
tutions matter is not logically inconsistent with a theory that emphasizes the role