1132 The Methods of Growth Econometrics
of geographic characteristics. A set ofKpotential growth theories, all of which are
logically compatible with combinations of one another, implies that there exist
2 K−1 potential specifications of the form (24.13), each one of which corresponds
to a particular combination of theories.
One approach to this model uncertainty is to examine robustness with respect
to variation in the model specification. This is the idea behind the classic Levine
and Renelt (1992) paper which, building on Leamer (1978, 1983) and Leamer and
Leonard (1983), used extreme bounds analysis to assess growth determinants. For a
modelm∈Mwithin the space of possible models, the growth process is specified as:
γi=ψmSi+πmRi,m+εi,m, (24.14)where themsubscripts reflect the model specific nature of the parameters and asso-
ciated errors. Letψˆmdenote the point estimate ofψfor everym∈Mand let the
vectorSbe composed of a variable of interest,sl, and other variables which are
included in all the specifications considered. Motivated by Leamer (1983), Levine
and Renelt (1992) use the following rule: there is strong evidence thatslaffects
growth if (and only if) the sign of the associated regression coefficientψˆl,mis con-
stant and the coefficient estimate is statistically significant across allm∈M. In their
analysis, the vectorSincludes the constant term, initial income, the investment
share of GDP, the secondary school enrollment rate, and the population growth
rate, as suggested by the augmented Solow model. The possible models are dis-
tinguished by alternative combinations of between one and three variables, taken
from a set of seven; these correspond to alternative choices ofRi,m. Applying their
rule, they conclude that the only robust growth determinants are initial income
and the share of investment in GDP.
These two findings are confirmed in subsequent work by Kalaitzidakis,
Mamuneas and Stengos (2000), who allow for potential nonlinearities in (24.14)
by considering models of the form:
γi=ψmSi+fm(
πRi,m)
+εi,m, (24.15)wheref(·)is a function allowed to vary across specifications ofR. Like Levine
and Renelt, they find that initial income and physical capital investment rates are
robust determinants of growth, but also find that inflation volatility and a measure
of exchange rate distortions are robust, providing an example of how failing to
account for nonlinearity in one set of variables can mask the importance of another.
A related exercise by Minier (2007) allows for nonlinearities in a parametric way
(including squared and interaction terms) and also examines what happens when
the Levine–Renelt sample is restricted to the lowest 75% of countries when ranked
by initial income, which broadly corresponds to a sample of developing countries.
She shows that a wider range of variables is found to be robust, including several
fiscal indicators that Levine and Renelt had classed as fragile. An open question here
is the extent to which certain kinds of nonlinearity, such as quadratic terms, may
be highly sensitive to outliers. Temple (2000b) discussed how an extreme bounds
analysis could be combined with robust estimation methods.