1158 The Methods of Growth Econometrics
uncertainty and instrumental variable selection can be integrated simultaneously
into methods for model averaging and model selection. The recent work of Hendry
and Krolzig (2005) on automated methods includes an ambitious approach to sys-
tematic model selection for simultaneous equation models, in which identifying
restrictions are primarily determined by the data.
24.6.3 Instrumental variables and heterogeneous effects
Another issue that arises in applying instrumental variable methods to cross-
country data is the possible heterogeneity in the effects of the instrument, and
in the marginal effect of the explanatory variable that is instrumented. This is
closely related to the idea of “local” average treatment effects. Stock and Watson
(2004, sec. 11.7) provide a useful discussion of the issues in the context of 2SLS.
Assume that the parameters in the first stage and second stage of 2SLS vary across
countries, and are distributed independently of the variables (and instruments) in
the model and the error terms. It can then be shown that the probability limit
of the 2SLS estimate of the coefficient on the endogenous explanatory variable is
not the average causal effect, but a weighted average of the effects for individual
countries. The weighted average gives most weight to the countries for which the
instrument has the largest effect on the endogenous explanatory variable. A corol-
lary is that, when heterogeneity is present, the estimated effect depends on the
choice of instrument. A further consequence is that claims for the exogeneity of
the instruments become harder to sustain.
We can illustrate the potential importance of this by considering some of the
most influential papers that apply IV methods to cross-country data, using the
“levels regressions” approach discussed in section 24.3.3 above. In particular, Ace-
mogluet al.(2001), Frankel and Romer (1999), and Hall and Jones (1999) all study
the determinants of income levels using IV methods. The dependent variable is
a measure of (log) GDP per capita or per worker, and the explanatory variables
include one or more regressors that may determine income levels, but that are
themselves likely to be endogenous to the level of development.
What direction of bias should be expected when estimating such models by
OLS? The usual expectation would be that policy variables like institutional quality
“improve” (that is, move in the direction of promoting development) as GDP per
capita increases. Under this view of the world, an OLS estimate of the effect of
variables like institutions is likely to overstate their importance. The OLS slope
coefficient will be biased away from zero, and correcting for this using IV should
lead to a parameter estimate closer to zero, sampling variability aside. But the
papers of Acemogluet al.(2001), Frankel and Romer (1999) and Hall and Jones
(1999) all have in common the opposite result. Somewhat surprisingly, the IV
estimate associated with the variable of interest, such as the quality of institutions,
is typically larger in magnitude than the OLS estimate.
There are a number of possible explanations. One is sampling variability, while
another is measurement error. But if we take the view that development is likely
to encourage improvements in (say) institutions, so that OLS estimates of their
effect on output per worker are biased away from zero, the required extent of