Paul Johnson, Steven Durlauf and Jonathan Temple 1159measurement error is unlikely to be trivial. It has to be large enough to more than
offset the effect of the simultaneity bias acting in the other direction.
A more sceptical view is that the IV coefficient may be larger because either (i)
the effects may be heterogeneous; or (ii) the exclusion restrictions used in these
papers are not genuinely valid; or some combination of the two. One interesting
perspective on the IV results in the cross-country literature is that the instruments
might have a more powerful effect on the endogenous explanatory variable (such
as institutions) in those countries where the explanatory variable has an especially
powerful effect on development outcomes. To give a concrete example, this would
be the case if the Acemogluet al.(2001) instrument, namely mortality rates of colo-
nial settlers, had greatest influence on institutional development in sub-Saharan
Africa, and if the marginal effect of institutions on development outcomes is most
powerful in Africa. Were this true, the estimated effect of institutions will be larger
than the average causal effect, because the IV estimate gives more weight to the
causal effect for countries where the instrument has greatest influence. This does
not invalidate the finding that institutions matter, but does make it harder to
generalize about the extent to which they matter.
This is admittedly a speculative hypothesis, but there is some possible supporting
evidence in Table 4 of Acemogluet al.(2001). The 2SLS coefficient on institutions is
roughly halved when African countries are excluded from the sample, although still
precisely estimated. The sensitivity of the 2SLS estimate suggests that the effects
of institutions differ substantially across countries. A deeper and more rigorous
investigation would be possible when there is at least one additional instrument,
so that estimates can be compared across different instrument sets. If the effects of
policy are homogeneous across countries, the estimated effect should be the same
regardless of the choice of instrument (abstracting from sampling variability). That
invariance no longer holds under heterogeneous effects. Then, as we have seen, it
is likely that the IV estimate will be influenced by the choice of instrument, and
the estimated effect will no longer relate to the whole population.
24.7 Other econometric issues
In this section we consider a range of questions that arise in growth econometrics
from the properties of data and errors. Starting with data issues, section 24.7.1
examines how one may handle outliers in growth data. Section 24.7.2 examines
the problem of measurement error. This is an important issue since there are good
reasons to believe that the quality of the data is sometimes poor for less developed
economies. In section 24.7.3 we consider the case where data are missing. Turning
to issues of the properties of model errors, section 24.7.4 examines the analysis of
heteroskedasticity in growth contexts. Finally, section 24.7.5 addresses the problem
of cross-section error dependence.
24.7.1 Outliers
Empirical growth researchers often work with small datasets and estimate relatively
simple models. In these circumstances, OLS regressions are almost meaningless