Paul Johnson, Steven Durlauf and Jonathan Temple 1157Since growth theories are often mutually compatible, the validity of an instru-
ment requires a positive and explicit argument that it cannot be a direct growth
determinant or correlated with an omitted growth determinant. For many of the
instrumental variables that have been proposed, such an argument is difficult to
construct.
Discussions of the validity of instruments inevitably suffer from some degree
of imprecision because of the need to make qualitative and subjective judgments.
When one researcher claims that it is implausible that a given instrument is valid,
unless this claim is made on the basis of a joint model of the instruments and
the variable of original interest, another researcher can always reject the asser-
tion as unpersuasive. To be clear, this element of subjectivity does not mean that
arguments about validity are pointless.^24 Rather, one must recognize that not all
statistical questions can be adjudicated on the basis of formal tests.
To see how different instruments might be assigned different levels of plausi-
bility, we consider some examples. Hall and Jones (1999) use various indicators
of Western European influence as instruments for openness to trade and institu-
tional quality. As subsequent authors, including Acemoglu (2005), have pointed
out, these indicators of Western European influence may have affected long-run
development through a variety of channels, in which case their usefulness as instru-
ments appears doubtful at best. The case for exclusion is easier to make for the
measure of Western European influence constructed by Acemogluet al.(2001),
namely the mortality rates of colonial settlers. Glaeseret al.(2004) discuss some of
the relevant issues in more detail.
As an example where instrument validity may be relatively plausible, consider
Cook (2002). He employs measures of the damage caused by World War II as instru-
ments for various growth regressors, such as saving rates. The validity of Cook’s
instruments again relies on the orthogonality of World War II damage with omitted
post-war growth determinants. It may be that levels of wartime damage had con-
sequences for post-war growth performance in other respects, such as institutional
change. Nevertheless, that argument would clearly be more involved, and specu-
lative, than would be necessary for some other examples in the growth literature.
To be clear, this discussion is nowhere near sufficient to conclude that one set
of instruments is valid and another is not. Our central point is that exclusion
restrictions need to rest on careful and explicit arguments. In particular, it is not
enough to appeal to a variable being predetermined. The fact that a variable may
be exogenous from an economic point of view is not enough to ensure that it
is uncorrelated with the disturbances in the structural equation being estimated.
This implies that historical information has a vital role to play in evaluating the
plausibility of exclusion restrictions.
This discussion of instrumental variables indicates another important, albeit
neglected, issue in empirical growth analysis: the relationship between model spec-
ification and instrumental variable selection. One cannot discuss the validity of
particular instruments independently from the choice of the specific growth deter-
minants under study and decisions about how to specify their relationship with
growth. As we noted earlier, an important research question is whether model