1150 The Methods of Growth Econometrics
Hence, at least one of the explanatory variables in the first-differenced equation
will be correlated with the disturbances, and instrumental variable procedures are
required.
Arellano and Bond (1991), building on work by Holtz-Eakin, Newey and Rosen
(1988), developed the GMM approach to dynamic panels in detail, including spec-
ification tests and methods suitable for unbalanced panels. Caselliet al.(1996)
applied their estimator in the growth context and obtained a much faster rate of
conditional convergence than found in cross-section studies, consistent with the
view that OLS estimates, by ignoring country effects, will yield an upward bias on
the lagged dependent variable.
The GMM approach is typically based on using lagged levels of the series as
instruments for lagged first differences. If the error terms in the levels equation (εit)
are serially uncorrelated thenlogyi,t− 1 can be instrumented using logyi,t− 2 and
as many earlier lagged levels as are available. This corresponds to a set of moment
conditions that can be used to estimate the first-differenced equation by GMM.
Bond (2002) and Roodman (2006) provide especially accessible introductions to
the theory and application of this approach.
In principle, this strategy can alleviate biases due to measurement error and
endogenous explanatory variables. In practice, many researchers are sceptical that
lags, or “internally generated” instruments, are appropriate choices for instru-
ments. It is easy to see that a variable such as educational attainment may influence
output with a considerable delay, so that the exclusion of lags from the growth
equation can look arbitrary. More generally, the GMM approach relies on a lack of
serial correlation in the error terms of the growth equation (before differencing).
This assumption can be tested using the methods developed in Arellano and Bond
(1991), and can also be relaxed by an appropriate choice of instruments, but will
sometimes be restrictive.
In practice, many applications of these methods have used “too many” moment
conditions. The small-sample performance of the GMM panel data estimators is
known to deteriorate as the number of moment conditions grows relative to the
cross-section dimension of the panel. In that case, the coefficient estimates can be
severely biased, and a further consequence is that the power of Sargan-type tests of
overidentifying restrictions may collapse, as shown in Bowsher (2002). When tests
of the overidentifying restrictions yieldp-values near unity, this is an important
warning sign that too many moment conditions are in use, and this problem can
be seen relatively frequently in the literature. This can be avoided by using only a
sub-set of the available lags as instruments, or summing moment conditions over
time, while retaining enough overidentifying restrictions to ensure that Sargan-
type tests will have some power. Roodman (2007) discusses these issues in more
detail.
Another concern is that the explanatory variables may be highly persistent, as
is clearly true of output. Lagged levels can then be weak instruments for first dif-
ferences, and the GMM panel data estimator is likely to be severely biased in short
panels. Bond, Hoeffler and Temple (2001) illustrate this point by comparing the
Caselliet al.(1996) estimates of the coefficient on lagged output with OLS and