14 the FE estimator is biased in the other direction, meaning that theoretically superior estimates, such as difference- or system-GMM estimators, should lie within or near the range of these estimates (Bond 2002; Roodman 2009a).

The obvious way to solve the endogeneity problem is to use instrumental variables. To avoid the problem of finding suitable instruments in each case, difference- and system-GMM methods were developed, with which the fixed effects are eliminated and where longer lags of the regressors are available as instruments. Difference-GMM, the first difference transformation of equations (5) or (6), does exactly this. However, considerable concern has been expressed, for example, that in a context where the time series are persistent and the time dimension is small “the first-differenced GMM estimator is poorly behaved” (Bond et al. 2001). In particular, under those circumstances - which evidently apply to the data used in this paper, in Forbes (2000), and most of the cross-country growth literature - the two-period lagged dependent-variable (in levels) used as instruments for the firstdifferences in the second stage are weak instruments. When instruments are weak, large finite sample biases can occur, and these problems have been documented in the context of first-difference GMM models (Blundell and Bond, 1998; Bond et al. 2001).

To deal with these issues and increase efficiency, “system-GMM” models, using an additional set of moment restrictions, combine the usual equation in first-differences using lagged levels as instruments, with an additional equation in levels, using lagged first-differences as instruments. According to Blundell and Bond (1998), Blundell et al. (2000) and Bond et al. (2001), this approach results in substantial reductions in finite-sample biases in Monte-Carlo experiments. Although system GMM estimation is, for these reasons, now generally preferred to difference GMMs, it is not problem-free. In particular, Roodman (2009a) urges caution with the effect of instrument proliferation on the Hansen test of joint validity of instruments. Although a significant Hansen statistic suggests that the instrument set is not valid, Roodman points out that implausibly good p-values (of or very close to 1.0) are telltale signs of the fact that the Hansen test has been weakened to the point of no longer being informative. To limit the number of instruments in GMM estimation, two approaches have been proposed (and incorporated into the Stata command xtabond2). First, one can collapse the instrument set, which makes the instrument count linear in time periods T rather than quartic.<sup>24</sup> Second, one can apply principal component analysis (pca) to the instruments and limit the number of instruments by retaining components of the instruments with eigenvalues above a certain threshold.<sup>25</sup> This has the advantage of being purely datadriven and, hence, a less arbitrary strategy for instrument reduction: Bontempi and Mammi (2012) suggest that this method is a promising approach compared with lag truncation and collapsing the instrument set.

To be transparent and thorough in checking the robustness of any finding in our empirical analysis, we present four GMM estimates in each table: Difference-GMM in Column (4), system-GMM with the full set of available instruments, the collapsed set of instruments, and instruments replaced with their

> 24 The _collapse_ option in Stata’s _xtabond2_ command performs this, and the resulting instrument matrix, according to Roodman (2009a), “embodies the same expectation but conveys slightly less information” than the uncollapsed instrument set. Roodman (2009b) suggests that collapsing the instrument set still retains more information than limiting the use of only certain lags as instruments rather than the full set of available lags.

> 25 For example, the _pca_ option in Stata’s _xtabond2_ command retains components with eigenvalues greater than 1.