dependent variable coe¢ cient should lie in the range between the FE estimate and the OLS estimate. This bracketing range thus provides a natural speci...cation check (Bond 2002).

The D-GMM solution to this endogeneity problem is to instrument for �yi;t�1 using yi;t�2 and possibly earlier lags. Notice that the lagged values of the dependent variable are useful instruments unless yi;t is close to a random walk, in which case past levels convey little information about future changes. Table 5 presents unit root test results for the three measures of ...scal performance. The IPS test statistic safely rejects the null of unit root in each case.<sup>27</sup> In the same fashion, one can instrument �MTFFi;t, which is also endogenous to �yi;t, with MTFFi;t�2 and possibly earlier lags (and similarly for the higher MTEF phases). In this way D-GMM generates internal instruments for the budget institutions. To improve estimation e¢ ciency we supplement the internal instruments with external instruments based on MTEF penetration in a country’s geographic region, computed according to equation (4). The external instruments are inspired by the regional penetration patterns noted in the previous section; see Subsection 2.2.<sup>28</sup> Because our panel is unbalanced, we use the orthogonal deviations transform (Arellano and Bover 1995) in the baseline speci...cations: yi;t<sup>�=</sup> q TTi;ti;+1t �yi;t � T1i;t Ps>t<sup>yi;s</sup> �, where Ti;t is the number of available future observations; we also report estimates based on the di¤erence transform yi;t<sup>�= yi;t�yi;t�1in the alternative speci...cations.Orthogonal deviations,</sup> instead of subtracting the previous observation from the current observation, subtracts the average of all future available observations from the current observation. This maximizes sample size in panels with gaps.

The moment conditions are based on orthogonality between the transformed errors and the lagged values of the dependent variable. To test for this condition one can run two diagnostics, namely ...rst-order and second-order serial correlation in the idiosyncratic error �i;t: The test should reject the null of no ...rst-order serial correlation, and not reject the absence of second-order serial correlation. We include year ...xed e¤ects in all speci...cations to strengthen the case for the assumption of no correlation in the idiosyncratic errors across countries.

> 27An alternative approach would be to use the System GMM estimator proposed by Arellano and Bover (1995) and Blundell and Bond (1998); this estimator requires an additional identifying assumption, namely that ...rst di¤erences of the instrumenting variables are exogenous to the ...xed e¤ects. This is the strategy we employ in World Bank (2012). There we also include a larger set of covariates which should mitigate omitted variable bias, but may also increase the possibility of additional endogeneity bias. The consistency in ...ndings between the two approaches adds to the robustenss to our results.

> 28By themselves the external instruments are not strong enough to justify a di¤-in-di¤s IV strategy. The lack of strength is driven in particular by insu¢ cient variation in MTPF adoption.

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