52: “however, budget support has limits, and project aid has been growing. The problems associated with poorly integrated project aid still loom large. The bigger challenge, therefore, is to bring project aid on budget.”) In section IV, I discuss how we can gain insight into the degree of fungibility of IP and ONM aid despite the greater uncertainty regarding the extent to which these types of aid are onor off-budget.

> 19As explained in Devarajan et al. (2007), unconditional resources _R_ (or their component parts, domestic revenue and net borrowing) should be excluded from the estimated equation to ensure that the full effect of earmarked aid on sectoral spending is captured. For instance, if sectoral aid reduces tax revenue but the latter is held fixed, then the effect of aid on spending may be overestimated. This twostep procedure entails the inclusion of the residual from a regression of _R_ on the right-side variables in equation (11) as an explanatory variable in the model. Because this residual is, by construction, orthogonal to the other right-side variables, its inclusion does not alter the sectoral aid coefficients, which capture the full effect of earmarked aid. However, its inclusion facilitates the estimation of<sup>_∂SSP_</sup> _∂Rit_<sup>_<u>it</u>_.</sup>

20This test is performed in Stata using the xtoverid command (Schaffer and Stillman, 2006).

> 21For instance, the coefficient on education SP aid is almost halved, to 0.64, and full fungibility is therefore rejected less strongly. The coefficient on health aid is reduced to 0.07, whereas in the disaggregated model, the coefficients on health IP and health ONM are much closer to zero. In both sectors, the coefficient on support to NGOs is estimated less precisely and/or substantially reduced in magnitude. The only exception is that the coefficient on health SP aid nearly doubles with the short-cut method (from 0.84 to 1.61), but its standard error rises commensurably.

22I am grateful to Nicolas Depetris Chauvin for sharing these data.

23In addition, no clear evidence is found to suggest that the degree of fungibility depends on the quality of institutions.

> 24The most extreme deviation occurs when the birth rate is added: the sample size in the health model decreases to 612, and the effect of health SP aid in the FE model rises to 1.34.

> 25To address zero values in the public expenditure, aid and debt variables, I add 1 before taking the log. Because GDP per capita growth can be negative, I include this variable without taking its log.

> 26Without Eritrea, the estimated effect of education TC becomes -0.33. Without Guinea-Bissau, the effect is 0.16.

> 27Using SP aid as an example, I calculate _DFBETAi_ as _DFBETAiSP_<sup>=(</sup><sup>_β_�</sup> _SP_<sup>_i−β_�</sup><sup>_SP_)</sup><sup>_/_(</sup> _SE_<sup>�</sup> � _βSPi_<sup>), where</sup><sup>_β_�</sup><sup>_SP_is the estimated</sup> coefficient in the full sample, _β_<sup>�</sup> _SP_<sup>_i_istheestimatewhencountry</sup><sup>_i_iseliminatedand</sup> _SE_<sup>�</sup> � _βSPi_<sup>istheestimatedstandarderrorofthe</sup> coefficient in the model without country _i_ (see, e.g., Bollen and Jackman, 1990). 28These countries are Burkina Faso, Cˆote d’Ivoire, Eritrea, Guinea-Bissau, Guyana, Lesotho, Mozambique, Nicaragua, Papua New Guinea, Samoa, Seychelles, Sierra Leone, Tajikistan and Tonga for education and Eritrea, Guinea-Bissau, Sierra Leone, Tajikistan, and Zambia for health.

> 29The elimination of outliers that are identified by either the method proposed by Hadi (1992, 1994) (hadimvo in Stata) or the method proposed by Billor, Hadi, and Velleman (2000) (bacon in Stata, see Weber, 2010) yields similar results. I follow Roodman (2007) in applying these methods to the partialled-out versions of public sectoral expenditure and sectoral SP aid and TC (i.e., the residuals that are obtained from the FE regressions of these variables on the other variables).

> 30Under the null hypothesis of no serial correlation, the residuals in the first-differenced model should have an autocorrelation of -0.5. Thus, a Wald test of this hypothesis can be performed to test for the presence of serial correlation in _εit_ (Wooldridge, 2002, p. 283; Drukker, 2003). I conduct this test in Stata using the xtserial command.

31Briefly, the GMM estimator differences equation (12) to remove the fixed effect and uses suitably lagged levels of the dependent variable and the right-side variables as instruments for the differenced equation. In addition, the system GMM estimator utilizes the equation in levels, using suitably lagged differences as instruments.

32I examine a number of different instrument configurations, from the use of a single lag of each variable to instrument the differenced equation to the use of four lags of each variable.

29