The further disaggregation of sectoral aid markedly changes the results. In both sectors, the marginal effect of SP aid in the FE model is close to 1; this result suggests that the bulk of SP aid is used in the intended sector. Full fungibility can be rejected, but the null hypothesis of no fungibility cannot be rejected. The effect of TC is close to zero in both sectors, and the null hypothesis of full fungibility is strongly rejected. The hypothesis of no fungibility cannot be rejected; thus, there is no evidence that sectoral TC displaces a recipient government’s own expenditure in either sector. The TC effect is similar in OLS, whereas the coefficients of SP aid become larger but are also estimated less precisely. The larger SP aid coefficients in OLS may indicate that time-invariant unobservables are positively correlated with both SP aid and sectoral public expenditures. In the FE estimation, the coefficients are identified from the within-country variation in the data, which reduces the problem of omitted variables in instances in which such variables do not change substantially over time.

For the FE results in Tables 3 and 4, a generalized Hausman test that allows for heteroskedasticity and serial correlation is reported (Arellano, 1993; Wooldridge, 2002, pp. 290-291).<sup>20</sup> The null hypothesis that _ηi_ is uncorrelated with the regressors is always rejected; this result suggests that FE should be preferred over RE. Growth consistently has a negative effect, which suggests that education and health expenditures do not immediately adjust to a higher (lower) level in the event of a positive (negative) short-term shock to GDP per capita (Dreher, 2006, obtains a similar result for total and social expenditures in OECD countries).

As a robustness test, I obtain qualitatively similar FE results with aid variables that are constructed by scaling up sectoral CRS disbursements to ensure that their sum matches the aggregate DAC2a disbursements (equation (5) but applied to CRS disbursements rather than commitments). The main change is that for some aid variables, the estimated coefficients are closer to zero and/or estimated less precisely, which is consistent with greater measurement error in the aid data that are constructed using this short-cut method.<sup>21</sup> Table 4 illustrates that a failure to properly address the presence of off-budget aid may yield misleading conclusions. After on- and off-budget aid are separated and their effects are assessed against appropriate benchmarks, the FE results suggest that there is little if any fungibility. This conclusion is robust to a large number of specification changes. I replace the PV of debt with a non-PV measure of long-term external public and publicly guaranteed debt expressed as a percentage of GDP (from World Bank, 2006b). I also add to the model, in turn, two different measures of the PV of debt relief constructed by Depetris Chauvin and Kraay (2005).<sup>22</sup> Because debt relief is often linked to higher social expenditure, one might expect it to have a larger positive effect on public education and health expenditure than the effect achieved by a reduction in debt or debt service that arises through means other than debt relief. If this effect is indeed larger, then we would expect a positive effect of debt relief even after controlling for the level of debt and debt service. However. I do not find evidence of this effect. Even without controlling for debt and debt service, I find no effect of the PV of debt relief. I further include GDP per capita in log form rather than in thousands of dollars. I add 16