and leads to an overestimation of the degree of fungibility. A marginal effect that is smaller than 1 does not necessarily indicate that aid is fungible; such a value could simply indicate that some aid is not recorded on a recipient government’s budget. This bias in the assessment of the degree of fungibility is larger if the variance of off-budget health aid is larger than the variance of on-budget health aid.<sup>4</sup> Other studies have estimated fungibility for a single country using a time series of recipient-based aid data (e.g., Pack and Pack, 1990, 1993; Franco-Rodriguez, Morrissey, and McGillivray, 1998; Feeny, 2007). In this case, because a recipient government’s reports of aid, by definition, exclude off-budget aid, only the effect of on-budget aid on government expenditures is estimated: Hence, the first problem is that we cannot estimate the degree of fungibility of off-budget health aid. Moreover, because off-budget health aid acts as an omitted variable and off- and on-budget health aid are most likely correlated, _β_<sup>�</sup> _ON_ is biased unless the marginal effect of off-budget health aid on health spending is zero. The sign of the bias is ambiguous because it depends on the partial correlation between on- and off-budget health aid, which could be positive or negative.

This section has clarified the criticism of McGillivray and Morrissey (2000, p. 422), who claim that because a large portion of the aid that is reported by donors is not reflected in the public sector accounts of recipients, such aid measures “. . . are inappropriate for analyzing fungibility”. In addition, this section has shown that the use of recipient-reported aid data is also problematic unless separate data exist that can measure off-budget aid such that equation (1) can be estimated rather than equation (4). Off-budget aid is likely to be sizable in many countries and to vary both between and within countries. Thus, the effects of its inappropriate treatment may be important. With regard to aggregate aid, Fagern ̈as and Roberts (2004a) show that OECD DAC figures for Uganda exceed the external financing recorded by the government by substantial margins (in some years, in excess of 10% of GDP). In Zambia, the gap is as wide as 20-40% of GDP in some years (Fagern ̈as and Roberts, 2004b). In both countries, the amount of off-budget aid varies substantially over time. Thus, for aggregate aid, _σOFF_<sup>2in (3) is unlikely to be small relative to</sup><sup>_σ_</sup> _ON_<sup>2.For Senegal,Ouattara (2006) finds that OECD DAC aid</sup> during the 1990s was, on average, twice as high as the aid reported by the local Ministry of Finance (12% vs. 6% of GDP, respectively), although his plots appear to suggest that the variation in aggregate aid over time is predominantly driven by on-budget aid.<sup>5</sup> The correct method of assessing whether earmarked aid is fungible involves separating on- and off-budget sectoral aid and comparing the marginal effect of on-budget aid on recipient sectoral spending to 1 and the marginal effect of off-budget aid to 0. The aim of this paper is to apply this method in the education and health sectors using a newly constructed dataset of disaggregated aid disbursements. Before presenting the empirical 4