suggests that a handful of high values on aid share could be influential in producing its negative and significant coefficient. Accordingly, in equation 4 we re-run equation 1, but dropping the 29 observations in which a donor’s aid share exceeds one-third. The aid share coefficient remains negative and significant, and even increases in magnitude.

The majority of aid share values in the data are under 1%. Arguably donors have no leverage in these cases (Munro, 2005), or if they do, there is no real increase in leverage from providing (say) 0.8% instead of 0.2%. We therefore checked to ensure that our results were not sensitive to the possibly spurious variation among these small values. Specifically, we tested an alternative aid share variable in which all values greater than 0% but under 1% were set equal to 1%. Results are shown in equation 5. The coefficient and significance of the aid share variable are affected only trivially, compared to the base specification of equation 1.

The majority of tied aid values in the panel data are equal to one of the extreme points, 0 or 1. We are unable to use a tobit estimator, because fixed-effects tobit estimates are biased. The value added of tobit estimation is relatively small in any case, according to Angrist and Pischke (2009). However, we report results in equation 6 for the smaller sample of values strictly between 0 and 1. Aid share remains highly significant in this limited set of observations.

Amegashie et al. (2007) raise the possibility that the costs of tying aid must be balanced against losses from graft when aid is untied. Where corruption levels are high, tying aid does not necessarily reduces its development benefits. A testable implication is that the negative relationship between aid shares and aid tying should strengthen when the most corrupt recipient countries are dropped from the sample. Accordingly, in equation 1 of table 4 we retain only the less corrupt 50% of observations, namely those scoring above the median value on the “Control of Corruption” variable from the Worldwide Governance Indicators project (higher scores indicate lower perceived corruption). The aid share coefficient increases in absolute value from -.4 (from the base specification of table 3, equation 1) to -.53 (in equation 5) and remains highly significant.<sup>10</sup> For the more corrupt half of the sample (equation 2), the aid share coefficient remains negative, but drops to -.25 and is not significantly different from zero<sup>11</sup> . This result is consistent with the view that theory is ambiguous regarding the effect of aid share on aid tying when losses from aid tying must be balanced against losses from embezzling aid funds where corruption is high.

In equation 3, we return to using the full sample but add Control of Corruption as a regressor. Where recipient-country procurement systems are believed to be more corrupt, donors are more likely to bypass them and use their own rules and procedures, including aid tying. This reasoning implies the coefficient on Control of Corruption should be negative. It turns out to be positive, but very small and not significant. Results for the key aid

> 10Dividing the sample by the median value of the corruption perceptions indicator is arbitrary, but results are very similar if many alternative cutpoints are used. Even if we retain only the least corrupt 30% of observations, aid share remains significant at the .04 level with a coefficient of -0.6.

> 11The .34 difference between these two coefficients is not statistically significant at conventional levels, however.

11