share variable are unaffected. Similar results are obtained if we instead use the well-known Corruption Perceptions Index from Transparency International. However, corruption is associated with higher rates of aid tying in cross-sectional tests reported below.

There are potentially many more recipient-country characteristics, other than those explicitly controlled for thus far, that could affect the level of aid tying. The most effective way to correct for any omitted-variables bias in our results for the key aid share variable is simply to replace the recipient-country variables with a full set of recipient country dummies. Equation 4 reports results from this two-way fixed effects regression. The coefficient on aid share declines slightly, from about -0.4 to -0.37, but statistical significance is slightly strengthened.

In equations 5 and 6 we report tests of the effects of costs of aid tying for donors, using donor size and income as rough proxies for costs. The value of aid in general should be reduced by more when it is tied to purchases in smaller donor countries, because the pool of qualified firms or consultants is likely to be smaller. Consultant fees (and thus tying costs) are likely to be higher in higher-income donor countries<sup>12</sup> . In equation 5, tying costs are measured by the log of population and log of per capita income in current US dollars (both for 2006). In equation 6 we substitute for population the log of total aid, measured in constant US dollars and averaged over the years 1995-2006. The rationale for this proxy is that the number of firms and consultants residing in the country with expertise pertinent to development assistance increases (but at a diminishing rate) with past and present aid expenditures. To test these donor-level variables we have to drop the donor fixed effects, and we instead use recipient fixed effects, and correct standard errors for recipient-clustered rather than donor-clustered observations. Aid tying is positively and significantly related to both donor size measures, as expected, in equations 5 and 6. Income, as predicted, is inversely (and significantly) related to the incidence of aid tying in both tests. We cannot rule out the possibility that smaller and wealthier donors tie less of their aid for other reasons, but the relationships are consistent with our theoretical framework. Donor aid share remains highly significant in both tests.

# _4.3. Endogeneity of Aid Share_

– Regressions in tables 3 and 4 treat aid share as exogenous. It is conceivable but – unlikely in our view that the negative coefficient on aid share reflects endogeneity bias. Suppose recipients discourage aid from donors that tie more of their aid, and lobby for more aid from other donors. Then, higher tied aid would be associated with lower aid shares, due to reverse causation. However, most recipients appear to accept whatever aid they are offered, and when they can be selective regarding aid offers they may care more about conditionality, sector, modality, and other issues than about tying status. Moreover, aid shares are probably determined much more by donor than by recipient decisions. If so, any reverse causation would likely produce a positive bias. For example, a donor agency (under pressure from lobby groups or parliament) may increase aid to recipients where it

> 12Admittedly, the quality of consultants may also tend to be somewhat higher in higher-income countries.

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