we constructed and tested three alternative measures of tied aid share in estimating both models:

1. the sum of tied and partially tied aid divided by the sum of tied, partially tied and untied aid;

2. the amount of tied aid divided by the sum of tied, partially tied and untied aid; 3. the sum of tied, partially tied, and aid for which tying status was unreported, divided by the total commitment amount<sup>9</sup> .

Several independent variables were also taken from the AidData portal, including the number of donors present in a recipient country, and each donor’s share of the aid given to each recipient. Total aid as a share of recipient GNI, population and GDP per capita were obtained from the World Bank’s World Development Indicators. The LDC dummy is constructed based on the definition in the 2001 DAC recommendation (DAC, 2001).

# _4.2. Empirical Findings_

Results for model 4.1 are presented in table 3, for each of the three alternative definitions of tied aid. Consistent with the model’s predictions, coefficients for a donor’s share in the total amount of aid are significantly negative. Using either definition 1 or 2, each percentage point increase in a donor’s share in total aid is associated with a reduction of 0.4 percentage points in the share of tied aid. To illustrate, an increase in aid share from the mean value of 3% to 8% other things equal would be associated with a decline in tied aid from the mean of about 20% to 18%. For definition 3, the coefficient on aid share is somewhat larger (in absolute value).

The LDC coefficient is also significantly negative, consistent with the DAC recommendation on aid untying. Other things equal, the share of tied aid is 7 percentage points lower in LDCs, or 10 percentage points based on results in equation 3. Tied aid tends to be higher in larger countries: the coefficient on log of population is positive and marginally significant in equations 1 and 2. Tied aid is significantly lower where aid volumes are higher. These results are consistent with the spirit of the DAC recommendation on aid untying, namely that it is particularly important to maximize the value of aid by untying it in countries more dependent on aid. However, aid/GNI is not significant, and income per capita is significant (with the expected positive coefficient) only in equation 3.

The DAC’s reports on aid tying focus on definition 1. This is also the aid untying indicator included in the Paris Declaration monitoring framework. In describing robustness of our results on aid share to changes in specification or sample, we therefore also use definition 1, where space constraints lead us to select only one of the three indicators. First, we consider the possibility of influential observations. Figure 1 depicts the partial relationship between tied aid and aid share, based on equation 1. Visual examination

> 9Nine donor countries did not report the tying status of some of their aid in 2007. In definition 3, we follow Easterly (2002) in treating aid with unreported tying status as tied. Such aid is disproportionately technical assistance, which is more often tied than other aid categories (DAC, 2001). Definition 3 therefore overestimates tied aid, but definitions 1 and 2 underestimate it, for the nine donors in question.

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