method that uses a common variance-covariance matrix for the different regressions.<sup>12</sup> The observation numbers across equations are unbalanced because the World Bank managed far more SDTFs than MDTFs over the 2002-2013 period. Robust estimation can flexibly handle this lack of balance. To test our hypotheses, we conduct Wald tests to compare coefficients across equations.

For each block of three regressions corresponding to the three categories of funds, we use exactly the same specification. The first block includes only six variables corresponding to the six hypotheses listed above, without fixed effects or other controls. The second block includes fixed effects for donor countries and for trust fund starting years.<sup>13</sup> The third block adds more controls, including variables related to bi- and multilateral aid as alternative funding options to multi-bi aid as a whole. Moreover, they include a variety of indicators capturing the (development-related and general) know-how and capacity of the donor country. Such capacity should generally reduce the need to use the multilateral channel. Finally, we include a binary indicator variable for particularly contentious issues, as identified from a small expert survey carried out within the World Bank (2013b). Creating a trust fund pertaining to one of these issues allows donors to circumvent lengthy or divisive debates within a multilateral’s decision-making body, where not only the big traditional donors but also MICs have an influential voice. All variables and their sources are described in more detail in the Annex, Tables A-2 and A-5.

In the Annex, we also show a replication of the same regressions for different definitions of small versus large MDTFs. Because the cutoff point is somewhat arbitrary, we should be able to confirm that a small change will not substantially affect our results. In addition to the cutoff between 4 and 5 donors used so far, Tables A-3 and A-4 present estimations for cutoffs between 6 and 7, and between 10 and 11 donors. Given that few funds comprise many more than 10 members, the latter is already a relatively big step that tends to blur the distinction between the two categories. The outcomes are generally in line with these expectations.

Another important methodological issue is the definition of the choice set. In line with the model, all possible trust funds should be considered here. However, information is available only for trust funds that actually exist. To generate the full data set, we proceed with two alternative assumptions. First, we assume that within each group of trust funds (SDTFs, small MDTFs, and large MDTFs), any fund that is used by at least one of the bilateral donors could have been chosen by any other donor too (choice set A). As an example, when Switzerland agrees with the World Bank on a SDTF in any specific area, we assume that any other donor could have made the same kind of arrangement. Similarly, if there is a MDTF in a given area, we assume that those donors that do not participate in this fund would in principle also have had the option to do so.

Second, we assume that beyond the choices included in choice set A, for all funds that exist in the form of one particular fund type, the two other fund types would also have been

> 12 We employ the _suest_ routine for STATA to run these estimations (McDowell 2004). This approach also follows the standard guidance on the estimation of fixed-effects panel data systems (Blackwell 2005).

> 13 A Hausman test indicates that random effects specifications would lead to inconsistent coefficients.

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