the geographical allocation of World Bank project funding within the country.<sup>16</sup> These initial calculations do not take into account other confounding factors mentioned in section 2 that may influence the targeting of aid. Nonetheless, high correlations are taken as an indication of effective geographic targeting insofar as a high proportion of resources go to those areas with a high presence of the bottom 40.

To account for other factors affecting the allocation of World Bank funding within countries, in particular the population size of the areas examined, regressions are estimated using, as the dependent variable, the share of World Bank funding each area receives. Zero-inflated beta regressions are undertaken because beta distributions are well suited in the case of continuous variables bound between 0 and 1.<sup>17</sup> Furthermore, the model is able to account for a not insignificant share of zero values, that is, areas that do not receive any investment project funding during the period of observation.<sup>18</sup> The estimation equation is as follows: where ��� is the share of World Bank funding going to area _i_ in country _c_ ; �� �40�� is the logarithm of the number of persons within the country’s bottom 40 living in area _i_ of country _c_ ; _X_ is a set of control variables; �� represents country fixed effects; and ��� is an idiosyncratic error term.<sup>19</sup> Standard errors are clustered at the country level.

A control is applied for population (in log) to identify the effect of the number of the bottom 40 living in an administrative area independent of the population size of the area. Furthermore, two variables are used to control for the ease of access to this area. The first is a dummy variable equal to one (zero) if the capital is (not) located in the area. Second, the travel time to the capital (in log) by road (with private transportation) from all other administrative areas is calculated from a database constructed from estimates gathered through Internet searches.<sup>20</sup> Besides access, the variables are also proxies for the visibility of projects, which is important for donor reputations. Projects in a capital city are expected to be more visible than those in remote areas. In addition, conflict-related deaths per 100,000 inhabitants are used to gauge security and the risks in administrative areas more generally. Government expenditures and the aid of other donors—only available in a limited sample of 15 and 11 countries, respectively—are included in robustness tests because the World Bank may take

> 16 While the World Bank projects variable runs from 2005–14, survey data on the distribution of the bottom 40 are scarcer and only available for some years within this period. Surveys are therefore used that are as close as possible to the center of the range of years, prioritizing older surveys if they are equidistant from the center to reflect more accurately the information available in allocation decisions and their lag relative to actual funding. In practice, most surveys (14) are from 2007. Other years account for fewer surveys (2011: 11, 2010: 10, 2009: 8, 2012: 6, 2008: 5, 2005: 3, and 2006: 1).

> 17 Beta distributions are characterized by high flexibility, thereby allowing varying degrees of skewness.

> 18 A fractional logit model might have also been estimated (Papke and Wooldridge 1996). However, unlike a beta regression, it would not generate an estimate of a separate process for the probability of the value of zero. Nonetheless, fractional logit models have been estimated to ensure robustness. For example, see Ospina and Ferrari (2012) for zero-or-one-inflated beta estimates.

> 19 Using the log of the number of the bottom 40 or the log of the share of the national bottom 40 living in an area is econometrically equivalent once one controls for country fixed effects.

> 20 Depending on data availability in a particular administrative area, the estimations took official speed limits, recommended speeds, likely speeds on certain road types, historical average or actual speed records, and realtime traffic information into account.

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