fore dropped from the sample.<sup>43</sup> Finally, ...ve districts had been split since the initial survey; Kaberamaido previously part of Soroti, Kayunga previously part of Mukono, Mayuge previously part of Iganga, Sironko previously part of Mbale, and Wakiso previously part of Mpigi. As a result, for some districts, we end up with too few facilities. The districts with too few (less than four) facilities were therefore dropped. Altogether, we end up with a sample of 50 government facilities/catchment areas (CA).

Combining information on geographical location (from the detailed maps provided by Uganda Bureau of Statistics (UBOS)) and census data, we could list all villages and enumeration areas and their size (number of households) for each catchment area (CA). Summary data on the number of villages in CA are provided in Tables A.1A.3. Altogether, there are 804 enumeration areas, covering 1,194 villages and 109,296 households in the 50 CAs. On average, a CA consists of 20 enumeration areas and 29 villages, half of which are outside the 3 km radius. The average (median) village has 92 (84) households.

Three general principles governed our choice of sample. First, we wanted our sample of households to be representative of the potential users of the facility in the CA. This, in turn, is a function of both the size of the population in the CA and the distance to the facility. Second, for the intervention to be feasible (and within our budget constraint), we wanted to restrict the number of villages to be surveyed within a given CA. For the same reason, we wanted to ensure that the villages surveyed are clustered together in a smaller set of clusters within each CA. Finally, we wanted to include the village where the facility was located (typically the village where the sta¤ resides).

To ensure this, we chose a four-stage sampling design. First, we determined how many villages should be selected from each CA. Balancing the need of being representative of the potential users of the facility in the CA and designing a ...nancially and logistically feasible survey strategy, the “village rule”was set to Second, we determined the share of these villages that should be sampled from the one, three, and ...ve kilometer radius (strata 1, 3, and 5), i.e., the “strata rule”.<sup>44</sup> For each CA, these shares were set so as to replicate the shares of villages in the di¤erent strata in the CA, with one exception. Since households in villages closer to the facility, everything else equal, are more likely to visit the facility, we oversampled the villages from the one-kilometer radius by a factor of 2 and undersampled the share of facilities within the ...ve-kilometer radius (excluding the facilities within the three-kilometer radius) by a factor of 0.7.

Third, to ensure that the villages surveyed are clustered together and that the 43 Speci...cally, we dropped facilities/catchment areas where more than 25, [33] or {50} percent of the catchment area were outside the 1 [3] {5} km radius.

44Strata 1 is de...ned as the area within the one-kilometer area; strata 3 is de...ned as the area within the three-kilometer area excluding the area within the one-kilometer area; strata 5 is de...ned as the area within the ...ve-kilometer area excluding the area within the three-kilometer area.

31