of facilities lacked both services. Figures 2 and 3 demonstrate the evidence of the gap in access to infrastructure for health facilities in Kenya, with some rural facilities far from the most populated cities lacking electricity and internet connectivity.

# _Road connectivity_

We use two sources of road data: the Global Friction Surface 2015 and georeferenced road network data from government sources (Kenya Road Fund 2018). The Global Friction Surface 2015 enumerates land-based travel speed for all land pixels between 85 degrees north and 60 degrees south for a nominal year 2015.<sup>7</sup> It was produced through a collaboration between the University of Oxford Malaria Atlas Project (MAP), Google, the European Union Joint Research Centre (JRC), and the University of Twente, Netherlands. The underlying data sets used to produce the map include roads (comprising all Open Street Map and Google roads data sets), railways, rivers, lakes, oceans, topographic conditions (slope and elevation), landcover types, and national borders. A speed of travel in terms of time to cross is allocated to each pixel. The final map represents the travel speed from this allocation process, expressed in units of minutes required to travel one meter. We also use a road network from the Kenya Road Board for 2018 that relies at least partially on actual road surveys. The road network data set features surface type and road conditions.

We use the Global Friction Surface 2015 to calculate the catchment area of population for each health facility, which represents the number of people that can be reached in a certain amount of time given the time allocated on the Global Friction Surface. We use the road network to calculate the orthogonal distance of each facility to the nearest fair- or good-quality road.<sup>8</sup>

# _Socioeconomic factors_

We use local estimates of deprivation scores, a proxy for poverty, calculated by the Poverty Global Practice at the World Bank. These calculations were done in small areas for the whole country, providing helpful information for comparisons within counties in Kenya. The methodology used and leveraged the "Small Area Estimation of Poverty under Structural Change" by Lange, Pape, & Putz, 2018. Poverty is estimated for each sub-location in two stages by estimating household consumption using census data.<sup>9</sup> In the first one, a consumption model is developed using survey data<sup>10</sup> but including non-variable household characteristics from the census. In the second stage, the estimated parameters are applied to census data, providing estimates for welfare at the sub-location level. In Kenya, 7,110 sub-locations were used in the analysis; on average, each had 120 households. The measure of poverty is included in the analysis as a control and proxy for the facility's resources.

- 3.2. Key Variables and Summary Statistics

We first merge the SDI data set and the Master List of facilities which results in a subset of 2,578 facilities. This means that 15% of the 2018 SDI facilities could not be found in Kenya's Master List of facilities. This final sample was complemented with information on road, electricity, and cellphone internet access, with additional data described in the previous subsection.<sup>11</sup>

> 7 D.J. Weiss, A. Nelson, H.S. Gibson, W. Temperley, S. Peedell, A. Lieber, M. Hancher, E. Poyart, S. Belchior, N. Fullman, B. Mappin, U. Dalrymple, J. Rozier, T.C.D. Lucas, R.E. Howes, L.S. Tusting, S.Y. Kang, E. Cameron, D. Bisanzio, K.E. Battle, S. Bhatt, and P.W. Gething. A global map of travel time to cities to assess inequalities in accessibility in 2015. (2018). Nature. doi:10.1038/nature25181.

> 8 For quality road we followed the definition of the Rural Access Index: “ _Good roads are paved roads that look dark and are not eroded. Fair roads are either paved roads in fair condition or good gravel roads that are motorable_ ” (Iimi, et al., 2016).

> 9 10% of the Kenya Population and Housing Census (KPHC), randomly selected.

> 10 The Kenya Integrated Household Budget Survey (KIHBS) conducted between 2015 and 2016.

> 11 The restricted sample works with the facilities that merges with the reviewed Master List. Moreover, an initial inclusion of “Distance to the nearest Facility” made it necessary to work with facilities in the 10,131 list.

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