imperfect proxy.<sup>12</sup> Various indicator variables are used in relation to DPOs. In the sample, 49 percent of the projects were in countries that had DPOs relating to any sector in the preceding five years, 42 percent of the projects were in countries that had public policy reform, and only 13 percent of the projects were in countries that had transport-related DPOs (table 1).<sup>13</sup>

# **3.4. Wider Economic Benefits**

We use remotely sensed measurements of nighttime lights emission intensity to measure the WEBs. Nighttime lights are considered a relatively good proxy for human and economic activity. The assumption is that the amount of light emitted at night is highly correlated with consumption, which increases with higher incomes. Following Henderson, Storeygard, and Weil (2012), who find a strong correlation between the growth of nighttime light intensity and GDP at the national level, multiple studies have expanded this approach and used nighttime lights to estimate economic development at much smaller geographic units. For example, Storeygard (2016) utilizes nighttime lights to study intercity transport costs and their impact on population income in Sub-Saharan African cities, and Harari (2017) uses nightlights to measure the shapes of urban areas in India. Because persistent light emitted at night is often associated with manmade structures, it is assumed that if the intensity of a pixel exceeds a given threshold, this pixel represents a populated location or some level of economic activity.

To measure WEBs, nighttime light data from the U.S. Air Force Defense Meteorological Satellite Program Operational Linescan System (DMSP-OLS) were used. Pixels in DMSP-OLS have a resolution of 30 arc seconds, or approximately 1 by 1 kilometer at the equator. These data are available for the period between 1992 and 2012. For each pixel, the digital number of calibrated light intensity ranges from 0 to 63, which is often referred to as the nightlight intensity (we use the “stable lights” band, where ephemeral events, such as fires, have been discarded). We inter-calibrate the data to account for the lack of on-board calibration between satellites (see annex 2).

However, there are well-known limitations to DMSP-OLS data (see, for example, Donaldson and Storeygard (2016)). These include saturation effects, in which the amplification of light detection to capture low levels of light leads to right censoring in detection in highly-lit areas (for example, city centers); and blooming effects (or the “diffusion of light”), in which light emitted in one pixel or over an area is detected in nearby pixels, making highly lit areas appear to be larger than they are.

For this paper, a grid of hexagons, each covering 260 square kilometers (20 kilometers from vertex to vertex), was created. The nighttime lights intensities at the pixel level were summed by hexagon to represent an overall value of light.<sup>14</sup> A global artificial hexagon data set was created to allow a standardized level of analysis for all projects across the globe. Hexagons are appropriate and efficient for management and analysis of geospatial data (Tong, Ben, and Wang 2010) and are increasingly popular as bases for discrete spatial simulations (Sahr, White, and Kimerling 2003). Hexagonal tessellation has been adopted by previous studies in the remote sensing domain (Potere 2009; Goldblatt et al. 2018). Using hexagons is advantageous over square pixels because of their higher symmetry, sampling efficiency, equidistance,

> 12 We cannot use alternative measures, such as the World Bank Country Policy and Institutional Assessment scores, because the series starts only in 2005.

> 13 Obvious candidates for capturing complementary policies and institutions are variables related to doing business, but there is no series that covers the entire period of the analysis.

> 14 Hexagons for which the observed nighttime light was zero were excluded from the analysis. This is done to exclude areas where no economic development is expected, for example, forests and deserts. Since international development organizations tend to have strong environmental safeguards to prevent the depletion of the natural environment, the exclusion of these hexagons is intuitive.

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