in income with respect to changes in light is 0.17 (Table 1, column 3). This elasticity stays in the range 0.169 to 0.171 whether six province-level aggregates of small MDs (used to preserve confidentiality) are included or excluded, and whether topcoded household incomes are modeled at the topcoded value or 1.5 times that amount (not shown). The analogous t-statistic ranges from 2.96 to 3.08.

For the present study, several steps were taken to convert the pixel-level lights data into cities. Figures 4–6 document these steps for Tanzania. The 30 satellite-years of lights data were first combined into one binary grid encoding whether a pixel was lit in at least one satellite-year (Figure 4). These ever-lit areas were then converted to polygons: contiguous ever-lit pixels were aggregated, and their digital numbers were summed within each satellite-year. Polygons not corresponding to a known city, based on census populations with latitude-longitude pairs, were dropped.<sup>20</sup> Figure 5 shows all the lit polygons and city points. For those light polygons that did contain one or more census cities, the populations of all such cities were summed to obtain a population. Most lights correspond to at most one census city.<sup>21</sup> Figure 6 shows those lights that correspond to known cities. In most countries, census information about cities with populations as small as 10 thousand was available, but in some, the cutoff was higher. For all regressions below, I restrict to cities with combined population over 20 thousand and lit in at least 2 years. The dropped lights most likely correspond to forest fires or random noise not flagged by NOAA’s algorithm, or smaller towns, and contain 13 to 16 percent of total DN in the 15-country sample. The total DN was recorded for each city polygon for each year, averaging across multiple satellite-years where necessary.<sup>22</sup> The light in each country with the largest associated population in 1992 is designated the primate.<sup>23</sup> 2001 are 10 percent samples of the full census.

> 20City Population, http://www.citypopulation.de. Accessed 19 March 2010.

> 21Light pixels for a given satellite-year actually represent the average light from several slightly larger overlapping pixels from many orbits within the satellite-year. Because of this, the lit area of a given city tends to be somewhat larger than its actual size. Among densely populated high and middle income countries, this means, for example, that the majority of land in the United States east of the Mississippi River or in continental Western Europe is contiguously lit, so that cities cannot be defined purely based on light contiguity. In Africa, this is much less of a problem because of sparser light overall. Snow also tends to increase the footprint and magnitude of lights. Again, this is less of a problem in Africa than elsewhere. And even if the area of a given city is overestimated, the light summed for that city in still presumably coming from that city or its outskirts—it may just be partially displaced a pixel or two from where it actually originates.

> 22Lights arising from gas flares, as delineated by Elvidge et al. (2009) were also removed. These affected only 4 populated lights in the 15-country sample.

> 23In practice, the primate designation does not change over the course of the sample period in any sample country.

10