satellite F15 in orbit in 2008 gave an average DN value of 16.6 across 0.9 million lit pixels in China, while F16 in orbit in the same year gave an average DN value of only 10.7 but spread over 1.7 million lit pixels. Similarly, Gibson et al (2015) show that satellites F14 and F15 differ by 85 km<sup>2</sup> (11 percent of the two-satellite mean), when estimating area for Bangalore in 2001. A related issue is that night-lit activity with a particular DN value on one day may not map to the same DN on another day due to sensor adjustments and inter-satellite differences.

We respond to these measurement issues in four ways.<sup>16</sup> First, we use an annual composite of non-ephemeral lights so unrecorded adjustments may wash out over the course of the year as repeated observations converge to some average amplification level. Second, we average over all satellite-year observations in a two-year window centered on the timing of the NSS rounds to ameliorate errors due to inter-satellite differences. Third, we measure smaller cities using two different luminosity thresholds, of 20 percent and 30 percent of the maximum (equivalent to DN values of 13 and 19), to check that the patterns we find are not sensitive to a particular choice of DN values.<sup>17</sup> Finally, we use the decomposition of night lights into lit area effects and average DN values within lit areas. We note in passing that most studies using DMSP data are not from economics and are typically concerned with urban area rather than with average DN values, while studies in economics typically just use average DN values.

In order to distinguish between cities and towns, and between towns and rural areas, we need luminosity thresholds. Several are used in practice, with examples of some close to what we use including Small and Elvidge (2013), who use DN  12 for their Asia-wide study of urban areas, and Alvarez-Berrios et al (2013), who use DN  20 for intermediate urban areas in Latin America. Lower thresholds are needed for towns than are used for cities because even some million-plus agglomerations were undetectable at a 50 percent threshold (DN>31). Conversely, a low threshold for all urban areas clumps big cities together along lit

> no record kept of these adjustments and produce data that are top-coded at DN=63. Also, comparability between satellites and sensor decay were less important for daily cloud monitoring than for measuring long-term changes in ground-level lights.

> 16 Various ‘calibrated’ night lights series are also available but these typically involve extrapolations from spatially and temporally limited episodes when amplification levels on the sensors were adjusted to suit the needs of researchers rather than of Air Force pilots (Hsu et al, 2015) or extrapolations from areas such as Sicily that were assumed to have stable lights (Elvidge _et al_ , 2009). These assumptions may not be broadly acceptable. 17 We refer to percentages of the maximum DN value to make the point that it is relative luminosity that is being measured, rather than the DN being a constant unit of measurement like a kilometer. For big cities, we use a single threshold of 50 percent because Gibson et al (2015) show the robustness of temporal and spatial patterns to using alternative thresholds of 40 and 60 percent. Cross-validation exercises also supported results using the 50 percent threshold, which contrasts with findings from Abrahams et al (2015) who found greatly exaggerated city sizes if night lights are used without correcting for various features causing blurring.

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