population size for 21 countries. The elasticity was 0.920. Sutton et al (2001) used night-time lights data to estimate the total urban population. They were able to estimate the total human population only by using additional information about the urban share of the population of each country. They estimated the global population was 6.3 billion in 1997 compared to a UN estimate of 5.9 billion.

Night-time lights are also positively correlated with the stock of physical capital. Most sources of manmade illumination are associated with physical capital. The main sources of man-made illumination include residences, offices, retail shopping areas, factories, street lighting, road vehicles, fishing boats, and gas flaring facilities.<sup>10</sup> Each of these sources can be classified as some form of physical capital: buildings, infrastructure, and vehicles. Much of this capital can be attributed to production but some of it is associated with consumption, particularly in the areas devoted to housing and retail market services. The literature focuses on two kinds of physical capital, urban areas (buildings) and roads. Satellite data could be useful in overcoming difficulties in aggregating a variety of inconsistent definitions of what is urban held by different countries and various levels of government jurisdictions. Satellite data could also help in gathering data at more frequent intervals than the usual 5 or 10 year survey cycles used in most countries. Imhof et al (1997) conducted some of the early research in this regard, comparing illuminated areas with data on total urban area for 48 states within the USA. They found a strong, positive correlation between _AoL_ and recorded total urban area. Akiyama (2012) found a strong, positive correlation between _AoL_ and road distribution in urban and suburban areas and with building distribution in rural areas.

The research cited above was conducted with data in levels, across countries, for single time periods. Three papers have extended the analysis in new directions by looking at growth within countries or regions. Elvidge et al (2013) used a very clean, reprocessed, inter-calibrated data set to explore the correlation of _SoL_ data with population and GDP on a country-by-country basis. They found that most, but far from all, countries in the sample displayed positive correlations with one or both variables. Some of the correlations were quite strong. A surprisingly high number of countries, however, showed rather weak correlations, no correlation or negative correlations. They propose that some of the correlations between GDP and nighttime lights may have been confounded by the efforts of some countries to install more efficient lighting. Another possibility is that some countries are making efforts to reduce light pollution. They also suspected that the data from observations at high latitudes are unstable due to the annual snow cycle. Henderson et al (2009) examined the suitability of night-time lights to serve as supplemental data that could help improve existing GDP estimates. To do this, they needed estimates of the elasticity of GDP to night-time lights data.<sup>11</sup> They made several estimates, including one based on long-run (13 year) cross-country _growth rates_ of average radiance, _R_ . The resulting positive correlation could not be rejected but the explanatory power was weak.

The third paper, by Bickenbach et al (2014), is closer in spirit to this paper. They test the hypothesis that night-lights data could serve as a suitable proxy for sub-national GDP. To do this, they test the relationship between long-term growth rates of GDP per square kilometer and the long-term growth rates of _SoL_ per square kilometer for sub-regions of Brazil, India, Europe and the United States. They find that the resulting growth elasticities are not stable across the geography of each country or region. They infer from this that night-lights data are not a good proxy for sub-regional GDP.

This paper is similar to Bickenbach et al (2014) in using growth rates as the basis for testing the suitability of night-lights data as a proxy for GDP. It goes further, however, in examining whether the data could also

> 10 Many fishing boats create intense light.  Illuminating the ocean tempts fish and squid to come to the surface where they are more easily caught. http://earthobservatory.nasa.gov/Features/Malvinas/ 11 Chen and Nordhaus (2012) explored the same topic.