technology and relative prices evolve.<sup>16</sup> Moreover, as was famously shown by Solow (1957), however, the combined movements of labor and capital explain only a fraction of GDP growth.

As a final caution, Doll et al (2006) note that international trade, and the growth of global value-chains in particular, imply that at least some of the light observed coming from one country may actually be contributing to the GDP of other countries, possibly thousands of miles away.

H2: Growth in night-time lights should be positively correlated with growth in electricity consumption. According to IEA/OECD 2006, only 1 percent of all lighting is fuel based rather than electrical. Thus, there ought to be a strong correlation between lights and electricity consumption. This correlation could extend into growth rates if there is a fixed ratio of external illumination to electricity consumption regardless of location of time. Yet, such an assumption is unlikely to be true. The ratio between illumination and electricity use is also likely to vary by country, perhaps in accord with degree of urbanization-more densely urbanized areas may be brighter than suburban areas. It is very likely that rapidly growing countries may initially increase the share of electricity used for illumination and then see that share fall after sufficient illumination has been achieved, as other uses continue growing. Many countries are beginning to install more efficient lighting and some middle and high income countries are making increased use of shielding to reduce light pollution. It is also the case that night-time lights data cannot detect electricity leakages in the transmission lines between generators and lights. In some countries, these losses can be as high as 60 percent and can grow when countries cannot afford to maintain their lines.<sup>17</sup> H3: Growth in night-time lights data should be positively correlated with population growth. This is a reasonable expectation because there are usually people located where there are lights. Expecting such a correlation to remain true in growth rates, however, requires several assumptions. First, there must be a fixed elasticity (or ratio) of illuminated settlements to non-illuminated settlements.<sup>18</sup> Yet, Tobler (1969) showed that the relationship between urban area and urban population varied regionally and it is clear that the urban (illuminated) share of a population can change fairly rapidly over time. Second, there must be a fixed relationship between population and area used for settlement. This, of course, is not true: growing cities often build upwards (and sometimes downwards) in addition to expanding outwards. Third, there must be a fixed ratio between population density and the intensity of illumination. As noted above, however, some wealthy countries actually decreased their illumination in order to become more energy efficient and/or reduce light pollution. The findings by Sutton et al (2001) are instructive. They found that there was a linear relationship between the natural logarithm of _urban_ populations and the natural logarithm of _AoL_ . Yet, they also found that the slope and intercept of that relationship varied by country. Most notably, they found that the intercept tended to vary with income per-capita. Wealthier countries tended to have smaller intercepts (fewer urban population counts per illuminated square kilometer).

H4: Growth in night-time lights should be positively correlated with growth in the stock of physical capital. It is certainly true that much of humanity’s buildings and roads are illuminated. Thus it is reasonable to expect a positive correlation in levels between night-lights and constructed capital. The correlation could extend into growth rates as well, if there is a fixed elasticity of illuminated to total capital.

> 16 Normally there is a quasi-fixed ratio of intermediates to gross output which slowly falls as productivity improves. Countries that import most of their intermediates will be subject to external shocks (trading partner demand, terms of trade) that disrupt this relationship.

> 17 From a sample of 166 countries in 2010, from the World Development Indicators.  The average loss was 13 percent.

> 18 According to OECD (2006), as many as 1.6 billion people live in areas _without_ electric lighting.