rejected, and both have similar elasticities, then one could infer that _SoL_ would be sufficient since _SoL_ = _AoL_ × _R_ .

# **IV. Night-Lights Hypotheses**

Several hypotheses taken from the literature are reviewed below. Most of the previous literature did not include much thinking about the implicit assumptions needed to justify the correlations they tested. Almost none reviewed the assumptions needed to maintain a positive correlation between growth in night-lights data and growth in economic variables. That task is taken up below in a preliminary way.

H1: Growth in night-time lights data should be positively correlated with real GDP growth. There are at least three ways to think of the link between night-time lights and GDP : by sectors, by factor inputs, and by energy usage. For example, one could assume there is a fixed elasticity of growth in total GDP to growth in illuminated GDP, perhaps urban manufacturing.<sup>14</sup> If so, then growth in the illuminated sector would be matched by growth in total GDP. Such a fixed elasticity is unlikely, so several researchers have introduced supplementary information about non-illuminated GDP to allow for changes in the ratio of illuminated to non-illuminated GDP. For example, Doll et al (2006) propose that the accuracy of GDP estimates based on night-lights would be much improved by data on the different ways land is used, notably for agriculture.<sup>15</sup> Ebener et al (2005) implemented this suggestion along with additional information on the size of informal economies in a large sample of countries to improve their GDP estimates. Souknilanh et al (2015) find their night-light based _GDP_ estimates are improved when supplemented by ground cover data from a second satellite (MODIS). Especially intriguing is their finding that the elasticity of GDP to _SoL_ decreases as agricultural land use increases. They also find that the area of ground cover is not sufficient because agricultural GDP growth can occur even if the area under crops does not change, for example, from the introduction of better yields or higher value-added crops.

One could assume all observed radiance is the consequence of physical capital, assume a fixed elasticity of illuminated to total capital, a fixed elasticity of labor to capital and constant total factor productivity. Alternatively, one could assume all observed radiance is the consequence of human populations, that there is a fixed ratio between population and employment and a fixed elasticity of GDP to employment.

One could also assume a fixed elasticity of GDP to electricity consumption, with the further assumption that _SoL_ is proportional to electricity consumption. A large number of researchers have also explored the correlation between growth in electricity consumption and real GDP growth. This effort has been somewhat disappointing. As Ozturk (2010) documented, there is no consensus on whether there is a correlation and, if so, what direction causality flows. Part of the problem is that some countries have consciously reduced their energy (and hence electricity) consumption, notably after the first and second OPEC petroleum price shocks and have continued to grow despite this policy. Other countries have seen their energy use grow faster than GDP.

In the medium-term, unemployment and low capacity utilization can occur with high probability. In the longer-run, the mix of capital, labor, energy and intermediate goods can vary in substantial ways as

> 14 If the assumed elasticity is equal to 1, then this is equivalent to assuming there is a fixed ratio of illuminated _GDP_ to total _GDP_ .

> 15 This paper is also very interesting for its careful exploration of challenges associated with data aggregation at different scales.