serve as proxies for electricity use, population or the stock of capital. Unlike Bickenbach et al (2014), however, this paper is constrained to national boundaries.

It is important to set out clearly our criteria for what constitutes a good proxy. First and foremost, the proxy variable (night-lights) should have a statistically significant and positive correlation with the variable it would substitute for. Second, that relationship should hold up when the data are expressed in growth rates rather than levels. In other words, one should expect to find statistically significant elasticities of growth between night-lights and one or more economic variables. Third, the elasticity should be constant over time. In this regard, we disagree with Bickenbach et al (2014) that instability of elasticities across subregions is a problem. To the contrary, growth in sub-regional night-lights data can serve as a good proxy for growth sub-regional GDP as long as the corresponding disparate sub-regional elasticities remain constant over time.<sup>12</sup> Moreover, growth in national GDP will be a simple weighted average of growth in sub-regional GDP, with the elasticities serving as weights.

Examining correlations in terms of growth rates within countries is an important feature that sets this paper as well as Bickenbach et al (2014) apart from most of the previous literature. As illustrated below, it is possible that the positive correlation between two variables observed in one time period (Figure 3) may not be representative of a positive relationship across time. Figure 4 illustrates such a possibility. In that figure, for any selected country, the difference in the dependent variable between any two points in time is zero, implying the absence of any within-country relationship over time. This points to a simple test. A hypothesized relationship can be rejected if there is no correlation between the growth rates of the dependent variable and the growth rates of the independent variable.

**Figure 3:  Apparent Cross-Country Correlation**

**Figure 4:  Within Country Correlations**

<!-- Start of picture text --> 8 8<br>7 7 Country G<br>6 6 Country F<br>5 5 Country E<br>4 4 Country D 2010<br>3 3 Country C 2011<br>2 2 Country B 2012<br>1 1 Country A<br>2013<br>0 0<br>0 3 6 9 12 15 18 21 24 27 30 1 3 6 8 11 13 16 18 20 22 24 26 28 30<br>Natural Log of Independent Variable<br>Natural Log Independent Variable<br>Natural Log Dependent Variable Natural Log Dependent Variable<br><!-- End of picture text --> Several other features also set this paper apart from its predecessors. One is a more rigorous examination of the night-time lights data for their own sake. We start with a careful review of the properties of the DMSP-OLS data and examine how _AoL_ , _R_ and _SoL_ interact over time. Problems associated with omitted observations due to cloudy weather, light blooming beyond its geographic origins, saturation of sensors, and censoring of data are explored. This led us to introduce various control variables into our testing framework – something we have not seen attempted in other papers.<sup>13</sup> Our attempts were not successful but we hope they will inspire others – there is a demonstrated need. We also construct our hypothesis tests to allow for the possibility that _AoL_ might be preferred over _R_ or vice versa in some cases. If neither are

> 12 There might be at least one circumstance where one would want growth elasticities to be equal across regions: one might be concerned about changes in the spatial distribution of growth, moving from one sub-region to another. 13 Abrahams et al (2015) proposes a correction for blurring (blooming) but not in the context of econometric testing.