# **VII. Hypothesis Testing**

We explore two basic questions. First, could night-time lights data serve as a good proxy for any of the economic variables considered in this paper? Second, which night-time lights variable or variables serve best? Will it be _R_ by itself, _AoL_ by itself, _R_ and _AoL_ together (with different coefficient values), or _SoL_ by itself? With only a few exceptions, such as Elvidge _et al_ (1997), most researchers used _SoL_ . This seems like it should be the best choice because it captures the combined effects of illuminated area and the intensity of illumination. In this paper, however, we will allow for the possibility that _AoL_ and _R_ might contribute in differing degrees. Thus, the test equation is written as:

##   _ln_ X = c0 + c1·  _lnAoL_ + c2·  _lnR_

where the growth rates here are calculated as logged first differences. The coefficients c1 and c2 can be interpreted as growth elasticities.

The hypothesis test is simple: for any dependent variable _X_ , our expectation is the coefficients associated with _R_ and _AoL_ are positive.<sup>32</sup> The null hypothesis, which can be rejected by regression analysis, is that one or both of the coefficients associated with _R_ and _AoL_ are not statistically different from zero. If the null hypothesis is rejected, then we will conclude that night-time lights variables can serve as a good proxy for an economic variable if: one or both of the elasticities c1 and c2 is (i) positive; (ii) the sum of the elasticities (that are statistically different from zero) is close to 1.0; and (iii) these elasticities are stable over time.

In order to filter out some of the noise in the data, as documented in section V above, we repeat the test using ten-year intervals in addition to annual intervals. In our sample, this means there 10 observations per country for the ten year point-to-point growth rates and 20 observations for the annual growth rates.

To test for the stability of the elasticities over time, we also calculated the elasticities for the first half of all available observations, 5 observations for the ten-year intervals and 10 observations for the annual intervals. If the estimated elasticities for the shorter time periods are noticeably different (no econometric test needed) from those of the longer time period, then we conclude they are not stable over time. In addition, if the elasticities c1 and c2 are not statistically different from one another, then we can conclude that _SoL_ can be used instead of _R_ and _AoL_ .

In addition, because growth in night-time lights is likely biased downwards for the well illuminated, high income countries, we also make this test excluding the high income countries. The full sample includes 69 countries while the reduced sample includes 53 countries.<sup>33</sup> The econometric tests will be conducted using fixed effects for time and for countries. In this, we follow Chen and Nordhaus (2012) and Henderson et al (2009). By using fixed effects for time, we should be able to reduce systematic errors coming from the satellite sensors and the inter-calibration process. By using fixed effects for countries, we allow for country-specific variations in the relationships between night-time lights and the dependent variables.

> 32 The portrayal of GDP, population, electricity consumption and capital stocks as dependent rather than independent variables is deliberate.  We wish to know if night-time lights data carry statistical power as proxies for the dependent variables. This is only possible if the night-time lights variables appear on the right-hand side of the test equation.

> 33 We use the World Bank list of high-income countries prevailing in the first five years of the sample, 1992-96.