tics along the Sanderson-Windmeijer statistic for comparative purposes and robustness. It follows that our first stage is strong.

# **4.2.2 Instrumental variable for electricity**

We exploit terrain topography and lightning intensity to generate two instruments for electricity. The use of geographical instruments such as weather variations, terrain roughness, slope, or land elevation is common in existing empirical work. Indeed, the random nature of these geographical instruments gives them the same properties as those of exogenous variables. For example, previous research has used exogenous changes in rainfall as an instrument for economic growth (Edward Miguel and Sergenti, 2004; Miguel, 2005; Paxson, 1992). Other research has relied on terrain elevation as a proxy for the cost of constructing electric grids (Amorim et al., 2018; Durante, 2009; Dinkelman, 2011; Ostrom, 1990).

To construct the instrument for access to electricity grids, we exploit the fact that lightning is a significant contributor to power disruptions in most sub-Saharan African countries (Alvehag and Soder, 2010; Minnaar et al., 2012), which is strictly exogenous. For example, in South Africa, lightning damage accounts for about 65 percent of all over-voltage damage to electrical distribution networks, and is believed to account for one-third of all outages. More than 50% of power outages on transmission lines in Eswatini are attributed to lightning. In Africa, every year lightning strikes and thunderstorms damage circuits and knock out electric power lines, crippling coverage (Minnaar et al., 2012). The recovery time depends on the extent of damage; in some cases changing the route of electricity lines is necessary. The recovery period is generally long (Karagiannis et al., 2017); maintenance is costly. Hence, frequent lightning strikes in a location negatively affect the electric-energy supply and household access to the electricity by damaging electricity grids. Following Andersen and Pablo (2012); Andersen et al. (2011); Andersen and Dalgaard (2013); Agrawal (2021), we use lightning density as an exogenous determinant of power disturbances and disruption to access to electricity that can affect the individuals’ location ”proximity”to the electricity grids. Note that while some of these papers have used lightning intensity as an instrument for the penetration of the Internet (Agrawal, 2021), the main argument in those papers is that lightning strikes damage electrical infrastructure useful to the functioning of the Internet.

In addition, bearing in mind that topography can be viewed as a geographic obstacle that makes infrastructure construction more expensive (Ostrom, 1990; Durante, 2009; Amorim et al., 2018; Dinkelman, 2011), we add terrain elevation to the exogenous variables that we consider as a determinant of the proximity to electrification grids. Therefore, in our empirical model, the proximity to the electrification grids is partly explained by the topography of the land on which the households are located, and the lightning intensity in that area defined by the mean of lightning strikes per square km each year.

We use satellite data generated by the National Aeronautics and Space Administration (NASA) on lightning strike intensity and aggregated by Manacorda and Tesei (2020); Cecil et al. (2014). They compute average lightning strike intensity between 1995 and 2010 in 0.5<sup>_◦_</sup> _×_ 0 _._ 5<sup>_◦_</sup> for Africa. In the DHS, we matched the closest location mean lightning density for a specific year with an individual’s location. As reported in Manacorda and Tesei (2020), with an average of 17.3 lightning strikes per square km per year, Africa has the highest lightning density on earth. The world average is 2.9 lightning strikes per square km per year. With almost half a million lightning strikes per year in each cell, the Democratic Republic 18