I’ve seen several papers using the number or density of lightning strikes in an area as an instrumental variable in the past few years, so thought I’d note some brief thoughts down as we sit through a sweltering few days in D.C. without the usual evening thunderstorms that normally come at the end of a hot summer day here.
Examples of the lightning strike IV
Google scholar has 132 papers come up when I search for “lightning strikes” and “instrumental variable”. A leading example is as follows:
Manacorda and Tesei (2020) use this instrument in their Econometrica paper on the impact of mobile phones on political mobilization in Africa. Using data at the level of small geographic regions (55x55km cells), they instrument mobile phone coverage with the average incidence of lightning strikes. Their argument for why this matters for mobile coverage they summarize as “Frequent electrostatic discharges during storms are known to damage mobile phone infrastructures and, in particular, antennas on the ground that transmit the signal in their vicinity, thus negatively affecting connectivity. As a consequence, this reduces both the supply of (as power surge protection is costly and poor connectivity makes the investment in technology less profitable) and the demand for (as the risk of intermittent communications discourages adoption of) mobile phone services … Hence, one would expect to see slower adoption of mobile phone technology in areas subject to higher incidence of lightning strikes… we show that, in fact, areas with higher than average incidences of lightning display slower adoption of mobile phone technology over the period under examination: conditional on a large number of cell-level controls, a 1 standard deviation (s.d.) increase in lightning intensity leads to a lower penetration rate of mobile phone technology of approximately 0.25 percentage points (p.p.) per year or 7 percent of the overall continental growth.”
They note that the exclusion restriction requires that lightning incidence only affects protest activity through mobile coverage and not through other channels. They acknowledge that this “might not hold unconditionally, as lightning strikes could be correlated with geographical variables (i.e. distance to the coast or longitude and latitude), climatic variables (i.e. rainfall and temperature), or the availability of other infrastructures or services (i.e. electricity) – and so control for time-varying temperature, rainfall, night light intensity, and a lot of cross-sectional variables (e.g. km of electrical grid) interacted with a time trend. They also do placebo tests to show there is no correlation between lightning strikes and protests in the periods before mobile technology became available. They also try to rule out heavy lightning periods directly affecting political protest participation by looking at months where lightning activity is lowest.
Mensah (2024) in the JDE uses lightning strikes as an instrument for electricity outages when looking at the impact of electricity outages on jobs in Africa. He argues “Lightning strikes contain about a billion volts of electricity; therefore when it strikes a transmission line or transformer, it induces a voltage surge, thereby destroying the transmission lines and equipment “. and curtailing the flow of electricity. Electrical infrastructure destroyed by lightning-induced voltage spikes and dips could take several days to be repaired and often entail a high cost of replacement. As a result, affected communities often go for several days without electricity. In South Africa for instance, lightning is estimated to account for nearly 65% of all over-voltage damages to the electricity transmission network”
Anderson et al. (2011) in the WBER use lightning strikes as an instrument for internet diffusion in the U.S. and across countries, when looking at the impact of the internet on corruption, noting that lightning strikes can crash computers and low the value of owning a computer.
Guriev et al. (2021) in the QJE use lightning strikes as an instrument for 3G mobile broadband internet coverage when looking at the impacts of mobile coverage on government approval across the world.
Yu et al. (2023) in the China Economic Review use lightning strikes as an instrument for landline telephone coverage when looking at the impact of ICT on labor allocation in China.
So why am I asking if lightning strikes at the new rainfall IV?
So we have what seems to be a clever new instrument, used in papers published in several prestigious journals, and subjected to several different checks for plausibility. So it is not surprising it is being increasingly used, especially given interest in the effects of mobile technology on different outcomes. So what are the concerns?
Exclusion?
There is a recent paper on rainfall instruments by Jonathan Mellon, which notes that weather has been used as an IV for at least 195 different variables – suggesting that all of the exclusion restrictions cannot possibly hold. While we are not yet at this stage, the above already shows how lightning have been used as instruments for multiple different types of electrical infrastructure and internet roll-out: electricity, fixed land telephone, computer infrastructure, the internet, 2G, and 3G broadband. So one needs to be worried if using lightning strikes as an instrument for one of these that it might also be having impacts through the others.
Second, while it can be very hard to predict the exact timing and location of a particular lightning strike, variation in intensity, which is the cross-sectional instrument being used, is something people can observe and learn over time. It may therefore affect where fire hazards and other weather events have happened throughout history, where people have set up cities, etc. It will be correlated with lots of other stuff, and the solution of Manacorda and Tesei of chucking in lots of other variables and assuming this captures everything takes us much closer to an identification conditional on observables than IV approach to identification in my opinion.
It might then be best used in a shift-share type of set-up, where there is some new exogenous shock to technology, and the lightning strike densities are then the shares that determine how responsive different locations are to this new technology shock - rather than assuming that the variation in the densities is exogenous. But then we still need to worry that these same shares have also influenced the responsiveness to other types of electrical infrastructure which may still be having lasting impacts.
Relevance and LATE?
Guriev et al. (2021) note the instrument is stronger in countries with below median GDP “because providers in these countries typically have fewer resources to protect equipment from being damaged—for instance, by using power-surge protection technology—or to repair it in case of damage.” Let’s think about where the key factor determining whether mobile technology or broadband is in a place is going to be the prevalence of lightning strikes – it is not going to be in large prosperous cities with vibrant markets and productive economies, where it will always be worth the cost of installing and protecting such infrastructure. Instead, this instrument seems like it will at best be relevant for explaining electrical infrastructure roll-out into the poorest, least dynamic, least prosperous places. This matters for what sort of LATE we can hope to identify from such an IV – it won’t be telling us the effect of mobile technology on the places where it has the highest profits or where the political pressure for installing it is the greatest – but instead will tell us impacts for much more marginal places.
So if you are going to use such an instrument, it seems important to discuss in a lot more detail where the identification is coming from, and what one could hope to learn from the LATE. Most of the papers I glanced through do not do this, although a notable exception is Guriev et al. (2021). In discussing the difference with OLS, they note the issue of what LATE identifies as “It is probable that the population of the complier regions is particularly affected by political messages on social media. This may be because the ability to get power-surge protection when needed is positively correlated with the overall level of development in the region, which, in turn, is correlated with how informed the regional population is. Therefore, one could expect the population in the complier regions to be relatively less informed, making them more receptive to new political information compared with the residents of noncomplier regions”.
Inference: finally note that lightning strike densities are unlikely to be distributed i.i.d. but instead are likely to be spatially correlated – and so standard errors which treat these as independent shocks will overstate precision. Spatial errors or a Borusyak and Hull re-centering approach might be needed to calculate correct standard errors.
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