education-related inputs from a single study that was not designed to explore this particular aspect.<sup>28</sup> Therefore, our findings may still imply that the solar lanterns had a limited impact on children’s academic performance, while other education-related inputs remained constant. While this may not be the only reason for the sizable impacts of solar lamps on educational inputs but not on achievement, the empirical results should still be considered of the first order of importance, and future research should aim to validate this educated conjecture.<sup>29</sup>

# **S.3 Threats to statistical inference**

This section discusses several threats to the findings of this study.

## **S.3.1 Bounds on treatment**

While the number of households lost in the follow-up survey – due to attrition – was small, the sample selection associated with the missing outcome data remains an empirical concern. A possible solution to this problem is to use a selection correction methodology by explicitly modeling the selection process. However, this approach cannot be adopted in the current research due to difficulties in precisely modeling the selection mechanisms and the lack of effective instruments that would explain the selection but not the outcomes.

As an alternative, we estimated the bounds of the treatment effects, based on Lee (2009)’s methodology. However, it is acknowledged that this approach is not free from limitations. First, it has to be assumed that the treatment assignment monotonically affects the selection, which cannot clearly be tested. Second, the estimates are the treatment effects on the sub-population that would always be observed regardless of the treatment assignment; however, they may not always be the main interest of the study. Nevertheless, it remains useful to assess the already identified estimates based on this approach.

First, Lee (2009) demonstrated that in randomized experimental settings, if the sample attrition rates are similar between the treatment and control groups, a simple comparison between these groups can still be interpreted as a valid average treatment effect on the aforementioned local population. With controls of the baseline family characteristics and village-fixed effects, Table S.27 in this supplemental appendix reports the impacts of the solar products on the non-attrition probability (which is one if the outcome data are not missing at follow-up) for the relevant previously estimated outcomes.<sup>30</sup> Based on the results, we can see, for example, that the treatment groups were more likely to provide missing information on kerosene expenditure in the follow-up survey than the control groups. This is

> 28For example, other school inputs not explored here may play a significant role in improving students’ performance.

> 29Another possible explanation is that our target population might have been too young to enjoy a noticeable improvement in academic performance (e.g., Stinebrickner and Stinebrickner, 2008).

> 30Notably, the estimation results of school attendance, reported in Table 6 in the article are free from the selection problem because the analysis exploited the data that pertained to all 882 respondents.

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