the solar lanterns had a limited impact on children’s academic performance, while other education-related inputs remained constant. In Section S.2 in the supplemental appendix, we discussed this possibility more carefully.

# **VI Spillover effects**

The potential for spillover effects is a threat to the previous findings.<sup>21</sup> In other words, as the randomization was carried out within a specific grade level at each sample school, it is certainly possible that a student who did not receive solar products could have benefited from her friends who did receive the products, or from having access to SHSs for nighttime study. However, visiting a friend’s home at night in _unelectrified river islands_ is quite risky, for both boys and girls. In fact, in a follow-up household survey, we collected information on whether treated students shared solar lamps with non-household members, and identified only three such cases, where solar lamps were shared with cousins. Hence, this possibility may not have been a valid concern in our setting.

Other spillover effects could have resulted from interactions in school and during exams. Non-treated students could have learned from their treated peers in school, minimizing the difference in outcomes between the treatment and control groups. However, if such spillover effects artificially blurred the academic performance gap between the treatment and control groups, they also may have made it difficult to detect significant differences in educational inputs among students. Finding significant increases in study time and school attendance among treated students could reduce this concern. However, it is still important to consider this possibility more carefully.<sup>22</sup> Two exercises were conducted. First, we collected information on the average progression rates in one of the studied districts, Kurigram, in 2012, 2013, and 2014; these were 0.93, 0.98, and 0.97 for primary-school students and 0.83, 0.89, and 0.86 for secondary-school students, respectively (i.e., a marginal increase in the progression rate from 2012 to 2014). In our control group, the progression rates in 2012, 2013, and 2014 were 0.80, 0.78, and 0.70 for 4<sup>_th_</sup> to 5<sup>_th_</sup> grade students and 0.67, 0.64, and 0.58 for 6<sup>_th_</sup> to 8<sup>_th_</sup> grade students, respectively (i.e., a decline in the progression rate from 2012 to 2014). Thus, we have no evidence to suggest that, on average, the academic performance of our control students improved in a more pronounced way during the sample periods than did the performance of all the Kurigram students.

Second, we exploited the insight obtained from Baird et al. (2014) that the fraction of those offered treatment in

> 21Further threats also exist. First, 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. Second, continuous rainfall struck northern Bangladesh in August 2014 and this weather shock might have made the subsequent learning of all the sample students indiscriminate. Third, in this study exploring the impacts of two treatment arms on multiple outcomes, we may accidentally have found statistically significant treatment effects for some arms and outcomes, even where true causal effects were absent. These concerns are carefully addressed in Section S.3 in the supplemental appendix.

> 22On the other hand, it is also possible that the control students were disappointed at losing the lottery, and therefore did not study as hard during the sample periods. This possible discouraging effect (if any) would have led us to overestimate the treatment effects on children’s educational achievement. If so, the true performance impact of solar products would be smaller than current estimates, while further supporting the result of “no academic performance effects” found with modern lighting technology.

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