the number of unsafe wells that cease to be used for drinking. Individual sales (A) are second-best, followed by either free provision (under the high-switching scenario) or sales with placards (C), while free provision is the worst under the assumption of switching rates as low as those observed in arm A. Note that the relative performance of the different strategies does not depend on the prevalence of unsafe wells. In contrast, the average cost ‘per switch’ from an unsafe well decreases with the fraction of unsafe wells, as this leads to an increase in the number of households who may benefit from switching, while the fraction that does is not affected under our assumptions.

These estimates also show that even the strategies with the highest average cost per unsafe well averted are highly cost-effective. The cost ranges from USD1.15 (group sales with high prevalence of unsafe wells) to USD14.4 (free provision with low switching rates and low prevalence of unsafe wells). However, Pitt et al. (2015) estimated a present discounted value of per-household gains from switching to safe water sources over twenty years ranging from USD1400 to USD1000 for discount rates of 3% to 8%. Such estimates only take into account income gains that result from avoiding productivity losses due to consumption of arsenic-contaminated water, while they ignore the additional utility gains from better health and reduced mortality. Argos et al. (2010) estimate substantial declines in all-cause mortality over a 10-year period associated with high arsenic content of drinking water, with hazard rates ranging from 1.09 to 1.68 relative to ‘safe’ wells with arsenic below 10 ppb. In addition, Keskin et al. (2017) find that testing campaigns also reduced mortality among young children because arsenic risk induced mothers to breastfeed longer. Such reductions in mortality would make testing even more cost-effective.<sup>21</sup> Note also that testing would remain cost-effective even if only a fraction of switchers actually moved to a safe source.

Last but not least, it must be highlighted that while group sales with cost-sharing appears to be the most cost-effective strategy for a given budget, it comes at a high cost in terms of equity. This is of course a by-product of low demand, which leads three quarter of households not to learn about the safety status of their well. For instance, even under the scenario of only 20% of unsafe wells, while 4,444 unsafe wells would be identified, and 2,178 of them would no longer be used for drinking, we also find that in the same communities where sales took place there would be an additional 13,333 unsafe wells that would not be tested. Equity concerns, if individuals sales are not allowed, may be particularly serious for households who are isolated, either geographically or socially.

# **7 Conclusions**

Information on household-specific environmental health risks can be a relatively inexpensive policy tool to mitigate those risks. However, the design of information campaigns often has to contend with resistance to behavioral change even when the presence of such risks has been revealed to target

> 21There are few estimates of the value of a statistical life (VLS) for Bangladesh, and their range is very broad. For instance Mahmud et al. (2019), using data on willingness to pay to reduce mortality risk from air pollution in urban Bangladesh estimates a value of 17,500-22,500 in PPP terms, or about 10-12 times per capita GDP, while Viscusi and Masterman (2017) use a figure about ten times larger.

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