Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
In order to ensure that our design is powered to detect reasonably-sized
treatment effects, we conduct a series of power calculations. All power
calculations use a standardized outcome variable, with control mean 0 and SD 1; are based
on a two-sided hypothesis test with a 5% significance level; and use a sample of 300 villages
containing a total of 1,800 households. We present two sets of power calculations: a “two-
group” calculation, which compares villages without insurance to villages with insurance
(Panel A), and a “three-group” calculation, comparing no insurance to low-payout and high-
payout insurance (Panel B). In the two-group calculation, we compare a control group of 125
villages to a treatment group of 175 villages. In the three-group calculation, we compare a
control group of 125 villages to a treatment group of 125 villages (representing the control vs.
high-payout insurance comparison, our main effect of interest). In both cases, we present
ICCs of 0, 0.05, 0.1, and 0.15. In the two-group calculation, we are powered to 80% for
effects of approximately 0.15–0.2 SD. In the three-group calculation, we are powered to 80%
for effects of approximately 0.2–0.25 SD. Since the insurance treatment is free to farmers,
we expect take-up to be close to 100%. In practice, these calculations are likely somewhat
conservative, as we will use specifications which control for baseline data, removing residual
variation in the outcome.
These calculations give us confidence that the experiment is powered to detect treat-
ment effects within the literature of impacts across prior agricultural studies in low-income
countries (e.g., Mobarak and Rosenzweig (2014); Karlan et al. (2014); Emerick et al. (2016);
Carter et al. (2017); Cole and Xiong (2017)). As perhaps a particularly helpful benchmark, Burlig et al. (2024) stimated that an index insurance product which had a maximum pay-
out two-thirds the size of that described in our proposed experiment, which was provided
50 villages (with a control group of 100 villages), yielded impacts on agricultural investment
of 0.12 SD, statistically significant at the 10% level. Because we are providing insurance to
175 villages (125 at the high payout level and 50 at the low payout level), we expect to be
able to estimate precise treatment effects on agricultural outcomes. We ultimately conclude
that these power calculations support our study design