effects. Most importantly, it provides a framework to disentangle these quantities and assess external validity.

We focus on effects on farmer investment decisions and examine five outcomes: cultivated area, fertilizers, pesticides, seeds, and a risk index.<sup>3</sup> We construct these outcomes using original data from each study.<sup>4</sup> We estimate intention-to-treat effects – that is the effects of being offered insurance regardless of the decision to subscribe or not – because it is arguably the most relevant parameter for a policymaker interested in the economy-wide effects of index insurance programs.<sup>5</sup> Using the traditional pooling model, we find that farmers who are offered index insurance cultivate more land (+0.09 SD), and use more seeds (+0.10 SD), pesticides (+0.09 SD), and fertilizers (+0.07 SD). The effect on the risk index is smaller and non-significant. Using the Bayesian hierarchical model, we find similar point estimates (around 0.06–0.11 SD), however, effects are much more uncertain and can be close to zero or negative. The 95% posterior intervals are [ _−_ 0.02 SD, +0.26 SD] for cultivated area, [ _−_ 0.02 SD, +0.25 SD] for seeds, [ _−_ 0.02 SD, _− −_ +0.15 SD] for pesticides, [ 0.05 SD, +0.21 SD] for fertilizers, and [ 0.09 SD, +0.09 SD] for the risk index. These results tend to confirm the potential of index insurance to foster smallholder farmers’ productive investments, however, they also show that effects are more uncertain than suggested by the pooling model. In fact, the pooling model is misleading because it considers that impacts are homogeneous across studies (thus understating the uncertainty around treatment effects).

We then use estimates from the Bayesian hierarchical model to gauge the external validity of index insurance experiments. We report evidence on the conventional pooling factor, a metric which emphasizes the percentage of total variation in treatment effects stemming from sampling variation (the higher this metric, the more suggestive it is of external validity). Averaged across all outcomes and studies, we find moderate pooling of information: 52% of the observed variation in treatment effects stems from sampling variation. We obtain similar results using two complementary metrics: the brute force pooling metric and the generalized pooling factor. This suggests moderate external validity of index insurance experiments. We note however that with few experiments the pooling factor cannot be precisely estimated: the

> 3The risk index is defined as _Rik_ = ∑ _rmkdimk_ / ∑ _dimk_ , where _rmk_ is the coefficient of variation of the yield of crop _m_ in study _k_ , and _dimk_ is the amount of land devoted by household _i_ to the cultivation of crop _m_ in study _k_ . It captures the riskiness of crop portfolios.

> 4 To derive the coefficient of variation _rmk_ of the risk index, we complement survey data from the original studies with time series on agricultural yields (see Section 3.1 below for more details).

> 5For reference, we compare the study-specific estimates of the ITT (intent-to-treat effect) and of the ATET (average treatment effect on the treated). If anything, we see larger heterogeneity in the ATET estimates (Figure A3).

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