# **1 Introduction**

Index insurance has generated worldwide interest in recent decades because of its potential to help smallholder farmers manage risks. Unlike traditional indemnity-based insurance products, which compensate farmers based on the losses they experience, index insurance products delink payouts from the assessment of individual losses and compensate farmers on the basis of an exogenous, easily observable index that is highly correlated but not identical to individual losses.<sup>1</sup> The theoretical appeal of index insurance is that it reduces information asymmetry problems (adverse selection and moral hazard) as well as transaction and verification costs. Index insurance is particularly appealing in low- and middle-income countries because traditional forms of insurance are prohibitively expensive for smallholder farmers (Hazell, 1992; Cole and Xiong, 2017). According to Carter et al. (2017), it represents " _one of the most important current opportunities to designing new institutions that can help developing countries achieve the goal of increased investment in agriculture, accelerated growth, and poverty reduction_ ".

In this paper, we aggregate evidence from existing experiments on index insurance and explore the external validity of their results. While each individual study is commendable for the care with which it estimates impacts, critics have called into question the external validity of such estimates (Deaton and Cartwright, 2018; Peters et al., 2018; Bédécarrats et al., 2020; Ogden, 2020; Ravallion, 2020). Each study is rooted in a specific context (period, location, intervention, population) and it is not clear to which extent the estimates are informative about impacts in other contexts. We follow the seminal paper by Meager (2019) and use a Bayesian hierarchical model to aggregate data from six studies on investment response to index insurance (Elabed and Carter, 2014; Karlan et al., 2014; Cole et al., 2017; Bulte et al., 2019; Hill et al., 2019; Stoeffler et al., 2022).<sup>2</sup> This framework offers an appealing statistical tool, not only to study the external validity of the studies, but also to estimate the average impact across settings as well as the potential sources of heterogeneity. In contrast with traditional meta-analyses, which consider that individual studies estimate a common effect and that variations in observed treatment effects are solely driven by (random) sampling variation, the hierarchical model allows for the presence of heterogeneous effects across studies. More specifically, it assumes that variations in observed treatment effects reflect both sampling variation and (true) heterogeneity in treatment

> 1Examples of indices include weather (e.g., rainfall, temperature), area production (e.g., average yield at the county or district level), and satellite images of vegetation.

> 2These studies cover a large set of regions and countries (Bangladesh, Burkina Faso, Ghana, Kenya, India and Mali), evaluate a wide range of insurance products, and thus offer an excellent opportunity to aggregate evidence and explore external validity. We explain in detail the inclusion criteria in Section 2.1.

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