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Dynamics of informal risk sharing in collective index insurance

Nature Sustainability volume 4, pages 426–432 (2021)Cite this article

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Abstract

Extreme weather events often prevent low-income farmers from accessing high-return technologies that would enhance their productivity. As a result, they often fall into poverty traps, a problem likely to worsen as the frequency of weather disasters increases due to climate change. Insurance offers, in principle, a solution for this conundrum and a means to guarantee households’ wellbeing. Group collective index insurance constitutes an alternative to indemnity or individual index insurance, and has the potential to alleviate basis risk through within-group informal transfers. Here we show that collective index insurance introduces a coordination dilemma of insurance adoption: socially optimal outcomes are obtained when everyone adopts insurance; however, a minimum fraction of contributors is necessary before the effects of basis risk can be averaged out and individuals start taking up insurance. We further show that additional mechanisms—such as local peer monitoring and defector exclusion—are necessary to stabilize informal transfers and collective index insurance adoption. Together, collective index insurance and informal transfers may thus constitute a practical instrument to improve sustainability in developing countries.

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Fig. 1: Average fraction of individuals adopting index insurance in the absence of risk-sharing pools.
Fig. 2: Adoption of CII with informal risk sharing.
Fig. 3: Risk-sharing pool induces a coordination dilemma of cooperation.
Fig. 4: Peer-monitoring efficacy and success of CII adoption.

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This paper relies on theoretical results following direct implementation of the equations provided in the Methods. Further details are provided in the Supplementary Information.

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Acknowledgements

F.P.S. acknowledges support from the James S. McDonnell Foundation 21st Century Science Initiative in Understanding Dynamic and Multi-scale Systems Postdoctoral Fellowship Award. J.M.P. and F.C.S. acknowledge the support from FCT-Portugal (grants PTDC/MAT/STA/3358/2014, PTDC/MAT-APL/6804/2020, UIDB/04050/2020, UIDB/50021/2020 and PTDC/CCI-INF/7366/2020). S.A.L. acknowledges funding from the Army Research Office grant no. W911NF-18-1-0325. F.P.S. thanks J. A. Swan and the Princeton University WRI 503 Spring 2020 participants for discussions on the text of this manuscript.

Author information

Authors and Affiliations

  1. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA

    Fernando P. Santos & Simon A. Levin

  2. Center for BioComplexity, Princeton Environmental Institute, Princeton University, Princeton, NJ, USA

    Fernando P. Santos & Simon A. Levin

  3. CBMA and Departamento de Matemática e Aplicações, Universidade do Minho, Braga, Portugal

    Jorge M. Pacheco

  4. ATP-Group, IST-Taguspark, Porto Salvo, Portugal

    Jorge M. Pacheco & Francisco C. Santos

  5. INESC-ID and Instituto Superior Técnico, Universidade de Lisboa, IST-Taguspark, Porto Salvo, Portugal

    Francisco C. Santos

  6. Resources for the Future, Washington DC, USA

    Simon A. Levin

  7. Beijer Institute of Ecological Economics, Stockholm, Sweden

    Simon A. Levin

  8. Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ, USA

    Simon A. Levin

Authors
  1. Fernando P. Santos
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Contributions

F.P.S., J.M.P., F.C.S. and S.A.L. conceived and designed the project. F.P.S. performed the numerical calculations and analysed the results. F.P.S., J.M.P., F.C.S. and S.A.L. discussed the results. F.P.S., J.M.P., F.C.S. and S.A.L. wrote and edited the manuscript.

Corresponding authors

Correspondence to Fernando P. Santos or Simon A. Levin.

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The authors declare no competing interests.

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Peer review information Nature Sustainability thanks Yichao Zhang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Effect of basis risk and risk-aversion in CII dynamics.

In the absence of risk-sharing pools (δ = 0) adoption of index insurance depends on the risk-aversion (γ) of individuals. a, As we consider an actuarially unfair insurance (from the consumer point of view, that is, qαw < c) only risk-averse individuals (high γ) adopt index insurance, which is evident by the positive gradients of selection for high γ. b, If basis risk is high, however, individuals do not adopt index insurance, which is evident by the negative gradients, implying a relative high probability of adopting No-CII compared with CII-C. c, The high rates of adoption of index insurance when the population is composed of risk-averse individuals is here evident by the peak in the stationary distribution over states with a high prevalence of CII-C individuals, when γ is high. d, Conversely, for high basis risk there is a peak in the stationary distribution over states with a high prevalence of No-CII, regardless of γ. Please note that, since δ = 0, strategies CII-C and CII-D are equivalent in this context. Other parameters: \(N = 1,w = 1,c = 0.18,p = q = 0.2,\alpha = 0.8,\beta = 10,Z = 100,\mu = 0.01\).

Source data

Extended Data Fig. 2 Effect of group size in CII dynamics.

The existence of sizeable groups in which individuals take part in informal risk-sharing (contributing to a common pool when they receive a payout without suffering a loss) promotes the adoption of index insurance. a, Sufficiently large groups introduce a coordination: if the number of individuals in the population goes above a critical fraction, the population will most likely evolve to a state where everyone adopts CII. b, If the basin of attraction towards CII is sufficiently large, we observe a high prevalence of individuals adopting CII, resulting in high index insurance take-up rates. Here we consider the prevalence of CII-C when only CII-C and No-CII can exist in a population. Other parameters: \(r = 0.1,w = 1,c = 0.18,p = q = 0.2,\alpha = 0.8,\delta = 0.5,\)\(\beta = 10,Z = 100,\mu = 0.01\).

Source data

Extended Data Fig. 3 The dilemma of CII adoption (and the need of peer-monitoring to solve it) in the context of less destructive events (lower values of α).

As in Figure 3 (main text) in all scenarios explored above the socially optimum outcome is achieved when all individuals adopt CII-C. In the absence of peer-monitoring (panels a and c) the most prevalent configurations are, however, those where individuals refuse insurance. The existence of peer-monitoring and defector exclusion from the informal pool (panels b and d) confers CII-C the relative advantage to be evolutionary robust. Other parameters: \(r = 0.1,w = 1,p = q = 0.2,\delta = 0.5,\beta = 50,Z = 50,N = 40,\mu = 0.02\).

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Supplementary Information

Supplementary Figs. 1–3, Table 1 and Notes.

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Santos, F.P., Pacheco, J.M., Santos, F.C. et al. Dynamics of informal risk sharing in collective index insurance. Nat Sustain 4, 426–432 (2021). https://doi.org/10.1038/s41893-020-00667-2

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