Dynamics of informal risk sharing in collective index insurance

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

Data availability

Source data are provided with this paper.

Code availability

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

References

  1. 1.

    Clarke, D. J. & Dercon, S. Dull Disasters? How Planning Ahead will Make a Difference (Oxford Univ. Press, 2016).

  2. 2.

    The Impact of Natural Hazards and Disasters on Agriculture and Food Security and Nutrition: A Call for Action to Build Resilient Livelihoods (FAO, 2015); http://www.fao.org/3/a-i4434e.pdf

  3. 3.

    Hallegatte, S. et al. Shock Waves: Managing the Impacts of Climate Change on Poverty (The World Bank, 2015).

  4. 4.

    Schaefer, L. & Waters, E. Climate Risk Insurance for The Poor & Vulnerable: How to Effectivelly Implement the Pro-Poor Focus of Insuresilience (Munich Climate Insurance Initiative, 2016).

  5. 5.

    Panda, A., Lambert, P. & Surminski, S. Insurance and Financial Services Across Developing Countries: An Empirical Study of Coverage and Demand Centre for Climate Change Economics and Policy Working Paper 367 & Grantham Research Institute on Climate Change and the Environment Working Paper 336 (London School of Economics and Political Science, 2020).

  6. 6.

    Cottrell, R. S. et al. Food production shocks across land and sea. Nat. Sustain. 2, 130–137 (2019).

    Article  Google Scholar 

  7. 7.

    Barnett, B. J. & Mahul, O. Weather index insurance for agriculture and rural areas in lower-income countries. Am. J. Agric. Econ. 89, 1241–1247 (2007).

    Article  Google Scholar 

  8. 8.

    Hansen, J. et al. Climate risk management and rural poverty reduction. Agric. Syst. 172, 28–46 (2019).

    Article  Google Scholar 

  9. 9.

    Barnett, B. J., Barrett, C. B. & Skees, J. R. Poverty traps and index-based risk transfer products. World Dev. 36, 1766–1785 (2008).

    Article  Google Scholar 

  10. 10.

    Noritomo, Y. & Takahashi, Y. Can insurance payouts prevent a poverty trap? Evidence from randomised experiments in northern Kenya. J. Dev, Stud. 56, 2079–2096 (2020).

    Article  Google Scholar 

  11. 11.

    Janzen, S. A. & Carter, M. R. After the drought: The impact of microinsurance on consumption smoothing and asset protection. Am. J. Agric. Econ. 101, 651–671 (2019).

    Article  Google Scholar 

  12. 12.

    Hazell, P. B. & Hess, U. Drought insurance for agricultural development and food security in dryland areas. Food Secur. 2, 395–405 (2010).

    Article  Google Scholar 

  13. 13.

    Transforming Our World: The 2030 Agenda for Sustainable Development (United Nations, 2015).

  14. 14.

    Carter, M., de Janvry, A., Sadoulet, E. & Sarris, A. Index insurance for developing country agriculture: a reassessment. Annu. Rev. Resour. Econ. 9, 421–438 (2017).

    Article  Google Scholar 

  15. 15.

    Binswanger-Mkhize, H. P. Is there too much hype about index-based agricultural insurance? J. Dev. Stud. 48, 187–200 (2012).

    Article  Google Scholar 

  16. 16.

    Clarke, D. J. A theory of rational demand for index insurance. Am. Econ. J. Microecon. 8, 283–306 (2016).

    Article  Google Scholar 

  17. 17.

    Budhathoki, N. K., Lassa, J. A., Pun, S. & Zander, K. K. Farmers’ interest and willingness-to-pay for index-based crop insurance in the lowlands of Nepal. Land Use Policy 85, 1–10 (2019).

    Article  Google Scholar 

  18. 18.

    Sibiko, K. W., Veettil, P. C. & Qaim, M. Small farmers’ preferences for weather index insurance: insights from Kenya. Agric. Food Secur. 7, 53 (2018).

    Article  Google Scholar 

  19. 19.

    Trærup, S. L. Informal networks and resilience to climate change impacts: a collective approach to index insurance. Glob. Environ. Change 22, 255–267 (2012).

    Article  Google Scholar 

  20. 20.

    Pacheco, J. M., Santos, F. C. & Levin, S. A. Evolutionary dynamics of collective index insurance. J. Math. Biol. 72, 997–1010 (2016).

    Article  Google Scholar 

  21. 21.

    Dercon, S., Hill, R. V., Clarke, D., Outes-Leon, I. & Taffesse, A. S. Offering rainfall insurance to informal insurance groups: evidence from a field experiment in Ethiopia. J. Dev. Econ. 106, 132–143 (2014).

    Article  Google Scholar 

  22. 22.

    De Janvry, A., Dequiedt, V. & Sadoulet, E. The demand for insurance against common shocks. J. Dev. Econ. 106, 227–238 (2014).

    Article  Google Scholar 

  23. 23.

    Dercon, S., De Weerdt, J., Bold, T. & Pankhurst, A. Group-based funeral insurance in Ethiopia and Tanzania. World Dev. 34, 685–703 (2006).

    Article  Google Scholar 

  24. 24.

    Mobarak, A. M. & Rosenzweig, M. R. Selling Formal Insurance to the Informally Insured Working Paper (Yale Univ., 2012).

  25. 25.

    Arnott, R. & Stiglitz, J. E. Moral hazard and nonmarket institutions: dysfunctional crowding out of peer monitoring? Am. Econ. Rev 81, 179–190 (1991).

    Google Scholar 

  26. 26.

    Takahashi, K., Barrett, C. B. & Ikegami, M. Does index insurance crowd in or crowd out informal risk sharing? Evidence from rural Ethiopia. Am. J. Agric. Econ. 101, 672–691 (2019).

    Article  Google Scholar 

  27. 27.

    Mobarak, A. M. & Rosenzweig, M. R. Informal risk sharing, index insurance, and risk taking in developing countries. Am. Econ. Rev. 103, 375–380 (2013).

    Article  Google Scholar 

  28. 28.

    Kunreuther, H. C. & Michel-Kerjan, E. O. At War With the Weather: Managing Large-Scale Risks in a New Era of Catastrophes (MIT Press, 2011).

  29. 29.

    van Valkengoed, A. M. & Steg, L. Meta-analyses of factors motivating climate change adaptation behaviour. Nat. Clim. Change 9, 158–163 (2019).

    Article  Google Scholar 

  30. 30.

    Lo, A. Y. The role of social norms in climate adaptation: mediating risk perception and flood insurance purchase. Glob. Environ. Change 23, 1249–1257 (2013).

    Article  Google Scholar 

  31. 31.

    Cai, J., De Janvry, A. & Sadoulet, E. Social networks and the decision to insure. Am. Econ. J. 7, 81–108 (2015).

    Google Scholar 

  32. 32.

    Cole, S. et al. Barriers to household risk management: Evidence from India. Am. Econ. J. 5, 104–135 (2013).

    Google Scholar 

  33. 33.

    Dixit, A. K., Levin, S. A. & Rubenstein, D. I. Reciprocal insurance among Kenyan pastoralists. Theor. Ecol. 6, 173–187 (2013).

    Article  Google Scholar 

  34. 34.

    Hilbe, C., Chatterjee, K. & Nowak, M. A. Partners and rivals in direct reciprocity. Nat. Hum. Behav. 2, 469–477 (2018).

    Article  Google Scholar 

  35. 35.

    Molho, C., Tybur, J. M., Van Lange, P. A. & Balliet, D. Direct and indirect punishment of norm violations in daily life. Nat. Commun. 11, 3432 (2020).

    Article  Google Scholar 

  36. 36.

    Tilman, A. R., Levin, S. & Watson, J. R. Revenue-sharing clubs provide economic insurance and incentives for sustainability in common-pool resource systems. J. Theor. Biol. 454, 205–214 (2018).

    Article  Google Scholar 

  37. 37.

    Mwenda, E. R. Mongolia—Index-Based Livestock Insurance Project Policy Research Working Paper Series 3528 (The World Bank, 2012).

  38. 38.

    Arrow, K. J. Uncertainty and the welfare economics of medical care. Am. Econ. Rev. 53, 941–973 (1963).

    Google Scholar 

  39. 39.

    Why wait for death? How a Ugandan hospital delivers health insurance through burial groups. The Economist (30 January 2020); https://go.nature.com/33Zvazv

  40. 40.

    Góis, A. R., Santos, F. P., Pacheco, J. M. & Santos, F. C. Reward and punishment in climate change dilemmas. Sci. Rep. 9, 16193 (2019).

  41. 41.

    Santos, F. P., Santos, F. C. & Pacheco, J. M. Social norm complexity and past reputations in the evolution of cooperation. Nature 555, 242–245 (2018).

    CAS  Article  Google Scholar 

  42. 42.

    Dixit, A. & Levin, S. in The Theory of Externalities and Public Goods (eds Buchholz, W. & Rübbelke, D.) 127–143 (Springer, 2017).

  43. 43.

    Tilman, A. R., Dixit, A. K. & Levin, S. A. Localized prosocial preferences, public goods, and common-pool resources. Proc. Natl Acad. Sci. USA 116, 5305–5310 (2019).

    CAS  Article  Google Scholar 

  44. 44.

    Molina, C., Akçay, E., Dieckmann, U., Levin, S. A. & Rovenskaya, E. A. Combating climate change with matching-commitment agreements. Sci. Rep. 10, 10251 (2020).

    CAS  Article  Google Scholar 

  45. 45.

    Wang, Z. et al. Communicating sentiment and outlook reverses inaction against collective risks. Proc. Natl Acad. Sci. USA 117, 17650–17655 (2020).

    CAS  Article  Google Scholar 

  46. 46.

    Carattini, S., Levin, S. & Tavoni, A. Cooperation in the climate commons. Rev. Environ. Econ. Policy 13, 227–247 (2019).

    Article  Google Scholar 

  47. 47.

    Nyborg, K. et al. Social norms as solutions. Science 354, 42–43 (2016).

    CAS  Article  Google Scholar 

  48. 48.

    Pratt, J. W. Risk aversion in the small and in the large. Econometrica 32, 122–136 (1964).

    Article  Google Scholar 

  49. 49.

    Arrow, K. J. Aspects of the Theory of Risk-Bearing (Yrjö Jahnssonin Säätiö, 1965).

  50. 50.

    Traulsen, A., Nowak, M. A. & Pacheco, J. M. Stochastic dynamics of invasion and fixation. Phys. Rev. E 74, 011909 (2006).

    Article  Google Scholar 

Download references

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

Affiliations

Authors

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.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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: \(r = 0.1,w = 1,p = q = 0.2,\delta = 0.5,\beta = 50,Z = 50,N = 40,\mu = 0.02\). Source data

Supplementary information

Supplementary Information

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

Reporting Summary

Source data

Source Data Fig. 1

Raw data corresponding to plots represented.

Source Data Fig. 2

Raw data corresponding to plots represented.

Source Data Fig. 3

Raw data corresponding to plots represented.

Source Data Fig. 4

Raw data corresponding to plots represented.

Source Data Extended Data Fig. 1

Raw data corresponding to plots represented.

Source Data Extended Data Fig. 2

Raw data corresponding to plots represented.

Source Data Extended Data Fig. 3

Raw data corresponding to plots represented.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing