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Natural disaster and risk-sharing behavior: Evidence from rural Bangladesh

Abstract

Using a unique field experiment in rural Bangladesh, this paper investigates how exposure to a natural disaster affects risk-sharing behavior. We conducted a risk-sharing experiment that randomly assigned different levels of risk-sharing commitments to individuals who were exposed and unexposed to a recent natural disaster and asked them to form risk-sharing groups. Our results show that disaster-affected individuals are less likely to defect from risk-sharing groups, regardless of the level of ex-ante commitment. Interestingly, individuals from disaster-affected villages chose riskier bets and realized higher average returns compared with individuals from non-disaster-affected areas. Our results have important implications for the design of financial risk-transfer mechanisms in developing countries.

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Fig. 1

Notes

  1. The design in the first stage is also used by other related studies such as Carvalhoa et al. (2016) and Cameron and Shah (2015).

  2. We conducted the survey immediately after flood in 2010 event, and conducted the experiment two and half years after this flood from December 2012 to January 2013. Although the flood in 2010 was after 2009 Aila cyclone, it is hard for the affected people to assess the impacts of the two events separately since the same communities were affected by both events in 2009 and 2010.

  3. For a graphical illustration, refer to Figure B1 in the Online Appendix that overlays the location of the treatment and control villages with a digital elevation model.

  4. Figure B2 in the Online Appendix presents a visualisation of the results from this simulation exercise.

  5. The exposure index of a village is a weighted index (with value from 0 to 1) created based on how much that village is affected in 12 different aspects. The four most important aspects (agro-crops, domestic animals, road, house) account for 80% of the total weight. The remaining 20% of the weight is made up by the eight less important aspects (dam, educational institutions, government offices, electricity, water, fish gar, tree plantation, water height). The exposure in each aspect is indicated in either one of three levels: low, average, and high. We give these numerical values of 1, 2, and 3, respectively.

  6. Table C1 in the Online Appendix presents the payoffs associated with each lottery game.

  7. Because Aila could have affected the social network structure in the affected villages, we examine if there are differences in the social networks between participants in the affected and non-affected villages. In our survey, we collected information on 10 different measures of social networks among all participants. Table E2 in the Online Appendix compares the average responses to these social network questions between affected and non-affected villages. The results show no sysmtematic differences in the social networks in disaster and non-disaster villages.

  8. The properties of ui(x|γi) satisfy the standard conditions shared by constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions.

  9. As the Appendix shows, these costs are necessary to prevent defection for all \(\tilde {x}_{i}\) realizations under any symmetric risk-pooling equilibrium.

  10. Refer to Online Appendix C.

  11. Refer to footnote 5 for details of the construction of the index. The results, reported in the Online Appendix, are qualitatively very similar.

  12. The one exception that could prevent this conclusion is for subjects in disaster regions to be so risk averse (while also being less risk averse than controls) that the predication (ii) of Section 3.1 is reversed. The Appendix shows that predication (ii) indeed holds over a plausible range of γi under CRRA preferences and under the lottery choice set of the experimental design. We focus on CRRA, which has the attractive feature of a decreasing coefficient of absolute risk aversion.

  13. All results maintain in a neighbourhood of the class of 50/50 lotteries by continuity of expected utility.

References

  • Ahlin, C. (2009). Matching for credit: Risk and diversification in Thai micro-credit borrowing groups. Michigan: Michigan State University Mimeo.

    Google Scholar 

  • Attanasio, O., Barr, A., Cardenas, J.C., Genicot, G., & Meghir, C. (2012). Risk pooling, risk preferences, and social networks. American Economic Journal Applied Economics, 4(2), 134–67.

    Google Scholar 

  • Barr, A., & Genicot, G. (2008). Risk sharing commitment and information: An experimental analysis. Journal of the European Economic Association, 6(6), 1151–1185.

    Google Scholar 

  • Botzen, W.J., & Van den Bergh, J. (2012a). Risk attitudes to low-probability climate change risks: WTP for flood insurance. Journal of Economic Behavior and Organization, 82(1), 151–166.

    Google Scholar 

  • Botzen, W.W.J., & Van Den Bergh, J.C.J.M. (2012b). Monetary valuation of insurance against flood risk under climate change. International Economic Review, 53(3), 1005–1026.

    Google Scholar 

  • Botzen, W.W.J., Kunreuther, H, & Michel-Kerjan, E. (2015). Divergence between individual perceptions and objective indicators of tail risks: Evidence from floodplain residents in New York City. Judgment and Decision Making, 10(4), 365–385.

    Google Scholar 

  • Botzen, W.W.J., Kunreuther, H, & Michel-Kerjan, E. (2019). Protecting against disaster risks: Why insurance and prevention may be complements. Journal of Risk and Uncertainty, 59(2), 151–169.

    Google Scholar 

  • Botzen, W.W.J., Aerts, J.C.J.H., & Van Den Bergh, J.C.J.M. (2009). Willingness of homeowners to mitigate climate risk through insurance. Ecological Economics, 68(8), 2265–2277.

    Google Scholar 

  • Browne, M.J., Knoller, C., & Richter, A. (2015). Behavioral bias and the demand for bicycle and flood insurance. Journal of Risk and Uncertainty, 50(2), 141–160.

    Google Scholar 

  • Bubeck, P., Botzen, W.W.J., & Aerts, J.C.J.H. (2012). A review of risk perceptions and other factors that influence flood mitigation behavior. Risk Analysis, 32(9), 1481–1495.

    Google Scholar 

  • Cameron, L., & Shah, M. (2015). Risk-taking behavior in the wake of natural disasters. Journal of Human Resources, 50(2), 484–515.

    Google Scholar 

  • Carvalhoa, L.S., Prinab, S., & Sydnor, J. (2016). The effect of saving on risk attitudes and intertemporal choices. Journal of Development Economics, 120(C), 41–52.

    Google Scholar 

  • Cassar, A., Healy, A., & Von Kessler, C. (2017). Trust, risk and time preferences after natural disasters. World Development p 94.

  • Cettolin, E., & Tausch, F. (2015). Risk taking and risk sharing: Does responsibility matter? Journal of Risk and Uncertainty, 50(3), 229–248.

    Google Scholar 

  • Charness, G., Gneezy, U., & Imas, A. (2013). Experimental methods: Eliciting risk preferences. Journal of Economic Behavior and Organization, 87, 43–51.

    Google Scholar 

  • Eckel, C.C., El-Gamal, M.A., & Wilson, R.K. (2009). Risk loving after the storm: A Bayesian network study of Hurricane Katrina evacuees. Journal of Economic Behavior and Organization, 69(2), 110–124.

    Google Scholar 

  • Fafchamps, M., & Gubert, F. (2007). The formation of risk sharing networks. Journal of Development Economics, 83(2), 326–350.

    Google Scholar 

  • Fafchamps, M., & Lund, S. (2003). Risk-sharing networks in rural Philippines. Journal of Development Economics, 71(2), 261–287.

    Google Scholar 

  • Fleming, D.A., Chong, A., & Bejarano, H.D. (2014). Trust and reciprocity in the aftermath of natural disasters. Journal of Development Studies, 50 (11), 1482–1493.

    Google Scholar 

  • Freeman, P., & Kunreuther, H. (2002). Environmental risk management for developing countries. The Geneva Papers on Risk and Insurance Issues and Practice, 27(2), 196–214.

    Google Scholar 

  • Gallagher, J. (2014). Learning about an infrequent event: evidence from flood insurance take-up in the United States. American Economic Journal Applied Economics, 6(3), 206–323.

    Google Scholar 

  • Ghatak, M. (1999). Group lending, local information and peer selection. Journal of Development Economics, 60(1), 27–50.

    Google Scholar 

  • Gray, C.L., & Mueller, V. (2012). Natural disasters and population mobility in Bangladesh. Proceedings of the National Academy of Sciences, 109(16), 6000–6005.

    Google Scholar 

  • Hanaoka, C., Shigeoka, H., & Watanabe, Y. (2018). Do risk preferences change? Evidence from panel data before and after the great east Japan earthquake. American Economic Journal: Applied Economics, 10(2), 298–330.

    Google Scholar 

  • Haushofer, J., & Fehr, E. (2014). On the psychology of poverty. Science, 344(6186), 862–867.

    Google Scholar 

  • Holzmann, R., Packard, T., & Cuesta, J. (2000). Extending coverage in multi-pillar pension systems: Constraints and hypotheses, preliminary evidence and future research agenda. Social Protection Discussion Paper Series, pp. no. SP 0002. Washington, D.C.: The World Bank.

  • Kousky, C. (2010). Learning from extreme events: risk perceptions after the flood. Land Economics, 86(3), 395–422.

    Google Scholar 

  • Kousky, C., Michel-Kerjan, E., & Raschky, P.A. (2018). Does federal disaster assistance crowd out flood insurance? Journal of Environmental Economics and Management, 87, 150–164.

    Google Scholar 

  • Kousky, C., Luttmer, E.F.P., & Zeckhauser, R.J. (2006). Private investment and government protection. Journal of Risk and Uncertainty, 33(1), 73–100.

    Google Scholar 

  • Kriesel, W., & Landry, C. (2004). Participation in the National Flood Insurance Program: An empirical analysis for coastal properties. Journal of Risk and Insurance, 71(3), 405–420.

    Google Scholar 

  • Kunreuther, H. (1996). Mitigating disaster losses through insurance. Journal of Risk and Uncertainty, 12(2-3), 171–187.

    Google Scholar 

  • Kunreuther, H., & Pauly, M. (2002). Neglecting disaster: Why don’t people insure against large losses? Journal of Risk and Uncertainty, 28(1), 5–21.

    Google Scholar 

  • Kunreuther, H., Novemsky, N., & Kahneman, D. (2001). Making low probabilities useful. Journal of Risk and Uncertainty, 23(2), 103–120.

    Google Scholar 

  • Kunreuther, H., Meyer, R., & Michel-Kerjan, E. (2009). Overcoming decision biases to reduce losses from natural catastrophes, mimeo.

  • Landry, C.E., Ahmadiani, M., & Colson, G. (2016). Structural empirical analysis of decisions under natural hazard risk. Working paper University of Georgia: Athens.

  • Li, J.-Z., Li, S., Wang, W.-Z., Rao, L.-L., & Liu, H. (2011). Are people always more risk averse after a major snow-hit and a major earthquake in China in 2008. Applied Cognitive Psychology, 25, 104–111.

    Google Scholar 

  • Loewenstein, G., & Angner, E. (2003). Predicting and indulging changing preferences. In Read , D, Loewenstein, G., & Baumeister, R. (Eds.) Time and decision: Economic and psychological perspectives on intertemporal choice. New York: Russell Sage Foundation.

  • Lybbert, T.J., Barrett, C.B., Desta, S., & Coppock, D.L. (2004). Stochastic wealth dynamics and risk management among a poor population. The Economic Journal, 114(498), 750–777.

    Google Scholar 

  • Malmendier, U., & Nagel, S. (2011). Depression babies: Do macroeconomic experiences affect risk taking? Quarterly Journal of Economics, 126(1), 373–416.

    Google Scholar 

  • Mazzocco, M., & Saini, S. (2012). Testing efficient risk sharing with heterogeneous risk preferences. American Economic Review, 102(1), 428–68.

    Google Scholar 

  • Morduch, J. (1991). Consumption smoothing across space: Tests for village-level responses to risk. Cambridge: Harvard University Mimeo.

    Google Scholar 

  • Munshi, K., & Rosenzweig, M. (2016). Networks and misallocation: Insurance, migration, and the rural-urban wage gap. American Economic Review, 106(1), 46–98.

    Google Scholar 

  • Page, L., Savage, D., & Torgler, B. (2014). Variation in risk seeking behaviour following large losses: A natural experiment. European Economic Review, 71(C), 121–131.

    Google Scholar 

  • Petrolia, D.R., Landry, C.E., & Coble, K.H. (2013). Risk preferences, risk perceptions, and flood insurance. Land Economics, 89(2), 227–245.

    Google Scholar 

  • Pratt, J.W., & Zeckhauser, R.J. (1989). The impact of risk sharing on efficient decision. Journal of Risk and Uncertainty, 2(3), 219–234.

    Google Scholar 

  • Raschky, P.A., & Weck-Hannemann, H. (2007). Charity hazard - a real hazard to natural disaster insurance? Environmental Hazards, 7(4), 321–329.

    Google Scholar 

  • Raschky, P.A., Schwarze, R., Manijeh, S., & Ferdinand, Z. (2013). Uncertainty of governmental relief and the crowding out of flood insurance. Environmental and Resource Economics, 54(2), 179–200.

    Google Scholar 

  • Ravallion, M., & Dearden, L. (1988). Social security in a moral economy: An empirical analysis for java. Review of Economics and Statistics, 70, 36–44.

    Google Scholar 

  • Solnit, R. (2009). A paradise built in hell: The extraordinary communities that arise in disaster Viking Books.

  • Takahashi, K., Barrett, C.B., & Ikegami, M. (2018). Does index insurance crowd in or crowd out informal risk sharing? Evidence from rural Ethiopia. American Journal of Agricultural Economics, 101(3), 672–691.

    Google Scholar 

  • Tausch, F., Potters, J., & Riedl, A. (2014). An experimental investigation of risk sharing and adverse selection. Journal of Risk and Uncertainty, 48(2), 167–186.

    Google Scholar 

  • Thieken, A.H., Petrow, T., Kreibich, H., & Merz, B. (2006). Insurability and mitigation of flood losses in private households in Germany. Risk Analysis, 26(2), 383–395.

    Google Scholar 

  • Townsend, R.M. (1994). Risk and insurance in village India. Econometrica, 62, 539–591.

    Google Scholar 

  • Toya, H., & Skidmore, M. (2014). Do natural disasters enhance societal trust? Kyklos, 67, 255–279.

    Google Scholar 

  • United Nations. (2010). Aila cyclone aila: joint UN multisector assessment & response framework, Dhaka, June.

  • Viscusi, W. K, & Zeckhauser, R.J. (2006). National survey evidence on disasters and relief: Risk beliefs, self-interest, and compassion. Journal of Risk and Uncertainty, 33(1), 13–36.

    Google Scholar 

  • Voors, M.J., Nillesen, E.E.M., Verwimp, P., Bulte, E.H., Lensink, R., & Van Soest, D.P. (2012). Violent conflict and behavior: A field experiment in Burundi. American Economic Review, 102(2), 941–64.

    Google Scholar 

  • Weerdt, J.D., & Dercon, S. (2006). Risk-sharing networks and insurance against illness. Journal of Development Economics, 81(2), 337–356.

    Google Scholar 

  • Yamamura, E. (2016). Natural disasters and social capital formation: The impact of the great Hanshin-Awaji earthquake. Papers in Regional Science, 95 (95), S143–S164.

    Google Scholar 

  • Zylberberg, Y., & Gröger, A. (2016). Internal labor migration as a shock coping strategy: Evidence from a typhoon. American Economic Journal: Applied Economics, 8(2), 123–153.

    Google Scholar 

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Acknowledgments

We would like to thank the editors and one anonymous referee for their comment. We are very grateful for the support from our dedicated field team. Shaun Astbury, Kashem Khan, and Chau Nguyen provided excellent research assistance. We thank Daniel Aldrich and Yasuyuki Sawada as well as the participants at the ESA World Meeting in Sydney 2015, the Mini-Conference on Disasters and Recovery in Tokyo 2016, and seminar participants at Monash University for their helpful comments. Funding from Monash University is gratefully acknowledged.

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Appendix

Appendix

A model of risk-sharing and defection

Here, we develop a model of risk-sharing and defection. For simplicity, we assume a common defection cost c ≥ 0, which may depend on whether a natural disaster previously occurred in the region, the public visibility of defection, and prevailing social norms. We let \( u_{i} \left (x \vert \gamma _{i} \right )\) denote agent i’s vNM utility function over certain monetary payments x > 0, for γi > 0 agent i’s risk aversion parameter. \( u_{i} \left (x \vert \gamma _{i} \right )\)is assumed to be increasing and strictly concave in x, and:

$$ \frac{\partial }{\partial \gamma_{i}}\frac{\frac{\partial^{2}}{\partial x^{2}}u_{i} \left( x \vert \gamma_{i} \right) }{\frac{\partial }{\partial x}u_{i} \left( x \vert \gamma_{i} \right) }<0. $$

We also assume that \( \frac {\partial }{\partial \gamma _{i}}u_{i} \left (x \vert \gamma _{i} \right ) \leq 0\), \( \frac {\partial }{\partial \gamma _{i}}\frac {\partial }{\partial x}u_{i} \left (x \vert \gamma _{i} \right ) \leq 0\) and \( \frac {\partial }{\partial \gamma _{i}}\frac {\partial ^{2}}{\partial x^{2}}u_{i} \left (x \vert \gamma _{i} \right ) \leq 0\) when x is non-negative. That is, the utility agents receive from cash payments is decreasing as they become more risk-averse. These properties are satisfied for both constant relative risk aversion (CRRA):

$$ u_{i} \left( x \vert \gamma_{i} \right) = \left\{ \begin{array}{ll} \frac{x^{1- \gamma_{i}}-1}{1- \gamma_{i}} & if \gamma_{i} \neq 1\\ ln \left( x \right) & if \gamma_{i}=1 \end{array}\right. $$

and constant absolute risk aversion (CARA):

$$ u_{i} \left( x \vert \gamma_{i} \right) =\frac{1-e^{- \gamma_{i}x}}{ \gamma_{i}} $$

Players choose (i) whether to share risk by joining a pool, (ii) a lottery \(\tilde {x}_{i}\), and when joining a pool (iii), a defection strategy di, which we describe as follows: if player i joins a pool P (a set of pool members), their expected payoff is:

$$ {V_{i}^{P}} \left( \tilde{x},d \right) =E_{\tilde{x}} \left[ u_{i} \left( d_{i} \left( \tilde{x}_{i} \right)\tilde{x}_{i}+ \left( 1-d_{i} \left( \tilde{x}_{i} \right) \right) \tilde{y} \vert \gamma_{i} \right) \right] -E_{\tilde{x}_{i}} \left[ d_{i} \left( \tilde{x}_{i} \right) \right] c $$

where \(\tilde {x} \equiv \left (\tilde {x}_{j} \right )_{j \in P}\) denotes the profile of lotteries that players in P choose, we denote:

$$ y=\frac{ {\sum}_{j \in P}^{}d_{j} \left( x_{j} \right) x_{j}}{ {\sum}_{j \in P}^{}d_{j} \left( x_{j} \right) }, $$

equal to the total payment to i when in the pool, \( d_{i} \left (x_{i} \right ) \in \left \{ 0,1 \right \}\) gives i’s lottery-outcome-contingent defection strategy (i.e., \( d_{i} \left (x_{i} \right ) =1\) iff defect), and we denote the profile of defection strategies by \( d \equiv \left (d_{j} \right )_{j \in P}\). Each player’s action is the choice \(\tilde {x}_{i} \in X\), where X gives the set of lotteries to choose from and the defection strategy \( d_{i} \left (x \right )\), which is either “no defection” or “defection” depending on the outcome of \(\tilde {x}_{i}\) (i.e. xi). We assume that X is ordered, with a “greater” \(\tilde {x}_{i}\) yielding a greater expected return and greater variance (riskiness). To simplify the environment, we focus on the experimental design where lotteries are determined via a fair coin toss. That is, \(\tilde {x}_{i}\) is xi,HIGH and xi,LOW with probability 1/2 each.Footnote 13 When convenient, we assume that the set X is smooth, with \( x_{i,HIGH} \left (\tilde {x}_{i} \right )\) and \( x_{i,LOW} \left (\tilde {x}_{i} \right )\) continuous and differentiable in the chosen lottery \(\tilde {x}_{i}\) (note that the implemented design takes finite |X| = 6).

If player i does not join a pool, their expected payoff is simply:

$$ V_{i}^{NP} \left( \tilde{x}_{i} \right) =E_{\tilde{x}_{i}} \left[ u_{i} \left( \tilde{x}_{i} \vert \gamma_{i} \right) \right] . $$

Thus, i will choose between the optimal strategy d maximizing \( {V_{i}^{P}} \left (\tilde {x}^{P},d \right )\) versus not joining the pool which yields \( V_{i}^{NP} \left (\tilde {x}_{i}^{NP} \right )\), where \(\tilde {x}^{P}\) gives the profile of optimal lotteries when entering the pool and \(\tilde {x}_{i}^{NP}\) gives i’s optimal lottery when not entering the pool.

Whether agent i joins a pool or not, their choice of \(\tilde {x}_{i}\) will determine the expected return and riskiness associated with the lottery. If this agent does not join a pool, this lottery is simply \(\tilde {x}_{i}=\tilde {x}_{i}^{NP}\). If the agent does join a pool, this lottery is \(\tilde {y}\) under \( \tilde {x}_{i}=\tilde {x}_{i}^{P}\). In either case, the expected return and riskiness of the lottery that i faces is increasing in the expected return and riskiness of \(\tilde {x}_{i}\). Under our assumptions on \( u_{i} \left (x | \gamma _{i} \right )\) and X, the following can be shown:

Proposition 1

The expected return and riskiness of optimal \(\tilde {x}_{i}\) in X is decreasing in γi.

Proof

Online Appendix A. □

Observation 1

Proposition 1 is consistent with the conclusion that individuals directly exposed to a disaster become more risk tolerant in order to secure increased gains.

We turn to defection incentives when agents join a risk-sharing pool. If i enters the pool and takes a defection strategy \( d_{i} \left (x_{i} \right ) =1\) if xi = xi,HIGH and \( d_{i} \left (x_{i} \right ) =0\) if xi = xiLOW, then \( V_{i} \left (\tilde {x},d \right )\) can be written as follows:

$$ V_{i} \left( \tilde{x},d \right) =V_{i}^{P-D} \left( \tilde{x},d_{-i} \right) \equiv \frac{1}{2} \left( u_{i} \left( x_{i,HIGH} \vert \gamma_{i} \right) -c \right) +\frac{1}{2}E_{\tilde{x}_{-i}} \left[ u_{i} \left( y_{i,LOW} \vert \gamma_{i} \right) \right] , $$

where:

$$ y_{i,LOW}=\frac{x_{i,LOW}+ {\sum}_{j \in P}^{}d_{j} \left( x_{j} \right) x_{j}}{1+ {\sum}_{j \in P^{}d_{j}} \left( x_{j} \right) }. $$

If i takes a no-defection strategy (\( d_{i} \left (x_{i} \right ) =0\) always), then:

$$ V_{i} \left( \tilde{x},d \right) =V_{i}^{P-ND} \left( \tilde{x},d_{-i} \right) \equiv \frac{1}{2}E_{x_{-i}} \left[ u_{i} \left( y_{i,HIGH} \vert \gamma_{i} \right) \right] +\frac{1}{2}E_{x_{-i}} \left[ u_{i} \left( y_{i,LOW} \vert \gamma_{i} \right) \right] , $$

where:

$$ y_{i,HIGH}=\frac{x_{i,HIGH}+ {\sum}_{j \in P}^{}d_{j} \left( x_{j} \right) x_{j}}{1+ {\sum}_{j \in P}^{}d_{j} \left( x_{j} \right) }. $$

Clearly, defection is preferred to no defection iff \( V_{i}^{P-D} \left (\tilde {x},d_{-i} \right ) >V_{i}^{P-ND} \left (\tilde {x},d_{-i} \right )\), equivalently:

$$ u_{i} \left( \tilde{x}_{i,HIGH} \vert \gamma_{i} \right) -E_{\tilde{x}_{-i}} \left[ u_{i} \left( y_{i,HIGH} \vert \gamma_{i} \right) \right] >c. $$

This provides our next result.

Proposition 2

The incentives to defect in a pool depend on the pool size, the lotteries and defection strategies of others in the pool, the cost of defection c, and on the size of the high outcome of the lottery chosen by the defecting individual; incentives to defect are independent of the low outcome of the lottery chosen by the defecting individual.

Now, further assume that ui = u and γi = γ for all i (γ may still depend on the treatment). Then, by the symmetry of the setting, a symmetric-pool equilibrium can be obtained where each member of the pool takes a similar strategy, both in their chosen lottery and defection strategies. Indeed, when a symmetric-pool equilibrium is obtained all pool members choose a lottery \(\tilde {x}^{P\ast }\), and the value to defection upon realizing \( x_{i,HIGH}^{P\ast }\), equal to \( u \left (x_{i,HIGH}^{P\ast } \vert \gamma \right ) -E_{\tilde {x}_{-i}} \left [ u \left (\tilde {y}_{i,HIGH}^{P\ast } \vert \gamma \right ) \right ]\), is always positive. When all others do not defect, then \(\tilde {y}_{i,HIGH}^{P\ast }=\tilde {y}_{i,HIGH}^{ND\ast } \equiv \left (x_{i,HIGH}^{P\ast }+ {\sum }_{j \in P}\tilde {x}_{j}^{P\ast }\right )/n\), for n = |P| giving the size of the pool. Alternatively, when all others choose to defect, the incentives to enter and contribute to the pool (by not defecting) dissolve. Therefore, the value to defection \({\Delta }^{D\ast } \equiv u \left (x_{i,HIGH}^{P\ast } \vert \gamma \right ) -E_{x_{-i}} \left [ u \left (y_{i,HIGH}^{ND\ast } \vert \gamma \right ) \right ]\) when all others do not defect pins the threshold such that no members defect in equilibrium if c ≥ΔD, and the pool disbands if c < ΔD. Indeed, ΔD defines the equilibrium propensity to defect, which we describe next.

A.1 Comparative statics

Given that many variables are changing upon moving between the control and treatment (the risk aversion parameter γ, the optimal \( x_{i}^{NP}\) and xP, the defection cost c, and the size of the pool n ), here we will assess the comparative statics of a symmetric-pool equilibrium with respect to each variable, ceteris paribus(i.e., we provide a partial-equilibrium analysis). The broad takeaway will be that an increase in the defection cost c is necessary to rationalize an observed decrease in defection in disaster regions.

A.1.1 Risk-sharing and defection

For our first set of comparative statics results, we focus on defection behaviour under risk-sharing (i.e., joining a pool), and set aside the endogenous \(\tilde {x}_{i}^{NP}\) and the corresponding choice between joining and not joining a pool. We then consider the incentives to join the pool as risk preferences change in the following subsection.

First, we hold the endogenous \(\tilde {x}^{P\ast }\) and n fixed and marginally increasing γ (note that the former will hold for local changes to γ).

Proposition 3

In the symmetric-pool equilibrium, the cut-off ΔD is decreasing in the coefficient of risk aversion γ.

Proof

Online Appendix A. □

In words, holding all else equal, the incidence of defection (i.e., the range of c < ΔD) decreases as the agents become more risk-averse. The reason is as follows: as agents become more risk averse, the gain to absconding with the high payment \( x_{i,HIGH}^{P\ast }\) decreases. Conversely, the opportunity cost of remaining in the pool decreases less abruptly, and approaches the value to defection. In total, the defection gain ΔD decreases.

Observation 2

With subjects exhibiting significantly less risk aversion in the disaster treatment (revealed in the first task), the finding that less defection is observed in the disaster treatment is inconsistent with Proposition 3.

Second, we hold γ and n fixed and increase the risk of endogenous \(\tilde {x}^{P\ast }\) chosen from X. With an increase to the mean and standard deviation of \(\tilde {x}^{P\ast }\), the effect on \( E_{\tilde {x}_{-i}} \left [ u_{i} \left (\tilde {y}_{i,HIGH}^{ND\ast } \vert \gamma \right ) \right ]\) is ambiguous. Therefore, for the following result, we impose an additional structure to the form of \( u \left (x \vert \gamma \right )\) and to the ordering of X. First, we assume that \( u \left (x \vert 0 \right ) =a+bx\) for some b > 0 (as with CRRA utility). Second, we take lotteries \(\tilde {x}\) and \(\tilde {x}^{\prime }\) such that \(\tilde {x}- \delta \) gives a mean-preserving spread of \(\tilde {x}^{\prime }\) for some δ ≥ 0. In the experimental design, δ = 40 Taka between lottery options 1 through 5 (δ = 0 between options 5 and 6). We say that \(\tilde {x}\) and \(\tilde {x}^{\prime }\) are ordered simply if \(\tilde {x}\) can be obtained from \(\tilde {x}^{\prime }\) via such homogenous upward shifts coupled with mean-preserving spreads. For the next result, which establishes sufficient conditions for ΔD to be increasing in the riskiness of \(\tilde {x}^{P\ast }\), we assume the lotteries \(\tilde {x}^{P\ast } \in X\) are ordered simply.

Proposition 4

In the symmetric-pool equilibrium, there is some γ > 0 and δ > 0 such that for all γ < γ and δ < δ, the cut-off ΔD is increasing in the riskiness of \(\tilde {x}^{P\ast }\).

Holding all else equal, the incidence of defection (i.e., the range of c < ΔD) increases as the agents bring greater risk to the risk-sharing pool, provided that the agents are not too risk averse and the additional expected value of each lottery is not too large. The intuition is as follows: as agents bring more risk to the pool, the gain from absconding with the high payment \( x_{i,HIGH}^{P\ast }\) increases. Conversely, the opportunity cost of remaining in the pool increases more slowly, provided the agents are not too risk-averse and the additional expected return is not too large. Consequently, greater xP under small γ and δ yields an increasing value to defection.

We exhibit the bounds of the result numerically, as follows: Table 8 provides ΔD values for various γ values under CRRA utlity. For γ values of 0.5 and 1, ΔD increases monotonically across the lottery choices of the experimental design; note that ΔD = 0 for lottery 1. For γ = 2, this trend reverses between lottery 4 and 5, and for γ = 4, the trend reverses across lotteries 1 to 5. For lottery 6, which gives a mean-preserving spread of lottery 5, ΔD always increases.

Table 8 Lottery Table 1

In Table 9 , 1000 Taka is added to all payoffs, capturing a non-zero initial level of wealth. Now, the ΔD increases monotonically across all lottery choices. We see that the domain of Proposition 4 is quite broad, particularly when including non-zero initial wealth.

Table 9 Lottery Table 2

Observation 3

With subjects taking significantly greater risk to the pool in the disaster treatment, the findings that agents are less risk-averse and less defection in the disaster treatment are inconsistent with Proposition 4.

Next, we hold γ and xP fixed and increase the size of the pool n. Now, the risk associated with staying in the pool decreases (because of the diversification in \(y_{i,HIGH}^{ND \ast }\) ), while the expected return remains fixed. It is straight forward to show the following:

Proposition 5

In the symmetric-pool equilibrium, the cut-off ΔD is decreasing in n.

Proof

Online Appendix A. □

Observation 4

With the average size of the pools in the disaster treatment significantly smaller than those of the control, the finding that less defection is observed in the disaster treatment is inconsistent with Proposition 5.

Main Observation

Given that Propositions 3, 4 and, 5 are each inconsistent with the experimental findings, a significant increase in the defection cost c is necessary to rationalize the observation that defection decreases significantly in the disaster treatment.

A.1.2 Risk-sharing choice

The comparative statics for the values of agents choosing not to pool are straight-forward. Precisely, given that the expected return and variance options from lottery choices in set X remain the same, facing less aversion to risk implies that agent i enjoys greater expected utility, both directly through a decrease in γ and indirectly through the chosen riskier \(\tilde {x}_{i}^{NP}\) (under our assumptions on \( u_{i} \left (x \vert \gamma \right )\)). That is, each i faces less cost when it comes to bearing risk and reaps more gains when it comes to greater expected return. The comparative statics on values to agents choosing to share risk, however, are less straight-forward given that the expected utilities depend on the risk choices of other pool members. For simplicity, we consider the comparative static holding fixed \(\tilde {x}=\tilde {x}^{NP}\) = \(\tilde {x}^{P\ast }\). Moreover, we consider the case of c > ΔD, where the pool can exist. The following is immediate:

Proposition 6

In the symmetric-pool equilibrium, the gain to sharing risk via joining the pool without defection, \(V_{i}^{P-ND} \left (\tilde {x},d_{-i}^{ND} \right ) -V_{i}^{NP} \left (\tilde {x} \right )\), is non-decreasing in both γ and n.

Intuitively, incentives to share risk are increasing with risk aversion and the size of the pool.

Observation 5

With subjects exhibiting significantly less risk aversion in the disaster treatment (revealed in the first task), the finding that the frequency of subjects joining a pool is significantly lower in the disaster treatment is consistent with Prediction 5.

Note that the observed lower frequency of joining pools and the significantly lower pool size in the disaster treatment group are complementary observations.

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Islam, A., Leister, C.M., Mahmud, M. et al. Natural disaster and risk-sharing behavior: Evidence from rural Bangladesh. J Risk Uncertain 61, 67–99 (2020). https://doi.org/10.1007/s11166-020-09334-5

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  • DOI: https://doi.org/10.1007/s11166-020-09334-5

Keywords

  • Risk preference
  • Risk-sharing
  • Intrinsic motivation
  • Asymmetric information
  • Natural disaster
  • Field experiment

JEL Classification

  • C90
  • C93
  • D03
  • D71
  • D81
  • O12
  • Q54