Risk sharing contracts with private information and one-sided commitment

  • Eduardo ZilbermanEmail author
  • Vinicius Carrasco
  • Pedro Hemsley
Research Article


In a repeated unobserved endowment economy in which agents negotiate long-term contracts with a financial intermediary, we study the risk sharing implications of the interaction between incentive compatibility constraints (due to private information) and participation constraints (due to one-sided commitment). In particular, we assume that after a default episode, agents consume their endowment and remain in autarky forever. We find that once they are away from autarky today, if the probability of drawing the highest possible endowment shock is sufficiently small, the optimal contract prevents agents from reaching autarky tomorrow and, thus, from being “impoverished.” Moreover, an invariant cross-sectional distribution of lifetime utilities (or values) exists. A numerical example shows that the mass of agents living in autarky can be zero in the limit.


Risk sharing contracts private information One-sided commitment 

JEL Classification

D31 D82 D86 

Supplementary material

199_2018_1112_MOESM1_ESM.pdf (266 kb)
Supplementary material 1 (pdf 265 KB)


  1. Ales, L., Maziero, P., Yared, P.: A theory of political and economic cycles. J. Econ. Theory 153, 224–251 (2014)CrossRefGoogle Scholar
  2. Atkeson, A., Lucas, R.E.: Efficiency and equality in a simple model of efficient unemployment insurance. J. Econ. Theory 66(1), 64–88 (1995)CrossRefGoogle Scholar
  3. Attanasio, O., Ríos-Rull, J.V.: Consumption smoothing in island economies: Can public insurance reduce welfare? Eur. Econ. Rev. 44(7), 1225–1258 (2000)CrossRefGoogle Scholar
  4. Broer, T., Kapička, M., Klein, P.: Consumption risk sharing with private information and limited enforcement. Rev. Econ. Dyn. 23, 170–190 (2017)CrossRefGoogle Scholar
  5. Doepke, M., Townsend, R.M.: Dynamic mechanism design with hidden income and hidden actions. J. Econ. Theory 126(1), 235–285 (2006)CrossRefGoogle Scholar
  6. Farhi, E., Werning, I.: Inequality and social discounting. J. Polit. Econ. 115(3), 365–402 (2007)CrossRefGoogle Scholar
  7. Fernandes, A., Phelan, C.: A recursive formulation for repeated agency with history dependence. J. Econ. Theory 91(2), 223–247 (2000)CrossRefGoogle Scholar
  8. Gobert, K., Poitevin, M.: Non-commitment and savings in dynamic risk-sharing contracts. Econ. Theory 28(2), 357–372 (2006)CrossRefGoogle Scholar
  9. Hertel, J.: Efficient and sustainable risk sharing with adverse selection. Job Market Paper (2004)Google Scholar
  10. Kehoe, T.J., Levine, D.K.: Liquidity constrained markets versus debt constrained markets. Econometrica 69(3), 575–598 (2001)CrossRefGoogle Scholar
  11. Kocherlakota, N.R.: Implications of efficient risk sharing without commitment. Rev. Econ. Stud. 63(4), 595–609 (1996)CrossRefGoogle Scholar
  12. Krueger, D., Perri, F.: Does income inequality lead to consumption inequality? Evidence and theory. Rev. Econ. Stud. 73(1), 163–193 (2006)CrossRefGoogle Scholar
  13. Krueger, D., Perri, F.: Public versus private risk sharing. J. Econ. Theory 146(3), 920–956 (2011)CrossRefGoogle Scholar
  14. Laczó, S.: Does risk sharing increase with risk aversion and risk when commitment is limited? J. Econ. Dyn. Control 46, 237–251 (2014)CrossRefGoogle Scholar
  15. Ligon, E., Thomas, J., Worrall, T.: Informal insurance arrangements with limited commitment: theory and evidence from village economies. Rev. Econ. Stud. 69(1), 209–244 (2002)CrossRefGoogle Scholar
  16. Ljungqvist, L., Sargent, T.: Recursive Macroeconomic Theory. The MIT Press, Cambridge (2012)Google Scholar
  17. Milgrom, P., Segal, I.: Envelope theorems for arbitrary choice sets. Econometrica 70(2), 583–601 (2002)CrossRefGoogle Scholar
  18. Opp, M.M., Zhu, J.Y.: Impatience versus incentives. Econometrica 83(4), 1601–1617 (2015)CrossRefGoogle Scholar
  19. Phelan, C.: Repeated moral hazard and one-sided commitment. J. Econ. Theory 66(2), 488–506 (1995)CrossRefGoogle Scholar
  20. Phelan, C.: On the long run implications of repeated moral hazard. J. Econ. Theory 79(2), 174–191 (1998)CrossRefGoogle Scholar
  21. Sleet, C., Yeltekin, Ş.: Dynamic labor contracts with temporary layoffs and permanent separations. Econ. Theory 18(1), 207–235 (2001)CrossRefGoogle Scholar
  22. Stokey, N.L., Lucas, R.E.L.: Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge (1989)Google Scholar
  23. Thomas, J., Worrall, T.: Self-enforcing wage contracts. Rev. Econ. Stud. 55(4), 541–54 (1988)CrossRefGoogle Scholar
  24. Thomas, J., Worrall, T.: Income fluctuation and asymmetric information: an example of a repeated principal-agent problem. J. Econ. Theory 51(2), 367–390 (1990)CrossRefGoogle Scholar
  25. Tian, G., Zhang, Y.: When can we do better than autarky? Econ. Lett. 119(3), 328–331 (2013)CrossRefGoogle Scholar
  26. Wang, C.: Dynamic insurance with private information and balanced budgets. Rev. Econ. Stud. 62(4), 577–595 (1995)CrossRefGoogle Scholar
  27. Wang, C.: Dynamic costly state verification. Econ. Theory 25(4), 887–916 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Eduardo Zilberman
    • 1
    Email author
  • Vinicius Carrasco
    • 2
  • Pedro Hemsley
    • 3
  1. 1.Economic Research DepartmentCentral Bank of ChileSantiagoChile
  2. 2.Department of EconomicsPUC-RioRio de JaneiroBrazil
  3. 3.Department of EconomicsUERJRio de JaneiroBrazil

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