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Efficient Risk Sharing with Limited Commitment and Hidden Saving

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  • Sarolta Laczo

    (University of California, Los Angeles)

  • Arpad Abraham

    (European University Institute)

Abstract

In the typical model of risk sharing with limited commitment (e.g. Kocherlakota, 1996) agents do not have access to any technology transferring resources intertemporally. In our model, agents have a private (non-contractible and/or non-observable) saving technology. We first show that, under general conditions, agents would like to use their private saving technology, i.e. their Euler constraints are violated at the constrained-optimal allocation of the basic model. We then study a problem where both the default and saving incentives of the agents are taken into account. We show that when the planner and the agents have access to the same intertemporal technology, agents no longer want to save at the constrained-optimal allocation. The reason is that endogenously incomplete markets provide at least as much incentive for the planner to save, because she internalizes the effect of aggregate assets on future risk sharing. This implies that aggregate savings are positive in equilibrium even when there is no aggregate uncertainty and the return to saving is below the discount rate. Further, we show that assets remain stochastic whenever only moderate risk sharing is implementable in the long run, but become constant if high but still imperfect risk sharing is the long-run outcome. In contrast, if the return on saving is as high as the discount rate, perfect risk sharing is always self-enforcing in the long run. We also show that higher consumption inequality implies higher public asset accumulation. In terms of consumption dynamics, two counterfactual properties of limited commitment models, amnesia and persistence, do not hold in our model when assets are stochastic in the long run. We also provide an algorithm to solve the model, and illustrate the effects of changing the discount factor and the return to saving by computed examples.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2012 Meeting Papers with number 680.

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Date of creation: 2012
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Handle: RePEc:red:sed012:680

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  1. Ábrahám, Árpád & Koehne, Sebastian & Pavoni, Nicola, 2011. "On the first-order approach in principal-agent models with hidden borrowing and lending," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1331-1361, July.
  2. Albert Marcet & Ramon Marimon, 2011. "Recursive Contracts," CEP Discussion Papers dp1055, Centre for Economic Performance, LSE.
  3. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2002. "Informal Insurance Arrangements with Limited Commitment: Theory and Evidence from Village Economies," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 209-244.
  4. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  5. Allen, Franklin, 1985. "Repeated principal-agent relationships with lending and borrowing," Economics Letters, Elsevier, vol. 17(1-2), pages 27-31.
  6. Narayana Kocherlakota, 2010. "Figuring out the impact of hidden savings on optimal unemployment insuranc," Levine's Working Paper Archive 506439000000000291, David K. Levine.
  7. Arpad Abraham & Nicola Pavoni, 2008. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending: A Recursive Formulation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 781-803, October.
  8. Thomas, Jonathan & Worrall, Tim, 1988. "Self-enforcing Wage Contracts," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 541-54, October.
  9. Maurizio Mazzocco, 2007. "Household Intertemporal Behaviour: A Collective Characterization and a Test of Commitment," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 857-895.
  10. Dirk Krueger & Fabrizio Perri, 2006. "Does Income Inequality Lead to Consumption Inequality? Evidence and Theory -super-1," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 163-193.
  11. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
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