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Efficient Risk Sharing with Limited Commitment and Storage

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  • Ábrahám, Árpád; Laczó, Sarolta

Abstract

We extend the model of risk sharing with limited commitment (Kocherlakota, 1996) by introducing both a public and a private (unobservable and/or non-contractible) storage technology. Positive public storage relaxes future participation constraints, hence it can improve risk sharing, contrary to the case where hidden income or effort is the deep friction. The characteristics of constrained-efficient allocations crucially depend on the storage technology’s return. In the long run, if the return on storage is (i) moderately high, both assets and the consumption distribution may remain time-varying; (ii) sufficiently high, assets converge almost surely to a constant and the consumption distribution is time-invariant; (iii) equal to agents’ discount rate, perfect risk sharing is self-enforcing. Agents never have an incentive to use their private storage technology, i.e., Euler inequalities are always satisfied, at the constrained-efficient allocation of our model, while this is not the case without optimal public asset accumulation. We compare the dynamics of consumption in simulated data and data from Indian villages, and find that past incomes matter in a similar way in our model with storage and the data but not in the basic limited-commitment model.

Suggested Citation

  • Ábrahám, Árpád; Laczó, Sarolta, 2016. "Efficient Risk Sharing with Limited Commitment and Storage," Economics Working Papers ECO2016/06, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2016/06
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    References listed on IDEAS

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    1. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2000. "Mutual Insurance, Individual Savings and Limited Commitment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 216-246, April.
    2. 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.
    3. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2002. "Informal Insurance Arrangements with Limited Commitment: Theory and Evidence from Village Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 209-244.
    4. Jonathan Thomas & Tim Worrall, 1994. "Foreign Direct Investment and the Risk of Expropriation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 81-108.
    5. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
    6. Krueger, Dirk & Uhlig, Harald, 2006. "Competitive risk sharing contracts with one-sided commitment," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1661-1691, October.
    7. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    8. Sarolta Laczó, 2015. "Risk Sharing With Limited Commitment And Preference Heterogeneity: Structural Estimation And Testing," Journal of the European Economic Association, European Economic Association, vol. 13(2), pages 265-292, April.
    9. Wataru Nozawa, 2016. "Failure of the first-order approach in an insurance problem with no commitment and hidden savings," Economics Bulletin, AccessEcon, vol. 36(4), pages 2422-2429.
    10. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    11. Bulow, Jeremy & Rogoff, Kenneth, 1989. "Sovereign Debt: Is to Forgive to Forget?," American Economic Review, American Economic Association, vol. 79(1), pages 43-50, March.
    12. Narayana Kocherlakota, 2004. "Figuring out the Impact of Hidden Savings on Optimal Unemployment Insurance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(3), pages 541-554, July.
    13. Tobias Broer, 2013. "The Wrong Shape of Insurance? What Cross-Sectional Distributions Tell Us about Models of Consumption Smoothing," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(4), pages 107-140, October.
    14. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
    15. Kimball, Miles S, 1988. "Farmers' Cooperatives as Behavior Toward Risk," American Economic Review, American Economic Association, vol. 78(1), pages 224-232, March.
    16. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    17. Ogaki, Masao & Zhang, Qiang, 2001. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometrica, Econometric Society, vol. 69(2), pages 515-526, March.
    18. Ethan Ligon, 1998. "Risk Sharing and Information in Village Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(4), pages 847-864.
    19. Kehoe, Patrick J. & Perri, Fabrizio, 2004. "Competitive equilibria with limited enforcement," Journal of Economic Theory, Elsevier, vol. 119(1), pages 184-206, November.
    20. Tobias Broer, 2009. "Stationary equilibrium distributions in economies with limited commitment," Economics Working Papers ECO2009/39, European University Institute.
    21. Harold L. Cole & Narayana R. Kocherlakota, 2001. "Efficient Allocations with Hidden Income and Hidden Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 523-542.
    22. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, December.
    23. Maurizio Mazzocco, 2007. "Household Intertemporal Behaviour: A Collective Characterization and a Test of Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 857-895.
    24. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 541-554.
    25. Maurizio Mazzocco & Shiv Saini, 2012. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences," American Economic Review, American Economic Association, vol. 102(1), pages 428-468, February.
    26. Dirk Krueger & Fabrizio Perri, 2006. "Does Income Inequality Lead to Consumption Inequality? Evidence and Theory -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 163-193.
    27. Jeremy Lise & Ken Yamada, 2019. "Household Sharing and Commitment: Evidence from Panel Data on Individual Expenditures and Time Use," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 2184-2219.
    28. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
    29. Allen, Franklin, 1985. "Repeated principal-agent relationships with lending and borrowing," Economics Letters, Elsevier, vol. 17(1-2), pages 27-31.
    30. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
    31. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 595-609.
    32. 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.
    33. Alexander Karaivanov & Robert M. Townsend, 2014. "Dynamic Financial Constraints: Distinguishing Mechanism Design From Exogenously Incomplete Regimes," Econometrica, Econometric Society, vol. 82(3), pages 887-959, May.
    34. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    35. Christian Sigouin, 2003. "Investment Decisions, Financial Flows, and Self-Enforcing Contracts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(4), pages 1359-1382, November.
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    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Efficient Risk Sharing with Limited Commitment and Storage
      by Christian Zimmermann in NEP-DGE blog on 2013-07-14 08:58:49

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    9. Bredemeier, Christian & Gravert, Jan & Juessen, Falko, 2021. "Accounting for Limited Commitment between Spouses When Estimating Labor-Supply Elasticities," IZA Discussion Papers 14226, Institute of Labor Economics (IZA).
    10. Li, Zhimin & Ligon, Ethan, 2020. "Inferring informal risk-sharing regimes: Evidence from rural Tanzania," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 941-955.
    11. Daniel J. Hernandez & Fernando Jaramillo & Hubert Kempf & Fabien Moizeau & Thomas Vendryes, 2023. "Limited Commitment, Social Control and Risk-Sharing Coalitions in Village Economies," Economics Working Paper Archive (University of Rennes & University of Caen) 2023-03, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
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    More about this item

    Keywords

    Risk Sharing; LC; Hidden Storage; Dynamic Contracts;
    All these keywords.

    JEL classification:

    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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