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Differentiability of the Efficient Frontier when Commitment to Risk Sharing is Limited

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  • Koeppl Thorsten V.

    (Department of Economics, Queen’s University, Kingston, Ontario)

Abstract

This paper shows that the value function describing efficient risk sharing with limited commitment is not necessarily differentiable everywhere. We link differentiability of the value function to history dependence of efficient allocations and provide sufficient conditions for both properties.

Suggested Citation

  • Koeppl Thorsten V., 2006. "Differentiability of the Efficient Frontier when Commitment to Risk Sharing is Limited," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(1), pages 1-6, April.
    • Handle: RePEc:bpj:bejmac:v:topics.6:y:2006:i:1:n:10
    DOI: 10.2202/1534-5998.1419
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    References listed on IDEAS

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    1. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    2. 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.
    3. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-598, May.
    4. Coate, Stephen & Ravallion, Martin, 1993. "Reciprocity without commitment : Characterization and performance of informal insurance arrangements," Journal of Development Economics, Elsevier, vol. 40(1), pages 1-24, February.
    5. 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.
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    Cited by:

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    2. Pierre Dubois & Bruno Jullien & Thierry Magnac, 2008. "Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence," Econometrica, Econometric Society, vol. 76(4), pages 679-725, July.
    3. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    4. Rincón-Zapatero, Juan Pablo & Santos, Manuel S., 2009. "Differentiability of the value function without interiority assumptions," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1948-1964, September.
    5. Huang, Pidong, 2013. "Optimal Unemployment Insurance With Different Types of Job," MPRA Paper 46626, University Library of Munich, Germany.
    6. Neele Balke & Thibaut Lamadon, 2022. "Productivity Shocks, Long-Term Contracts, and Earnings Dynamics," American Economic Review, American Economic Association, vol. 112(7), pages 2139-2177, July.
    7. Thibaut Lamadon, 2014. "Productivity Shocks, Dynamic Contracts and Income Uncertainty," 2014 Meeting Papers 243, Society for Economic Dynamics.
    8. Lippi, Francesco & Fuchs, William, 2003. "Monetary Union with Voluntary Participation," CEPR Discussion Papers 4122, C.E.P.R. Discussion Papers.
    9. Popov, Latchezar, 2016. "Stochastic costly state verification and dynamic contracts," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 1-22.
    10. Guilherme Carmona, 2006. "On the optimality of the equality matching form of sociality," Nova SBE Working Paper Series wp489, Universidade Nova de Lisboa, Nova School of Business and Economics.
    11. Tessa Bold, 2008. "Implications of Endogenous Group Formation for Efficient Risk-Sharing," Economics Series Working Papers 387, University of Oxford, Department of Economics.
    12. Kai Arvai, 2021. "The Political Economy of Currency Unions," Working papers 850, Banque de France.

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    More about this item

    Keywords

    risk sharing; limited commitment; differentiability;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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