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The Wrong Shape of Insurance? What Cross-Sectional Distributions Tell Us about Models of Consumption Smoothing

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  • Tobias Broer

Abstract

This paper shows how two standard models of consumption risk-sharing?self-insurance through borrowing and saving and limited commitment to insurance contracts?replicate similarly well the standard, second-moment measures of insurance observed in US micro data. A nonparametric analysis, however, reveals strongly contrasting and counterfactual joint distributions of consumption, income and wealth. Method of moments estimation shows how measurement error in consumption eliminates excessive skewness and smoothness of consumption growth. Moreover, counterfactual nonlinearities disappear at high-estimated risk aversion under selfinsurance, but are a robust feature of limited commitment. Its "shape of insurance" thus argues in favor of the self-insurance model.

Suggested Citation

  • 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.
    • Handle: RePEc:aea:aejmac:v:5:y:2013:i:4:p:107-40
    Note: DOI: 10.1257/mac.5.4.107
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    Cited by:

    1. Zhang, Yuzhe, 2013. "Characterization of a risk sharing contract with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 794-809.
    2. Xavier Mateos-Planas & Giulio Seccia, 2014. "Consumer default with complete markets: default-based pricing and finite punishment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 549-583, August.
    3. Tessa Bold & Tobias Broer, 2021. "Risk Sharing in Village Economies Revisited [Efficient Risk Sharing with Limited Commitment and Storage]," Journal of the European Economic Association, European Economic Association, vol. 19(6), pages 3207-3248.
    4. Etheridge, Ben, 2015. "A test of the household income process using consumption and wealth data," European Economic Review, Elsevier, vol. 78(C), pages 129-157.
    5. Röhrs, Sigrid & Winter, Christoph, 2015. "Public versus private provision of liquidity: Is there a trade-off?," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 314-339.
    6. Broer, Tobias, 2020. "Consumption insurance over the business cycle," CEPR Discussion Papers 14579, C.E.P.R. Discussion Papers.
    7. Tobias Broer & Marek Kapicka & Paul Klein, 2017. "Consumption Risk Sharing with Private Information and Limited Enforcement," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 170-190, January.
    8. Broer, Tobias, 2014. "Domestic or global imbalances? Rising income risk and the fall in the US current account," Journal of Monetary Economics, Elsevier, vol. 64(C), pages 47-67.
    9. Tobias Broer & Tessa Bold, 2015. "Risk-Sharing in Village Economies Revisited," 2015 Meeting Papers 1232, Society for Economic Dynamics.
    10. Lancia, Francesco & Russo, Alessia & Worrall, Tim S, 2020. "Optimal Sustainable Intergenerational Insurance," CEPR Discussion Papers 15540, C.E.P.R. Discussion Papers.
    11. Árpád Ábrahám & Sarolta Laczó, 2018. "Efficient Risk Sharing with Limited Commitment and Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1389-1424.
    12. Swapnil Singh & Christian A. Stoltenbergz, 2018. "How Much Do Households Really Know About Their Future Income?," Bank of Lithuania Working Paper Series 55, Bank of Lithuania.
    13. Wöhrmüller, Stefan, 2022. "Consumption Insurance and Credit Shocks," VfS Annual Conference 2022 (Basel): Big Data in Economics 264088, Verein für Socialpolitik / German Economic Association.
    14. Krueger, Dirk & Uhlig, Harald, 2022. "Neoclassical Growth with Limited Commitment," CEPR Discussion Papers 17757, C.E.P.R. Discussion Papers.
    15. Swapnil Singh, 2018. "Public insurance of married versus single households in the US: trends and welfare consequences," Bank of Lithuania Working Paper Series 54, Bank of Lithuania.
    16. Denderski, Piotr & Stoltenberg, Christian A., 2020. "Risk sharing with private and public information," Journal of Economic Theory, Elsevier, vol. 186(C).
    17. Xavier Mateos-Planas & Giulio Seccia, 2013. "Consumer Default with Complete Markets: Default-based Pricing and Finite Punishment," Working Papers 711, Queen Mary University of London, School of Economics and Finance.
    18. Thomas, Jonathan P. & Worrall, Tim, 2018. "Dynamic relational contracts under complete information," Journal of Economic Theory, Elsevier, vol. 175(C), pages 624-651.
    19. Thomas, Jonathan P. & Worrall, Tim, 2014. "Dynamic Relational Contracts under Complete Information," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-47, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    20. Stefan Wöhrmüller, 2025. "Consumption insurance and credit shocks," Working Papers 825, DNB.
    21. Christian A. Stoltenberg & Swapnil Singh, 2020. "Consumption insurance with advance information," Quantitative Economics, Econometric Society, vol. 11(2), pages 671-711, May.
    22. Townsend, Robert M., 2025. "“Information frictions in macroeconomics: The legacy of Robert E. Lucas, Jr.”," Journal of Monetary Economics, Elsevier, vol. 155(S).
    23. Martin Ellison & Charles Brendon, 2015. "Time-Consistent Institutional Design," 2015 Meeting Papers 495, Society for Economic Dynamics.

    More about this item

    JEL classification:

    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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