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Stationary equilibrium distributions in economies with limited commitment

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  • Tobias Broer
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    Abstract

    Limited commitment to contracts can explain imperfect risk sharing even when individuals have access to complete insurance markets. Past contributions have focused on the resulting cross-sectional distribution of consumption (Cordoba 2008, Krueger and Perri 2006). In contrast, this paper looks at the joint dynamics of income, consumption and wealth implied by the asymmetric nature of partial insurance under limited commitment, where negative income shocks are largely insured but positive shocks can lead to large rises in consumption. A theoretical section proves the existence and uniqueness of equilibrium in a limited commitment continuum economy where incomes follow a standard markov process, and solves analytically for the joint equilibrium distribution of consumption, income and wealth. I show that individual consumption follows, at least locally, a left-skewed geometric distribution. Also, the conditional distributions of consumption and wealth are highly non-linear and have a characteristic form of heteroscedasticity, with declining conditional variances as income increases. In a quantitative part, the paper compares the exact distributions in the Krueger and Perri (2006) model to non-parametric estimates of their counterparts in US micro-data, and in a simple Ayagari economy.

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    Bibliographic Info

    Paper provided by European University Institute in its series Economics Working Papers with number ECO2009/39.

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    Date of creation: 2009
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    Handle: RePEc:eui:euiwps:eco2009/39

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    Keywords: Risk Sharing; Limited Commitment; Inequality; Wealth and Consumption Distribution; Participation Constraints; Default;

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    1. 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.
    2. Richard Blundell & Luigi Pistaferri & Ian Preston, 2008. "Consumption Inequality and Partial Insurance," American Economic Review, American Economic Association, vol. 98(5), pages 1887-1921, December.
    3. Orazio Attanasio & Steven J. Davis, 1994. "Relative Wage Movements and the Distribution of Consumption," NBER Working Papers 4771, National Bureau of Economic Research, Inc.
    4. Cordoba, Juan Carlos, 2010. "US Inequality: Debt Constraints or Incomplete Asset Markets?," Staff General Research Papers 32120, Iowa State University, Department of Economics.
    5. Harald Uhlig, 2010. "A Law of Large Numbers for Large Economies," Levine's Working Paper Archive 2070, David K. Levine.
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    7. Dirk Krueger & Harald Uhlig, 2003. "Competitive Risk Sharing Contracts with One-Sided Commitment," Levine's Bibliography 666156000000000407, UCLA Department of Economics.
    8. Abigail Barr & Garance Genicot, 2008. "Risk Sharing, Commitment, and Information: An Experimental Analysis," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1151-1185, December.
    9. Andrew Atkeson & Robert E Lucas, 2010. "On Efficient Distribution with Private Information," Levine's Working Paper Archive 2179, David K. Levine.
    10. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2010. "The Macroeconomic Implications of Rising Wage Inequality in the United States," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 681-722, 08.
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    12. Kocherlakota, Narayana R, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 595-609, October.
    13. Pedro Albarran & Orazio P. Attanasio, 2003. "Limited Commitment and Crowding out of Private Transfers: Evidence from a Randomised Experiment," Economic Journal, Royal Economic Society, vol. 113(486), pages C77-C85, March.
    14. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-98, May.
    15. 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.
    16. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2009. "Indeterminacy Of Competitive Equilibrium With Risk Of Default," Levine's Working Paper Archive 814577000000000313, David K. Levine.
    17. Kehoe, Timothy J & Levine, David K, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 865-88, October.
    18. Orazio Attanasio & Nicola Pavoni, 2007. "Risk Sharing in Private Information Models with Asset Accumulation: Explaining the Excess Smoothness of Consumption," NBER Working Papers 12994, National Bureau of Economic Research, Inc.
    19. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    20. 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.
    21. Townsend, R.M., 1991. "Risk and Insurance in Village India," University of Chicago - Economics Research Center 91-3, Chicago - Economics Research Center.
    22. 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.
    23. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
    24. Thomas, Jonathan & Worrall, Tim, 1988. "Self-enforcing Wage Contracts," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 541-54, October.
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    Cited by:
    1. Zhang, Yuzhe, 2012. "Characterization of a Risk Sharing Contract with One-Sided Commitment," MPRA Paper 42820, University Library of Munich, Germany, revised Aug 2012.
    2. Gervais, Martin & Klein, Paul, 2009. "Measuring consumption smoothing in CEX data," Discussion Paper Series In Economics And Econometrics 0906, Economics Division, School of Social Sciences, University of Southampton.

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