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Stationary equilibrium distributions in economies with limited commitment

  • Tobias Broer
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    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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    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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    1. 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.
    2. Orazio P. Attanasio & Nicola Pavoni, 2011. "Risk Sharing in Private Information Models With Asset Accumulation: Explaining the Excess Smoothness of Consumption," Econometrica, Econometric Society, vol. 79(4), pages 1027-1068, 07.
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    4. Dirk Krueger & Harald Uhlig, 2005. "Competitive Risk Sharing Contracts with One-Sided Commitment," SFB 649 Discussion Papers SFB649DP2005-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. 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.
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    7. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2008. "The Macroeconomic Implications of Rising Wage Inequality in the United States," NBER Working Papers 14052, National Bureau of Economic Research, Inc.
    8. Abigail Barr & Garance Genicot, 2007. "Risk Sharing, Commitment and Information: An experimental analysis," Economics Series Working Papers WPS/2007-17, University of Oxford, Department of Economics.
    9. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-91, May.
    10. Stephen P. Zeldes, . "Consumption and Liquidity Constraints: An Empirical Investigation," Rodney L. White Center for Financial Research Working Papers 16-88, Wharton School Rodney L. White Center for Financial Research.
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    13. Richard Blundell & Luigi Pistaferri & Ian Preston, 2004. "Consumption inequality and partial insurance," IFS Working Papers W04/28, Institute for Fiscal Studies.
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    18. Atkeson, Andrew & Lucas, Robert E, Jr, 1992. "On Efficient Distribution with Private Information," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 427-53, July.
    19. Kocherlakota, Narayana R, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 595-609, October.
    20. Orazio Attanasio & Steven J. Davis, 1994. "Relative Wage Movements and the Distribution of Consumption," NBER Working Papers 4771, National Bureau of Economic Research, Inc.
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    22. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer, vol. 8(1), pages 41-50.
    23. 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.
    24. Erich Battistin & Richard Blundell & Arthur Lewbel, 2007. "Why is consumption more log normal than income? Gibrat's law revisited," IFS Working Papers W07/08, Institute for Fiscal Studies.
    25. 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.
    26. 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.
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