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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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    8. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
    9. Timothy J Kehoe & David K Levine, 1993. "Debt Constrained Asset Markets," Levine's Working Paper Archive 1276, David K. Levine.
    10. 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.
    11. 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.
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    18. 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.
    19. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
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    21. 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.
    22. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2009. "Indeterminacy Of Competitive Equilibrium With Risk Of Default," Levine's Working Paper Archive 814577000000000313, David K. Levine.
    23. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-98, May.
    24. 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.
    25. Atkeson Andrew & Lucas Jr. , Robert E., 1995. "Efficiency and Equality in a Simple Model of Efficient Unemployment Insurance," Journal of Economic Theory, Elsevier, vol. 66(1), pages 64-88, June.
    26. 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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