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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. Attanasio, Orazio & Davis, Steven J, 1996. "Relative Wage Movements and the Distribution of Consumption," Journal of Political Economy, University of Chicago Press, vol. 104(6), pages 1227-62, December.
    2. Bloise, Gaetano & Reichlin, Pietro & Tirelli, Mario, 2009. "Indeterminacy of Competitive Equilibrium with Risk of Default," CEPR Discussion Papers 7477, C.E.P.R. Discussion Papers.
    3. 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.
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    7. 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.
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    20. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
    21. Richard Blundell & Luigi Pistaferri & Ian Preston, 2004. "Consumption inequality and partial insurance," IFS Working Papers W04/28, Institute for Fiscal Studies.
    22. Andrew Atkeson & Robert E Lucas, 2010. "On Efficient Distribution with Private Information," Levine's Working Paper Archive 2179, David K. Levine.
    23. 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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    Cited by:
    1. Gervais, Martin & Klein, Paul, 2010. "Measuring consumption smoothing in CEX data," Journal of Monetary Economics, Elsevier, vol. 57(8), pages 988-999, November.

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