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Stationary equilibrium distributions in economies with limited commitment

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  • Tobias Broer

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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  • Tobias Broer, 2009. "Stationary equilibrium distributions in economies with limited commitment," Economics Working Papers ECO2009/39, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2009/39
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    References listed on IDEAS

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    1. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 541-554.
    2. 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 1227-1262, December.
    3. Zeldes, Stephen P, 1989. "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 305-346, April.
    4. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2009. "Indeterminacy Of Competitive Equilibrium With Risk Of Default," Levine's Working Paper Archive 814577000000000313, David K. Levine.
    5. 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.
    6. Krueger, Dirk & Uhlig, Harald, 2006. "Competitive risk sharing contracts with one-sided commitment," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1661-1691, October.
    7. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
    8. 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.
    9. 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.
    10. Cordoba, Juan-Carlos, 2008. "U.S. inequality: Debt constraints or incomplete asset markets?," Journal of Monetary Economics, Elsevier, vol. 55(2), pages 350-364, March.
    11. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    12. 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.
    13. 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.
    14. Storesletten, Kjetil & Telmer, Christopher I. & Yaron, Amir, 2004. "Consumption and risk sharing over the life cycle," Journal of Monetary Economics, Elsevier, vol. 51(3), pages 609-633, April.
    15. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 865-888.
    16. 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, August.
    17. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
    18. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-598, May.
    19. Erich Battistin & Richard Blundell & Arthur Lewbel, 2009. "Why Is Consumption More Log Normal than Income? Gibrat's Law Revisited," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1140-1154, December.
    20. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Oxford University Press, vol. 63(4), pages 595-609.
    21. 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.
    22. 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, July.
    23. Andrew Atkeson & Robert E. Lucas, 1992. "On Efficient Distribution With Private Information," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 427-453.
    24. 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.
    25. 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 77-85, March.
    26. 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.
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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. Gervais, Martin & Klein, Paul, 2010. "Measuring consumption smoothing in CEX data," Journal of Monetary Economics, Elsevier, vol. 57(8), pages 988-999, November.
    3. Árpád Ábrahám & Sarolta Laczó, 2013. "Efficient Risk Sharing with Limited Commitment and Storage," Working Papers 697, Barcelona Graduate School of Economics.
    4. Sarolta Laczo & Arpad Abraham, 2012. "Efficient Risk Sharing with Limited Commitment and Hidden Saving," 2012 Meeting Papers 680, Society for Economic Dynamics.

    More about this item

    Keywords

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

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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