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Stationary equilibrium distributions in economies with limited commitment

Listed author(s):
  • Tobias Broer

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
Handle: RePEc:eui:euiwps:eco2009/39
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  1. Kjetil Storesletten & Chris Telmer & Amir Yaron, 1997. "Consumption and risk sharing over the life cycle," GSIA Working Papers 228, Carnegie Mellon University, Tepper School of Business.
  2. 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.
  3. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  4. Dirk Krueger & Harald Uhlig, 2003. "Competitive Risk Sharing Contracts with One-Sided Commitment," Levine's Bibliography 666156000000000407, UCLA Department of Economics.
  5. Timothy J. Kehoe & David K. Levine, 1992. "Debt constrained asset markets," Working Papers 445, Federal Reserve Bank of Minneapolis.
  6. 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.
  7. 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).
  8. 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.
  9. Jonathan Heathcote, 2003. "The Macroeconomic Implications of Rising Wage Inequality in the United States," Working Papers gueconwpa~03-03-19, Georgetown University, Department of Economics.
  10. Andrew Atkeson & Robert E Lucas, 2010. "On Efficient Distribution with Private Information," Levine's Working Paper Archive 2179, David K. Levine.
  11. 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.
  12. 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.
  13. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
  14. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2009. "Indeterminacy Of Competitive Equilibrium With Risk Of Default," Levine's Working Paper Archive 814577000000000313, David K. Levine.
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  17. 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.
  18. 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.
  19. Cordoba, Juan Carlos, 2010. "US Inequality: Debt Constraints or Incomplete Asset Markets?," Staff General Research Papers Archive 32120, Iowa State University, Department of Economics.
  20. 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.
  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. 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.
  23. 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.
  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. 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.
  26. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-598, May.
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