Martingale properties of self-enforcing debt

Bidian, Florin and Bejan, Camelia (2011): Martingale properties of self-enforcing debt.

Abstract

Not-too-tight (NTT) debt limits are endogenous restrictions on debt that prevent agents from defaulting and opting for a specified continuation utility, while allowing for maximal credit expansion. For an agent facing some fixed prices for the Arrow securities, we prove that discounted NTT debt limits must differ by a martingale. Discounted debt limits are submartingales (martingales) under an interdiction to trade (borrow), and can be supermartingales under a temporary interdiction to trade. Asset price bubbles limited by the size of the total martingale components in debt limits can be sustained in equilibrium. They can counteract the effects of a credit tightening in the economy.

• Item Type: MPRA Paper
• Language: English
• Keywords: rational bubbles, endogenous debt limits, limited enforcement, credit crunch, not-too-tight debt constraints
• Subjects: E - Macroeconomics and Monetary Economics > E0 - General; G - Financial Economics > G0 - General

References

Alvarez, F., and U. J. Jermann (2000): “Efficiency, Equilibrium, and Asset Pricing with Risk of Default,” Econometrica, 68(4), 775–797.

Alvarez, F., and U. J. Jermann (2001): “Quantitative Asset Pricing Implications of Endogenous Solvency Constraints,” Review of Financial Studies, 14(4), 1117–1151.

Antinolfi, G., C. Azariadis, and J. B. Bullard (2007): “Monetary policy as equilibrium selection,” Federal Reserve Bank of St. Louis Review, July, 331–342.

Azariadis, C., and L. Kaas (2008): “Endogenous credit limits with small default costs,” mimeo, Washington University.

Bejan, C., and F. Bidian (2012): “Limited Enforcement, Bubbles and Trading in Incomplete Markets,” Working Paper 2012-03, CEAR, Georgia State University.

Bidian, F. (2011): “Essays on Asset Price Bubbles,” Ph.D. thesis, University of Minnesota.

Bidian, F., and C. Bejan (2012): “Supplement to “Martingale Properties of Self-Enforcing Debt”,” mimeo, Rice University and Georgia State University.

Bloise, G., and P. Reichlin (2011): “Asset prices, debt constraints and inefficiency,” Journal of Economic Theory, 146(4), 1520–1546.

Bulow, J., and K. Rogoff (1989): “Sovereign Debt: Is to Forgive to Forget?,” American Economic Review, 79(1), 43–50.

Farhi, E., and J. Tirole (2011): “Bubbly Liquidity,” NBER Working Papers 16750, National Bureau of Economic Research, Inc.

Forno, A. D., and L. Montrucchio (2003): “Optimality Conditions and Bubbles in Sequential Economies and Bounded Relative Risk-Aversion,” Decisions in Economics and Finance, 26(1), 53–80.

Guerrieri, V., and G. Lorenzoni (2011): “Credit Crises, Precautionary Savings, and the Liquidity Trap,” NBER Working Papers 17583, National Bureau of Economic Research, Inc.

Hellwig, C., and G. Lorenzoni (2009a): “Bubbles and Self-Enforcing Debt,” Econometrica, 77(4), 1137–1164.

(2009b): “Supplement to “Bubbles and Self-Enforcing Debt”,” Econometrica Supplementary Material.

Huang, K. X. D., and J. Werner (2000): “Asset Price Bubbles in Arrow-Debreu and Sequential Equilibrium,” Economic Theory, 15(2), 253–278.

Kehoe, T. J., and D. K. Levine (1993): “Debt-Constrained Asset Markets,” Review of Economic Studies, 60(4), 865–888.

Kehoe, T. J., and D. K. Levine (2001): “Liquidity Constrained Markets versus Debt Constrained Markets,” Econometrica, 69(3), 575–598.

Kocherlakota, N. R. (1992): “Bubbles and Constraints on Debt Accumulation,” Journal of Economic Theory, 57(1), 245–256.

Kocherlakota, N. R. (2008): “Injecting Rational Bubbles,” Journal of Economic Theory, 142(1), 218–232.

Kocherlakota, N. R. (2009): “Bursting bubbles: consequences and cures,” mimeo.

Kopp, P. (1984): Martingales and stochastic integration. Cambridge University Press.

Krueger, D., and F. Perri (2006): “Does Income Inequality Lead to Consumption Inequality? Evidence and Theory,” Review of Economic Studies, 73(1), pp.163–193.

Leroy, S., and J. Werner (2001): Principles of financial economics. Cambridge University Press, 1 edn.

Martin, A., and J. Ventura (2011): “Economic Growth with Bubbles,” forthcoming, American Economic Review.

Santos, M. S., and M. Woodford (1997): “Rational Asset Pricing Bubbles,” Econometrica, 65(1), 19–57.

Severo, T., and S. Giglio (2011): “Intangible Capital, Relative Asset Shortages and Bubbles,” forthcoming, Journal of Monetary Economics.

Woodford, M. (1990): “Public Debt as Private Liquidity,” American Economic Review, 80(2), 382–88.