# Consumer default with complete markets: default-based pricing and finite punishment

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## Abstract

This paper studies economies with complete markets where there is positive default on consumer debt. In a simple tractable two-period model, households can default partially, at a finite punishment cost, and competitive intermediaries price loans of different sizes separately. This environment yields only partial insurance. The default-based pricing of debt makes it too costly for the borrower to achieve full insurance, and there is too little trade in securities. This framework is in contrast to existing literature. Unlike the literature with default, there are no restrictions on the set of state contingent securities that are issued. Unlike the literature on lack of commitment, limited trade arises without need of debt constraints that rule default out. Compared with the latter, the present approach appears to imply more consumption inequality. An extended model with an infinite horizon, idiosyncratic risk and more realistic assumptions is used to demonstrate the general validity of this approach and its main implications.

## Keywords

Consumer default Complete markets Endogenous incomplete markets Risk-based pricing Risk sharing## JEL Classification

E21 E44 D52## References

- Ábrahám, Á., Cárceles-Poveda, E.: Endogenous trading constraints with incomplete asset markets. J. Econ. Theory
**145**(3), 974–1004 (2010)Google Scholar - Alvarez, F., Jermann, U.: Efficiency, equilibrium, and asset pricing with risk of default. Econometrica
**68**(4), 775–797 (2000)Google Scholar - Andolfatto, D., Gervais, M.: Endogenous debt constraints in a life-cycle model with an application to social security. J. Econ. Dyn. Control
**32**(12), 3745–3759 (2008)Google Scholar - Araujo, A.P., Páscoa, M.R.: Bancruptcy in a model of unsecured claims. Econ. Theory
**20**(3), 455–481 (2002)Google Scholar - Araujo, A., Monteiro, P., Páscoa, M.: Incomplete markets, continuum of states and default. Econ. Theory
**11**(1), 205–213 (1998)Google Scholar - Arellano, C.: Default risk and income fluctuations in emerging economies. Am. Econ. Rev.
**98**(3), 690–712 (2008)Google Scholar - Arellano, C., Mateos-Planas, X., Ríos-Rull J.V.: Partial Default. Manuscript (2013)Google Scholar
- Athreya, K., Tam, X., Young, E.: Unsecured credit markets are not insurance markets. J. Monet. Econ.
**56**(1), 83–103 (2009)Google Scholar - Benjamin, D., Mateos-Planas, X.: Formal Versus Informal Default in Consumer Credit. Manuscript (2012)Google Scholar
- Benjamin, D., Wright, M.: Recovery Before Redemption: A Theory of Delays in Sovereign Debt Renegotiations, Working Paper (2009)Google Scholar
- Broer, T.: The Wrong Shape of Insurance? What Cross-Sectional Distributions Tell Us About Models of Consumption-Smoothing, CEPR Discussion Paper No. DP8701 (2011)Google Scholar
- Chatterjee, S.: An equilibrium model of the timing of bankruptcy filings. Presented at Credit, Default and Bankruptcy Conference, LAEF, UCSB (2010)Google Scholar
- Chatterjee, S., Eyigungor, B.: Maturity, indebtedness, and default risk. Am. Econ. Rev.
**102**(6), 2674–99 (2012)Google Scholar - Chatterjee, S., Corbae, D., Nakajima, M., Ríos-Rull, J.: A quantitative theory of unsecured consumer credit with risk of default. Econometrica
**75**(6), 1525–1589 (2007)Google Scholar - Cordoba, J.: US inequality: debt constraints or incomplete asset markets? J. Monet. Econ.
**55**(2), 350–364 (2008)Google Scholar - Dawsey, A., Ausubel, L.: Informal Bankruptcy, unpublished (2004)Google Scholar
- Dawsey, A., Hynes, R., Ausubel, L.: The Regulation of Non-judicial Debt Collection and the Consumer’s Choice Among Repayment, Bankruptcy and Informal Bankruptcy, University of Virginia Legal Working Paper Series, p. 42 (2008)Google Scholar
- Diamond, D.W.: Financial intermediation and delegated monitoring. Rev. Econ. Stud.
**51**(3), 393–414 (1984)Google Scholar - Díaz-Giménez, J., Glover, A., Ríos-Rull, J.: Facts on the distributions of earnings, income, and wealth in the United States: 2007 update. Fed. Reserve Bank Minneap. Q. Rev.
**34**(1), 2–31 (2011)Google Scholar - Dubey, P., Geanakoplos, J., Shubik, M.: Default and punishment in general equilibrium1. Econometrica
**73**(1), 1–37 (2005)Google Scholar - Eaton, J., Gersovitz, M.: Debt with potential repudiation: theoretical and empirical analysis. Rev. Econ. Stud.
**48**(2), 289–309 (1981)Google Scholar - Fernandez-Villaverde, J., Krueger, D.: Consumption and saving over the life cycle: how important are consumer durables? Macroecon. Dyn.
**15**(5), 725 (2011)Google Scholar - Heathcote, J., Storesletten, K., Violante, G.L.: The macroeconomic implications of rising wage inequality in the United States. J. Polit. Econ.
**118**(4), 681–722 (2010)Google Scholar - Herkenhoff, K.: Informal Unemployment Insurance and Labor Market Dynamics. FRB of St, Louis Working Paper No (2012)Google Scholar
- Kaplan, G., Violante, G.: How much consumption insurance beyond self insurance? Am. Econ. J.: Macroecon.
**38**(2), 53–87 (2010)Google Scholar - Kehoe, T., Levine, D.: Debt-constrained asset markets. Rev. Econ. Stud.
**60**(4), 865–888 (1993)Google Scholar - Kehoe, T., Levine, D.: Liquidity constrained markets versus debt constrained markets. Econometrica
**69**(3), 575–598 (2001)Google Scholar - Kehoe, T., Levine, D.: Bankruptcy and Collateral in Debt Constrained Markets, NBER Working Paper (2006)Google Scholar
- Kehoe, P., Perri, F.: International business cycles with endogenous incomplete markets. Econometrica
**70**(3), 907–928 (2002)Google Scholar - Kilenthong, W.T.: Collateral premia and risk sharing under limited commitment. Econ. Theory
**46**(3), 475–501 (2011)Google Scholar - Koeppl, T.V.: Optimal dynamic risk sharing when enforcement is a decision variable. J. Econ. Theory
**134**(1), 34–60 (2007)Google Scholar - Krueger, D., Perri, F.: Does income inequality lead to consumption inequality? Evidence and theory1. Rev. Econ. Stud.
**73**(1), 163–193 (2006)Google Scholar - Livshits, I., MacGee, J., Tertilt, M.: Consumer bankruptcy: a fresh start. Am. Econ. Rev.
**97**(1), 402–418 (2007)Google Scholar - Livshits, I., MacGee, J., Tertilt, M.: Accounting for the rise in consumer bankruptcies. Am. Econ. J. Macroecon.
**2**(2), 165–193 (2010)Google Scholar - Mateos-Planas, X.: Credit limits and bankruptcy. Econ. Lett.
**121**(3), 469–472 (2013)Google Scholar - Mateos-Planas, X., Ríos-Rull, J.V.: Credit Lines, Manuscript (2013)Google Scholar
- Mateos-Planas, X., Seccia, G.: Welfare implications of endogenous credit limits with bankruptcy. J. Econ. Dyn. Control
**30**(11), 2081–2115 (2006)Google Scholar - Peiris, M.U., Vardoulakis, A.P.: Savings and default. Econ. Theory
**54**(1), 1–28 (2011)Google Scholar - Poblete-Cazenave, R., Torres-Martínez, J.P.: Equilibrium with limited-recourse collateralized loans. Econ. Theory
**53**(1), 1–31 (2010)Google Scholar - Wang, M.: Optimal education policies under endogenous borrowing constraints. Econ. Theory, 1–25 (2011). doi: 10.1007/s00199-013-0743-5
- Yue, V.: Sovereign default and debt renegotiation. J. Int. Econ.
**80**(2), 176–187 (2010)Google Scholar - Zame, W.: Efficiency and the role of default when security markets are incomplete. Am. Econ. Rev.
**83**(5), 1142–1164 (1993)Google Scholar - Zhang, H.: Endogenous borrowing constraints with incomplete markets. J. Financ.
**52**(5), 2187–2209 (1997)Google Scholar