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Endogenous Trading Constraints with Incomplete Asset Markets

Listed author(s):
  • Eva Carceles Poveda
  • Arpad Abraham

The present project introduces the possibility of default on the trading contracts in an infinite horizon incomplete markets model, relaxing the usual assumption made in the literature with respect to the trading limits, which are chosen to be fixed or independent of the characteristics of the economy. In particular, it assumes that households can break their trading contracts by going into autarky, in which case they are seized from their total assets and only receive labour income from the default period on. Further, to avoid this happening in equilibrium, the trading limits are endogenously determined at the level where the participation constraint is satisfied at each possible date and state. Using this set-up, the main objectives are to quantify and characterize the endogenous limits resulting from the option of default and to study their real and financial implications along the growth path and during the business cycle. Our work is of considerable relevance, since it builds a bridge between several important strands of literature. First, it is related to the usual incomplete market models with ad hoc trading limits, such as Heaton and Lucas (1996), Marcet and Singleton (2001) or Telmer (1993), who study asset prices in two agent exchange economies, and Aiyagari (1994) or Krussel and Smith (1997) and (1998), who study production economies with a large number of households. In addition, it also relates to a recent literature, where a number of authors have introduced the possibility of default through participation constraints, resulting in agent and state specific endogenous trading limits. Among others, Kehoe and Levine (1993) and Alvarez and Jermann (2000) introduce this type of limits in exchange economies, while Kehoe and Perri (2002) analyse a production economy where investors are interpreted as countries. All these authors, however, introduce the option of default into a complete markets context, which they compare to an exogenous incomplete markets environment without explicitly characterizing the trading limits. In contrast to this, the present framework allows for a direct comparison of economies with the same asset structure, making it possible to isolate the effects of no default on the equilibrium allocations. Finally, our work is also related to the papers of Zhang (1997a) and (1997b), where the author derives the endogenous borrowing limits resulting from the possibility of default in a Lucas type exchange economy with one asset. In contrast to this, our work introduces different types of assets and incorporates a production sector, leading to state-dependent autarky values and trading limits, which considerable complicate the computations. In this respect, the contribution of the present project is also methodological, since it extends the standard policy iteration algorithm to incorporate state dependent limits and state dependent lower bounds for the grid of the endogenous states. To summarize, the present work fills an important gap in the literature, since it links the incomplete markets models with fixed trading limits and the complete markets models with the option of default, allowing for a complete characterization of the no-default endogenous trading constraints and for a better understanding of the endogenous portfolio choice problems in the absence of full commitment. Further, while our methodological contribution will enhance the understanding on the numerical techniques used to solve problems with default, it is very likely to be of use to other researchers in the field. Preliminary results on the characterization of the endogenous trading limits for the case in which a finite number of households can trade in shares of aggregate capital already shed light on important implications of the present work that can have a considerable impact on the different strands of literature studying risk sharing in infinite horizon economies. As expected, the endogenous limits do vary to a great extent with the aggregate state of the economy. In particular, when aggregate capital is scarce, and the incentives to default are relatively low, limits on individual capital shares are relatively loose. On the other hand, as the economy accumulates capital, they become tighter. Apart from this, the endogenous limits computed using a preliminary but reasonable calibration allow for short-selling of the stock in the magnitude of ten to fifteen percent of aggregate capital in the stationary distribution, being surprisingly close to the zero fixed limits usually imposed in the literature with fixed trading limits. While this is good news for the models studying steady state behaviour, it suggests that it can be dangerous to impose fixed limits during transition to the steady state, since at earlier stages of development and a relatively low capital they can vary to a great extent. In this case, the different risk sharing opportunities resulting from the presence of endogenous limits also lead to important implications concerning asset wealth and consumption inequality, which are sensitive of the particular stage on the transition path.

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Paper provided by Society for Economic Dynamics in its series 2004 Meeting Papers with number 667.

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Date of creation: 2004
Handle: RePEc:red:sed004:667
Contact details of provider: Postal:
Society for Economic Dynamics Marina Azzimonti Department of Economics Stonybrook University 10 Nicolls Road Stonybrook NY 11790 USA

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  1. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  2. Krusell, Per & Smith, Anthony A., 1997. "Income And Wealth Heterogeneity, Portfolio Choice, And Equilibrium Asset Returns," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 387-422, June.
  3. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2005. "Default and Punishment in General Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 1-37, 01.
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  5. Alvarez, Fernando & Jermann, Urban J, 2001. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1117-1151.
  6. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
  7. Zhang, Harold H., 1997. "Endogenous Short-Sale Constraint, Stock Prices And Output Cycles," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 228-254, January.
  8. Aiyagari, S Rao, 1995. "Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1158-1175, December.
  9. Judd, Kenneth L., 1985. "Redistributive taxation in a simple perfect foresight model," Journal of Public Economics, Elsevier, vol. 28(1), pages 59-83, October.
  10. Kehoe, Patrick J. & Perri, Fabrizio, 2004. "Competitive equilibria with limited enforcement," Journal of Economic Theory, Elsevier, vol. 119(1), pages 184-206, November.
  11. Zhang, Harold H, 1997. " Endogenous Borrowing Constraints with Incomplete Markets," Journal of Finance, American Finance Association, vol. 52(5), pages 2187-2209, December.
  12. Satyajit Chatterjee & Dean Corbae & Makoto Nakajima & José-Víctor Ríos-Rull, 2007. "A Quantitative Theory of Unsecured Consumer Credit with Risk of Default," Econometrica, Econometric Society, vol. 75(6), pages 1525-1589, November.
  13. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 865-888.
  14. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-487, June.
  15. Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 385-403, August.
  16. 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.
  17. 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.
  18. 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.
  19. Telmer, Chris I, 1993. " Asset-Pricing Puzzles and Incomplete Markets," Journal of Finance, American Finance Association, vol. 48(5), pages 1803-1832, December.
  20. David Domeij & Jonathan Heathcote, 2004. "On The Distributional Effects Of Reducing Capital Taxes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 523-554, 05.
  21. S. Rao Aiyagari & Albert Marcet & Thomas J. Sargent & Juha Seppala, 2002. "Optimal Taxation without State-Contingent Debt," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1220-1254, December.
  22. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
  23. 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.
  24. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-622, May.
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