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Endogenous Trading Constraints with Incomplete Asset Markets

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  • Eva Carceles Poveda
  • Arpad Abraham

Abstract

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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Bibliographic Info

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

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Date of creation: 2004
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Handle: RePEc:red:sed004:667

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Keywords: Asset prices; Incomplete markets; Heterogeneous Agents; No-default constraints;

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References

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  1. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
  2. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2001. "Default and Punishment in General Equilibrium," Cowles Foundation Discussion Papers 1304, Cowles Foundation for Research in Economics, Yale University.
  3. Chamley, Christophe, 1986. "Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives," Econometrica, Econometric Society, vol. 54(3), pages 607-22, May.
  4. John Heaton & Deborah Lucas, 1993. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," NBER Working Papers 4249, National Bureau of Economic Research, Inc.
  5. Enrique G. Mendoza & Assaf Razin & Linda L. Tesar, 1994. "Effective Tax Rates in Macroeconomics: Cross-Country Estimates of Tax Rates on Factor Incomes and Consumption," NBER Working Papers 4864, National Bureau of Economic Research, Inc.
  6. Albert Marcet & Thomas J. Sargent & Juha Seppala, 1996. "Optimal taxation without state-contingent debt," Economics Working Papers 170, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2001.
  7. Telmer, Chris I, 1993. " Asset-Pricing Puzzles and Incomplete Markets," Journal of Finance, American Finance Association, vol. 48(5), pages 1803-32, December.
  8. Kehoe, Timothy J & Levine, David K, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 865-88, October.
  9. S. Rao Aiyagari, 1994. "Optimal capital income taxation with incomplete markets, borrowing constraints, and constant discounting," Working Papers 508, Federal Reserve Bank of Minneapolis.
  10. Kenneth L. Judd, 1982. "Redistributive Taxation in a Simple Perfect Foresight Model," Discussion Papers 572, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. 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.
  12. 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.
  13. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  14. 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.
  15. Kehoe, Patrick J. & Perri, Fabrizio, 2004. "Competitive equilibria with limited enforcement," Journal of Economic Theory, Elsevier, vol. 119(1), pages 184-206, November.
  16. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  17. Fernando Alvarez & Urban J. Jermann, 1999. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," NBER Working Papers 6953, National Bureau of Economic Research, Inc.
  18. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  19. 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.
  20. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns," GSIA Working Papers 1997-45, Carnegie Mellon University, Tepper School of Business.
  21. 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.
  22. 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.
  23. 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.
  24. Zhang, Harold H, 1997. " Endogenous Borrowing Constraints with Incomplete Markets," Journal of Finance, American Finance Association, vol. 52(5), pages 2187-2209, December.
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