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Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

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  • Beker, Pablo
  • Chattopadhyay, Subir

Abstract

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually--so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 6 (November)
Pages: 2133-2185

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2133-2185

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: General equilibrium Dynamically incomplete markets Consumption Survival Market selection hypothesis Asset prices;

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References

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  1. Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
  2. Krebs, Tom, 2004. "Non-existence of recursive equilibria on compact state spaces when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 115(1), pages 134-150, March.
  3. Tarek Coury & Emanuela Sciubba, 2006. "Belief Heterogeneity and Survival in Incomplete Markets," Birkbeck Working Papers in Economics and Finance 0613, Birkbeck, Department of Economics, Mathematics & Statistics.
  4. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  5. Pablo F Beker & Emilio Espino, 2007. "The Dynamics of Efficient Asset Trading with Heterogeneous Beliefs," Levine's Bibliography 122247000000001715, UCLA Department of Economics.
  6. David K. Levine & William Zame, 2001. "Does Market Incompleteness Matter," Levine's Working Paper Archive 78, David K. Levine.
  7. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, 07.
  8. David K. Levine & William R. Zame, 1992. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," UCLA Economics Working Papers 666, UCLA Department of Economics.
  9. Magill,Michael & Quinzii,Martine, 1992. "Infinite horizon,Incomplete markets," Discussion Paper Serie A 384, University of Bonn, Germany.
  10. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  11. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-40, April.
  12. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
  13. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
  14. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  15. Krebs, Tom, 2004. "Testable implications of consumption-based asset pricing models with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 191-206, February.
  16. repec:fth:starer:8415 is not listed on IDEAS
  17. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  18. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1998. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Discussion Papers 1228, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  19. Becker, Robert A, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, MIT Press, vol. 95(2), pages 375-82, September.
  20. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
  21. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211.
  22. Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122-140, July.
  23. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  24. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
  25. Gary Chamberlain & Charles A. Wilson, 2000. "Optimal Intertemporal Consumption Under Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 365-395, July.
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Citations

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Cited by:
  1. Ani Guerdijkova & Emanuela Sciubba, 2012. "Survival with Ambiguity," Birkbeck Working Papers in Economics and Finance 1216, Birkbeck, Department of Economics, Mathematics & Statistics.
  2. Tarek Coury & Emanuela Sciubba, 2006. "Belief Heterogeneity and Survival in Incomplete Markets," Birkbeck Working Papers in Economics and Finance 0613, Birkbeck, Department of Economics, Mathematics & Statistics.
  3. Dan Cao, 2011. "Collateral Shortages, Asset Price and Investment Volatility with Heterogeneous Beliefs," Working Papers gueconwpa~11-11-01, Georgetown University, Department of Economics.
  4. Braido, Luis H. B., 2013. "Ergodic Markov equilibrium with incomplete markets and short sales," Theoretical Economics, Econometric Society, vol. 8(1), January.

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