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Consumption Dynamics in General Equilibrium : A Characterisation when Markets are Incomplete

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  • Beker, Pablo

    (University of Warwick)

  • Subir Chattopadhyay

    (University of York)

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 e?ectively 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) and Blume and Easley (2006) 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. JEL Codes: D52 ; D61

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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 921.

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Date of creation: 2009
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Handle: RePEc:wrk:warwec:921

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  1. Larry Blume & David Easley, 2001. "If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Cowles Foundation Discussion Papers 1319, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  4. David K. Levine & William R. Zame, 2002. "Does Market Incompleteness Matter?," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.
  5. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
  6. 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.
  7. Magill,Michael & Quinzii,Martine, 1992. "Infinite horizon,Incomplete markets," Discussion Paper Serie A 384, University of Bonn, Germany.
  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. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
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  17. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  18. Beker, Pablo F. & Espino, Emilio, 2011. "The dynamics of efficient asset trading with heterogeneous beliefs," Journal of Economic Theory, Elsevier, vol. 146(1), pages 189-229, January.
  19. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
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Cited by:
  1. Tarek Coury & Emanuela Sciubba, 2012. "Belief heterogeneity and survival in incomplete markets," Economic Theory, Springer, vol. 49(1), pages 37-58, January.
  2. Dan Cao, 2011. "Collateral Shortages, Asset Price and Investment Volatility with Heterogeneous Beliefs," Working Papers gueconwpa~11-11-01, Georgetown University, Department of Economics.
  3. Ani Guerdijkova & Emanuela Sciubba, 2012. "Survival with Ambiguity," Birkbeck Working Papers in Economics and Finance 1216, Birkbeck, Department of Economics, Mathematics & Statistics.
  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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