Consumption dynamics in general equilibrium: A characterisation when markets are incomplete
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)  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.
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- 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.
- Woodford, Michael & Santos, Manuel S., 1995.
"Rational asset pricing bubbles,"
UC3M Working papers. Economics
3913, Universidad Carlos III de Madrid. Departamento de Economía.
- Constantinides,George & Duffie,Darrel, 1992.
"Asset pricing with heterogeneous consumers,"
Discussion Paper Serie A
381, University of Bonn, Germany.
- Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
- David K. Levine & William R. Zame, 1993.
"Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets,"
UCLA Economics Working Papers
703, UCLA Department of Economics.
- Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
- 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.
- David K. Levine & William Zame, 1996. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," Levine's Working Paper Archive 1954, David K. Levine.
- Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
- Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999.
"Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited,"
Econometric Society, vol. 67(4), pages 875-894, July.
- 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.
- Magill,Michael & Quinzii,Martine, 1992.
"Infinite horizon,Incomplete markets,"
Discussion Paper Serie A
384, University of Bonn, Germany.
- Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," Papers 413a, California Davis - Institute of Governmental Affairs.
- Magill, M. & Quinzii, M., 1993. "Infinite Horizon Incomplete Markets," Papers 9320, Southern California - Department of Economics.
- Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," DELTA Working Papers 92-26, DELTA (Ecole normale supérieure).
- Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
- Lawrence Blume & David Easley, 2001.
"If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets,"
01-06-031, Santa Fe Institute.
- 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.
- 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.
- Tom Krebs, 2002.
"Non-Existence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete,"
2002-17, Brown University, Department of Economics.
- 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.
- 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.
- Tarek Coury & Emanuela Sciubba, 2012. "Belief heterogeneity and survival in incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 37-58, January.
- 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.
- Pablo F Beker & Emilio Espino, 2007. "The Dynamics of Efficient Asset Trading with Heterogeneous Beliefs," Levine's Bibliography 122247000000001715, UCLA Department of Economics.
- Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375-382.
- Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
- Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
- Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
- Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
- 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.
- David K. Levine & William Zame, 2001.
"Does Market Incompleteness Matter,"
Levine's Working Paper Archive
78, David K. Levine.
- Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, June.
- 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.
- Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211.
- Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122-140, July.
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