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 eventuallyso 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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 145 (2010)
Issue (Month): 6 (November)
Pages: 21332185
Handle:  RePEc:eee:jetheo:v:145:y:2010:i:6:p:21332185 
Contact details of provider:  Web page: http://www.elsevier.com/locate/inca/622869

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
 Constantinides, George M & Duffie, Darrell, 1996.
"Asset Pricing with Heterogeneous Consumers,"
Journal of Political Economy,
University of Chicago Press, vol. 104(2), pages 219240, April.
 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 745781, July.
 Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284306, April.
 Manuel S. Santos & Michael Woodford, 1997.
"Rational Asset Pricing Bubbles,"
Econometrica,
Econometric Society, vol. 65(1), pages 1958, January.
 Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
 Woodford, Michael & Santos, Manuel S., 1995. "Rational asset pricing bubbles," UC3M Working papers. Economics 3913, Universidad Carlos III de Madrid. Departamento de Economía.
 Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122140, July.
 Magill, Michael & Quinzii, Martine, 1994.
"Infinite Horizon Incomplete Markets,"
Econometrica,
Econometric Society, vol. 62(4), pages 853880, July.
 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 9226, DELTA (Ecole normale supérieure).
 Magill,Michael & Quinzii,Martine, 1992. "Infinite horizon,Incomplete markets," Discussion Paper Serie A 384, University of Bonn, Germany.
 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 3758, January.
 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.
 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 365395, July.
 David K. Levine & William R. Zame, 2002.
"Does Market Incompleteness Matter?,"
Econometrica,
Econometric Society, vol. 70(5), pages 18051839, September.
 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, July.
 Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211211.
 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 103131.
 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 R. Zame, 1993. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," UCLA Economics Working Papers 703, 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.
 Krebs, Tom, 2004. "Testable implications of consumptionbased asset pricing models with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(12), pages 191206, February.
 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 875894, 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.
 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 929966, 07.
 Lawrence Blume & David Easley, 2001. "If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Working Papers 0106031, Santa Fe Institute.
 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.
 Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(12), pages 91104, February.
 Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381412, March.
 Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(23), pages 233267, September.
 Beker, Pablo F. & Espino, Emilio, 2011.
"The dynamics of efficient asset trading with heterogeneous beliefs,"
Journal of Economic Theory,
Elsevier, vol. 146(1), pages 189229, January.
 Pablo F Beker & Emilio Espino, 2007. "The Dynamics of Efficient Asset Trading with Heterogeneous Beliefs," Levine's Bibliography 122247000000001715, UCLA Department of Economics.
 Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219236, October.
 Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173184, February.
 Krebs, Tom, 2004.
"Nonexistence of recursive equilibria on compact state spaces when markets are incomplete,"
Journal of Economic Theory,
Elsevier, vol. 115(1), pages 134150, March.
 Tom Krebs, 2002. "NonExistence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete," Working Papers 200217, Brown University, Department of Economics.
 Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
 Robert A. Becker, 1980. "On the LongRun Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375382.
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.
When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:21332185. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.