On Trees and Logs
In this paper we critically examine the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), extended to include heterogeneous agents and multiple goods, and contrast it to the benchmark model in financial equilibrium theory, the real assets model (RA-Model). Households in the LT-Model trade goods together with claims to Lucas trees (exogenous stochastic dividend streams specified in terms of a particular good) and long-lived, zero-net-supply real bonds, and are endowed with share portfolios. The RA-Model is quite similar to the LT-Model except that the only claims traded there are zero-net-supply assets paying out in terms of commodity bundles (real assets) and households' endowments are in terms of commodity bundles as well. At the outset, one would expect the two models to deliver similar implications since the LT-Model can be transformed into a special case of the RA-Model. We demonstrate that this is simply not correct: results obtained in the context of the LT-Model can be strikingly different from those in the RA-Model. Indeed, specializing households' preferences to be additively separable (over time) as well as log-linear, we show that for a large set of initial portfolios the LT-Model -- even with potentially complete financial markets -- admits a peculiar financial equilibrium (PFE) in which there is no trade on the bond market after the initial period, while the stock market is completely degenerate, in the sense that all stocks offer exactly the same investment opportunity -- and yet, allocation is Pareto optimal. We then thoroughly investigate why the LT-Model is so much at variance with the RA-Model, and also completely characterize the properties of the set of PFE, which turn out to be the only kind of equilibria occurring in this model. We also find that when a PFE exists, either (i) it is unique, or (ii) there is a continuum of equilibria: in fact, every Pareto optimal allocation is supported as a PFE. Finally, we show that most of our results continue to hold true in the presence of various types of restrictions on transactions in financial markets. Portfolio constraints however may give rise other types of equilibria, in addition to PFE. While our analysis is carried out in the framework of the traditional two-period Arrow-Debreu-McKenzie pure exchange model with uncertainty (encompassing, in particular, many types of contingent commodities), we show that most of our results hold for the analogous continuous-time martingale model of asset pricing.
|Date of creation:||05 Jun 2002|
|Contact details of provider:|| Postal: MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT), SLOAN SCHOOL OF MANAGEMENT, 50 MEMORIAL DRIVE CAMBRIDGE MASSACHUSETTS 02142 USA|
Web page: http://mitsloan.mit.edu/
More information through EDIRC
|Order Information:|| Postal: MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT), SLOAN SCHOOL OF MANAGEMENT, 50 MEMORIAL DRIVE CAMBRIDGE MASSACHUSETTS 02142 USA|
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.:
- Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
- K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 91-96.
- Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
- Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
- Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
- Angel Serrat, 2001. "A Dynamic Equilibrium Model of International Portfolio Holdings," Econometrica, Econometric Society, vol. 69(6), pages 1467-1489, November.
- Harold L. Cole & Maurice Obstfeld, 1989.
"Commodity Trade and International Risk Sharing: How Much Do Financial Markets Matter?,"
NBER Working Papers
3027, National Bureau of Economic Research, Inc.
- Cole, Harold L. & Obstfeld, Maurice, 1991. "Commodity trade and international risk sharing : How much do financial markets matter?," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 3-24, August.
- Bottazzi, Jean-Marc, 1995. "Existence of equilibria with incomplete markets: The case of smooth returns," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 59-72.
- Balasko, Yves & Cass, David, 1989. "The Structure of Financial Equilibrium with Exogenous Yields: The Case of Incomplete Markets," Econometrica, Econometric Society, vol. 57(1), pages 135-162, January.
- Zapatero, Fernando, 1995. "Equilibrium asset prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 787-811, May.
- Geanakoplos, J. & Magill, M. & Quinzii, M. & Dreze, J., .
"Generic inefficiency of stock market equilibrium when markets are incomplete,"
CORE Discussion Papers RP
916, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Geanakoplos, J. & Magill, M. & Quinzii, M. & Dreze, J., 1990. "Generic inefficiency of stock market equilibrium when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 113-151.
- John Geanakoplos & Michael Magill & Martine Quinzii & J. Dreze, 1988. "Generic Inefficiency of Stock Market Equilibrium When Markets Are Incomplete," Cowles Foundation Discussion Papers 863, Cowles Foundation for Research in Economics, Yale University.
- Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
- Gaetano Antinolfi & Todd Keister, 1998. "Options and sunspots in a simple monetary economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 295-315.
- Magill, Michael J. P. & Shafer, Wayne J., 1990. "Characterisation of generically complete real asset structures," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 167-194.
When requesting a correction, please mention this item's handle: RePEc:mit:sloanp:665. 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: (Christian Zimmermann)
If references are entirely missing, you can add them using this form.