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 financi...
| Main Authors: | , |
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| Language: | en_US |
| Published: |
2002
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/665 |
| _version_ | 1811092008558657536 |
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| author | Cass, David Pavlova, Anna |
| author_facet | Cass, David Pavlova, Anna |
| author_sort | Cass, David |
| collection | MIT |
| description | 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.
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| first_indexed | 2024-09-23T15:11:11Z |
| id | mit-1721.1/665 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:11:11Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | mit-1721.1/6652019-04-12T08:22:47Z On Trees and Logs Cass, David Pavlova, Anna Equilibrium Theory Lucas Tree Model Nonuniqueness of Equilibria Peculiar Financial Equilibrium Portfolio Constraints 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. 2002-06-05T20:14:06Z 2002-06-05T20:14:06Z 2002-06-05T20:14:18Z http://hdl.handle.net/1721.1/665 en_US MIT Sloan School of Management Working Paper;4233-02 462065 bytes application/pdf application/pdf |
| spellingShingle | Equilibrium Theory Lucas Tree Model Nonuniqueness of Equilibria Peculiar Financial Equilibrium Portfolio Constraints Cass, David Pavlova, Anna On Trees and Logs |
| title | On Trees and Logs |
| title_full | On Trees and Logs |
| title_fullStr | On Trees and Logs |
| title_full_unstemmed | On Trees and Logs |
| title_short | On Trees and Logs |
| title_sort | on trees and logs |
| topic | Equilibrium Theory Lucas Tree Model Nonuniqueness of Equilibria Peculiar Financial Equilibrium Portfolio Constraints |
| url | http://hdl.handle.net/1721.1/665 |
| work_keys_str_mv | AT cassdavid ontreesandlogs AT pavlovaanna ontreesandlogs |