IDEAS home Printed from https://ideas.repec.org/p/cla/penntw/e046baf19b9659b668c46a5f975816ee.html
   My bibliography  Save this paper

On Trees and Logs

Author

Listed:
  • David Cass
  • Anna Pavlova

Abstract

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
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • David Cass & Anna Pavlova, "undated". "On Trees and Logs," Penn CARESS Working Papers e046baf19b9659b668c46a5f9, Penn Economics Department.
    • Handle: RePEc:cla:penntw:e046baf19b9659b668c46a5f975816ee
    as

    Download full text from publisher

    File URL: http://www.econ.upenn.edu/Centers/CARESS/
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Angel Serrat, 2001. "A Dynamic Equilibrium Model of International Portfolio Holdings," Econometrica, Econometric Society, vol. 69(6), pages 1467-1489, November.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Partha Dasgupta & Douglas Gale & Oliver Hart & Eric Maskin (ed.), 1992. "Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262541599, April.
    7. Zapatero, Fernando, 1995. "Equilibrium asset prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 787-811, May.
    8. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    9. 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.
    10. 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.
    11. 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.
    12. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    13. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    14. 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.
    15. David Cass, 1991. "Perfect Equilibrium with Incomplete Financial Markets: An Elementary Exposition," International Economic Association Series, in: Lionel W. McKenzie & Stefano Zamagni (ed.), Value and Capital: Fifty Years Later, chapter 5, pages 121-144, Palgrave Macmillan.
    16. 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.
    17. David Cass, 1989. "Sunspots and Incomplete Financial Markets: The Leading Example," Palgrave Macmillan Books, in: George R. Feiwel (ed.), The Economics of Imperfect Competition and Employment, chapter 25, pages 677-693, Palgrave Macmillan.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michael Ehrmann & Marcel Fratzscher & Roberto Rigobon, 2011. "Stocks, bonds, money markets and exchange rates: measuring international financial transmission," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 948-974, September.
    2. Anna Pavlova & Roberto Rigobon, 2008. "The Role of Portfolio Constraints in the International Propagation of Shocks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1215-1256.
    3. Ghironi, Fabio & Lee, Jaewoo & Rebucci, Alessandro, 2015. "The valuation channel of external adjustment," Journal of International Money and Finance, Elsevier, vol. 57(C), pages 86-114.
    4. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
    5. Anna Pavlova & Roberto Rigobon, 2007. "Asset Prices and Exchange Rates," The Review of Financial Studies, Society for Financial Studies, vol. 20(4), pages 1139-1180.
    6. Elahi, M.A., 2011. "Essays on financial fragility," Other publications TiSEM 882f55bb-10dc-4e49-95ef-e, Tilburg University, School of Economics and Management.
    7. Curatola, Giuliano, 2017. "Portfolio choice and asset prices when preferences are interdependent," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 197-223.
    8. Ehling, Paul & Heyerdahl-Larsen, Christian, 2015. "Complete and incomplete financial markets in multi-good economies," Journal of Economic Theory, Elsevier, vol. 160(C), pages 438-462.
    9. Eugeni, Sara, 2024. "Nominal exchange rates and net foreign assets' dynamics: The stabilization role of valuation effects," Journal of International Money and Finance, Elsevier, vol. 141(C).
    10. Cass, David, 2006. "Musings on the Cass trick," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 374-383, August.
    11. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.
    12. Basak, Suleyman & Cass, David & Licari, Juan Manuel & Pavlova, Anna, 2008. "Multiplicity in general financial equilibrium with portfolio constraints," Journal of Economic Theory, Elsevier, vol. 142(1), pages 100-127, September.
    13. Berrada, Tony & Hugonnier, Julien & Rindisbacher, Marcel, 2007. "Heterogeneous preferences and equilibrium trading volume," Journal of Financial Economics, Elsevier, vol. 83(3), pages 719-750, March.
    14. Lukasz Prorokowski, 2013. "Lessons from financial crisis contagion simulation in Europe," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 30(2), pages 159-188, May.
    15. Soumare, Issouf, 2007. "International capital markets and redundant securities," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 1037-1050, March.
    16. Pavlova, Anna & Rigobon, Roberto, 2010. "An asset-pricing view of external adjustment," Journal of International Economics, Elsevier, vol. 80(1), pages 144-156, January.
    17. Felix Kubler & Larry Selden & Xiao Wei, 2014. "When Is a Risky Asset "Urgently Needed"?," American Economic Journal: Microeconomics, American Economic Association, vol. 6(2), pages 131-162, May.
    18. Suleyman Basak & David Cass & Juan Manuel Licari & Anna Pavlova, 2006. "Multiplicity in General Financial Equilibrium with Portfolio Constraints, Second Version," PIER Working Paper Archive 06-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 17 Jul 2006.
    19. Rigobon, Roberto & Pavlova, Anna, 2005. "Wealth Transfers, Contagion and Portfolio Constraints," CEPR Discussion Papers 5117, C.E.P.R. Discussion Papers.
    20. Chaban, Maxym, 2009. "Commodity currencies and equity flows," Journal of International Money and Finance, Elsevier, vol. 28(5), pages 836-852, September.
    21. Curatola, Giuliano & Dergunov, Ilya, 2017. "International capital markets with time-varying preferences," SAFE Working Paper Series 176, Leibniz Institute for Financial Research SAFE.
    22. Curatola, Giuliano, 2016. "Preference evolution and the dynamics of capital markets," SAFE Working Paper Series 128, Leibniz Institute for Financial Research SAFE.
    23. George Constantinides & John Donaldson & Rajnish Mehra, 2007. "Junior is rich: bequests as consumption," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(1), pages 125-155, July.
    24. Suleyman Basak & David Cass & Juan Manuel Licari & Anna Pavlova, 2006. "Multiplicity and Sunspots in General Financial Equilibrium with Portfolio Constraints," PIER Working Paper Archive 06-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    25. Roszkowska Paulina & Prorokowski Łukasz, 2013. "Model of Financial Crisis Contagion: A Survey-based Simulation by Means of the Modified Kaplan-Meier Survival Plots," Folia Oeconomica Stetinensia, Sciendo, vol. 13(1), pages 22-55, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    2. Ehling, Paul & Heyerdahl-Larsen, Christian, 2015. "Complete and incomplete financial markets in multi-good economies," Journal of Economic Theory, Elsevier, vol. 160(C), pages 438-462.
    3. Pascal Stiefenhofer, 2009. "Production in General Equilibrium with Incomplete Markets," Discussion Papers 09/06, Department of Economics, University of York.
    4. Tirelli, Mario, 2008. "Constrained inefficiency in GEI: A geometric argument," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1197-1214, December.
    5. Anna Pavlova & Roberto Rigobon, 2007. "Asset Prices and Exchange Rates," The Review of Financial Studies, Society for Financial Studies, vol. 20(4), pages 1139-1180.
    6. Jean-Marc Tallon, 1995. "Théorie de l'équilibre général avec marchés financiers incomplets," Revue Économique, Programme National Persée, vol. 46(5), pages 1207-1239.
    7. Yves Balasko & Enrique Kawamura, 2010. "Pareto-Improving Defaul," Working Papers 102, Universidad de San Andres, Departamento de Economia, revised May 2010.
    8. Mas-Colell, Andreu & Zame, William R., 1996. "The existence of security market equilibrium with a non-atomic state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 63-84.
    9. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research.
    10. Bottazzi, Jean-Marc & Luque, Jaime & Páscoa, Mário R., 2012. "Securities market theory: Possession, repo and rehypothecation," Journal of Economic Theory, Elsevier, vol. 147(2), pages 477-500.
    11. Bhamra, Harjoat S. & Coeurdacier, Nicolas & Guibaud, Stéphane, 2014. "A dynamic equilibrium model of imperfectly integrated financial markets," Journal of Economic Theory, Elsevier, vol. 154(C), pages 490-542.
    12. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    13. Philippe Bich, 2005. "On the existence of approximated equilibria in discontinuous economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00287685, HAL.
    14. Philippe Bich, 2005. "On the existence of approximated equilibria in discontinuous economies," Post-Print halshs-00287685, HAL.
    15. Jean-Marc Bottazzi & Jaime Luque & Mário Páscoa, 2010. "Re-hypotecation of securities," Post-Print halshs-00476004, HAL.
    16. Rahi, Rohit, 1995. "Partially revealing rational expectations equilibria with nominal assets," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 137-146.
    17. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    18. Rigobon, Roberto & Pavlova, Anna, 2005. "Wealth Transfers, Contagion and Portfolio Constraints," CEPR Discussion Papers 5117, C.E.P.R. Discussion Papers.
    19. Basak, Suleyman & Cass, David & Licari, Juan Manuel & Pavlova, Anna, 2008. "Multiplicity in general financial equilibrium with portfolio constraints," Journal of Economic Theory, Elsevier, vol. 142(1), pages 100-127, September.
    20. Bowman, David & Faust, Jon, 1997. "Options, Sunspots, and the Creation of Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 105(5), pages 957-975, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cla:penntw:e046baf19b9659b668c46a5f975816ee. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: David K. Levine (email available below). General contact details of provider: http://www.dklevine.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.