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On Trees and Logs

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  • 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
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  • David Cass & Anna Pavlova, "undated". "On Trees and Logs," CARESS Working Papres 00-01, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    • Handle: RePEc:wop:pennca:00-01
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    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. 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.
    8. 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).
    9. Cass, David, 2006. "Musings on the Cass trick," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 374-383, August.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Pavlova, Anna & Rigobon, Roberto, 2010. "An asset-pricing view of external adjustment," Journal of International Economics, Elsevier, vol. 80(1), pages 144-156, January.
    15. Chaban, Maxym, 2009. "Commodity currencies and equity flows," Journal of International Money and Finance, Elsevier, vol. 28(5), pages 836-852, September.
    16. 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.
    17. 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.
    18. Curatola, Giuliano, 2017. "Portfolio choice and asset prices when preferences are interdependent," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 197-223.
    19. 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.
    20. Soumare, Issouf, 2007. "International capital markets and redundant securities," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 1037-1050, March.
    21. 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.
    22. Rigobon, Roberto & Pavlova, Anna, 2005. "Wealth Transfers, Contagion and Portfolio Constraints," CEPR Discussion Papers 5117, C.E.P.R. Discussion Papers.
    23. Curatola, Giuliano & Dergunov, Ilya, 2017. "International capital markets with time-varying preferences," SAFE Working Paper Series 176, Leibniz Institute for Financial Research SAFE.
    24. Curatola, Giuliano, 2016. "Preference evolution and the dynamics of capital markets," SAFE Working Paper Series 128, Leibniz Institute for Financial Research SAFE.
    25. 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.

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