IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpfi/0509021.html
   My bibliography  Save this paper

How Equilibrium Prices Reveal Information in Time Series Models with Disparately Informed, Competitive Traders

Author

Listed:
  • Todd B. Walker

    (University of Iowa)

Abstract

Accommodating asymmetric information in a dynamic asset pricing model is technically challenging due to the problems associated with higher-order expectations. That is, rational investors are forced into a situation where they must forecast the forecasts of other agents (i.e., form higher-order expectations). In a dynamic setting, this problem telescopes into the infinite future and the dimension of the relevant state space approaches infinity. By employing the frequency domain approach of Whiteman (1983) and Kasa (2000), this paper demonstrates how information structures previously believed to lead to disparate expectations in equilibrium (e.g., Singleton (1987)) converge to a symmetric equilibrium. The “revealing” aspect of the price process lies in the invertibility of the observed state space, which makes it possible for agents to infer the economically fundamental shocks, thus eliminating the need to forecast the forecasts of others.

Suggested Citation

  • Todd B. Walker, 2005. "How Equilibrium Prices Reveal Information in Time Series Models with Disparately Informed, Competitive Traders," Finance 0509021, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0509021
    Note: Type of Document - pdf; pages: 33
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0509/0509021.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sargent, Thomas J, 1981. "Interpreting Economic Time Series," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 213-248, April.
    2. Franklin Allen & Stephen Morris & Hyun Song Shin, 2003. "Beauty Contests, Bubbles and Iterated Expectations in Asset Markets," Cowles Foundation Discussion Papers 1406, Cowles Foundation for Research in Economics, Yale University.
    3. Lippi, Marco & Reichlin, Lucrezia, 1994. "VAR analysis, nonfundamental representations, blaschke matrices," Journal of Econometrics, Elsevier, vol. 63(1), pages 307-325, July.
    4. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, January.
    5. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    6. He, Hua & Wang, Jiang, 1995. "Differential Information and Dynamic Behavior of Stock Trading Volume," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 919-972.
    7. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, January.
    8. Pearlman, Joseph & Currie, David & Levine, Paul, 1986. "Rational expectations models with partial information," Economic Modelling, Elsevier, vol. 3(2), pages 90-105, April.
    9. Futia, Carl A, 1981. "Rational Expectations in Stationary Linear Models," Econometrica, Econometric Society, vol. 49(1), pages 171-192, January.
    10. Jiang Wang, 1993. "A Model of Intertemporal Asset Prices Under Asymmetric Information," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 249-282.
    11. Philippe Bacchetta & Eric Van Wincoop, 2006. "Can Information Heterogeneity Explain the Exchange Rate Determination Puzzle?," American Economic Review, American Economic Association, vol. 96(3), pages 552-576, June.
    12. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    13. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    14. Kenneth Kasa, 2000. "Forecasting the Forecasts of Others in the Frequency Domain," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 726-756, October.
    15. McCafferty, Stephen & Driskill, Robert, 1980. "Problems of Existence and Uniqueness in Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 48(5), pages 1313-1317, July.
    16. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, January.
    17. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, January.
    18. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    19. Christian Hellwig, 2005. "Knowing What Others Know: Coordination Motives in Information Acquisition (March 2007, with Laura Veldkamp)," UCLA Economics Online Papers 369, UCLA Department of Economics.
    20. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    21. Sargent, Thomas J., 1991. "Equilibrium with signal extraction from endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 245-273, April.
    22. Michael Woodford, 2001. "Imperfect Common Knowledge and the Effects of Monetary Policy," NBER Working Papers 8673, National Bureau of Economic Research, Inc.
    23. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    24. Wang, Jiang, 1994. "A Model of Competitive Stock Trading Volume," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 127-168, February.
    25. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, January.
    26. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, January.
    27. Joseph G. Pearlman & Thomas J. Sargent, 2005. "Knowing the Forecasts of Others," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 480-497, April.
    28. Kenneth Kasa & Todd B. Walker & Charles H. Whiteman, 2006. "Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders," CAEPR Working Papers 2006-010, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    29. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-588, August.
    30. Lucas, Robert E, Jr, 1975. "An Equilibrium Model of the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 83(6), pages 1113-1144, December.
    31. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics :theory and applications," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
    32. Admati, Anat R, 1985. "A Noisy Rational Expectations Equilibrium for Multi-asset Securities Markets," Econometrica, Econometric Society, vol. 53(3), pages 629-657, May.
    33. Franklin Allen & Stephen Morris & Hyun Song Shin, 2006. "Beauty Contests and Iterated Expectations in Asset Markets," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 719-752.
    34. Foster, F Douglas & Viswanathan, S, 1996. "Strategic Trading When Agents Forecast the Forecasts of Others," Journal of Finance, American Finance Association, vol. 51(4), pages 1437-1478, September.
    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. Tan, Fei, 2018. "A Frequency-Domain Approach to Dynamic Macroeconomic Models," MPRA Paper 90487, University Library of Munich, Germany.
    2. Philippe Bacchetta & Eric Van Wincoop, 2008. "Higher Order Expectations in Asset Pricing," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(5), pages 837-866, August.
    3. Kristoffer Nimark, 2007. "Dynamic Higher Order Expectations," 2007 Meeting Papers 542, Society for Economic Dynamics.
    4. Eric R. Young & Ponpoje Porapakkarm, 2008. "Information Heterogeneity in the Macroeconomy," 2008 Meeting Papers 67, Society for Economic Dynamics.
    5. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    6. Pengfei Wang & Yi Wen, 2007. "Incomplete information and self-fulfilling prophecies," Working Papers 2007-033, Federal Reserve Bank of St. Louis.
    7. George-Marios Angeletos & Chen Lian, 2016. "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination," NBER Working Papers 22297, National Bureau of Economic Research, Inc.
    8. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    9. Rondina, Giacomo & Walker, Todd B., 2021. "Confounding dynamics," Journal of Economic Theory, Elsevier, vol. 196(C).
    10. Lanne Markku & Saikkonen Pentti, 2011. "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-32, October.
    11. Todd Walker, 2017. "Confounding Dynamics," 2017 Meeting Papers 141, Society for Economic Dynamics.
    12. P. Seiler & B. Taub, 2008. "The dynamics of strategic information flows in stock markets," Finance and Stochastics, Springer, vol. 12(1), pages 43-82, January.
    13. Kristoffer Nimark, 2009. "Speculative dynamics in the term structure of interest rates," Economics Working Papers 1194, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2012.
    14. repec:zbw:bofrdp:2009_018 is not listed on IDEAS

    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. Philippe Bacchetta & Eric Van Wincoop, 2006. "Can Information Heterogeneity Explain the Exchange Rate Determination Puzzle?," American Economic Review, American Economic Association, vol. 96(3), pages 552-576, June.
    2. Philippe Bacchetta & Eric Van Wincoop, 2008. "Higher Order Expectations in Asset Pricing," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(5), pages 837-866, August.
    3. Makarov, Igor & Rytchkov, Oleg, 2012. "Forecasting the forecasts of others: Implications for asset pricing," Journal of Economic Theory, Elsevier, vol. 147(3), pages 941-966.
    4. Philippe Bacchetta & Eric van Wincoop, 2005. "Can Information Heterogeneity Explain the Exchange Rate Determination?," FAME Research Paper Series rp155, International Center for Financial Asset Management and Engineering.
    5. Yuriy Gorodnichenko, 2008. "Endogenous information, menu costs and inflation persistence," NBER Working Papers 14184, National Bureau of Economic Research, Inc.
    6. Christian Hellwig, 2004. "Heterogeneous Information and the Benefits of Public Information Disclosures (October 2005)," UCLA Economics Online Papers 283, UCLA Department of Economics.
    7. Rondina, Giacomo & Walker, Todd B., 2021. "Confounding dynamics," Journal of Economic Theory, Elsevier, vol. 196(C).
    8. Kenneth Kasa & Todd B. Walker & Charles H. Whiteman, 2014. "Heterogeneous Beliefs and Tests of Present Value Models," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 1137-1163.
    9. Assaf Razin & Itay Goldstein, 2012. "Review Of Theories of Financial Crises," 2012 Meeting Papers 214, Society for Economic Dynamics.
    10. Evstigneev, Igor & Taksar, Michael, 2009. "Dynamic interaction models of economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 166-182, January.
    11. Piersanti, Giovanni, 2012. "The Macroeconomic Theory of Exchange Rate Crises," OUP Catalogue, Oxford University Press, number 9780199653126, Decembrie.
    12. Todd Walker, 2017. "Confounding Dynamics," 2017 Meeting Papers 141, Society for Economic Dynamics.
    13. Elmar Mertens, 2016. "Managing Beliefs about Monetary Policy under Discretion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(4), pages 661-698, June.
    14. Guido Lorenzoni, 2009. "A Theory of Demand Shocks," American Economic Review, American Economic Association, vol. 99(5), pages 2050-2084, December.
    15. Leonardo Melosi, 2017. "Signalling Effects of Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 853-884.
    16. George-Marios Angeletos & Chen Lian, 2016. "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination," NBER Working Papers 22297, National Bureau of Economic Research, Inc.
    17. Mordecai Kurz, 2007. "Rational Diverse Beliefs and Economic Volatility," Discussion Papers 06-045, Stanford Institute for Economic Policy Research.
    18. John Geanakoplos & Robert Axtell & J. Doyne Farmer & Peter Howitt & Benjamin Conlee & Jonathan Goldstein & Matthew Hendrey & Nathan M. Palmer & Chun-Yi Yang, 2012. "Getting at Systemic Risk via an Agent-Based Model of the Housing Market," American Economic Review, American Economic Association, vol. 102(3), pages 53-58, May.
    19. Gärtner, D.L. & Zhou, J., 2012. "Delays in Leniency Application : Is There Really a Race to the Enforcer’s Door?," Other publications TiSEM cbb8fac0-0cd7-4a0c-a6d4-a, Tilburg University, School of Economics and Management.
    20. Dan Bernhardt & P. Seiler & B. Taub, 2010. "Speculative dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 1-52, July.

    More about this item

    Keywords

    Asymmetric Information; Asset Pricing; Frequency Domain;
    All these keywords.

    JEL classification:

    • G - Financial Economics

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpfi:0509021. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.