IDEAS home Printed from https://ideas.repec.org/p/red/sed007/542.html
   My bibliography  Save this paper

Dynamic Higher Order Expectations

Author

Listed:
  • Kristoffer Nimark

    (Reserve Bank of Australia)

Abstract

In models where privately informed agents interact, agents may need to form higher order expectations, i.e. expectations of other agents' expectations. This paper explores dynamic higher order expectations in a setting where it is common knowledge that agents are rational Bayesians. This structure allows any order of expectation at any horizon to be determined recursively. The usefulness of the approach is illustrated by solving a version of Singleton's (1987) asset pricing model with disparately informed traders but without assuming that shocks can be observed perfectly with a lag. In this context, we prove that both the impact of expectations on the asset's price and the variance of expectations are decreasing as the order of expectation increases. We use these results to derive a finite dimensional state representation that can be made arbitrarily accurate. The solution method exploits the Euler-type structure of the asset pricing function and should be applicable to a variety of settings where privately informed agents optimize intertemporally.

Suggested Citation

  • Kristoffer Nimark, 2007. "Dynamic Higher Order Expectations," 2007 Meeting Papers 542, Society for Economic Dynamics.
    • Handle: RePEc:red:sed007:542
    as

    Download full text from publisher

    File URL: https://red-files-public.s3.amazonaws.com/meetpapers/2007/paper_542.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Olivier Coibion & Yuriy Gorodnichenko, 2012. "What Can Survey Forecasts Tell Us about Information Rigidities?," Journal of Political Economy, University of Chicago Press, vol. 120(1), pages 116-159.
    2. Guido Lorenzoni, 2010. "Optimal Monetary Policy with Uncertain Fundamentals and Dispersed Information ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 305-338.
    3. Hellwig, Christian & Venkateswaran, Venky, 2009. "Setting the right prices for the wrong reasons," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 57-77.
    4. Hansen, Lars Peter & Sargent, Thomas J., 1981. "A note on Wiener-Kolmogorov prediction formulas for rational expectations models," Economics Letters, Elsevier, vol. 8(3), pages 255-260.
    5. Giovanni Cespa & Xavier Vives, 2012. "Dynamic Trading and Asset Prices: Keynes vs. Hayek," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 539-580.
    6. 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.
    7. Stephen Morris & Hyun Song Shin, 2006. "Inertia of Forward-Looking Expectations," American Economic Review, American Economic Association, vol. 96(2), pages 152-157, May.
    8. George-Marios Angeletos & Alessandro Pavan, 2007. "Efficient Use of Information and Social Value of Information," Econometrica, Econometric Society, vol. 75(4), pages 1103-1142, July.
    9. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    10. Walker, Todd B., 2007. "How equilibrium prices reveal information in a time series model with disparately informed, competitive traders," Journal of Economic Theory, Elsevier, vol. 137(1), pages 512-537, November.
    11. Nimark, Kristoffer P., 2015. "A low dimensional Kalman filter for systems with lagged states in the measurement equation," Economics Letters, Elsevier, vol. 127(C), pages 10-13.
    12. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-588, August.
    13. 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.
    14. Guido Lorenzoni, 2009. "A Theory of Demand Shocks," American Economic Review, American Economic Association, vol. 99(5), pages 2050-2084, December.
    15. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
    16. 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.
    Full references (including those not matched with items 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. 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.
    2. Rondina, Giacomo & Walker, Todd B., 2021. "Confounding dynamics," Journal of Economic Theory, Elsevier, vol. 196(C).
    3. George-Marios Angeletos & Chen Lian, 2016. "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination," NBER Working Papers 22297, National Bureau of Economic Research, Inc.
    4. George-Marios Angeletos & Chen Lian, 2018. "Forward Guidance without Common Knowledge," American Economic Review, American Economic Association, vol. 108(9), pages 2477-2512, September.
    5. Benhima, Kenza, 2019. "Booms and busts with dispersed information," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 32-47.
    6. Giacomo Rondina & Todd Walker, 2016. "Learning and Informational Stability of Dynamic REE with Incomplete Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 21, pages 147-159, July.
    7. Todd Walker, 2017. "Confounding Dynamics," 2017 Meeting Papers 141, Society for Economic Dynamics.
    8. Angeletos, George-Marios & La’O, Jennifer, 2009. "Incomplete information, higher-order beliefs and price inertia," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 19-37.
    9. Thomas Lustenberger & Enzo Rossi, 2022. "The Social Value of Information: A Test of a Beauty and Nonbeauty Contest," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 54(7), pages 2125-2148, October.
    10. 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.
    11. Guido Lorenzoni, 2009. "A Theory of Demand Shocks," American Economic Review, American Economic Association, vol. 99(5), pages 2050-2084, December.
    12. Leonardo Melosi, 2017. "Signalling Effects of Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 853-884.
    13. Jonathan J Adams, 2019. "Macroeconomic Models with Incomplete Information and Endogenous Signals," Working Papers 001004, University of Florida, Department of Economics.
    14. Lerby Ergun & Andreas Uthemann, 2020. "Strategic Uncertainty in Financial Markets: Evidence from a Consensus Pricing Service," Staff Working Papers 20-55, Bank of Canada.
    15. Candian, Giacomo, 2019. "Information frictions and real exchange rate dynamics," Journal of International Economics, Elsevier, vol. 116(C), pages 189-205.
    16. 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.
    17. Drenik, Andrés & Perez, Diego J., 2020. "Price setting under uncertainty about inflation," Journal of Monetary Economics, Elsevier, vol. 116(C), pages 23-38.
    18. George‐Marios Angeletos & Fabrice Collard & Harris Dellas, 2018. "Quantifying Confidence," Econometrica, Econometric Society, vol. 86(5), pages 1689-1726, September.
    19. 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.
    20. Walker, Todd B., 2007. "How equilibrium prices reveal information in a time series model with disparately informed, competitive traders," Journal of Economic Theory, Elsevier, vol. 137(1), pages 512-537, November.

    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:red:sed007:542. 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: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    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.