(Translated by https://www.hiragana.jp/)
Indeterminacy and imperfect information
IDEAS home Printed from https://ideas.repec.org/p/zbw/bubdps/012020.html
   My bibliography  Save this paper

Indeterminacy and imperfect information

Author

Listed:
  • Lubik, Thomas A.
  • Matthes, Christian
  • Mertens, Elmar

Abstract

We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less informed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. In this environment, we identify a new channel that leads to equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to self-fulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with a monetary policy problem where an imperfectly informed central bank follows an interest rate rule.

Suggested Citation

  • Lubik, Thomas A. & Matthes, Christian & Mertens, Elmar, 2020. "Indeterminacy and imperfect information," Discussion Papers 01/2020, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdps:012020
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/213861/1/1689860634.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    2. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-1026, November.
    3. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    4. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    5. Bu, Chunya & Rogers, John & Wu, Wenbin, 2021. "A unified measure of Fed monetary policy shocks," Journal of Monetary Economics, Elsevier, vol. 118(C), pages 331-349.
    6. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(1), pages 147-180.
    7. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
    8. Faust, Jon & Svensson, Lars E O, 2002. "The Equilibrium Degree of Transparency and Control in Monetary Policy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(2), pages 520-539, May.
    9. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    10. Jess Benhabib & Pengfei Wang & Yi Wen, 2015. "Sentiments and Aggregate Demand Fluctuations," Econometrica, Econometric Society, vol. 83, pages 549-585, March.
    11. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252, Elsevier.
    12. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    13. Evans, George W. & McGough, Bruce, 2005. "Stable sunspot solutions in models with predetermined variables," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 601-625, April.
    14. 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.
    15. 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.
    16. Acharya, Sushant & Benhabib, Jess & Huo, Zhen, 2021. "The anatomy of sentiment-driven fluctuations," Journal of Economic Theory, Elsevier, vol. 195(C).
    17. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November.
    18. Emi Nakamura & Jón Steinsson, 2018. "High-Frequency Identification of Monetary Non-Neutrality: The Information Effect," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1283-1330.
    19. Nimark, Kristoffer, 2008. "Monetary policy with signal extraction from the bond market," Journal of Monetary Economics, Elsevier, vol. 55(8), pages 1389-1400, November.
    20. Kristoffer P. Nimark, 2014. "Man-Bites-Dog Business Cycles," American Economic Review, American Economic Association, vol. 104(8), pages 2320-2367, August.
    21. Kristoffer Nimark, 2007. "Dynamic higher order expectations," Economics Working Papers 1118, Department of Economics and Business, Universitat Pompeu Fabra, revised Mar 2011.
    22. Lubik, Thomas A. & Matthes, Christian, 2016. "Indeterminacy and learning: An analysis of monetary policy in the Great Inflation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 85-106.
    23. 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.
    24. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
    25. Bernanke, Ben S & Woodford, Michael, 1997. "Inflation Forecasts and Monetary Policy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(4), pages 653-684, November.
    26. Athanasios Orphanides & John C. Williams, 2006. "Monetary Policy with Imperfect Knowledge," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 366-375, 04-05.
    27. Athanasios Orphanides, 2001. "Monetary Policy Rules Based on Real-Time Data," American Economic Review, American Economic Association, vol. 91(4), pages 964-985, September.
    28. Julian Kozlowski & Laura Veldkamp & Venky Venkateswaran, 2020. "The Tail That Wags the Economy: Beliefs and Persistent Stagnation," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 2839-2879.
    29. Angeletos, George-Marios & Iovino, Luigi & La'O, Jennifer, 2020. "Learning over the business cycle: Policy implications," Journal of Economic Theory, Elsevier, vol. 190(C).
    30. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    31. 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.
    32. Aoki, Kosuke, 2006. "Optimal commitment policy under noisy information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 81-109, January.
    33. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
    34. Orphanides, Athanasios, 2003. "Monetary policy evaluation with noisy information," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 605-631, April.
    35. Svensson, Lars E. O. & Woodford, Michael, 2004. "Indicator variables for optimal policy under asymmetric information," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 661-690, January.
    36. Taylor, John B, 1977. "Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations," Econometrica, Econometric Society, vol. 45(6), pages 1377-1385, September.
    37. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    38. Carboni, Giacomo & Ellison, Martin, 2011. "Inflation and output volatility under asymmetric incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 40-51, January.
    39. Baxter, Brad & Graham, Liam & Wright, Stephen, 2011. "Invertible and non-invertible information sets in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 295-311, March.
    40. Farmer, Roger E.A. & Khramov, Vadim & Nicolò, Giovanni, 2015. "Solving and estimating indeterminate DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 54(C), pages 17-36.
    41. Dotsey, Michael & Hornstein, Andreas, 2003. "Should a monetary policymaker look at money?," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 547-579, April.
    42. Nimark, Kristoffer, 2008. "Dynamic pricing and imperfect common knowledge," Journal of Monetary Economics, Elsevier, vol. 55(2), pages 365-382, March.
    43. Orphanides, Athanasios & Williams, John C., 2007. "Robust monetary policy with imperfect knowledge," Journal of Monetary Economics, Elsevier, vol. 54(5), pages 1406-1435, July.
    44. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-118, May.
    45. Stephen Morris & Hyun Song Shin, 2018. "Central Bank Forward Guidance and the Signal Value of Market Prices," AEA Papers and Proceedings, American Economic Association, vol. 108, pages 572-577, May.
    46. Pearlman, Joseph & Currie, David & Levine, Paul, 1986. "Rational expectations models with partial information," Economic Modelling, Elsevier, vol. 3(2), pages 90-105, April.
    47. Siemroth, Christoph, 2019. "The informational content of prices when policy makers react to financial markets," Journal of Economic Theory, Elsevier, vol. 179(C), pages 240-274.
    48. Schmitt-Grohe, Stephanie, 1997. "Comparing Four Models of Aggregate Fluctuations due to Self-Fulfilling Expectations," Journal of Economic Theory, Elsevier, vol. 72(1), pages 96-147, January.
    49. Sargent, Thomas J & Wallace, Neil, 1975. ""Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 241-254, April.
    50. Farmer Roger E. A. & Guo Jang-Ting, 1994. "Real Business Cycles and the Animal Spirits Hypothesis," Journal of Economic Theory, Elsevier, vol. 63(1), pages 42-72, June.
    51. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    52. Guido Ascari & Paolo Bonomolo & Hedibert F. Lopes, 2019. "Walk on the Wild Side: Temporarily Unstable Paths and Multiplicative Sunspots," American Economic Review, American Economic Association, vol. 109(5), pages 1805-1842, May.
    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. Sorge Marco M., 2020. "Computing sunspot solutions to rational expectations models with timing restrictions," The B.E. Journal of Macroeconomics, De Gruyter, vol. 20(2), pages 1-10, June.
    2. Angelini, Giovanni & Sorge, Marco M., 2021. "Under the same (Chole)sky: DNK models, timing restrictions and recursive identification of monetary policy shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    3. Haque, Qazi & Groshenny, Nicolas & Weder, Mark, 2021. "Do we really know that U.S. monetary policy was destabilizing in the 1970s?," European Economic Review, Elsevier, vol. 131(C).
    4. Paul Levine & Joseph Pearlman & Stephen Wright & Bo Yang, 2023. "Imperfect Information and Hidden Dynamics," School of Economics Discussion Papers 1223, School of Economics, University of Surrey.

    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. Thomas Lubik & Christian Matthes & Elmar Mertens, 2023. "Indeterminacy and Imperfect Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 49, pages 37-57, July.
    2. Hatcher, Michael, 2022. "Solving linear rational expectations models in the presence of structural change: Some extensions," Journal of Economic Dynamics and Control, Elsevier, vol. 138(C).
    3. Elmar Mertens, 2010. "Discreet Commitments and Discretion of Policymakers with Private Information," 2010 Meeting Papers 763, Society for Economic Dynamics.
    4. Lubik, Thomas A. & Matthes, Christian, 2016. "Indeterminacy and learning: An analysis of monetary policy in the Great Inflation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 85-106.
    5. Francesco Bianchi & Giovanni Nicolò, 2021. "A generalized approach to indeterminacy in linear rational expectations models," Quantitative Economics, Econometric Society, vol. 12(3), pages 843-868, July.
    6. Givens, Gregory E. & Salemi, Michael K., 2015. "Inferring monetary policy objectives with a partially observed state," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 190-208.
    7. 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.
    8. repec:spo:wpecon:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    9. Angelini, Giovanni & Sorge, Marco M., 2021. "Under the same (Chole)sky: DNK models, timing restrictions and recursive identification of monetary policy shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    10. McClung, Nigel, 2020. "E-stability vis-à-vis determinacy in regime-switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).
    11. repec:hal:wpspec:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    12. repec:hal:spmain:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    13. Paul Hubert, 2010. "Monetary policy, imperfect information and the expectations channel [Politique monétaire,information imparfaite et canal des anticipations]," SciencePo Working papers Main tel-04095385, HAL.
    14. repec:spo:wpmain:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    15. Mariano Kulish & Adrian Pagan, 2017. "Estimation and Solution of Models with Expectations and Structural Changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 255-274, March.
    16. Farmer, Roger E.A. & Khramov, Vadim & Nicolò, Giovanni, 2015. "Solving and estimating indeterminate DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 54(C), pages 17-36.
    17. Yasuo Hirose & Takushi Kurozumi & Willem Van Zandweghe, 2020. "Monetary Policy and Macroeconomic Stability Revisited," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 255-274, July.
    18. Svensson, Lars E.O., 2010. "Inflation Targeting," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 22, pages 1237-1302, Elsevier.
    19. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    20. Evans, George W. & McGough, Bruce, 2020. "Stable near-rational sunspot equilibria," Journal of Economic Theory, Elsevier, vol. 186(C).
    21. Pengfei Wang & Yi Wen, 2006. "Solving linear difference systems with lagged expectations by a method of undetermined coefficients," Working Papers 2006-003, Federal Reserve Bank of St. Louis.
    22. Aoki, Kosuke, 2006. "Optimal commitment policy under noisy information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 81-109, January.
    23. Olivier Coibion & Yuriy Gorodnichenko, 2011. "Monetary Policy, Trend Inflation, and the Great Moderation: An Alternative Interpretation," American Economic Review, American Economic Association, vol. 101(1), pages 341-370, February.
    24. Haque, Qazi & Groshenny, Nicolas & Weder, Mark, 2021. "Do we really know that U.S. monetary policy was destabilizing in the 1970s?," European Economic Review, Elsevier, vol. 131(C).

    More about this item

    Keywords

    limited information; rational expectations; signal extraction; belief shocks;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

    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:zbw:bubdps:012020. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/dbbgvde.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.