IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v31y2007i4p1376-1391.html
   My bibliography  Save this article

E-stability vis-a-vis determinacy results for a broad class of linear rational expectations models

Author

Listed:
  • McCallum, Bennett T.

Abstract

It is argued that learnability/E-stability is a necessary condition for a RE solution to be plausible. A class of linear models considered by Evans and Honkapohja (2001) is shown to include all models of the form used by King and Watson (1998) and Klein (2000), which permits any number of lags, leads, and lags of leads. For this broad class it is shown that, if current-period information is available in the learning process, determinacy is a sufficient condition for E-stability. It is not a necessary condition, however; there exist cases with more than one stable solution in which the solution based on the decreasing-modulus ordering of the system's eigenvalues is E-stable. If in such a case the other stable solution(s) are not E-stable, then the condition of indeterminacy may not be important for practical issues.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • McCallum, Bennett T., 2007. "E-stability vis-a-vis determinacy results for a broad class of linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1376-1391, April.
  • Handle: RePEc:eee:dyncon:v:31:y:2007:i:4:p:1376-1391
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(06)00099-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. John H. Cochrane, 1999. "A Frictionless View of US Inflation," NBER Chapters, in: NBER Macroeconomics Annual 1998, volume 13, pages 323-421, National Bureau of Economic Research, Inc.
    3. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
    4. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
    5. 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.
    6. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    7. McCallum, Bennett T., 2001. "Indeterminacy, bubbles, and the fiscal theory of price level determination," Journal of Monetary Economics, Elsevier, vol. 47(1), pages 19-30, February.
    8. George W. Evans & Seppo Honkapohja, 2003. "Expectations and the Stability Problem for Optimal Monetary Policies," Review of Economic Studies, Oxford University Press, vol. 70(4), pages 807-824.
    9. Klaus Adam & George W. Evans & Seppo Honkapoja, 2003. "Are Stationary Hyperinflation Paths Learnable?," CESifo Working Paper Series 936, CESifo.
    10. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
    11. Woodford, Michael, 1995. "Price-level determinacy without control of a monetary aggregate," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 1-46, December.
    12. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    13. Klaus Adam, 2003. "Learning and Equilibrium Selection in a Monetary Overlapping Generations Model with Sticky Prices," Review of Economic Studies, Oxford University Press, vol. 70(4), pages 887-907.
    14. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
    15. Robert G. King, 2000. "The new IS-LM model : language, logic, and limits," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 45-103.
    16. Binder, M. & Pesaran, H., 1996. "Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation," Cambridge Working Papers in Economics 9619, Faculty of Economics, University of Cambridge.
    17. Binder, Michael & Pesaran, M. Hashem, 1997. "Multivariate Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 13(6), pages 877-888, December.
    18. Michael Woodford, 1994. "Nonstandard Indicators for Monetary Policy: Can Their Usefulness Be Judged from Forecasting Regressions?," NBER Chapters, in: Monetary Policy, pages 95-115, National Bureau of Economic Research, Inc.
    19. 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.
    20. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
    21. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics 9415, Faculty of Economics, University of Cambridge.
    22. Sims, Christopher A, 1994. "A Simple Model for Study of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 381-399.
    23. McCallum, Bennett T., 1998. "Solutions to linear rational expectations models: a compact exposition," Economics Letters, Elsevier, vol. 61(2), pages 143-147, November.
    24. 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.
    25. Evans, George W & Honkapohja, Seppo, 1992. "On the Robustness of Bubbles in Linear RE Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 1-14, February.
    26. George Evans, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, Oxford University Press, vol. 100(4), pages 1217-1233.
    27. Stephen J. DeCanio, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, Oxford University Press, vol. 93(1), pages 47-57.
    28. Narayana R. Kocherlakota & Christopher Phelan, 1999. "Explaining the fiscal theory of the price level," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 23(Fall), pages 14-23.
    29. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    30. Adam, Klaus & Evans, George W. & Honkapohja, Seppo, 2006. "Are hyperinflation paths learnable?," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2725-2748, December.
    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. McCallum, Bennett T., 2003. "Multiple-solution indeterminacies in monetary policy analysis," Journal of Monetary Economics, Elsevier, vol. 50(5), pages 1153-1175, July.
    2. Bennett T. McCallum, 2002. "The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models," GSIA Working Papers 2003-25, Carnegie Mellon University, Tepper School of Business.
    3. Bennett T. McCallum, 2009. "Determinacy, Learnability, and Plausibility in Monetary Policy Analysis: Additional Results," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 7, pages 203-225, Central Bank of Chile.
    4. Bennett T. McCallum, 2000. "Role of the Minimal State Variable Criterion," NBER Working Papers 7087, National Bureau of Economic Research, Inc.
    5. Bennett T. McCallum, 2009. "Indeterminancy from inflation forecast targeting : problem or pseudo-problem?," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 95(Win), pages 25-51.
    6. Olivier Loisel, 2004. "Monetary policy rules to preclude booms and busts," Money Macro and Finance (MMF) Research Group Conference 2003 56, Money Macro and Finance Research Group.
    7. Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
    8. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
    9. Bennett T. Mccallum, 2003. "Is The Fiscal Theory of the Price Level Learnable?," Scottish Journal of Political Economy, Scottish Economic Society, vol. 50(5), pages 634-649, November.
    10. Petia Ivanova, 2007. "The Fiscal Theory for the Cost Level and Monetarism," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 1, pages 60-79.
    11. Blake, Andrew P. & Zampolli, Fabrizio, 2011. "Optimal policy in Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1626-1651, October.
    12. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    13. 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.
    14. George-Marios Angeletos & Chen Lian, 2021. "Determinacy without the Taylor Principle," NBER Working Papers 28881, National Bureau of Economic Research, Inc.
    15. Ellison, Martin & Pearlman, Joseph, 2011. "Saddlepath learning," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1500-1519, July.
    16. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    17. Bennett McCallum, 1999. "Role of the Minimal State Variable Criterion in Rational Expectations Models," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 6(4), pages 621-639, November.
    18. Philip Arestis & Alexander Mihailov, 2011. "Classifying Monetary Economics: Fields And Methods From Past To Future," Journal of Economic Surveys, Wiley Blackwell, vol. 25(4), pages 769-800, September.
    19. Meyer-Gohde, Alexander, 2010. "Linear rational-expectations models with lagged expectations: A synthetic method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 984-1002, May.
    20. Onatski, Alexei, 2006. "Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 323-345, February.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

    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:eee:dyncon:v:31:y:2007:i:4:p:1376-1391. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.