IDEAS home Printed from https://ideas.repec.org/p/rba/rbardp/rdp2012-08.html
   My bibliography  Save this paper

Estimation and Solution of Models with Expectations and Structural Changes

Author

Listed:
  • Mariano Kulish

    (Reserve Bank of Australia)

  • Adrian Pagan

    (University of Sydney)

Abstract

Standard solution methods for linearised models with rational expectations take the structural parameters to be constant. These solutions are fundamental for likelihood-based estimation of such models. Regime changes, such as those associated with either changed rules for economic policy or changes in the technology of production, can generate large changes in the statistical properties of observable variables. In practice, the impact of structural change on estimation is often addressed by selecting a sub-sample of the data for which a time-invariant structure seems valid. In this paper we develop solutions for linearised models in the presence of structural changes using a variety of assumptions relating to agents' beliefs when forming expectations, and whether the structural changes are known in advance. The solutions can be put into state space form and the Kalman filter used for constructing the likelihood function. Structural changes and varying beliefs trigger movements in the reduced-form coefficients and hence model variables follow a time-varying coefficient VAR. We apply the techniques to two examples: a disinflation program and a transitory slowdown in trend growth.

Suggested Citation

  • Mariano Kulish & Adrian Pagan, 2012. "Estimation and Solution of Models with Expectations and Structural Changes," RBA Research Discussion Papers rdp2012-08, Reserve Bank of Australia.
  • Handle: RePEc:rba:rbardp:rdp2012-08
    as

    Download full text from publisher

    File URL: https://www.rba.gov.au/publications/rdp/2012/pdf/rdp2012-08.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Adam Cagliarini & Mariano Kulish, 2013. "Solving Linear Rational Expectations Models with Predictable Structural Changes," The Review of Economics and Statistics, MIT Press, vol. 95(1), pages 328-336, March.
    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. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    4. Harald F. Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
    5. 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.
    6. Peter N. Ireland, 2004. "Technology Shocks in the New Keynesian Model," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 923-936, November.
    7. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2011. "Minimal state variable solutions to Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2150-2166.
    8. Anderson, Gary S., 2010. "A reliable and computationally efficient algorithm for imposing the saddle point property in dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 472-489, March.
    9. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    10. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    11. 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.
    12. 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.
    13. 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.
    14. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    15. 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.
    16. Atsushi Inoue & Barbara Rossi, 2011. "Identifying the Sources of Instabilities in Macroeconomic Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1186-1204, November.
    17. 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.
    18. 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.
    19. Cúrdia, Vasco & Finocchiaro, Daria, 2005. "An Estimated DSGE Model for Sweden with a Monetary Regime Change," Seminar Papers 740, Stockholm University, Institute for International Economic Studies.
    20. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    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. Fabio Canova & Filippo Ferroni & Christian Matthes, 2015. "Approximating Time Varying Structural Models With Time Invariant Structures," Working Paper 15-10, Federal Reserve Bank of Richmond.
    2. Jesper Lindé & Mathias Trabandt, 2018. "Should we use linearized models to calculate fiscal multipliers?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 937-965, November.
    3. Hashem Pesaran & Ron Smith, 2014. "Tests of Policy Ineffectiveness in Macroeconometrics," Cambridge Working Papers in Economics 1415, Faculty of Economics, University of Cambridge.
    4. Gomez-Gonzalez, Patricia & Rees, Daniel M., 2018. "Same Spain, less pain?," European Economic Review, Elsevier, vol. 110(C), pages 78-107.
    5. Kapetanios, George & Millard, Stephen & Price, Simon & Petrova, Katerina, 2018. "Time varying cointegration and the UK Great Ratios," Essex Finance Centre Working Papers 23320, University of Essex, Essex Business School.
    6. Pablo Cuba‐Borda & Luca Guerrieri & Matteo Iacoviello & Molin Zhong, 2019. "Likelihood evaluation of models with occasionally binding constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1073-1085, November.
    7. M. Hashem Pesaran & Ron P. Smith, 2014. "Tests of Policy Ineffectiveness in Macroeconometrics," CESifo Working Paper Series 4871, CESifo.
    8. Mariano Kulish & Adrian Pagan, 2016. "Issues in Estimating New Keynesian Phillips Curves in the Presence of Unknown Structural Change," Econometric Reviews, Taylor & Francis Journals, vol. 35(7), pages 1251-1270, August.
    9. García-Cicco, Javier & García-Schmidt, Mariana, 2020. "Revisiting the exchange rate pass through: A general equilibrium perspective," Journal of International Economics, Elsevier, vol. 127(C).
    10. M. Hashem Pesaran & Ron P. Smith, 2018. "Tests of Policy Interventions in DSGE Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(3), pages 457-484, June.
    11. Castelnuovo, Efrem & Pellegrino, Giovanni, 2018. "Uncertainty-dependent effects of monetary policy shocks: A new-Keynesian interpretation," Journal of Economic Dynamics and Control, Elsevier, vol. 93(C), pages 277-296.
    12. Gibbs, Christopher G. & Kulish, Mariano, 2017. "Disinflations in a model of imperfectly anchored expectations," European Economic Review, Elsevier, vol. 100(C), pages 157-174.
    13. Christoffel, Kai & Mazelis, Falk & Montes-Galdón, Carlos & Müller, Tobias, 2020. "Disciplining expectations and the forward guidance puzzle," Working Paper Series 2424, European Central Bank.
    14. Gibbs, Christopher G. & McClung, Nigel, 2019. "Does my model predict a forward guidance puzzle?," Research Discussion Papers 19/2019, Bank of Finland.
    15. Han Gao & Mariano Kulish & Juan Pablo Nicolini, 2020. "Two Illustrations of the Quantity Theory of Money Reloaded," Working Papers 774, Federal Reserve Bank of Minneapolis.
    16. Sergei Seleznev, 2016. "Solving DSGE models with stochastic trends," Bank of Russia Working Paper Series wps15, Bank of Russia.

    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. Elmar Mertens & Christian Matthes & Thomas Lubik, 2017. "Indeterminacy and Imperfect Information," 2017 Meeting Papers 337, Society for Economic Dynamics.
    2. Baele, Lieven & Bekaert, Geert & Cho, Seonghoon & Inghelbrecht, Koen & Moreno, Antonio, 2015. "Macroeconomic regimes," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 51-71.
    3. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    4. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    5. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2011. "Minimal state variable solutions to Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2150-2166.
    6. Smith, A. Lee, 2016. "When does the cost channel pose a challenge to inflation targeting central banks?," European Economic Review, Elsevier, vol. 89(C), pages 471-494.
    7. Liu, Zheng & Waggoner, Daniel F. & Zha, Tao, 2007. "Asymmetric Expectation Effects of Regime Shifts and the Great Moderation," Kiel Working Papers 1357, Kiel Institute for the World Economy (IfW).
    8. Francesco Bianchi & Cosmin Ilut, 2017. "Monetary/Fiscal Policy Mix and Agent's Beliefs," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 113-139, October.
    9. Troy Davig & Taeyoung Doh, 2014. "Monetary Policy Regime Shifts and Inflation Persistence," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 862-875, December.
    10. 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.
    11. Carravetta, Francesco & Sorge, Marco M., 2011. "On the Solution of Markov-switching Rational Expectations Models," Bonn Econ Discussion Papers 05/2011, University of Bonn, Bonn Graduate School of Economics (BGSE).
    12. 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.
    13. Neusser, Klaus, 2019. "Time–varying rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    14. 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.
    15. Adam Cagliarini & Mariano Kulish, 2013. "Solving Linear Rational Expectations Models with Predictable Structural Changes," The Review of Economics and Statistics, MIT Press, vol. 95(1), pages 328-336, March.
    16. Francesco Bianchi & Leonardo Melosi, 2017. "Escaping the Great Recession," American Economic Review, American Economic Association, vol. 107(4), pages 1030-1058, April.
    17. Qazi Haque, 2017. "Monetary Policy, Inflation Target and the Great Moderation: An Empirical Investigation," School of Economics Working Papers 2017-13, University of Adelaide, School of Economics.
    18. Chen, Xiaoshan & Kirsanova, Tatiana & Leith, Campbell, 2017. "How optimal is US monetary policy?," Journal of Monetary Economics, Elsevier, vol. 92(C), pages 96-111.
    19. Shayan Zakipour-Saber, 2019. "Monetary policy regimes and inflation persistence in the United Kingdom," Working Papers 895, Queen Mary University of London, School of Economics and Finance.
    20. Andrew T. Foerster, 2016. "Monetary Policy Regime Switches And Macroeconomic Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 211-230, February.

    More about this item

    Keywords

    expectations; structural change; regime change; DSGE; maximum likelihood; Kalman filter;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

    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:rba:rbardp:rdp2012-08. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Paula Drew). General contact details of provider: http://edirc.repec.org/data/rbagvau.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.