IDEAS home Printed from https://ideas.repec.org/p/een/camaaa/2020-46.html
   My bibliography  Save this paper

Information weighting under least squares learning

Author

Listed:
  • Jaqueson K. Galimberti

Abstract

This paper evaluates how adaptive learning agents weight different pieces of information when forming expectations with a recursive least squares algorithm. The analysis is based on a renewed and more general non-recursive representation of the learning algorithm, namely, a penalized weighted least squares estimator, where a penalty term accounts for the effects of the learning initials. The paper then draws behavioral implications of alternative specifications of the learning mechanism, such as the cases with decreasing, constant, regime-switching, adaptive, and age-dependent gains, as well as practical recommendations on their computation. One key new finding is that without a proper account for the uncertainty about the learning initial, a constant-gain can generate a time-varying profile of weights given to past observations, particularly distorting the estimation and behavioral interpretation of this mechanism in small samples of data. In fact, simulations and empirical estimation of a Phillips curve model with learning indicate that this particular misspecification of the initials can lead to estimates where inflation rates are less responsive to expectations and output gaps than in reality, or “flatter†Phillips curves.

Suggested Citation

  • Jaqueson K. Galimberti, 2020. "Information weighting under least squares learning," CAMA Working Papers 2020-46, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2020-46
    as

    Download full text from publisher

    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2020-05/46_2020_galimberti1.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Berardi, Michele & Galimberti, Jaqueson K., 2017. "On the initialization of adaptive learning in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 26-53.
    2. Giorgio E. Primiceri, 2006. "Why Inflation Rose and Fell: Policy-Makers' Beliefs and U. S. Postwar Stabilization Policy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(3), pages 867-901.
    3. Berardi, Michele & Galimberti, Jaqueson K., 2013. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Economics Letters, Elsevier, vol. 118(1), pages 139-142.
    4. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    5. Orphanides, Athanasios & Williams, John C., 2005. "The decline of activist stabilization policy: Natural rate misperceptions, learning, and expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1927-1950, November.
    6. Albert Marcet & Juan P. Nicolini, 2003. "Recurrent Hyperinflations and Learning," American Economic Review, American Economic Association, vol. 93(5), pages 1476-1498, December.
    7. George W. Evans & Seppo Honkapohja & Noah Williams, 2010. "Generalized Stochastic Gradient Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 237-262, February.
    8. 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.
    9. Sophocles Mavroeidis & Mikkel Plagborg-Møller & James H. Stock, 2014. "Empirical Evidence on Inflation Expectations in the New Keynesian Phillips Curve," Journal of Economic Literature, American Economic Association, vol. 52(1), pages 124-188, March.
    10. Thomas Sargent & Noah Williams & Tao Zha, 2006. "Shocks and Government Beliefs: The Rise and Fall of American Inflation," American Economic Review, American Economic Association, vol. 96(4), pages 1193-1224, September.
    11. Sergey Slobodyan & Raf Wouters, 2012. "Learning in a Medium-Scale DSGE Model with Expectations Based on Small Forecasting Models," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 65-101, April.
    12. Markiewicz, Agnieszka & Pick, Andreas, 2014. "Adaptive learning and survey data," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PB), pages 685-707.
    13. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    14. George W. Evans & Seppo Honkapohja, 1993. "Adaptive forecasts, hysteresis, and endogenous fluctuations," Economic Review, Federal Reserve Bank of San Francisco, pages 3-13.
    15. Robert J. Gordon, 2011. "The History of the Phillips Curve: Consensus and Bifurcation," Economica, London School of Economics and Political Science, vol. 78(309), pages 10-50, January.
    16. Milani, Fabio, 2014. "Learning and time-varying macroeconomic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 94-114.
    17. Noah Williams, 2019. "Escape Dynamics in Learning Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(2), pages 882-912.
    18. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
    19. Carceles-Poveda, Eva & Giannitsarou, Chryssi, 2007. "Adaptive learning in practice," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2659-2697, August.
    20. Chevillon, Guillaume & Massmann, Michael & Mavroeidis, Sophocles, 2010. "Inference in models with adaptive learning," Journal of Monetary Economics, Elsevier, vol. 57(3), pages 341-351, April.
    21. Berardi, Michele & Galimberti, Jaqueson K., 2014. "A note on the representative adaptive learning algorithm," Economics Letters, Elsevier, vol. 124(1), pages 104-107.
    22. Galimberti, Jaqueson K., 2019. "An approximation of the distribution of learning estimates in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 29-43.
    23. Ulrike Malmendier & Stefan Nagel, 2016. "Learning from Inflation Experiences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 53-87.
    24. Markiewicz, Agnieszka & Pick, Andreas, 2014. "Adaptive learning and survey data," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PB), pages 685-707.
    25. Kostyshyna, Olena, 2012. "Application Of An Adaptive Step-Size Algorithm In Models Of Hyperinflation," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 355-375, November.
    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. Cole, Stephen J. & Milani, Fabio, 2021. "Heterogeneity in individual expectations, sentiment, and constant-gain learning," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 627-650.

    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. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    2. Berardi, Michele & Galimberti, Jaqueson K., 2017. "On the initialization of adaptive learning in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 26-53.
    3. Michele Berardi, 2020. "A probabilistic interpretation of the constant gain learning algorithm," Bulletin of Economic Research, Wiley Blackwell, vol. 72(4), pages 393-403, October.
    4. Galimberti, Jaqueson K., 2019. "An approximation of the distribution of learning estimates in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 29-43.
    5. Berardi, Michele & Galimberti, Jaqueson K., 2019. "Smoothing-Based Initialization For Learning-To-Forecast Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 23(3), pages 1008-1023, April.
    6. Cole, Stephen J. & Milani, Fabio, 2021. "Heterogeneity in individual expectations, sentiment, and constant-gain learning," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 627-650.
    7. Michele Berardi & Jaqueson K. Galimberti, 2012. "On the initialization of adaptive learning algorithms: A review of methods and a new smoothing-based routine," Centre for Growth and Business Cycle Research Discussion Paper Series 175, Economics, The University of Manchester.
    8. Kobielarz, Michal, 2018. "The economics of monetary unions," Other publications TiSEM b0293536-68ec-4905-bffd-6, Tilburg University, School of Economics and Management.
    9. Carlos Carvalho & Stefano Eusepi & Emanuel Moench & Bruce Preston, 2023. "Anchored Inflation Expectations," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(1), pages 1-47, January.
    10. Gáti, Laura, 2023. "Monetary policy & anchored expectations—An endogenous gain learning model," Journal of Monetary Economics, Elsevier, vol. 140(S), pages 37-47.
    11. Michele Berardi & Jaqueson K. Galimberti, 2012. "On the plausibility of adaptive learning in macroeconomics: A puzzling conflict in the choice of the representative algorithm," Centre for Growth and Business Cycle Research Discussion Paper Series 177, Economics, The University of Manchester.
    12. Christina Strobach & Carin van der Cruijsen, 2015. "The formation of European inflation expectations: One learning rule does not fit all," DNB Working Papers 472, Netherlands Central Bank, Research Department.
    13. Marine Charlotte André & Meixing Dai, 2015. "Central bank accountability under adaptive learning," Working Papers of BETA 2015-32, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    14. Berardi, Michele & Galimberti, Jaqueson K., 2013. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Economics Letters, Elsevier, vol. 118(1), pages 139-142.
    15. Alexander Mayer, 2022. "Estimation and inference in adaptive learning models with slowly decreasing gains," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 720-749, September.
    16. André, Marine Charlotte & Dai, Meixing, 2017. "Is central bank conservatism desirable under learning?," Economic Modelling, Elsevier, vol. 60(C), pages 281-296.
    17. KevinX.D. Huang & Zheng Liu & Tao Zha, 2009. "Learning, Adaptive Expectations and Technology Shocks," Economic Journal, Royal Economic Society, vol. 119(536), pages 377-405, March.
    18. Dave, Chetan & Malik, Samreen, 2017. "A tale of fat tails," European Economic Review, Elsevier, vol. 100(C), pages 293-317.
    19. Audzei, Volha, 2023. "Learning and cross-country correlations in a multi-country DSGE model," Economic Modelling, Elsevier, vol. 120(C).
    20. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.

    More about this item

    Keywords

    bounded rationality; expectations; adaptive learning; memory;
    All these keywords.

    JEL classification:

    • E70 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • 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

    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:een:camaaa:2020-46. 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: Cama Admin (email available below). General contact details of provider: https://edirc.repec.org/data/asanuau.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.