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Information weighting under least squares adaptive learning

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  • Jaqueson K. Galimberti

    (School of Economics, Auckland University of Technology)

Abstract

This note evaluates how adaptive learning agents weigh different pieces of information when forming expectations with a recursive least squares algorithm. The analysis is based on a new and more general non-recursive representaion 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 diferent specifications of the learning mechanism, such as the cases with decreasing-, constant-, regime-switching, and age-dependent gains. The latter is shown to imply the emergence of "dormant memories" as the agents get old.

Suggested Citation

  • Jaqueson K. Galimberti, 2020. "Information weighting under least squares adaptive learning," Working Papers 2020-04, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:202004
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    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.
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    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.

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    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

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