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Statistical Learning With Time-Varying Parameters

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  • McGough, Bruce

Abstract

In their landmark paper, Bray and Savin note that the constant-parameters model used by their agents to form expectations is misspecified and that, using standard econometric techniques, agents may be able to determine the time-varying nature of the model's parameters. Here, we consider the same type of model as employed by Bray and Savin except that our agents form expectations using a perceived model with parameters that vary with time. We assume agents use the Kalman filter to form estimates of these time-varying parameters. We find that, under certain restrictions on the structure of the stochastic process and on the value of the stability parameter, the model will converge to its rational expectations equilibrium. Further, the restrictions on the stability parameter required for convergence are identical to those found by Bray and Savin.

Suggested Citation

  • McGough, Bruce, 2003. "Statistical Learning With Time-Varying Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 7(1), pages 119-139, February.
    • Handle: RePEc:cup:macdyn:v:7:y:2003:i:01:p:119-139_01
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    Cited by:

    1. 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.
    2. Gaballo, Gaetano, 2013. "Good luck or good policy? An expectational theory of macro volatility switches," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2755-2770.
    3. In-Koo Cho & Kenneth Kasa, 2017. "Gresham's Law of Model Averaging," American Economic Review, American Economic Association, vol. 107(11), pages 3589-3616, November.
    4. Georges Prat & Remzi Uctum, 2016. "Do markets learn to rationally expect US interest rates? Evidence from survey data," Post-Print hal-01411824, HAL.
    5. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    6. In-Koo Cho & Kenneth Kasa, 2015. "Learning and Model Validation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 45-82.
    7. Mitra, Kaushik & Evans, George W. & Honkapohja, Seppo, 2012. "Baysian Model Averaging, Learning and Model Selection," SIRE Discussion Papers 2012-11, Scottish Institute for Research in Economics (SIRE).
    8. Mathew B. Chylinski & John H. Roberts & Bruce G. S. Hardie, 2012. "Consumer Learning of New Binary Attribute Importance Accounting for Priors, Bias, and Order Effects," Marketing Science, INFORMS, vol. 31(4), pages 549-566, July.
    9. Georges Prat & Remzi Uctum, 2016. "Do markets learn to rationally expect US interest rates? Evidence from survey data," Working Papers hal-04141591, HAL.
    10. 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.
    11. Eric Gaus, 2013. "Time-Varying Parameters and Endogenous Learning Algorithms," Working Papers 13-02, Ursinus College, Department of Economics.
    12. Orlando Gomes, . "Volatility, Heterogeneous Agents and Chaos," The Electronic Journal of Evolutionary Modeling and Economic Dynamics, IFReDE - Université Montesquieu Bordeaux IV.
    13. Evans, David & Evans, George W. & McGough, Bruce, 2022. "The RPEs of RBCs and other DSGEs," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    14. Bullard, James & Suda, Jacek, 2016. "The stability of macroeconomic systems with Bayesian learners," Journal of Economic Dynamics and Control, Elsevier, vol. 62(C), pages 1-16.
    15. 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).
    16. Carravetta, Francesco & Sorge, Marco M., 2013. "Model reference adaptive expectations in Markov-switching economies," Economic Modelling, Elsevier, vol. 32(C), pages 551-559.
    17. J. Huston McCulloch, 2005. "The Kalman Foundations of Adaptive Least Squares: Applications to Unemployment and Inflation," Computing in Economics and Finance 2005 239, Society for Computational Economics.
    18. In-Koo Cho & Ken Kasa, 2012. "Model Validation and Learning," Discussion Papers dp12-07, Department of Economics, Simon Fraser University.

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