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Adaptive Learning In Regime-Switching Models

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  • Branch, William A.
  • Davig, Troy
  • McGough, Bruce
Abstract
We study adaptive learning in economic environments subject to recurring structural change. Stochastically evolving institutional and policymaking features can be described by regime-switching models with parameters that evolve according to finite state Markov processes. We demonstrate that in nonlinear models of this form, the presence of sunspot equilibria implies two natural schemes for learning the conditional means of endogenous variables: under mean value learning, agents condition on a sunspot variable that captures the self-fulfilling serial correlation in the equilibrium, whereas under vector autoregression learning (VAR learning), the self-fulfilling serial correlation must be learned. We show that an intuitive condition ensures convergence to a regime-switching rational expectations equilibrium. However, the stability of sunspot equilibria, when they exist, depends on whether agents adopt mean value or VAR learning: coordinating on sunspot equilibria via a VAR learning rule is not possible. To illustrate these phenomena, we develop results for an overlapping-generations model and a New Keynesian model.

Suggested Citation

  • Branch, William A. & Davig, Troy & McGough, Bruce, 2013. "Adaptive Learning In Regime-Switching Models," Macroeconomic Dynamics, Cambridge University Press, vol. 17(5), pages 998-1022, July.
    • Handle: RePEc:cup:macdyn:v:17:y:2013:i:05:p:998-1022_00
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    Citations

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    Cited by:

    1. Troy Davig & Eric M. Leeper, 2010. "Generalizing the Taylor Principle: Reply," American Economic Review, American Economic Association, vol. 100(1), pages 618-624, March.
    2. Guido Ascari & Sophocles Mavroeidis & Nigel McClung, 2023. "Coherence without Rationality at the ZLB," DEM Working Papers Series 212, University of Pavia, Department of Economics and Management.
    3. Troy Davig & Eric Leeper, 2009. "Reply To “Generalizing The Taylor Principle: A Comment”," CAEPR Working Papers 2009-008, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    4. Cho, Seonghoon, 2021. "Determinacy and classification of Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    5. Dennis Wesselbaum, 2022. "Cheap Talk in a New Keynesian Model," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(3), pages 661-691, September.
    6. Stefano Eusepi & Bruce Preston, 2008. "Stabilizing Expectations under Monetary and Fiscal Policy Coordination," NBER Working Papers 14391, National Bureau of Economic Research, Inc.
    7. Best, Gabriela, 2017. "Policy Preferences And Policy Makers' Beliefs: The Great Inflation," Macroeconomic Dynamics, Cambridge University Press, vol. 21(8), pages 1957-1995, December.
    8. Eusepi, Stefano & Preston, Bruce, 2011. "Learning the fiscal theory of the price level: Some consequences of debt-management policy," Journal of the Japanese and International Economies, Elsevier, vol. 25(4), pages 358-379.
    9. Ascari, Guido & Mavroeidis, Sophocles & McClung, Nigel, 2023. "Coherence without rationality at the zero lower bound," Journal of Economic Theory, Elsevier, vol. 214(C).
    10. Eo, Yunjong & McClung, Nigel, 2021. "Determinacy and E-stability with interest rate rules at the zero lower bound," Bank of Finland Research Discussion Papers 14/2021, Bank of Finland.
    11. Cole, Stephen J., 2020. "The influence of learning and price-level targeting on central bank forward guidance," Journal of Macroeconomics, Elsevier, vol. 65(C).
    12. Reed, Jason R., 2019. "The forward premium puzzle and Markov-switching adaptive learning," Journal of Macroeconomics, Elsevier, vol. 59(C), pages 1-17.
    13. Carravetta, Francesco & Sorge, Marco M., 2013. "Model reference adaptive expectations in Markov-switching economies," Economic Modelling, Elsevier, vol. 32(C), pages 551-559.
    14. Cone, Thomas E., 2022. "Learning with unobserved regimes," Journal of Macroeconomics, Elsevier, vol. 73(C).
    15. McClung, Nigel, 2020. "E-stability vis-à-vis determinacy in regime-switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).

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