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Adaptive Learning in Practice

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  • Chryssi Giannitsarou
  • Eva Carceles-Poveda

Abstract

While there is an extensive literature on identifying the asymptotic properties of adaptive learning algorithms, little is explicitly mentioned on how to actually implement these algorithms on the computer to analyze the quantitative effects of learning in dynamic macroeconomic models. The aim of this paper is twofold. First, we provide a detailed practical description of how to numerically implement least squares learning in the context of a reduced form forward looking model with an endogenous lag. Second, while we give a brief overview of the asymptotic properties of least squares learning for the reduced form at hand, the analysis focuses on illustrating the importance of the initial conditions of the learning algorithm for the study of medium and short run dynamics. In particular, we propose and discuss two ways of initializing the algorithm, one that is based on randomly generated data and a second that is ad-hoc. Using several variations of the basic real business cycle model, we then compare the behavior of the variables of interest for a variety of initializations. Our results indicate that, for short time horizons of up to 300 periods (corresponding to 75 years of quarterly data), the evolution of aggregate variables depends crucially on the initial conditions of the algorithm, and the learning dynamics might deviate significantly from the corresponding rational expectations case depending on the initialization.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 271.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:271

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Keywords: Adaptive learning; least squares estimation; computational methods; short-run dynamics;

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References

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  1. Giannitsarou, Chryssi, 2006. "Supply-side reforms and learning dynamics," Journal of Monetary Economics, Elsevier, vol. 53(2), pages 291-309, March.
  2. Bullard, James & Cho, In-Koo, 2003. "Escapist policy rules," CFS Working Paper Series 2003/38, Center for Financial Studies (CFS).
  3. Campbell, John, 1994. "Inspecting the Mechanism: An Analytical Approach to the Stochastic Growth Model," Scholarly Articles 3196342, Harvard University Department of Economics.
  4. Cho, In-Koo & Williams, Noah & Sargent, Thomas J, 2002. "Escaping Nash Inflation," Review of Economic Studies, Wiley Blackwell, vol. 69(1), pages 1-40, January.
  5. Bennett T. McCallum, 1981. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc.
  6. Eva Carceles-Poveda & Chryssi Giannitsarou, 2008. "Asset Pricing with Adaptive Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 629-651, July.
  7. Fabio Milani, 2005. "Adaptive Learning and Inflation Persistence," Working Papers 050607, University of California-Irvine, Department of Economics.
  8. Orphanides, Athanasios & Williams, John C, 2005. "Inflation Scares and Forecast-Based Monetary Policy," CEPR Discussion Papers 4844, C.E.P.R. Discussion Papers.
  9. Orphanides, Athanasios & Williams, John C, 2005. "The Decline of Activist Stabilization Policy: Natural Rate Misperceptions, Learning and Expectations," CEPR Discussion Papers 4865, C.E.P.R. Discussion Papers.
  10. Fabio Milani, 2005. "Expectations, Learning and Macroeconomic Persistence," Working Papers 050608, University of California-Irvine, Department of Economics.
  11. Fabio Milani, 2005. "Learning, Monetary Policy Rules, and Macroeconomic Stability," Macroeconomics 0508019, EconWPA.
  12. Albert Marcet & Juan P. Nicolini, 1995. "Recurrent hyperinflations and learning," Economics Working Papers 244, Department of Economics and Business, Universitat Pompeu Fabra, revised Nov 2001.
  13. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," NBER Technical Working Papers 0317, National Bureau of Economic Research, Inc.
  14. Giannitsarou, Chryssi, 2005. "E-Stability Does Not Imply Learnability," Macroeconomic Dynamics, Cambridge University Press, vol. 9(02), pages 276-287, April.
  15. James Bullard & Stefano Eusepi, 2003. "Did the Great Inflation Occur Despite Policymaker Commitment to a Taylor Rule?," Computing in Economics and Finance 2003 129, Society for Computational Economics.
  16. Evans, George W. & Honkapohja, Seppo, 1998. "Convergence of learning algorithms without a projection facility," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 59-86, August.
  17. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The Conquest of South American Inflation," NBER Working Papers 12606, National Bureau of Economic Research, Inc.
  18. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
  19. 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.
  20. McCallum, Bennett T., 2007. "E-stability vis-a-vis determinacy results for a broad class of linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1376-1391, April.
  21. William Poole, 2002. "Flation," Speech 49, Federal Reserve Bank of St. Louis.
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