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Adaptive Learning in Practice

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Author Info

  • 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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Related research

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

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References

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  1. Athanasios Orphanides & John C. Williams, 2003. "Inflation scares and forecast-based monetary policy," Finance and Economics Discussion Series 2003-41, Board of Governors of the Federal Reserve System (U.S.).
  2. Bennett T. McCallum, 2006. "E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models," NBER Working Papers 12441, National Bureau of Economic Research, Inc.
  3. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," University of Oregon Economics Department Working Papers 2005-17, University of Oregon Economics Department, revised 18 May 2008.
  4. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
  5. 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.
  6. Bullard, James & Cho, In-Koo, 2005. "Escapist policy rules," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1841-1865, November.
  7. Fabio Milani, 2005. "Adaptive Learning and Inflation Persistence," Working Papers 050607, University of California-Irvine, Department of Economics.
  8. Athanasios Orphanides & John C. Williams, 2004. "The decline of activist stabilization policy: natural rate misperceptions, learning, and expectations," International Finance Discussion Papers 804, Board of Governors of the Federal Reserve System (U.S.).
  9. Fabio Milani, 2005. "Expectations, Learning and Macroeconomic Persistence," Macroeconomics 0510022, EconWPA.
  10. Marcet, Albert & Nicolini, Juan Pablo, 1998. "Recurrent Hyperinflations and Learning," CEPR Discussion Papers 1875, C.E.P.R. Discussion Papers.
  11. James B. Bullard & Stefano Eusepi, 2004. "Did the Great Inflation occur despite policymaker commitment to a Taylor rule?," Working Papers 2003-013, Federal Reserve Bank of St. Louis.
  12. Chryssi Giannitsarou, 2004. "Supply-side reforms and learning dynamics," Money Macro and Finance (MMF) Research Group Conference 2003 36, Money Macro and Finance Research Group.
  13. Uhlig, H., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
  14. Eva Carceles Poveda & Chryssi Giannitsarou, 2006. "Asset pricing with adaptive learning," Computing in Economics and Finance 2006 25, Society for Computational Economics.
  15. Campbell, John Y., 1994. "Inspecting the mechanism: An analytical approach to the stochastic growth model," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 463-506, June.
  16. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The conquest of South American inflation," Working Paper 2006-20, Federal Reserve Bank of Atlanta.
  17. Giannitsarou, Chryssi, 2005. "E-Stability Does Not Imply Learnability," Macroeconomic Dynamics, Cambridge University Press, vol. 9(02), pages 276-287, April.
  18. In-Koo Cho & Thomas J. Sargent, 2000. "Escaping Nash inflation," Working Paper Series 23, European Central Bank.
  19. Milani, Fabio, 2008. "Learning, monetary policy rules, and macroeconomic stability," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3148-3165, October.
  20. 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.
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