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Learning and Model Validation

  • In-Koo Cho


    (Economics University of Illinois)

  • Kenneth Kasa

This paper studies the following problem. An agent takes actions based on a possibly misspecified model. The agent is 'large', in the sense that his actions influence the model he is trying to learn about. The agent is aware of potential model misspecification and tries to detect it, in real-time, using an econometric specification test. If his model fails the test, he formulates a new better-fitting model. If his model passes the test, he uses it to formulate and implement a policy based on the provisional assumption that the current model is correctly specified, and will not change in the future. We claim that this testing and model validation process is an accurate description of most macroeconomic policy problems. Unfortunately, the dynamics produced by this process are not well understood. We make progress on this problem by relating it to a problem that is well understood. In particular, we relate it to the dynamics of constant-gain stochastic approximation algorithms. This enables us to appeal to well known results from the large deviations literature to help us understand the dynamics of testing and model revision. We show that as the agent applies an increasingly stringent specification test, the large deviation properties of the discrete model validation dynamics converge to those of the continuous learning dynamics. This sheds new light on the recent constant-gain learning literature.

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Paper provided by Society for Economic Dynamics in its series 2006 Meeting Papers with number 178.

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Date of creation: 03 Dec 2006
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Handle: RePEc:red:sed006:178
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Society for Economic Dynamics Marina Azzimonti Department of Economics Stonybrook University 10 Nicolls Road Stonybrook NY 11790 USA

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  1. Philippe Aghion & Philippe Bacchetta & Abhijit Banerjee, 2000. "Currency Crises and Monetary Policy in an Economy with Credit Constraints," Working Papers 00.07, Swiss National Bank, Study Center Gerzensee.
  2. Hansen, Lars Peter & Sargent, Thomas J., 1993. "Seasonality and approximation errors in rational expectations models," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 21-55.
  3. Thomas J. Sargent & Noah William, 2005. "Impacts of Priors on Convergence and Escapes from Nash Inflation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 360-391, April.
  4. Brock,W.A. & Durlauf,S.N. & West,K.D., 2004. "Model uncertainty and policy evaluation : some theory and empirics," Working papers 19, Wisconsin Madison - Social Systems.
  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. Timothy Cogley & Thomas Sargent & Riccardo Colacito, 2005. "Benefits from U.S. Monetary Policy Experimentation in the Days of Samuelson," 2005 Meeting Papers 791, Society for Economic Dynamics.
  7. Sargent, Thomas J, 1976. "The Observational Equivalence of Natural and Unnatural Rate Theories of Macroeconomics," Journal of Political Economy, University of Chicago Press, vol. 84(3), pages 631-40, June.
  8. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  9. Timothy Cogley & Riccardo Colacito & Thomas J. Sargent, 2007. "Benefits from U.S. Monetary Policy Experimentation in the Days of Samuelson and Solow and Lucas," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 67-99, 02.
  10. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
  11. Evan W. Anderson & Lars Peter Hansen & Thomas J. Sargent, 2003. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 68-123, 03.
  12. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  13. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695, December.
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