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Speed of convergence of recursive least squares learning with ARMA perceptions

  • Albert Marcet
  • Thomas J. Sargent

This paper fills a gap in the existing literature on least squares learning in linear rational expectations models by studying a setup in which agents learn by fitting ARMA models to a subset of the state variables. This is a natural specification in models with private information because in the presence of hidden state variables, agents have an incentive to condition forecasts on the infinite past records of observables. We study a particular setting in which it suffices for agents to fit a first order ARMA process, which preserves the tractability of a finite dimensional parameterization, while permitting conditioning on the infinite past record. We describe how previous results (Marcet and Sargent [1989a, 1989b] can be adapted to handle the convergence of estimators of an ARMA process in our self--referential environment. We also study ``rates'' of convergence analytically and via computer simulation.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 15.

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Date of creation: May 1992
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Handle: RePEc:upf:upfgen:15
Contact details of provider: Web page: http://www.econ.upf.edu/

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  1. Kuan, C.M. & White, H., 1991. "Strong Convergence of Recursive M-Estimators for Models with Dynamic Latent Variables," Papers 25, Stanford - Institute for Thoretical Economics.
  2. Vives, Xavier, 1993. "How Fast Do Rational Agents Learn?," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 329-47, April.
  3. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-88, August.
  4. Sargent, Thomas J., 1991. "Equilibrium with signal extraction from endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 245-273, April.
  5. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  6. Hansen, Lars Peter & Sargent, Thomas J., 1982. "Instrumental variables procedures for estimating linear rational expectations models," Journal of Monetary Economics, Elsevier, vol. 9(3), pages 263-296.
  7. Marcet, Albert & Sargent, Thomas J, 1989. "Convergence of Least-Squares Learning in Environments with Hidden State Variables and Private Information," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1306-22, December.
  8. Futia, Carl A, 1981. "Rational Expectations in Stationary Linear Models," Econometrica, Econometric Society, vol. 49(1), pages 171-92, January.
  9. Sargent, Thomas J & Wallace, Neil, 1973. "Rational Expectations and the Dynamics of Hyperinflation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 328-50, June.
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