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The Endogenous Kalman Filter

Author

Listed:
  • Brad Baxter

    (Department of Economics, Mathematics & Statistics, Birkbeck)

  • Liam Graham
  • Stephen Wright

    (Department of Economics, Mathematics & Statistics, Birkbeck)

Abstract

We relax the assumption of full information that underlies most dynamic general equilibrium models, and instead assume agents optimally form estimates of the states from an incomplete information set. We derive a version of the Kalman filter that is endogenous to agents' optimising decisions, and state conditions for its convergence. We show the (restrictive) conditions under which the endogenous Kalman filter will at least asymptotically reveal the true states. In general we show that incomplete information can have significant implications for the time-series properties of economies. We provide a Matlab toolkit which allows the easy implementation of models with incomplete information.

Suggested Citation

  • Brad Baxter & Liam Graham & Stephen Wright, 2007. "The Endogenous Kalman Filter," Birkbeck Working Papers in Economics and Finance 0719, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:0719
    as

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    File URL: https://eprints.bbk.ac.uk/id/eprint/26893
    File Function: First version, 2007
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    References listed on IDEAS

    as
    1. Graham, Liam & Wright, Stephen, 2010. "Information, heterogeneity and market incompleteness," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 164-174, March.
    2. Aoki, Kosuke, 2003. "On the optimal monetary policy response to noisy indicators," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 501-523, April.
    3. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    4. Svensson, Lars E. O. & Woodford, Michael, 2003. "Indicator variables for optimal policy," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 691-720, April.
    5. McCallum, Bennett T., 1998. "Solutions to linear rational expectations models: a compact exposition," Economics Letters, Elsevier, vol. 61(2), pages 143-147, November.
    6. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    7. 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.
    8. Bomfim, Antulio N., 2001. "Measurement error in general equilibrium: the aggregate effects of noisy economic indicators," Journal of Monetary Economics, Elsevier, vol. 48(3), pages 585-603, December.
    9. Liam Graham & Stephen Wright, 2007. "Information, heterogeneity and market incompleteness in the stochastic growth model," CDMA Conference Paper Series 0704, Centre for Dynamic Macroeconomic Analysis.
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    Cited by:

    1. Hauk, Esther & Lanteri, Andrea & Marcet, Albert, 2021. "Optimal policy with general signal extraction," Journal of Monetary Economics, Elsevier, vol. 118(C), pages 54-86.
    2. Eric R. Young & Ponpoje Porapakkarm, 2008. "Information Heterogeneity in the Macroeconomy," 2008 Meeting Papers 67, Society for Economic Dynamics.

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    More about this item

    Keywords

    Dynamic general equilibrium; Kalman filter; imperfect information; signal extraction;
    All these keywords.

    JEL classification:

    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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