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The Lucas Imperfect Information Model with Imperfect Common Knowledge

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  • Takashi Ui

    (Hitotsubashi University)

Abstract

In the Lucas Imperfect Information model, output responds to unanticipated monetary shocks. We incorporate more general information structures into the Lucas model and demonstrate that output also responds to (dispersedly) anticipated monetary shocks if the information is imperfect common knowledge. Thus, the real effects of money consist of the unanticipated part and the anticipated part, and we decompose the latter into two effects, an imperfect common knowledge effect and a private information effect. We then consider an information structure composed of public and private signals. The real effects disappear when either signal reveals monetary shocks as common knowledge. However, when the precision of private information is fixed, the real effects are small not only when a public signal is very precise but also when it is very imprecise. This implies that a more precise public signal can amplify the real effects and make the economy more volatile.

Suggested Citation

  • Takashi Ui, 2019. "The Lucas Imperfect Information Model with Imperfect Common Knowledge," Working Papers on Central Bank Communication 007, University of Tokyo, Graduate School of Economics.
    • Handle: RePEc:upd:utmpwp:007
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    References listed on IDEAS

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    1. Hyun Song Shin & Jeffery D. Amato, 2003. "Public and private information in monetary policy models," BIS Working Papers 138, Bank for International Settlements.
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    3. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-334, June.
    4. Takashi Ui, 2009. "Bayesian potentials and information structures: Team decision problems revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 271-291, September.
    5. Takashi Ui & Yasunori Yoshizawa, 2013. "Radner's Theorem on Teams and Games with a Continuum of Players," Economics Bulletin, AccessEcon, vol. 33(1), pages 72-77.
    6. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
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    9. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
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    12. Ui, Takashi & Yoshizawa, Yasunori, 2015. "Characterizing social value of information," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 507-535.
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    Cited by:

    1. Kosuke Aoki & Hibiki Ichiue & Tatsushi Okuda, 2019. "Consumers' Price Beliefs, Central Bank Communication, and Inflation Dynamics," Bank of Japan Working Paper Series 19-E-14, Bank of Japan.

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    Keywords

    real effects; neutrality of money; iterated expectations; the Lucas model; imperfect common knowledge;
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