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Optimal Policy with General Signal Extraction

Author

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  • Esther Hauk
  • Andrea Lanteri
  • Albert Marcet

Abstract

We study optimal policy when the planner has partial information in a general setup where observed signals are endogenous to policy. In this context, signal extraction and policy have to be determined jointly. We derive a general non-standard first order condition of optimality from first principles and we use it to find numerical solutions. This first order condition allows us to identify widely-used special cases in the literature in which the signal extraction and the optimal decision problems can be solved separately, using the well-known separation principle. Our general setup, which does not feature any separation, is relevant for most available dynamic models in macro. We apply our results to a model of fiscal policy and show that optimal taxes are often a very non-linear function of observed hours, calling for tax smoothing in normal times, but for a strong fiscal reaction to output in a deeper recession. This non-linearity arises because signal extraction interacts differently with optimal policy depending on the range of observed signals. The non-linearity is stronger near the top of the Laffer curve or near a debt limit. In a fully dynamic model taxes react with a delay to adverse deficit shocks due to partial information, and this can lead to larger low-frequency fluctuations.

Suggested Citation

  • Esther Hauk & Andrea Lanteri & Albert Marcet, 2016. "Optimal Policy with General Signal Extraction," Working Papers 932, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:932
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    File URL: https://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/932.pdf
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Sargent, Thomas J., 2012. "Three types of ambiguity," Journal of Monetary Economics, Elsevier, vol. 59(5), pages 422-445.
    2. Narayana R. Kocherlakota, 2010. "The New Dynamic Public Finance," Economics Books, Princeton University Press, edition 1, number 9222, March.
    3. Pearlman, Joseph & Currie, David & Levine, Paul, 1986. "Rational expectations models with partial information," Economic Modelling, Elsevier, vol. 3(2), pages 90-105, April.
    4. Mirman, Leonard J & Samuelson, Larry & Urbano, Amparo, 1993. "Monopoly Experimentation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 549-563, August.
    5. Svensson, Lars E. O. & Woodford, Michael, 2004. "Indicator variables for optimal policy under asymmetric information," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 661-690, January.
    6. Ellison, Martin & Valla, Natacha, 2001. "Learning, uncertainty and central bank activism in an economy with strategic interactions," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 153-171, August.
    7. Hansen, Lars Peter & Sargent, Thomas J., 2012. "Three types of ambiguity," Journal of Monetary Economics, Elsevier, vol. 59(5), pages 422-445.
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    More about this item

    Keywords

    optimal policy; partial information; separation; calculus of variations; fiscal policy;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General
    • H60 - Public Economics - - National Budget, Deficit, and Debt - - - General

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