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Aggregation over time and the inverse optimal predictor problem for adaptive expectations in continuous time

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  • Lars Peter Hansen
  • Thomas J. Sargent

Abstract

This paper describes the continuous time stochastic process for money and inflation under which Cagan?s adaptive expectations model is optimal. It then analyzes how data formed by sampling money and prices at discrete points in time would behave.

Suggested Citation

  • Lars Peter Hansen & Thomas J. Sargent, 1981. "Aggregation over time and the inverse optimal predictor problem for adaptive expectations in continuous time," Staff Report 74, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:74
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    References listed on IDEAS

    as
    1. Lars Peter Hansen & Thomas J. Sargent, 1980. "Methods for estimating continuous time Rational Expectations models from discrete time data," Staff Report 59, Federal Reserve Bank of Minneapolis.
    2. Marc Nerlove, 1967. "Distributed Lags and Unobserved Components in Economic Time Series," Cowles Foundation Discussion Papers 221, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2016. "Risks for the long run: Estimation with time aggregation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 52-69.
    2. Thomas J. Sargent, 1982. "The Ends of Four Big Inflations," NBER Chapters, in: Inflation: Causes and Effects, pages 41-98, National Bureau of Economic Research, Inc.
    3. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
    4. Tourinho, Octávio A. F ., 1997. "The Demand and Supply of Money Under High Inflation: Brazil 1974-1994," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 17(2), November.
    5. Mercenier, Jean & Michel, Philippe, 2001. "Temporal aggregation in a multi-sector economy with endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1179-1191, August.
    6. Roberto Gómez‐Cram, 2022. "Late to Recessions: Stocks and the Business Cycle," Journal of Finance, American Finance Association, vol. 77(2), pages 923-966, April.
    7. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    8. Christiano, Lawrence J. & Eichenbaum, Martin, 1987. "Temporal aggregation and structural inference in macroeconomics," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 26(1), pages 63-130, January.
    9. Lawrence J. Christiano, 1981. "Rational expectations, hyperinflation, and the demand for money," Working Papers 163, Federal Reserve Bank of Minneapolis.

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