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Formulating and estimating continuous time rational expectations models

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  • Lars Peter Hansen
  • Thomas J. Sargent

Abstract

This paper proposes a method for estimating the parameters of continuous time, stochastic rational expectations models from discrete time observations. The method is important since various heuristic procedures for deducing the implications for discrete time data of continuous time models, such as replacing derivatives with first differences, can sometimes give rise to very misleading conclusions about parameters. Our proposal is to express the restrictions imposed by the rational expectations model on the continuous time process generating the observable variables. Then the likelihood function of a discrete time sample of observations from this process is obtained. Parameter estimates are computed by maximizing the likelihood function with respect to the free parameters of the continuous time model.

Suggested Citation

  • Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:75
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    References listed on IDEAS

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    1. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-681, September.
    2. Wilson, Charles A, 1979. "Anticipated Shocks and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 87(3), pages 639-647, June.
    3. 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.
    4. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-113, May.
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    6. Lars Peter Hansen & Thomas J. Sargent, 1983. "Identification of continuous time rational expectations models from discrete time data," Staff Report 73, Federal Reserve Bank of Minneapolis.
    7. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
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    10. Sargent, Thomas J, 1981. "Interpreting Economic Time Series," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 213-248, April.
    11. Hansen, Lars Peter & Sargent, Thomas J, 1983. "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, Econometric Society, vol. 51(2), pages 377-387, March.
    12. Hansen, Lars Peter & Sargent, Thomas J, 1983. "Aggregation over Time and the Inverse Optimal Predictor Problem for Adaptive Expectations in Conginuous Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 1-20, February.
    13. Milton Friedman, 1962. "The Interpolation of Time Series by Related Series," NBER Books, National Bureau of Economic Research, Inc, number frie62-1, June.
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    17. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    18. Hansen, Lars Peter & Sargent, Thomas J., 1981. "A note on Wiener-Kolmogorov prediction formulas for rational expectations models," Economics Letters, Elsevier, vol. 8(3), pages 255-260.
    19. Saracoglu, Rusdu & Sargent, Thomas J., 1978. "Seasonality and portfolio balance under rational expectations," Journal of Monetary Economics, Elsevier, vol. 4(3), pages 435-458, August.
    20. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
    21. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
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    25. R. Dornbusch, 1975. "Exchange Rate Dynamics," Working papers 167, Massachusetts Institute of Technology (MIT), Department of Economics.
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    Cited by:

    1. Christiano, Lawrence J & Eichenbaum, Martin & Marshall, David, 1991. "The Permanent Income Hypothesis Revisited," Econometrica, Econometric Society, vol. 59(2), pages 397-423, March.
    2. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
    3. 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.

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