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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. Sargent, Thomas J, 1981. "Interpreting Economic Time Series," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 213-248, April.
    4. 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.
    5. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-113, May.
    6. Treadway, Arthur B., 1970. "Adjustment costs and variable inputs in the theory of the competitive firm," Journal of Economic Theory, Elsevier, vol. 2(4), pages 329-347, December.
    7. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
    8. 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.
    9. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-823, September.
    10. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, 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., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    13. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
    14. 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.
    15. 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.
    16. 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.
    17. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    18. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    19. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
    20. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    21. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-577, May.
    22. Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-665, July.
    23. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    24. R. Dornbusch, 1975. "Exchange Rate Dynamics," Working papers 167, Massachusetts Institute of Technology (MIT), Department of Economics.
    25. Taylor, John B., 1980. "Output and price stability: An international comparison," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 109-132, May.
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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(02), 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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