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Formulating and estimating continuous time rational expectations models

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Author Info
Lars Peter Hansen
Thomas J. Sargent

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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.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 75.

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Date of creation: 1982
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Handle: RePEc:fip:fedmsr:75

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-75, November. [Downloadable!] (restricted)
  2. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-81, September. [Downloadable!] (restricted)
  3. Wilson, Charles A, 1979. "Anticipated Shocks and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 87(3), pages 639-47, June. [Downloadable!] (restricted)
  4. Sargent, Thomas J, 1981. "Interpreting Economic Time Series," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 213-48, April. [Downloadable!] (restricted)
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  5. 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. [Downloadable!]
  6. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May. [Downloadable!] (restricted)
  7. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-13, May. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
  11. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July. [Downloadable!] (restricted)
  12. 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. [Downloadable!]
  13. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-77, May. [Downloadable!] (restricted)
  14. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-23, September. [Downloadable!] (restricted)
  15. Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-65, July. [Downloadable!] (restricted)
  16. R. Dornbusch, 1975. "Exchange Rate Dynamics," Working papers 167, Massachusetts Institute of Technology (MIT), Department of Economics.
  17. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-41, November. [Downloadable!] (restricted)
  18. Lars Peter Hansen & Thomas J. Sargent, 1981. "A note on Wiener-Kolmogorov prediction formulas for rational expectations models," Staff Report 69, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  19. Lars Peter Hansen & Thomas J. Sargent, 1981. "The dimensionality of the aliasing problem in models with rational spectral densities," Staff Report 72, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  20. 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. [Downloadable!] (restricted)
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  21. 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. [Downloadable!] (restricted)
  22. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis. [Downloadable!]
  23. 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. [Downloadable!] (restricted)
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  24. 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. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Andrew W. Lo, 1986. "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," NBER Technical Working Papers 0059, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Lawrence J. Christiano & Martin Eichenbaum & David Marshall, 1987. "The Permanent Income Hypothesis Revisited," NBER Working Papers 2209, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Lawrence J. Christiano & Martin Eichenbaum, 1987. "Temporal aggregation and structural inference in macroeconomics," Working Papers 306, Federal Reserve Bank of Minneapolis. [Downloadable!]
    Other versions:
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