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Formulating and estimating continuous time rational expectations models

  • Lars Peter Hansen
  • Thomas J. Sargent

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
Date of revision:
Handle: RePEc:fip:fedmsr:75
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  1. 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.
  2. 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.
  3. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-41, November.
  4. 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 377-87, March.
  5. 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.
  6. 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.
  7. 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.
  8. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-77, May.
  9. 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.
  10. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-13, May.
  11. R. Dornbusch, 1975. "Exchange Rate Dynamics," Working papers 167, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Thomas J. Sargent, 1980. "Interpreting economic time series," Staff Report 58, Federal Reserve Bank of Minneapolis.
  13. Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-65, July.
  14. 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.
  15. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
  16. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May.
  17. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-81, September.
  18. 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.
  19. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-23, September.
  20. 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.
  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.
  22. 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.
  23. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
  24. 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.
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