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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.

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Bibliographic Info

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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References

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  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. 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.
  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. 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.
  5. 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.
  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. Rusdu Saracoglu & Thomas J. Sargent, 1976. "Seasonality and portfolio balance under rational expectations," Working Papers 58, Federal Reserve Bank of Minneapolis.
  8. 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.
  9. R. Dornbusch, 1975. "Exchange Rate Dynamics," Working papers 167, Massachusetts Institute of Technology (MIT), Department of Economics.
  10. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
  11. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-23, September.
  12. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-77, May.
  13. 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.
  14. 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.
  15. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
  16. 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.
  17. 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.
  18. Thomas J. Sargent, 1980. "Interpreting economic time series," Staff Report 58, Federal Reserve Bank of Minneapolis.
  19. Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-65, July.
  20. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-81, September.
  21. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May.
  22. 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.
  23. Taylor, John B, 1979. "Staggered Wage Setting in a Macro Model," American Economic Review, American Economic Association, vol. 69(2), pages 108-13, May.
  24. 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.
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Citations

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Cited by:
  1. Lawrence J. Christiano & Martin Eichenbaum & David Marshall, 1990. "The permanent income hypothesis revisited," Staff Report 129, Federal Reserve Bank of Minneapolis.
  2. Lawrence J. Christiano & Martin S. Eichenbaum, 1986. "Temporal Aggregation and Structural Inference in Macroeconomics," NBER Technical Working Papers 0060, National Bureau of Economic Research, Inc.
  3. Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.

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