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Methods for estimating continuous time Rational Expectations models from discrete time data

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  • Lars Peter Hansen
  • Thomas J. Sargent

Abstract

This paper describes methods for estimating the parameters of continuous time linear stochastic rational expectations models from discrete time observations. The economic models that we study are continuous time, multiple variable, stochastic, linear-quadratic rational expectations models. The paper shows how such continuous time models can properly be used to place restrictions on discrete time data. Various heuristic procedures for deducing the implications for discrete time data of these models, such as replacing derivatives with first differences, can sometimes give rise to very misleading conclusions about parameters. The idea is to express the restrictions imposed by the rational expectations model on the continuous time process of the observable variables. Then the likelihood function of a discrete-time sample of observations from this process is obtained. Estimators are obtained 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 59.

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Date of creation: 1980
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Handle: RePEc:fip:fedmsr:59

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References

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  1. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  2. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-81, September.
  3. Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-65, July.
  4. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis.
  5. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-41, November.
  6. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May.
  7. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-77, May.
  8. 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.
  9. 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.
  10. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
  11. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-23, September.
  12. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
  13. Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, vol. 75, pages 321.
  14. 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 & Robert J. Vigfusson, 1999. "Maximum likelihood in the frequency domain: a time to build example," Working Paper 9901, Federal Reserve Bank of Cleveland.
  2. 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.
  3. Lawrence J. Christiano & Martin Eichenbaum & David Marshall, 1987. "The Permanent Income Hypothesis Revisited," NBER Working Papers 2209, National Bureau of Economic Research, Inc.
  4. 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.
  5. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis.
  6. Jean Mercenier & Philippe Michel, 1995. "Temporal aggregation in a multi-sector economy with endogenous growth," Working Papers 554, Federal Reserve Bank of Minneapolis.
  7. Lawrence J. Christiano, 1987. "Estimating continuous time rational expectations models in frequency domain: a case study," Working Papers 301, Federal Reserve Bank of Minneapolis.
  8. Christiano, Lawrence J. & Vigfusson, Robert J., 2003. "Maximum likelihood in the frequency domain: the importance of time-to-plan," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 789-815, May.
  9. Lawrence J. Christiano, 1986. "Temporal aggregation bias and government policy evaluation," Working Papers 302, Federal Reserve Bank of Minneapolis.
  10. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
  11. 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.

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