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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.

Suggested Citation

  • 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.
  • Handle: RePEc:fip:fedmsr:59
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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. 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.
    3. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
    4. 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.
    5. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-577, May.
    6. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis.
    7. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-823, September.
    8. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    9. 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.
    10. 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.
    11. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    12. Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-665, July.
    13. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    14. Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, vol. 75, pages 321-321.
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    Citations

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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. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
    3. Mercenier, Jean & Michel, Philippe, 2001. "Temporal aggregation in a multi-sector economy with endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1179-1191, August.
    4. 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.
    5. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis.
    6. 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.
    7. 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.
    8. Lawrence J. Christiano, 1987. "Estimating continuous time rational expectations models in frequency domain: a case study," Working Papers 301, Federal Reserve Bank of Minneapolis.
    9. 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.
    10. 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.
    11. Lawrence J. Christiano, 1986. "Temporal aggregation bias and government policy evaluation," Working Papers 302, Federal Reserve Bank of Minneapolis.

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