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Analytic Derivatives for Linear Rational Expectations Models

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  • Andrew P. Blake

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Abstract

This paper sets out the analytic solution for the calculation of exact derivatives in linear rational expectations models with reference to the optimal simple rule problem. We argue that there are substantial computational advantages of using analytic derivatives and compare the likely computational costs of using approximate and exact derivatives when calculating optimal coefficients for simple feedback rules. A specific algorithm for finite time optimization is also outlined, which will reduce the computational time required and is simple to implement. We discuss modifications to allow for stochastic models.

Suggested Citation

  • Andrew P. Blake, 2004. "Analytic Derivatives for Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 77-96, August.
  • Handle: RePEc:kap:compec:v:24:y:2004:i:1:p:77-96
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    References listed on IDEAS

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    5. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
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    8. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    9. Dennis, Richard, 2004. "Solving for optimal simple rules in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(8), pages 1635-1660, June.
    10. Gable, Jeff & van Norden, Simon & Vigfusson, Robert, 1997. "Analytical Derivatives for Markov Switching Models," Computational Economics, Springer;Society for Computational Economics, vol. 10(2), pages 187-194, May.
    11. Blake, Andrew P., 2000. "Solution and control of linear rational expectations models with structural effects from future instruments," Economics Letters, Elsevier, vol. 67(3), pages 283-288, June.
    12. Zadrozny, Peter, 1988. "Analytic Derivatives for Estimation of Discrete-Time,," Econometrica, Econometric Society, vol. 56(2), pages 467-472, March.
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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01053484, HAL.
    2. Andrew P. Blake & Tatiana Kirsanova, 2012. "Discretionary Policy and Multiple Equilibria in LQ RE Models," Review of Economic Studies, Oxford University Press, vol. 79(4), pages 1309-1339.
    3. Stradi-Granados, Benito A. & Haven, Emmanuel, 2010. "The use of interval arithmetic in solving a non-linear rational expectation based multiperiod output-inflation process model: The case of the IN/GB method," European Journal of Operational Research, Elsevier, vol. 203(1), pages 222-229, May.
    4. Andrew P Blake & Fabrizio Zampolli, 2006. "Optimal monetary policy in Markov-switching models with rational expectations agents," Bank of England working papers 298, Bank of England.
    5. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Working Papers halshs-01044432, HAL.
    6. Blake, Andrew P. & Zampolli, Fabrizio, 2011. "Optimal policy in Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1626-1651, October.

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