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Analytic Derivatives for Linear Rational Expectations Models

  • Andrew P. Blake

    ()

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.

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Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 24 (2004)
Issue (Month): 1 (08)
Pages: 77-96

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Handle: RePEc:kap:compec:v:24:y:2004:i:1:p:77-96
Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=100248

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  1. Gable, Jeff & van Norden, Simon & Vigfusson, Robert, 1997. "Analytical Derivatives for Markov Switching Models," Computational Economics, Society for Computational Economics, vol. 10(2), pages 187-94, May.
  2. Athanasios Orphanides & John C. Williams, 2005. "Inflation scares and forecast-based monetary policy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 498-527, April.
  3. Michael Woodford, 2003. "Optimal Interest-Rate Smoothing," Review of Economic Studies, Oxford University Press, vol. 70(4), pages 861-886.
  4. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  5. Nicoletta Batini & Edward Nelson, 1999. "Optimal Horizons for Inflation Targeting," Computing in Economics and Finance 1999 1052, Society for Computational Economics.
  6. Richard Dennis, 2000. "Solving for optimal simple rules in rational expectations models," Working Paper Series 2000-14, Federal Reserve Bank of San Francisco.
  7. Leith, Campbell B & Wren-Lewis, Simon, 1997. "Interest Rate Feedback Rules in an Open Economy with Forward Looking Inflation," Discussion Papers 9704, Exeter University, Department of Economics.
  8. Karakitsos, E. & Rustem, B., 1984. "Optimally derived fixed rules and indicators," Journal of Economic Dynamics and Control, Elsevier, vol. 8(1), pages 33-64, October.
  9. Currie, David, 1985. "Macroeconomic Policy Design and Control Theory-A Failed Partnership?," Economic Journal, Royal Economic Society, vol. 95(378), pages 285-306, June.
  10. 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.
  11. Clare, Andrew, et al, 1998. "Macroeconomic Shocks and the CAPM: Evidence from the UK Stockmarket," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 3(2), pages 111-26, April.
  12. Fiorentini,G. & Calzolari,G. & Panattoni,L., 1995. "Analytic Derivatives and the Computation of Garch Estimates," Papers 9519, Centro de Estudios Monetarios Y Financieros-.
  13. Rustem, B. & Zarrop, M.B., 1979. "A newton-type method for the optimization and control of non-linear econometric models," Journal of Economic Dynamics and Control, Elsevier, vol. 1(3), pages 283-300.
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