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On the application of automatic differentiation to the likelihood function for dynamic general equilibrium models

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Author Info

  • Houtan Bastani
  • Luca Guerrieri

Abstract

A key application of automatic differentiation (AD) is to facilitate numerical optimization problems. Such problems are at the core of many estimation techniques, including maximum likelihood. As one of the first applications of AD in the field of economics, we used Tapenade to construct derivatives for the likelihood function of any linear or linearized general equilibrium model solved under the assumption of rational expectations. We view our main contribution as providing an important check on finite-difference (FD) numerical derivatives. We also construct Monte Carlo experiments to compare maximum-likelihood estimates obtained with and without the aid of automatic derivatives. We find that the convergence rate of our optimization algorithm can increase substantially when we use AD derivatives.

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File URL: http://www.federalreserve.gov/pubs/ifdp/2008/920/default.htm
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File URL: http://www.federalreserve.gov/pubs/ifdp/2008/920/ifdp920.pdf
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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 920.

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Date of creation: 2008
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Handle: RePEc:fip:fedgif:920

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Keywords: Econometric models ; Equilibrium (Economics);

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  1. Anderson, Gary, 1987. "A procedure for differentiating perfect-foresight-model reduced-from coefficients," Journal of Economic Dynamics and Control, Elsevier, vol. 11(4), pages 465-481, December.
  2. Andrew Levin & Christopher J. Erceg & Dale W. Henderson, 1999. "Optimal Monetary Policy with Staggered Wage and Price Contracts," Computing in Economics and Finance 1999 1151, Society for Computational Economics.
  3. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
  4. Christopher J. Erceg & Luca Guerrieri, 2004. "Can Long-Run Restrictions Identify Technology Shocks?," Computing in Economics and Finance 2004 3, Society for Computational Economics.
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Cited by:
  1. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 642-654.
  2. Tore Selland Kleppe & Jun Yu & Hans J. Skaug, 2011. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers CoFie-04-2011, Sim Kee Boon Institute for Financial Economics.
  3. Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
  4. Adolfson, Malin & Lindé, Jesper, 2011. "Parameter Identification in a Estimated New Keynesian Open Economy Model," Working Paper Series 251, Sveriges Riksbank (Central Bank of Sweden).

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