Summary
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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References
Anderson, G.: A procedure for differentiating perfect-foresight-model reduced-form coefficients. Journal of Economic Dynamics and Control 11, 465–81 (1987)
Anderson, G., Moore, G.: A linear algebraic procedure for solving linear perfect foresight models. Economic Letters 17, 247–52 (1985)
Bischof, C.H., Bücker, H.M., Lang, B.: Automatic differentiation for computational finance. In: E.J. Kontoghiorghes, B. Rustem, S. Siokos (eds.) Computational Methods in Decision-Making. Springer (2002)
Erceg, C.J., Guerrieri, L., Gust, C.: Can long-run restrictions identify technology shocks? Journal of the European Economic Association 3(6), 1237–1278 (2005)
Erceg, C.J., Henderson, D.W., Levin, A.T.: Optimal monetary policy with staggered wage and price contracts. Journal of Monetary Economics 46(2), 281–313 (2000)
Giles, M.: Monte Carlo evaluation of sensitivities in computational finance. In: E.A. Lipitakis (ed.) HERCMA The 8th Hellenic European Research on Computer Mathematics and its Applications Conference (2007)
Hascoët, L.: Tapenade: A tool for automatic differentiation of programs. In: Proc. 4th European Congress on Computat. Methods, ECCOMAS’2004, Jyvaskyla, Finland (2004)
Hascoët, L., Greborio, R.M., Pascual, V.: Computing adjoints by automatic differentiation with TAPENADE. In: B. Sportisse, F.X. LeDimet (eds.) Ecole INRIA-CEA-EDF “Problemes non-lineaires appliques”. Springer (2005). Forthcoming
Hascoët, L., Pascual, V., Dervieux, D.: Automatic differentiation with TAPENADE. In: V. Selmin (ed.) Notes on Numerical Fluid Dynamics. Springer (2005). Forthcoming
M. Giles, P.G.: Smoking adjoints: Fast Monte Carlo greeks. Risk Magazine 19, 88–92 (2006)
Papadopoulo, T., Lourakis, M.I.A.: Estimating the jacobian of the singular value decomposition: Theory and applications. Lecture Notes in Computer Science 1842/2000, 554–570 (2000)
Smets, F., Wouters, R.: An estimated dynamic stochastic general equilibrium model of the euro area. Journal of the European Economic Association 1(5), 1123–1175 (2003)
Yun, T.: Nominal price rigidity, money supply endogeneity, and business cycles. Journal of Monetary Economics 37, 345–370 (1996)
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Bastani, H., Guerrieri, L. (2008). On the Application of Automatic Differentiation to the Likelihood Function for Dynamic General Equilibrium Models. In: Bischof, C.H., Bücker, H.M., Hovland, P., Naumann, U., Utke, J. (eds) Advances in Automatic Differentiation. Lecture Notes in Computational Science and Engineering, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68942-3_27
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DOI: https://doi.org/10.1007/978-3-540-68942-3_27
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