Abstract
We propose to apply to the simulation of general nonlinearrational-expectation models a method where the expectation functions areapproximated through a higher-order Taylor expansion. This method has beenadvocated by Judd (1998) and others for the simulation of stochasticoptimal-control problems and we extend its application to more general cases.The coefficients for the first-order approximation of the expectation functionare obtained using a generalized eigenvalue decomposition as it is usual forthe simulation of linear rational-expectation models. Coefficients forhigher-order terms in the Taylor expansion are then obtained by solving asuccession of linear systems. In addition, we provide a method to reduce abias in the computation of the stochastic equilibrium of such models. Theseprocedures are made available in DYNARE, a MATLAB and GAUSS based simulationprogram.This method is then applied to the simulation of a macroeconomic modelembodying a nonlinear Phillips curve. We show that in this case a quadraticapproximation is sufficient, but different in important ways from thesimulation of a linearized version of the model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, G. and Moore, G. (1985). A linear algebraic procedure for solving linear perfect foresight models. Economic Letters, 17.
Blanchard, O. and Kahn, C. (1980). The solution of linear difference models under rational expectations. Econometrica, 48, 1305–1311.
Debelle, G. and Laxton, D. (1997). Is the Phillips curve really a curve? Some evidence for Canada, the United Kingdom, and the United States. IMF Staff Papers, 44, 249–282.
Gaspard, J. and Judd, K. (1997). Solving large-scale rational expectation models. Macroeconomic Dynamics, 1, 45–75.
Kim, J. and Kim, S.H. (1999). Inaccuracy of loglinear approximation in welfare calculations: The case of international risk sharing. Paper presented at the Fifth Conference of the Society for Computational Economics, Boston College, June 1999.
Klein, P. (1997). Using the generalized Schur form to solve a system of linear expectational difference equations. In Papers on the Macroeconomics of Fiscal Policy. Dissertation, Monograph Series No. 33, Institute for International Economic Studies, Stockholm University.
Judd, K. (1998). Numerical Methods in Economics. The MIT Press, Cambridge.
Judd, K. and Guu, S.-M. (1997). Asymptotic methods for aggregate growth models. Journal of Economic Dynamics and Control, 21, 907–942.
Juillard, M. (1999). The dynamical analysis of forward-looking models. In A. Hughes-Hallett and P. McAdam (eds.), Analysis in Macroeconomic Modelling. Kluwer Academic Publishers, Boston.
Marimon, R. and Scott, A. (eds.) (1999). Computational Methods for the Study of Dynamic Economies. Oxford University Press.
Sims, C. (1995). Solving linear rational expectation models. Mimeo, Yale University, New Haven, CT.
Söderlind, P. (1999). Solution and estimation of RE macromodels with optimal policy. European Economic Review, 43, 813–823.
Zadrozny, P. (1998). An eigenvalue method of undetermined coefficients for solving linear rational expectations models. Journal of Economic Dynamics and Control, 22, 1353–1373.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Collard, F., Juillard, M. A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model. Computational Economics 17, 125–139 (2001). https://doi.org/10.1023/A:1011624124377
Issue Date:
DOI: https://doi.org/10.1023/A:1011624124377