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Résolution d'un modèle macroéconomique avec anticipations rationnelles

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  • Jean-Pierre Laffargue

Abstract

The simulation of a model with rational expectations requires the solution of a system of difference equations with initial and terminal conditions over an infinite time period. This paper first considers the linear case and investigates the kind of errors which result from the substitution of a finite horizon to the infinite one. The results which are found are applied to the evaluation of the various methods of choice of this horizon and the terminal conditions which are related to it, when the model is nonlinear. Then the paper gives a short review of the methods of simulation which are currently used in macroeconomics. Finally it presents a method of relaxation which has not been used yet in economics: this method rests upon the algorithm of Newton-Raphson and the triangulation of a large matrix by Gauss' elimination.

Suggested Citation

  • Jean-Pierre Laffargue, 1990. "Résolution d'un modèle macroéconomique avec anticipations rationnelles," Annals of Economics and Statistics, GENES, issue 17, pages 97-119.
    • Handle: RePEc:adr:anecst:y:1990:i:17:p:97-119
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    1. Cacciatore, Matteo & Duval, Romain & Fiori, Giuseppe & Ghironi, Fabio, 2016. "Market reforms in the time of imbalance," Journal of Economic Dynamics and Control, Elsevier, vol. 72(C), pages 69-93.
    2. Bergin, Paul R., 2022. "Currency undervaluation and comparative advantage," European Economic Review, Elsevier, vol. 150(C).
    3. Cacciatore, Matteo & Fiori, Giuseppe & Ghironi, Fabio, 2016. "Market deregulation and optimal monetary policy in a monetary union," Journal of International Economics, Elsevier, vol. 99(C), pages 120-137.
    4. Javier Andres & Oscar Arce & Dominik Thaler & Carlos Thomas, 2020. "When Fiscal Consolidation Meets Private Deleveraging," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 214-233, July.
    5. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    6. Helton Saulo & Leandro Rêgo & Jose Divino, 2013. "Fiscal and monetary policy interactions: a game theory approach," Annals of Operations Research, Springer, vol. 206(1), pages 341-366, July.
    7. Coenen, Günter & Montes-Galdón, Carlos & Schmidt, Sebastian, 2021. "Macroeconomic stabilisation and monetary policy effectiveness in a low-interest-rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 132(C).
    8. Günter Coenen & Carlos Montes‐Galdón & Frank Smets, 2023. "Effects of State‐Dependent Forward Guidance, Large‐Scale Asset Purchases, and Fiscal Stimulus in a Low‐Interest‐Rate Environment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 55(4), pages 825-858, June.
    9. Cacciatore, Matteo, 2014. "International trade and macroeconomic dynamics with labor market frictions," Journal of International Economics, Elsevier, vol. 93(1), pages 17-30.
    10. Jean-Pierre Laffargue, 1997. "Chômage des non qualifiés et progrès technique. Le modèle "Charlotte"," Revue Économique, Programme National Persée, vol. 48(5), pages 1311-1335.
    11. Cacciatore, Matteo & Duval, Romain & Fiori, Giuseppe & Ghironi, Fabio, 2016. "Short-term pain for long-term gain: Market deregulation and monetary policy in small open economies," Journal of International Money and Finance, Elsevier, vol. 68(C), pages 358-385.
    12. Gomes, Sandra, 2018. "Euro area structural reforms in times of a global crisis," Journal of Macroeconomics, Elsevier, vol. 55(C), pages 28-45.
    13. 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.

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