Global Solutions to DSGE Models as a Perturbation of a Deterministic Path

Ajevskis, Viktors (2014): Global Solutions to DSGE Models as a Perturbation of a Deterministic Path.

Abstract

This study presents an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i.e. the model where the volatility of the shocks vanishes. If a deterministic path is global in state variables, then so are the constructed solutions to the stochastic model, whereas these solutions are local in the scaling parameter. Under the assumption that a deterministic path is already known the higher order terms in the expansion are obtained recursively by solving linear rational expectations models with time-varying parameters. The present work proposes a method rested on backward recursion for solving this type of models.

• Item Type: MPRA Paper
• Language: English
• Keywords: DSGE, perturbation method, rational expectations models with time-varying parameters, asset pricing model
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D58 - Computable and Other Applied General Equilibrium Models; D - Microeconomics > D9 - Intertemporal Choice

References

Abraham, R., J. Marsden, and T. Ratiu (1988) Manifold, Tensor Analysis, and applications, Applied Mathematical Sciences, 75. Springer-Verlag Berlin Heidelberg.

ADJEMIAN, S., H. BASTANI, M. JUILLARD, F. MIHOUBI, G. PERENDIA, M. RATTO, AND S. VILLEMOT (2013) Dynare: Reference Manual, Version 4, Dynare Working Papers 1, CEPREMAP.

ANDERSON, G. S., MOORE, G. (1985). A Linear Algebraic Procedure for Solving Linear Perfect Foresight Models. Economics Letters, vol. 17, issue 3, pp. 247–252.

BLANCHARD, O. J., KAHN, C. M. (1980). The Solution of Linear Difference Models under Rational Expectations. Econometrica, vol. 48, No. 5, July, pp. 1305–1312.

Borovička J. and Hansen L.P.(2013). Examining Macroeconomic Models through the Lens of Asset Pricing. Working paper.

Burnside C.(1998). Solving asset pricing models with Gaussian shocks. Journal of Economic Dynamics and Control 22, 329-340.

COLLARD, F., JUILLARD, M. (2001). Accuracy of Stochastic Perturbation Methods: the Case of Asset Pricing Models. Journal of Economic Dynamics and Control, No. 25, pp. 979–999.

DEN HAAN, W. J., DE WIND, J. (2012). Nonlinear and Stable Perturbation-Based Approximations. Journal of Economic Dynamics and Control, vol. 36, issue 10, October, pp. 1477–1497.

FAIR, R., TAYLOR, J. (1983). Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models. Econometrica, vol. 51, issue 4, July, pp. 1169–1185.

GASPAR, J., AND K. L. JUDD (1997). Solving Large-Scale Rational-Expectations Models,Macroeconomic Dynamics, 1(01), 45–75.

GOMME, P. and KLEIN, P. (2011). Second-Order Approximation of Dynamic Models without the Use of Tensors. Journal of Economic Dynamics and Control, vol. 35, issue 4, April, pp. 604–615.

HARTMAN, P. (1982). Ordinary Differential Equations. New York : Wiley. 628 p.

Holmes, M. H. (2013). Introduction to Perturbation Methods, Springer-Verlag, Berlin-Heidelberg-New-York-Tokyo.2nd ed. 436 p.

JIN, H., JUDD, K. L. (2002). Perturbation Methods for General Dynamic Stochastic Models. Stanford University Working Paper, April. 44 p.

JUDD, K. L. (1998). Numerical Methods in Economics. Cambridge : The MIT Press. 633 p.

JUDD, K. L., and S.-M. GUU (1997). Asymptotic Methods for Aggregate Growth Models, Journal of Economic Dynamics and Control, 21(6), 1025–1042.

Kim, J., Kim, S., Schaumburg, E.t, and Sims C. (2008). Calculating and Using Second-Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models. Journal of Economic Dynamics and Control, vol. 32, issue 11, November, pp. 3397–3414.

KLEIN, P. (2000). Using the Generalized Schur form to Solve a Multivariate Linear Rational Expectations Model. Journal of Economic Dynamics and Control, No. 24, pp. 1405–1423.

LOMBARDO, G. (2010). On Approximating DSGE Models by Series Expansions. European Central Bank Working Paper Series, No. 1264, November. 31 p.

Mehra, R., Prescott, E.C., 1985. The equity premium: a puzzle. Journal of Monetary Economics 15, 145-161.

SCHMITT-GROHÉ, S., URIBE, M. (2004). Solving Dynamic General Equilibrium Models Using as Second-Order Approximation to the Policy Function. Journal of Economic Dynamics and Control, No. 28, pp. 755–775.

SIMS, C. (2001). Solving Linear Rational Expectations Models. Computational Economics, No. 20, issue 1–2, October, pp. 1–20.

UHLIG, H. (1999). A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily. In: Computational Methods for the Study of Dynamic Economies. Ed. by R. Marimon and A. Scott. Oxford, UK : Oxford University Press, pp. 30–61.