Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function
Since the seminal papers of Kydland and Prescott (1982) and King, Plosser and Rebelo (1988), it has become commonplace in macroeconomics to approximate the solution to nonlinear, dynamic general equilibrium models using linear methods. Linear approximation methods are useful to characterize certain aspects of the dynamic properties of complicated models. First-order approximation techniques are not however, well suited to handle questions such as welfare comparisons across alternative stochastic of policy environments. The problem with using linearized decision rules to evaluate second-order approximations to the objective function is that some second-order terms of the objective function are ignored when using a linearized decision rule. Such problems do not arise when the policy function is approximated to second-order or higher. In this paper we derive a second order approximation to the policy function of a dynamic, rational expectations model. Our approach follows the perturbation method described in Judd (1998) and developed further by Collard and Juillard(2001). We follow Collard and Juillard closely in notation and methodology. An important difference separates this Paper from the work of Collard and Juillard. Namely, Collard and Juillard apply what they call a bias reduction procedure to capture the fact that the policy function depends on the variance of the underlying shocks. Instead, we explicitly incorporate a scale parameter for the variance of the exogenous shocks as an argument of the policy function. In approximating the policy function, we take a second order Taylor expansion with respect to the state variables as well as this scale parameter. To illustrate its applicability, the method is used to solve the dynamics of a simple neoclassical model. The Paper closes with a brief description of a set of MATLAB programs designed to implement the method.
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- Collard, Fabrice & Juillard, Michel, 1999.
"Accuracy of stochastic perturbuation methods: the case of asset pricing models,"
CEPREMAP Working Papers (Couverture Orange)
- Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
- Kim, Jinill & Kim, Sunghyun Henry, 2003.
"Spurious welfare reversals in international business cycle models,"
Journal of International Economics,
Elsevier, vol. 60(2), pages 471-500, August.
- Jinill Kim & Sunghyun Henry Kim, 1999. "Spurious Welfare Reversals in International Business Cycle Models," Virginia Economics Online Papers 319, University of Virginia, Department of Economics.
- Jinill Kim and Sunghyun Henry Kim, 2001. "Spurious Welfare Reversals in International Business Cycle Models," Computing in Economics and Finance 2001 3, Society for Computational Economics.
- Michael Woodford, 2001.
"Inflation Stabilization and Welfare,"
NBER Working Papers
8071, National Bureau of Economic Research, Inc.
- Baoline Chen & Peter A. Zadrozny, 2003.
"Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem,"
Society for Computational Economics, vol. 21(1_2), pages 45-64, 02.
- Baoline Chen & Peter Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Society for Computational Economics, vol. 21(1), pages 45-64, February.
- Kydland, Finn E & Prescott, Edward C, 1982.
"Time to Build and Aggregate Fluctuations,"
Econometric Society, vol. 50(6), pages 1345-70, November.
- Finn E. Kydland & Edward C. Prescott, 1982. "Web interface for "Time to Build and Aggregate Fluctuations"," QM&RBC Codes 4a, Quantitative Macroeconomics & Real Business Cycles.
- Finn E. Kydland & Edward C. Prescott, 1982. "Executable program for "Time to Build and Aggregate Fluctuations"," QM&RBC Codes 4, Quantitative Macroeconomics & Real Business Cycles.
- Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
- Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
- Jinill Kim & Sunghyun Henry Kim, 1999. "Inaccuracy of Loglinear Approximation in Welfare Calculations: the Case of International Risk Sharing," Computing in Economics and Finance 1999 251, Society for Computational Economics.
- Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
- Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Wiley Blackwell, vol. 37(4), pages 537-42, October.
- King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
- King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
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