Solving DSGE models with perturbation methods and a change of variables

Abstract This paper explores the application of the changes of variables technique to solve the stochastic neoclassical growth model. We use the method of Judd [2003. Perturbation methods with nonlinear changes of variables. Mimeo, Hoover Institution] to change variables in the computed policy functions that characterize the behavior of the economy. We report how the optimal change of variables reduces the average absolute Euler equation errors of the solution of the model by a factor of three. We also demonstrate how changes of variables correct for variations in the volatility of the economy even if we work with first-order policy functions and how we can keep a linear representation of the laws of motion of the model if we use a nearly optimal transformation. We discuss how to apply our results to estimate dynamic equilibrium economies.

[1]  K. Judd.  Numerical methods in economics , 1998 .

[2]  S. Boragan Aruoba,et al.  Finite Elements Method , 2003 .

[3]  Jesús Fernández-Villaverde,et al.  Comparing Solution Methods for Dynamic Equilibrium Economies , 2003 .

[4]  S. Boragan Aruoba,et al.  Linear and Log-Linear Approximation , 2003 .

[5]  Harald Uhlig,et al.  A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily , 1995 .

[6]  R. Hall.  The Dynamic Effects of Fiscal Policy in an Economy with Foresight , 1971 .

[7]  Ching-Sheng Mao,et al.  How well do linear approximation methods work , 1992 .

[8]  Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function , 2002 .

[9]  Stephanie Schmitt-Grohé,et al.  The Perils of Taylor Rules , 1999, J. Econ. Theory.

[10]  C. Sims.  Matlab Code for Solving Linear Rational Expectations Models , 2001 .

[11]  Manuel S. Santos.  ACCURACY OF NUMERICAL SOLUTIONS USING THE EULER EQUATION RESIDUALS , 2000 .

[12]  Finn E. Kydland,et al.  Time to Build and Aggregate Fluctuations , 1982 .

[13]  Sy-Ming Guu,et al.  Asymptotic methods for aggregate growth models , 1997 .

[14]  P. Klein,et al.  Using the generalized Schur form to solve a multivariate linear rational expectations model q , 1997 .

[15]  C. Sims.  Solving Linear Rational Expectations Models , 2002 .

[16]  S. Boragan Aruoba,et al.  Perturbation (2nd and 5th order) , 2003 .

[17]  Charles I. Plosser,et al.  Growth and Business Cycles I. The Basic Neoclassical Model , 1988 .

[18]  Albert Marcet,et al.  Accuracy in Simulations , 1994 .

[19]  S. Boragan Aruoba,et al.  Value Function Iteration , 2003 .

[20]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[21]  Sergio Rebelo,et al.  Production, Growth and Business Cycles: Technical Appendix , 2002 .

[22]  Manuel S. Santos,et al.  Convergence Properties of the Likelihood of Computed Dynamic Models , 2004 .

[23]  Thomas F. Cooley.  Frontiers of business cycle research , 1995 .

[24]  Edward C. Prescott,et al.  Economic Growth and Business Cycles , 2020, Frontiers of Business Cycle Research.

[25]  Charles M. Kahn,et al.  THE SOLUTION OF LINEAR DIFFERENCE MODELS UNDER RATIONAL EXPECTATIONS , 1980 .

[26]  T. J. Rivlin.  The Chebyshev polynomials , 1974 .

[27]  George Tauchen,et al.  Finite state markov-chain approximations to univariate and vector autoregressions , 1986 .

[28]  Charles I. Plosser,et al.  Production, growth and business cycles , 1988 .

[29]  C. Sims,et al.  Calculating and Using Second Order Accurate Solutions of Discrete Time , 2003 .

[30]  Jesús Fernández-Villaverde,et al.  Convergence Properties of the Likelihood of Computed Dynamic Models , 2004 .

[31]  Andrew Scott,et al.  Computational Methods for the Study of Dynamic Economies , 1998 .

[32]  Christopher A. Sims,et al.  SECOND ORDER ACCURATE SOLUTION OF DISCRETE TIME DYNAMIC EQUILIBRIUM MODELS , 2003 .

[33]  Toni Braun.  A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily , 1995 .

[34]  Sy-Ming Guu,et al.  Perturbation Solution Methods for Economic Growth Models , 1993 .

[35]  Michael Woodford,et al.  Interest and Prices , 2011 .