Parametric Path Method: An alternative to Fair-Taylor and L-B-J for solving perfect foresight models

The parametric path method applies projection methods to compute the equilibrium path of economic variables in infinite-horizon dynamic models. We exploit the special structure of economic time paths common in such models. This structure drastically reduces dimensionality and reduces computing time. We apply the parametric method to a simple example which illustrates how one applies the ideas to produce an efficient implementation.

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

[2]  Raouf Boucekkine,et al.  An alternative methodology for solving nonlinear forward-looking models , 1995 .

[3]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[4]  R. Fair,et al.  Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rationalexpectations Models , 1980 .

[5]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[6]  M. Miranda,et al.  The Effects of Commodity Price Stabilization Programs , 1988 .

[7]  Michel Juillard,et al.  Dynare: a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm , 1996 .

[8]  Brian D. Wright,et al.  The Welfare Effects of the Introduction of Storage , 1984 .

[9]  A. H. Hallett,et al.  Simple reordering techniques for expanding the convergence radius of first-order iterative techniques , 1998 .

[10]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[11]  R. Gustafson.  Carryover levels for grains: A method for determining amounts that are optimal under specified conditions , 1958 .

[12]  Paul Fisher,et al.  Rational expectations in macroeconomic models , 1992 .

[13]  Philippe Michel,et al.  A criterion for time aggregation in intertemporal dynamic models , 1994, Math. Program..

[14]  Kenneth L. Judd,et al.  Projection methods for solving aggregate growth models , 1992 .

[15]  Jean-Pierre Laffargue,et al.  Rsolution d'un modle macroconomique avec anticipations rationnelles , 1990 .

[16]  Philippe Michel,et al.  Discrete-time finite horizon approximation of infinite horizon optimization problems with steady-state invariance , 1994 .

[17]  Manfred Gilli,et al.  Krylov methods for solving models with forward-looking variables , 1998 .

[18]  A. H. Hallett,et al.  Efficient solution techniques for dynamic non-linear rational expectations models , 1986 .

[19]  Michel Juillard,et al.  An algorithm competition: First-order iterations versus Newton-based techniques , 1998 .

[20]  S. Hall.  On the Solution of Large Economic Models with Consistent Expectations , 1985 .