Projection methods for solving aggregate growth models

Abstract We describe a general numerical approach, the projection method, to solve operator equations which arise in economic models. Principles from numerical analysis are then used to develop efficient implementations of the projection method for solving aggregate growth models. Since any numerical approach will involve error, we derive error measures which are related to optimization errors by agents and argue that the numerical approximations can be viewed as equilibria with boundedly rational agents. The results are programs which run hundreds of times faster than competing methods in the literature while achieving high accuracy.

[1]  Albert Marcet,et al.  Solving the Stochastic Growth Model by Parameterizing Expectations , 1990 .

[2]  R. Lucas.  ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[3]  M. A. Krasnoselʹskii,et al.  Geometrical Methods of Nonlinear Analysis , 1984 .

[4]  T. J. Rivlin.  Chebyshev polynomials : from approximation theory to algebra and number theory , 1990 .

[5]  Lawrence J. Christiano.  Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration , 1990 .

[6]  Harald Uhlig,et al.  Solving Nonlinear Stochastic Growth Models: a Comparison of Alternative Solution Methods , 1989 .

[7]  Leonard J. Mirman,et al.  Optimal economic growth and uncertainty: The discounted case , 1972 .

[8]  Brian D. Wright,et al.  The Roles of Public and Private Storage in Managing Oil Import Disruptions , 1982 .

[9]  G. Golub,et al.  Scientific Computing and Differential Equations: An Introduction to Numerical Methods , 1991 .

[10]  Ellen R. McGrattan,et al.  Solving the Stochastic Growth Model by Linear-Quadratic Approximation , 1990 .

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

[12]  E. Prescott,et al.  Recursive Competitive Equilibrium: The Case of Homogeneous Households , 1980 .

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

[14]  Marianne Baxter,et al.  Solving the Stochastic Growth Model by a Discrete-State-Space, Euler-Equation Approach , 1990 .

[15]  K. Judd,et al.  Taxation and Uncertainty , 1989 .

[16]  Wilbur John Coleman.  Solving the Stochastic Growth Model by Policy-Function Iteration , 1990 .

[17]  A. Bensoussan.  Perturbation Methods in Optimal Control , 1988 .

[18]  M. Magill.  A local analysis of N-sector capital accumulation under uncertainty , 1977 .

[19]  Kendall E. Atkinson.  An introduction to numerical analysis , 1978 .

[20]  R. Mehra,et al.  On some computational aspects of equilibrium business cycle theory , 1988 .

[21]  George Tauchen.  Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations , 1990 .

[22]  Christopher A. Sims,et al.  Solving the Stochastic Growth Model by Backsolving With a Particular Nonlinear Form for the Decision Rule , 1990 .

[23]  Brian D. Wright,et al.  The Economic Role of Commodity Storage , 1982 .

[24]  Brian D. Wright,et al.  Storage and Commodity Markets , 1991 .

[25]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[26]  J. Danthine,et al.  Stochastic Properties of Fast vs. Slow Growing Economies , 1981 .

[27]  John Rust.  Maximum likelihood estimation of discrete control processes , 1988 .

[28]  P. M. Prenter.  Splines and variational methods , 1975 .