A Note on the Time-Elimination Method for Solving Recursive Dynamic Economic Models
28 Pages Posted: 8 Feb 2001 Last revised: 27 Oct 2024
Date Written: November 1991
Abstract
The Time-Elimination Method for solving recursive dynamic economic models is described. By defining control-like and state-like variables, one can transform the equations of motion describing the economy's evolution through time into a system of differential equations that are independent of time. Unlike the transversality conditions, the boundary conditions for the system in the state-like variable are not asymptotic boundary conditions. In theory, this reformulation of the problem greatly facilitates numerical analysis. In practice, problems which were impossible to solve with a popular algorithm - shooting - can be solved in short order. The reader of this paper need not have any knowledge of numerical mathematics or dynamic programming or be able to draw high dimensional phase diagrams. only a familiarity with the first order conditions of the 'Hamiltonian' method for solving dynamic optimization problems is required. The most natural application of Time-Elimination is to growth models. The method is applied here to three growth models.: the Ramsey/Cass/Koopmans one sector model, Jones & Manuelli's(1990) variant of the Ramsey model, and a two sector growth model in the spirit of Lucas (1988). A very simple - but complete - computer program for numerically solving the Ramsey model is provided.
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Transitional Dynamics in Two-Sector Models of Endogenous Growth
-
Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure
By Timo Trimborn, Karl-josef Koch, ...
-
By Guido Cazzavillan and Ignazio Musu
-
Transitional Dynamics and Endogenous Growth Revisited. The Case of Public Capital
-
Environmental Fiscal Policy in an Endogenous Growth Model with Human Capital
-
The Reduction of Dimension in the Study of Economic Growth Models