A Note on the Time-Elimination Method for Solving Recursive Dynamic Economic Models

28 Pages Posted: 8 Feb 2001

See all articles by Casey B. Mulligan

Casey B. Mulligan

University of Chicago; National Bureau of Economic Research (NBER)

Xavier Sala-i-Martin

Columbia University, Graduate School of Arts and Sciences, Department of Economics

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

Mulligan, Casey B. and Sala-i-Martin, Francesc Xavier, A Note on the Time-Elimination Method for Solving Recursive Dynamic Economic Models (November 1991). NBER Working Paper No. t0116. Available at SSRN: https://ssrn.com/abstract=236665

Casey B. Mulligan (Contact Author)

University of Chicago ( email )

1126 East 59th Street
Chicago, IL 60637
United States
773-702-9017 (Phone)
773-702-8490 (Fax)

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

Francesc Xavier Sala-i-Martin

Columbia University, Graduate School of Arts and Sciences, Department of Economics ( email )

420 W. 118th Street
New York, NY 10027
United States
212-854-7055 (Phone)

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