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

Casey B. Mulligan, Xavier Sala-i-Martin

NBER Technical Working Paper No. 116
Issued in November 1991
NBER Program(s):   EFG

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.

download in pdf format
   (254 K)

email paper

This paper is available as PDF (254 K) or via email.

Machine-readable bibliographic record - MARC, RIS, BibTeX

Users who downloaded this paper also downloaded these:
Mulligan w14729 What Caused the Recession of 2008? Hints from Labor Productivity
Mulligan and Sala-i-Martin w3986 Transitional Dynamics in Two-Sector Models of Endogenous Growth
Mulligan w15681 Aggregate Implications of Labor Market Distortions: The Recession of 2008-9 and Beyond
Barro and Redlick w15369 Macroeconomic Effects from Government Purchases and Taxes
King and Rebelo w3185 Transitional Dynamics and Economic Growth in the Neoclassical Model

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us