TY - JOUR AU - Mulligan,Casey B. AU - Sala-i-Martin,Xavier TI - A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models JF - National Bureau of Economic Research Technical Working Paper Series VL - No. 116 PY - 1991 Y2 - November 1991 UR - http://www.nber.org/papers/t0116 L1 - http://www.nber.org/papers/t0116.pdf N1 - Author contact info: Casey B. Mulligan University of Chicago Department of Economics 1126 East 59th Street Chicago, IL 60637 Tel: 773/702-9017 Fax: 773/702-8490 E-Mail: c-mulligan@uchicago.edu Xavier Sala-i-Martin Department of Economics Columbia University 420 West 118th Street, 1005 New York, NY 10027 Tel: 212/854-7055 Fax: 212/854-8059 E-Mail: xs23@columbia.edu AB - 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. ER -