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Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations

Опубликовано на портале: 01-07-2004
Journal of Business and Economic Statistics. 1990.  Vol. 8. No. 1. P. 49-51. 
Solution algorithm that uses value-function iterations on a discrete state space is presented for the capital growth model set forth by Taylor and Uhlig (1990). The grid for the exogenous process is set using the quadrature technique, and the grid for the endogenous capital process is set using a simple equispaced scheme in logarithms. The discretized model is then solved with value-function iterations. The algorithm is coded in GAUSS and run on a Compaq 386-25 computer. It appears to be very successful. When applied to a slightly different version of the problem in which the exact solution is known, the algorithm can approximate the exact solution with 4-digit accuracy and with a computational time of about 40 to 45 minutes. While the algorithm approximates the decision rule closely, it still might appear to do poorly on criteria that test for statistical violations of orthogonality conditions implied by the Euler equation. This is because a value-function approach does not impose the Euler equation explicitly on the discrete model.