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.