"PROJECTIONS PEA"

These programs use the techniques described in Ken Judd's 1992 "Journal of Economic Theory" article to solve the standard growth model using parameterized expectations. Another good reference for the solution methods used in these programs is the working paper "Algorithms for Solving Dynamic Models with Occasionally Binding Constraints" by Larry Christiano and Jonas Fisher. All algorithms have the following properties.

1. They use the tensor method to approximate the conditional expectation with orthogonal Chebyshev polynomials.

2. The coefficients of the approximating function are such that they minimize the distance between the approximating function and the numerically calculated conditional expectation at a set of grid points.

3. The grid points are Chebyshev nodes.

4. The numerical integration procedure used to calculate the conditional expectation is Hermite Gaussian Quadrature. In my experience it is easier to obtain an accurate solution fast with quadrature methods than with Monte Carlo methods. An example of a PEA algorithm that uses Monte Carlo methods can be found at Simulations PEA

5. The "iterative" programs iterate on a projection procedure to find the coefficients of the approximating function.

6. The "equation-solver" programs use a nonlinear equation solver to find the value of the coefficients at which the approximating function equal the numerically calculated conditional expectation.

These programs are written by Christian Haefke with support of NSF grant 9708587.

FORTRAN:

GAUSS:

MATLAB: