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
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
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.