Creator: Christiano, Lawrence J. and Fisher, Jonas D. M. (Jonas Daniel Maurice), 1965- Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 171 Abstract:
We describe several methods for approximating the solution to a model in which inequality constraints occasionally bind, and we compare their performance. We apply the methods to a particular model economy which satisfies two criteria: It is similar to the type of model used in actual research applications, and it is sufficiently simple that we can compute what we presume is virtually the exact solution. We have two results. First, all the algorithms are reasonably accurate. Second, on the basis of speed, accuracy and convenience of implementation, one algorithm dominates the rest. We show how to implement this algorithm in a general multidimensional setting, and discuss the likelihood that the results based on our example economy generalize.
Keyword: Occasionally binding constraints, Parameterized expectations, Collocation, and Chebyshev interpolation Subject (JEL): C68 - Computable General Equilibrium Models, C60 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General, and C63 - Computational Techniques; Simulation Modeling
Creator: McGrattan, Ellen R. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 164 Abstract:
Since it is the dominant paradigm of the business cycle and growth literatures, the stochastic growth model has been used to test the performance of alternative numerical methods. This paper applies the finite element method to this example. I show that the method is easy to apply and, for examples such as the stochastic growth method, gives accurate solutions within a second or two on a desktop computer. I also show how inequality constraints can be handled by redefining the optimization problem with penalty functions.
Keyword: Growth model and Finite element method Subject (JEL): C68 - Computable General Equilibrium Models and C63 - Computational Techniques; Simulation Modeling