Judd Maliar Maliar
Lilia and Serguei Maliar and I have developed some methods for solving rational expectations models which make it feasible to solve high-dimensional problems. The key insight is that a solution to a rational expectations problem often visits a small fraction of the potential state space. We adaptively approximate the ergodic set, and then use approximation methods that will work on any domain, not just the classical domains of hypercubes and hyperspheres.
The examples in our papers are simple multicountry RBC models. We are currently working on applying this method to New Keynesian models and dynamic programming problems. We believe that this method can also solve dynamic games if the approximation method used conforms to the topological properties of the equilibrium definition.
These methods are also highly parallelizable. We show how to formulate the problem so as to maximized the ability to use parallel processing.