A Homotopy Approach to Solving Nonlinear Rational Expectation Problems

Many numerical methods have been developed in an attempt to find solutions to nonlinear rational expectations models. Because these algorithms are numerical in nature, they rely heavily on computing power and take sizeable cycles to solve. In this paper we present a numerical tool known as homotopy theory that can be applied to these methods. Homotopy theory reduces the computing time associated with an iterative algorithm by using a rational expectation problem with known solutions and transforming it into the problem at hand. If this transformation is preformed slowly, homotopy theory will also help the global convergence properties of the numerical algorithm. We apply homotopy theory to Den Haan and Marcet's Parameterized Expectation Approach to show how homotopies improves the computing speed and global convergence properties of this algorithm.