Improving tatonnement methods for solving heterogenous agent models

This paper develops a globally convergent algorithm which modifies standard block Gauss-Seidel iterations used by tatonnement methods for solving large scale deterministic heterogenous agent models. It is shown that the restrictions on the structure of the Jacobi matrix implicit in any such first-order iterative method can easily be relaxed for these models. Instead of relying on {\it ad hoc} and fixed dampening factors, standard Quasi-Newton methods can be used to determine the exact Jacobi matrix for steady state calculations and to update its elements by Broyden's method as the iteration proceeds. By transforming variables such that they are constant in the steady states, very few elements of the Jacobian have to be determined. For transition calculations the resulting steady state Jacobi matrix can be used as an approximation of the true transition Jacobi matrix. This extension of standard Gauss-Seidel iterations is shown to considerably improve convergence both in terms of speed as well as robustness relative to an ad hoc choice of fixed dampening factors. In addition, the relative advantage of the modified algorithm increases in the number of state variables of the model. The algorithm is particularly attractive since it is easy to implement - it only augments conventional and intuitive tatonnement iterations by standard numerical methods