Analytical and Numerical Solution of Multivariate Nonlinear Rational Expectations Models

Michael Binder, M. Hashem Pesaran - University of Cambridge, and S. Hossein Samiei - IMF

In this paper, we propose a new solution method for multivariate nonlinear rational expectations models. Previous solution methods for this class of models have either invoked certainty equivalence, have used state-space discretization techniques, or have been based on approximations of expectations of nonlinear functions appearing in these models. Our approach, in contrast, is based on simulating future paths of the forcing variables of these models. We provide conditions under which, conditional on specific realizations of such paths as well as terminal conditions, one can solve these models by solving deterministic problems recursively backward. We show that our solution method is feasible in practice as the number of future paths of the forcing variables for which the backward recursions have to be carried out is not exponentially increasing in the forecasting horizon.

We illustrate our solution method by applying it to a life-cycle/permanent income model of consumption in the presence of precautionary savings as well as liquidity constraints. We use the model to study the effects of changes in labor income uncertainty on the life-time profile of consumers' savings.

Scheduled for Session 2.4 Rational Expectations Analysis - I