Analytical and Numerical Solution of Finite-horizon Nonlinear Rational Expectations Models

This paper considers the solution of nonlinear rational expectations models resulting from the optimality conditions of a finite-horizon intertemporal optimisation problem satisfying Bellman's principle of optimality (and possibly involving inequality constraints). A backward recursive procedure is used to characterise and solve the time- varying optimal decision rules generally associated with these models. At each stage of these backward recursions, either an analytical or numerical solution of the optimality conditions is required. When an analytical solution is not possible, a minimum weighted residual approach is used. The solution technique is illustrated using a life-cycle model of consumption under labour income and interest rate uncertainties (and possibly involving liquidity constraints). Approximate numerical solutions are provided and compared with certainty-equivalent solutions and, when possible, with exact solutions.