Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function

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Abstract
This paper derives a second-order approximation to the solution of a general class of discrete-time rational expectations models. The main theoretical contribution of the paper is to show that for any model belonging to the general class considered, the coefficients on the terms linear and quadratic in the state vector in a second-order expansion of the decision rule are independent of the volatility of the exogenous shocks. In other words, these coefficients must be the same in the stochastic and the deterministic versions of the model. Thus, up to second order, the presence of uncertainty affects only the constant term of the decision rules. In addition, the paper presents a set of MATLAB programs designed to compute the coefficients of the second-order approximation. The validity and applicability of the proposed method is illustrated by solving the dynamics of a number of model economies.

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