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This chapter provides a review of solution and estimation methods available in the literature for the analysis of multivariate linear rational expectations models, and proposes new techniques which are straightforward to implement and allow the incorporation of many forms of nonstationarity and nonlinearity (the latter being restricted to the models’ forcing variables) into the analysis of multivariate rational expectations models. The proposed method decomposes the solution into a backward and a forward component, and employs familiar martingale or martingale difference techniques to obtain all the solutions for the forward component. The method is relatively straightforward to apply and requires solution of a quadratic determinantal equation, the roots of which provide a complete characterization of all the possible classes of solutions, namely the unique stable solution, the multiple stable solutions, and the case where no stable solution exists. Since we only need to impose very weak assumptions on the forcing variables of the model, this solution method is applicable to cases where the forcing variables are first-order integrated, or display conditional variance dynamics, or other forms of nonstationarities or nonlinearities in the forcing variables. The quadratic determinantal equation solution method also renders a convenient (restricted) VAR framework for purposes of full ... log in or subscribe to read full text