A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models
完整刻画了含未来内生变量预期的标量线性理性预期模型的所有ARMA解，证明最大阶解为ARMA(k+l, k)且可通过特征多项式直接得到，低阶解通过删除AR和MA滞后多项式的公因子获得，并应用于多个宏观经济例子。
Linear rational expectations models with expectations of future endogenous variables have multiple equilibria. For a scalar model with k forward expectational lags and l backward lags, this paper characterizes the complete set of ARMA solutions. It is shown that the maximum degree solutions are ARMA (k + l, k), that the solutions of maximum degree are obtained directly from the characteristic polynomial but have arbitrary MA parameters, and that all lower degree ARMA solutions are obtained by deleting common factors in the AR and MA lag polynomials. The results are applied to several macroeconomic examples.