The Solution of Singular Linear Di¤erence Systems Under Rational Expectations
نویسندگان
چکیده
Many linear macroeconomic models can be cast in the rst-order form, AEtyt+1 = Byt +CEtxt; if the matrix A is permitted to be singular. For this singular linear di¤erence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinental polynomial jAz ¡ Bj is not zero for some value of z, and (ii) a rank condition is satis ed which is a direct generalization of Blanchard and Kahns (1980) requirement for the nonsingular system. The unique solution is characterized using a familiar approach: a canonical variables transformation which separates the dynamics associated with stable and unstable eigenvalues. In singular models, however, there are also canonical variables associated with in nite eigenvalues. These new canonical variables arise from nonexpectational behavioral relations or dynamic identities present in the singular linear di¤erence system.
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