THE SOLUTION OF SINGULAR LINEAR DIFFERENCE-SYSTEMS UNDER RATIONAL-EXPECTATIONS

Many linear rational expectations macroeconomic models can be cast in the first-order form, AE(t)y(t+1) = By(t) + CE(t)x(t), if the matrix A is permitted to be singular. We show that there is a unique stable so lution under two requirements: (i) the determinantal polynomial \Az-B\ is not zero for some value of z, and (ii) a rank condition. The uniqu e solution is characterized using a familiar approach: a canonical var iables transformation separating dynamics associated with stable and u nstable eigenvalues. In singular models, however, there are new canoni cal variables associated with infinite eigenvalues. These arise from n onexpectational behavioral relations or dynamic identities present in the singular linear difference system.