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The Solution of Singular Linear Difference Systems under Rational Expectations
Robert G. King and Mark W. Watson
International Economic Review
Vol. 39, No. 4, Symposium on Forecasting and Empirical Methods in Macroeconomics and Finance (Nov., 1998), pp. 1015-1026
Published by: Wiley for the Economics Department of the University of Pennsylvania and Institute of Social and Economic Research, Osaka University
Stable URL: http://www.jstor.org/stable/2527350
Page Count: 12
You can always find the topics here!Topics: Eigenvalues, Economic expectations, Macroeconomic modeling, Matrices, Rational expectations theory, Economic models, Solvability, Polynomials, Zero, Macroeconomics
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Many linear rational expectations macroeconomic models can be cast in the first-order form, AEtyt+1 = Byt + CEtxt, if the matrix A is permitted to be singular. We show that there is a unique stable solution under two requirements: (i) the determinantal polynomial |Az-B| is not zero for some value of z, and (ii) a rank condition. The unique solution is characterized using a familiar approach: a canonical variables transformation separating dynamics associated with stable and unstable eigenvalues. In singular models, however, there are new canonical variables associated with infinite eigenvalues. These arise from nonexpectational behavioral relations or dynamic identities present in the singular linear difference system.
International Economic Review © 1998 Economics Department of the University of Pennsylvania