System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations

Authors:
Robert G. King;Mark W. Watson
Affiliations:
Boston University, Department of Economics, 270 Bay State Road, MA 02215, Boston, U.S.A.;Princeton University
Venue:
Computational Economics
Year:
2002

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Abstract

A first-order linear difference system under rational expectations is, AEyt+1|It=Byt+C(F)Ext|It , where yt is a vector of endogenous variables;xt is a vector ofexogenous variables; Eyt+1|It is the expectation ofyt+1 givendate t information; and C(F)Ext|It =C0xt+C1Ext+1|It+∣dot;s +CnExt+n|It. If the model issolvable, then yt can be decomposed into two sets of variables:dynamicvariables dt that evolve according toEdt+1|It = Wdt + ¶sid(F)Ext|It and other variables thatobey the dynamicidentities ft =−Kdt−¶sif(F)Ext|It. We developan algorithm for carrying out this decomposition and for constructing theimplied dynamic system. We also provide algorithms for (i) computing perfectforesight solutions and Markov decision rules; and (ii) solutions to relatedmodels that involve informational subperiods.