System Reduction and Solution Algorithms for Singular Linear Di¤erence Systems Under Rational Expectations
نویسندگان
چکیده
A rst-order linear di¤erence system under rational expectations is, AEyt+1jIt = Byt +C(F)ExtjIt; where yt is a vector of endogenous variables; xt is a vector of exogenous variables; Eyt+1jIt is the expectation of yt+1 given date t information; and C(F)ExtjIt = C0xt+ C1Ext+1jIt + ::: + CnExt+njIt. Many economic models can be written in this form, especially if the matrix A is permitted to be singular. If the model is solvable, yt can be divided into two sets of variables: dynamic variables dt that evolve according Edt+1jIt =Wdt +ad(F)ExtjIt and other variables which that obey the dynamic identities ft = ¡Kdt ¡af (F)ExtjIt. This paper provides an algorithm that constructs the reduced system Edt+1jIt = Wdt+ad(F)ExtjIt for any solvable linear di¤erence system. We also provide algorithms for computing (i) perfect foresight solutions and (ii) Markov decision rules that can be used when there is a unique solution.
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