## System Reduction and Solution Algorithms for Singular Linear Difference Systems Under Rational Expectations (1997)

Venue: | Computational Economics |

Citations: | 25 - 2 self |

### BibTeX

@ARTICLE{King97systemreduction,

author = {Robert G. King and Mark W. Watson},

title = {System Reduction and Solution Algorithms for Singular Linear Difference Systems Under Rational Expectations},

journal = {Computational Economics},

year = {1997},

volume = {20},

pages = {57--86}

}

### Years of Citing Articles

### OpenURL

### Abstract

A first-order linear difference system under rational expectations is, AEy t+1 jI t = By t +C(F)Ex t jI t ; where y t is a vector of endogenous variables; x t is a vector of exogenous variables; Ey t+1 jI t is the expectation of y t+1 given date t information; and C(F)Ex t jI t = C 0 x t + C 1 Ex t+1 jI t + ::: + C n Ex t+n jI t . Many economic models can be written in this form, especially if the matrix A is permitted to be singular. If the model is solvable, y t can be divided into two sets of variables: dynamic variables d t that evolve according Ed t+1 jI t = Wd t + d (F)Ex t jI t and other variables which that obey the dynamic identities f t = Kd t f (F)Ex t jI t . This paper provides an algorithm that constructs the reduced system Ed t+1 jI t = Wd t + d (F)Ex t jI t for any solvable linear difference 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.