### Abstract

A first-order linear difference system under rational expectations is, AEy_{t+1}{pipe}I_{t}=By_{t}+C(F)Ex_{t}{p ipe}I_{t}, where y_{t} is a vector of endogenous variables;x_{t} is a vector ofexogenous variables; Ey_{t+1}{pipe}I_{t} is the expectation ofy_{t+1} givendate t information; and C(F)Ex_{t}{pipe}I_{t} =C_{0}x_{t}+C_{1}Ex_{t+1}{pipe}I_{t}+...+C_{n}Ex_{t+n}{pipe}I_{t}. If the model issolvable, then y_{t}can be decomposed into two sets of variables:dynamicvariables d_{t} that evolve according to Ed_{t+1}{pipe}I_{t} = Wd_{t} + Ψ_{d}(F)Ex_{t}{pipe}I_{t} and other variables thatobey the dynamicidentities f_{t} =-Kd_{t}-Ψ_{f}(F)Ex_{t}{pipe}I_{t}. 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.

Original language | English (US) |
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Pages (from-to) | 57-86 |

Number of pages | 30 |

Journal | Computational Economics |

Volume | 20 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2002 |

### All Science Journal Classification (ASJC) codes

- Economics, Econometrics and Finance (miscellaneous)
- Computer Science Applications

### Keywords

- algorithm
- in practice
- models
- solutions
- system reduction