Practice Problem

Simultaneous Equation Models

Practice Problem 13.1

Substituting equations (13.4) through (13.6) into (13.7) , we get
Yt = 0 + 1 (Yt - Tt ) + 2 (Yt-1 - Tt-1 ) + ut + 0 + 1Yt  + 2Yt-1 + vt  + Gt
Regrouping terms, this becomes
(1 - 1 - 1) Yt = (0 + 0 ) + ( 2 + 2 ) Yt-1  - 1Tt  - 2Tt-1 + Gt + ut + vt
The reduced form equation for Yt is therefore given by
 Yt = [ (0 + 0 ) / (1 - 1 - 1) ] + [( 2 + 2 ) / (1 - 1 - 1) ] Yt-1  - [ 1 / (1 - 1 - 1) ] Tt  - [ 2 / (1 - 1 - 1) ] Tt-1  + ( Gt + ut + vt ) / (1 - 1 - 1)
or
 Yt = 0  + 1Yt-1  + 2 Tt  + 3 Tt-1 + 4Gt + error

The other reduced form equations are easily derived from this.

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Updated March 20, 2000
noelroy@morgan.ucs.mun.ca