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The reduced form matrix ir can be partitioned into submatrices such
that
Yt do + + D2Xt + 5t
where Yt is a g*l vector of endogenous variables, Yt_^ is a g*l vector
of endogenous variables lagged one period, Xt is a kxl vector of the
exogenous variables, dg is a vector of constant terms, Dj^ is a g*g
matrix of derived reduced form estimates for the lagged endogenous
variables, D2 is a g>4c matrix of derived reduced form estimates for the
exogenous variables, and is a g*l vector of disturbances. The ele
ments in Dj and are impact multipliers. For the sake of simplicity,
no lagged exogenous variables are included in this discussion and the
endogenous variables are only lagged one period. To obtain a final form
expression for the system, Yt must be expressed in a form free of lagged
endogenous variables. The expression Yfc lagged one period and substi
tuted back into Yt gives
Repeating this procedure s times yields
However, note that if
lim D = 0,
S -H
then
lim E D*
S-H i**0
- (I-D^-1.
Then by dropping the time subscript, Y can be written as
Y = D + XX + E