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 The SIMLIN Procedure

## Dynamic Multipliers

For models that have only first-order lags, the equation of the reduced form of the system can be rewritten

D is a matrix formed from the columns of 1 plus some columns of zeros, arranged in the order in which the variables meet the lags. The elements of 2 are called impact multipliers because they show the immediate effect of changes in each exogenous variable on the values of the endogenous variables. This equation can be rewritten as

The matrix formed by the product D2 shows the effect of the exogenous variables one lag back; the elements in this matrix are called interim multipliers and are computed and printed when the INTERIM= option is specified in the PROC SIMLIN statement. The ith period interim multipliers are formed by Di2.

The series can be expanded as

A permanent and constant setting of a value for x has the following cumulative effect:

The elements of (I-D)-12 are called the total multipliers. Assuming that the sum converges and that (I-D) is invertible, PROC SIMLIN computes the total multipliers when the TOTAL option is specified in the PROC SIMLIN statement.

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