as a “global influence”, which is decomposed into a series of “total influences”. These, in
turn, are decomposed into “direct influences” multiplied by the “path multiplier”:
ma i = IG = ∑n IT = ∑n ID *Mp (20)
maji=I(i→j)=p∑=1I(i→j)p =p∑=1I(i→j)p Mp (20)
Where:
maji is the (j,i)th element of the Ma (accounting multipliers) matrix, which quantifies the
full effect of a unitary injection xj on the endogenous variable yj;
I(Gi→ j) is the Global Influence of pole i on pole j;
p is the nth elementary path - the arc linking two different poles, oriented in the direction of
the expenditure, located between i and j, with i being the pole of origin of the
elementary path 1 (the first) and j the pole of destination of the elementary path n
(the last);
T
I(i→ j) is the Total Influence transmitted from i to j along the elementary path p;
ID is the Direct Influence of i on j transmitted along the elementary path p, which
(i→ j)p
measures the magnitude of the influence transmitted between its two poles through
the average expenditure propensity;
Mp is the Multiplier of the path p, or the path Multiplier, which expresses the extent to
which the influence along elementary path p is amplified through the effects of
adjacent feedback circuits10:
Mp = δΔP (21)
where: ∆ = the determinant of matrix ∣ I-An I of the structure represented by the SAM,
∆p = the determinant of the submatrix of ∣ I-An ∣ obtained by removing the row
and the column associated with the poles of the elementary path p.
10 A circuit is a path for which the first pole (pole of origin) coincides with the last pole (pole of destination)
(Defourny and Thorbecke, 1984, p. 119).
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