Thus, l = Al * yn= Al * (I-An)-1* x = Al * Ma *x.
(12)
So, with the accounting multipliers, the impact of changes in receipts is analysed at the
moment, assuming that the structure of expenditure in the economy does not change. This
type of methodology allows for a static analysis to be made, assuming also that there is excess
capacity, prices remain constant and the production technology and resource endowment are
given.
To have an idea about the level of veracity of the calculated accounting multipliers, a test
was carried out in accordance with such a methodology, for the beginning of our series. In
order to do this, accounting multipliers were first calculated from the Portuguese SAM for
1995, whilst the changes that really occurred from 1995 to 1996 were also considered, i.e. the
“x” vector of the Portuguese SAM for 1996, and the new vector of receipts of the endogenous
accounts (yn) was calculated. From this, and with the aid of the matrices of average
expenditure propensities (An and Al) for 1995, the endogenous part of the SAM was re-
calculated for 1996, where the value of aggregate household income showed a percentage
difference in relation to the real SAM values of 1.12%, whilst the difference in
investment/investment funds was 29.62%. The corresponding percentage difference, i.e. the
difference between the calculated and the real total values, was 1.12% for account 9 (labour),
2.20% for account 10 (capital), 1.54% for account 11 (activities), and 1.53% for account 12
(products).
In previous studies (Santos, 1999, 2003b), lower differences were obtained, probably due
to a higher level of disaggregation of the SAM accounts.
Taking into account these results and the assumptions referred to before, we will analyse
our results in an indicative fashion.
b) Decomposition of the accounting multipliers
Accounting multipliers can be decomposed if we consider the An matrix and two other
ones with the same size (Bn - with the diagonal of An, whilst all the other elements are null -
and Cn - with a null diagonal, but with all the other elements of An). In this way, it can be
written that
An = Bn + Cn. (13)
Thus, from equation (6):
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