187.
A social accounting matrix
is a tablethat shows
the flows from each sector
in an economy
to each other sector. Here
is sirnple
fivesector
example, with blank entries
indicating
flows known
to be zero:
I,AB
P1
YZ
I,AB
H1
H2
P1
P2
15
3
130
80
?
,)
15
130
20
25
40
55
total
220
i
190
105
If the matrix were estimated perfectly, it would be balanced: each row sum (the flow out of a sec
tot) would equal the corresponding column sum (the flow in). As a practical matter, however,
there are several difficulties:

Some entries, marked ? above, have no reliable estimates.

In the estimated table, the row sums do not necessarilyequal the column surns.

We have sepdate estimates of the total flows into (or out of) each sector, shown to the right of
the rows in our table. These do not necessarily equal the sums of the estimated
rows or columns.
illonlinear prograrnming can be used to adjust this matrix by finding the balanced matrix that is
closest,
in some sense,
to the one given.
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 Spring '07
 SHMOYS/LEWIS
 Operations Research, Avril Lavigne, surns., H2 P1 P2, corresponding column sum

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