With the special use of proportional scaling RAS outlined below, it is possible to balance a matrix for which one or more row and/or column total is not known with reasonable certainty. The method, which allows these uncertain totals to change during the balancing process, (a) opens up a row and/or column of zeros and (b) subtracts the uncertain totals from the final row or column (leaving a zero in the final row or column) and from the corresponding position of the new row or column of zeros. As the uncertain totals now are inside the matrix, they are treated as part of the matrix and will change as the matrix is balanced. Finally, it is possible to use the precondition option in the *psras* command to control the change in any of the uncertain totals. This command depends critically on the ability of the proportional scaling algorithm to scale rows and/or columns that sum to zero.

The example that follows will make the procedure more clear. It uses a 5x4 matrix of factor payments from a three-sector input-output table (in which total value added is in the last row and total factor payments is in the last column) and subsequently published national accounts data for total value added.

First, expand the matrix to five columns and insert a column of zeros as column four; then move the total factor payments (now in column five) to column four and change their sign.

```
Primary Secondary Tertiary FactPay Total
EstDep 58.5 563.7 409.0 -1031.2 0.0
EstWages 1297.9 1759.9 1096.2 -4154.0 0.0
EstTaxes 43.3 694.1 287.1 -1024.5 0.0
EstSurplus 74.5 943.2 343.0 -1360.7 0.0
NatActVA 1421.1 3722.3 2302.9 -7446.3 0.0
```

The matrix now is ready to balance. The command is:

**psras [<-f|c>] <matrix>[(r rgroup)][(c cgroup)]<rowctrl><colctrl>[yr][r|c][-maxiter][-precon]**

or in this example:

```
psras VA (r 1-4)(c 1-4) VA 5 VA 5 1997 r
```

To see how it works, download and run the script SPECIALPSRAS.ADD available on the *G7* demo page of the Inforum web site.