Chapter 9: Balancing Supply and Uses

EN/SUT/2014/Doc/11

Chapter 9: Balancing supply and uses

9.1. Introduction

1.  If the supply and use tables were based on perfect knowledge, the two sides would automatically balance for each commodity. But of course in the real world both the supply and uses sides contain many estimates that had to be made to fill gaps. The data sources for almost all commodities are incomplete and the two sides will usually not be in balance. The SUT compiler’s task is to bring the two sides into balance. There are two ways of doing this – manual balancing and automatic balancing.

9.2. Manual balancing

2.  “Manual balancing” means that the SUT compiler inspects the supply and use of each commodity and adjusts one or more entries so that the two sides are equal. The balancing must be done at the most detailed level – that is for each of the commodities listed in the first column of the SUT. In manual balancing we use the identity Supply ≡ Uses and one estimate will always be derived as a residual.

3.  Here is an example of manual balancing for the commodity garments. Here are the unbalanced statistics:

Figure 1: Example on garments – unbalanced statistics
Domestic production at basic prices / 48,920
Imports at c.i.f values / 145,770
Transport costs / 5,841
Trade margins / 74,345
Product taxes / 21,990
Subsidies / 0
Total supply / 296,776
Intermediate consumption / 4800
Government final consumption expenditure / 0
NPISH final consumption expenditure / 0
Household final consumption expenditure / 291,175
Gross fixed capital formation / 0
Change in inventories / -75
Exports at fob values / 46,980
Total uses / 342,880

Total uses are more than 15% higher than total supply. If the difference had been only one or two percent we could have made an automatic adjustment using the RAS method explained later but as the difference is so large we need to look carefully at each estimate to see where the error may lie:

·  Some figures are quite firm and we should not change them. The SUT compiler decides to treat the following as firm estimates: imports, exports, product taxes and subsidies, intermediate consumption reported by government and NPISH (4,800) and change in inventories. The zero for gross fixed capital formation is also a firm figure.

·  Household final consumption expenditure is taken from a household expenditure survey. The problem with the survey is that coverage of low income households is weak. Richer households tend to spend more on garments than poorer households, so the SUT compiler assumes that the household expenditure survey has overestimated expenditure on garments. After discussion with the survey specialists, the compiler decides that expenditure on garments may be overestimated by between 4% and 5%.

·  Domestic production is taken from an establishment survey but the survey was made three years ago. In addition it only covered enterprises with five or more employees but a lot of garments are made by tailors working from their homes with help from family workers and these small enterprises were not covered in the survey.

·  The compiler decides to reduce the household consumption estimate by 4% and to keep all the other uses the same. This gives a new estimate of total use of 331,233 – slightly lower than the unbalanced estimate of 342,880. This becomes the new control figure for total supply.

·  Transport margins were originally estimated as 3% of domestic production plus imports at basic prices, and trade margins were estimated as 37% of supply at basic prices plus transport costs. Both these percentages are based on a recent trade and transport survey and are thought to be accurate. However the new domestic production that has been “discovered” is production by very small enterprises – usually just one person - and the garments they produce are sold directly to the purchaser so there are no trade margins or transport costs and no taxes on products. These three items- transport costs, trade margins and product taxes will not be changed.

·  Domestic production now becomes the balancing item i.e.

331,233 – 145,770 – 5,841 – 74,345 – 21,990 = 83,287 – see Figure 6.

Figure 6: Example on garments– results of manual balancing
Supply/Use / Unbalanced estimates / Balanced estimates
Domestic production at basic prices / 48,920 / 83,287
Imports at c.i.f. values / 145,770 / 145,770
Transport costs / 5,841 / 5,841
Trade margins / 74,345 / 74,345
Product taxes / 21,990 / 21,990
Subsidies / 0 / 0
Total supply / 296,776 / 331,233
Intermediate consumption / 4800 / 4800
Government final consumption expenditure / 0 / 0
NPISH final consumption expenditure / 0 / 0
Household final consumption expenditure / 291,175 / 279,528
Gross fixed capital formation / 0 / 0
Change in inventories / -75 / -75
Exports at fob values / 46,980 / 46,980
Total uses / 342,880 / 331,233

In the balanced supply and use estimates for garments, a small downward adjustment has been made to household consumption expenditure on the supply side and on the uses side a large upward revision has been made for domestic production. These revisions were based on the compiler’s assessment of the reliability of the underlying data sources. The revision for domestic supply is large but there had to be a mistake somewhere and the compiler has used his knowledge of the data sources to make the best possible adjustment.

Note that both GDP (P) and GDP(E) will need to be revised: there is now more value added in garments manufacture and less household consumption expenditure on garments. The two new revised estimates of GDP (P) and GDP (E) with respect to garments will now balance and, we hope, will be more accurate.

4.  Here is another example – advertising services. Below are the unbalanced statistics:

Figure 7. Example of advertising services – unbalanced statistics
Domestic production at basic prices / 68,000
Imports at CIF values / 0
Transport costs / 0
Trade margins / 0
Product taxes / 48
Subsidies / 0
Total supply / 68,048
Intermediate consumption / 0
Government final consumption expenditure / 0
NPISH final consumption expenditure / 45
Household final consumption expenditure / 0
Gross fixed capital formation / 0
Change in inventories / 0
Exports at fob values / 0
Total uses / 45

Most of the cells in the unbalanced table are zero. For services there are never any transport costs, trade margins, or changes in inventories and there is usually no gross fixed capital formation. In this case there were no imports or exports either.

The only uses recorded were purchases of 45 by NPISH, but the three advertising agencies in the country reported sales of 68,000. How were the other 67,955 of advertising services used?

The SUT compiler decides that:

·  Government does not usually purchase any advertising services so government intermediate consumption expenditure is assumed zero. This means that the rest of the advertising services must have been purchased by either enterprises as intermediate consumption or by households as final consumption expenditure.

·  The only product taxes are value added taxes. These must have been paid by households because enterprises do not pay VAT on intermediate consumption and NPISH do not pay VAT either. VAT is charged at 10% so households must have purchased advertising services valued at 480 before tax and advertising services including VAT of 480 + 48 = 528

·  The rest of the advertising services (67,475) must have been purchased by enterprises as intermediate consumption.

Here is the balanced table for advertising services:

Figure 8: Example on advertising – results of manual balancing
Supply/Use / Unbalanced estimates / Balanced estimates
Domestic production at basic prices / 68,000 / 68,000
Imports at cif values / 0 / 0
Transport costs / 0 / 0
Trade margins / 0 / 0
Product taxes / 48 / 48
Subsidies / 0 / 0
Total supply / 68,048 / 68,048
Intermediate consumption / 0 / 67,475
Government final consumption expenditure / 0 / 0
NPISH final consumption expenditure / 45 / 45
Household final consumption expenditure / 0 / 528
Gross fixed capital formation / 0 / 0
Change in inventories / 0 / 0
Exports at fob values / 0 / 0
Total uses / 45 / 68,048

5.  In these examples we have been balancing the rows of the SUT, but once these have been balanced and the uses equal supply, the column totals will also need to be balanced. For example, when new figures are introduced into the column for household final consumption expenditure, the column will not equal the control total for HFCE. Similarly when new estimates are made for intermediate consumption in order to balance supply and use, the new totals for intermediate consumption by each kind of activity will not agree with the control totals. This means that the columns will now need to be corrected but this will, in turn, disturb the row totals. An iterative procedure is therefore required in which the rows and columns are adjusted one after the other until they agree with the correct marginal figures. This is a challenging and time-consuming exercise and when the largest differences have been eliminated, automatic balancing procedures are often used to eliminate any small discrepancies that remain.

9.3. Automatic balancing

6.  The most widely used method of automatic balancing is called the RAS method. It is used to revise the internal entries in a matrix so that they agree with the margin totals. RAS is used when the margin totals – total supply/use of commodities, or total gross output by kind of activity, for example – are believed to be correct but the breakdown inside the matrix is not consistent with the margin totals. Lagrangean multipliers are an alternative to RAS and are used in both Norway and Thailand for balancing supply and use and input-output tables. However RAS is far more commonly used and is the method described in detail in the United Nations Handbook of Input-output Table Compilation and Analysis.

7.  When a benchmark SUT is being compiled, manual balancing should be carried on until the remaining differences have been reduced to a minimum. A good rule of thumb is that the row and column totals should sum to within ±5% of the known correct marginal figures before resorting to automatic balancing. RAS and similar procedures will produce a balanced matrix even if the discrepancies are large but the resulting table may be very misleading. Automatic balancing methods cannot judge the reliability of the numbers they are adjusting. That is the job of the compiler.

8.  The RAS method is often described in terms of matrix algebra and an algebraic description is given in Chapter 10 where we consider how to update an SUT. But when we are balancing a benchmark (first-time) SUT, the RAS method is best regarded as a purely mechanical process. This process can be seen as an iterative one in which the rows and columns of the matrix are alternately forced to agree with the correct marginal totals. An example follows.

9.  The figure below is a matrix of domestic production showing three commodities and three kinds of activity. The margin totals are assumed to be known accurately while the internal entries have been estimated from various less reliable sources and do not sum to the correct marginal totals. The task now is to revise the internal entries so that they agree with the correct margin totals.

Figure 9: Automatic balancing procedure
Automatic balancing - Basic data: Correct Margins but Internal Entries Not Consistent
Agriculture / Industry / Services / Row total / Correct total
Crops / 20,0 / 30,0 / 15,0 / 65,0 / 70,0
Manufactures / 10,0 / 60,0 / 20,0 / 90,0 / 80,0
Services / 40,0 / 55,0 / 5,0 / 100,0 / 120,0
Column total / 70,0 / 145,0 / 40,0
Correct total / 80,0 / 140,0 / 50,0
As noted, the RAS adjustment can be seen as an iterative process in which columns and rows (or rows and columns) are successively forced to sum to the correct marginal totals. In this example the internal entries rapidly converge to the correct row and column margin totals. After four iterations the sums of the three rows are within 0.2 of the correct row totals and by the fifth iteration the rows and columns sum to the correct margin total at one decimal place.
Figure 9(a): First iteration - Recalculate the Rows
Agriculture / Industry / Services / Row total / Correct total
Crops / 21,5 / 32,3 / 16,2 / 70,0 / 70,0
Manufactures / 8,9 / 53,3 / 17,8 / 80,0 / 80,0
Services / 48,0 / 66,0 / 6,0 / 120,0 / 120,0
Column total / 78,4 / 151,6 / 39,9
Correct total / 80,0 / 140,0 / 50,0
In this first iteration, each row is forced to agree with its correct row total. To achieve this, each row entry was multiplied by the ratio of the correct row total to the actual row total. The first row (Crops) was multiplied by 70/65, the second row (Manufactures) was multiplied by 80/90 and the third row (Services) by 120/100. The rows in Figure 9(a)now sum to the correct totals, but the column totals are still wrong.
Figure 9(b):Second iteration - Recalculate the Columns
Agriculture / Industry / Services / Row total / Correct total
Crops / 22,0 / 29,8 / 20,2 / 72,0 / 70,0
Manufactures / 9,1 / 49,2 / 22,3 / 80,6 / 80,0
Services / 49,0 / 60,9 / 7,5 / 117,4 / 120,0
Column total / 80,0 / 140,0 / 50,0
Correct total / 80,0 / 140,0 / 50,0
In the second iteration, the new column totals obtained in Figure 9(a)are forced to agree with the correct column totals. Each entry in the column for agriculture is multiplied by 80/78.4, entries in the column for industry by 140/151.6, and entries in the column for services by 50/39.9. The column totals in Figure 9(b)are now correct but the row totals are wrong again.
Figure 9( c).Third iteration: Recalculate the Rows
Agriculture / Industry / Services / Row total / Correct total
Crops / 21,4 / 29,0 / 19,7 / 70,0 / 70,0
Manufactures / 9,0 / 48,9 / 22,1 / 80,0 / 80,0
Services / 50,0 / 62,3 / 7,7 / 120,0 / 120,0
Column total / 80,4 / 140,2 / 49,4
Correct total / 80,0 / 140,0 / 50,0
In the third iteration the new row totals that were obtained in Figure 9(b) are forced to agree with the correct row totals: crops, manufactures and services are multiplied by 70/72.0, 80/80.6, and 120/117.4 respectively
Figure 9(d). Fourth iteration: Recalculate the Columns
Agriculture / Industry / Services / Row total / Correct total
Crops / 21,2 / 29,0 / 19,9 / 70,1 / 70,0
Manufactures / 9,0 / 48,8 / 22,4 / 80,1 / 80,0
Services / 49,8 / 62,2 / 7,8 / 119,8 / 120,0
Column total / 80,0 / 140,0 / 50,0
Correct total / 80,0 / 140,0 / 50,0
In the fourth iteration the new columns totals that were obtained in Figure 9( c) are forced to agree with the correct totals. The entries for Agriculture, Industry, and Services are multiplied by 80/80.4,140/140.2 and 50/49.4 respectively.
Figure 9(e) Fifth Iteration:Recalculate the Rows
Agriculture / Industry / Services / Row total / Correct total
Crops / 21.2 / 29.0 / 19.9 / 70.0 / 70.0
Manufactures / 9.0 / 48.7 / 22.3 / 80.0 / 80.0
Services / 49.9 / 62.3 / 7.8 / 120.0 / 120.0
Column total / 80.0 / 140.0 / 50.0
CorrectTotal / 80.0 / 140.0 / 50.0
In the fifth iteration the new rows that were obtained in Table are forced to agree with the correct totals. The entries for crops, manufactures, and services are multiplied by 70/70.1, 80/80.1 and 120/119.8 respectively.
It can be seen that by the fifth iteration, RAS has forcedthe originally incorrect internal cells to sum to the correct marginal totals. No further iterations are required

10. RAS can be used in either a complete or modified form. In the complete form all the internal entries in the matrix will be revised. In the modified RAS any cells or vectors which are believed to be accurate are removed from the matrix and new margins are calculated without these correct figures. The RAS is then performed as described above and when enough iterations have been made the vectors or cells that were thought to be accurate are reinserted. It is always best to use RAS in the modified form because this makes use of the compiler’s assessment of the reliability of the basic statistics. If compilers are confident in a particular cell or vector they should prevent RAS from changing it.