Social accounting matrix

From SUT to SAM

We now want to come to a presentation of the SUT tables in matrix form, with row and column totals being equal, as in the SIOT, but with the supply and use tables in their original form. To do this we need both industries and products in the header and the stub of the table, as in the table below, where columns (1) and (2) and rows (1) and (2) are for products and columns/rows (3) and (4) are for industries. From now on we will use the term “Commodities” (abbreviated as “Com”) for products and “Activities” (“Act”) for industries. This way the main parts of the use table easily fit in rows (1) and (2) of the matrix, with the intermediate consumption table in columns (3) and (4) and the final use categories in columns (5) – (8). Column (9) gives total use. Note that all column data are specified by product, as in the original use table.

To fit in the supply table in this matrix, we need to transpose it, i.e. to change rows and columns and “rotate the data” accordingly. It can then be inserted in columns (1) and (2), with the output table in rows (3) and (4), the net taxes in row (7) and imports in row (8). Total supply is given in row (9). Note that output data are specified by industry on the stub, as in the original transposed supply table.

We can also insert the value added part of the use table in columns (3), (4), rows (5), (6). Remember that the net taxes in row (6) are net taxes on production (net meaning the difference between taxes and subsidies), whereas the net taxes in row (7) are net taxes on products. The value added components are correctly given by industry, as in the use table.

Note that for the columns / rows (1), (2), (3) and (4) the row totals indeed equal the column totals. For columns / rows (1), (2) these are the horizontal product balances of the SUT. For columns / rows (3), (4) these are the vertical industry balances of the SUT. So far our matrix form has been successful in representing the SUT. However, for columns / rows (5), (6), (7) and (8) we run into trouble. Stub and header do not represent the same items, and the column and row totals are not equal.

To solve these problems, let us first make the stub and header entries equal. Before we do this, let us aggregate the two product groups into one entry “Com” (commodities) and the two industries into one entry “Act” (activities). Also, we aggregate the value added components into a single entry “Fact”, from “factor of production” (the two production factors are labour and capital, remunerated with the value added components CE and OS respectively). Next, let us replace the transaction header labels in columns (5), (6) and (8) and the stub label for row (8) with sector labels: “HH” for households, “GG” for government and “ROW” for rest-of-the-world. Finally, we replace the label “Net taxes” with “Tx”.

We can now make header and stub equal by inserting the missing stub entries “Fact” and “Tx” into the header, and inserting the missing header entries “HH”, “GG” and “GCF” into the stub. Since we now have the three sectors households, government and ROW in our presentation, it stands to reason to include the fourth main sector “Corporations” (abbreviated as “Corp”) as well. Finally, we change “GCF” (gross capital formation) to “Cap” (Capital), effectively including all entries of the capital account under this label. Applying all these changes gives us the table below. This matrix presentation is precisely that of a typical Social Accounting Matrix (SAM). Of course we are still left with the second problem noted earlier, that for columns / rows (3) – (9), column and row totals are not equal. We can fix this by inserting additional data into the matrix. These entries can appear in any cell of the matrix. By way of example we have added some representative entries, labeled as “(Aij)”, with “i” the row number and “j” the column number.

Some remarks on the SAM:

• The particular SAM structure introduced here is by no means the only one possible. Many other structures are possible and in fact used. Our structure was determined by our aim to fit the SUT into a matrix form resembling that of the SIOT.

• Each cell of the above table is the total of a “sub matrix”. For example, the number 1883 in row (1), column (2) is the total for the product by industry table of intermediate consumption. The presentation here is commonly known as the “Macro SAM”. Replacing the cells of the macro SAM with their respective sub matrices yields the “Micro SAM”.

• For the “Com” and “Act” columns / rows we do not necessarily have to use the same product and industry breakdowns as used in the SUT. For the SAM any suitable aggregation can be used. Different aggregations can be chosen for different analytical purposes.

• The main additional breakdowns introduced in the SAM are those for the “Fact” and “HH” columns / rows.

• The production factor labour is typically broken down in many different types of employment, such as self-employed labor, unskilled labor, skilled labor. Also, the production factor capital can be broken down in a number of types, e.g. in agriculture-specific capital, other capital and land. Again, different breakdowns can be chosen for different analytical purposes.

• The sector households is also typically broken down in different types, such as urban and rural households.

• The additional details on labour and households are the reason of the term “Social” in “Social Accounting Matrix”.

• The more detail is introduced in “Fact” the more detailed data needs to be found by the cells affected by the “Fact” breakdown, such as value added by industry (the number 1721 in row (3), column (2)). Data constraints usually limit the possible breakdowns for production factors and household types.

• Column (10) gives the row totals. For row (1) this is total use. But for the other rows this label does not make sense. For the other rows the entries are “uses” in the sense of “receipts” or “incomes”. The entries represent products or money “coming in”. In the SAM, rows stand for receipts, in the SIOT rows stand for inputs.

• Row (10) gives the column totals. For column (1) this is total supply. But for the other columns this label also does not make sense. For the other columns the entries are “supplies” in the sense of “costs”, “expenditures”, “payments” or “outlays”. The entries represent products or money “going out”. In the SAM, columns stand for outlays, in the SIOT columns stand for outputs.

• For the SIOT the input totals equal the output totals for each row / column. For the SAM the receipt totals equal the outlay totals for each row / column. This equality implies that there is one cell in each row and corresponding column for which the value can be obtained residually, i.e. by subtracting all remaining entries of the same row or column for the known total from the corresponding column / row.

• Although additional data need to be added, the SUT balances present in the “Com” and “Act” rows / columns will usually persist. In this sense the SAM is dependent on the SUT. But for the remaining rows / columns, row and column totals will usually be quite different, since data from many data sources need to be used. Hence the SAM needs to be balanced, i.e. row totals made equal to column totals, as was the case for the SUT. Hence, NA Builder is very well suited for SAM work.

• As is the case in the table above, a typical Macro SAM has many empty cells. This reflects the fact that stub and header contain quite diverse items (products, industries, transactions, sectors, accounts), of which some combinations simply will not be meaningful.

• The heterogeneous nature of the header and stub of the SAM also means that it is a flexible instrument. As is done for taxes in the example, if a transaction is judged to be important for analytical purposes, it can be added as a separate item.

• Elsewhere, we briefly outlined the use of the SIOT in input-output analysis, underlying economic policy studies. The balanced SAM can serve similar purposes with respect to socio-economic policy. The SAM is widely used in this respect, especially in developing countries.

SAMs in NA Builder

NA Builder contains an example SAM, taken from “A 2005 Social Accounting Matrix (SAM) For Ghana (Ghana Statistical Services (GSS) and International Food Policy Research Institute (IFPRI) under the Ghana Strategy Support Program (GSSP) October, 2007”

The template for the SAM looks as follows:

The classification list:

As usual, the can be expanded to any size required.

On the system sheet “Aggr” we can view the Ghana SAM at top level (the cell notes will show additional information):

The example also contains activity and product views:

Which can be generated with scripts. In the “Aggr” sheet these give:

SAMs from Sector Accounts

In many cases the totals of the Macro SAM can be obtained from the institutional sector accounts. Using a simplified version of the SNA 2008 example with only four institutional sectors (Corp = non-financial and financial corporations; GG = Government; HH = Households and Non-Profit Institutions Serving Households (NPISH); ROW = Rest-of-the-World) and only transactions at a high level of aggregation the sequence of SNA accounts presented can be structured as follows (with the accounts included underlined):

Current Accounts

Production Account

Distribution of income accounts

Primary distribution of income accounts

Generation of income account

Allocation of primary income account

Secondary distribution of income account

Use of income account

Use of disposable income account

Capital Accounts

Capital account

In the current accounts flows are recorded in terms of uses and resources. For our purpose it is best to look at monetary flows:

Resource (R) = incoming flow; e.g. output is incoming money;

Use (U) = outgoing flow; e.g. intermediate consumption is outgoing money.

The table below presents the main transactions of the current accounts and the capital account with for each sector resource and use columns. Note that for the capital account the use column represents the changes in assets and the resource column the changes in liabilities and net worth.

Note that we are interested in monetary receipts and outlays for the institutional sectors. Hence, we leave out all balancing items and account totals.

To see how we can use these institutional sector account data to fill the Macro SAM, let us examine households. From the resource column we see that the following money is coming in (total = 1943):

• Output (302)

• Compensation of Employees (1154)

• Property income (83)

• Social benefits other than social transfers in kind (379)

• Other current transfers, net (-1) (is in fact negative, can be positive as well)

• Adjustment for the change in pension entitlements (11)

• Capital transfers (15) (can be negative as well)

From the use column we see that the following money is going out (total = 1757):

• Intermediate Consumption (132)

• Compensation of Employees (22)

• Current taxes on income, wealth, etc. (178)

• Net social contributions (329)

• Final consumption expenditure (1031)

• Gross capital formation (60)

• Acquisitions less disposals of non-produced assets (5)

The surplus money coming in for households (1943 – 1757 = 186) is the net lending in the use column. Total net lending of the household sector is equal to the sum of total net borrowing of the corporate sector (57), the government sector (119) and ROW (10).

Note that for ROW we look at flows from the perspective of the ROW. So exports are a use item (money going out of ROW, i.e. coming into the country). Likewise, imports are a resource item.

We can use data from this table to fill in some of the macro SAM, e.g. some of the ROW entries in column (9) and some of the savings entries in row 8. For other cells the sector account information is not sufficient. For example, although the total of household transfers is known from the sector accounts, it cannot be determined from the accounts alone how much comes from individual sectors such as “GG” or “Corp”. Also, transfers between households are not recorded in the sector accounts, but they are part of the SAM. To complete the Macro SAM and to disaggregate the macro totals to come to the Micro SAM requires additional data sources. Given the focus on employment and households, major additional data sources are household surveys and labour force surveys.