SAMs are square (columns equal rows) in the sense that all institutional agents (Firms,Households, Government and 'Rest of Economy' sector) are both buyers and sellers. Columns represent buyers (expenditures) and rows represent sellers (receipts). SAM's were created to identify all monetary flows from sources to recipients, within a disaggregated national account. The SAM is read from column to row, so each entry in the matrix comes from its column heading, going to the row heading. Finally columns and rows are added up, to ensure accounting consistency, and each column is added up to equal each corresponding row. In the illustration below for a basic open economy, the item C (consumption) comes from Households and is paid to Firms.
Illustrative Open Economy SAM:
|Firm||Household||Government||Rest of Economy||Net Investment||Total (Received)|
|Rest of Economy||(X-M)K||(X-M)C||(X-M)K+(X-M)C|
SAMs can be easily extended to include other flows in the economy, simply by adding more columns and rows, once the standard national account (SNA) flows have been set up. Often rows for ‘capital’ and ‘labor’ are included, and the economy can be disaggregated into any number of sectors. Each extra disaggregated source of funds must have an equal and opposite recipient. So the SAM simplifies the design of the economy being modeled. SAMs are currently in widespread use, and many statistical bureaus, particularly in OECD countries, create both a national account and this matrix counterpart.
A theoretical SAM always balances, but empirically estimated SAM’s never do in the first collation. This is due to the problem of converting national accounting data into money flows and the introduction of non-SNA data, compounded by issues of inconsistent national accounting data (which is prevalent for many developing nations, while developed nations tend to include a SAM version of the national account, generally precise to within 1% of GDP). This was noted as early as 1984 by Mansur and Whalley, and numerous techniques have been devised to ‘adjust’ SAMs, as “inconsistent data estimated with error, [is] a common experience in many countries”.
The traditional method of benchmarking a SAM was simply know as the "Row-and-Columns" (RoW) method where one finds an arithmetic average of the total differences between the row and column in question, and adjust each individual cell until the row and column equal.
Robinson et al. (2001) suggests an improved method for ‘adjusting’ an unbalanced SAM in order to get all the rows and columns to equal, and gives the example of a SAM created for Mozambique’s economy in 1995, where the process of gathering the data, creating the SAM and ‘adjusting’ it, is thoroughly covered by Arndt et al (1997). On inspecting the changes made to the Mozambique’s 1995 SAM to achieve balance is an adjustment of $295m USD which meant that $227m USD was added to the SAM net, just to balance the rows and columns. For 1995 this adjustment is equivalent to 11.65% of GDP! More disconcerting is perhaps the fact that agricultural producers (which according to FAO (1995) employed 85% of the labor force in 1994) were given a $58m USD pay rise in the SAM, meaning that 10% of agricultural income (equivalent to 5% of GDP) in the SAM was created, out of thin air. In other words, for a country where 38% of the population lived for less than $1 in the period 1994-2004 (UNICEF 2008), this SAM ‘adjustment’ added $4.40 to each persons income in the agricultural sector – more than any of the later trade and tax models using this SAM could arguably hope to achieve.
"By the early 1980s, CGE models were heavily ensconced as the approach of the World Bank for development analysis. Social Accounting Matrices (SAMs) were similarly a mainstay of Bank analysis, which had been adopted as a presentational device by the CGE modelers" (Mitra-Kahn 2008: 23)