Social Accounting Matrix Research Paper

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A social accounting matrix (SAM) gives a snapshot of all the transactions between different actors or agents in an economy (Pyatt 1988). The economy can be that of a nation, a province, or even a city. The scope of a SAM— that is, how many groups of actors are considered or the level of disaggregation within a group—depends on the availability of data. Transactions are organized in the form of a square matrix. The (i, j) element of the matrix represents the expenditure of actor j on actor i. Equivalently, it is also the income of actor i that originates from the activities of actor j. Expressed in accounting jargon, the concept of SAM is simply that of a double-entry bookkeeping in which the incomings of an actor are also the outgoings of another actor. Thus each row sum must be equal to the corresponding column sum.

It is the choice of actors that distinguishes SAM from both traditional national accounts and an input-output matrix. In terms of broad groups of actors, SAM typically considers production sectors, households, factors of production, and institutions. Each broad group is further disaggregated. For example, a typical SAM involves specific types of households and specific factors of production in order to reflect the economic and social structure of the economy under consideration. Production activities create incomes for various factors of production. These incomes then get distributed to different types of households and corporations. Household and corporate incomes generate private consumption and savings/investments. Government income is generated from direct taxation of household and corporate incomes and from indirect taxation and is translated into public expenditure and investments. The actual task of collecting and collating the information necessary to construct a SAM is quite formidable. Often data from different sources need to be combined. For this and many other reasons, the row and column sums frequently differ. There are, however, numerical methods to reconcile these differences.

The concept of representing transactions between actors in an economy in the form of a matrix was first introduced by Wassily Leontief in his classic work The Structure of American Economy (1941, 1951). For Leontief, the actors were mainly producing sectors, and the matrix represented intermediate inputs in production. However, in one of his later reviews of input-output analysis, he writes:

Households must not necessarily be considered to be part of the exogenous sectors. … In dealing with problems of income generation in its relation to employment, the quantities of consumers’ goods and services absorbed by households can be considered (in a Keynesian manner) to be structurally dependent on the total level of employment in the same way as the quantities of coke and ore absorbed by blast furnaces are considered to be structurally related to the amount of pig iron produced by them. (Leontief 1966, pp. 141-142)

From these conceptual foundations, Leontief extends the input-output matrix to include transactions between households, factors of production, and so on.

The applications of SAMs can be wide-ranging. They can, and often do, form the backbone of computable general equilibrium models. SAMs are particularly useful for any exercise in which a researcher or policy maker is interested in analyzing the distributional implications of particular policy measures (Pyatt and Round 1979, 1985, and 2006). In such cases, the overall matrix multiplier (which gives the total “activity” level of all the actors in an economy to produce a given level of final use as the sum of direct activity levels and an infinite series of indirect ones) is typically broken down into a number of multiplicative components (Pyatt and Round 1979). Each of these components represents a particular connection between or within groups’ effects. An analysis of these disaggregated multipliers not only tells us the effects of an injection of a particular shock to various socioeconomic groups, it also tells us the mechanisms through which such effects come about. There are now many studies that construct SAMs for developing countries and examine the distributional consequences of policy measures (Pyatt and Round 1985). One hopes that as time goes by, SAMs for more and more countries will be constructed, as they could only help in the formulation and effective implementation of development policies benefiting the poor.


  1. Leontief, Wassily. 1951. The Structure of American Economy, 1919–1939: An Empirical Application of Equilibrium Analysis. 2nd enlarged ed. New York: Oxford University Press.
  2. Originally published as The Structure of American Economy, 1919–1929 (Cambridge, MA: Harvard University Press, 1941).
  3. Leontief, Wassily. 1966. Input-Output Economics. New York: Oxford University Press.
  4. Pyatt, Graham. 1988. A SAM Approach to Modeling. Journal of Policy Modeling 10 (3): 327–352.
  5. Pyatt, Graham, and Jeffery I. Round. 1979. Accounting and Fixed Price Multipliers in a Social Accounting Matrix Framework. Economic Journal 89 (356): 850–873.
  6. Pyatt, Graham, and Jeffery I. Round, eds. 1985. Social Accounting Matrices: A Basis for Planning. Washington, DC: World Bank.
  7. Pyatt, Graham, and Jeffery I. Round. 2006. Multiplier Effects and the Reduction of Poverty. In Poverty, Inequality, and Development: Essays in Honor of Erik Thorbecke, eds. Alain de Janvry and Ravi Kanbur, 233–259. New York: Springer.

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