The starting point for many models is a balanced Social Accounting Matrix (SAM). SAMs are presented as a square matrices where row i and column i refer to a single account. Rows correspond to receipts (sale) and columns are expenditures (purchase). SAM can be quite detailed in their representation of an economy, and they are also quite flexible. A SAM is balanced when the vector of row sums equals the vector of column sums.

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Example 6: SAM

X,Y - two produced commodities

L,K - two factors of production

CONS - one consumer

W - aggregate consumption index

A 9 x 9 SAM describes the benchmark equilibrium for the next model we consider

		supply					total cost			expenditures
		PX	PY	PW	PL	PK	X	Y	W	CONS
demand	PX								100
	PY								100
	PW									200
	PL						40	60
	PK						60	40
total revenue	X	100
	Y		100
	W			200
income	CONS				100	100

Reading SAM: 100 units is spent on good X by sector W

40 units is spent on L by sector X

60 units is spent on L by sector Y

For MPSGE models, it is convenient to use a different SAM type. This structure will emphasizes how the MPSGE program is connected to the benchmark data:

· We will have one row for every market. In the current example, we have 5 markets (for goods - X,Y,W and for factors - L,K).

· There are two types of columns - corresponding to (1) production sectors and (2) consumers. In the example, we have 3 sectors and 1 consumer.

The numbers which appear in a SAM are typically positive, but not in the MPSGE models. A positive and negative entry signifies a sale and purchase in a particular market respectively. Reading down a production column, we then observe a complete list of the transactions associated with that activity. This SAM is balanced when row and column sums are zeros (the total amount of commodity flowing into the economy equals the total amount of commodity flowing out of the economy). This is market clearance condition for each commodity in the model.

The following MPSGE SAM conveys the same information as the traditional SAM presented above

Markets	Production sectors			Consumers
	X	Y	W	CONS
PX	100		-100
PY		100	-100
PW			200	-200
PL	-40	-60		100
PK	-60	-40		100

where expenditures/costs are presented as negative numbers, while revenue/income – positive numbers.

A production sector column (sum of rows) is zero if the value of outputs equals the cost of inputs. A consumer column is balanced if the sum of primary factor sales equals the value of final demands.