National accounting identities and the sectoral balance approach
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Flows are derived from the National Accounting relationship between aggregate spending and income. So:
(1) Y = C + I + G + (X – M)
where Y is GDP (income), C is consumption spending, I is investment spending, G is government spending, X is exports and M is imports (so X – M = net exports).
Another perspective on the national income accounting is to note that households can use total income (Y) for the following uses:
(2) Y = C + S + T
where S is total saving and T is total taxation (the other variables are as previously defined).
You than then bring the two perspectives together (because they are both just “views” of Y) to write:
(3) C + S + T = Y = C + I + G + (X – M)
You can then drop the C (common on both sides) and you get:
(4) S + T = I + G + (X – M)
Then you can convert this into the familiar sectoral balances accounting relations which allow us to understand the influence of fiscal policy over private sector indebtedness.
So we can re-arrange Equation (4) to get the accounting identity for the three sectoral balances – private domestic, government budget and external:
(S – I) = (G – T) + (X – M)
The sectoral balances equation says that total private savings (S) minus private investment (I) has to equal the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents.
Another way of saying this is that total private savings (S) is equal to private investment (I) plus the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents.
All these relationships (equations) hold as a matter of accounting and not matters of opinion.
Thus, when an external deficit (X – M < 0) and public surplus (G - T < 0) coincide, there must be a private deficit. While private spending can persist for a time under these conditions using the net savings of the external sector, the private sector becomes increasingly indebted in the process.