An alternative sectoral balance equation.

This is a popular equation with Modern Monetary Theory sectoral balance enthusiasts:

(I – S) + (G – T) + (X – M) = 0

I=investment, S=savings, G=government spending, T=tax, X=exports, and M=imports. The equation is cited for example here, here, here and here.

And there is a picture of Warren Mosler displaying the equation here!

However, the equation and the reasoning leading to it are flawed. I’ll argue below that investment (I) should be omitted from the equation.

Here is Bill Mitchell’s reasoning (in grey italics), leading to the equation.

From the sources perspective we write:

GDP = C + I + G + (X – M)

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

However, there is a problem here: in the real world there is no clear distinction between consumption items (C) and investment items (I). To illustrate, is something designed to last three months an investment? How about one year . . . three years? The distinction between the two is arbitrary.

Bill continues:

From the uses perspective, national income (GDP) can be used for:

GDP = C + S + T

which says that GDP (income) ultimately comes back to households who consume (C), save (S) or pay taxes (T) with it once all the distributions are made

Hang on: why doesn’t investment (I) appear on the right hand side? If we define anything designed to last more than say five years as an investment (e.g. cars), then rather a large proportion of what the average household “consumes” has been omitted (cars in particular).

Bill continues:

Equating these two perspectives we get:

C + S + T = GDP = C + I + G + (X – M)

So after simplification (but obeying the equation) we get the sectoral balances view of the national accounts.

(I – S) + (G – T) + (X – M) = 0

That is the three balances have to sum to zero. The sectoral balances derived are:

• The private domestic balance (I – S) – positive if in deficit, negative if in surplus.
• The Budget Deficit (G – T) – negative if in surplus, positive if in deficit.
• The Current Account balance (X – M) – positive if in surplus, negative if in deficit.

I suggest the above should read:

Equating these two perspectives we get:

C + I + S + T = GDP = C + I + G + (X – M)

So after simplification (but obeying the equation) we get the sectoral balances view of the national accounts.

S + (G – T) + (X – M) = 0

Perhaps the above mistake occurred because some microeconomics was applied at the macroeconomic level. That is, if a household or firm makes an investment, it normally runs down its savings. However, that idea does not apply at the macroeconomic level. That is, all else equal (external balance and budget deficit in particular), one household or firm running down its savings must cause another household or firm accumulating savings.

P.S. 23rd Feb. More discussion of the above points here, and here.


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