Friday, 2 March 2012

The sectoral balance equation again.

That ‘s the equation (I – S) + (G – T) + (X – M) = 0

There has been much discussion about this since my last post on this topic. E.g. here.

I’m sticking to my original point, namely that “I” (investment) should be scrubbed from the equation. But my reasons are now better thought out. They are as follows.

The sectoral balance equation must work as long as it refers simply to movements of cash or the movement of goods and services. But the two cannot be mixed.

Reason is that if goods worth $X move from sector A to sector B, the relevant entities in sector B certainly OUGHT to pay for the goods, but they might not. Moreover, even if they do pay, they might not pay during the time period under consideration.

The equation must work where it refers, for example, just to movements of cash, because a movement of cash from one sector must be matched by a movement of cash into another. (And if you want to do the equation on a goods and services basis, rather than a cash basis, then the same point applies: a movement of goods from one sector must equal a movement into another sector).

So if we go for a cash basis, then the defintions of I,S,G etc must be such that they clearly refer to movements of cash and nothing else.

For example, the definiton of exports (X) in the equation CANNOT BE the conventional one which is something like “value of goods sold to foreigners”. It must be something like “payments by foreigners to domestic entities for ANY reason including payments by foreigners for goods supplied by domestic entities”.

Investment should be scrubbed from the equation.

As for the idea that “investment” ought to be in the equation, I’m sticking to my point that investment should be scrubbed from the equation. Reasons are as follows.

If one private sector entity purchases an investment item from another, cash does not leave the private sector, so that particular “investment” is irrelevant to the equation. In contrast, if a private sector entity purchases an investment item off governemnt (e.g. some land), then cash crosses a sectoral boundary. Thus it must be included in the equation somehow.

One way of doing this is to scrub “investment” from the equation and replace it with something like “ non-tax payments made by private sector entities to governemnt for goods or services supplied by government”.

Alternatively, investment can be scrubbed from the equation, and “tax” could be replaced with “all cash received by government including tax and payments to government not normally classified as tax”.

And the final nail in the “investment coffin” is that it is perfectly possible for a private sector entity to make an investment without purchasing anything from anyone – never mind purchasing stuff from another sector. For example if the value of shares I own rise, that increases my “investments”, but I haven’t purchased anything from anyone to bring that about. Or if I make an improvement to my house which will last say ten years, and using materials I’ve got lying around in my garage, that is an investment which needn’t involve a purchase from anyone during the relevant time period.

Here endeth the lesson. 


P.S. (3rd March). (X-M) and (G-T) are by their very nature CHANGES to a stock, i.e. a flow. That means that if “I” is scrubbed from the equation (leaving just S), then S must also refer to a “change in a stock” (i.e. a change in the total of private sector cash savings). Thus the equation is arguably best written:
∆S + (G-T) + (X-M) = 0
(h/t to Paulie46)



  1. You scrub I from the equation by making everything consumption.

    'I' is just accounting capitalisation. It is pure opinion on whether things should be seen as consumed over multiple accounting periods.

    Shift your accounting period to a week and most consumption becomes 'I' - which then naturally increases Gross Saving.

    So its really a load of rubbish.

    What we need is a classic 'cash flow statement' for the macro economy.

    Cash is fact, accounts are opinion

  2. Gordon Bennet – that was quick, Neil. Between putting that post online and you making a comment, I didn’t even have time to have a cup of coffee. In fact the poor old “Blogger” system I use didn’t have time to get your comment onto this comment section: I learned about your comment via email.

  3. Time is short on a morning. Kids to get to school ;)


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