Does S = I? One for the economics wonks

Posted on

A commentator called Nick asked on the blog:

I’ve seen you use the national income identity repeatedly when talking about MMT:

Y = C + I + G + (X-M)

Where Y = GDP, C = consumption, I = investment, G = government spending and X-M = net exports.

But it is also true that:

Y = C + S + T

where S = private saving and T = taxes paid

Equating, this gives:

C + S + T = C + I + G + (X-M)

Rearranging you get:

I = S + (T-G) + (M-X)

Where T-G is public saving and M-X is capital inflow.

Which states that investment I equals the sum of public and private saving, plus net capital inflow. Which suggests tha investment is directly linked to saving.

However, in your blog above you say that:

“There is no tie between investment and saving”

Which is incorrect, given these accounting identities. So is this statement you have made wrong, or are the accounting identities wrong, at which point they would also be wrong when applied to MMT.

Which is it?

That's a good question and so it deserves an answer. But let's be clear in the first instance that the answer is in the question. If, as example, S = 0 (and that is quite possible) then, of course, there would be no link between I and S (investment and savings).

But let me expand another term forst. As I (and Stephanie Kelton, and Bill Mitchell, with slight variation on the theme in his case as I recall it) have all argued:

G = T +∆B + ∆F

where G and T are as above, B is government borrowing and F is government-created money (or funding)and ∆ simply represents the change in the stock over a period, so measuring a flow.

In that case:

G - T = ∆B + ∆F

Since G - T can be a negative or positive sum the ordering in which they are written is inconsequential: the same is then true of ∆B and ∆M, which can both have positive and negative value in the same period and need not be similarly signed.

In that case it is possible to rewrite your rearranged formula as:

I = S + (∆B + ∆F) + (M-X)

For the sake of argument hold foreign flows constant: it just makes the formulas eaier to follow and the assumption could be realxed if desired but the same conclusion would be reached.

No let's assume the savings ratio is zero (which is entirely plausible).


I = ∆B + ∆F

In other words, it's entirely possible that if the overseas sector holds constant and that savings do too then investment is all funded by net governmment flows.

I make the point for a simple reason. There could be a relationship between I and S. But you have to make assumptions to make that relationship. And the fact is that if, as has been the case of late the savings ratio has been small or even negative, then investment can be financed by the government, or by government-created money or by overseas interests (to relax that condition, once more). In other words, there is nothing that says there is an immutable relationship between S and I. There is just a funding mix and it is my suggestion that the relationship is weak at best, and that other factors can be and almost certainly are more powerful, and that can and should now include government-created money to be used for this purpose.

And quite specifically, investment need not be funded by saving, at all. Hence my claim, which I think holds true.

Other opinion is, of course, welcome.