# Briefly Revisiting S = I + (S-I)

By JKH (cross posted at Monetary Realism)

Introduction

Some readers of Pragmatic Capitalism and Monetary Realism have been underwhelmed by the aesthetics of this equation:

S = I + (S – I)

This says that private sector saving consists of an amount required to fund investment I plus an additional amount (S – I). The structure of the equation is a tautology that cannot be falsified in purely symbolic form, of course. There has been some criticism of it for that reason. For example, one reaction (from a few people) is that a 6 year old could derive the same thing. That criticism is perhaps understandable – absent further consideration of the reason for this decomposition.

Those interested in reviewing the reasoning behind the tautological form – or perhaps seeing it explained for the first time – may wish to read further.

But before that, some earlier references:

Michael Sankowski provided an excellent, brief introduction here:

http://monetaryrealism.com/s-i-s-i-the-most-important-equation-in-economics/

I elaborated at length here:

http://monetaryrealism.com/jkh-on-the-recent-mmrmmt-debates-2/

And Cullen Roche summarized it in part 6 of his paper here:

http://pragcap.com/understanding-modern-monetary-system

With that background, we briefly revisit the reasoning behind the equation. Despite its simple appearance, there is a more nuanced explanation behind it, based on an element of Keynesian style macroeconomic intuition.

Expenditure/Income Sector Decomposition

The standard expenditure/income model:

C + I + G + (X – M) = C + S + T

For purposes of this discussion, the pivotal variable is S, which corresponds to private sector saving.

S = I + (G – T) + (X – M)    *

This says that private sector saving is an amount required to fund investment I, the government budget deficit (G – T) and a current account surplus (X – M).

Subtracting investment I from both sides,

(S – I) = (G – T) + (X – M)  **

This decomposes (S – I) into its two components – funding for the government budget deficit and a current account surplus.

Substituting the left side of **  into the right side of *:

S = I + (S – I)

And that is the equation in question. It says that private sector saving is the amount required to fund investment I plus a residual amount in excess of that, equal to (S – I). The excess amount is deliberately left un-decomposed. The occasional complaint about this form is that it is a self-referencing tautology, since it can also be derived by simple rearrangement of symbols without reference to their underlying meaning.

The ‘Keynesian Skew’

Assume temporarily that the government budget and the current account are both in balance.

Then, from the Keynesian expenditure income model above:

S = I

This equation does not mean that S is the same ‘thing’ as I.

Suppose private sector saving in the current period consists entirely of household saving of S, with the result being an addition to household net worth and a corresponding bank deposit. Suppose also that a corporation has borrowed an amount equal to S to make a new investment I during the same period. Under these assumptions, S = I. But it is obvious that the substance of I (the material substance whose value is recorded on the corporate balance sheet) is different than the substance of S (a net worth increase whose value is measured on the household balance sheet and which equals an amount held in bank deposit form).

It is measured value and not substance that is being equated in S =I.

While this may seem too obvious, it is an important distinction in following the meaning of national income accounting construction and sector financial balances using such symbols.

For purposes of this post, we’ll coin the phrase “Keynesian skew”. This will refer to the idea that government deficits are a rational response to shortages in aggregate demand, as roughly prescribed by Keynes. This translates directly to corresponding saving dynamics. According to the Keynesian skew, the private sector generally desires to save in excess of what might achievable in the absence of government deficits. This means that, unless the country is running a sufficiently large current account surplus that adds to saving, there will be a tendency for S to be insufficient in quantity to satisfy private sector saving desires in full.

Our temporary assumption above was that saving S equals investment I. The Keynesian skew suggests that the quantity of investment I will be insufficient in allowing for enough private sector saving. Aggregate demand and economic output and employment will be stopped out below potential – because the private sector is starving for more saving. A temporary equilibrium has been reached where S = I, but the economy has not yet created GDP sufficient to reach potential.

Again, suppose S = I now holds in a real world situation, and that the economy is performing below potential. There are two ways in which the economy can expand from here. Either investment I increases or something else has to give. In framing the situation, we also make the upfront assumption that investment I has pretty well maxed out.

So assume the government starts to run a deficit as a deliberate policy response.

Then:

S = I + (G – T)

Recalling the distinction mentioned above between substance and the measure of substance, the above equation means:

Private sector saving S equals an amount of saving equal to the amount of investment I, plus saving in the amount of the budget deficit (G – T). Thus, private sector saving funds both private sector investment and the government budget deficit.

(The term “fund” is used here in the sense of standard flow of funds accounting and sources and uses of funds accounting. This does not contradict the dynamic of macroeconomic construction, which is that for any accounting period, it is the expenditure on investment and the act of government deficit spending (as well as foreign sector effects in the more general case) that allows the actual private sector saving result. This dual interpretation is analogous to that emphasized in the case of banking, as described in a previous post on ‘loans create deposits’, where it is also the case that ‘deposits fund loans’:

Now bring an active current account into the picture:

S = I + (G – T) + (X – M)

That says that the quantity of private sector saving funds private sector investment, the government budget deficit, and a current account surplus.

This equation might be represented as:

S = I + SAVEGAP

Where SAVEGAP = (G – T) + (X – M)

So,

Why not just write:

S = I + (G – T) + (X – M)

Or,

S = I + SAVEGAP

S = I + (S – I)?

This is the question.

The Keynesian skew suggests that investment alone is not capable of delivering an adequate supply of saving to the private sector. Notwithstanding the amount of saving that must be generated by the same amount of investment, there is a residual shortage of saving relative to private sector desires in total – a shortage that can only be alleviated by finding outlets other than investment.

Thus, there need to be two components of private sector saving:

a) The amount corresponding to investment I – which is the amount of saving that at the macro level is created by investment, and which funds investment in the sense of both macro/micro flow of funds accounting and micro level competition for the form of financial intermediation

b) An additional amount, which by residual (tautological) equivalence, is (S – I)

And according to that decomposition,

S = I + (S – I)

This decomposition is logical, according to the assumption of the Keynesian skew. The equation is derived without direct reference to further detail in the national income equations. And that accounts for the simple term (S – I), instead of the explicit sector decomposition (government deficit and current account surplus) noted earlier.

As an alternative, the notation might have been something like:

S = ISAVE + SAVEGAP

But the logical association still holds:

ISAVE = I

SAVEGAP = (S – I)

Those whose instinct is to dismiss the relevance of such a tautology might consider that the chosen decomposition has a meaning that supersedes the mere observation that it is a tautology. The message of the decomposition is that the Keynesian skew suggests a natural inclination by the private sector to save more than the amount required to fund private sector investment alone – i.e. an excess amount which is (S – I) by residual decomposition.

More generally, the basic idea behind a residual or tautological decomposition is found in Boolean Algebra and Venn diagrams – where a given set is split in two subsets, according to the defined outer set (S), a known subset (I), and the residual gap that remains (S – I).

S = I + (S – I) delineates the idea that (S – I) is the additional saving component, when investment I alone is insufficient to deliver enough saving to achieve economic capacity. That said, a good deal of saving comes from investment I, not (S – I), and that should be a point of emphasis as well. The comparison between those two quantities is important. From there, further sector decomposition of the component (S – I) is naturally of interest. And the full expansion as derived earlier, is:

S = I + (G – T) + (X – M).

The Keynesian skew suggest that the private sector wants to save more than the amount that corresponds to investment I alone. It doesn’t exactly specify that desire as a desire for net financial assets (NFA). The fact that the demand for saving gets satisfied through net financial assets is a consequence of monetary configuration. If investment I is assumed to be maxed out, then additional private sector saving is forced into net financial asset form. But that’s not necessarily because the private sector seeks net financial assets because of their financial form alone. It’s because net financial assets is the only form in which that additional saving can be manifested, given the assumption of maxed out investment I. If investment I could be expanded, a similar aggregate demand impetus and overall private sector saving result might be achieved. In this sense, the NFA ‘solution’ is the result of the ‘failure’ of private sector investment to produce enough saving on its own. It is consistent with the judgment that government needs to act in these circumstances, absent additionally compensating export expansion.

Moreover, the circumstantial nature of NFA compositional demand can be revealed further by looking one more level down in sector decomposition terms. The private sector is composed of the household sub-sector and the business sub-sector. From the perspective of their own balance sheets, households save in the form of both real assets (e.g. residential real estate) and net financial assets (e.g. bank accounts, bonds, stocks; net of financial liabilities). And the household NFA component is present even when private sector S = I. This is because much of investment I is present on corporate balance sheets, from where it is intermediated back to household wealth through financial claims. And that puts the household sector into its own ‘NFA long position’, even when S = I. So when the private sector as a whole is in a state of seeking additional saving beyond the level of investment I  – i.e. seeking positive (S – I) – one should remember that the household sector already holds considerable NFA of its own via financial intermediation from the business sector. It is saving that is the primary quest – not so much NFA – and the NFA result at the private sector level is a function of the assumption that investment has been maxed out, with NFA expansion being the private sector saving outlet beyond that.

(MMT was the original blogosphere promoter of the NFA concept. Like most ideas, it’s been subject to scrutiny and interpretation. The equation in question has been involved in that process.)

### JKH

1. Tim says:

You lost me at:

“The structure of the equation is a tautology that cannot be falsified in purely symbolic form, of course”

Time to print this out get a cup of coffee…..

• Johnny Evers says:

It means the equation balances no matter what the value of ‘S’ and ‘I’.

If 3 = 3 + (3-3) …

Then if S goes to 4, then 4 = 3 + (4-3).

Of if I goes to 4, then 3 = 4 + (3-4)

THe rest of it loses me. I suspect it says that if you add money without having to subtract a future obligation, you’ll get growth.

2. SS says:

Cullen. can you explain this to us in layman’s terms? That math is too hard to understand for many people.

• Cullen Roche says:

Yes, just wrapping up a busy morning so let me reload on coffee and I’ll write it out for you. Though it helps to reinforce the points JKH makes here because, if you can digest the math, it really helps….

• Cullen Roche says:

Okay. First of all, some background is helpful in understanding this. Back when I was using the MMT framework (which I still think is quite good, btw) I kept running into a problem with their focus on net financial assets. We were always presenting the NFA view of the world through the identity (S – I) = (G – T) + (X – M). Tie this in with the idea that “taxes destroy money” and government spending “creates money” and it’s easy to see how someone can come to the conclusion that saving is only possible if there is a current account surplus (X – M) OR if the government spends more than it takes in in taxes (G – T). Okay so far?

Of course, there are two issues here. First, taxes don’t “destroy money”. Banks distribute almost all of our money and the govt is a user of that money by choice. There is a very specific legally mandated flow of funds occurring here. And it starts and ends with bank money (inside money). See this conversation for a simple breakdown of why the MMT reserve accounting is misleading. So you have to jettison the concept that the govt is a creator of money in our system. They only create NFA as bonds when they deficit spend. The govt is a massive redistributor of money. Not its creator.

BUT, the more important point is understanding the composition of the actual private sector balance sheet and how the flow of funds turns into a stock of financial assets that help us generate savings and ultimately growth. For instance, in the USA, there is only about 15T in NFA in pvt balance sheet that is 65T. Where does the rest come from? It comes from the I component of (S – I). But by netting out I in the original equation you essentially net out the most important piece of the entire economy. As we say, Investment is the backbone of private financial assets. The other 50T in net worth exists because the private sector takes out claims against itself. Things like common stocks, corporate bonds, etc.

So, it’s more important to understand the I component of S than it is to understand S-I. Not that NFA doesn’t matter or can’t help. But you have to keep things in perspective. When MMT says silly things like “From inception, the purpose of the monetary system is to move resources to the public sphere” they’re doing the same thing when they obsess over NFA. It’s a govt centric focus on the economy. The monetary system doesn’t exist solely for public purpose. It actually exists primarily for private purpose. So I can feed my family, buy the things I need. We build govt on as a facilitating feature to support broader public purposes. But we don’t live to pay taxes into a socialized system. That is not its “purpose”.

Anyhow, I hope that helps. Let me know if you have questions.

• SS says:

• HankB says:

Your evolution into and out of MMT has been a great development for our understanding. Most people don’t have the guts to say they were wrong. You’ve grown from your MMT experiences. Kudos and thanks.

• Cullen Roche says:

It’s about growth to me. I’ve never claimed I have all the answers. I am just a guy with a decent amount of experience, maybe above average IQ and a furious curiosity. My only real desire is to figure out how “the machine” works. A lot of people involved in economics think they have everything figured out and they take it very personally when you claim they might not. One of my strengths (the few) is that I know I can be wrong. And I know I can grow from being wrong. So in the end it’s about developing a better understanding. That’s it. If you let politics and ideology get in the way of that process it will cloud your judgement. It’s all about learning and growing to me.

• GLG34 says:

The key to understanding the monetary system is about understanding how the private sector works. I don’t care how many economists want to focus on the Fed, the Treasury, the deficit, “job guarantees” or whatever else they theorize about from their ivory towers funded by state spending. Almost none of these people have sufficient private sector experience to understand the monetary system. So they start with something they can understand which is the government. And they build their whole model around it.

As Cullen showed, the monetary system is built around the private sector. Everything else is secondary. That doesn’t mean it’s not important, but getting the emphasize right is half the ball game.

• Cullen Roche says:

Yep. For instance, it looks like MMTers put the dogs out on me this weekend because of my back and forth with Stephanie Kelton on Twitter. The author writes in the comments:

“In order for there to be any money at all, someone (the government) must issue it. But what is the debt payable in? Well, it’s circular – more money!”

This is patently wrong. The govt is not the issuer of all money. It is a designed user of money and a strategic issuer (as in, it can always procure funds or issue money if legal changes are made). Banks issue most the money. The govt just redistributes it. This author, who appears new to MMT, is still in the process of error that people go through when they first learn MMT. He has yet to get over the stage in learning MMT where you realize that taxes don’t actually destroy money at all….I went through it. It was informative and important.

Looks like someone called him out on it. We’ll see if he responds with the usual reserve accounting nonsense….

• Cullen Roche says:

He didn’t even get to the reserve accounting. My guess is this author doesn’t understand MMT entirely or that would have been his certain “go to” point here. Ah well. Many of them still haven’t understood how the reserve accounting is wrong. Many others don’t want to think it’s wrong because then the paradigm starts to crack at its very foundation….

• Cullen Roche says:

Here we go. Someone came to his rescue once again showing that MMT does exactly what all of neoclassical econ does by bringing everything back to the currency or reserves.

“You are only telling a portion of the story and making it seem to the uninitiated here as if the “private banking industry” controls the issuing of the currency , and that is patently false. Or that it can raise the money supply all by its lonesome.”

Yes, banks raise the money supply ALL BY THEIR LONESOME. What the commenter doesn’t point out is that currency (notes here) is created by the Tsy and delivered to Fed banks on demand due to the demand of bank customers who….wait for it….have accounts they want to draw upon in INSIDE MONEY. Currency (including reserves) is a facilitating feature of the money supply. Inside money precedes outside money just like resources precede taxation and private use of the money system precedes public use. MMT, like all of neoclassical econ, designs a govt centric model, when our system is pvt centric.

3. The trouble with tautological arguments is that you’re never quite sure what you’re REALLY saying. So, for example, here’s a similar argument:
Since GDP = C + G + I + (X – M) and GDP = C + S + T, it follows that

(X – M) = (S – I) + (T – G), where

(X – M) = net exports; (S- I) = private savings and (T – G)= government savings

Another way of looking at this relationship is that since GDP = C + G + I + (X – M)

(X – M) = GDP -(C+I+G), that is (X – M) = GDP – Domestic Demand

It follows that GDP – C – G = I+(X – M), that is to say National Savings = I + (X – M)

That is then to say that National Savings – Investment = (Net Exports).

So, the great point neutralizes itself with the way X – M then moves. These are interesting relationships to consider, contextually – but, there are always ultimately several moving parts and a pure isolation isn’t really possible. Unless I’m mis-reading the point of the article – which I may be.

4. Tom Brown says:

JKH, I never claimed that S = I + (S – I) was obvious to a six year old… just a sixth grader (pre-algrebra).

• Tom Brown says:

As for the rest of your post… I’ll have to think about it a bit.

• JKH says:

sorry, Tom

that wasn’t ‘aimed’ at you

it’s a type of reaction from a few people, although maybe inadvertently exaggerated on my part

• Tom Brown says:

Thanks for writing a post on this, BTW!

Isn’t this the same as saying S >= I?

6. John Carney says:

Thanks this is very useful.

One question that arises in my mind is about “crowding out.”

Let’s say the private sector desires Savings of \$1000. Let’s say that the private sector has Investment opportunities of \$1000. In that case, S=I. Everything is honky-dory.

But what if the government runs a \$100 deficit by issuing savings bonds. This injects extra income into the private sector but doesn’t necessarily create a demand for higher savings. If the government offers a high risk-adjusted interest rate (which may be as low as 0.25 percent, depending on risk discounting of the public), couldn’t it crowd out private investment. That is, savings would equal \$1000 but instead of investment equalling \$1000, it would equal just \$900.

To put it in the form of the equation,

we go from
S=I
\$1000=\$1000

to:
S=I+(G-T)
\$100=\$900+(\$100)

Which means:
I=S-(G-T)
\$900=\$1000-(\$100)

In other words, in a world in which private sector savings and investment demand are at equilibrium, private sector investment is reduced by the size of the deficit.

Thoughts?

• LVG says:

The problem with the traditional “crowding out” definition is that it states that the government competes in the loanable funds market with the private sector. That’s not right. But the government can definitely “crowd out” private investment by competing with it. For instance, when the government decides to build a government building on a plot of land outside Washington DC they are competing with the private sector to invest in that land. Now, it might be more beneficial for society to have that government building, but that doesn’t mean it doesn’t crowd out the private sector from using that land in other useful ways.

• JKH says:

There’s no financial crowding out.

If the economy is operating near capacity, there might conceivably be some element of real crowding out – due to government spending on stuff that the private sector might have invested in instead.

Apart from that, private sector investment creates saving the same way that deficits create saving.

So provided the government and the private sector are spending/investing in different real stuff, the deficit is additive, and saving would become 1,100.

• John Carney says:

JKH: I don’t mean to be obstinate but I also don’t mind occasionally sounding dumb if it helps me ask the right questions. So let me ask about what I’m missing.

If the Keynesian skew ever holds, it means that savings desire aggregates to a fixed number rather than a percentage of funds available in the economy. Let’s say aggregate savings desired is \$1000. (I like using small numbers because it helps small minds like mine not get bogged down.)

S=\$1000.

Now let’s say that the business community offers \$1000 of Investments.

I=\$1000.

Assume, for a moment, a balanced budget where government spends \$250 and taxes \$250.

G=T=\$250.
G-T=\$0

We’ll also assume a balance of trade so that X-M amounts to \$0.

Now imagine that the government decides that it wants to spend an additional \$100 to dam up rivers. It decides to fund these expenditures by issuing bonds worth \$100. So now G-T=\$100.

Where does that \$100 borrowed come from/go to?

Remember that savings desire is fixed at \$1000. It is not a function of income, as we’ve seen (or else we’d never worry about a Keynesian skew).

With the public now able to achieve \$100 of desired savings by buying government savings bonds, doesn’t there result in a \$100 shortfall for the private sector investments? Aren’t \$100 of would-be investments being crowded out?

To put it differently, now that government saving accounts are competing with private sector investment accounts, won’t interest rates rise for the private sector as it seeks to win back savings from the government?

In short, where have I gone wrong here? Why isn’t this crowding out story true?

• JKH says:

John,

Assume that the private sector has made its investment of 1000 and that’s assumed for purposes of the analysis.

That generates 1000 in macroeconomic saving – expenditures on investment are paid to the factors of production – labor and capital. That amount of money is saved in the same accounting period as the expenditure. Investment matches saving at the macro level.

(Easy to think of this as the 1000 being borrowed from a bank and paid to the factors of production which leave it in bank deposits – as in ‘loans create deposits’ idea.)

Suppose the government spends 100 on the dam.

Simplistically, it first borrows the 100 using bonds, and then spends that into the economy.

The spending generates 100 in income (similar to the case of investment) for the factors of the production of the dam.

At the macro level, that amount of money has to be saved by the non-government economy – because the income that has been earned cannot be spent by non-government on what has been produced (the dam) – because the government has already paid for the dam.

So saving by non-government is now 1,100 in total.

Regarding saving ‘desire’ – again simplistically, if it’s the case that the private sector already had all the saving it wanted, then the knock on effect of the government ‘forcing’ an additional 100 in saving is in theory a sort of hyperactive multiplier effect – in which the private sector as a result of being 100 richer than what they really want then spends in the next accounting period – and very likely puts inflation pressure on the system in doing so. The idea simplified is that when saving ‘desire’ is fully satiated, the private sector will starting spending at the margin like mad – which puts inflation pressures on the system. So the idea that private sector saving desires can be satiated as a demand doesn’t mean that the economy and specifically the government can’t force additional saving as a supply.

On the pure finance side, there’s no such thing as crowding out really – it’s all a matter of pricing. And pricing will include the effect of hyper-stimulated aggregate demand on inflation – and that’s what would cause government bond yields to rise in these circumstances. More generally, crowding out in the financing sense is always a reflection of pricing on competing financial forms and the result of that on preferences for different financial forms, as opposed to being a macro constraint on the size of overall financing.

That’s rushed; hope it makes a bit of sense (unfortunately, I have to go off line for 24 hours now).

• JKH says:

forgot to say that the 100 saved in the case of government spending is saved by the private sector as ‘net financial assets’ – in the form of bonds

• JKH says:

It’s a very good question, so let me try to answer it again (back on-line temporarily here).

Maybe there are two different ways of framing the type of question you ask:

a) The version used in my previous response, where the private sector has financed and invested I = 1000 by assumption. That produces 1000 in saving as described. But if the private sector is satiated at 1000 in saving, why would it want to save another 100 in the form of (S – I) of 100 as in the case of government deficit spending in that amount? That’s what I attempted to answer above.

b) The version that I think was more the question you posed: the government has deficit financed 100 in spending, which creates 100 of corresponding saving in the form of (S – I). If the private sector is satiated when S overall reaches 1000 (by your assumption), why would it now facilitate investment I of greater than 900? Why wouldn’t there be crowding out of investment I of 100 due to satiated private sector saving desires at that level?

So let me try and answer version b) more directly.

By assumption, the private sector has saved 100 in (S –I) as a result of government deficit spending in that amount.

Somebody then envisages a private sector investment opportunity for 1000.

There are two possibilities for how the real economy investor can obtain 1000 in financing (and we’re talking about a real economy investor here, before we get to the financial economy saver.)

The real investor either has the cash on hand to invest or he needs to finance the investment externally somehow – bank loan, debt, equity stock, etc.

If he has the cash, then he goes ahead and invests 1000. He’s really not thinking so much about the fact that his investment will generate 1000 in additional macroeconomic saving. As an investor, his issue is not the Keynesian skew relative to saving. His issue is the economic viability of a particular real investment at the micro level.

But his investment of 1000 generates private sector saving in the same accounting period, according to the necessary macro accounting result, roughly as described in my prior comment. So the private sector then has 1,100 in saving in total for the current accounting period.

From a “Keynesian skew” perspective, the combination of the two sources of saving at that point has tipped the private sector into ‘negative-skew’ territory so to speak, because the private sector is no longer short of either the investment I or the (S – I) it needs at the margin to ensure that its saving desire is met in total. It has exceeded that amount.

And that circumstance likely coincides with a state in which the economy has now been put into overdrive in aggregate demand terms, because the private sector with its saving desire now satiated will be motivated to spend more in the next accounting period. And that may put inflation pressure on the economy.

Now suppose the private sector investor doesn’t have the cash and needs to finance the 1000 externally. I think maybe this case is where your question comes into play more directly.

So in this case, I think your question is why doesn’t the private sector only facilitate 900 in financing for the investment, given that this is the amount that will be satisfactory to meet its own saving desires? Why isn’t there ‘crowding out’ of financing for the final 100 of the full 1000 sought by the real investor in such circumstances?

I think the key part of the answer is that financing is operationally and analytically separate from investment and saving.

And at the macro analytic level, flow of funds accounting is separate from national income accounting.

First, the real investor is looking at an investment opportunity. He’s not really concerned with the subsequent macroeconomic effect on saving of his 1000 real investment project – not directly.

Second, the agent providing the finance – whether it’s a bank or a non-bank – isn’t really that concerned about the subsequent macroeconomic effect on saving either.

Financing is an asset swap – with no direct income or saving effects considered as a single operation in the economy. The financing agent is concerned about swapping his own cash (or creating a loan in the case of a bank) into a specific alternative financial asset form with new risk and reward characteristics. The prospective financier will do his financial analysis on that basis, including his evaluation of project success, etc. And the financier will price his offering of finance on that basis. In the context of this discussion, he will consider his own outlook for the economy and its risks, including any implications for inflation. (Those implications should already be priced into the government bond yield curve, which serves as a reference point for private sector financing credit spreads and yield curves.) But financing as an operation gets done before the real economy investor spends the money on the project.

And it’s not the financing of the project that produces the macroeconomic saving effect – its the money that is spent on the real project that does it.

(Again I emphasize the difference between macroeconomic flow of funds accounting, which has mostly to do with asset swaps – versus national income accounting, which has to do with expenditure, income, and saving.)

The money spent on the project produces income for the factors of production. And the private sector at the macro level has to save that income, because investment generates saving at the margin in the same accounting period.

From a national income accounting perspective, what is invested (expenditure that is not consumption) corresponds to income that cannot then be double counted as an offset that also corresponds to consumption in the same period.)

Thus, the investment of 1000 is not constrained by the subsequent macroeconomic saving effect of that investment – not directly. So the project gets done, with the result that private sector saving becomes 1,100 at the end of the accounting period. The result is that the economy has now overshot the level of saving implied as sufficient according to the “Keynesian skew”.

At the end of the accounting period, the overshoot of 100 in desired private sector saving causes “animal spirits” (or something akin to that in the general aggregate demand sense) to perk up, with the private sector now poised to add to aggregate demand in the next accounting period. The economy has tipped over into “negative skew” mode, so to speak, because the 100 in deficit spending has been too aggressive in this sense.

Now, returning to my earlier explanation that pertains to the a) case noted above, where the assumption was that investment I of 1000 has already been completed, resulting in private sector saving of 1000.

So the question there is – why would the private sector now accommodate deficit financing of 100 so that the government could spend 100 and thereby create additional saving of 100 in the form of (S – I)? Why wouldn’t there be ‘crowding out’ in this case?

The government Treasury is an operational currency user – just like the private sector. So it finances with bonds prior to spending – or at least not after spending.

(BTW, the MMT assumption that bonds ‘drain’ bank reserves after “spending by crediting bank balances” is at least implicitly misleading in the government finance context, something I’ve written about at some length previously, and which Cullen Roche has been emphasizing steadily for some time now. When government deficit spends, it borrows money at least as quickly as it spends it, first draining and then resupplying existing private sector bank balances in the process. Treasury is in fact an operational currency user (of private sector bank balances).)

Similar to the case of private sector financing, the government sells bonds to the private sector as an asset swap – cash for bonds. Getting this done operationally is a matter of pricing only. It is not a function of how much the economy has saved. The private sector expresses the degree of its preference for bonds over existing bank deposits it currently holds by pricing in that preference through its bids in the bond auction process. Saving doesn’t come into that decision – not right away at least – because that transaction in itself is not a saving event – it is an asset swap.

The government then spends 100 on its project, which produces 100 in (S – I) type saving for the private sector in the same accounting period.

It is at that point that the private sector ‘realizes’ that it has overshot its saving desires by 100, and animal spirits in the form of increased aggregate demand take over in the next accounting period, same as example b).

The government in this case has overplayed its “Keynesian skew” card in effect, with deficit spending and corresponding private sector saving that will have implications for “animal spirits” of additional aggregate demand in the next accounting period.

Note: the government deficit is usually considered to be endogenous in total, due to the complexity of dynamic feedback between strength of the economy and actual tax revenue and the amount required for economically sensitive government spending assistance programs. But government has discretion to adjust spending or tax rates at the margin. This discretionary exogenous component is implied in the idea of the “Keynesian skew”.

7. Frederick says:

Elegant in its simplicity and eye opening in its importance. Thanks, JKH!

8. jt26 says:

For the layperson, I think I would understand S=I+(S-I) as a parable.
Consider a 2 person economy.
I spend 7 hours hunting deer; you spend 7 hours getting wheat.
Additionally, I spend 1 hour, inventing a wheat seeder; you spend 1 hour inventing a crossbow. We exchange both. The seeder and crossbow are investments.
In aggregate, S-I=0, which is a downer.
But, we do have a beautiful new seeder and crossbow, and we get a lot fatter next year.
(Side note: no government NFAs required; MMT ring sent to Mordor.)

9. jt26 says:

Test.

10. S-I says:

Isn’t this simpler to just say that

GDP = C + S + T

So in this GDP eqn a portion of national income goes to consumption, a portion goes to taxes. The remainder is designated S for savings. But this definition of savings is not the laymans definition because investment I has to be funded from this portion — where else can it come from?

That is why I have written previously here that for digesting this stuff the GDP eqn could be re-written as

GDP = C + S (laymans) + I + T

In this way the S is now the residual after outflows on consumption, taxes and investment which is how the man on the street thinks about savings., i.e. it is the stuff you have left over after your outlays.

This treatment also makes the sectorial model easier to understand conceptually:

(X – M) = (G – T) + S (laymans)

so we can speak of external sector surplus/deficit, government sector surplus/deficit and private sector surplus/deficit in a way that makes more intuitive sense IMO.

11. GLG34 says:

I was thinking about this a bit more. The biggest problem in this discussion seems to be the understanding of private sector liabilities. A huge amount of corporate Americas liabilities are common stocks. This is not debt or a liability in the same way that most of us think about debt. It’s just an obligation that foregoes some ownership. And this is one of the primary ways that private investment occurs.

12. Mark Caplan says:

If a credit-worthy corporation needs money to invest, say in a new plant, it can get a loan from a bank. The bank creates the loan out of thin air. That is a core principle of Monetary Realism. Banks can create money for private investment. There is no requirement that money for investment come only from savings.

Given that, there must be a flaw in Cullen’s statement:

“Assume temporarily that the government budget and the current account are both in balance. Then [...] S = I.”

Investment I is elastic and is based on the willingness of banks to lend, not on the totality of savings S.

• Crossover says:

The money that the credit-worthy corporation “spent” as part of its invetsment will end up as someone else’s savings.

13. Nichol Brummer (@Twundit) says:

Somewhere I don’t get it.

What if people have part of their savings as money, stored in an old sock, or under the matress. That isn’t free for use for Investment.

On the other hand: investments are usually done based on credit based on loans from banks. Banks have the privilege that they can give out loans based on money that is instantly created. Maybe backed-up with a certain fraction of other assets, that may be again be loans.

Should not these two effects feature somewhere in those equations?

14. Iluvatar says:

JKH:
First, thanks for posting this. +3

I had a couple questions, that I don’t beleive were covered in the comments. I will admit that I still need to read your interchange w/ John Carney however; I’ll get that done tonight.

I will admit that I am not having any difficulty w/ your algebra here, but the tautological phrasing does lead to confusion. I think we are better off with the equation I copied below. Because later in your discussion you add them back in when describing how the PVT sector’s desire for more savings is taken up the last 2 terms below. Just a thought.

Here are my terse questions:

#1: “S = I + (G – T) + (X – M) *

This says that private sector saving is an amount required to fund investment I, the government budget deficit (G – T) and a current account surplus (X – M).”

I guess the key word is *fund* above. That seems like a very awkward way to phrase it. It is certainly something I am not “getting”.

You have a parenthetical paragraph wherein you discuss flow of funds accounting terms, and I believe that is your meaning of the term *fund* above.

Please keep in mind your typical reader here isn’t a double-entry accounting major. Is there a more casual down-to-earth way to re-phrase the meaning and point you are trying to make here?

You use this phrasing multiple times in the remaining discussion.

#2: The discussion of measured value vs. substance seems like back-pedaling, almost. If money is money, does one really care?

#3: Later in the paper: “The Keynesian skew suggests that investment alone is not capable of delivering an adequate supply of saving to the private sector.”

This really confuses me, and I am having a real hard time connecting the dots here.

Except for direct hiring for an investment project, I did not see the direct connection to investment leads to savings? Can you explain this to me?

4: Your second to last paragraph went smoothly enough, but the last one was not clear. And while I have long been an advocate of breaking up the PVT sector into the BNK, CORP, and HH sectors, the NFA arguments you are making here aren’t coming across to the simple layman (which would be me, thank-you very much!). Is there a way to re-phrase this so simpletons can get it? Maybe expand this into six smaller paragraphs?

I enjoy your posts and the (obvious) hard work you put in to these efforts.

In the meantime, I am going to try and understand your interchange w/ John Carney.

Thanks again, Iluv

• JKH says:

Yes, the tautology form has some people perplexed – with some of those absolutely apoplectic about it, like I’m pretending to change the laws of the universe or something.

It’s simpler than that.

It’s a presentation that’s designed to emphasize the importance of real investment I in generating saving for the private sector and the idea that investment I is really the core of private sector saving – as opposed to (S – I), which is the net financial asset component.

So it splits S into 2 parts – investment I and ‘the rest of it’ – to emphasize that basic difference – that’s all – i.e. to get across the idea that private saving arises from 2 quite different sources in the economy.

One of the original motivations for this was that there was considerable confusion about the use of the term ‘saving’ as it related to these 2 different components. Some people were speaking regularly of saving as being equivalent to (S – I) when that was only part of it.

So the point of it is not that it’s a tautology – but that it’s a partition – for emphasis – of what the sources of saving are. The fact that it looks like a tautology is incidental to the identification of those separate components.

That’s really all there is to it. It’s a starting point for sector analysis. In other words, it’s a particular type of sector balance decomposition that emphasizes investment as a source of saving.

The term “fund” is from flow of funds accounting terminology. I think I’ll leave that one there.

“measured value vs. substance”

This is a very minor point about substance within equations. If I = S, then I is real investment and S is (financial) saving. So there is a distinction of substance between the two. Also, in S = I + (S – I), the symbol I equates to an amount of saving equal to I. So the two terms on the right hand side are subsets of saving that add to total saving.

Investment creates saving:

Maybe a simple way to see this is to consider an economy that only produces investment goods – perhaps for a short period of time, for example. The producer of the investment goods will pay for the cost of production by paying all of the factor inputs – such as wages, interest payments, and profits. All of that is income. And if none of it is spent on consumer goods (by assumption only investment goods are produced) and if the definition of saving is income that is not consumed (which it is), then all income is saved and investment equals saving. Moreover, the income that was saved could not have been earned without the investment expenditure. So investment creates saving in that sense.

“The Keynesian skew suggests that investment alone is not capable of delivering an adequate supply of saving to the private sector.”

Investment creates saving in the macro economy. The “skew” is assumed to be a bias toward the likelihood that the private sector wants to save more than what is generated by investment alone. It will tend to want more saving – otherwise it will not spend enough to get the economy up to full speed. So the government creates that saving for the private sector (through government spending) in order to encourage more private sector spending as well. Like pump priming in a way. The idea is that the private sector gradually takes over spending as its saving and wealth position improves.

There’s a lot condensed in the last paragraph of the post. I’ll try and come back on that later.

• JKH says:

yikes

Looks good at first glance, but I’ll come back to this tomorrow

Yes, the flexible use of the term ‘fund’ is tricky – its use in banking is pretty well standard, and its use in the flow of funds accounts is implicit

Later then

• Matthijs says:

Fully agree with Iluvatar. Have read the article on this page and the other references on S = I + (S-I) and it’s still wildly confusing. Even though I think I understand the fundamentals now. In this equation S is used 2 times and I is used 2 times. Supposedly to imply an important distinction. However, if both S’s and both I’s have a different meaning, why use the same letter? Why not S1 and S2 or something else? It’s just very confusing. And only the most motivated and intelligent readers of this blog might understand it. After reading, no, intensily studying many thousands of words on the subject. And even then it can be confusing.

This way, you’re not going to reach any wider audience.

Is there really no easier way to explain things? From reading an equation two things must be very, very clear:
1) What the terms mean exactly
2) What the causality is

Something Iluvatar says comes closer to something that is easier to understand: ““S” is what is left over after “I” got done, “G-T” got done, and “X-M” got done.”

In the end it’s all about the stories you tell or want to dismiss. Like a very important one, which most people don’t understand/know about: a bank creates new money for a company, which gets spend on a factory and loans, which ends up being the savings of the workers. That’s a different story then for example “person A gets his money to the bank which allows the bank to loan it out to company X” (the multiplier story)

Or the story like the one you hear all the time now by austerity proponents, “we must spend less now, otherwise our children have to pay the bill”.

So I’m not sure the S = I + (S – I) is really helping in that sense.

15. Cullen Roche says:

YOu’re always “in”. It’s just that the spam filter doesn’t always like your formatting so it gets caught. I always release them, but can’t always do so in a timely fashion so keep that in mind!

16. Iluvatar says:

JKH:

I just visited the MR site where there are currently 98 comments on your posting!

Dear lord.

And who is this Phil P guy? Honestly, I never seen you cuss in a post before this.

Btw, an identity *is* an equation, and accounting *has* equations (where did he come up w/ this stuff?).

Whew!