Noah Smith starts to get S = I + (S – I)

Seems like our little corner of the internet got a bit more popular. Noah Smith is nosing around S = I + (S-I).

The It-boy of economics, Noah Smith, has stumbled across an issue which we hold dear. Saving/Savings, and Investment/Investments are hard to understand, and yet I feel even slightly better understanding is extremely useful.

Noah Smith points out in the absence of a government sector, saving and therefore a stock of saving called savings, can still exist. Defining the government out of existence does not break accounting, so the S = I relationship holds. Still, as we’ve pointed out, even smart people like Nick Rowe routinely forget we live in a world with government and foreign sectors – and even beyond that assumption, the relationship between Saving/Savings and Investment/Investments is slightly magical.*

He gets confused for a bit, but then sorts out that surpluses and Savings are different, which makes it all work for him.

“Some people are telling me that “private-sector surplus”, as used by Hatzius and others, does not mean “private saving”, but rather “private saving minus private investment”. In that case, the accounting clearly makes sense, and does not conflict with my example (since storing salted venison is investment).

However, he hints at a more interesting question here:

“OK, so what about the nominal value of the real assets (salted venison) sitting in the sheds? This is determined by the nominal price of a pound of salted venison – i.e., how many pounds of fresh venison must be exchanged for a pound of salted venison. The total stock of nominal assets in the economy is given by: (lbs of salted venison) * (lbs of fresh venison / lb of salted venison)

Can this rise? It seems to me that it can. Suppose that the stock of salted venison increases, s per the previous example, but the price of salted venison stays fixed (which we can assume because we’re just looking at accounting identities, not at the determinants of prices). It seems that aggregate nominal saving is positive.”

This is a massive simplification of the real world. Still, it’s useful. It makes us think about the S = I relationship. I’ll give massive kudos to the venison/salted venison idea, because it sure makes the flow/stock idea much easier to understand. It’s a very useful thought experiment simply due to this distinction. unsalted venison is the flow, salted is the stock. Nice!

When we add in a few details, it becomes clear the relationship he is talking about here is not trivial.

  • If we make the stock of venison large to the economy, things become much more uncertain.
  • If we allow other assets to become savings, but which are still valued in venison, the world becomes more complex.
  • If we abstract to paper fiat money rather than commodity money (venison), the stock of savings becomes something entirely different in real and nominal terms.
  • If we then allow banking to create money against the stock of savings – like we do with our real estate monetary standard – then things become even more complex.

The S = I relationship is only useful in a very, very limited world, and our modern world is not simple.

About that “*”. Magical in this case means “something which has not been well figured out”. As we know, any sufficiently advanced technology is indistinguishable from magic. We know S = I + (S-I) because it must. Yet, the workings seem “magical”. Godley helped to scientize (neologisim warning) some of this magic, but it sure seems like there is a lot of work left to do.

I’ll circle back with my favorite economic quote of all time, because it helps to scientize the magic. From the paper “Fiscal Policy will Matter“:

“It is thirty years since Carl Christ, of Johns Hopkins University, had the brilliant insight that should an economy ever reach stationary equilibrium, all stock variables as well as all flow variables would be constant; and that if all stock variables, including government debt, were constant, government receipts would have to equal government payments. It would then follow that if the economy were moving toward stock-flow equilibrium and if taxes were levied as a proportion of income, the GDP of a (closed) economy would always be tracking, perhaps with a long lag, government outlays divided by the average tax rate – the very same concept that we call fiscal stance. Therefore, a necessary condition for the expansion of the economy, at least in the long term, is that the fiscal stance should rise: Government expenditure must rise relative to the average tax rate. If the tax rate were held constant, government expenditure would have to rise absolutely for output to grow; if government expenditure were held constant, the tax rate would have to fall.”

In a closed economy, if you balanced the budget over a long time, the economy cannot not grow in nominal terms.

But I also love this quote because he uses it as a launching pad to demonstrate the importance of credit to the economy. The next thing he does in the paper is to say: “You need to add government and the foreign sector to make it more accurately match the real world.” Then he notes even adding these sectors to the fiscal stance is not enough.You need to add credit to these numbers to get the best match to what we see in the economy.

Adding in credit creation/destruction makes all the difference, which he then shows in his deceptively simple prose and method.

Yet, the amount of credit created in an economy has limits. Nearly all credit is created against the stock of Savings which the economy has created for itself over time. This stock is not infinite. This stock can also vary in value. Different parts of this stock can also be expanded to devalue that sector of the stock relative to other parts of the stock.

All of this relates back to the venison/salted venison story Noah told, and is related to the safe asset debate which David Beckworth is spearheading.

We are faced with a huge dilemma:

  1. We want nominal GDP to grow faster than real GDP because hoarding causes bad effects on our economy; but,
  2. Credit creation is constrained by it’s relationship to the stock of Savings, government is constrained by credibility issues, and foreign investment is…heh.
Nearly all of the debate around this issue is about how to get that lump of real Savings to become nominally useful in some way, but it’s already Investements, and so these need to be repurposed in some way, or using the (S-I) magic to make our economy gainfully employ the full population.
So, thanks Noah for bringing this up.


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124 Comments on "Noah Smith starts to get S = I + (S – I)"

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3 years 9 months ago

“a stock of saving called savings,”

In national accounts language savingS is used as a plural of saving.

In ordinary language savings refers to a stock.

However the former is definitely the usage of practitioners, so it is better to not using savingS as a stock.

What is InvestmentS?

3 years 9 months ago

Do you see savings used as a plural? I think I would tend to talk about the combined saving of all sectors, rather than the combined savings. I don’t know. Anyway, if you can use the plural of saving, I guess you can use the plural of investment. Probably best avoided though, as it’s bound to cause confusion.

3 years 9 months ago

Yeah one talks of savings ratio (not saving ratio) or a saving rate and no savings rate – although they are equal. I think it is saving when one talks of disposable income less consumption but savings when it is the counterpart – the saving allocated into various assets even for a single sector or a unit.

Yes savings is also used as combined saving of many sectors.

3 years 9 months ago

Good point. A lot of confusion seems to arise from ambiguity of terms.

The flow of income less consumption is saving and the stock is called “wealth.” A portfolio is comprised of monetary, financial, and real assets. In ordinary language, monetary assets are called savings, and financial and real assets are called “investments.” Total assets minus total liabilities are net worth. Most people are going to understand the terms in portfolio terms, and it seems strange to them that they are used technically in a different sense in other contexts.

How to overcome this ambiguity at this point, when the use of terms in context is well-embedded culturally and institutionally?

3 years 9 months ago

Talking of ambiguity, here is how physicists live with ambiguities without any problem. See footnote 12 here in this funny website page:

on how they use the symbol “pi” in the same context to mean two different things!

3 years 9 months ago

We want nominal GDP to grow faster than real GDP because hoarding causes bad effects on our economy; but,

I’m not convinced by this. I still think it would have more chance of working if an asset tax were used as the way to ensure that resources were put to productive use rather than being locked up due to hoarding.
Expanding nominal GDP faster than real GDP still lets you keep ahead of inflation by speculating in secondary markets in an entirely unproductive way (that is hoarding too in its own way).

If hoarding were discouraged by an asset tax, then real GDP expansion due to improving technology and organization, could continue apace with no increase in nominal GDP and instead falling prices as occur today for computers, DNA sequencing, solar power etc.