Explaining S=I: Inventories vs Adding up Individuals

It's easy to teach students the arithmetic showing that actual saving must equal actual investment (S=I). But many students (quite rightly) want more than the arithmetic. Because S=I is not intuitive, and good students want to understand the intuition. I think that most profs will try to explain the intuition by talking about inventories of unsold goods. But I think it would be better to explain the intuition behind S=I by talking about the difference between individual saving and aggregate saving; some types of individual saving don't add up to aggregate saving.

A student's email is what prompted me to write this post. He's read three textbooks on the subject, and has read my old post, and understands the arithmetic, but still doesn't understand the intuition. Here's one of his questions: "Or, suppose I buy a used car. Is it saving? How will in this example saving be equal to investment?". Here's how I would answer his question: "Yes, your buying a used car is saving, because you spent part of your income on something that is not a newly-produced consumption good. Which is how we define "saving" in National Income Accounting. But someone else must have sold you that same used car, so if you were saving (buying an asset), that someone else was dissaving (selling an asset). It is impossible for everyone to save by buying used cars."

My Twitter poll suggests the student is not alone. And I suspect that many of those who answered "Easy" did so because they were taught the "Inventory" intuition: "If saving exceeds desired investment, then firms produce more goods than they sell, so unsold goods pile up as undesired inventory accumulation, which counts as actual investment. The orchard sold the unsold apples to itself!"

Here's why I don't like that "Inventory" way of explaining the intuition. S=I is an accounting identity, and accounting identities are true by definition. So it's wrong to try to explain an accounting identity by smuggling in an assumption about the world: that firms decide on the level of production before knowing how many goods they will sell. S=I is still true in an economy where firms produce goods to order, so never find themselves unable to sell goods they have produced. And S=I is still true in an economy where all goods are pure services, like haircuts (consumption) and teaching haircutting (investment), that can't be produced then stored in inventory waiting for a buyer. And, I think that what students have difficulty understanding is not about inventories but about the difference between individuals vs aggregates. And Macro is supposed to be about the difference between individuals and aggregates (fallacies of composition etc.) anyway.

Here's how I think about "saving":

I earn $1,000 income this month (or year or whatever) from producing goods. What can I do with that $1,000?

1. I can spend it on newly-produced consumption goods.

All the remaining categories count as "saving":

2. I can spend it on newly-produced investment goods.

3. I can spend it on anything that is not a newly-produced consumption good or newly-produced investment good. The list is endless, but would include used cars, old paintings, land, bonds (when I lend money I am buying an IOU or bond), etc.

4. I can not spend the money at all, but leave it sitting in my pocket or chequing account.

When we add up across individuals, category 3 above disappears. If I buy your used car, then you sold that used car. If I buy your old painting, then you sold that old painting. If I buy your land, then you sold that land. If I buy your IOU (lend you money), then you sold your IOU (borrowed money). It all cancels out in aggregate.

If it weren't for Category 4, I could stop here. Since Category 3 saving cancels out in aggregate, that leaves only Category 2 saving, so aggregate saving must equal aggregate investment. The only way we can all accumulate more assets (saving) is if we produce more assets (investment). Anything else is just one individual transferring an asset to another individual.

Category 4 is where the fun starts.

You might say that Category 4 is like Category 3, and in a way it is. If I accumulate money, then you or someone else must deccumulate money, if there's a fixed stock of money. Or if a bank creates money, so I can accumulate money, it does so by buying an IOU, so you must have sold an IOU, and the money the bank creates is the bank's IOU, so all the IOUs cancel out, so categories 3 and 4 together cancel out.

But there's a difference between Category 3 and Category 4.

Category 3 saving is voluntary exchange. I can't buy your used car, and you can't sell your used car to me, unless both of us agree to the deal. I want to save, and you want to dissave. Category 3 saving is a bilateral decision with desired saving by me and desired dissaving by you. Category 4 saving is a unilateral decision. If I want to save by leaving the money I have earned sitting in my pocket, I just do it. I don't need to ask your permission and persuade you to dissave.

But since my expenditure is your income, if I spend $100 less money on anything, your money income is $100 less. And it's the same for me if you spend $100 less money on anything. Each of us as individuals can save by reducing the flow of money out of our pockets, without it affecting the flow of money into our pockets. But collectively the flow in equals the flow out, so collectively we can't save that way. Our individual attempts to save by accumulating money must collectively fail, but would have caused our money income to fall until we stopped trying. [I have edited the previous sentence in response to Andy Harless' comment below.]

Addendum: Here's the arithmetic of S=I:

Define Y as market value of newly-produced final goods (and services). In a closed economy (no net exports NX) with no government spending G or taxes T we divide Y into consumption goods C and investment goods I, so Y=C+I. And we define saving S as S=Y-C. Substitute the first equation into the second to get S=Y-C=C+I-C=I, so S=I. If we bring government into the picture it changes to Y=C+I+G. And private saving is now Sp=Y-T-C, government saving is Sg=T-G, and national saving is S=Sp+Sg=Y-C-G=C+I+G-C-G=I. If we bring foreigners into the picture it changes to Y=C+I+G+NX, so S=I+NX (saving that is not invested domestically is lent to foreigners to finance net exports).

Comments

[Kyle A]

As someone who responded "difficult" to your initial poll, let me say that this was a helpful post.

Category 2 was always easy to understand.
Category 3 now is crystal clear
Category 4 is now clearer, but still a little foggy

If I'm reading you correctly, in Category 3, for every bilateral transaction there is a buyer and a seller, which in other words means there are equal amounts of savings and dissavings. Category 4 is similar. For every singular, unilateral decision to keep money in a bank account or a wallet (savings), there is an equal and opposite amount of displaced money income (dissavings). Because you didn't spend $1 on apples, the apple seller is now $1 poorer in income.

So since Categories 3 and 4 in the aggregate cancel out, all that's left is Category 2.

Did I get that right?

[Stephen Gordon]

I wonder to what extent this is similar to the 'immaculate rebalancing' school of balance of payments analyses. There, too, one is tempted to use accounting identities as theories, so people forget that things like exchange rates and interest rates have to move in order to get people to make the decisions that make things balance.

[Market Fiscalist]

I think the reason that economic professors talk about inventories of unsold goods is because that is the area where the term Investment is used in a way that is contrary to everyday parlance.

If I produce 100 consumer goods to sell but only succeed in selling 80 of them then this would not sound like Investment to the average non-accountant. In my opinion it is the transformation of Potential C into Actual I (based upon what is sold) that is implicit in the equations that is non intuitive and confusing to people.

This confusion does not exist in economies where all goods are produced to order , or there are only services and in those economies the equations would not be at all non-intuitive.

[Nick Rowe]

Kyle: thanks! Yes, I think you've got that right. Category 4 is always the tricky one, because money is not like other assets. We use money as medium of exchange, so it flows both into and out of our pockets whenever we sell or buy anything else. So there are always two ways to accumulate money: increase the flow in (which is a bilateral decision); decrease the flow out (which is a unilateral decision).

Stephen: I think there's a similarity. But there's also a difference, because the open economy is, in a sense, a bit like an individual household. We Canadians *can* all save by buying used cars, if we buy them from the US (and export new cars or whatever in exchange).

MF: I think you might be right. And when I used to teach Intro, I would talk about inventory accumulation when I explained why production had to be equal to expenditure. "Accountants cheat, to make the accounting identities come true! They say you bought those unsold apples from yourself!"

[Roger Sparks]

Following the assumption that I earn $1000 this month, I much prefer to consider how the person who enriched me got this $1000 and why did he give it to me. This approach causes me to question the accounting identity S=I when applied to macroeconomics.

The giver could be taking the money from long term savings, from HIS last pay check (short term savings), or he could be borrowing from himself (as when government borrows from the central bank). I, as a receiver of money, could have earned it by building a new product but in this modern world, only a small number of people actually build products that actually have an inventory presence. Most 'inventory' is the result of constructive accounting.

By beginning with income and then discerning the source, we recognize that when we divide output "Y into consumption goods C and investment goods I, so Y=C+I, we are looking at a small part of the economy, albeit a very important part. Having defined Y as representing goods (either consumption or investment), we cannot go on to add government spending (as in "Y=C+I+G") because doing so would increase Y to the extend of government spending.

Of course, "Y=C+I+G" is accepted macro accounting so we have an incongruity. In my own mind, I redefine the macro investment term 'I' into a balancing term having meaning only so far as it balances the equation. I would conclude that term I has nothing to do with inventories.

[Andy Harless]

Your explanation is different from mine. But I have a bit of a problem with yours in that it seems to be a story about the future, not about the present. "Our individual attempts to save by accumulating money will collectively fail, but will cause our money income to fall until we stop trying." But the identity has to work even in an arbitrarily short time period, where there might not be time for our money income to fall.

Of course you could argue that my story is a story about the past. "You did invest or dissave, and now that I am receiving income from your act of investment of dissaving, I'm saving that income." But the time span involved is inherently infinitessimal.

[Benoit Essiambre]

I'm surprised to hear that the standard teaching story is about inventory. Isn't this kind of narrow? What about infrastructure, equipment, buildings, factories, tools, upgrades, improvements, renovations, durable goods etc. Even things like education, teaching, skills building, scientific discovery or data gathering can be "stored" as knowledge in people's heads or on paper. Or are all these things considered "inventory" in economics? I guess they all vaguely fall under inventory or production capacity. "Capital" might be to polysemous of a word to use in teaching. It might add to the confusion.

To me, the point of S=I is that to be considered net S or I, it has to add to the worth of the stock of intrinsically valuable physical things or stored useful information and not be just promises, financial instruments or numbers in an account.

[Nick Rowe]

Roger: sorry, but you lost me there.

Andy: good point. I think I worded that wrong, because, as you say, this accounting identity says nothing about future (or past) time periods. Is this better?: "Our individual attempts to save by accumulating money must collectively fail, but will have caused our money income to have fallen to a point where we stop trying."

Benoit: "What about infrastructure, equipment, buildings, factories, tools, upgrades, improvements, renovations, durable goods etc. Even things like education, teaching, skills building, scientific discovery or data gathering can be "stored" as knowledge in people's heads or on paper."

Those are all investments. But those are desired or planned investments. What's different about inventory accumulation is: we don't normally think of it as "investment, so it's counter-intuitive, and needs explaining; it can be unplanned/undesired, like when you produce goods planning to sell them, but fewer get sold than you had expected.

[Steve Roth]

Here’s the key conceptual difficulty IMO, which (as you're aware) I spent years struggling with:

Saving is not a flow. (Though it is a flow as opposed to a stock measure — tallied over a period of time, not at an instant.) It’s a residual of two flows — income minus (consumption) expenditure.

So you can’t point to any transaction and say “that’s saving.” Buying Apple shares or a work of art is just an asset swap. It has no effect on your total assets or net worth — only the composition of your portfolio assets. Depositing a paycheck in your checking account isn't saving, until you don't spend it. Saving is, by its very nature, a non- flow. That's its sine qua non.

You can point to a transaction and say “that’s investment (spending)”: paying people to create goods which will not be consumed within the accounting period (or in practice and measurement, buying such newly created long-lived goods).

But if you conflate this investment spending with saving, you have a very troublesome conundrum: spending is saving? That's a difficult thing to intuit, for undergrads inevitably thinking in terms of household "saving"; (almost) all household spending is consumption spending, so saving is just...income minus expenditures.

This embodies a broader problem, the almost universal confution of wealth with real stuff (wealth is market-traded and -priced claims on stuff) that I think is most perfectly expressed in the phrase "financial capital" a confusion which is pervasive across economics — from Marx and Ricardo to Lucas and (very much so) Piketty — he explicitly makes wealth and capital synonymous...except when he doesn't.

[Andy Harless]

Steve: In my version I point to the transaction in which you received the income and say "that is saving" (on your part). Somebody else is spending, but you are saving what they have just spent.

[Steve Roth]

Andy: So then, condensed, "income...is saving"? That seems deeply problematic.

[Nick Rowe]

Steve: I think I get what you are saying. We can identify the flow of income, and identify the flow of consumption, but saving is just the residual difference between the two. Saving is not a thing, it's an "anything else" category, a "non-thing".

And ordinary people's concept of saving (=not spending) isn't the same as economists', true.

But I think it's useful to break down that "non-thing" saving into: transactions where we buy new investment goods; transactions where we buy other assets (real and financial); the residual where we don't buy anything at all but just accumulate money. Because, even though it makes very little difference to me as an individual whether I buy a newly-produced house or a one-year old house, or whether I buy a bond or leave the money I earned in my pocket, it makes a macroeconomic difference.

"Financial capital/wealth" makes sense for an individual, but doesn't add up right. I hear it from Marxists, but didn't think Lucas uses that concept?

[Steve Roth]

Nick: >Saving is not a thing, it's an "anything else" category, a "non-thing".

Sure. But when we resort to the word “thing,” we know we’re in trouble. I think it’s clearer to call it a non-flow. (While it’s obviously a flow measure.) Really, that’s what makes it what it is. Saving is not-spending. (Out of, relative to, income, over a period. I think spending out of wealth/assets is a more pertinent and transparent concept, but that’s a further discussion.)

Takeaway: saving, being a non-flow, does not, cannot, increase any imagined stock of “savings.” (Whatever stock measure that undefined but pervasive plural is referring to.)

When you “save” — spend less than you receive — you have more money/wealth. We don’t. When you eat less corn, we have more corn. When you spend less money, we have no more money.

Real goods and balance-sheet assets/claims are created and destroyed through utterly different mechanisms. Income - Consumption is trying to subtract apples from dollars. (Intuitive?)

Production creates stuff; it doesn’t create balance-sheet assets. Those are created by the government/financial system through three mechanisms: 1. bank net new lending, 2. gov def spending, and 3. (overwhelmingly dominant) holding gains. (That system is “looking at” the stock of real goods when it creates those assets. If there’s new stuff out there, it creates new claims, balance-sheet assets, reflecting ownership of that stuff.)

>[1.] transactions where we buy new investment goods; [2.] transactions where we buy other assets (real and financial); [3. ] the residual where we don't buy anything at all but just accumulate money.

My definition of “spending” might help here: “transferring assets from the lefthand side of one balance sheet to the lefthand side of another, in exchange for newly-produced goods and services.” (Physical cash is just a convenient technology for making that balance-sheet transfer.)

By this definition, #2 is not spending. It’s swapping existing claims/assets. That’s why GDP ignores these transactions.

Gonna stop here, but a last key point I think: national-accounts Saving (a residual of national accounts Income) doesn’t even come close to explaining balance sheet changes — ∆ total assets and net worth. Intuitively, it should, right? As in normal business accounting statements?

Maybe useful: images in this tweet and thread, responding to Josh Mason’s preceding tweet image from the BEA:

https://twitter.com/asymptosis/status/960531936241422337

[thomas michl]

I don't see any reason to stop using the inventory story--its worked for me for a couple of decades. The important point is that *actual* investment is defined to include any change in inventories. That is what makes Actual I=S an identity. The inventory story comes in handy because it provides a (primitive) explanation of why AD=Y or Planned I=S describe equilibrium: if you produce too much (Y>AD), inventory accumulation sends a clear signal to reduce production.

Its true the inventory story would collapse in a pure service economy. But then you'd always be in goods market equilibrium with Y=AD and no distinction between actual and planned investment.

[Dan Kervick]

To derive S = I as an "identity" that is "true by definition", one must assume that the equality S = Y - C is also true by definition. Far be it from me to deny economists the right to make whatever stipulative definitions they want for the letters they introduce into their alphabetic manipulations, and to attach English words to them in various Pickwickian ways that might suit their fancy. But simply stipulating that "S" shall be taken to be Y - C, where Y is the total output in a closed economy during some given period of time, and C is the total output of consumables in that closed economy during some period of time, does not correspond to any sensible prior understanding of saving at the social, macro level.

A society should be deemed to have saved during a given period of time if it has made a net addition to its stock of wealth during that time. The value of it's wealth stock entering that period consists in whatever investment goods it has produced previously that still exist and have not depreciated into valuelessness, along with whatever consumable goods it produced in the past that have not either been consumed already or gone to waste:

W(initial) - CS(initial) + IS(initial)

During the period in question there is a gross output of new consumables and new investment goods. This is income:

Y = C + I

During that same period there will be a loss of some previously existing wealth, and of some of the potential additions of new wealth, due to the consumption of either new or previously existing consumables, plus the depreciation of either new or previously existing investment goods. Call this "outgo" - in contrast to income" - and represent it like this:

Y* = C* + I*

Note that these three variables typically represent negative numbers, if the previous variables are assigned positive numbers.

So, we have:

W(final) = W(initial) + Y + Y*, or

W(final) - W(initial) = Y + Y*.

This quantity W(final) - W(initial) = Y + Y* represents what it means for a society to have saved in the net. The society has positive saving during a period if it is wealthier at the end of the period than it was at the beginning, i.e., if it has made a net addition to it's stock of wealth. How does this relate to investment? Well, net investment is I + I*. We have:

S = Y + Y* = (C + I) + (C* + I*)

S = (C + C*) + (I + I*)

In English, saving is the net addition of consumables plus the net addition of investment goods.

The attempt to measure and approach these clear and useful notions by looking at transfers of income or wealth stock (which includes purchases) is bound to be misleading. At the macro level, goods of any kind changing hands, whether as gifts, takings or part of an exchange, make no difference to the income, saving and wealth of the society as a whole. Measuring the purchases of newly produced consumables doesn't even tell you about consumption and saving, because it doesn't tell you whether those consumables were actually consumed, or were added to the wealth stock.

[Matt Young]

S=I because we mostly use double entry accounting. We use double entry accounting because any triple entry accounting system can be decomposed into a set of double entry accounts.

When S=I we are in compliance with the savings = loan ratio managed by central banker. Any deviation from S=I is considered a random mis-pricing and gets a separate liability account, and that account tracks the disequilibrium of the currency.

The real question is why do all natural processes appear as a yin and yang (look it up). That is a question for all things natural, not just accounting.

[Nick Rowe]

thomas: fair point. But I might be planning to invest in a machine, but be unable to buy one, because I can't find a willing seller.

Matt: for every apple sold, there's an apple bought. I think that's the origin of this particular identity.

[Jamie]

I’ve been reading about economics for a decade. When I started, I thought that accounting identities would be a good way into the subject as accounting seemed to be a bridge between the real world of business and the more esoteric world of economics. However, it has turned out that accounting identities form an almost insurmountable hurdle to a shared understanding. The most interesting question for me is to ask: what are the main obstacles to any shared understanding?

Nick’s student: "Or, suppose I buy a used car. Is it saving? How will in this example saving be equal to investment?"”

This makes me want to scream in frustration.

Suppose Nick’s student buys his used car from me. We are both households so the business sector (including investment) is irrelevant. In this transaction, Nick’s student gains a used car and I lose a used car. Nick’s student loses the money he paid for the used car, and I gain the same amount of money. If we think about the TRANSACTION, we can see that the two sets of gains and losses cancel out leaving a net change of zero. There is no net saving and no net anything else. This is obvious, as no cars or money were created during this transaction, so the total of cars and money in the economy did not change. Obviously, this is true at the macro level too. If we add up a million similar transactions, there will still be no net effect.

The key problem here is that Nick’s student seems to imagine that he can buy a used car without someone else also selling that car. It is thinking about the INDIVIDUAL, in isolation, rather than the TRANSACTION that causes this problem. And that is the first, and biggest, insurmountable hurdle to a shared understanding between business people like me (who think about TRANSACTIONS) and economists (who think about isolated INDIVIDUALS). I might add that it is the failure to think about both halves of transactions that results in the paradox of thrift. There is no paradox if you think about both halves.

There are other problems in developing a shared understanding but most of them stem from this very basic problem. I would argue that this problem is also at the heart of the mainstream versus heterodox schism. I have yet to hear ANY economist explain why thinking about half of any economic exchange, while ignoring the other half, makes any sense at all. If anyone has such an explanation, I would like to understand it.

[Nick Rowe]

Jamie: well, economists *do* talk about demand *and* supply, so we are thinking about the people on both sides of the transaction.

But "demand" and "supply" aren't exactly the same as "buying" and "selling". Because we are talking about how many apples some individuals *want* to buy, and how many apples other individuals *want* to sell. And the wants/plans of those different individuals may be inconsistent, and we talk about how the price of apples adjusts to make them consistent. Even though the actual number of apples bought must necessarily equal the number sold, because, as you say, it's just two sides of the same transaction.

We start with individual choices, and then ask what (if anything) adjusts so that individuals' choices to buy and sell become mutually consistent. It's the problem of the coordination of millions of individuals' plans.

With "saving" and "investment" it's similar. But "saving" is a much harder concept to grasp than "apples bought". And it's less obvious what adjusts to bring desired saving equal to desired investment.

(By the way, households, not just businesses, can invest.)

[Steve Roth]

Coming back to this, trying to be more concise on the intuitive problem I’ve wrestled with:

Investment — paying people to create new stuff that will not be consumed within the accounting period (usually a year in practice) — increases our collective stock of stuff.

But it does not create new monetary “savings” — balance-sheet assets and net worth. Those are only created by bank lending, gov def spending, and capital gains (all in response to an expanded stock of real stuff).

Likewise individual saving does not create new collective balance-sheet assets. (It does increase an individual’s assets/NW, of course.) Saving just means you hold assets in your account rather than transferring them to another’s. The stock of assets only increases via the three mechanisms above.

And since saving doesn’t create “savings,” assets, wealth, “loanable funds,” it can’t fund investment.

(I’d say that the proximate “funding” source for most investment is just portfolio/asset churn: people swapping treasuries for cash, and swapping the cash for shares in a real-estate development venture.)

[Egmont Kakarot-Handtke]

#DrainTheScientificSwamp

Links on Nick Rowe’s ‘Explaining S=I: Inventories vs Adding up Individuals’

Macroeconomics is one of the most embarrassing failures in the history of modern science. Fact is that economists do NOT understand to this day that I=S is provably false since Keynes.

I is never equal S and even Nick Rowe will eventually grasp it
https://axecorg.blogspot.com/2018/01/i-is-never-equal-s-and-even-nick-rowe.html

How Keynes got macro wrong and Allais got it right
https://axecorg.blogspot.com/2016/09/how-keynes-got-macro-wrong-and-allais.html

Kalecki and Keynes: The double macroeconomic false start
https://axecorg.blogspot.com/2018/11/kalecki-and-keynes-double-macroeconomic.html

Heterodox economics: When stupidity becomes a public danger
https://axecorg.blogspot.com/2018/09/heterodox-economics-when-stupidity.html

Keynesians ― terminally stupid or worse?
https://axecorg.blogspot.com/2017/08/keynesians-terminally-stupid-or-worse.html

For details of the big picture see cross-references Refutation of I=S
http://axecorg.blogspot.com/2015/01/is-cross-references.html

Egmont Kakarot-Handtke

[Roger Sparks]

Does the following example help make S=I intuitive?

Two workers receive cash for their labor during the year. One worker makes beer and the second makes cars. At the end of the year, most of the beer has been consumed but most of the car production remains. There may or may not have been a change in the amount of cash during the year.

The reader can see that this example begins with cash used to pay workers. Unlike Nick's example, each worker worked because someone wanted to dis-save cash. At least for an instant, each worker traded labor for cash and each dis-saver traded cash for inventory. During that brief period, S would have equaled I. Over the longer period of one year, most of the beer would have been consumed and some of the cars. There is no reason to think that S should continue to equal I over the longer period unless we arbitrarily made the two items equal for accounting purposes.

MERRY CHRISTMAS TO ALL!

[Nick Rowe]

Merry Christmas Roger, and to all!

[Egmont Kakarot-Handtke]

Roger Sparks

I is NEVER equal to S. Therefore, it is a futile exercise to ‘explain’ I=S with some silly examples.

Here is the proof.

The elementary production-consumption economy is given with three macroeconomic axioms: (A1) Yw=WL wage income Yw is equal to wage rate W times working hours. L, (A2) O=RL output O is equal to productivity R times working hours L, (A3) C=PX consumption expenditures C is equal to price P times quantity bought/sold X.

In the elementary production-consumption economy, three configurations are logically possible: (i) consumption expenditures are equal to wage income C=Yw, (ii) C is less than Yw, (iii) C is greater than Yw.

In case (i) the monetary saving of the household sector Sm≡Yw−C is zero and the monetary profit of the business sector Qm≡C−Yw, too, is zero. The product market is cleared, i.e. X=O in all three cases. Accordingly, the market clearing price as the dependent variable is given by P=C/X=W/R.
In case (ii) monetary saving Sm is positive and the business sector makes a loss, i.e. Qm is negative. The market clearing price P is less than W/R.
In case (iii) monetary saving Sm is negative, i.e. the household sector dissaves, and the business sector makes a profit, i.e. Qm is positive.

It always holds Qm+Sm=0 or Qm=−Sm, in other words, the business sector’s profit is equal to the household sector’s dissaving and the business sector’s loss is equal to the household sector’s saving. In still other words, saving is NOT equal to investment because there is NO investment in the elementary production-consumption economy.

Under the condition that the price remains constant, the market does not clear if saving is greater zero, i.e. O−X>0 if Sm>0, i.e. the business sector’s inventory increases. The valuation of the inventory is NOT predetermined. For example, if it is valued with zero, then inventory investment is zero and I is NOT equal to Sm. If it is valued higher, then inventory investment is positive but still unequal to Sm.#1

Keynes started macroeconomics with false premises and ended with false conclusions: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (GT, p. 63)

Keynes’ premise income = value of output is false. From the correct macroeconomic axioms follows:
(1) Qm=−Sm in the elementary production-consumption economy,
(2) Qm=I−Sm in the elementary investment economy,
(3) Qm=Yd+I−Sm in the investment economy with profit distribution.
(4) Qm=Yd+I−Sm+(G−T)+(X−M) the general case with government in an open economy.

Simple algebra tells everyone that saving is NEVER equal to investment. Both Orthodox and Heterodox economists are too stupid for the elementary mathematics that underlies macroeconomic accounting.#2

Egmont Kakarot-Handtke

#1 Primary and Secondary Markets
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1917012

#2 For more details see cross-references Refutation of I=S
http://axecorg.blogspot.com/2015/01/is-cross-references.html

[Roger Sparks]

Egmont Kakarot-Handtke

The simple two worker model (producing beer and cars) introduces production on two levels of duration. Excepting the moment of initial exchange (of labor for cash for production), there is no logical expectation of equality of value. In fact, logically, the exchange would only happen if labor values cash more than time, and the initial purchaser values production more than the cash he dissaves.

Next we turn to the the resale of the items produced.

If indeed the new owners value production higher than they originally paid, then we would never expect workers to be able to buy the goods they produce. They (labor) accepted cash that buyers dissaved. Labor could only buy back those goods (in their entirety) when the initial buyer was ready to resell them at a discount.

Turning to your math analysis, I followed it OK, but, I think that your "household sector" is better described as the narrower "labor part of the household sector". This change is needed to recognize the difference between sellers-of-labor and buyers at the moment of initial exchange. Their motivations are diametrically different at that initial event.

Later, you write "(3) Qm=Yd+I−Sm in the investment economy with profit distribution.". How is Yd defined?

Changing the focus of discussion, I think macroeconomics makes an error when we create two sectors, households and business. instead, we have workers and those who have savings. When paid, workers have savings and, therefore, become a member of the savings sector.

[Egmont Kakarot-Handtke]

Roger Sparks

Nick Rowe writes: “It’s easy to teach students the arithmetic showing that actual saving must equal actual investment (S=I).” and “S=I is an accounting identity, and accounting identities are true by definition.”

Fact is that “S=I is an accounting identity, and accounting identities are true by definition.” is one of the most stupid statements in the history of the failed/fake science of economics.#1, #2, #3 And the fact that all student generations since Keynes parrot this manifest arithmetic garbage is a metric of the desperately low IQ of economics students.

Take notice that the correct accounting identity for the elementary investment economy reads Qm=I−Sm, that is, monetary profit Qm is the difference of investment expenditures of the business sector I and monetary saving of the household sector Sm.

Saving has never been nor will ever be equal to investment. So, ‘explaining’ I=S is not easy, just the opposite, it is impossible.

The fact that economists still claim ― 80+ years after Keynes committed the lethal blunder ― that I equals S is due to their utter scientific incompetence. This thread is the very proof that Nick Rowe and Roger Sparks and the rest (except Jamie, who got it: “This makes me want to scream in frustration”) are too stupid for the elementary mathematics that underlies macroeconomic accounting.#4, #5

Egmont Kakarot-Handtke

#1 Wikipedia and the promotion of economists’ idiotism
https://axecorg.blogspot.com/2018/07/wikipedia-and-promotion-of-economists.html

#2 MMT and the single most stupid physicist
https://axecorg.blogspot.com/2018/09/mmt-and-single-most-stupid-physicist.html

#3 Truth by definition? The Profit Theory is axiomatically false for 200+ years
https://axecorg.blogspot.com/2018/07/truth-by-definition-profit-theory-is.html

#4 A crash course in macro accounting
https://axecorg.blogspot.com/2017/07/a-crash-course-in-macro-accounting.html

#5 For details see cross-references Accounting
http://axecorg.blogspot.com/2016/12/accounting-cross-references.html

[George]

What about separating firms and private consumers and assuming that firms do not own inputs? In this case they firms can only invest by borrowing from the banks, whereas the banks only have on their deposits whatever we've "saved" (assuming that our income goes towards consumption, investment goods and bank deposits). In this case firms can borrow only whatever we've saved (essentially, like in the loanable funds model)which together with private consumers' spending on investment goods gives us S=I. Is such an intuition wrong for Econ 101?

[Mike Sax]

Question Nick: so buying a new car ISN"T saving but a used car IS saving?

Happy New Year by the way

[Peter J.]

Buying a new car and keeping it for 10 years = buying a used car now, then savings may have to go towards to buying another rust bucket in 5 years.
2 rust buckets spread over 10 years = 1 new car?
Savings intuition for me is not a reduction in consumption at all, but spreading that consumption out over time. Surely no one expects any real returns on savings these days. ;)

[Egmont Kakarot-Handtke]

Nick Rowe

You write: “Here’s the arithmetic of S=I: Define Y as market value of newly-produced final goods (and services). In a closed economy … we divide Y into consumption goods C and investment goods I, so Y=C+I. And we define saving S as S=Y−C. Substitute the first equation into the second to get S=Y−C=C+I−C=I, so S=I.”

This is Keynes’ argument of GT p. 63. It is false because Keynes got macroeconomic profit wrong: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end, he gave up and discarded the draft chapter dealing with it.” (Tómasson et al.)

Let this sink in: the economist Keynes NEVER understood the foundational concept of his subject matter. And After-Keynesians NEVER spotted Keynes’ blunder.

In order to get the arithmetic right, one has to go back to the MOST ELEMENTARY macroeconomic configuration, that is, the elementary production-consumption economy which consists of the household and the business sector.

In this elementary economy, three configurations are logically possible: (i) consumption expenditures are equal to wage income C=Yw, (ii) C is less than Yw, (iii) C is greater than Yw.

In case (i) the monetary saving of the household sector S≡Yw−C is zero and the monetary profit of the business sector Q≡C−Yw, too, is zero. The product market is cleared, i.e. X=O, i.e. there is NO change of inventory.
In case (ii) monetary saving S is positive and the business sector makes a loss, i.e. Q is negative.
In case (iii) monetary saving S is negative, i.e. the household sector dissaves, and the business sector makes a profit, i.e. Q is positive.

It always holds Q+S=0 or Q=−S, in other words, at the heart of the monetary economy is an identity: the business sector’s surplus (deficit) equals the household sector’s deficit (surplus). In other words, profit is the counterpart of dissaving and loss is the counterpart of saving. This is the most elementary form of the macroeconomic Profit Law.

For the elementary investment economy the Profit Law reads Q=I−S. As everyone can see, there is NO such thing as an accounting identity I=S or an equilibrium of saving and investment.

Since 80+ years, I=S is a monument of economists’ mathematical incompetence: “S=I is an accounting identity, and accounting identities are true by definition.” will forever stand out as one of the most idiotic statements in the history of so-called economic thought.

Egmont Kakarot-Handtke

[Roger Sparks]

Egmont Kakarot-Handtke

"the elementary production-consumption economy which consists of the household and the business sector."

These two sectors control two different economic resources. Households control labor and the business sector controls money. Elementary production trades labor for money, with production (a product) the result.

Consumption is a second step in the analysis. Having traded labor for money, households can now trade money for product. Your three cases outline the three possible secondary trading combinations. You can see that business would control the pricing of the products consumed but households would control whether consumption (the second exchange) would occur and when.

[Egmont Kakarot-Handtke]

Roger Sparks

You say: “You can see that business would control the pricing of the products consumed but households would control whether consumption (the second exchange) would occur and when.”

What I indeed see is that you are one of those undereducated blatherers who overpopulate economics. The point at issue is the macroeconomic “arithmetic” and not human behavior/control. More specifically, the point at issue is the refutation of the brain-dead assertion: “S=I is an accounting identity, and accounting identities are true by definition.”

The point at issue is that I=S is mathematically false and by NO means “true by definition” and that economists are too stupid for macroeconomic accounting#1 and that they, after 200+ years, still do not understand what profit is.

Make no mistake, I=S is not only disqualifying for you and Nick Rowe but for the entire profession.#2

In the elementary production-consumption economy, the price is under the condition of market clearing, i.e. X=O, and budget balancing, i.e. C=Yw, the dependent variable, i.e. P=W/R. If the condition of market clearing is dropped and the firm sets the price then the market is NOT cleared and the change of inventory is given by O−X.

All these cases have been dealt with elsewhere#3 and they are NOT relevant for the point at issue. So, they can be left out for the moment. Again, the point is that investment is NEVER equal to saving and that Nick Rowe’s attempt to explain I=S is 200+ light years beside the point, as usual.#4

This is the state of economics: Walrasian microfoundations are false and Keynesian macrofoundations are false. There is NO economics that satisfies the criteria of science, only senseless blather.

Egmont Kakarot-Handtke

#1 The Common Error of Common Sense: An Essential Rectification of the Accounting Approach
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2124415

#2 Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2392856

#3 Primary and Secondary Markets
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1917012

#4 Cryptoeconomics ― the best of Nick Rowe’s spam folder
https://axecorg.blogspot.com/2018/01/cryptoeconomics-best-of-nick-rowes-spam.html