I=S

There's a lot of people wandering around the internet who are very confused about Investment = Saving. Maybe they have been mistaught, or maybe they have mislearned? I don't know. But I'm doing this as a public service, even though it's a thoroughly boring job for me. Someone's got to do it. And since I've done it almost every year for the last 33 years, it might as well be me. "Ours the task eternal" is Carleton's motto.

Let's get the arithmetic out of the way first, then I'm going to simplify, back up, and explain what it all means.

Start with the standard national income accounting identity:

1. Y = C + I + G + X - M

On the left hand side of we've got sales of (Canadian) newly-produced final goods (and services) Y. On the right hand side we've got purchases of (Canadian) newly-produced final goods (and services), divided up into various categories. Consumption, Investment, Government expenditure, eXports, and iMports.

2. S = Y - T - C

This is a definition of Saving as income from the sale of newly-produced goods minus Taxes (net of transfers, which are like negative taxes because the government gives you money instead of taking it away) minus Consumption.

Substitute equation 1 into 2 to eliminate Y and you get:

3. S = C + I + G + X - M - T - C

You can eliminate C in 3, and rearrange terms to get:

4. I - S + G - T + X - M = 0

If you simplify, by assuming a closed economy with no exports or imports, you get:

5. I - S = T - G

If you simplify further, by assuming no government spending or taxes, you get:

6. I = S

(Or, if you like, you could define S as "national saving" to include both private saving plus government saving, which is defined as T-G.)

Now let's talk about what it means.

Equation 1 is an accounting identity. It is just like saying "the number of apples sold = the number of apples bought". You can't sell an apple without somebody else buying it. That's what the words "buy" and "sell" mean. If we add up all the apples sold, and add up all the apples bought, we should get exactly the same answer. If we didn't, it means we miscounted, or had a different definition of "apple" in the two counts, or did the two counts over different time periods, or made some other screw-up. And National Income Accounting is the art of checking all the possible screw-ups we might make, and trying to make them as small as possible, so we can get as accurate a picture as possible of economic data.

For example, if you are counting apples sold by the Canadians who produced them, and counting apples bought by Canadians, you have to remember that some Canadian apples get sold to foreigners, and some apples bought by Canadians weren't produced in Canada. That's why you have to add exports and subtract imports in equation 1 to make it add up right.

Since apples sold = apples bought, and bananas sold = bananas bought, then apples and bananas sold = apples and bananas bought. If it adds up for each good, it also has to add up across all the goods. So it really doesn't matter if we add up the physical number of apples and bananas, or add up the market values of apples and bananas, or add up the market values adjusted for inflation, or what. A+B=A+B. A+2B=A+2B. 24A+32B=24A+32B. Whatever. Equation 1 is true in nominal terms, without any inflation adjustment. Equation 1 is true in real terms, adjusted for inflation. Equation 1 is even true if we adjust for inflation in some totally daft manner, just as long as we are consistent in our daftness on both sides of the equation. Of course, we get a different number for Y depending on which we choose, and some of those numbers will be more useful than others, but we should (unless we screw up) get the exact same number on both sides.

(There are lots more potential screw-ups we could make: like how exactly we define and count "Canadian" "newly-produced" "final" goods. But go read any intro economics textbook if you are interested, because it's not the main topic of this post.)

Now, I have defined Y as goods sold. Normally, we think of Y as "income", or "production". And you can think of cases where these don't seem to be the same.

For example, suppose you produce 100 apples and you don't sell them? If we want Y to measure the production of apples, and not just sales of apples, we have to remember to include apples that the grower consumes himself, or adds to his inventory of apples. "He sold them to himself, either for Consumption or for inventory Investment". That's a fudge, of course, but it's a fudge we need to make if we want Y to mean "production" as well as "sales".

Here's a second example. Suppose you have 100 apples in inventory, that were produced last year, and the price of apples suddenly goes up $1. You have just made a capital gain of $100. Shouldn't that capital gain be included in your income?  Well perhaps it should, or perhaps it shouldn't. But if you want Y to mean "income", you had better not include it. Y has to be restricted to mean "income from newly-produced goods".

All the above was accounting. It wasn't really economics at all. "Apples sold = apples bought" is always true. But it tells us nothing whatsoever about what determines the number of apples traded. It is totally silent on what causes the number of apples bought-and-sold to increase or decrease. Or why it is bigger in some countries than in others. Is it the weather? Is it people's preferences for apples? Is it government rationing? Is it the rotation of the planets? There are 1,001 different theories of what determines the quantity of apples traded, and all of those theories are consistent with the accounting identity of apples sold = apples bought. Because "apples sold" and "apples bought" are just two different ways of describing the exact same number.

One of those 1,001 theories is the simple economic theory taught in Intro Economics. Supply and demand. Quantity demanded is the quantity of apples people would like to buy, given the price of apples, their income, etc.. Quantity supplied is the quantity of apples people would like to sell, given the price of apples, their productive abilities, etc.. The demand curve shows how quantity demanded varies with price, holding other things like income etc. constant. The supply curve shows how quantity supplied varies with price, holding other things like productive capacity etc. constant. And, according to this theory, the price of apples adjusts to make quantity demanded equal to quantity supplied, where the demand and supply curves cross. At that equilibrium price, and only at that equilibrium price, all 3 quantities are equal. Quantity demanded = quantity bought-and-sold = quantity supplied. According to this theory it is the supply and demand curves that determine quantity bought-and-sold.

That theory could be wrong. That's one of the dangers of having a theory that actually attempts to explain what causes or determines the facts. It could be wrong. But if we want to explain the world, that's the risk we have to take. One can easily think of examples where this theory would be wrong. For example, if the government imposes a binding price floor on apples it will be wrong. In that case, Intro Economics would replace it with a slightly modified theory: the quantity of apples traded is determined by the demand curve and the price the government sets; the supply curve plays no role. With the price fixed above where supply and demand curves cross, quantity demanded = quantity bought-and-sold < quantity supplied. In that "semi-equilibrium" actual purchases will be equal to and determined by the quantity of apples people want to buy (demand) at the fixed price. But the actual quantity sold will not be equal to nor determined by the quantity people want to sell (supply).

And if the government instead sets a binding price ceiling on apples the original supply and demand theory will also be wrong, but in a different way. In this case, according to the Intro Economics textbook, it's the supply curve and price that determine quantity bought-and-sold. In "semi-equilibrium", quantity demanded > quantity bought-and-sold = quantity supplied. Actual purchases will be equal to and determined by the the quantity people want to sell (supply) at the fixed price.

(The key assumption in all three of the above theories is that trade is voluntary. You can't force people to buy more than they want to buy; and you can't force people to sell more than they want to sell. So quantity actually bought-and-sold will equal whichver is less: quantity demanded; or quantity supplied. Only in full equilibrium, at exactly the right price, are all three quantities equal. Otherwise we are in what i call "semi-equilibrium", where only two of the three quantities are equal, and the third is bigger than the other two.)

"Apples sold = apples bought" is an accounting identity that is always true, but tells us nothing about what determines that quantity.

"Apples demanded = apples supplied" is an equilibrium condition. It might not be true. It is part of a theory that does try to explain what determines the quantity of apples bought-and-sold. That theory might be true, or might be false. But it is a theory about the world, and the risk of being false is an unavoidable occupational hazard of trying to explain the world.

Now, that was microeconomic theory. Let's switch back to macroeconomic theory. What's that got to do with I=S?

Look back at equation 1, and assume a closed economy with no government. You get Y = C + I. That equation is exactly the same as I = S. The two are mathematically equivalent. Just different ways of saying the same thing. But Y = C + I is a lot easier to compare to the microeconomic equilibrium condition "supply = demand". So I'm going to do that first, then come back to I = S.

For an economy that produced only apples, "Y = C + I" tells us that apples sold equals apples bought (some for consumption, some to be added to stocks as an inventory investment). But that accounting identity tells us absolutely nothing about what determines the quantity of newly-produced goods bought-and-sold. It does not explain why it changes over time, or is higher in some countries than in others. There are 1,001 different theories, all compatible with that accounting identity, that do try to explain what determines Y.

Here is just one of those 1,001 theories. This theory will be found in most Intro Economics textbooks. It's the simple "Keynesian Cross" theory. This theory is very similar to the microeconomic theory above of a market for apples with a binding price floor, where quantity supplied exceeds quantity demanded. This theory says that the quantity of goods bought-and-sold will be equal to and determined by the quantity demanded, and will be less than the quantity supplied. But there's a clever macro twist. The macro twist is that the quantity of goods demanded depends on income, and income is equal to the quantity of goods bought-and sold.

This theory can be described by three equations:

7. Y = Cd + Id

Cd means "desired consumption". It's the quantity of consumption goods people would like to buy, given their income etc. Some economists call Cd "ex ante consumption". But a simpler name would be "quantity of consumption goods demanded", just like in micro. And Id is just the same, except it's "desired investment", or the quantity of investment goods demanded. And equation 7 is a "semi-equilibrium condition". It says that actual quantity of goods bought-and-sold (Y) will equal quantity of goods demanded (Cd+Id).

8. Cd = a + bY   (where a>0 and 0<b<1)

9. Id = Ibar

Equations 8 and 9 are the behavioural equations. They tell us what determine desired consumption and desired investment. Desired consumption is an increasing function of actual income, and desired investment is fixed at some exogenous number, called Ibar. (That's supposed to be a bar over the I, but I can't write it).

Substitute 8 and 9 into the equilibrium condition 7, to get:

10. Y = a + bY + Ibar

Solving for Y we get:

11. Y = [1/(1-b)][a+Ibar]

Now that's a theory of the world. It might be false. But if true, it explains what determines the quantity of goods bought-and-sold. It says Y is determined by desired investment (and by the parameters a and b in the consumption demand function).

And it is a simple matter of math to relate that back to I=S. Simply define "desired saving" Sd as:

12. Sd = Y - Cd

So "desired saving" means "that part of income that people do not desire to spend on (newly-produced) consumption goods". What do they want to do with it instead? It could be anything, except spend on (newly-produced) consumption goods. They might want to spend it on newly-produced investment goods, they might want to buy government bonds, or corporate bonds or shares, or buy antique furniture, or add to their stocks of currency under the mattress. You name it, and if it's something you can want to do with your income (after taxes), other than spend it on newly-produced consumption goods, it's "desired saving".

We can re-write the old semi-equilibrium condition 7 as:

13. Y - Cd = Id

And substitute the definition for Sd into the left hand side to get:

14. Sd = Id

We can read 14 as "desired saving equals desired investment". Or "ex ante saving equals ex ante investment". It is mathematically equivalent to the semi-equilibrium condition 7. It's just another way of saying "quantity of goods bought-and-sold equals quantity of goods demanded". Only now it gets rearranged to become "quantity of goods bought-and-sold minus quantity of consumption goods demanded equals quantity of investment goods demanded". Which is a bit of a mouthful.

Substitute 8 into 12 to derive the desired saving function from the desired consumption function:

15. Sd = -a + (1-b)Y

Desired saving is an increasing function of income.

Substitute the desired investment and desired savings functions 9 and 15 into the "semi-equilibrium condition" 14 to get:

16. -a + (1-b)Y = Ibar

Rearrange 15 to get

17. Y = [1/(1-b)][a+Ibar]

Which, you will notice, is exactly the same as 11. You get exactly the same results whether you start from Y=Cd+Id or Id=Sd. And of course you should, They are exactly the same semi-equilibrium condition, just re-written.

But if you start with the same semi-equilibrium condition and add different behavioural functions you will get a very different theory of the world. For example another macroeconomist would say that desired investment and desired saving also depend on the rate of interest, and that the central bank will adjust the interest rate so that desired saving equals desired investment at potential output. In which case you cannot say that desired investment determines desired saving (or vice versa) because they are both endogenous variables, and it is the central bank that determines the equilibrium level of income. And yet another macroeconomist would say that that's not quite right either, because if the central bank tries to set the interest rate too high or too low the result will be accelerating deflation or inflation, so in the long run, if it doesn't want to destroy the monetary system, the central bank can only set it at some "natural rate" where desired saving equals desired investment at the level of income determined by the long-run supply of output.

In other words, the semi-equilibrium condition Sd=Id leaves open the question of what variable(s) adjust (or is adjusted) to bring the two sides into equality. It might be Y, as the Keynesian Cross model assumes. But it might be the rate of interest. Or the price level. Or anything else.

Let me sum up the main lessons.

First, you can't get anywhere with just accounting identities, if you want to explain the world. Convert that accounting identity into an equilibrium condition, and add some assumptions about people's behaviour, and what adjusts to what, and you might have a theory.

Second. The I=S approach is exactly equivalent to the Y=C+I approach. The latter is more easily re-interpreted as the semi-equilibrium condition Y=Cd+Id, which is the macroeconomic version of "apples bought-and-sold = quantity of apples demanded", but Id=Sd  is saying the exactly the same thing. (I was taught both these methods of representing the old Keynesian Cross model back in high school).

Third. The key question is not just the equilibrium condition you assume, but what variable or variables you assume adjust to make that equilibrium condition hold. What are the behavioural functions? Different behavioural functions will give you a very different theory.

Fourth. A lot of economists wasted an awful lot of time and ink getting this stuff straight 50 years ago. If you start your theory with I=S as an accounting identity, it really is your responsibility to try to explain to anyone reading the difference between I=S as an accounting identity, and Id=Sd as some sort of equilibrium condition, and why that difference matters. Because, as I said at the beginning, there's an awful lot of poor lost souls wandering around the internet who have just discovered the marvellous truth of I=S as an accounting identity, and think they have found some magical philosopher's stone that "mainstream" economists have never heard about, and that this blinding flash of divine truth will lead them to the Promised Land. It's a bit like being accosted at airport terminals by people with a glow in their eyes repeating "apples sold equals apples bought". Because that's exactly what they are saying.

Comments

[Nick Rowe]

Ron T. : let's just say that you were one of the people who *inspired* this post ;-)

Your 5 comments above are confirming what I said in the post. As an *accounting identity*, nothing needs to adjust to get S=I. Apples bough = apples sold. But as an *equilibrium condition* something needs to adjust to get desired S = desired I.

[Patrick]

I think I'm perceiving a yearning for a conservation law here. A Gauge Theory for macroeconomics?

[rsj]

JKH,

This is a behavioral question. My answer is that if the CB did not engage in any QE, but government continued to deficit spend and sell more bonds, then banks would have had a larger *net* bond position. You can interpret that as meaning that they would have held more bonds on the asset side, or that they would have fewer bond liabilities -- the elasticity analysis can't distinguish between these two options, and in any case the net position is all that the other sectors see.

[RonT]

Nick, simplyfiying my post above, in the absence of government Sd=Id trivilally, because each investment transaction (I) will be recorded as someone's income Y (income of the seller of the investment good), and this income reflects a sale of good that not consumed by the buyer (thus it is classified as saving Y-C=S) by definition. So assuming the private sector has some investment plans Id, if they choose to realize them, this will consitute the unconsumed income, so you can say that the demanded Sd equals to demanded Id, by construction. By making an investment you are giving someone an income that you won't consume (by definition, since it is an investment). So by demanding investment you are demanding savings at the same time, there is one without the other. Talking about Sd vs Id makes no sense. Sd is not independently measurable anyway so talking about Sd alone makes no sense.

[RonT]

In other words, say Sd=100000000, Id=100. Realizing their investment desires, people make ivnestment purchases to the tune of 100. Accounting will produce: S=I=100. S was equilibrated with I by the transactions, although the desired S was 1 million times larger than desired I. So what? Any disequilibrum, no matter how huge, will be easily taken care of by the transactions that will take place.

[JKH]

RSJ,

BTW, recapitalization includes internally generated capital, which includes a substantial effect from across the board dividend cuts, cuts that have not been reversed. US commercial banks are engaging in their own form of deposit liability quantitative tightening, by debiting deposit accounts for loan interest payments, but failing to credit them for dividend payments.

[RonT]

I know what is going on here, you are thinking of Sd as desired unspent income, whereas the definition of S is unconsumed income. If you don't change the definitions on the fly and keep the definition (S =unconsumed income) the desired Sd is equal to the desired spending on investment goods = Id. The paradox goes away.

in absence of govt: (private income)=(private spending).
There can be no unspent income in the economy as a whole, because income = spending. Whatever is unspent ceases to be income.
So w/o govt there is no saving in the colloquial sense (in aggregate - some agents can save, but others have to dissave), yet there is S in the accounting sense = accounting record of investment, S=I.

[RonT]

Me again here:

"savings in colloquial sense"="unspent income" = income -taxes - (private spending)=Y-(C+I)=C+I+G-C-I-T=G-T=S-I

"savings in accounting sense" = S = Y-C-T

You are confusing S-I (savings in the colloquial sense) and S (saving in the accounting sense). Desired savings in the accounting sense = desired spending on non-consumption goods - taxes.

In (transaction 2) in my long 5-series post, the agent D could very well intend never to spends the 60 he received for his comsumption good sold to agent C, yet this transaction will be recorded as C (consumption), not S (saving).

[rsj]

JKH,

"US commercial banks are engaging in their own form of deposit liability quantitative tightening, by debiting deposit accounts for loan interest payments, but failing to credit them for dividend payments."

Agreed. But I don't think this is a useful way of approaching the problem.

We are after a general equilibrium solution, taking into account all the actions and responses of all the sectors that results in the observed time path of household deposits.

Households take delivery of all wealth as deposits, and the question becomes how much of that wealth do they keep in the form of deposits, and how much do they allocate as bonds, equity, etc.

As households decide to not keep all of their wealth as deposits, they bid to purchase other assets. In the course of doing so, the yield on those other assets declines somewhat, and the supply of those assets increases. Simultaneously, this makes households more indifferent between holding the deposit and holding the other asset.

Therefore it boils down to an elasticity argument -- which sector responds first to supply households with assets as a result of a (small) decrease in yields. Moreover, by how much does household demand for non-deposit assets decrease as a result of a small decrease in yields. Keeping track of all of these effects -- in a simplified model -- is the purpose of the excess demand diagram in my second post.

I am arguing that household demand for non-deposit assets declines much less in response to a small decrease in yields than the financial sector's supply of those assets. Similarly, I am arguing that the non-fianancial business sector's supply will also change much less in response to a small change in yield than that supply-response of the financial sector.

And that's all you need to get a rule of thumb argument that the financial sector's net supply of non-deposit assets is the primary equilibrating mechanism that clears household demands to hold those assets.

Equivalently, it is the main equilibrating mechanism to ensure that households are able to keep the proportion of their wealth stored as deposits that they demand.

Note that if you had a different model of the economy -- for example, if you assumed that household net bond holdings were always zero, and that households only owned (physical) capital, which in each period is fixed in quantity, then you would reach the opposite conclusion.

In that model -- which is incompatible with inside money -- the price of capital would always adjust so that households no longer wished to buy it, and the quantity of money (there are no deposits) would be exogenous. It seems to me that Nick primarily works with that model, whereas I'm working with almost the exact opposite model. Both models are correct, in the accounting sense, and the question becomes which is more useful. Perhaps in the very long run, the first model is all you need, but certainly not in the short run.

The only difference between these two extremes is the parameters that you assign to the interest-elasticity of net bond supply by each sector.

In Nick's model, bonds are perfectly inelastic, as households can never own more than 0 bonds, and banks will never sell *any* bonds to households, no matter the price. Households only hold capital, the supply of which is relatively inelastic in the short run.

Therefore primarily interest rates adjust in response to an increased demand for non-deposit assets, or in response to an increase in the quantity of outside money.

In my model, it is primarily the quantity of financial sector bonds that adjust. In Nick's model, there can be crowding out of real investment by government debt sales. In my model, crowding out only occurs in the financial sector's net bond supply. Real capital is not crowded out.

Obviously both models are extremes, but you can transition from one to the other by changing the elasticities of net bond supply by each sector in your model.

[Nick Rowe]

Ron T.: "I know what is going on here, you [Nick] are thinking of Sd as desired unspent income, whereas the definition of S is unconsumed income."

"You [Nick] are confusing S-I (savings in the colloquial sense) and S (saving in the accounting sense). Desired savings in the accounting sense = desired spending on non-consumption goods - taxes."

Nope.

Oh Christ.

Scott: you see? This is the sort of thing that MMT *followers* say. And this, after my very careful attempts to lay it all out as simply and clearly as possible. You see why MMT gets a bad rep on the blogosphere? They accuse *us* of being confused about accounting identities, definitions, and equilibrium conditions!

Maybe one of you MMT guys could try explaining it to Ron. I think I have gone way above and beyond the call of duty on this one.

[Nick Rowe]

rsj: "In Nick's model, bonds are perfectly inelastic, as households can never own more than 0 bonds, and banks will never sell *any* bonds to households, no matter the price. Households only hold capital, the supply of which is relatively inelastic in the short run."

WHAAAAAAAAT!!!!!! Which "Nick" are you speaking of? Because around here I'm "Nick". And that sure ain't *my* model!

[RonT]

Nick, in the absence of govt the desired unconsumed spending = desired investment spending, because investment is by definition spending on non consumed goods. Tautology. Id=Sd. Nothing deep there, although you want to make it look so. No equilibrium will be needed to bring them together like in my example with Sd=10M, Id=100. S will record the size of investment I.

Your confusion of S with S-I is the only explanation why you would care about Sd.

It makes no sense to think of Sd separately from Id. The same people are saving and investing in the economy w/o the govt. (unless, again you confuse "saving" with "not spending"). If people are schizophrenic and want to spend a different amount on non consummable goods than invest, S will still be equal to whatever I will and up being.

Similarly for a coin toss there is no sense of thinking about the number of heads separately from a number of tails. There is no equilibrium that gets you to #heads + #tails=#tosses.

[rsj]

"WWHAAAAAAAAT!!!!!!"

LOL

Sorry!

But in discussions, you often start with: assume there is only outside money and there is no separate banking sector. That *seems* to be your favorite mental model -- at least on WCI. I am not saying that this is the sum total of all models you have explicated here, though.

Apart from the teasing, interpret this as a request for more models with banks in them, in which money is defined as one type of claim on the banking system that competes with other types of claims (e.g. bank shareholders). Households have the option of purchasing a deposit claim (which pays no interest, but provides the benefit of "money" -- or purchasing bank equity which does pay a stochastic interest rate, but is not "money".)

[Nick Rowe]

Ron T. : "Nick, in the absence of govt the desired unconsumed spending = desired investment spending, because investment is by definition spending on non consumed goods. Tautology. Id=Sd. Nothing deep there, although you want to make it look so. No equilibrium will be needed to bring them together like in my example with Sd=10M, Id=100. S will record the size of investment I."

Scott (or any other MMTers): he's one of your kids (at least, he says he is). Can one of *you* straighten him out (or at least disown him)? (Because if you don't straighten out your kids, you can't really complain when people suspect you share their beliefs.)

[RonT]

Nick, you said:
But as an *equilibrium condition* something needs to adjust to get desired S = desired I.
.

No, in an economy w/o govt no adjustment is necessary. If they never adjust, there is no problem whatsoever. S will end up equal to the level of actual investment even is a nanosecnd ago the desired S was different by many orders of magnitude.

You may be implicitly assuming that the level of investment is itself predicated by the level of savings, but again this "savings" would be the colloquial meaning of "stock of accumulated cash", not the accounting sense.

In absence of govt:
By looking at transactions it is obvious that it is the same people that generate S the moment they spend I on investment goods. They make the desires of savings the same moment the desire investment. Savings is created the moment investment occurs by people who spend on investment, Andy Harless' post is pretty clear here.

So, in the economy w/o govt, desired S=desired I by definition. If people are irrational and don't understand this, the fact that someone wants at the same to spend 1M on unconsummed goods (saving) and only spend 100 on investment goods (investment), there is no disequilibrium to speak of.

I agree that there is a problem in case the govt is present, then desired S can be different from desired I: and not necessarily equal to G-T desired by the govt. The matter boils down to how govt spending G and taxes T are constructed - are they done thru automatic stabilizers etc. Yes, S-I may end up being different from desired. All these issues are gone in absence of the govt though.

[Nick Rowe]

rsj: "But in discussions, you often start with: assume there is only outside money and there is no separate banking sector. That *seems* to be your favorite mental model -- at least on WCI. I am not saying that this is the sum total of all models you have explicated here, though."

That's a fair caricature! Really simple model: no banks, and the government issues currency and bonds. Change in currency + change in bonds = G-T. (I'm also assuming the government never sells off old assets like national parks!).

But then that simple model assumes that *all* government bonds are held by households. (Which is why I went "WHAAAAAAAT?" when you said I assumed households never held positive stocks of bonds!)

[RonT]

Nick,
I agree that accoutning S=I doesn't tell you anything about the level of I (or S), but what I claim is that you cannot have Id<>Sd without making a math error (that would show up as Cd<>Cd). It not a coincidence that you got Id=Sd for all consumption functions you chose.

I challenge you to come up with a theory with Id<>Sd (in absence of govt) -you can't (w/o violating algebra).

[Nick Rowe]

Ron T.: "I challenge you to come up with a theory with Id<>Sd (in absence of govt) -you can't (w/o violating algebra)."

Good challenge Ron. But I'm going to give all the MMTers reading this a chance to respond to Ron's challenge. (And also, without imports and exports, because I take it Ron was implicitly assuming X=M as well as G=T).

[RonT]

Nick,
You think that similarly for a market for apples there is a market offering "savings" from which "investment" is bought, so that S(sold savings)=I(bought investment), like apples. Investment and savings is nothing like a market for apples. It is like income and spending. Income equals spending (by accounting - sorry), but there is no equlibrating process that brings them together, they are equal in every transaction. You can plan your spending, but you cannot plan your income because your income depends on someone else's decision (to buy whatever you have for sale).

I bet each period our desired income is (much) higher than the actual one (which is dictated by our desired spending - we earn only as much as we spend, sadly) and the world goes on. Constant disequilibrium. Thinking what would equilibrate desired income with desired spending is useless because they never equilibrate. It makes thinking about "desired income" useless.

[Nick Rowe]

Hang on Ron. We have to wait for an MMTer to respond to your challenge, before you go running off off on other tangents.

Oh, by the way. You *are* an MMTer, aren't you? At least, you learned (most of) your economics from reading MMT blogs? And you basically agree with the MMT approach?

(And rsj, JKH, and everyone else, just hold off posting on other stuff for the minute please. I don't see why you guys should be having all the fun while you leave me here to educate one of your presumed (at least half-) siblings!)

[RonT]

Nick,
Yes, I am an "MMT sympatiser". So if you prove that I am confused you will have proved MMT wrong. Right? Fingers crossed then.

For the record, I never claimed that S=I determines the level of I. I took issue with your claim at Sumner's blog that some equilibrating process is needed to bring about S=I. You wanted to equilibrate I-S+G-T+X-M (to zero, I hope).

I will happily get "disowned" by any more experienced MMT-er here, so go ahead, from you guys it will at least mean something ;)

[Nick Rowe]

Ron "Yes, I am an "MMT sympatiser". So if you prove that I am confused you will have proved MMT wrong. Right?"

No. If some MMTer comes on here, and says you are confused, and gives any halfway reasonable response to your challenge, there is no way I could say I have proven MMT wrong. I am pretty sure Scott (to give just one name) could do this. If you read his earlier comments above, you can see that he and I have little (if any) disagreement on substantive questions about the difference between accounting identities and equilibrium conditions.

So, we're just going to wait for a bit. (Plus, I have a car I need to check over this evening).

[JKH]

"we're just going to wait for a bit"

http://www.youtube.com/watch?v=f4zyjLyBp64

[JKH]

Nick,

I don’t really know the answer to your question. The following is exploratory, and not really an argument. And I’m not taking sides here:

Suppose you have an economy that produces only investment goods. Or suppose it produces only investment goods for an assumed period of time. Either way, you then examine that economy in the context of the theory in the post.

I = S as an accounting identity, as usual.

Y = I = S is also an accounting identity, in this particular case.

I assume your “short side rule” would determine I, the amount of investment goods produced, based on supply and demand for I. (Do I have that right, or am I off base right away there?)

So if that’s correct, it’s a “non-MMT” behavioural condition on the determination of I.

Backtracking slightly, it then seems to me that your generic argument about S and I actually depends on C > 0.

Particularly starting around your equation 12:

12. Sd = Y - Cd

But what happens to your argument if C is zero, as in my example? If I is determined based on Id and Is (like apples would be), then:

a) Why is there any remaining issue regarding the determination of S in either accounting identity terms or behavioural terms?

b) Does the theory you described in the post theory depend on C > 0?

c) If the answer to c) is yes, is that really a legitimate logical constraint on the relationship between S and I as per the theory in the post? It's obviously a real world concern, but why does the theory relating S to I in both an accounting identity and behavioral sense need to make that assumption?

Just asking.

[JKH]

meant "If the answer to b) is yes"

[Nick Rowe]

JKH: It's good to see you having a try (though I understand it's not really your cup of tea)!

(Your Youtube lead me to this, straight afterwards! http://www.youtube.com/watch?v=dxPVyieptwA&NR=1 )

"I assume your “short side rule” would determine I, the amount of investment goods produced, based on supply and demand for I. (Do I have that right, or am I off base right away there?)"

You have that right. I'm following fine so far.

"So if that’s correct, it’s a “non-MMT” behavioural condition on the determination of I."

Are you sure about that? I would have thought that *any* economic theory would accept the short-side rule. Actual quantity traded is whichever is less: quantity buyers wish to buy; or quantity sellers wish to sell. You can't force people to buy if they don't want to; you can't force people to sell if they don't want to. Mafia aside. Maybe a couple of other weird cases aside, where buyers or sellers feel they have an obligation to buy or sell, in order to maintain an ongoing relationship.

"b) Does the theory you described in the post theory depend on C > 0?"

No. Maybe (though I agree it's a bit strange) people want to save *all* their income (for a short time, anyway, otherwise they would starve).

[RonT]

My take on JKH's example:
In absence of demand and supply of consumption goods, we have:

Sd=desired income from selling non-consumption (investment) goods = supply of investment goods.
Id=desired spending on investment goods (demand for investment goods).

How much is bought/sold will be determined by the smaller of the two: Y=min(supply, demand). (Post Keynesians, not sure about the MMT bunch, believe in a cost mark-up pricing set by firms, rather than price being given by demand=supply, so the price is "given").

Y=min(Sd,Id)=I=S.

I think Post Keynesians tend to believe that the economy is demand- rather than supply-constrained (most of industry is running below capacity most of the time etc.), although some markets can become bottlenecks where supply is the limiting factor. But in no way it is an economic "law" that defines MMT.

In my previous rants I implicitly assumed that whatever is demanded will be met with supply, I should have made it clear, sorry.

[Nick Rowe]

Ron: "How much is bought/sold will be determined by the smaller of the two: Y=min(supply, demand)."

Good so far. (If I wanted to be picky I would say it should be min{*quantity* supplied; *quantity* demanded}

But you don't mean this, surely: "Y=min(Sd,Id)=I=S."

"I think Post Keynesians tend to believe that the economy is demand- rather than supply-constrained (most of industry is running below capacity most of the time etc.), although some markets can become bottlenecks where supply is the limiting factor."

Yep.

"In my previous rants I implicitly assumed that whatever is demanded will be met with supply, I should have made it clear, sorry."

Let me be picky again. You implicitly assumed that whatever is demanded will be met with *output and sales*, not "supply". Remember, "quantity supplied* is the amount sellers *would like to* sell. You were implicitly assuming that quantity supplied exceeded quantity sold, which was equal to and determined by quantity demanded.

So, still nobody up to the Ron T. challenge?

[JKH]

Nick,

By "non-MMT" I meant that this is the idea that the "non-MMT" side of the debate (i.e. primarily you Nick) seems to be promoting - not that it isn't or shouldn't be accepted by MMT.

Not sure you've answered my question yet Nick. If it doesn't depend on C > 0, then it should work with C = 0, which is the case where I don't yet see your argument prevailing.

[Nick Rowe]

JKH: I am 99% sure that serious MMTers (people like Scott F.) would agree with the "short-side rule", and would automatically assume it's true (barring the few weird exceptions to that rule that I would probably agree with them on).

"Not sure you've answered my question yet Nick. If it doesn't depend on C > 0, then it should work with C = 0, which is the case where I don't yet see your argument prevailing."

? I thought I just said. Nothing in my post depends on C>0.

Come on guys, who's up to the Ron T challenge? Or do you believe that it's logically impossible for Sd =/= Id??

[JKH]

Nick,

We're not communicating at all.

I didn't say it wouldn't be accepted by MMT'ers.

And with regard to the other, you didn't answer this:

a) Why is there any remaining issue regarding the determination of S in either accounting identity terms or behavioural terms?

But that's it for me, for now.

[RonT]

Nick,

Haven't I answered my challenge myself? I was wrong, it is indeed possible to have Sd<>Id, exactly like in JKH's example, without consumption. C can be zero, or whatever. Because Yd has two sides: Y=income=spending, but income_desired<>spending_desired, so there is no single Yd, like I said at 5:18pm.

Income is from selling goods, so desired income is equal to the quantity supplied (offered for sale):

income_desired=supply(consumption goods)+supply(investment goods)

spending_desired=demand(consumption goods)+demand(investment goods)

in absence of (demand and supply) of consumption:

income_desired=Sd (Sd=desired "unconsumed income", and since w/o consumption all income is unconsumed, Sd=desired income=supply of investment goods for sale)

spending_desired=Id (demand of investment goods, as all spending/demand is on investment)

And yes, I did mean that ex post Y=I=S=min(Sd,Id). What is the problem with this? Are you objecting to: income_desired=supply=Sd and spending_desired=demand=Id?

Y will happily be min(Sd,Id) although Sd<>Id, so perpetual disequilibrium. Post Keynesians tend to believe supply>demand.

Some discussion of the causation by the MMT camp:
http://bilbo.economicoutlook.net/blog/?p=12914
http://heteconomist.com/?p=641
http://heteconomist.com/?p=2360

[Nick Rowe]

Ron: you can't answer your own challenge! That's not fair!

And I had 6 really good examples, all ready to go!

But what ever are you thinking with this "Y=I=S=min(Sd,Id)" business"?? What about C? If Cd>0, and if Id=Sd, then Y=Cd+Id=Cd+Sd > min{Sd,Id}.

[RonT]

Nick,
we assumed consumption away, only then Y=min{Sd,Id}.

If C is allowed to be nonzero,

Cd<>Cd on both sides of Cd+Id=Cd+Sd, because one is desired_spending_on_consumption (demand for consumption goods), the other is desired_income_from_selling_consumption_goods (supply of consumption goods), they are not necessarily equal.

[Nick Rowe]

Ron: "Nick, we assumed consumption away, only then Y=min{Sd,Id}."

Aha! OK.

You are using a *slightly* non-standard definition of Sd. You are defining Sd as Ys-T-Cd. The standard definition is Y-T-Cd.

Yours is not wrong. Few people ever notice there's a difference.

[Min]

@ Nick Rowe:

Thanks for your response. :) I have been offline for a few days, and only now have managed to read it.

"2a. (This is the innocuous part, that most would agree with).

"Suppose people used barter exchange. They traded goods for goods directly, without using a medium of exchange. But accountants, including national income accountants, might still use some common measure of market value to add up the values of apples and bananas. They might, for example, use kilograms of carrots as the unit of account. That doesn't mean people use carrots as the medium of exchange -- only buying and selling things for carrots -- it just means that accountants reduce everything to carrots as the common denominator.

"2b (A wild, outrageous claim, that I only thought up while writing this post, and I still can't quite get my head around. I'm not even sure it doesn't violate all the normal rules of science. I made this claim in the post, but nobody has yet called me on it. So, I'm going to repeat this wild statement, then call myself on it.)

"Here's the claim, made as provocatively as possible: National Income Accounts allow us to add kilograms of apples with kilowatt-hours of electricity."

Well, I guess I am not everybody. ;) I find the idea of reducing everything to carrots to be far from innocuous, while adding kilograms with kilowatt hours in the manner you indicate, where you keep the different sums separate, is simply using vectors correctly, and hardly outrageous. :)

[Min]

Nick Rowe:

"Accounting identities are true by definition. (OK, if somebody said that sometimes the *meanings of words* has to adjust to keep the accounting identities intact, I would not disagree.)"

Oh, Jeebus! Since accounting identities are true by definition, the meanings of words has to **stay the same** to keep them intact.

[Min]

Nick Rowe: "Here's the claim, made as provocatively as possible: National Income Accounts allow us to add kilograms of apples with kilowatt-hours of electricity."

Let me clarify a bit. I said that, as you are doing it, you are handling vectors correctly by keeping the sums separate.

You write, A + E = A + E, even though A and E are in different units. What you do not do is write A + E = Z, where A, E, and Z are in incomparable units. What you are doing is using '+' as a connector, not as an arithmetic operator. In the usual vector notation we would write, (A,E) = (A,E). :)

[Nick Rowe]

Min: "Oh, Jeebus! Since accounting identities are true by definition, the meanings of words has to **stay the same** to keep them intact."

Agreed. I meant the meanings of words sometimes has to adjust from the *everyday* meanings of words.

[Nick Rowe]

Min: "What you are doing is using '+' as a connector, not as an arithmetic operator. In the usual vector notation we would write, (A,E) = (A,E). :)"

Maybe that's what I'm doing. I still can't quite get my head around the "fact" that 5 kg of apples sold "+" 6 kwhrs of electricity sold = 5 kg of apples bought "+" 6kwhrs of electricity bought! (But I'm not going to lose sleep over it.)

*Any* set of prices, (not just market prices, but prices picked at random), would make the units line up, and the identity would be perfectly true.

[RonT]

Nick,
So I agree that we may have Id<>Sd and (w/o consumption) Y=min{Sd,Id}, but:

I still have issue with your statement: "But as an *equilibrium condition* something needs to adjust to get desired S = desired I."

It seems to me that there is no need for Sd to end up equal with Id. The smaller of the two will be what ends up being bought/sold. What do you think?

[Nick Rowe]

Ron: "It seems to me that there is no need for Sd to end up equal with Id. The smaller of the two will be what ends up being bought/sold. What do you think?"

I can imagine a world where Sd and Id never get to equality, except by sheer chance. I can build a theory of such a world. But usually, Sd and/or Id will depend on Y, and/or interest rates, and/or the price level, and (at least) one of those 3 variables will adjust to bring Sd and Id into equality. Sometimes the adjustment will be immediate, and sometimes slow.

[Oliver]

Here's the claim, made as provocatively as possible: National Income Accounts allow us to add kilograms of apples with kilowatt-hours of electricity.

Sounds like you're describing the nature of money as such, not only that of National Income Accounts. In that case, the accounts are only the map by which we can attain some sort of macro view over the real happenings initiated through flows of money. The only outrageous part of this claim to me is the implication that all that cannot be expressed (and thus ultimately traded) through the common unit of account is per definition worthless. JKH's objection seems more a matter of convention than of content.

Very interesting discussion overall though! Thanks guys.

Proves my ongoing suspicion that accounting identities are not some kind of secret weapon by which MMTers can debunk all other schools of thought, but rather an instrument that all economists should use to control their own theories and those of others for quality. And of course, even with the best tools at hand, bad or ill-informed scholars on all sides can easily make a hash of things - MMT soldiers are no exception.

[Too Much Fed]

"I can imagine a world where Sd and Id never get to equality, except by sheer chance. I can build a theory of such a world. But usually, Sd and/or Id will depend on Y, and/or interest rates, and/or the price level, and (at least) one of those 3 variables will adjust to bring Sd and Id into equality. Sometimes the adjustment will be immediate, and sometimes slow."

Can the amount of medium of exchange adjust?

[Min]

Nick Rowe: " I meant the meanings of words sometimes has to adjust from the *everyday* meanings of words."

Thanks for the clarification, Nick. :)

BTW, I have noticed that at times you offer redefinitions which still satisfy the mathematical relations. That is a powerful technique. Is that usual in economics, or is it your specialty? :)

[rsj]

I admit to having a difficult time understanding what Income supplied could mean (to the degree that it differs from actual income).

Although, curiously, I have no difficulty understanding what income demanded would mean.

[mdm]

Nick Rowe: "Scott (or any other MMTers): he's one of your kids (at least, he says he is). Can one of *you* straighten him out (or at least disown him)? (Because if you don't straighten out your kids, you can't really complain when people suspect you share their beliefs.)"

To be fair, if an economist is taking the word of an autodidact MMTer rather than consulting the academic literature, then in my opinion that reflects poorly on the academic -- dare I say it, the academic lacks academic integrity.

[Nick Rowe]

Min: "That is a powerful technique. Is that usual in economics, or is it your specialty? :)"

It's very usual in economics (or economic accounting, rather). "Investment" is a perfect example. To us, it means "newly-produced capital goods" only. You don't "invest" in the stock market, or by buying an old house.

And see my response to rsj for another example:

rsj: in an economy that produces only apples/wheat/haircuts, the quantity of apples/wheat/haircuts supplied (i.e. the quantity they want to sell) is desired income, or income supplied. Normal people might call it income demanded. But we *sell* goods to earn income, therefore it's "supplied".

mdm: Oh, you dare say that all right, safely anonymous. But you don't have the guts to take the Ron T. challenge, and risk making yourself look foolish.

[rsj]

"the quantity of apples/wheat/haircuts supplied (i.e. the quantity they want to sell) is desired income, or income supplied."

OK, I would say that is the quantity of *product* supplied, in an attempt to obtain a quantity of income demanded.

The problem here is that "income" = consumption + change in net-worth.

It is certainly possible to demand consumption + change in net-worth, but I don't see how you can supply it.

[Nick Rowe]

rsj: fair enough. I'm not really wanting to disagree/argue with you on this point.

Notice though, how we might want to describe it differently in a barter economy than in a monetary exchange economy.

In a barter economy, when I supply the goods I have produced to earn income, I am *in the very same act* demanding other goods to consume or save. My desired level of income is both a supply of and a demand for goods.

In a monetary exchange economy, first I supply the goods I have produced in exchange for money to earn income, then I take (some, all, or more than all) of that money and demand other goods. My demand for non-money goods is not always the same as the income I desire to earn by supplying goods. We can imagine (an extreme case) where we plan to hold 100% of our income in extra money. We don't *normally* talk of "wanting to buy money". (Only economists talk like that, sometimes).

[Alex Plante]

When you deposit money in a bank, you're effectively lending money to the bank. Most people confuse that lending with saving.

[RonT]

Nick,
"I can imagine a world where Sd and Id never get to equality, except by sheer chance. ... But usually, Sd and/or Id will depend on Y, and/or interest rates, and/or the price level, and (at least) one of those 3 variables will adjust to bring Sd and Id into equality. Sometimes the adjustment will be immediate, and sometimes slow."

so your grand critique of how "stupid, stupid" MMT is fizzles down to: "Id, Sd can equilibrate, or not, fast or slow".

???

Yeah, so what? I bet academic MMT-ers knew all that, but how relevant is that?

Each time you set out to undermine MMT it ends up in nothing. The you swiotch to calling it a cult. And then the cycle repeats.

[Roscoe]

BT: "Private sector net savings (S - I) are just the money added into circulation by government deficit spending and an export surplus."
Nick: “That is really wrong, unless you are using ‘money’ in a very strange way.”
I have to side with BT on this one. It seems to me that his statement is correct, no matter what open market operations the Central Bank may simultaneously undertake (e.g. selling a national park or government bonds). BT did not say or imply that an increase in (S-I) was related to a change in the money supply, but rather to government spending. They are not the same thing. Is it not so that there are two different ways to increase the money supply (1) government spending (2) Central Bank purchasing of government bonds? The former increases (S-I) as per the sector balance identities. The latter has no effect on (S-I), although it may affect the levels of S and I. That is my current understanding. Am I missing something?

[Nick Rowe]

Roscoe: we may all be arguing at cross-purposes. But this bit of what you said definitely caught my eye: "...no matter what open market operations the Central Bank may simultaneously undertake (e.g. selling a national park..."

In my way of thinking, central banks do not own national parks and do not sell national parks. It is the government (as distinct from the central bank) that owns national parks, and sells them.

The way in which economists normally think of an increase in G-T increasing the money supply is as follows: the government sells a bond to the central bank (for CB money), and uses the proceeds to buy newly produced goods. In other words, if the government finances its deficit by borrowing from the central bank, the deficit is money-financed. There is a direct increase in the money supply.

If instead the government finances its deficit by borrowing from the public (selling bonds to anyone other than the central bank) then the deficit is bond-financed. There is no direct increase in the money supply.

The central bank (and the commercial banks too) may or may not choose to respond to bond-financed government deficits by changing the money supply, of course. If they do, then government deficits my indirectly lead to an increase in the money supply.