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.
Worthwhile Canadian Initiative 
Damn! I can see my graph, but my link just shows NGDP. It doesn’t show MZM any more. I have screwed it up somewhere.
rsj: do me a favour please. Can you draw a graph showing your same MZM, but compared to nominal GDP (that’s the first one in their GDP list). Thanks.
Nick, if you click on Fred link (e.g. MZM) and then edit the graph to get MZM/NGDP, the URL in your browser does not change as a result of your edit, so you if then cut and paste the URL, it will point to your original graph (MZM) not the modified one.
To get a link to your modified graph, there is a “link” link just above the graph you created. Click on it, and you will get a URL that will point to just the .PNG file, or the entire page.
Here is a graph of MZM/NGDP and Debt held by Public/NGDP.
http://research.stlouisfed.org/fred2/graph/?g=1HK
And yes, my graph was a behavioral, not an accounting relationship. Very much like velocity! And like velocity, the relationship can break down if you push it to the extreme — e.g. attempting to issue a lot of debt in order to increase MZM will have the same non-result as engaging in QE to increase MZM.
Here MZM and the base:
http://research.stlouisfed.org/fred2/graph/?g=1HL
But the behavioral theory is that when the government deficit spends, it creates a deposit, so MZM goes up, but when the government sells a bond, the deposit does not go away, only the reserves backing the deposit go away.
So the deposit ends up “backed” (very loosely) by a bond, rather than by reserves. The seignorage income is transferred from the government to the banking system, but the private sector as a whole still demands to hold money roughly equal to the federal debt. Obviously, this relationship breaks down if the federal government were to issue too much or too little debt. But in the latter case, the deposit ends up backed by a mortgage (say), which is more fragile than a riskless treasury. Therefore when MZM went above federal debt, this could have been (and was, for my part) interpreted as a sign of financial sector fragility. And the rush to increase federal debt can be interpreted as allowing the deposits to be “backed” more by riskless bonds — it strengthens the financial sector.
Nick,
“An aggregation that works well for one theory does not work for another. We need to make our accounting categories fit our models, not vice versa”
Two different ideas in juxtaposition there –
MMT and the New Keynesian model and any other model should be able to map into the same basic accounting framework, in order to be able to “talk to each other”.
And everybody should map to national income accounting and financial accounting in general, in order to be able to talk to the real world. MMT accounting DOES derive from and map to national income accounting. You should too, Nick.
This is like saying that the rest of mathematics should be friendly and communicable with the natural numbers (please don’t attempt an exception to that, Nick).
Aggregation is separate. Aggregation can be done differently across and within the same accounting framework. (C + I + G + X – M) across is one aggregation. (G u G’) across is another. G’ within is another. Etc.
Pax out.
Nick Rowe: “First off, none of this has anything to do with the money supply. Y=C+I+G+X-M would still be true in a barter economy, with no money at all.”
You mean each of the variables would be vectors? I. e., not reduced to a single measure?
Nick Rowe: “And none of these variables determines the supply of money, even in a monetary economy.”
A somewhat ambiguous statement. 🙂 And one that appears to contradict MMT directly, which claims that the gov’t deficit injects money into the economy, increasing the money supply dollar for dollar. The simplest explanation for the apparent contradiction is differing definitions of money. Could you address that question more? Thanks. 🙂
Nick,
Interesting discussion on aggregation.
As someone has pointed out here, national accounting itself is based on a model – a way of looking at the complex world around us. And that is Institutionalism. New Keynesian economics seems to be built on utility-maximizing individuals and says little about the role of institutions.
Someone named Peter Kenway provided a taxonomy of the various income/expenditure models in Britain in a nice book. The first time someone aggregated in the way we are talking here (in an accounting language) – “private sector” was during the early 70s – Cambridge. So they would talk of the private sector “Net Acquisition of Financial Assets” in their models and would also combine the private and public sectors’ accounts stressing that the income less expenditure of a nation as a whole is the current balance of payments and this would lead to net incurrence of liabilities to foreigners and that process cannot go on forever.
The aggregation of all sectors of a nation as a whole exists independently – central banks have been maintaining the balance of payments and international investment position accounts since the World War – or maybe before (?). The numbers are also consolidated – so we have numbers such as net international investment (which combines the government and the domestic private sector into one) hitting the first page of an official press release.
Agree with you on the question you have posed here – what mechanism ensures that the accounting identities are maintained at all times ? I see you have commented that Y adjusts to keep the accounting identities intact, which nobody has appreciated so far!
Yes accounting identities don’t mean much. Some Austrian economist pointed out recently that he can criticize deficits using G-T=S-I by saying deficits reduce I! (The correct model IMO is that a fiscal expansion increases demand and would also increase investment)
“..this would lead to net incurrence of liabilities to foreigners and that process cannot go on forever.”
Sorry meant the other way – expenditure higher than income leading to net incurrence of liabilities to foreigners and that the process could become unsustainable.
“First, you need to stop talking about the “flow of funds“. What the heck are “funds”? You need to talk instead about the flow of money — the medium of exchange. Because it is money that we buy and sell stuff with. If we talk about demand and supply, and buying and selling, in a monetary exchange economy, we are talking about the flow of money.”
Can you stick to medium of exchange? IMO, there are too many definitions of “money”?
So in MV = PY should M equal the medium of exchange amount?
“But someone who says that lower interest rates will increase borrowing and therefore debt (which you hear a lot), has forgotten the other side of the accounting identity. Borrowing = lending. And lower interest rates reduce desired lending.”
What about banks and the capital requirement?
That sounds like the nominal interest rate(s) (I could be wrong about that). What about real interest rate(s)?
“You can eliminate C in 3, and rearrange terms to get:
4. I – S + G – T + X – M = 0”
That requires a medium of exchange supply that flows. Correct?
“Start with the standard national income accounting identity:
1. Y = C + I + G + X – M”
What if C, I, G, and/or (X-M) are coming from time periods outside of that measured by Y?
“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).”
Can that be applied to the medium of exchange amount and/or its composition?
I said: “You can eliminate C in 3, and rearrange terms to get:
4. I – S + G – T + X – M = 0
That requires a medium of exchange supply that flows. Correct?”
I see something about barter above. Skip that and replace “requires” with “usually has”.
this whole thread is talking past each other for one simple reason: we aren’t using the right terminology. Wynne godley’s main complaint was that in the mainstream model it isn’t clear who is a counterparty to each transaction, what form savings take and where the excess of spending over income actually goes. i think this 6 page sample from wynne godley’s monetary economics may be of use. http://goo.gl/jr0eS
Nick
Well, “borrowing” from foreigners is inapplicable to the USA but its also true that foreigners are a part of the non govt sector. They are part of the savers who are measured in the national debt. The MMT statement has never been “The national debt= AMERICAN CITIZEN savings only”. They have a demand to save in US dollars that is being “met” with the debt.
RSJ wrote:'”So the deposit ends up “backed” (very loosely) by a bond, rather than by reserves. The seignorage income is transferred from the government to the banking system, but the private sector as a whole still demands to hold money roughly equal to the federal debt. Obviously, this relationship breaks down if the federal government were to issue too much or too little debt. But in the latter case, the deposit ends up backed by a mortgage (say), which is more fragile than a riskless treasury. Therefore when MZM went above federal debt, this could have been (and was, for my part) interpreted as a sign of financial sector fragility. And the rush to increase federal debt can be interpreted as allowing the deposits to be “backed” more by riskless bonds — it strengthens the financial sector.”
Awesome! I’ve never seen the mechanics of government spending interacting with the banking sector explained that way. If I did, I wasn’t ready to understand it at the time. Initially it looks like banks have a large amount of control over the correlation between MZM and fed debt held by pub but their flexibility is determined by how much debt government is willing to issue. Basically it is the government’s choice to destabilize the banking system.
I’ve followed the amount of tsy secs held by commercial banks
http://research.stlouisfed.org/fred2/series/USGSEC?cid=99
and never had a good explanation for the recent step like nature to bank purchases of government debt. I never considered they might be due to supply issues. Interesting, thanks!
Or Winslow R., its their choice to stabilize it…anyway welcome to MMT
rsj said: “But the behavioral theory is that when the government deficit spends, it creates a deposit, so MZM goes up, but when the government sells a bond, the deposit does not go away, only the reserves backing the deposit go away.”
But when the gov’t sells a bond, does a different demand deposit that was saved also “go away” even if it was created by something bank-like?
So the deposit ends up “backed” (very loosely) by a bond, rather than by reserves.
So does that mean the new demand deposit (the new medium of exchange) was borrowed into existence?
“So the deposit ends up “backed” (very loosely) by a bond, rather than by reserves.” above is a rsj quote.
Min: I’m going to take your 2 questions in reverse order:
1. ” “Nick Rowe: “And none of these variables determines the supply of money, even in a monetary economy.”
A somewhat ambiguous statement. 🙂 And one that appears to contradict MMT directly, which claims that the gov’t deficit injects money into the economy, increasing the money supply dollar for dollar. The simplest explanation for the apparent contradiction is differing definitions of money. Could you address that question more? Thanks. :)”
Suppose a government buys $1billion worth of newly-produced tanks, or schools, or roads. That’s an increase in G. And suppose it finances this purchase by selling a national park for $1billion. That’s not part of G, because the national park is not a newly-produced good. And it’s not part of T either, by any standard definition. So G-T has increased by $1billion, but there’s no change in the money supply. (OK, you might say the money supply in public hands decreased by $1 billion when the government sold the park, but it immediately increased again by $1 billion when the government bought the tanks.)
Now, you might say that sales of government assets like national parks are perhaps rare. But it is very common for governments to finance deficits by selling bonds.
There are many different ways to define the stock of “money”. But most people, when they say “money”, do not include either national parks or bonds.
The stuff that people do call “money” that is a direct liability of the government and that the government can finance part of its deficit by issuing, is “base money” (i.e.currency plus deposits at the Bank of Canada). The stock of base money is normally around 5% of GDP in Canada and similar countries, while the public debt (accumulated deficits G-T) is (usually) many times bigger than that.
2. “Nick Rowe: “First off, none of this has anything to do with the money supply. Y=C+I+G+X-M would still be true in a barter economy, with no money at all.”
You mean each of the variables would be vectors? I. e., not reduced to a single measure?”
I’m going to make two responses to this:
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.
Apples sold = apples bought. That’s the same number, just looked at from two different sides. We might as well write it, A=A.
Same is true for bananas: B=B.
Normally, National Income Accountants add up the monetary values of goods. If Pa is the price of apples, and Pb the price of bananas, they will say that the total value of goods sold = the total value of goods bought: Pa.A + Pb.B = Pa.A + Pb.B (for an economy that produces only apples and bananas.
But look at the math. You can replace Pa and Pb with any pair of numbers (like 7 and 42), and the equation still holds true: 7A+42B=7A+42B
We could measure apples in kilograms, and bananas in pounds, and the equation would still hold true.
Now, replace bananas with electricity. We could measure apples in kilograms, and electricity in kilowatt hours, and it is still true that A+E=A+E. Even though A+E doesn’t mean anything at all, because the units are just…..wrong!
Weird, huh? What I say can’t be right! (But nobody called me on this when I wrote this in the post.)
I bet the Austrians will love this one! They always said that aggregation is meaningless (or something like that).
Ramanan: “Agree with you on the question you have posed here – what mechanism ensures that the accounting identities are maintained at all times ? I see you have commented that Y adjusts to keep the accounting identities intact, which nobody has appreciated so far!”
Hang on! That’s not what I said. I said that nothing needs to adjust to keep the accounting identities intact. 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.)
I said that something has to adjust to keep the equilibrium conditions (like desired saving = desired investment) intact. And I gave an example of one theory where Y alone did all the adjusting, just to illustrate the point. A different theory might say that r adjusts. Or maybe P. Or maybe some mixture of all 3. Or maybe a quite different theory says nothing can adjust, and desired saving never does adjust to equal desired investment.
“If Pa is the price of apples, and Pb the price of bananas, they will say that the total value of goods sold = the total value of goods bought”
Disagree.
They say the total value of goods sold/bought = total income earned.
The right hand side requires a homogeneous unit of measurement by construction.
It doesn’t allow the nonsensical examples you construct simply by invoking bought = sold.
Here’s the thing: there is no such thing as a theory derived from accounting identities; all you have done is re-written the accounting identities in a different way. Arranging things so that X is on the left-hand side and Y is on the right-hand side is not a demonstration that Y depends on X.
“Suppose a government buys $1billion worth of newly-produced tanks, or schools, or roads. That’s an increase in G. And suppose it finances this purchase by selling a national park for $1billion. That’s not part of G, because the national park is not a newly-produced good. And it’s not part of T either, by any standard definition. So G-T has increased by $1billion, but there’s no change in the money supply.”
So has the velocity of the medium of exchange supply changed because the gov’t has stopped saving?
I didn’t rewrite anything. It’s products on one side, and income on the other. Value of transactions (product side) equals income. Transactions, bought or sold, are stated on the product side. I said/inferred nothing about dependency or causality. It’s just accounting, not theory.
Sorry Nick you have lost me.
RSJ’s point (as I interpret).
1) ‘bank loans create bank deposits’
2) ‘government spending creates bank deposits and reserves’
3) ‘government taxes destroys bank deposits and reserves’
RSJ’s point regarding reserves and deposits can also address whether government bonds are purchased by banks or bank customers.
If the bank customer’s purchase bonds, reserves and deposits are destroyed.
Simple xplanation: initially the bank customer has a $10 deposit from which he requests $10 bill. He takes the $10 bill and purchases a $10 bond. Both reserves and deposits are destroyed, while customer gains a bond.
If the bank purchases government bonds, reserves are destroyed but deposits remain.
Simple xplanation: initially the bank has excess reserves. It exchanges the reserves for bonds. The reserves are destroyed while the bank gains a bond.
I’ll test RSJ’s theory against real numbers when I get back to civilization, hard to do on a smart phone, even an iPhone 🙂
Initially I don’t think the base money at 5% of GDP vs. Government debt being several times that is a concern because government does sell bonds which destroy reserves all the time and deposits almost all the time ( except when the bonds are sold to banks)
Winslow,
I am not saying that all government bonds are purchased by banks. But I am saying that the result of the behavior is that the system behaves as if the government is transacting directly with banks.
Each action — e.g. the government selling a bond — kicks off a chain of other actions — many other people/sectors buy and sell bonds as well. Interest rates change, quantities change, etc. The result of all of these actions is (typically) that the household sector bond to deposit ratio changes only slightly even as the other sectors significantly shift their net supply of bonds.
Primarily, it is the financial sector that adjusts its net bond holdings, allowing households to maintain a target level of bond to deposits in line with their own bond/deposit demand.
We would expect that target ratio to change with the interest rate, and it does, but the target ratio as demanded by households is much less sensitive to changes in the interest rate than the quantity of bonds supplied by the financial sector. Or equivalently, the financial sector, because it is leveraged, is much more sensitive to interest rate changes than the household sector, so it is the one to bear the brunt of the quantity adjustment.
This is basically an elasticity argument, that I tried to outline here with some graphs:
The actual data has been that household bond/deposit ratio remain relatively constant even as the government and foreign sector’s bond supply swing around, with the financial sector soaking up the difference. This data is available here:
That last post was by me, not “m” 🙂
Winslow R. said: “RSJ’s point regarding reserves and deposits can also address whether government bonds are purchased by banks or bank customers.
If the bank customer’s purchase bonds, reserves and deposits are destroyed.
Simple xplanation: initially the bank customer has a $10 deposit from which he requests $10 bill. He takes the $10 bill and purchases a $10 bond. Both reserves and deposits are destroyed, while customer gains a bond.
If the bank purchases government bonds, reserves are destroyed but deposits remain.
Simple xplanation: initially the bank has excess reserves. It exchanges the reserves for bonds. The reserves are destroyed while the bank gains a bond.”
Let me try to expand on the bank part. If the bank wants to purchase the gov’t bond, it creates a demand deposit (medium of exchange) out of thin air and immediately saves it. Next, both (central bank) reserves and demand deposit(s) are destroyed, while the bank gains the bond (a savings vehicle). Sound good?
Winslow R. said: “Simple xplanation: initially the bank customer has a $10 deposit from which he requests $10 bill. He takes the $10 bill and purchases a $10 bond. Both reserves and deposits are destroyed, while customer gains a bond.”
It seems to me you can skip the $10 bill part. Just markdown the customer’s account by $10 of demand deposit(s) and markup the same person’s account with $10 of a gov’t bond that yields interest.
That’s great stuff, RSJ. It fits quite well with the MMT view. I’m going to have to work with both posts a bit more (pushing on a string posts, that is) when I get some time to see how much of my own views I can fit in their and how much it clarifies/adjusts my own views. Thanks!
RSJ,
I took a quick look at your two posts for the first time. They look very interesting. A couple of first reactions:
a) Wouldn’t you expect off the top that most CB or Treasury bond sales/issues would end up in the financial sector directly anyway, based on the size and historic trend holdings of the household sector? If I’m not mistaken, your posts seem to develop it as if it is households that are taking on some sort of temporary intermediary function which results in “diffusion” of bonds out into the financial sector. But I’ll have a closer look at your posts when I get a chance.
b) I think your posts may be blending in and out of talking about banks versus the non-bank financial sector a bit. It’s still noteworthy to track the first round effect on bank deposits versus non-bank non-deposit liabilities, and to do it for the banks and non-bank FIs in distinction.
c) You’ve “universalized” the analysis to bond deposit liabilities versus bond liabilities. The big non-bank financial liabilities other than bonds that may be intertwined with bond purchases include mutual fund liabilities, investment fund liabilities, insurance liabilities, pension fund liabilities, etc. The bank bank liabilities of course include time deposits as opposed to bonds.
d) Just a caveat on flow of funds data, which you’re probably aware of. The household sector is a data residual, not directly collected data. As a quirk, it happens to include hedge funds, which have probably had a substantial impact on bond distribution since the QE programs started.
This is a quick response. Apologies if I’ve misrepresented anything you wrote.
meant bank deposit liabilities, not bond deposit liabilities, above
Final point, RSJ – it’s not clear to me that the CB would have an objective of creating household deposits with QE, given what you would think they would know and expect about the end distribution of bonds among sectors.
That’s another reason why the official explanations for QE motivation seem somewhat vague and ill-defined.
Winslow R.: “RSJ’s point (as I interpret).
1) ‘bank loans create bank deposits’
2) ‘government spending creates bank deposits and reserves’
3) ‘government taxes destroys bank deposits and reserves'”
Hang on. Isn’t there a central bank in there somewhere? What’s it doing?
Savings will NEVER be equal to investment, because their under-the-mattress portion cannot and will not be invested, NO MATTER WHAT YOUR ARITHMETIC SAYS.
Scott — thanks! I’d be happy to hear any criticism or corrections. The post was my interpretation of the data, but it may not be the only interpretation.
JKH,
Thanks. Regarding your points:
A) In the first post, I assumed that all bonds were sold to households or purchased from household, for purposes of exposition, not because this is important. As long as there is a law of one price, then it doesn’t matter who the government is transacting with. While the law of one of price is itself just an idealization, it’s good enough for my purposes.
But in the second post (the supply-demand version), I didn’t look at individual transactions at all, but merely asset demand — specifically net bond bond demand coming from different sectors. I think this is a better way of trying to understand the relationship between changes in government bond supply and the resulting shifts in both quantity and price that occur in each sector.
B) Perhaps. I am often sloppy. If you see an error, then point it out. But for my purposes, I don’t treat insurance/pension/mutual funds as “finance”, but I called them an “investment” sector. The sector membership definitions were defined in the first post. For me, the relevant part about finance is leverage, since my hypothesis is that leverage is what makes this sector more sensitive to rates and therefore the interest elasticity of net bond supply should be higher for leveraged institutions rather than non-leverage.
In the second post, I grouped most of the sectors together, purely for pedagogical purposes — there were enough lines in the drawing already! But again, in theory, if you have N different sectors, each with N different interest-elasticities, then you can calculate how quantities and interest rate shift as a result of one of the sectors (e.g. the central bank or foreign sector) changing their net bond demand, just by using the elasticities and sum of bond positions = 0. That is uncontroversial. It then becomes an econometric problem to estimate the elasticities using time series data or other data. My general argument about leverage increasing the elasticity is the low hanging fruit.
C) Yes. I ignored equity completely, as well as things like repo funding. The former was just too volatile, and I don’t imagine equity as directly competing with deposits in a way that bonds do. But the latter is important since I am ultimately looking at instruments that households can purchase and specifically looking at the effects of CB and foreign sector bond purchases.
Btw, I actually think that the foreign sector bond acquisitions were much more devastating to both household and financial sector balance sheets than the Clinton surpluses, and I think the data bears that out.
D) Yeah, the hedge fund data complicates every measure of household asset holdings. I think for this reason, it’s good to group the household and “investment” sectors (as I’ve defined it) together — another good reason to split off insurance and the like from “finance” and insert it into the household sector. Both groups tend to have fairly stable bond holdings under a variety of interest rate regimes, particularly in comparison with the other sectors.
Nick,
The CB is controlling the short rate, and — in the case of something like QE — it is causing the consolidated government bond demand curve to shift. I was examining the effect of the second.
Specifically, I was trying to understand why the various rounds of QE failed to cause MZM to increase — both here and previously in Japan.
I came to the conclusion that it boils down to the incidence of the CB purchases on overall bond holdings by each sector:
If the CB sells a bond to a household, and the household turns around and buys a bond from a bank. Then the result of both operations is that MZM remains unchanged. On the other hand, if the CB buys a bond from a household, and the household keeps the deposit, then MZM has increased. Of course there are many other possibilities in between, but the key aspect seemed to be how net bond holdings change among all the different sectors as a result of a shift in the bond demand curve of the government sector.
When looking at the historical time series, I noticed that households tend to keep their bond/deposit holdings constant, or at least the sensitivity of this ratio to changes in interest rates is quite low. However the opposite is true of the financial sector. This sector adjusts its bond holdings very rapidly, and it seems to make this adjustment in such a way as to keep household bond holdings roughly unchanged.
Then I hypothesized that because this sector is leveraged, its sensitivity to interest rates is much higher, and therefore leverage is the main reason why the CB has such difficulty affecting the size of MZM via quantity adjustments (e.g. OMO). Hope that makes sense.
“Specifically, I was trying to understand why the various rounds of QE failed to cause MZM to increase”
Without looking at the data as closely as you have, I’ve always just assumed its directly related to the impact of de-leveraging on the banking system: loans being paid down, which extinguishes deposits. And banking system losses leading to bank recapitalization, which moves money from deposits into capital. But maybe that’s too simplified.
JKH,
These issues are clouded by the fact the government has been stepping in to supply more net bonds and a lower trade deficit meant that the foreign sector was purchasing fewer bonds. If you consolidate CB + foreign sector + government, there hasn’t been a change in net bond supply by this consolidated sector.
If you are going to measure bond supply shocks on the household sector, it’s better to look at the foreign sector prior to the crisis, or, in the case of Japan, look at their QE effort.
Total borrowing by financial sectors is lower than before (but it seems to be have stabilized), so that if we group all types of bank borrowing — recapitalization as you put it, together with debt growth, then there has been less of it going on now that before the crisis.
Therefore deposits, in aggregate, have not been moved into more claims on banks. Rather household bond claims on banks have been replaced with bond claims on government and the foreign sector. Total household deposits and bonds haven’t changed a whole lot throughout this crisis.
I was the one who annoyed Nick at Sumner’s site by claiming that S=I (in absence of govt) by accounting and that equilibrium has nothing to do with it.
Here is why more generally the equality S-I=G-T has nothing to do with any equilibrium, and everything to with with accounting.
In the presence of govt, there are only 4 types of transactions, examples of which are below:
1) A buys investment good from B for 40.
(note that different parties accrue income and invest here: B accrues income, A invests.)
2) C buys consumption good from D for 60. (D accrues income, C consumes).
3) Govt G taxes party E 10. (no private sector income here)
4) Govt spends by crediting F’s account 20. (F gets income, G doesn’t consume anything)
This covers all possible transactions types in a closed economy with govt.
(cont.) part 2
Let’s looks at accounting:
Y=(outlays)=C+I+G
Y=(spending sinks)=C+S+T
The second equality is the definition of S=Y-C-T : Saving (S)=income (Y), unconsumed (-C), after taxes (-T).
I will show below that with this definition all transactions 1-4 obey S-I=G-T.
Note, that for this “saving” S to occur, there has to be a transaction (we need income). A stash of money we have in the bank, although commonly called “savings”, is a stock, not a flow, as S is – this is the source of the confusion.
(cont. part 3)
Here is how S-I=G-T is preserved in each of the above transactions:
1) Transaction 1
A buys investment good from B for 40.
Income incurred by B is 40, it records A’s investment (not consumption):
dY=40=dC+dI+dG=0+40+0
dY=40=dC+dS+dT=0+40+0
dS=40 here, by definition, because this the unconsumed income (40) after taxes (0) that was recorded in this transaction.
dS-dI=40-40
dG-dT=0-0
d(S-I)=d(G-T) in this transaction.
2) Transaction 2
C buys consumption good from D for 60.
dY=60=dC+dI+dG=60+0+0
dY=60=dC+dS+dT=60+0+0
dS-dI=0-0
dG-dT=0-0
d(S-I)=d(G-T) in this transaction.
(cont part 4)
3) Transaction 3
Govt G taxes party E 10. No private sector income is created here:
dY=0=dC+dI+dG=0+0+0
dY=0=dC+dS+dT=0-10+10
Here we have S=unconsumed income (0), minus taxes (-10)=-10
dS-dI=-10-0
dG-dT=0-10
d(S-I)=d(G-T) in this transaction.
4) Transaction 4
Govt spends by crediting F’s account 20. This income is not recording G’s consumption (thus belongs in S).
dY=20=dC+dI+dG=0+0+20
dY=20=dC+dS+dT=0+20+0
Here we have income of 20, which the private sector didn’t consume = it belongs to unconsumed income after taxes (S).
dS-dI=20-0
dG-dT=20-0
d(S-I)=d(G-T) in this transaction.
(cont part 5)
If the period in question contains transactions 1-4, the GDP equation is:
Y =C+I+G=60+40+20=120=C+S+T=60+50+10
Total saving S in this period: unconsumed income (Y-C=60), minus taxes (10)=50. Or, summing dS(i) accrued in each transaction: S=dS(1)+dS(2)+dS(3)+dS(4)=40+0+(-10)+20=50.
In this period:
S-I=50-40=10
G-T=20-10=10
Each larger period contains many of these transactions, yet each and every one of these transactions obeys S-I=G-T, no matter the size of the transaction, the interest rates, equilibrium presence and whatnot.
Interest rates or the presence or absence of equilibrium would have impact on the size of these transactions or their taking place or not in the first place, but it would have no impact on the equality S-I=G-T being obeyed or not (it will be obeyed no matter what).
S-I=G-T is preserved in each transaction that takes place in the economy.
In the absence of the govt, the transaction types 3) and 4) don’t take place and we have S-I=0 preserved in every single transaction, and hence in each period, however long or short.
(appologies for so many parts and a long comment.)
RSJ,
I’ll have to absorb that.
I’m being a bit lazy about this at this particular point, but one of the pieces of the puzzle here is what could be a somewhat stand-alone explanation about what’s happened to the banking system balance sheet. We know that reserves are up to due to QE. So what I’m looking to summarize in a lazy way is what is the offset to that instead of MZM on the liability side. It has to be some combination of asset adjustment and liability/equity adjustment that plugs the absence of MZM growth. No doubt it’s consistent with your explanation, but is there a way of summarizing the system balance sheet change in such a way as to explain that adjustment?
P.S.
And I expect not much of it at all is going to be explained by a decline in commercial bank holdings of government bonds.
P. Petropoulos: “Savings will NEVER be equal to investment, because their under-the-mattress portion cannot and will not be invested, NO MATTER WHAT YOUR ARITHMETIC SAYS.”
Aha! A man after my own quasi-monetarist leanings! Presumably you are saying that desired saving will not be equal to desired investment, if there is an excess demand for the medium of exchange.
You might enjoy this old post of mine:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/10/the-paradox-of-thrift-vs-the-paradox-of-hoarding.html