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 
There is no equilibrium in the real world. It would have been better and more realistic if you just dropped your equilibrium assumption together with Sd=Id and just stayed in the real world. Because this is where the real difficulty of S=I is.
“First, you can’t get anywhere with just accounting identities, if you want to explain the world.”
I assume all this is mostly the result of your frustration with MMT.
The inverse to your statement is:
“You can’t explain the world without conforming to accounting identities”.
If you examine a lot of the MMT thinking about economics, you’ll find that this latter idea is highly operative. Scott Fullwiler has some powerful ways of expressing this in some of his papers, but I’m too lazy to look them up right now.
In the most simple form, your accounting identity is S = I.
If you attempt to explain the world according to your economics as a change from time period 1 to time period 2, you must have:
S (1) = I (1)
And
S (2) = I (2)
This is the case no matter what the absolute temporal positioning of period 1 and period 2 are. Both can be in the past, one in the past and one in the future, or both in the future.
What this means is that accounting is a constraint on economics.
And that’s something you guys (you to be defined relative to attitude to MMT) are very loathe to accept.
Sergei: do you want to do away with I=S altogether, even as an accounting identity? Are you saying it’s false? OK, if that’s what you mean, I will leave you and JKH to have a fun argument (I will join JKH). Or are you saying that it’s not useful? I might have some sympathy with that.
If you think that demand and supply are both irrelevant in determining the quantity of apples actually bought and sold, that’s an interesting position. Not one I agree with, but interesting.
JKH: If I find a theory in which quantity of apples sold is not equal to quantity of apples bought, I am very happy to agree that’s not a very good theory. I’m not at all loathe to accept that. That goes whether we are talking about this year, last year, next year, or whatever year, century, month, week, etc. Or whether we are talking about apples, bonds, antique furniture, whatever, or even money.
JKH,
“What this means is that accounting is a constraint on economics”
You obviously missed the point of Nick’s post. Saying that apples bought equals apples sold doesn’t tell you anything meaningful about the market for apples. Saying that S=I in every period doesn’t tell you anything meaningful about the macroeconomy. All old-Keysian, New Keysian, Monetarist, Austrian, RBC and neoclassical growth theory models are all consistent with S=I. S=I is not a constraint on any of these theories.
I can’t think of any economic model that doesn’t impose the accounting identities. The whole point of Nick’s post is to point out that they are routinely incorporated into the development of the model en passant.
Are you thinking of some economic theory in which accounting identities are violated? Which one?
Gregor and Stephen: I was thinking on the same lines. I think I did once referee one paper that maybe (if my memory is correct) violated an accounting identity. (The model was over-determined). Just in case you need to ask, I recommended rejection.
Good refresher post. The “return to basics” S=I, made popular recently by certain individuals, could be akin to a “brilliant” physicist coming into a room and intuitively looking at a problem, surrounded by much complicated maths, empirical assumptions and the like, and stating the elegant solution on a single chalkboard, not necessarily with any equations beyond the basic one. It does happen (I’ve seen it) so I wouldn’t discount it.
Krugman claims his freshman economics class teachings are explaining the current economic environment rather well.
Let’s do this a different way.
1. What is your recommended path for the US govt budget balance over the next, say, 10 years? (in % of GDP terms would be most clear)
2. What is your assumption regarding the US current account balance?
3. Give answers to 1 and 2, what will S-I be?
4. Is your answer to 3 desirable or even sustainable?
BTW, using CBO assumptions for 1 and 2 during the late 1990s and 2000s and then answering 3 and 4 for ourselves made it clear that CBOs projections (and most everyone else’s) were dead on arrival. If the accounting identities were so obvious and trivial, why can’t CBO figure them out?
As JKH says, any relevant theory has to conform to accounting identities (and if one thinks that’s all there is to MMT, then that’s just silly, but I’ll leave that one for now). “apples sold= apples bought” just demonstrates the point hasn’t been properly understood.
The CBO example is more along the lines of what we’re talking about–or asking the Republicans in the US Congress to answer those 4 questions, for instance, particularly the ones against raising the debt ceiling. If you can find 1 neoclassical economist who teaches his/her students to answer my 4 questions above when teaching macroeconomic policy analysis, I’ll be more than moderately surprised. (Not to mention the fact that any neoclassical economist using DSGE models with a transversality condition can’t answer #4 anyway, as Charles Goodhart has pointed out over and over.)
No, I think the better challenge is to find an economic theory that doesn’t respect the accounting identities. My claim is that they all do. Saying that “any relevant theory has to conform to accounting identities” is telling us something we already know.
My suggestion was not that economic theory must conform to accounting identities, but that economic analysis must conform to it, including all forecasting and risk analysis. That is a stronger statement than the same for formal economic theory alone, which hopefully has been vetted for accounting integrity. So I think Scott’s question is a good example of what the issue is.
I’d still like to see an example of a ‘neoclassical’ economist failing to do so. Since apparently we’re all very loathe to accept the point, it shouldn’t be hard to find one.
“No, I think the better challenge is to find an economic theory that doesn’t respect the accounting identities. ”
That’s a straw man, as is Nick’s post. My questions above get at what MMT’ers are talking about.
Another example of not understanding the sector balances–Maastricht Criteria and the EMU triangle http://neweconomicperspectives.blogspot.com/2010/03/will-quest-for-fiscal-sustainability.html
Again, how could all those economists pushing for the EMU and Maastricht not have seen this coming. Somehow we did.
And here’s another on the household sector in 2005: http://www.levyinstitute.org/pubs/sa_mar_05.pdf
Apparently Milton Friedman was wrong. Making correct predictions isn’t good enough if you don’t have the “right” model.
Any takers on the four questions? Apparently you’ve all done this before and do it in every one of your classes, or so Steven suggests.
Scott: “BTW, using CBO assumptions for 1 and 2 during the late 1990s and 2000s and then answering 3 and 4 for ourselves made it clear that CBOs projections (and most everyone else’s) were dead on arrival.”
But most models I can think of wouldn’t make any assumptions about 2, given an assumption about 1. You make an assumption about the government budget balance (and maybe monetary policy), then let the model answer 2 and 3. I could maybe imagine someone like Pat Buchanan making an assumption about both 1 and 2. Because he’s planning to impose import quotas or something. Otherwise 2 and 3 are both endogenous variables (though the sum of 2 plus 3 is exogenous, of course, given 1).
“…(and if one thinks that’s all there is to MMT, then that’s just silly, but I’ll leave that one for now).”
I have come across too many followers of MMT who I can only interpret as believing that everything in MMT follows as a matter of logic from accounting identities. That’s one of the things that triggered this post (though I also wrote it because a lot of people, not just MMT followers, find I=S confusing). I can’t think that the leaders, like yourself, believe this. And I know one can’t be held responsible for everything one’s followers believe. But something weird is going on here. It happens far too often to be just a fluke. My guess is that a lot more will listen to you setting them straight on this than will listen to me.
“(Not to mention the fact that any neoclassical economist using DSGE models with a transversality condition can’t answer #4 anyway, as Charles Goodhart has pointed out over and over.)”
That sounds interesting. Does anyone have a link?
I haven’t done any macro in ages and can barely remember the IS-LM model. But, if i understand everything said in the post correctly when we plot the usual S and I curves in {S_I, r} space these are effective supply and demand curves for loanable funds for a given level of income. And if they intersect at a rate of interest that is negative so that the ZRLB holds then it must be that Income must fall given our equlibrium conditions that jointly determine Y and r.
N: you understand it. You just need to add that if they intersect at a negative rate of interest when Y is at potential Y you hit the ZLB problem. (Because the two curves shift when Y changes).
jesse: glad you found it a good refresher too. That’s what it was intended to be, for those who have already seen this stuff.
BTW: JKH: “My suggestion was not that economic theory must conform to accounting identities, but that economic analysis must conform to it, including all forecasting and risk analysis.”
Agreed. Certainly. (But if the forecast comes from a model that conforms to accounting identities, then the forecast will automatically conform to them too.)
Hi Nick, why did the mainstream models not see the GFC coming, while heterodox economists, including MTM economists did? Did you foresee it? Can you explain it in terms of your model? How about doing a post on that.
Nick,
Regarding the endogeneity, yes, obviously all three are endogenous in their own ways. The point is, then, for instance, why hasn’t the economics profession ever (to my knowledge) queried CBO on its assumptions for S-I when it makes its projections? Why doesn’t Laurence Kotlikoff tell us what he expects the effects on S-I to be if we follow his advice and permanently cut deficits by 6% or whatever his latest projection of the fiscal imbalance is?
My suspicion is that your model above isn’t what economists think about when they think of S-I. What shows up in all of the textbooks once it’s time to do analysis is I = S + T-G + M-X, the so-called national saving identity. Most analyses of this identity incorrectly assume that there is some pool of saving, and we easily go from here to the inapplicable loanable funds market and financial “crowding out” by govt (in terms of how “loanable funds” are actually generated in the aggregate, but not that there aren’t supply and demand in individual markets like, say, for venture capital; that’s another story, though).
Regarding Goodhart, see this as a quick overview: http://www.voxeu.org/index.php?q=node/4283
Thinking more about what Scott said about some forecasts violating accounting identities, this is my guess about what happened. Instead of using one consistent model to make the forecast for everything, the problem is broken up into bits. One group forecasts X, with one model, another group forecasts Y, with a different model, and a third group forecasts Z, with a third model. And it would only be by sheer fluke if X,Y, and Z are in any way consistent with each other. Even if they were (by fluke) accounting consistent, it would be very unlikely if all 3 were consistent with any reasonable economic theory.
And Scott is, of course, quite right to complain about such internally inconsistent forecasts.
Nick,
A detour of questions:
Is it possible to construct a prototypical example of how people are abusing accounting identities? I would have thought something in the way of an iconic error might be sticking in your mind as to exactly how people are going terribly wrong on this.
I’ve also noticed you touch on the nature of supply and demand curves a number of times. It seems to me as simple as acknowledging that both are functions of an independent variable that itself covers a fairly wide domain of possibilities. The eventual, operative value of the functional value (i.e. quantity sold or bought) reflects just one of those independent variable possibilities, depending on the interface between supply and demand functions as well as other possible influences (e.g. government intervention, etc.) I’m I wrong on this myself? How are people not understanding this?
Finally, is it possible that some of your concern is related to the outright MMT rejection of the loanable funds theory? (I wrote this before seeing Scott’s latest.) That is fundamental to MMT, and I would have thought that it rejects a great deal of related theory that you might otherwise expect to substantiate the extrapolation of accounting identities associated with economic outcomes. People are not bringing theories that you are comfortable with to the accounting party because they are not comfortable with the theories that you comfortable with.
I think you are missing an important viewpoint on I=S by not translating it back to the real world: In order to invest the national savings we need a financial system. That system is absent from the equation, because we always assumed it would function efficiently, moving the money from the place where it is saved to the place it is needed for investment. With a financial system that doesn’t function you will never get I=S. The problem we need to solve is thus: how do we get investments going without depending on the banking system?
The only ones that can invest the money without help are the ones saving the money, thus the government should stimulate that. The only other solution is taxation and have the government reinvest.
Scott: we were posting at the same time.
I think my 07.19 comment speaks partly to your first point.
But more generally (I don’t know who Laurence Kotlikoff is and what his theory is) not all models give the same salience to the same variables. It might be a bit like a traditional monetarist asking a New Keynesian what his forecast implied about the stock of money and velocity? The New Keynesian would just shrug his shoulders and reply “M and V will take care of themselves”.
On your second paragraph: When I first learned the Keynesian Cross, we were taught it two ways. The first was the standard Y=AE and AE=C+I+G+X-M way (with the two lines on the board). The second was the Withdrawals = inJections way. Same Y on the horizontal, then two curves: W=S+T+M, and J=I+G+X. Equilibrium Y determined where the two curves cross.
The two ways of showing the same theory are of course equivalent. The second has fallen out of favour. I think it’s because “S” is such a “non-thing”, and hard to interpret intuitively. The first has a much easier “output = output demanded” interpretation.
But, of course, both ways have really fallen out of favour past intro economics. It’s only old guys like me who understand what you are talking about (or part of it, anyway). Does Y adjust to equilibrate S=I? Or does r adjust to equilibrate S=I? (And some MMT followers don’t think anything has to adjust to equilibrate S=I, because they must be equal).
Thanks for the Goodhart link.
JKH: “Is it possible to construct a prototypical example of how people are abusing accounting identities? I would have thought something in the way of an iconic error might be sticking in your mind as to exactly how people are going terribly wrong on this.”
Scott Sumner’s blog seems to be overloaded, but it was some of the comments there that were the trigger. But let me make something up, to give you an illustration:
“It makes no sense to ask what variable adjusts to equilibrate S and I. S and I are always necessarily equal, so anybody (like Nick Rowe) who asks this question just doesn’t understand basic accounting.”
Yep, something like that did rather stick in my mind. It is terribly wrong. A good old-fashioned extreme Keynesian would also say that’s terribly wrong (and would answer “Y adjusts to equilibrate desired S and desired I, and that is precisely how Y gets determined”).
And saying the above is a terrible mistake is in no way related to the loanable funds theory per se. The loanable funds theory (at its crudest) says r adjusts to equilibrate S and I. Keynesian economics (at its crudest) says “no that’s wrong, it is Y that adjusts to equilibrate S and I; r adjusts to equilibrate Md and Ms”. Two very different theories (and one can imagine many more non-loanable funds theories of what adjusts to equilibrate S and I) but all are in conflict with the mistaken view that S and I don’t need equilibrating, because they are always equal.
(Funnily enough, in the olden days we used to associate the view that S is necessarily the same as I with Say’s Law, and the denial of the logical possibility of general gluts, which is about the most extreme opposite to MMT one can think of!)
Sorry. You lost me on your middle paragraph on supply and demand.
Paul Krugman regularly blogs on the ‘Doctrine of the Immaculate Transfer‘, which is another good example of the bad use of accounting identities.
Thanks for the replies, Nick–I’m feeling much better now.
Your 7:19 sounds good to me. If you don’t know who Kotlikoff is, then you’re way ahead, IMO!
Regarding this: “It makes no sense to ask what variable adjusts to equilibrate S and I. S and I are always necessarily equal, so anybody (like Nick Rowe) who asks this question just doesn’t understand basic accounting.”
I agree with you . . . that’s not correct at all. A lot of MMT supporters misinterpret or at the very least don’t have a very precise understanding of the sector balances (as we call s-i = g-t +x-m) as we explain and use them in analysis. Sort of like when I see someone write “the national debt is equal to private savings” or something like that–ouch.
Regarding this: “It might be a bit like a traditional monetarist asking a New Keynesian what his forecast implied about the stock of money and velocity? The New Keynesian would just shrug his shoulders and reply “M and V will take care of themselves”.”
I see where you’re going there–there has to be a reason why paying attention to the pvt sector balance is important to us, which obviously comes from our Minskyan approach. And it’s obviously not as important to others–Goodhart’s interpretation of DSGE models suggests that the latter ignore solvency issues for the pvt sector altogether. Further, it goes to a fundamental difference b/n fiscal and monetary policies–the latter can only “work” to end a recession if the pvt sector releverages, whereas with the former the pvt sector can deleverage and still sustain or perhaps even increase spending. We think that difference is important, but it doesn’t show up hardly anywhere in most discussions of the differences. (Clearly some of the reason for this is that fiscal policy is viewed as requiring releveraging for the pvt sector, too, in the neoclassical view, via adherence to the intertemporal budget constraint and potential Ricardian equivalence effects.)
Scott: we are very much on the same page.
I am going to take minor issue with you on one picky point.
“Further, it goes to a fundamental difference b/n fiscal and monetary policies–the latter can only “work” to end a recession if the pvt sector releverages, whereas with the former the pvt sector can deleverage and still sustain or perhaps even increase spending.”
I’m going to put words into your mouth here a bit, but bear with me.
One of the problems with S-I=G-T (ignore foreigners) is the level of aggregation. Even if G-T=0 the private sector can still deleverage. If the debtors increased their saving, and the creditors decreased theirs, leaving aggregate desired saving the same, private sector (gross) debt would decrease, and I would want to describe that as “deleveraging”.
You would I think agree. And this does not in any way contradict your model. But, to make the same point you made earlier, some ways of presenting the accounting identities do (in some weird way) lead our eyes to look towards certain things and ignore others.
Here’s my preferred way of doing the identity/equilibrium condition. Just ignore foreigners, government, and even investment, for simplicity:
S(creditors) = -S(debtors)
How will a change in r, or Y, affect that equilibrium condition? And how will it affect debt/Y?
OK, Nick, I’m going to come to the defense of your straw man:
“It makes no sense to ask what variable adjusts to equilibrate S and I. S and I are always necessarily equal, so anybody (like Nick Rowe) who asks this question just doesn’t understand basic accounting.”
The thing is, the accounting identity has to hold even out of equilibrium, so unless you believe in continuous equilibrium, it’s misleading to talk about equilibrating S and I. Something happens, out of equilibrium, that determines S and I in the very short run, and then something else happens that brings the model to equilibrium (possibly changing S and I in the process and possibly not).
In the simple Keynesian cross model (closed economy, no government, no inventories), the thing that happens initially out of equilibrium is that firms decide how much to invest. Their desired investment is then realized as actual investment, and, in the very short run, it determines saving, because everyone who receives income from that investment immediately saves it. (If you make the very short run short enough, that has to be the case, because they don’t have time to spend it.) And when the equilibration happens, it has no effect on these values of S and I. The equilibration happens through acts of matched saving and dis-saving without ever altering the level of investment. I would argue, therefore, that in the Keynesian cross model, nothing adjusts to equilibrate S and I; rather I immediately determines S, and then C and Y adjust to equilibrate each other.
I’m less clear on what happens out of equilibrium in the loanable funds model. Does it only work with continuous equilibrium? Otherwise, what happens in the very short run if, for example, people suddenly decide to save more? I’m thinking the immediate effect is to reduce, simultaneously, both income and interest rates without affecting investment. Then the equilibration happens when firms respond to the lower interest rates by investing more, thus bringing income and saving back up (and also causing interest rates to rise to some intermediate level, possibly feeding back on saving in a cobweb etc.). But again it’s misleading to say that r adjusts to equilibrate S and I. In my example, r changes before the equilibration, and then I adjusts (along with further changes in r) to equilibrate Y.
Nick
Here we see an example of the importance of understanding accounting.
If I am a debtor and I pay down my debt to you instead of spending, I have reduced my spending out of income and deleveraged.
But you have not received any income from this aside from debt service (interest), just a portfolio shift from a loan or bond to deposits. You would have to make an additional assumption that the creditor now spends more out of income (i.e., as a result of the portfolio shift now moves to spend instead of save), which I don’t see any inherent reason for; the creditor could desire to continue saving and just convert to a time deposit or whatever (the creditor could surely spend, but I don’t see the behavioral reason to spend BECAUSE the debt has been paid down).
Further, if it is a bank that is the creditor, the payment to reduce debt has simply resulted in a debited deposit of the payor and a debited loan for the bank. There is clearly no reason for the bank to “spend” more out of income.
Now to turn to traditional Keynesian macro . ..
In the aggregate, S-I will depend on a number of factors (interest rates, etc.) that will determine how or even if the reduced spending of one affects aggregate desired spending out of aggregate income (i.e., desired “net saving”). Yes, some others may spend more out of income as a result–perhaps the debtor’s reduced spending reduces someone else’s income, but that person doesn’t reduce spending but reduces saving. In other words, we certainly can get the same result as you do, but not necessarily via the creditor’s actions (and I would argue probably not because of the creditor’s actions). Or, interest rates could fall and others could as a result spend more out of income and again keep aggregate S-I from rising.
But if the desire to deleverage is widespread enough, then it reduces incomes and shows up as reduced spending on imports and/or reduced tax revenues in the aggregate, and S-I rises.
(Furthermore, it’s important to add that “deleveraging” could simply be reducing debt ratios or debt service ratios, so simply borrowing less or stop borrowing, rather than actually paying debt down. In that case, again, we aren’t talking about creditor behavior but the aggregate picture.)
So, what we have is the debtor spending less out of income and very possibly the creditor spending the same out of unchanged income.
In the end, I don’t necessarily agree with your overall point (we can have some deleveraging but keep S-I from changing, and the aggregation is complex and important to understand), but I don’t don’t think the creditor’s desire to spend/save is really the place to look either in the micro or macro case. I think this is one of the problems/flaws folks like Krugman have in not completely understanding what is meant by a balance sheet recession relative to a liquidity trap.
Andy,
I agree with you given the assumptions made (no govt, no foreign sector, etc.).
I was interpreting the statement differently, but it’s late and I’ve forgotten how (not real late, but I’m tired, so I’m using that as my excuse). When I first read Nick’s response to that quote above, I saw his point immediately, though, or so I thought–perhaps Nick can help me out (and I hope I agree with whatever Nick writes or I’ll feel really stupid–won’t be the first time, though, or last.)
Scott:
“monetary policies…can only “work” to end a recession if the pvt sector releverages”
Nick:
“If the debtors increased their saving, and the creditors decreased theirs, leaving aggregate desired saving the same, private sector (gross) debt would decrease, and I would want to describe that as ‘deleveraging’”
That could happen, but it does not seem to constitute monetary policy “working” to end a recession. At least it’s not the mechanism by which monetary policy would work.
However, I think what Scott is missing is that some other monetary policy mechanism that has the effect of ending the recession by other means could also result in deleveraging. In an open economy, currency depreciation would be an example. Indeed, currency depreciation operates very much like fiscal policy, except that the fiscal stimulus comes from exports and from import replacement rather than from the government.
Another example, or rather a class of examples, would be the effect of monetary policy on asset values. Even if no new borrowing happens, lower interest rates raise the value of long-lived assets, such as equity and houses, because interest-bearing assets become less attractive, making other assets more attractive in comparison. This has several effects. For one thing, it produces immediate deleveraging by raising the asset side of balance sheets without raising the liability side. It also has a wealth effect that induces people to spend more. And finally, by raising the value of investment goods relative to the cost of producing them, it makes it more advantageous to demand such goods.
Finally, I would note that monetary policy can operate by affecting expectations. If the central bank can convince people that it can and will raise the price level, there will be incentives to start raising prices and output immediately, and this will result in deleveraging by transferring wealth from creditors to debtors. This does require a certain Tinkerbell effect, but I believe a sufficiently aggressive central bank could apply a fairly effective whip to Tinkerbell’s back.
this post is all about flow consistency. i can’t think of any models off the top of my head that are flow inconsistent. MMT is referring to something different. it’s referring to the consistency between flows, stocks AND stocks. there are plenty of models that aren’t stock-flow consistent (the most glaring example being cbo forecasts).
“This has several effects. For one thing, it produces immediate deleveraging by raising the asset side of balance sheets without raising the liability side. It also has a wealth effect that induces people to spend more. And finally, by raising the value of investment goods relative to the cost of producing them, it makes it more advantageous to demand such goods.”
It’s extremely difficult to price the value of a firm when earnings from year 20 to year 100 are 80% of the firm’s value. Really you are just throwing a lot of dust in the eyes of investors, creating bubbles which will be followed crashes. Odds are more likely that the resulting prices are the wrong ones, and economic growth will suffer as a result.
Finally attempts to increase the value of in-place assets disproportionately favor the wealthy — as the starting concentration of assets is not uniform.
There are much better and simpler ways to stimulate demand and clear debts that don’t rely on throwing a wrench into the valuation process.
The Nikkei didn’t do very well since ZIRP, although it had a lot of volatility and in the short run ZIRP seemed to succeed in raising asset prices. Land didn’t do that well, either.
Andy: I think the Keynesian model you are talking about looks like this:
Cd(t) = a + bY(t-1)
Id(t) = Ibar
There’s a 1 period lag in your consumption function (the period could be as short as you like). So your model has a “slow multiplier”, as opposed to an instantaneous multiplier.
But then your implied equation for desired saving is Sd(t) = Y(t) -a – (1-b)Y(t-1).
You get a similar “slow multiplier” if you assume production responds slowly, and that any change in investment is initially met out of inventories, but in that case it’s desired saving that determines actual investment in the very short run. A change in desired investment causes no immediate change in actual investment, because there’s undesired inventory rundown.
Another different way to get a slow multiplier is to assume no inventories, but production responds slowly. A sudden increase in desired investment causes a line-up of frustrated buyers. Only later does output respond to restore the semi-equilibrium condition.
In the simplest loanable funds model, an increase in desired saving causes the rate of interest to fall, with no change in Y. If I is slow to respond to r, then r must fall by a larger amount, sufficient to completely offset the increase in desired S.
(My personal views on all this S=I Keynesian Cross vs loanable funds stuff are quite different again, but I’ve kept quiet about them in this post, because it would just be a distraction, since my views are too unorthodox. As you perhaps know, I don’t believe in the Paradox of Thrift, but I do believe in the paradox of hoarding. It is an excess demand for the medium of exchange, not an excess of desired saving over desired investment, that causes Y to fall. An excess demand for antique furniture is an excess of saving over investment, but it cannot cause a recession.)
Scott and Andy: the normal way of dividing the economy up is into: households; firms; government; and foreigners. That’s roughly in line with Y=C+I+G+(X-M). But that’s not the only way to divide up the economy. For questions of debt and deleveraging, I find it more useful to divide it up into creditors and debtors. Sure, that way of dividing up the economy doesn’t tell us anything by itself. We need to add some behavioural conditions. A fall in interest rates will cause borrowers to want to borrow more, but will also cause lenders to want to lend less. Y will presumably increase, but what is the net effect on the quantity of borrowing and lending, when we remember the accounting identity that borrowing=lending? It’s not obvious. It will depend on the differences between the two groups’ elasticities of borrowing and lending with respect to interest rates and income. (I confess I haven’t actually worked out the math.)
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.
Yep, it’s late, and my brain’s going too.
“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. ”
OK — if we assume that the government controls nominal borrowing rates, then the “demand to lend” falls out of the picture for purposes of clearing the lending markets. Banks can always create money and lend it out, irrespective of what individuals want.
In that case, the lack of a desire to lend shows up as inflation — it really means households don’t want to hold onto the deposits created by banks as a result of lending. It doesn’t mean that borrowers do not get funded, or that the lending does not occur.
Nick: do you want to do away with I=S altogether, even as an accounting identity?
No, surely I do not. But what makes this identity interesting is a dynamic process and not the static statement of S=I. Accounting world world lives in accounting periods but there are a lot of things happening within each and every period to render your Sd=Id completely useless if not misguiding.
The accounting identity S=I is an ex-post identity. That is why Sd=Id is meaningless outside of equilibrium. It is meaningless to this world which is never in the equilibrium. Therefore imposing Sd=Id on the real world is misguiding. Yet many theoretical and political conclusions are driven from such misguided understanding.
Nick wrote “One of the problems with S-I=G-T (ignore foreigners) is the level of aggregation. Even if G-T=0 the private sector can still deleverage. If the debtors increased their saving, and the creditors decreased theirs, leaving aggregate desired saving the same, private sector (gross) debt would decrease, and I would want to describe that as “deleveraging”.”
I don’t follow this at all. Mmt sees S’ as vertical money or S-I. Please say it is S’ you are referring to as savings?
Deleveraging relates to a reduction in horizontal money, not shifting vertical money from private creditors to private debtors which has no effect on gross savings(S’). Yes vertical money can be use to pay off a creditor of horizontal money, but the vertical money ends up with the horizontal creditor in order for there to be ‘deleveraging’.
Scott wrote:” Sort of like when I see someone write “the national debt is equal to private savings” or something like that–ouch.”
I hear Mmters say this all the time and assume they’ve not included cash, reserves or the word net ( as in net non-u.s. Government savings – ss surplus……) In Nick’s case he’d take out investment as he includes it in his savings (S). Though I don’t think he did above. It’s tough communicating clearly.
If economists had gotten this stuff straightened out 50 years ago, we would not be having this lovely discussion, but alas and alack. (And, it has been lovely. Thanks to all.)
I would like to do away with I = S, as an accounting identity. Contra Sergei, I find Sd = Id comparatively harmless; a necessity, prehaps of derivation.
The double-entry bookkeeping of the National Accounts is based on the idea that every observable transaction gives rise to at least one pair of entries. So, when some product is sold, that product is also bought; the sale can be recorded and the purchase can be recorded. If the statistician has access to a record of sale, she’s fully justified in inferring a purchase; in this way, somewhat spotty observation and records can be reconciled into a coherent picture of the whole. Two problems with “saving”: first, in its common-sense meaning saving does not necessarily involve a transaction; saving is not-spending, which is not a transaction. Of course, some forms of “saving” do involve a transaction; transactional saving is also lending. So, if the national accounts were consistent, they could define saving = lending, and that would be true as a matter of accounting identity in a straightforward way. (And, actually, that’s what they do, mostly.)
It seems to me that both the understanding of the national accounts and economic theory get twisted out of shape by this silly business of S = I. If the economist wants to posit an equilibrium in analysis, I’m fine with that, but the national accounts do not describe a system in equilibrium, so why should S = I? (I understand why; I’m arguing that the national accounts would be clearer, if this were not the convention. And, it is a convention, not an accounting identity, strictly speaking; since transactional saving/lending has no necessary, definitional relation to investment in inventories and capital equipment; it is just a matter of conventional presentation to make it so, to make Y equal to final product and estimate S with a big fudge.) The system described by the National Accounts is out of equilibrium; describe it as out of equilibrium. You may need equilibrium for derivation; you don’t need equilibrium to make the books balance.
Winslow, I’m afraid I’m not conversant with “horizontal” and “vertical”. Could you point to a succinct explanation?
I don’t think leverage/de-leverage means much outside a context of financial intermediation. It is not a single interest rate matching a market of would-be creditors with would-be debtors; it is a yield curve, along which intermediaries attempt, through arbitrage (the carry trade), maturity transformation and portfolio diversification, to manage risk. Money as a medium of exchange gives way to money as a store of value, and medium of insurance and calculation.
IF you think in terms of financial intermediaries as the primary manufacturers of private debt, it is easier to imagine how debt can expand and contract, and carry effective aggregate demand with it. Also, central bank policy becomes less a matter of a single policy rate, than about managing inversions of the yield curve to induce recession.
Bruce,
I don’t understand your 03.27AM post. You are right that Savings is an ambiguous term (and unfortunately the national accounting identity don’t destinguish clearly between the household sector and the corporate sector which doesn’t help in understanding). But the national accounts show a flow of money used to buy goods and services – and (in a closed economy without government for simplicity) income that is not spent on consumption goods and services (and that is how consumption is distinguished from investment) must both increase asset balances (i.e. savings net of depreciation) AND come from purchases of investment goods (since received income implies a transaction). There is no equilibrium involved with this – it is simply following firms and households income and expenditure. The key here is the somewhat arbitrary division of goods and services into final consumption and intermediate and capital goods. (Intermediate goods are of course mostly netted out).
Scott and Nick R.
Sectoral balances are flow measures. Private sector net savings (S – I) are just the money added into circulation by government deficit spending and an export surplus.
The money stock – as in total credit/debt on bank balance sheets – can go up and down due to private sector or government borrowing or repayment.
Sometimes a few people conflate private sector deleveraging with private sector net savings. This is obviously wrong. The better way to think about it is that total credit/debt will shrink with private sector deleveraging unless the government leverages up through increased deficit spending.
Maintaining a growing stock of money is important to maintain the flow of money in a growing economy. If the stock of money falls due to deleveraging, then the flow of money must also drop – reducing incomes (Y) and therefore affecting things like consumption (C), savings (S), taxes (T) or imports (M). But it’s not that paying down debt directly reduces I without reducing S. Any discrepancy between I and S only arises due to government deficit spending or the trade balance.
I agree that savings can be ambiguous. You hear people saying that we must increase savings to boost investment – when the truth is that loans create deposits. You also hear people talking about how the chinese are great savers – saving 50% of their income – when this is just the export surplus and government deficits adding to 50% of Y.
“Sometimes a few people conflate private sector deleveraging with private sector net savings. This is obviously wrong. The better way to think about it is that total credit/debt will shrink with private sector deleveraging unless the government leverages up through increased deficit spending.”
Yeah, I argued with Bill Mitchell about this. He insisted that deleveraging requires saving at the private sector level (not just saving by non-financial entities).
…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…
I suspect this is because the definitions of S and I are not quite intuitive to non-economists (and even to some economists, perhaps).
Imagine I earn $100 and put $10 in the bank, but the bank hasn’t yet found a business to lend it to, so it hasn’t been “invested”. An intuitive way to describe this is: S=10, I=0 – oh look, S=I is violated!
Of course S is not really 10, because my saving is cancelled out by the bank’s borrowing (or the bank’s shareholders’ borrowing if you like). That’s without even getting into the question of whether the $100 is actually income.
People who think in the above way (which is not unreasonable given the normal use of English language) are inevitably going to be surprised by the assertion that S=I. This will lead to one of two responses: “don’t be ridiculous, your economic theories of ‘equilibrium’ and ‘rationality’ are obviously wrong” or “wow, look at this amazing fact I discovered. Isn’t the world a strange place? I will now show off my new cleverness to my unenlightened friends/fellow bulletin board readers.”
If they were taught the technical meanings of S and I, or even that there are technical meanings, their amazement and confusion would quickly dissipate. Admittedly it would probably be replaced with boredom; good luck getting most of those people to read and understand this post. Thanks though – it’s a good refresher, especially for those (like me) not formally trained in economics. I’m sure I have made similar mistakes in the past.
rsj: money does (generally) change things. But I’m not sure financial intermediaries do. This would be one of those cases where I would start out slowly. Start with barter, get the “bonds bought = bonds sold” accounting identity and equilibrium conditions right, then bring in money and/or financial intermediaries one at a time.
Sergei: “The accounting identity S=I is an ex-post identity. That is why Sd=Id is meaningless outside of equilibrium. It is meaningless to this world which is never in the equilibrium.”
Dunno. If you were right, that would mean all of keynesian economics (plus all of classical and MMT and pretty well anything else that comes to mind) would be wrong. What would you replace it with?
Winslow: “I don’t follow this at all. Mmt sees S’ as vertical money or S-I. Please say it is S’ you are referring to as savings?”
And you expect me to follow what you are saying there? You are speaking some very strange language. “Vertical money”?? “S'”???
Look, Scott understood what I was saying. Suppose I have a debt to you of $100. Suppose I drop my consumption by $100, pay you the $100, and you increase your consumption by $100. Then private gross debt has fallen, private consumption and saving have stayed the same in aggregate, and nothing changed with I,G,T,X, or M. If your accounting identities are stopping you understanding that, then you are being mislead by your own accounting identities.
“Deleveraging relates to a reduction in horizontal money, not shifting vertical money from private creditors to private debtors which has no effect on gross savings(S’). Yes vertical money can be use to pay off a creditor of horizontal money, but the vertical money ends up with the horizontal creditor in order for there to be ‘deleveraging’.”
What?????
“In Nick’s case he’d take out investment as he includes it in his savings (S). Though I don’t think he did above.”
I have been using the absolutely standard economics definition of saving thoughout. S is defined as Y-T-C.
Bruce: “If economists had gotten this stuff straightened out 50 years ago, we would not be having this lovely discussion, but alas and alack.”
Well,…some of us got it straightened out, but others haven’t learned it. My post was an attempt to educate those latter people.
There is absolutely nothing new in my post, BTW. Any competent teacher of ECON1000 could have written something similar. (But I am sort of proud of the way I presented it, especially in relating Sd=Id back to “quantity demanded = quantity bougt-and-sold”. I don’t think many could have done that as clearly and accurately as I did, if you will excuse me blowing my own horn a little!)
I can’t decide whether I agree or disagree with the rest of your comment. When we actually build macro models, we normally simplify massively, so the accounting becomes trivial. And it gets built into the agents’ budget constraints. The problem starts when we try to relate variables in our models back to the data, which use NIA definitions of variables, which are necessarily based on a much more complicated world. Do the variables in our model mean the same things as the NIA data?
Bear in mind, from an accounting perspective:
– Saving is an income statement event
– Deleveraging is a balance sheet event
The two are severed in that way.
One can save without deleveraging.
And one can deleverage without saving.
But the desire to deleverage can induce the desire to save, in order to deleverage. That’s what’s happening in a “balance sheet recession”.
P.S.
And that’s why your example works Nick. You can have deleveraging in aggregation, without net saving in aggregation, essentially because the two are separable in general.