Accounting for ****

A commentator on my last post at Mike Norman Economics, who gives his name simply as ‘John’, made the following interesting comment:

I heard a nice, intuitive and very easy argument recently that puts loanable funds to bed. No fancy mathematics, no convoluted diagrams, just a straight simple argument that goes like this:

When the government borrows, from whom does it borrow? The private sector who have funds in the financial system, right? The government borrows these funds and spends it directly back into the economy. Where do these spent funds find their way to? Back into the private sector who on aggregate have the same amount of funds in the financial system that they had prior to the government borrowing. Where else can the government spending and private funds go, but back into the financial system?

At first I thought that surely even neoclassical economists who believe in the loanable funds model can’t be making such an elementary error.

And yet… if you look at the way national accounting gets treated in the textbooks I mentioned, it seems as if that’s exactly the error being taught. Here I want to explain why they make that mistake. But first, let’s look at the mistake in some detail.

The textbook loanable funds model is based on the idea that ‘when the government spends more than it taxes, the resulting deficit lowers national saving’ (Mankiw, see last post). National saving is explained in national accounting terms as follows (I’m sticking with the closed economy model – no net exports or imports):

S ≡ Y – C – G,

where Y is total income (GDP), C is expenditure on consumption, and G is expenditure by the government. Meanwhile Y is defined as the sum of consumption, investment (I) and government expenditure:

Y ≡ C + I + G.

How do we get to the idea that government deficits reduce national savings? The idea is that if G increases then Y – C – G will have to decrease. But so far it seems just as logical to argue that Y must increase, since G is a component of Y.

What we need to ask about any accounting identity is, of course, what the relevant accounts are. If we’re talking about bank deposits, then G will represent total credits to the accounts of sellers of public goods to the government (henceforth ‘public goods accounts’), C will represent total credits to the accounts of sellers of consumption goods (henceforth ‘consumption accounts’), I will represent total credits to deposits of sellers of investment goods (‘investment accounts’), and Y will represent the sum of these.

So suppose the government borrows £10m out of the ‘investment accounts’ (loanable funds seems to assume a fixed supply of deposits). Then we have this:

Screen Shot 2015-08-05 at 09.11.00

There is no change in Y, since one of its summands has only fallen by the same value as another has increased. And thus national savings, S, must have fallen, since S ≡ Y – C – G, Y and C have stayed the same, and G has increased. This is where we get the idea that government deficits reduce national savings:

Screen Shot 2015-08-05 at 11.30.59

But this shows that John is correct. If private investors want to borrow money to invest, the money is right there in the public goods accounts. The national savings level is irrelevant, because it doesn’t represent the amount of available funds to borrow. It’s an idle accounting construct, representing nothing of significance.

You can see how irrelevant the national savings measure is if you imagine the same scenario with one difference: the government borrows out of consumption accounts instead of investment accounts. Then we have:

Screen Shot 2015-08-05 at 11.31.07

There is now no change in national savings, Y – C – G, since C has come down by the amount that G has gone up, and again Y has stayed the same. How could the effect of government borrowing on national savings depend on which private accounts the government borrows from? The whole thing is a disaster of accounting.

The point becomes even clearer when we disaggregate the components of national saving into the government’s savings and the private sector’s savings. This is done in the textbooks in the following way:

S ≡ (Y – T – C) + (T – G)

T is tax revenue. Since we’re dealing with bank deposits, this will be credits to tax accounts. In the first pair of parentheses we have private saving. In the second, we have public saving. In terms of bank deposits, these represent, respectively:

  • Total credits to all bank accounts minus credits to public goods accounts and consumption accounts, and
  • Total credits to tax accounts minus credits to public goods accounts.

So what happens if the government borrows £10m from investment accounts? It will look like this:

Screen Shot 2015-08-05 at 09.14.00

Public saving falls by £10m, since £10m is credited to public goods accounts and nothing is credited to tax accounts to offset this. Private saving doesn’t change, since there are no new net payments into total bank accounts, Y, nor are there any credits or debits to tax accounts or consumption accounts.

This balance sheet should look very alarming to an accountant. Funds have flowed out of public savings, but there is no accounting for where they have gone. We have a debit but no corresponding credit. Anybody familiar with the sectoral balance approach will know how to account for this missing credit, but that’s not the point here.

The question is: where does this bizarre accounting in the textbooks come from? The answer is, of course, that even though the textbooks go on to talk about funds, the accounting is all in terms of real goods.

Suppose we switch from talking about bank deposits to talking about real resources. Imagine a simple Ricardian corn economy: all the economy produces is corn, and all it needs to produce corn is corn and labour. Y is now the total harvest of corn in some period, measured in terms of (say) weight. C is the corn eaten during that period. I is the corn planted as seed corn in order to grow more corn (yes, I know corn doesn’t work like this). T is the corn handed over to the government and put in its ‘tax silo’. G is the corn eaten by the government (no wonder William Cobbett called them ‘tax-eaters’). Now things begin to make a bit more sense.

First, it’s clear why there is less corn available for investment when the government runs a deficit – that is, T – G is negative. The government has eaten the corn, so it can’t be invested. Ingesting precludes investing. It’s also clear why the government can only ‘borrow’ out of I, not out of C. C represents corn that is eaten, and the government can’t ‘borrow’ this without resorting to unspeakable procedures. It can, however, borrow out of I – the corn planted as seed corn; it just has to dig it out. A seedbed is a granary in the ground. Finally, the measures of private and public saving now make sense. Private saving, Y – C – T, represents the corn that the private sector still has – what isn’t eaten or handed over to the tax-eaters. Public saving, T – G, represents the corn the government still has – whatever is in the tax silo that the tax-eaters haven’t eaten yet. If T – G is negative – a deficit – then the government must have eaten everything in the tax silo and more besides; this more can only come from the seedbeds accounted for in I.

The explanation of this:

Screen Shot 2015-08-05 at 09.14.00

is now clear enough. G is a measure of eating, not of spending, so we don’t need to ask where the corn has gone. In fact, maybe you’d rather not.

So loanable funds makes perfect sense in a world where the government taxes and borrows corn and eats it rather than spending it. If you find yourself in that possible world, remember your loanable funds training. But here we are in the actual world, so why are we talking about this?

I hesitate to suggest that mainstream economists fail to recognise the relevant difference between money and corn. And yet look at this blog post by Nick Rowe, arguing that deficits do, in fact, burden future generations (even though they patently don’t). His argument depends on a model in which the government borrows apples, people buy bonds using apples, and people eat the apples. Rowe happily extrapolates from this model to the case in which the government borrows money, unbothered by the crashingly obvious disanalogy. Maybe if you go into an economics department when they’re not expecting you, you will witness an unearthly feast of notes and coins. That would explain a bit.

Of course it isn’t just economists who are oblivious to the difference between corn (or apples) and money. People who complain about ‘their taxes’ going to benefit cheats, who spend it all on booze, fags, and big TVs, never consider that this means income for the (taxpaying) employees of supermarkets, indeed that most of the money flows back to all of us. They view the benefit cheats simultaneously as irresponsible spenders and as tax-eaters, failing to consider that you can’t spend your money and eat it too.

All the same, whether accounting in corn or in money, loanable funds is still based on the national accounting identity. Accounting must be done properly or not at all. So we still need to track all the relevant flows. A debit to public savings must be matched to a credit of some sort. So where does the corn go after being eaten? We all know the answer, but it would be indelicate to make it explicit. Let’s just call it ‘the mystery account’. Now:

Screen Shot 2015-08-05 at 09.15.33

This mystery account is the receptacle of all the corn-debits represented in consumption and government spending. Whenever there is negative public or private saving, the debits flow into the mystery account. But nothing ever flows out of the mystery account: the sources of public and private saving are the harvest, Y. Whatever isn’t saved out of the harvest goes into the mystery account.

And that’s what mainstream economics gets us: a ceaseless accumulation of the contents of that mystery account.

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60 thoughts on “Accounting for ****

  1. John

    If interested, the argument I laid out was found in one of Frank N. Newman’s books, either “Six Myths That Hold Back America” or “Freedom From National Debt”. I happened to be flicking through them on the train, but decided instead to return to finishing the captivating and powerful “Regeneration Trilogy” by Pat Barker.

    Apparently, Stephanie Kelton is a great admirer of Frank Newman (formerly a deputy secretary of the US treasury, CEO of Bankers Trust and currently CEO of the Chinese Shenzhen Development Bank) and whose analysis is said to be as close to MMT as it gets.

    A nice video of Frank Newman in action: https://www.youtube.com/watch?v=Ae7PO-j7TIc

    Reply
  2. Min

    I think that your memory has played you false here, that the relevant equations for a closed economy are actually these:

    1) Y = C + G + I
    and
    2) Y = C + S + T

    Now, each of these applies during a specified period of time. If we are interested in the change between two periods, we have

    3) ΔY = ΔC + ΔG + ΔI
    and
    4) ΔY = ΔC + ΔS + ΔT

    Solving the first equation for ΔG gives us

    5) ΔG = ΔY – ΔC – ΔI

    If all we know is that ΔG is positive, i. e., that gov’t spending has increased, then we may reasonably expect that the GDP has increased, that consumption has decreased, and that investment has decreased, to some extent. (This says nothing about causality, OC.)

    Substituting ΔY in 4) for ΔY in 5) and simplifying gives us

    6) ΔG = ΔS + ΔT – ΔI

    If all we know is that gov’t spending has increased, then we may reasonably expect that saving has increased (not decreased), taxes have increased, and investment has decreased, to some extent.

    If I understand you correctly, the textbook argument is that if, in one time period the gov’t runs a deficit ( G > T), then it the next time period saving decreases (ΔS 0

    Now, if in the next time period the gov’t balances the budget, then we have

    G – T = S – I = 0

    We may reasonably expect that saving decreases in the second period, and that investment increases, to some extent.

    Also, under the assumption that S and I tend to equalize, we may from that reasonably expect that S will decrease and I will increase in the next period.

    And if the gov’t runs a higher than usual deficit in any time period, we may expect a decrease in saving in the next time period — but again, that says nothing about causality.

    Reply
    1. axdouglas Post author

      You’re using a different ‘S’ from the one in the textbooks. Your S is private saving (Y – T – C) (you can see that because you can derive your identity 2 from S ≡ Y – T – C). The textbooks use S to stand for national saving: private plus public saving, which reduces to Y – T – G (you can check Mankiw on this if you like – look at p.97; he uses S in the same way in the textbook). Your S will have a different value from the textbook S unless G = T (you can see this by plugging in (Y – T – G) for S in your identity 2; you’ll get G = T).

      Of course accounting identities tell you nothing about causation. The textbook example I was using was one in which ΔG = –ΔI. That should be clear from my first balance sheet, in which ΔG is 10 and ΔI is –10. So I have no idea why you say: ‘If all we know is that ΔG is positive…’ In the textbook example that is decidedly NOT all we know; we also know, or it is assumed, that ΔG = –ΔI (I explain why the textbooks make this assumption; it’s based on their views about the causation involved, not derived directly from the identity).

      Even if you don’t make the textbook assumption, I don’t get why you say that if all we know is that ΔG is positive, we can ‘reasonably assume’ that all terms would be changing on the right-hand side of the identity ΔG ≡ ΔY – ΔC – ΔI. The accompanying change on the right-hand side could be a change in only one of the terms (as in the textbook example), or it could be in a combination of two, or it could be in all three as you propose. We can’t ‘reasonably assume’ which it is until we know something about the causation involved. So your statement is false as well as being irrelevant to the textbook example.

      Reply
      1. Min

        Thanks for clearing up the question of what the textbook S is. Then we have, as you say,

        1) S = Y – C – G
        2) Y = C + I + G

        From which we may derive

        3) S = I

        As for the relationship between ΔG and ΔI, Mankiw must also be using them in a different sense that I was. I meant the following:

        ΔG = G(t) – G(t-1)
        and
        ΔI = I(t) – I(t-1)
        where t-1 and t are successive time periods.

        From that we may derive

        4) ΔG = ΔY – ΔC – ΔI
        not
        5) ΔG = – ΔI

        OC, both are so if ΔY = ΔC. Mankiw isn’t assuming that is he?

        Now, to talk about the deficit we have to introduce T, which we can do by introducing private saving; let us use Sp to indicate that. That yields

        6) G – T = Sp – S
        and
        7) Δ(G – T) = ΔSp – ΔS

        As for Mankiw’s claim, ‘when the government spends more than it taxes, the resulting deficit lowers national saving’, at first blush it seems to mean that in any time period, t, if G(t) > T(t) then S(t-1) > S(t) (and I(t-1) > I(t)). But that seems farfetched. I don’t think that’s what he means, and you don’t, either. Perhaps he means that S when G > T is less than S when G = T.

        That is actually a reasonable claim. When G = T then Sp = S. When G > T then Sp > S. Now, OC, both Sp and S could increase, if Sp increases more, or both could decrease if Sp decreases less. But normally Sp will increase some and S will decrease some. (Because normally the increases and decreases are small.) If that is his claim, he left out that the resulting deficit raises private saving. For shame.

      2. Min

        axdouglas: “I don’t get why you say that if all we know is that ΔG is positive, we can ‘reasonably assume’ that all terms would be changing on the right-hand side of the identity ΔG ≡ ΔY – ΔC – ΔI. The accompanying change on the right-hand side could be a change in only one of the terms (as in the textbook example), or it could be in a combination of two, or it could be in all three as you propose. We can’t ‘reasonably assume’ which it is until we know something about the causation involved.”

        It is true that I was making the unstated assumption that the increases and decreases are small. I think that that is normally the case. A greater change would be unusual. I was also making use of the fact that there are only three variables on the right side of the equation. If there were only one, then its change would be equal to the change in G. If there were two, then the change could be all in one variable or the other, but usually it will be in both. If there were many, then the change is unlikely to be in all of them. But with only three, I think that the most likely thing is for there to be changes in all three. The smaller the changes need to be, the more likely that is.

        As for Mankiw’s claim about the effect of deficits, if it is about the counterfactual, there are only two variables on the right side, private saving and “national saving”; so it is likely both that private saving will increase and that “national saving” will decrease. (I put “national saving” in quotes because I am not sure why it is preferred to the term, investment.)

      3. Min

        BTW, over the past seven years I have asked about the difference between the S in the sectoral balances accounting and the S in S = I on a number of economics blogs, including those by prominent economists where several of the commenters were also economists. I said that the two S’s must stand for different things. What are they? Do you know how many economists told me the difference, that one S stood for private saving and one stood for national saving? Exactly zero.

        Bully for you! 🙂

      4. axdouglas Post author

        🙂 And boo to the economists. Thanks for your comments, btw; I’ll think about them and answer properly tomorrow.

      5. Min

        Oh! Amusing thought about
        Δ(G – T) = ΔSp – ΔS

        Mankiw argues that a gov’t deficit reduces S, while the Ricardian Equivalence argument is that it increases Sp. 😉 Neither says anything about the effect on the other variable.

      6. axdouglas Post author

        Yes, that’s because standard macro has very little interest in the sectoral balance identity. And that, in turn, is because they generally want supply-demand equilibriums to solve for, rather than models for tracking flows over time that may never find any equilibrium. This came up in my conversation with Prof. Rowe, but didn’t quite get resolved.

  3. Min

    The idea of loanable funds means two rather different things in the economic blogosphere. Often it is taken to mean that banks are mere intermediaries, lending only what they have on deposit (minus reserves, if any are required). As you say, deposits seem to be fixed. But according to Wikipedia and other references, under the loanable funds doctrine “loanable funds” refers to available credit, which is typically more than deposits, and is not fixed.

    Reply
    1. axdouglas Post author

      Your point seems quite straightforward. If I give you an apple today and then ten years later I steal an apple from Smith, it’s very much the same as if I had reached into the future, snatched the apple from Smith, and handed it to you. So far you’re quite right, and you hardly need OLG models to make that point.

      And the government can do the same with money, in a sense. But the overall productive capacity of the economy doesn’t depend on the volume of money. Money can either accommodate production at full capacity or somehow hold it back (through price-instability or paradox of thrift effects, e.g.). So in terms of the real level of production enjoyed by each generation, you can only have the ‘snatching’. You can’t have the ‘giving’.

      The real analogy in the apples case would be: I only steal one of your apples today, though I could steal two, but I ‘make up for it’ by stealing three of Smith’s apples ten years later. Since I could just as well have not stolen apples at all, this doesn’t really look like an intergenerational *transfer* at all. That’s the point.

      Reply
      1. Nick Rowe

        Or, I give an apple to the old today, and I get that apple by borrowing it from the young today, by promising to give them back an apple when they are old. And repay the borrowed apple by borrowing another apple. Repeat. Then, some time in the distant future, I steal an apple to pay off the loan.

      2. axdouglas Post author

        Yes. So you can, in effect, steal from the future to give to the present. And if you can do it, so can the government. That’s a point well made, and well taken. But to do that, the government would have to take *real goods* from people. It doesn’t. It only takes money. Yet taking money from people doesn’t deprive them *as a whole* of access to their full productive output. It can only change the distribution of their claims on that output.

      3. Nick Rowe

        Suppose initially the government borrows money from the young, and gives that money to the old. So the total stock of money stays the same.The old then use that money to buy apples from the young. It is exactly as if the government borrowed apples from the young, and gave apples to the old.

        Then, when it pays off the debt, the government takes money from the old, and gives them back that money to repay the debt. That means the old do not sell their bonds to the young for money, then give that money back to the young in exchange for apples. It is exactly as if the government took apples away from the old, and gave them back those apples to repay the debt.

      4. axdouglas Post author

        Yes. The government can, by taking and giving money, redistribute goods between two generations when they’re alive at the same time. As I said, you can use money to redistribute claims on existing production among people alive at one time.

        But you can’t use money to redistribute real stuff to/from ALL the people alive at time t to/from ALL the people alive at time t+n (it doesn’t matter whether they overlap or not, just treat them as two distinct aggregates). Of the first group, some will have more and others will have less access to the production available at t, but *in the aggregate* they’ll have access to all of it, unless the government takes some of it away (which it doesn’t do if it only takes money). Just the same can be said of the second group.

      5. axdouglas Post author

        I sort of see your point now. When A and B are alive at the same time, you can take from B and give to A. When B and C are alive at the same time, you can take from C and give to B. And then when C and D are alive at the same time, you can leave things equal between them. So A got a pretty good deal, C got a pretty bad deal, and B basically broke even. That’s true. But of course government deficits don’t have to work that way. So I think we agree on this one.

      6. axdouglas Post author

        So I apologise for misunderstanding… But of course it’s a moot point, as you say, since governments can use deficits to achieve lots of different distributions.

      7. Nick Rowe

        No apologies needed. You got it MUCH quicker than I did, many decades ago. Took me AGES to figure it out.

        Oh I do like arguing with philosophers who are interested in economics.

      8. axdouglas Post author

        🙂 I like arguing with economists too.

        So of course I believe in deficits for using up spare capacity, not redistributing resources when you’re already at full capacity! And of course you’re right that at full capacity the crowding out story has to be true. So it’s all about whether there can be a prolonged net savings desire in the private sector. I see the argument that this doesn’t make sense, because people desire stuff, not money as such. But it’s a philosophical point involving human psychology, and I’m trying to work on it.

      9. Nick Rowe

        Well, people do desire (to hold a stock of) money as well, because it is very useful stuff (as a medium of exchange). But the central bank needs to ensure the supply matches the demand for money (at something like “full employment potential” output), or adjust the inflation (or whatever) target or have Gessellian negative interest rates on money to adjust the demand for money to the supply. Needing to use deficit spending and intergenerational transfers to ensure “capacity” is an admission of central bank incompetence.

        Which does not mean that intergenerational transfers are always bad. But we want to do them because we think we ought to do them, not as a bodge-job to get around central bank incompetence. Right tool for the right job, and all that.

        (It’s not too much *saving* per se that causes recessions. It’s too much saving in the form of medium of exchange (money). I prefer to use the word “hoarding” for “saving in the form of money/medium of exchange. The national income accounting concept “saving” distorts our categories for theoretical thinking, like Borges’ emporium of celestial knowledge.)

      10. Min

        Nick Rowe: “Needing to use deficit spending and intergenerational transfers to ensure “capacity” is an admission of central bank incompetence.”

        Or of legal constraints upon CBs. Or that CBs are less omnipotent than they are assumed to be.

      11. axdouglas Post author

        Min, yes: Or that CBs were never omnipotent and the ‘Great Moderation’ was largely down to fiscal policy that constrained the economy from running at anywhere near full capacity.

      12. axdouglas Post author

        Amen to your last sentence, which sums up much of my motivation for writing this.

        And yes, what I call ‘net saving’ is what you call ‘hoarding’.

      13. Nick Rowe

        Suppose I want to take milk away from people on the east coast, and give it to people on the west coast. But I can only transport milk by horse, and it will spoil before it gets there. Or suppose I want to take food away from carnivores, and give it to vegetarians. Impossible, right? No. As long as there are people producing and consuming milk in a chain between both coats, or omnivores who eat both meat and veg, all I need do is take money away from one group and give it to the other group. The market will handle the rest. *Providing there is an overlapping chain*.

        http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/10/how-time-travel-is-possible.html

        Yes of course you can’t make goods literally travel back in time. But too many “sophisticated” economists have used that premise to laugh at the poor unsophisticated rubes on the street who think that the national debt is a burden on future generations. And the sophisticated economists should be embarrassed to use such a fallacious argument. The rubes are roughly right (under some assumptions).

      14. Min

        No, the rubes are not roughly right. The rubes think that gov’t deficits now will make **everybody** alive at some later time worse off. That is not anything like what you claim.

      15. Blissex

        «unless the government takes some of it away (which it doesn’t do if it only takes money)»

        In an open economy it can do it by borrowing from abroad to pay for the consumption of more goods than the national economy can produce now. Then the next generation has to reduce their consumption below production capacity to generate the exports with which to repay the debt.

        That’s not a special case…

      16. axdouglas Post author

        It’s an exceedingly special case inside reality and outside the textbooks, since countries like the UK run consistent trade deficits year on year. The way you describe it, a country that runs a trade deficit one year should have to run a trade surplus the next, in order to ‘repay the debt’. It’s another case of mistaking an intuitively convincing model for reality. The remedy is simply to consider obvious facts independently of any background theory.

      17. Min

        Nick, if you add money to yours and Murphy’s scenario from a few years ago, if the amount of money is fixed, then in order to get the money to pay interest, the velocity of money will have to increase, and since the supply of apples is constant over time, the price of apples will increase proportionally, right? Won’t the number of apples transferred between generations remain the same, so that the economy will be in a steady state, except for inflation, and there will be no crisis?

      18. Min

        Well, with inflation eventually the gov’t will have to print more money, but that is not a real crisis.

  4. Nick Rowe

    Three points:

    1. My little toy models about the burden of the debt were designed as counterexamples, to people who say it is *impossible* for the debt to create a burden on future generations, (unless taxes are distorting or the debt is owed to foreigners or debt reduces investment). All I need is one simple counterexample to show they are wrong. Whether debt does in fact create a burden on future generations…depends. I can easily tweak my little toy model to show other examples where debt benefits all future generations.

    2. Consider the statement “# of apples bought = # of apples sold”.

    That statement is true by definition. It’s a trivial tautology. It tells us nothing about what determines the number of apples bought-and-sold. Those are not two different quantities of apples; it is one quantity of apples, looked at in two different ways.

    All national income accounting identities are exactly like that statement above (they are just variations on that statement). They tell us about how we use words, like “saving” and “investment”. They tell us nothing about what determines the level of saving-and-investment. They have no substantive or empirical content.

    My old post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/08/is.html

    3. I am trying to reverse-engineer the (substantive) economic model at the back of your mind when you made the statements in your comment above about government bonds being automatically self-retiring. The nearest I can get is an old model by Carl Christ. Christ assumed that total taxes T were a fixed fraction t of income Y. So the government deficit is G-tY + rB, where B is the stock of bonds and r the interest rate. He also assumed that income is an increasing function of the stock of bonds Y=F(B). (It was a Keynesian model, where income was determined by demand, and a higher stock of bonds caused increased demand.) In that model, it was *possible* (though not certain) that bond-financed deficits would be automatically self-eliminating (it depends on the function F( ) ). Now if we assume that the increase in G is purely temporary, and if Christ’s conditions about F() are fulfilled, that would also generate your result that B must eventually return to its original level.

    Show me the model. But forget about that MMT “to the penny!!” rubbish.

    Reply
    1. axdouglas Post author

      Ah. You’ve replied to a comment I subsequently deleted, deciding it was too far off the main topic. Sorry about that. The comment I decided to leave is below.

      Reply
    2. axdouglas Post author

      One point on this, even though I’ve deleted the original comment. I wasn’t claiming that there is some long-run equilibrium at which all bonds are retired without an increase in taxes. So I don’t have a model that contains such an equilibrium. I don’t see the point of models like that.

      My point was more basic. One difference between apples and money is that accounting identities can tell you a lot *more* wrt money than they can wrt apples. If there’s a flow of apples out of one stock, it may either be increasing another stock or being consumed, or any combination of the two. But with money, it must be flowing into another stock.

      Given that, you can see that since (in a closed economy) Δpublic savings ≡ -Δnet private savings, any flow out of public savings (a government deficit) must build up the stock of (net) private savings. And so a reversal of that flow, as where the government builds up public savings by retiring its debt, is supplied from the stock built up by the original flow in the reverse direction. I’m not saying there is some equilibrium level towards which the flows tend. That’s the wrong kind of model. I’m just saying that any flow in one direction simply depletes the stock built up by a flow in the reverse direction.

      Reply
    3. Min

      Accounting identities do have empirical content. They set constraints upon what is empirically possible.

      Conservation of energy and of momentum are good examples. Consider the collision of billiard balls. The accounting identities tell us that the change in momentum after the collision is not enough to account for the kinetic energy of the balls. What happens to it? We observe that the extra energy is dissipated in sound waves, as the click of the balls. But how do the sound waves spread? In every direction, axdouglas, in every direction. The sound could be focused in one direction, or two, but it is not, as a rule. It is a question of probabilities, and each direction is equally probable.

      Now suppose that we have a game of billiards on the moon. With no air, no energy is dissipated by sound waves. What happens? We can draw a conclusion based upon the accounting identities. The balls heat up.

      We actually have empirical evidence of this effect. As ivory billiard balls became expensive, some were made of cellulose in the late 19th century. Cellulose does not make for loud clicks. So the cellulose balls heated up. The result was exploding billiard balls. 😉

      Reply
  5. Nick Rowe

    The loanable funds theory of the rate of interest can be interpreted as saying that the rate of interest adjusts to ensure that the quantity of apples people *want to* buy (at that rate of interest) always equals the number of apples people *want to* sell.

    If we have a central bank setting the rate of interest to keep inflation on target, the loanable funds theory will be (roughly) true. Because if the central bank sets the rate of interest above/below where the Loanable Funds Theory predicts, there will be an excess supply/demand for apples, and inflation will fall below/rise above target. So the LFT will be true, up to a (random?) error due to the central bank’s (random?) mistakes in hitting its inflation target.

    Reply
      1. axdouglas Post author

        Interesting. In my last post before this one I said almost the same thing: ONKM is disguised loanable funds theory.

        But then I see no evidence that the central bank policy rate on its own controls the level of inflation. So I have little interest in this sort of theory. So much the worse for ONKM.

      2. axdouglas Post author

        Put otherwise, if there were a single policy rate at which some target level of inflation were achieved, you could indeed call that the equilibrium point at which supply meets demand for loanable funds. But I reject the premise.

        Also, even if you defend LF this way, the crowding-out argument still doesn’t make sense, since the funds borrowed and spent by the government aren’t removed from the supply of loanable funds at all. This was the argument from John with which I began this post.

      3. Nick Rowe

        Alex: “But then I see no evidence that the central bank policy rate on its own controls the level of inflation.”

        Could you expand on what you mean by “on its own”? Because nobody says that the central bank policy rate is the *only* thing that affects demand (or supply) of apples. All we need is that the policy rate is *one of* the things that affects demand. So that by adjusting the policy rate, the central bank can offset those other things, and in principle keep inflation on target, just like the driver of a car can keep at the speed limit by moving the gas pedal despite all the hills and headwinds that affect the speed too. (Much harder in practice of course, unless the central bank has a crystal ball.)

        “Also, even if you defend LF this way, the crowding-out argument still doesn’t make sense, since the funds borrowed and spent by the government aren’t removed from the supply of loanable funds at all.”

        Yes it does make sense. If the government increases spending, which increases aggregate demand, the central bank will raise the policy rate to offset that increase in demand 100%, to prevent inflation rising above target. So (if the central bank gets it right) private consumption plus investment demand must fall dollar for dollar with the increased government demand. (If it’s investment demand that falls, the demand for loanable funds falls. If it’s consumption demand that falls, the supply of loanable funds increases.) If the central bank gets it exactly right, we can use the standard loanable funds diagram, shift the desired national savings curve left by the increase in G, and see a rise in the rate of interest that moves you along the S and I curves to the new intersection.

        But you would be quite right in saying that the crowding out argument would not make sense *if* the central bank held the policy rate constant. We would need Ricardian Equivalence plus the assumption that government spending is a perfect substitute for private spending to get crowding out in that sense.

      4. axdouglas Post author

        ‘So that by adjusting the policy rate, the central bank can offset those other things, and in principle keep inflation on target, just like the driver of a car can keep at the speed limit by moving the gas pedal despite all the hills and headwinds that affect the speed too.’

        Except that the acceleration of the car is a linear or at least a monotonic function of the depression of the pedal. Even that doesn’t seem like it’s the case with the policy rate. An increase in the rate might increase spending via the interest-income channel, for example.

        Remember that for loanable funds you need a *stable* equilibrium where S=I. To use as a proxy the policy rate at which (say) output is maximised but inflation is non-accelerating assumes that there is a stable equilibrium at that point. But, again, since we’re dealing with a function that may be non-monotonic, I see no reason to assume there will be any such stable equilibrium at all.

        ‘If the government increases spending, which increases aggregate demand, the central bank will raise the policy rate to offset that increase in demand 100%, to prevent inflation rising above target.’

        Waiving the point already made about whether raising the policy rate would actually have that effect, I don’t see why a rate rise should be necessary. More government spending means more income for the private sector, which reduces its need to borrow.

      5. Nick Rowe

        Can we build theoretical models with a multiplicity of natural rate equilibria? Yes. Does the world seem to be like that? Probably not. I’m an old guy, and I can remember back in the 1970’s when people (Post Keynesians especially) gave all sorts of arguments why the Bank of Canada’s raising the interest rate would cause inflation to rise, not fall. And nowadays, in the blogosphere, I hear “Neo-Fisherians” (who are very very different from Post Keynesians) making a very different argument for why raising the nominal interest rate will cause inflation to rise by an equal amount. But inflation in fact fell in the 1980’s, and the Bank of Canada has in fact succeeded in keeping inflation roughly equal to the 2% it said it would target.

        If the driver of a car tells me he presses the gas pedal down to go faster, and plans to drive at 100km/hr, and if I see him keeping the speed at roughly 100, despite hills going up and down, I figure he is probably right. Or extremely lucky.

        (But I’m not a fan of interest rate control either, but to address this point properly I would have to stop pretending to be a New Keynesian economist, and things would get complicated fast.)

        “Waiving the point already made about whether raising the policy rate would actually have that effect, I don’t see why a rate rise should be necessary. More government spending means more income for the private sector, which reduces its need to borrow.”

        Of course. That is standard Old Keynesian macro. Like in ISLM for example, where *both* Y and r adjust to equalise desired saving and desired investment, (and if the central bank holds r constant, by making the LM curve horizontal, then *all* the adjustment must come from Y). But that assumes a really incompetent central bank. A sensible central bank, doing something sensible, like targeting inflation (I would prefer targeting NGDP, but I’m pretending to be an Orthodox New Keynesian) would instead adjust r to keep Y at Y* (“potential output”) so that Y does to need to adjust to keep desired I = desired S, and that means the central bank chooses to make the LM curve vertical at Y* (or tries to), so that *all* the adjustment must come from r.

      6. Nick Rowe

        Typo in my last comment. I meant to say:
        A sensible central bank, doing something sensible, like targeting inflation (I would prefer targeting NGDP, but I’m pretending to be an Orthodox New Keynesian) would instead adjust r to keep Y at Y* (“potential output”) so that Y does NOT need to adjust to keep desired I = desired S, and that means the central bank chooses to make the LM curve vertical at Y* (or tries to), so that *all* the adjustment must come from r.

      7. Nick Rowe

        Alex: “Interesting. In my last post before this one I said almost the same thing: ONKM is disguised loanable funds theory.”

        Yep. I have put it like this: an orthodox New Keynesian central banker acts as if he is part of a conspiracy to make Loanable Funds look true even though it isn’t true. (And to make Say’s Law true in practice even though it isn’t true in theory, to steal Brad deLong’s line.)

        (But in the long run, on average, it can’t really do anything else, without imploding/exploding the monetary system.)

      8. Min

        Nick Rowe: “Can we build theoretical models with a multiplicity of natural rate equilibria? Yes. Does the world seem to be like that? Probably not. I’m an old guy, and I can remember back in the 1970’s when people (Post Keynesians especially) gave all sorts of arguments why the Bank of Canada’s raising the interest rate would cause inflation to rise, not fall.”

        Because in equilibrium the higher interest rate would be accompanied by a correspondingly higher inflation rate? Never argue from an equilibrium. 😉

  6. Min

    OK, I have done a bit more thinking about Δ(G-T) = ΔSp – ΔS = ΔSp – ΔI.

    Suppose that the signs of the differences on the right side are randomly increases or decreases. (I am basically setting up null hypotheses.) Then when Δ(G-T) > 0, 1/4 of the time both Sp and S will increase, 1/4 of the time both will decrease, and 1/2 of the time Sp will increase and S will decrease. (My sense was that the last will happen more than 50% of the time when the changes are small, but maybe I was mistaken. Anyway, I don’t have a theory about that.) Similarly, when 0 > Δ(G-T), 1/4 of the time both will increase, 1/4 of the time both will decrease, and 1/2 of the time S will increase and Sp will decrease. You can see how everything adds up. 🙂

    One interesting aspect is that when Δ(G-T) > 0, 3/4 of the time S will decrease, so that running a deficit as opposed to a balanced budget is likely to decrease national saving, as Mankiw indicates. Also, 3/4 of the time Sp will increase, so that the Ricardian Equivalence people will usually be part right. But note that these probabilities imply no causation, as they follow from an accounting identity. Who says that accounting identities have no empirical content? 😉

    Note that to establish a non-random connection between Δ(G-T) and ΔS, increasing the deficit would have to be accompanied by a decrease in national saving more than 3/4 of the time, not more than 1/2 the time, which is what the null hypothesis would be if there were no relevant accounting identity.

    Reply
  7. Egmont Kakarot-Handtke

    Accounting matters
    Comment on ‘Accounting for ****’

    Since theories have an architectonic structure it is clear that if there is a fault in the formal foundations the whole superstructure is bound to collapse eventually. Accounting matters because it provides the natural reality check for economic theories; it plays the same role in economics as a sophisticated instrument in physics.

    The first thing to realize is that there is no such thing as a ‘real’ economy. Hence economic phenomena are only explicable as the outcome of the interaction of real and nominal variables. The nominal variables can be easily related to national accounting.

    With regard to saving this means that all ‘real’ models of intertemporal shifting of consumption are pointless. In the monetary economy the process of saving and dissaving is independent from real output in different periods.

    For the correct theory of saving see (2013).

    Egmont Kakarot-Handtke

    References
    Kakarot-Handtke, E. (2013). Settling the Theory of Saving. SSRN Working Paper
    Series, 2220651: 1–23. URL http://ssrn.com/abstract=2220651.

    Reply
  8. Egmont Kakarot-Handtke

    ICYMI

    There is a parallel discussion on Mainly Macro under the heading
    ‘What is it with economists and accounting identities?’
    http://meansquarederrors.blogspot.de/2015/08/what-is-it-with-economists-and.html

    See in particular my answer ‘Either stupid or duplicitous’
    http://axecorg.blogspot.com/2015/08/either-stupid-or-duplicitous.html

    For the bigger picture see the cross-references
    http://axecorg.blogspot.com/2015/01/is-cross-references.html

    Reply
  9. Blissex

    The discussion above i a bit misleading, in part because so many people get lost in the technicalities of national accounting, which looks like a secret language that give access to magic knowledge. It does not.

    The main point is *substantive* and has nothing to do with the national accounts and whether they are in nominal or real terms and is that those who argue that government deficits damage “the economy” always implicitly assume that the government deficit spending multiplier is less than one, while the private spending multiplier is greater than one.

    That is the government spending is aat least in part a black hole: every dollar of income by the government generates less than a dollar of value.

    The extreme position is that the government deficit spending multiplier is zero, that is every dollar of deficit spending is completely wasted, in the sense it simply feeds the government. Which is a shorter and clearer way of saying “G is the corn eaten by the government”.

    As an additional note, as to the corn/money story, technically (and for very good reasons) GDP was properly defined as a vector of physical quantities, like tons of steel, number of cars, tons transported by rail, hours of lawyer work, number of surgeries, delivered in a year (“Gross Domestic Production”) gross of depreciation.

    Nominal GDP is not GDP, it is an *index* constructed by multiplying GDP with a price vector, chosen more or less arbitrarily, and “real” GDP is yet another index using another price vector.

    However mostly for propaganda-related reasons for decades the “sponsored” Economists clique have tried to prevaricate (in textbooks too) by talking of the nominal GDP index as if it were GDP.

    The propaganda related reasons seem to me that it is much easier to “adjust” an index, for example by cleverly “adjusting” the price vector. For example by pervasive use of the Gerschenkron effect. Also it seems little known that the USA is so-far the only country that “adjusts” GDP using also a vector of “hedonic” multipliers, not just prices. J Stiglitz recently wrote that:

    «Likewise, quality improvements – better cars rather than just more cars – account for much of the increase in GDP nowadays.»

    And a blogger who asked the BEA discovered that:

    «The most current figure I have for hedonic adjustment to the GDP is 2.257 TRILLION dollars which is roughly 22% of the GDP.»

    Reply
    1. axdouglas Post author

      Blissex: even if you assume full Ricardian Equivalence, a penny created by government deficit spending adds a penny to private sector net savings. So it’s not ‘wasted’; it’s saved.

      Reply
      1. Blissex

        The tentative explanation above is not assuming «full Ricardian Equivalence», which is completely different from the government spending multiplier. Ricardian equivalence says that “financing” deficits with bonds has the same effect as “financing” them with taxes; the government spending multiplier is about the cumulative effect on GDP of government spending, regardless of how it is “financed”.

        As to “wasted” imagine the government spending to build a “bridge to nowhere” or pay for “national self-esteem day” celebrations, where the private sectors instead would have discovered the cure for cancer or invented cheap fusion energy generators with the same money.

        Some “conservative” economists implicitly assume that private spending always generates value added and government spending never does.

      2. Blissex

        Ricardian equivalence matters when there is a recession caused by insufficient private+public spending, and the argument is that public deficit spending cannot fix that, because financing a public deficit with bonds does not generate any more private+public spending than financing it with taxes, because in both cases 1 dollar of extra public spending results in 1 dollar less of private spending. It is not used to discuss the case of full-employment (usually at least).

        The government spending multiplier applies all the time, and many “aligned” economists assume that it is always lower than the private spending multiplier, so *every* dollar of public spending, including during full-employment, reduces GDP compared to the situation where there is only private spending.

        Some “sponsored” economists seem to believe that not only the public spending multiplier is lower than the private one, but also that it is also lower than 1, so that any every dollar spent by the government instead of the private sector makes everybody poorer on average. Some even seem to assume that it is zero, so that every dollar spent by the government and financed with taxes (or bonds if they also believe in full Rircardian equivalence) is purely destructive.

        For the latter case imagine an example like: in a village the village chief orders 2 people with collecting 10% of the yearly corn harvest and then taking part of it to feed themselves as their wage and then burn it as an offering to the evil god Zokialismus. In that case that 10% of tax-and-spend is completely wasted because most of is burned in some pointless government purpose, and the corn consumed by the 2 government employees is also wasted because they are being paid to do that.

      3. Blissex

        «Some “sponsored” economists seem to believe that [ … ] it is zero»

        Some argue that the public spending multiplier is _negative_ in many cases if not in the aggregate: that 1 dollar of government spending can be not merely completely wasted, but instead destroy more than 1 dollar of private sector value, for example if the government spends that dollar on regulations that can do far reaching damage to the private sector, for example environmental regulations and their enforcement.

        For a more extreme case imagine the government spending millions of tax dollars to prosecute and convict “wealth creators” like Paulson, Fuld, Cayne, Mozilo, ONeil, which could result in trillions of loses in paper wealth in the private sector.

        Ricardian equivalence is a small matter by comparison :-).

  10. Blissex

    «In an open economy it can do it by borrowing from abroad to pay for the consumption of more goods than the national economy can produce now.»
    «It’s an exceedingly special case inside reality and outside the textbooks»

    But balance-of-trade crisises happen all the time, so they are not a special case. See Greece and several other countries recently, and many more examples in recent decades, usually from second-tier countries, but not just.

    «since countries like the UK run consistent trade deficits year on year.»
    «The way you describe it, a country that runs a trade deficit one year should have to run a trade surplus the next, in order to ‘repay the debt’.»

    That’s not quite how I described it by writing «Then the next generation» rather than “the next year”. Anyhow I agree that trade account crisises don’t happen every year, as they take time to build up. But some countries have one every generation or even more frequently (e.g. Greece).

    And as to the UK a few years ago the UK pound fell by 25% (it has since recovered a bit), after about a generation of “strong pound” benefiting the first half of the baby boomer property-owning generation. A sudden 25% devaluation is a massive event and it amazing that it largely passed without comment; while government deficits and welfare benefits are scandals few seem to care publicly about the trade account and the value of the currency or the effects of credit booms.

    Some large debtor/importer countries have so-far managed to cope with long runs of trade deficits by limiting the size of those trade deficits and relying on “vendor financing” from creditor/exporter countries, but eventually such situations always result in a readjustment, sometimes pretty sharp. The UK had several trade-account risises in the past decades, before the era of “vendor financing” by Japan and China began.

    When that policy regime changes we’ll see what happens to the UK…

    Reply
    1. mrkemail2

      The other thing is consumption imports can “crowd out” capital goods.
      You can’t choose what you export.
      You can choose what you import, and countries should introduce restrictions despite “free trade” nonsense.

      Reply

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