Why Am I Arguing with Scott Sumner?

This is going to be my third consecutive post about Scott Sumner (well, not only about Scott), and we seem to be arguing about something, but it may not be exactly clear what the argument is about. Some people, based on comments on this and other blogs, apparently think that I am defending the Keynesian model against Scott’s attacks. Others even accuse me of advocating – horrors! – tax and spend policies as the way to stimulate the economy. In fact, Scott himself seems to think that what I am trying to do is defend what he calls the hydraulic Keynesian model. That’s a misunderstanding; I am simply trying to enforce some basic standards of good grammar in arguing about economic models, in this case the hydraulic Keynesian model. I am not a fan of the hydraulic Keynesian model, but most economists, even anti-Keynesians like Hayek (see here), have acknowledged that in a severe recession or depression, when there is substantial unemployment of nearly all factors of production, the model does provide some insight. I have also explained (here and here) that it is possible to translate the simple Keynesian model of a depression and a liquidity trap into the language of the supply of and demand for money. So at some level of generality, the propositions of the Keynesian model can be treated as fairly trivial and non-controversial.

So what do I mean when I say that I am just trying to enforce basic standards of good grammar? I mean that good grammar is not about what you choose to say; it is about how you say it. Using good grammar doesn’t prevent you from saying anything you want to; it just prevents you from saying it in certain not very comprehensible ways. If you use good grammar, you enhance your chances of saying what you want to say coherently and avoiding needless confusion. Sure some grammatical rules are purely conventional or nitpicks, but good writers and speakers know which grammatical rules can be safely ignored and which can’t. Using bad grammar leads you make statements that are confusing or ambiguous or otherwise incoherent even though the point that you are trying to make may be perfectly clear to you. Making the point clear to someone else requires you to follow certain semantic rules that help others to follow what you are saying. It is also possible that when you make an ungrammatical statement, you are disguising (and at the same time revealing) some confusion that you yourself may not be aware of, and had you made the statement grammatically you might have become aware that you had not fully thought through what you were trying to say. So in a discussion about the Keynesian model, I regard myself as a neutral observer; I don’t care if you are making a statement for or against the model. But I want you to make the statement grammatically.

That’s right; my problem with Scott is that he is using bad grammar. When Scott says he can derive a substantive result about the magnitude of the balanced-budget multiplier from an accounting identity between savings and investment, he is making a theoretically ungrammatical statement. My problem is not with whatever value he wants to assign to the balanced-budget multiplier. My problem is that he thinks that he can draw any empirically meaningful conclusion — about anything — from an accounting identity. Scott defends himself by citing Mankiw and Krugman and others who assert that savings and investment are identically equal. I don’t have a copy of any of Krugman’s textbooks, so I don’t know what he says about savings and investment being identically equal, but I was able to find the statement in Mankiw’s text. And yes, he does say it, and he was speaking incoherently when he said it. Now, it is one thing to make a nonsense statement, which Mankiw obviously did, and it is another to use it as a step – in fact a critical step — in a logical proof, which is what Scott did.

The unfortunate fact is that the vast majority of economics textbooks starting with Samuelson’s classic text (though not until the fourth edition) have been infected by this identity virus, even including the greatest economics textbook ever written. The virus was introduced into economics by none other than Keynes himself in his General Theory. He was properly chastised for doing so by Robertson, Hawtrey, Haberler, and Lutz among others. Perhaps because the identity between savings and investment in the national income accounts reinforced the misunderstanding and misconception that the Keynesian model is somehow based on an accounting identity between investment and savings, the virus withstood apparently conclusive refutation and has clearly become highly entrenched as a feature of the Keynesian model.

The confusion was exacerbated because, in the most common form of the Keynesian model, the timeless, lagless form with the instantaneous multiplier, the model has meaning only in equilibrium for which the equality of savings and investment is a necessary and sufficient condition. This misunderstanding has led to completely illegitimate attempts to identify points on the Keynesian cross diagram away from the point of intersection as disequilibria characterized by a difference between planned (ex ante) and realized (ex post) savings or planned and realized investment. It is legitimate to refer to the equality of savings and investment in equilibrium, but you can’t extrapolate from a change in one or the other to determine how the equilibrium changes as a result of the specified change in savings or investment, which is what Scott tried to do. So, yes, the mistaken identification of savings and investment is distressingly widespread, but unfortunately Scott has compounded the confusion, taking it to an even higher level. Let me again cite as the key source identifying and tracking down all the confusions and misconceptions associated with treating savings and investment (or expenditure and income) as identically equal the classic paper by Richard Lipsey, “The Foundations of the Theory of National Income,” originally published in 1972 in Essays in Honour of Lord Robbins and reprinted in Lipsey Macroeconomic Theory and Policy: The Selected Essays of Richard G. Lipsey, vol. 2.

That’s all for now. I still need to respond to some of Scott’s arguments in detail, clear up a mistake in my previous post and say some more about the savings is identically equal to investment virus.

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26 Responses to “Why Am I Arguing with Scott Sumner?”


  1. 1 Hunter Pritchett January 19, 2012 at 11:49 pm

    Assuming no taxes/government spending:
    Y=C+I
    In your example:
    C=.5Y
    therefore by the definition above:
    I=.5Y
    and your example would more fully read
    Y=C+I=.5Y+.5Y=200+200=400
    If you introduce taxes you get:
    Y=.5(Y-T)+.5(Y-T)+G=.5(Y-100)+.5(Y-100)+100
    Y=.5Y-50+.5Y-50+100
    Y=.5Y+.5Y=C+I

    No multiplier. What you are missing is that if C=.5Y then I=.5Y. It may also equal 200 in an example, but when you change the equation for C you must change it for I as well. When Scott points out that S=I what he really should be pointing out is I=Y-C which is to say that one saves what one does not consume. S=I has almost nothing to do with his argument.

  2. 2 Bill Woolsey January 20, 2012 at 4:57 am

    David:

    I was also taken aback by Sumner’s odd statement that saving is the same thing as investment. I am also a bit taken aback by your claims that realized saving equals realized investment is not an identity.

    I believe it is in fact true that for society as a whole to save–shift consumption from the present to the future, then society as a whole must investment–use resources to produce capital goods.

    Sumner used the term “national saving” to mean something like “society as a whole.” National saving, in his view, requires the production of capital goods. (Producing consumer goods now and stroring them for the future would count as investment too.)

    Now, I think of national saving as the sum of personal saving, business saving, and government saving. I have never really identified it with the question of how society as a whole can shift consumption from the present to the future.

    As I have said before, I don’t fiind the identity of realized saving and realized investment very interesting. I have thought it an artifact of national income accounting. But I don’t think it is false.

    Expenditures = output = income. Any output that isn’t purchased in the ordinary way is inventory investment, including when it is unplanned. Any value of output that is not matched by incomes paid out in ordnary ways is profit for the residual claimants. That would include profit on unplanned inventory investment and even unplanned inventory investment.

    Rowe has pointed out that if nothing is storable, it is still true that expenditure equals output equals income. Things produced and not sold arent’ an issue. Subtract consumption from income and the result is saving. Subract it from output and the result is investment.

    I agree with Sumner’s point. If increased government spending is going to raise nominal expenditure on output, it must involve a decrease in the demand to hold money. (Of course, an increase in the quantity of money would have that effect too.) Sumner points out that the articles Lewis-Wren was critiquing did say that, though well after going through a list of reasons why fiscal policy would not be effective. (I would say, “should not” be effective.)

    Sumner’s argument, however, was that Lewis Wren implied that aggregate demand is just consumption and government spending. Sumner argued that investment is part of aggregate demand too. In the absense of monetary disequilibrium, a temporary increase in government spending matched by a temporary tax hike would result in more government spending and less consumption and investment. The reduction in investment would be due to consumption smoothing.

    It is possible, of course, that if there was a shortage of money, then the increase in government spendng and taxes would at least partly releave the shortage by reducing money demand. In my view, the consumption smoothing would be an important part of such an account. Money demand would fall, and consumption and investment would fall less than government spending rises.

    Sumner is insisting that the important part be made explicit. In Keynesian economics (both old and new,) the monetary disequilibrium is left hidden.

    To excuse Lewis Wren a bit, many (most?) new Keynesian models don’t have investment. In such a model, consumption plus government spending is aggregate demand. The consumer good isn’t storable, at least not across the discrete periods, and so inventory investment isn’t possible. I am pretty sure that in such a scenario, the increase in government spending and taxes, results in a shortage of consumer goods.

  3. 3 Scott Sumner January 20, 2012 at 6:03 am

    David, First of all I’m not attacking the Keynesian model in these recent posts, I’m attacking a bad argument by Wren-Lewis, which ignores some accounting identities. That’s very different.

    You said:

    “That’s right; my problem with Scott is that he is using bad grammar. When Scott says he can derive a substantive result about the magnitude of the balanced-budget multiplier from an accounting identity between savings and investment, he is making a theoretically ungrammatical statement.”

    I’m not claiming that at all, indeed just the opposite. Monetary policy determines the effect of changes in G on NGDP, not accounting identities. I am merely asking Wren-Lewis to make sure his claims don’t violate accounting identities.

    You said;

    “My problem is not with whatever value he wants to assign to the balanced-budget multiplier. My problem is that he thinks that he can draw any empirically meaningful conclusion — about anything — from an accounting identity.”

    I’m afraid you’ve completely misunderstood my argument. I’m not claiming you can derive any useful estimates of the multiplier, with or without the use of an accounting identity. I’m just claiming that if someone derives such an estimate, It ought not violate accounting identities. In your previous proof that showed I was wrong (in your view), you consistently adhered to accounting identities. Would it be OK to have a final answer where the change in AD is not equal to the change in C+I+G? If so, why couldn’t I do that as a way of avoiding your proof?

    I don’t agree with you on S=I, but then isn’t your real target the entire economics profession, not just me? Aren’t you really saying that Sumner, Krugman, Mankiw, Wren-Lewis, and almost all other major economists are making a mistake? I think the readers of this post might think it has something to do with me personally, whereas it really about the economics profession as a whole. I’m taking the view that is in all the textbooks.

    In my view S=I is a useful definition. Definitions can never be right or wrong, only useful or not useful (or if you prefer, widely accepted or not widely accepted.) If saving is defined as the funds put into investment, no empirical study could ever show that it is not the funds put into investment.

  4. 4 Scott Sumner January 20, 2012 at 6:11 am

    Bill, I agree with your comment. Perhaps I shouldn’t have said “same thing” I should have said equal by definition. But when you really think about it, both terms are “the funds put into investment projects.” There are only two other places to put income in a simple economy with no saving. One place is consumption, and we all agree that’s not saving, and the other place is to loan it to someone. In that case you do save, but the borrower dissaves, so no net national saving. Unless you put the funds into an investment project, there is no saving at all.

    If Wren-Lewis wanted to do a model with no investment, he should not have done an example where consumption was smoothed. He could have assumed no change in C. But he knew that wouldn’t have been a convincing explanation of why consumption smoothing showed Cochrane was wrong.

  5. 5 Scott Sumner January 20, 2012 at 6:29 am

    David, By the way in my previous comment to you I wasn’t trying to be defensive when I said the entire profession should be your real target (although it probably sounded that way.) Rather I was suggesting that now you’ve moved on from my dispute with Wren-Lewis, and begun a dispute over an issue where Wren-Lewis and I agree, but where you have another view. Since this is the 3rd in a series that address my criticism of Wren-Lewis, I think some readers might wrongly assume that this particular post continues that line of analysis, whereas now your on a completely separate issue where Wren-Lewis and I agree. if you are right, then Wren Lewis is wrong to claim S=I is an identity, as he recently did. I think that’s worth emphasizing.

  6. 6 John Hall January 20, 2012 at 6:55 am

    David,
    That paper you cited is in a book that costs $140. Any way there is a version available on the cheap?

  7. 7 David Glasner January 20, 2012 at 9:52 am

    Hunter, You are making a basic mistake, a mistake that illustrates very nicely the muddle that results from treating expenditure (E) as being identically equal income (Y). Your first equation should have been written E = C + I, where the equality is actually an identity because expenditure is just the name that we assign to the sum of consumption plus investment. C is a function of income and I may or may not be a function of income. In my example I was assuming it to be a fixed amount, namely 200. Then after you define an expenditure function in terms of income you apply an equilibrium condition E = Y, which allows you to find the unique value of Y which satisfies the two equations simultaneously and in graphical terms represents the intersection of the 45-degree line and the aggregate demand curve (the expenditure function) in the Keynesian cross diagram. The solution you came up with implies that every point on the 45-degree line is an equilibrium, so there is no unique solution. The model becomes incoherent. Speaking ungrammatically often leads people into making incoherent statements. Thanks for providing an example of how that can happen. It’s not your fault, you were just doing what the textbooks inadvertently tell you to do.
    .
    Bill, Realized savings are not the same thing as realized investment. Savings is household income not spent on consumption, investment is business spending on final goods and services. Since they are not the same things, their equality cannot be a necessary condition of every state of the world, which is possible only if they were the same thing or because we choose to define the terms in such a way that we will always measure them and come up with the same number, but that is the result of a semantic choice, not a property of the world.

    You say that the identity of realized saving and realized investment is an artifact of national income accounting. You are thus conceding my point, that the identity reflects a particular verbal convention to attach a particular label to a particular object. That definition cannot have any empirical content, because there is no conceivable state of the world in which the identity would not hold. That is a very different sort of equality than the equality between savings and investment that determines the equilibrium of the Keynesian model. The mistake in reasoning arises because people assume that there is an economic mechanism that ensures the equality of realized savings and realized investment e.g., involuntary inventory accumulation. There is no such mechanism. I don’t say that any accounting definition is false, but I do say that you have to keep track of whether you are applying an accounting identity that has no empirical content and an equilibrium condition because the accounting identity is defining terms differently from how they are defined in the theory.

    Your statement E = Q = Y can be interpreted either as a condition of equilibrium or as identity, and you are not carefully distinguishing between the two possible usages. I agree that if there were no lags, we would be in a world of instantaneous adjustment and we would always be in equilibrium. In a world of perpetual equilibrium, there would be no difference between E, Q and Y or between I and S, but that would reflect the constancy of equilibrium not the identity of the different magnitudes. The problems arise because people try to reason about what happens in disequilibrium or the adjustment from one equilibrium to another by reference to the identity of realized quantities. That is nonsense.

    About the demand to hold money, I agree that in a simple Keynesian model, the monetary side is kept hidden. An increase in G causes an increase in Y with M constant. In terms of MV=Y, if Y rises with M constant, you get a higher V, which means that the demand for money has gone down, so you can interpret the result whichever way you choose.

    Scott, As I have said, you do so many things, it’s hard to keep track of all them. I just can’t keep up with you.

    For the most part accounting identities should be ignored. They usually lead to confusion and fallacious reasoning, because the special meaning that they have is confused with the different meaning assigned to the terms by the theory. Does the theoretical demand for money have the same meaning as the inverse of the velocity in MV = Y accounting identity? Please, I beg of you, don’t answer “yes.”

    As for asking that Wren-Lewis make sure his claims don’t violate accounting identities, I say to __ with the accounting identities. You have to solve the model for an equilibrium, when you do that the equilibrium ensures whatever equalities we care about will be taken care of. Don’t go to the accounting identity as a short-cut way of finding the equilibrium. That leads to disaster. Equilibrium conditions are not the same as accounting identities. Repeat that 100 times. Alternatively keep reading Lipsey’s article until you are thoroughly convinced by it.

    About the economics profession, you are right. You have inspired me to go on a crusade to banish all accounting identities from the reaching of theoretical models. If you are writing a macro book, it is ok to have a chapter on the national income accounts, but only if you make clear that the meaning of the terms in the accounting identities are not the same as the meaning the terms have in the theory, and the solution of the model is in no way dependent on the identities posited by the income accounts.

    There is no difference between saying two things are the same thing and saying that they are equal by definition. If two things are equal by definition it can only be because you are defining them in such a way that they are the same thing. Savings causes investment and investment causes savings. You can’t have one without the other. That doesn’t mean that they are the same thing or that they must always be equal, any more than the fact that chickens cause eggs and eggs cause chickens prove that chickens and eggs are the same thing and that chickens always equal eggs.

    As I said the reason that I took up the cudgels against your attempt to refute Wren-Lewis was because of the particular way in which you were relying on the alleged investment-savings identity rather than an interest in whether the balanced budget multiplier is zero or one or in between. So there was a reason why I was singling you out for special treatment. But you are right that the specific issue that you are arguing about with Wren-Lewis was less important to me than the nonsensical nature of the savings-investment identity.

    John, I wish I had an easy to access source for Lipsey’s paper. How about a library?

  8. 8 rob January 20, 2012 at 10:33 am

    Looked at things in terms of physical goods in existence then savings and investments are just two names for the same set of goods. It is impossible for one to change without the other.

    Introduce money and as long as prices accurately reflects relative values then nothing changes. If that is not the case then you get wrinkles in the system. If money itself is .undervalued then one of the way that this will manifest itself is in of a smaller volumes of transactions taking place and a build up of inventories. This will mean a higher quantity of real savings (physical goods) than one would get in equilibrium until business cuts back on production to adjust. If money remains undervalued (prices of other goods don’t adjust) then a stable point may be reached where savings stay constant.but the economy is in disequilibrium.

    If the govt finances spending via a tax then this will be a wash in terms of its effect the value of money. However if individuals respond by changing the way they divide up their cash income in terms of more spending and less cash savings then this will have an effect. At first this additional cash spending will increase the volume of transactions and reduce the pool of real physical savings (inventories). This in turn will cause firms to rebuild inventories which will further increase the volume of transactions, reduce the value of money and move things back towards equilibrium.

  9. 9 gregransom January 20, 2012 at 10:53 am

    “chickens cause eggs and eggs cause chickens”

    You left out a step there. Unless that step is included, a chicken can cause an egg, but that egg itself _cannot_ cause a chicken.

    The various national accounting identities encourage economists to have sight blindness when it comes to an awareness of similar causal contingencies in the economy.

    E.g. the same set of goods not consumed (or saved) can be dedicated to different production processes, long production processes producing superior output, or shorter production processes producing inferior output.

    In value and money terms “S” does not strictly determine the size of the value of I, the value of I is determined by alternative production choices.

    The “S” = “I” misleads people into being unable to see or think such thoughts.

  10. 10 Bill Woolsey January 21, 2012 at 5:12 am

    David:
    R
    Realized saving and realized investment aren’t different names for the same thing. It is rather the second possibilty–they are defined so they are always equal. I don’t find it very interesting either.

    My view on it, about E = Q = Y is _not_ an equilibrium conditon.

    With storable goods, unplanned inventory investment and profits (including on unplanned inventory investment) adjust to make it true. Unplanned inventory investment is inconsistent with equilibrium.

    With no storable goods, it is still true, but that is because relized Q = realized E. Haircuts the barbers would like to sell, but no one buys, are not realized output. And people may want to get more haircuts than barbers will provide, but that isn’t a realized expenditure. Profits, I think, still make Y = Q, but there are no profits on inventories to worry about, particularly profits on goods produced for sale, but no one buys.

    Rowe is very good on explaining all of this. Think of basic supply and demand. Equilibrium is when quantity supplied equals quantity demanded. The identty is that actual purchases and sales always match. But that doesn’t tell you that the actual purchases are the same as desired purchases and the actual sales are equal to desired sales.

    With a price floor, the amount purchased, the amount sold, and the quantity demanded are all equal. It is not an equilibrium because the quantity supplied is greater than the amount sold. Only at the equilibrium price are all four the same.

    The Clower interpretation of Keynes is that we don’t want to assume we are at equilibrium. It would be like an argument that assumes actual production equals quantity supplied when there is a price floor. What happens to the demand for fertilizer when there is a higher price floor on corn? At the higher price, quantity supplied is higher, which implies more demand for fertilizer. But, in reality, production is lower, so the demand for fertilizer falls.

    Scott:

    In a consumption only economy, each individual can smooth consumption. They can save by lending or paying down loans or dissave by borrowing or collectng on loans. It is only in aggregate that saving must be zero. (You know this, of course.)

    With the typical new Keynesian model, everyone is the same, so there is never any saving. That makes it double wierd.

    Still, the government builds the bridge and this everyone with a huge tax bill. Everyone at the same times _tries_ to smooth consumption and so they all try to borrow money to pay most of the taxes. They plan to reduce consumption a bit each year in the future to pay down the loans.

    Since everyone is the same, everyone is trying to borrow exactly the same amount in the same way. No one is lending.

    If we assume the interest rate adjusts to clear markets, it rises until no one tries to borrow after all. Consumption falls to match the tax increase. Something like that would be your point.

    However, at the given interest rate, everyone wants reduce consumpton by less than the tax hike, so C desired plus G increases.

    With a new Keynesian model we assume that the interest rate really is fixed, and so there is an assumption that actual C + G rises.

    If the interest rate were fixed by a price ceiling, then this wouldn’t work. Everyone is trying to borrow and no one want to lend and so there is no borrowing or lending, and consumption falls.

    But, hidden in new Keynesian theory is that the central bank creates money out of thin air as needed to make sure that people can in fact borrow. We could also imagine that if people were hoarding money because market interest rates were at zero, then maybe lending could come out of those hoards.

    That, of course, is what you want to get at, right?

    Still, even in a model with no investment, there can be consumption smoothing for the individuals and at given levels of income and interest rates there can be desired consumption smoothng in the aggregate. That it can never actually happen doesn’t matter, really.

  11. 11 Michael Carroll January 21, 2012 at 10:14 am

    David Glasner: “The problems arise because people try to reason about what happens in disequilibrium or the adjustment from one equilibrium to another by reference to the identity of realized quantities. That is nonsense.”

    It occurs to me (as a thoroughly uneducated layperson) that the monetarist (?) counter arguments are glossing over time lags a fair amount and that this was the main point of PK’s comparative statistics post and much of what he and (perhaps) Wren-Lewis were getting at in the multi-period analysis, no?

  12. 12 Michael Carroll January 21, 2012 at 10:32 am

    Just read Bill Wolsey’s comment and so please free to delete my last post as I feel it contributes nothing to this discussion.

  13. 13 rob January 21, 2012 at 10:40 am

    Bill,

    I find the equality between realized saving and realized investment very interesting.

    Take the entire stock of physical goods in existence as total savings/investment. and start with an equilibrium where goods and services produced = goods and services consumed.

    Take the scenario that Wren Lewis describes. Scott’s model seems to have people increasing consumption and nothing else changes so the total pool of goods in existence diminishes. Savings/Investment has fallen.

    If in addition an increase in economic activity also takes place then we will see both an increase in additions to the stock of goods as well as an increase to the totality of goods and services consumed.

    What does this mean for the stock and flows of money.?

    If cash balances don’t change then the above examples would need falling prices.

    Most likely however we are talking about a situation where money is undervalued in terms of other goods.

    In this case it is easy to imagine a scenario where consumption smoothing not only causes people to reduce the amount they are savings out of cash income but actually to reduce cash balances to spend on consumption goods. If this happens then we can understand what happens to the stocks and flows of real goods and services in terms of the value of money decreasing towards its equilibrium vale as cash balances fall, as well as the Keynesian story of firms rebuilding inventories.

  14. 14 rob January 21, 2012 at 1:24 pm

    I thought about my last post and see that the cash flows would not be as I described them. Again assuming a starting point where money is undervalued but prices can’t adjust. Consumption smoothing would cause people to save less out of cash income. This would leave less cash for investment unless people also reduced cash balances. Increased consumption however .would provide an incentive for increased investment spending and cause cash balances to fall (One possible way of seeing this is that increased investment demand may raise interest rates above zero and allow money that had been dormant to be lent out. )

    The increased demand and need to rebuild inventories should then lead to a new equilibrium at a higher level of economic activity which would (because of the lower cash balances) reduce the value of money closer to its “true” value in relation to other goods.

  15. 15 nylund January 22, 2012 at 11:10 am

    I do not want to put words in anyone’s mouth (but I will), especially since everyone here is so much smarter than I am. I may very well be misinterpreting or misunderstanding people’s arguments.

    I think, at the heart of the matter, there’s confusion over this term Y, which means both income and expenditure. Everyone agrees that in equilibrium, they must be equal. The confusion/disagreements really comes down to whether or not the Y at the start of the analysis must be the same as the one at the end of the analysis?

    I think one side is saying:

    Initial expenditure = initial income

    and

    final expenditure = final income

    That is, at both the beginning and the end of the analysis, the equilibrium condition must be met (E=Y), but that doesn’t mean that at the two ends of the analysis, they must have the same equilibrium value. We can have Y1=E1 and Y2=E2 without necessarily having Y1=E1=Y2=E2. But since no one is really being clear about which Y they’re talking about or whether or not Y can change you get a confusing argument where some people are saying, “yes, Y=Y and Y=Y, but that doesn’t mean Y=Y=Y=Y,” and other’s are saying, “If Y=Y and Y=Y, then Y=Y=Y=Y. It’s all just Y you nincompoop!”

    It’d be clearer if people said, E1=Y1 and E2=Y2, then argued about whether or not Y1=Y2.

    I think this ultimately comes down to a point made on p. 325 of Mankiw’s “Macroeconomics” (7E).

    He states that the economy can be described with three equations, the first two of which are:

    Y = C(Y-T) + I(r) + G
    M/P = L(r,Y)

    The problem, he explains, is that there are three endogenous variables, Y, P, and r, but only two equations. We need a third equation.

    Keynesians who believe that prices are sticky in the short-run assume that P=Pbar. Thus, r and Y are the two that adjust to make sure all the identities and equilibrium conditions are satisfied.

    On the other hand, the classical approach completes the model by assuming that prices are flexible and that output reaches it’s natural level so that Y=Ybar. In this model, Y is fixed and it’s P and r that do all the adjustments.

    That’s a mix of direct quotes and paraphrasing from Mankiw’s book. And, I also think it’s the source of the fundamental disagreement here.

    One side is saying that since Y is fixed, an increase in G means that S and/or I must fall. The other is saying that since Y is flexible, that’s not necessarily true.

    It all just comes down to the fact that we have three variables and two equations, so in order to get the math to work, you have to hold one variable constant. It all comes down to whether you think prices are fixed and output is flexible, or if you think output is fixed and it’s prices that are flexible.

    Which one you choose changes your result. The classic dodge that Econ 101 professors make (including Mankiw in his book) is to say that you should use one for the short-run (Keynes), and the other for the long-run (Classical). For the most part, this is what Keynesian’s do (but some do forget about the long-run version). On the other hand, non-Keynesians simply always use the classical, regardless of whether or not you’re talking short or long-run.

    Point being, I don’t think anyone is “wrong.” People are just using different assumptions without explicitly stating them, and if those assumptions were made clearer, then people would start to understand why different people keep getting different answers to a very simple econ 101 question instead of accusing each other of not understanding basic econ 101.

    Both are right using basic econ 101! It just depends which version of Econ 101 you’re using. Bring up other points using reasoning beyond Econ 101 is just muddling the argument when all you really need to resolve is whether or not you think Y changes.

    And really, that’s what this is all about. Can the government increase Y via government spending? If by assumption you’re saying yes, then yes it can (but not necessarily). If by assumption you’re saying no, then no it can’t (no matter what).

    I think that some people started out trying to prove that while yes, in theory, it can change, it doesn’t necessarily. In trying to prove that by solely relying on a simple model, they somewhat accidentally drew upon a model where, by assumption, it can’t change and mistakenly thought this proved their point that it won’t change.

    As I said, everyone here is much smarter than I am and I’m not sure I’m following everyone’s logic correctly. But, to my novice mind, that’s what happened.

    PS. If this is a very stupid post and I’m way off on everything, feel free to delete.

  16. 16 David Glasner January 22, 2012 at 6:31 pm

    Rob, You are confusing a proposition about equilibrium with a proposition about what must necessarily always be true whether equilibrium obtains or not. In equilibrium the amount of investment, physical output in the current period not consumed, equals the amount of saving, the amount of income not consumed. But if equilibrium did not obtain, investment and savings would not be equal. Equilibrium need not prevail at all times and whenever it doesn’t, savings does not equal investment. This is true with or without money.

    Greg, I agree that we can, and perhaps should, make the model more complicated, but not until we properly understand the simple version.

    Bill, I don’t think that you can give a coherent interpretation of the Keynesian cross diagram unless you have E = Y as an equilibrium condition. That is what the 45-degree line represents: an equilibrium condition. Otherwise, how are you solving for Y? The natural interpretation of the model is that E always equals Q and that there is no unplanned inventory accumulation or decumulation, because inventories are not held or because they remain constant. The supply-demand analogy does not work because suppliers and demanders are both making plans about the same magnitude. Savers and investors are not making plans about the same magnitude. Savers are making plans about how much of their income not to consume and investors (firms) are making plans about how much to spend on capital equipment.
    I don’t know what Clower has to do with anything. We are talking about the proper interpretation of the Keynesian model. If Clower is right the Keynesian model is not a good representation of what Keynes wanted to say. But the model is what it is.

    Michael, This is probably a discussion that would be of interest only to a rather narrow selection of economists and students of economics.

    Rob, You are engaged in reasoning and speculation that is outside the boundaries of the very simplified model that we are discussing. It may be insightful reasoning and speculation, but it is not addressing the very specific point that I am trying to explain, which is how to think about what it means for the simple Keynesian model to be in equilibrium and what it means for the model to be out of equilibrium.

    Nylund. Sorry, but you got off to a bad start. Y means income, not expenditure. E means expenditure. Y is Y and E is E. Out of equilibrium E does not equal Y. In equilibrium E does equal Y. That’s all there is to it. The question whether Y is changing or constant, prices are flexible or fixed are separate from understanding the basic meaning of the simple model. I am not discussing any model but the Keynesian model and how to interpret it. I am not saying it is a good model or a bad model. I am just explaining what it means and how it works. Now you can go back and reread everything I wrote.

  17. 17 John Schultz January 22, 2012 at 8:57 pm

    @David Glasner

    Let’s say that some shock causes the private sector to want to save more by reducing its consumption.

    First, is that a coherent proposition?

    Second, assuming that it is a coherent proposition, then in a step-by-step walkthrough doesn’t a reduction in consumption lead directly and immediately to a build up in (business) inventories, which is part of “investment” in E = C + I + G?

    That is, every additional dollar not consumed leads directly to an additional dollar of (unplanned) inventories as a direct and immediate effect? Also, that every additional dollar not consumed is saved as a direct and immediate effect? Therefore, the direct and immediate changes in I and S are 1-for-1 in complete lockstep?

    From there you can go onto second order effects where (business) expenditure goes down because inventories are growing more than wanted, which in turn feeds back into consumption and saving and ultimately you can find the final equilibrium.

    However, I don’t see why S and I won’t stay in lockstep so long as your definition of I includes business inventories?

  18. 18 Greg Ransom January 23, 2012 at 12:20 am

    David, this isn’t a complicating factor.

    Iit is the guts of getting clear on the idea of savings being in an equilibrium relation with investment — and also the very guts of understanding how alternwtive interest rates and money supply growth rates can put savings out of equilibrium with investment.

    There is no other game in town that non-pathologically engages the economic way of thinking.

    How otherwise can we make sense of expansions or contractions of lending, money and credit which cause excess investment over savings or deficient investment in relation to savings, unless we avail ourselves of the logic of choice applied to alternative production and consumption streams requiring alternative lengths of time.

    If we do so, we can appreciate how investment can be increased via expansions in lending via bidding away from intermediate projects in favor of longer project promising superior output, a process which need not be underwritten by reductions in immediate cnsumption, i.e. via increased savings,

    So there you have savings out of equilibrium with investment, exactly what was needed to explain macroeconomic discoordination.

    The minimal demands of explanatory success dictate what is the minimum of conceptual simplicity — if we don’t know what we want to understand, we can’t know what sort of simplicity will serve to achieve anything worth understanding.

  19. 19 Bill Woolsey January 23, 2012 at 5:29 am

    David:

    C + I (the line with the slope of mpc) is planned expenditure.

    Y = E is the identity, not an equilibrium condition. On the graph it has a slope of one.

    The point of equilibrium (were the cross) is when output equals planned expenditures.

    Output always equals income and realized expenditures.

    Gaps between realized expenditure and planned expendture imply disequilibrium.

    This is how I see the Keynesian Cross. (Not that I think about it much.)

    You can, if you want, translate this into saving and investment talk. I don’t usually do it that way. (Not that I worry much about the Keynesian cross either.)

    Subract C from both sides of Y = E and your get saving equals realized investment.

    The equilibriium condition is the Y = C + I — income equals planned expenditure. Subtract C from both sides. Then saving equals planned investment. in equilibrium.

    Your argument about saving and investment being different things, I grant.

    However, the Keynesian cross isn’t about saving and investment. It is about income and expenditure.

    It is the same thing because expenditure is what is paid for output and income is what is received for output.

    Suppose all production is by yeoman farmers. There is no wage labor, interest income, or anything. Income appears as business profit. Farmers produce and sell corn, wheat, apples. Farmers buy corn, wheat, apples. Income equals expenditure. It is buying and selling.

    Of course, the supply and demand for apples can be both measured in numbers of apples. Expenditures on apples, wheat, and corn is measured in money and income earned from selling apples, wheat, and corn is measured in money. But it is money from the same transactions.

    When we add factor markets for labor and the like, then income equals output because profits are a residual and part of income. When we add storable goods, unplanned inventory inestment is a residual and a type of expenditure.

  20. 20 David Glasner January 23, 2012 at 9:51 am

    John, It is certainly a coherent proposition to assume that the private sector (households) decides to save more by reducing consumption – with or without a preceding shock.

    A reduction in consumption expenditures by households only leads “directly and immediately to a build-up in (business) inventories if you make an assumption about the real world – an assumption that could be either true or false – that businesses do not adjust production immediately to the change in expenditures. Since your conclusion requires making an assumption that, in some conceivable states of the world, might be false, you have not established that income and expenditure or investment and savings are identically equal. In some conceivable states of the world, they might not be equal. If two magnitudes are identically equal, then there is no conceivable state of the world in which the equality between them fails to obtain.

    Greg, I am not going to take the bait and engage with you on whether the income-expenditure is a satisfactory model of economic fluctuations for any purpose (even to make an observation about Hayek’s ambiguous stance on its relevance during periods in which all resources are less than fully employed). This discussion is restricted to the question of how to interpret the income-expenditure model. You may be right that the model itself is worthless as an explanation of reality, but as a matter of pure understanding or intellectual history or whatever, it is possible to discuss the right way to interpret the model without undertaking a more profound assessment of its validity.

    Bill, You are positing a distinction between planned expenditure and actual expenditure and actual expenditure. That is modeling choice that you have made there is no more reason to assume that planned expenditure is different from actual expenditure than there is to assume that expenditure can differ from income.

    If I take your definitions, we get the following:

    E ≡ C + I, where “≡” stands for “identically equal to,” or “equal by definition”

    If we write C as a function in the usual way C = a + bY, where b = mpc and if we take as I as fixed we can rewrite the expression for E as follows
    E ≡ A + bY, where A stands for the autonomous component of expenditure

    If E ≡ Y then the expression for E above can be rewritten as
    E ≡ A + bE

    Rearranging terms we get

    E ≡ A/(1-b)

    That means that expenditure is identically equal to A/(1-b).

    So instead of having an expenditure function, you have expenditure as identically equal to a specific number. That doesn’t make sense to me.

    The better interpretation of what is going on is to say that E = Y is an equilibrium condition, and to avoid trying to attach interpretations of the model outside of equilibrium, without specifying explicitly a lag structure between output and expenditure and income and then modeling the dynamic adjustment path of the model from one equilibrium situation to another.

    There is a simple translation from income and expenditure to savings and income. The two equilibrium conditions always imply precisely the same equilibrium, so there is only a semantic distinction between them. It’s all one model.

    I am not saying that it is impossible to model a dynamic system in which income and expenditure are identically equal, but that is a property of a model not a fundamental identity that must hold under all conceivable circumstances. It is also possible to say that we want to work with a model in which there are no lags, so that income, expenditure and output are always equal. Fine, but then adjustments to disturbances are instantaneous and it is meaningless to speak about the disequilibrium properties of the model and the notion of unplanned inventory investment has no representation or meaning in the model.

  21. 21 John Schultz January 23, 2012 at 10:11 am

    “A reduction in consumption expenditures by households only leads “directly and immediately to a build-up in (business) inventories if you make an assumption about the real world – an assumption that could be either true or false – that businesses do not adjust production immediately to the change in expenditures. Since your conclusion requires making an assumption that, in some conceivable states of the world, might be false, you have not established that income and expenditure or investment and savings are identically equal. In some conceivable states of the world, they might not be equal. If two magnitudes are identically equal, then there is no conceivable state of the world in which the equality between them fails to obtain.”

    David, if we use your counter example, then when production adjusts “immediately” to the change in consumption, then doesn’t income also adjust “immediately” to the change in production (and consumption)?

    Or do you think it logically possible that “one side” of an economy could exhibit no lag while the other did? That is, that incomes remained constant (for a while) even though production dropped immediately?

  22. 22 Bill Woolsey January 24, 2012 at 5:23 am

    David:

    I suppose you are correct about Y being equal to A/(1-b) in your example, but you are defining A, at least, given b.

    However, the basic identity of macroeconomics is not the same thing as the Keynesian cross. And realized saving equals realized investment by definition because of the basic identity of macroeconomics. It is not something that follows from the Keynesian cross.

    I think you have in mind something like expenditures generate revenues for firms, and then, firms take that revenue they just earned and pay it out as income. Then, households take that income they just earned, and then, they use the income to buy output.

    In equilibrium, the expenditures generate revenues which the firms then pay out as incomes which the households spend, which generates revenue…and these are all equal period after period.

    The basic identity of macroeconomics, however, is that the output produced during a period generates an equal income during that period and is all purchased during that same period. There is no first expenditure, then income, and then expenditure with all of these supposedly being equal period after period by definition.

    If firms adjust output to sales instantly, then to say that expeditures are less than output is just contradicted. Maybe this periods expenditures and output are less than last periods expenditures and output, but they are the same. Output is at the level of these expenditures and the income generated is equal to that output.

    In the story that you have in mind — first expendture, then income, then expenditure, there are three periods.

    In the first period, the expenditure, output, and income were all equal. (This is the initial expenditure that you imagne is creating the next periods revenue and income.)

    In the second period, income, expenditure, and output all remain the same as well. (This is the period where you imagine the household are getting the incomes from last periiods expenditure.)

    And then, in the third period, expenditure, output, and income are all the same, (This is the preriod where you imagine households are spending the inncome they earned in the previous period.

    Nothing says the third period’s expenditure equals the first period’s expenditure.

    How much was actually produced in each period? That was equal to the expenditures and the income in each period.

    With unplanned inventory investment, this identity looks a bit peculiar to me. As I have said before, when firms produce something for sale, and they don’t sell it, saying that they bought it themselves seems like cheatng. And to count the profit on those same unsold goods as income also seems like cheating.

    If you don’t “cheat” and say that unplanned inventory expenditure is not expendture at all, then expenditure can be less than output. If profit on unsold goods does’t count as income, then income can be less than output. If you count the unplanned inventory accumulation as expenditure, but the profit on those goods as not being income, then expenditure can be less than income. If you count the profit of the goods as income, but don’t count the unsold goods as being purchased, then income can be greater than expenditure.

    In a services only economy, this issue doesn’t arise. Ouput is produced as it is sold, so output and expenditure are equal. And an equal income is generated at the same time the output is produced. Of course, that has nothing to do with how many services the sellers would like to sell and so the income they would like to earn.

  23. 23 Bill Woolsey January 24, 2012 at 7:03 am

    I made a mistake. If you count unplanned inventory investment as expenditure, but don’t count the profit on those goods as income, then income can be less than expendture.

    If you count the profit on unsold goods as income, but don’t count goods produced for sale but unsold as expenditure, then expenditure can be less than income.

    However, the basic identify of macroeconomics doesn’t define things in those ways.

    Also, if anyone thinks that a definition is forcing people to take money they earn during some period and spend it on output, then they are very wrong.

    It is rather that if the expendenture doesn’t occur, then they don’t earn the income. With unplanned inventory investment, there is obviously some expendture and income that doesn’t involve any transfer of money.

    In a services only economy, however, where production is made with sales and ignoring credit, then all sales are money sales and the money receipts are money income to those selling the products. But nothing says they have to spending the money income recieved. It is that they don’t earn it if there are no money expenditures.

    It is exactly like purchases matching sales in the apple market, but that doesn’t tell us quantity supplied equals quantity demanded.

    The basic identity of macroeconomics is exactly like saying that the sellers receipts for apples equals to buyers purchases of apples. Of course, no one thinks that means that apple sellers must spend their receipts on apples.

    As for the saving equals investment identity, that starts with income equals expenditure by definition. Lets subtract spending on cars from both sides. Then we can say that spending on things other than cars matches that part of income not spent on cars.

  24. 24 David Glasner January 25, 2012 at 9:18 am

    John, The lag structure of an economy is a matter of fact, not logic. What stops me from assuming that production adjusts instantaneously to expenditure while assuming that payments by business firms to factor owners (households) are not made more frequently than biweekly and sometimes at longer intervals? In fact, both sorts of lag exist, but there is no logical barrier to assume that one does and one doesn’t. That is a matter of choice on the part of the modeler.

    Bill, I don’t know what you mean by “defining A, at least, given b.”
    I deny absolutely that there is any basic identity of macroeconomics whether in the Keynesian model or any other macroeconomic model. Realized savings equaling realized investment is merely a definitional convention of national income accounting and has no analytic status or function. I agree that I = S is an important equilibrium condition in a large class of macroeconomic models, but an identity is a very different concept from an equilibrium condition, and it is important not to confuse them. The I = S condition does not follow from the Keynesian cross. It is assumed by the Keynesian cross. That’s how you generate a solution to the model as the intersection between the AD curve and the 45-degree line, which represents the equilibrium condition (I = S) not the accounting identity (I ≡ S).

    I agree that if we assume that firms adjust output to expenditures instantaneously, then output always equals expenditure in every period. That is a convenient assumption in the Keynesian cross because there is no separate axis for output, so we just equate E and Q for convenience. There is no necessary identity, just a convenient assumption for modeling simplicity.

    I agree that the treatment of unplanned inventory investment is a tough problem. But it is an accounting issue, not a theoretical issue that is necessary part of the story, and it has no necessary interpretation in the Keynesian cross, which has no economic interpretation out of equilibrium and there is no unintended inventory accumulation in equilibrium.

    Again, I don’t know where “the basic identity of macroeconomics” comes from and I deny that it has any role in macroeconomic theory of any sort. You can posit an economy in which E always equals Y and I always equals S, but if that is the economy you want to talk about, you can’t meaningfully discuss any disequilibrium or adjustment path from one equilibrium to another. You are in the world of the instantaneous multiplier and any change in the model generates an instantaneous adjustment to a new equilibrium.


  1. 1 Advice to Scott: Avoid Accounting Identities at ALL Costs « Uneasy Money Trackback on January 22, 2012 at 10:33 am
  2. 2 Thompson’s Reformulation of Macroeconomic Theory, Part IV « Uneasy Money Trackback on October 19, 2012 at 12:36 pm

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About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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