I Figured Out What Scott Sumner Is Talking About

I won’t bother with another encomium to Scott Sumner. But how many other bloggers are there who could touch off the sort of cyberspace fireworks triggered by his series of posts (this, this, this, this, this and this) about Paul Krugman and Simon Wren-Lewis and their criticism of Bob Lucas and John Cochrane? In my previous post, after heaping well-deserved, not at all overstated, praise upon Scott, I registered my own perplexity at what Scott was saying. Thanks to an email from Scott replying to my post (owing to some technical difficulties about which I am clueless, his comment, and possibly others, to that post weren’t being accepted last Friday) and, after reading more of the back and forth between Scott and Wren-Lewis, I now think that I finally understand what Scott was trying to say. Unfortunately, I’m still not happy with him.

Excuse me for reviewing this complicated multi-sided debate, but I don’t know how else to get started. It all began with assertions by Lucas and Cochrane that that old mainstay of the Keynesian model, the balanced-budget multiplier theorem, is an absurd result because increased government spending financed by taxes simply transfers spending from the private sector to the public sector, without increasing spending in total. Lucas and Cochrane supported their assertions by invoking the principle of Ricardian equivalence, the notion that the effect of taxation on present consumption is independent of when the taxes are actually collected, because the expectation of future tax liability reduces consumption immediately (consumption smoothing). Paul Krugman and Simon Wren-Lewis pounced on this assertion, arguing that Ricardian equivalence actually reinforces the stimulative effect of government spending financed by taxes, because consumption smoothing implies that a temporary increase in taxation would cause current consumption to fall by less than would a permanent increase in taxation. Thus, the full stimulative effect of a temporary increase in government spending is felt right away, but the contractionary effect of a temporary increase in taxes is partially deferred to the future, implying that a temporary increase in both government spending and taxes has a net positive immediate effect.

[See update below] Now this response by Krugman and Wren-Lewis was just a bit opportunistic and disingenuous, the standard explanation for a balanced-budget multiplier equal to one having nothing to do with the deferred effect of temporary taxation. Rather, it seems to me that Krugman and Wren-Lewis were trying to show that they could turn Ricardian equivalence to their own advantage. It’s always nice to turn a favorite argument of your opponent against him and show that it really supports your position not his. But in this case the gambit seems too clever by a half.

Enter Scott Sumner. Responding to Krugman and Wren-Lewis, Scott tried to show that the consumption-smoothing argument is wrong, and the attempt to turn Ricardian equivalence into a Keynesian argument a failure. I don’t know about others, but it did not occur to me on first reading that Scott’s criticism of Krugman and Wren-Lewis was so narrowly focused. The other problem that I had with Scott’s criticism was that he was also deploying some very strange arguments about the alleged significance of accounting identities, which led me in my previous post to make some controversial assertions of my own denying Scott’s assertion that savings and investment are identically equal as well as the equivalent one that income and expenditure are identically equal.

So what Scott was trying to do was to show that consumption smoothing cannot be an independent explanation of why an equal temporary increase in government spending and in taxes increases equilibrium income.  Krugman and Wren-Lewis were suggesting that it is precisely the consumption-smoothing effect that produces the balanced-budget multiplier. Here’s Wren-Lewis:

Both make the same simple error. If you spend X at time t to build a bridge, aggregate demand increases by X at time t. If you raise taxes by X at time t, consumers will smooth this effect over time, so their spending at time t will fall by much less than X. Put the two together and aggregate demand rises.

This is not your parent’s proof of the balanced-budget multiplier, in which consumption decisions are based only on current income without consideration of future income or expected tax liability. It’s a new proof. And it drove Scott bonkers. So what he did was to say, let’s see if Wren-Lewis’s proof can work on its own. In other words, let’s assume that the standard argument for the balanced-budget theorem — that all government spending on goods and services is spent, but part of a tax cut is spent and part is saved, so that an equal increase in government spending and taxes generates a net increase in expenditure, leading in turn to a corresponding increase in income — is somehow false.  Could consumption smoothing rescue an otherwise disabled balanced-budget multiplier

This was a clever idea on Scott’s part. But implementing it is not so simple, because if you are working with the simple Keynesian model, you can’t help but get the balanced-budget multiplier automatically. (A balanced-budget multiplier of 1 is implied by the Keynesian cross. In the world of IS-LM, you must be in a liquidity trap to get a multiplier of 1. Otherwise the multiplier is between 0 and 1.) At this point, the way to proceed would have been for Scott to say, well, let’s assume that something in the Keynesian model changes simultaneously along with the temporary increase in both government spending and taxes that exactly offsets the expansionary effect of the increase in spending and taxes, so that in the new equilibrium, income is exactly where is started. So, let’s say that initially Y = 400, and G and T then increase by 100. The balanced-budget multiplier says that Y would rise to 500. But let’s say that something else also changed, so that the two changes together just offset one another, resulting in a new equilibrium with Y = 400, just as it was previously. At this point, Scott could have introduced consumption smoothing and determined how consumption smoothing would alter the equilibrium.

But that is not what Scott did.  Instead, he relied on arguments from irrelevant accounting identities, as if an accounting identity can be used to predict (even conditionally) the response of an economic variable to an exogenous parameter change. Let’s now go back to a more recent restatement of his argument against Wren-Lewis (a restatement with the really bad title “It’s tough to argue against an identity”). Here’s Scott responding to Paul Krugman’s jab that Lucas and Cochrane had committed “simple fail-an-undergraduate-level-quiz errors.”

First recall that C + I + G  = AD = GDP = gross income in a closed economy.  Because the problem involves a tax-financed increase in G, we can assume that any changes in after-tax income and C + I are identical.

By after-tax income, Scott means C + S, because in equilibrium, E (expenditure) ≡ C + I + G = Y (income) ≡ C + S + T. So if G = T, then C + S = C + I. Scott continues:

Suppose that because of consumption smoothing, any reduction in after-tax income causes C to fall by 20% of the fall in after-tax income.  Then by definition saving must fall by 80% of the decline in after-tax income.  So far nothing controversial; just basic national income accounting.

It is not clear what accounting identity Scott is referring to; the accounting identities of national income accounting do not match up with the equilibrium conditions of the Keynesian model. But the argument is getting confused, because there are two equilibria that Scott is talking about (the equilibrium without consumption smoothing and the one with smoothing), and he doesn’t keep track of the difference between them. In the equilibrium without consumption smoothing, Y is unchanged from the initial equilibrium. Because after-tax income must be less in the new equilibrium than in the old one, taxes having risen with no change in Y, private consumption must be less in the new equilibrium than the old one. By how much consumption fell Scott doesn’t say; it would depend on the assumptions of the model. But he assumes that in the equilibrium with consumption smoothing, consumption falls by 20%. Presumably, without consumption smoothing, consumption would have fallen by more than 20%. But here’s the problem. Instead of analyzing the implications of consumption smoothing for an increase in government spending and taxes that would otherwise fail to increase equilibrium income, while reducing disposable income by the amount of taxes, Scott simply assumes that consumption smoothing leaves Y unchanged. Let’s follow Scott to the next step.

Now let’s suppose the tax-financed bridge cost $100 million.  If taxes reduced disposable income by $100 million, then Wren-Lewis is arguing that consumption would only fall by $20 million; the rest of the fall in after-tax income would show up as less saving.  I agree.

Again, Scott is assuming a solution to a model without paying attention to what the model implies. The solution of a model must be derived, not assumed. The only assumption that Scott can legitimately make is that Wren-Lewis would agree that without consumption smoothing the $100 million bridge financed by $100 million in taxes would not change Y. The effect on Y (and implicitly on C and S) of consumption smoothing must be derived, not assumed. Next step.

But Wren-Lewis seems to forget that saving is the same thing as spending on capital goods.

I interrupt here to protest emphatically. There is simply no basis for saying that saving is the same thing as spending on capital goods, just as there is no basis for saying that eggs are chickens, or that chickens are eggs. Eggs give rise to chickens, and chickens give rise to eggs, but eggs are not the same as chickens. Even I can tell the difference between an egg and a chicken, and I venture to say that Scott Sumner can, too. Now back to Scott:

Thus the public might spend $20 million less on consumer goods and $80 million less on new houses.  In that case private aggregate demand falls by exactly the same amount as G increases, even though we saw exactly the sort of consumption smoothing that Wren-Lewis assumed. But Wren-Lewis seems to forget that saving is the same thing as spending on capital goods.  Thus the public might spend $20 million less on consumer goods and $80 million less on new houses.  In that case private aggregate demand falls by exactly the same amount as G increases, even though we saw exactly the sort of consumption smoothing that Wren-Lewis assumed.

Scott has illegitimately assumed a solution to a model after introducing a change in the consumption function to accommodate consumption smoothing, rather than derive the solution from the model. His numerical assumptions are therefore irrelevant even for illustrative purposes. Even worse, by illegitimately asserting an identity where none exists, he infers a reduction in investment that contradicts the assumptions of the very model he purports to analyze. To say “in that case private aggregate demand falls by exactly the same amount as G increases, even though we saw exactly the sort of consumption smoothing that Wren-Lewis assumed” is simply wrong. It is wrong precisely because saving is not “the same thing as spending on capital goods.” I know this is painful, but let’s keep going.

Those readers who agree with Brad DeLong’s assertion that Krugman is never wrong must be scratching their heads.  He would never endorse such a simple error.  Perhaps investment was implicitly assumed fixed; after all, it is sometimes treated as being autonomous in the Keynesian model.  So maybe C fell by $20 million and investment was unchanged.  Yeah, that could happen, but in that case private after-tax income fell by only $20 million and there was no consumption smoothing at all.

What Scott is saying is that if you were to assume that savings is not the same as investment, so that investment remains at its original level, then C + I goes down by only $20. Then in equilibrium, given that G = T, C + S, private after-tax income also went down by $20 million, in which case consumption accounted for the entire reduction in Y, which, if I understand Scott’s point correctly, contradicts the very idea of consumption smoothing. But the problem with Scott’s discussion is that he is just picking numbers out of thin air without showing the numbers to be consistent with the solution of a well-specified model.

Let’s now go through the exercise the way it should have been done. Start with our initial equilibrium with no government spending or taxes. Let C (consumption) = .5Y and let I (investment) = 200.

Equilibrium is a situation in which expenditure (E) equals income (Y).  Thus, E ≡ C + I = .5Y + 200 = Y. The condition is satisfied when E = Y = 400. Solving for C, we find that consumption equals 200. Income is disposed of by households either by spending on consumption or by saving (additional holdings of cash or bonds). Thus, Y ≡ C + S. Solving for S, we find that savings equals 200. Call this Equilibrium 1.

Now let’s add government spending (G) = 100 and taxes (T) = 100. Consumption is now given by C = .5(Y – T) = .5(Y – 100). Our equilibrium condition can be rewritten E ≡ C + I + G = .5(Y – 100) + 200 + 100 = .5Y + 250 = Y. The equilibrium condition is satisfied when E = Y = 500. So an increase in government spending and taxes of 100 generates an increase in Y of 100. The balanced budget multiplier is 1. Consumption and saving are unchanged at 200. Call this Equilibrium 2.

Now to carry out Scott’s thought experiment in which the balanced-budget multiplier is 0, we have to assume that something else is going on to keep income and expenditure from rising to 500, but to be held at 400 instead. What could be happening? Perhaps the increase in government spending causes businesses to reduce their planned investment spending either because the government spending somehow reduces the expected profits of business, by reducing business expectations of future sales. At any rate to reduce equilibrium income by 100 from the level it would otherwise have reached after the increase in G and T, private investment would have to fall by 50. Thus in our revised model we have E ≡ C + I + G = .5(Y – 100) + 150 + 100 = .5Y + 200 = Y. The equilibrium condition is satisfied when E = Y = 400. The increase in government spending and in taxes of 100 causes a reduction in investment of 50, and therefore generates no increase in Y. The balanced budget multiplier is 0. Consumption and savings both fall by 50 to 150. Call this Equilibrium 2′.

Now we can evaluate the effect of consumption smoothing. Let’s assume that households, expecting the tax to expire in the future, borrow money (or draw down their accumulated holdings of cash or bonds) by 10 to finance consumption expenditures, planning to replenish their assets or repay the loans in the future after the tax expires. The new consumption function can be written as C = 10 + .5(Y – T). The revised model can now be solved in terms of the following equilibrium condition: E ≡ C + I + G = 10 + .5(Y – 100) + 150 + 100 = .5Y + 210 = Y. The equilibrium condition is satisfied when E = Y = 420.  Call this equilibrium 3.  Relative to equilibrium 1, consumption and savings in equilibrium 3 fall by 30 to 170, and the balanced budget multiplier is .2.  The difference between equilibrium 2′ with a zero multiplier and equilibrium 3 witha multiplier of .2 is entirely attributable to the effect of consumption smoothing.  However, the multiplier is well under the traditional Keynesian balanced-budget multiplier of 1.

Scott could have avoided all this confusion if he had followed his own good advice: never reason from a price change. In this situation, we’re not dealing with a price change, but we are dealing with a change in some variable in a model. You can’t just assume that a variable in a model changes. If it changes, it’s because some parameter in the model has changed, which means that other variables of the model have probably changed. Reasoning in terms of accounting identities just won’t do.

Update (1/17/12):  Brad DeLong emailed me last night, pointing out that I was misreading what Krugman and Wren-Lewis were trying to do, which was pretty much what I was trying to do, namely to assume that for whatever reason the balanced-budget multiplier without consumption smoothing is zero, so that an equal increase in G and T leads to a new equilibrium in which Y is unchanged, and then introduce consumption smoothing.  Consumption smoothing leads to an increase in Y relative to both the original equilibrium and the equilibrium after G and T increase by an equal amount.  So I withdraw my (I thought) mild rebuke of Krugman and Wren-Lewis for being slightly opportunistic and disingenuous in their debating tactics.  I see that Krugman also chastises me in his blog today for not checking my facts first.  My apologies for casting unwarranted aspersions, though my rebuke was meant to be more facetious than condemnatory.


33 Responses to “I Figured Out What Scott Sumner Is Talking About”

  1. 1 Scott Sumner January 16, 2012 at 7:32 pm

    David, Sorry to make you go through all that work, but you haven’t correctly stated my argument. You seem intent on proving that the BBM can be positive with consumption smoothing. I agree. But in your final example you simply assume that consumption smoothing has no impact on investment. In that case it’s virtually a truism that consumption smoothing makes the multiplier bigger. After all, if you hold G and I fixed, then raising C via consumption smoothing raises GDP. Obviously I accept that. No need for algebra. However I don’t accept that investment would not change. If the fiscal multiplier is zero (as I believe), investment would fall to offset any rise in C due to consumption smoothing. Wren-Lewis simply ignores the change in I.

    I would add that in your example investment falls by 50 after the tax is imposed. In Wren-Lewis’s example there is no change in investment after the tax is imposed. In that case the games up, he’s assumed the multiplier is positive. There’s no argument, just an assumption.

    And I still don’t understand how you can question S=I. Both Krugman and Wren-Lewis agree with me that it’s an identity. Perhaps you should also critique their assertions. I simply pointed out that Wren-Lewis seemed to forget the identity when he talked about C falling less than disposable income, and yet investment being mysteriously unchanged. I made no behavioral assumptions, I just talked about what some equilibria might look like. You can use actual investment and saving for that purpose, and assume the identity is true.


  2. 2 Noah Smith January 16, 2012 at 10:50 pm

    David, if I ever meet you, I expect I will be incredibly surprised that you do not resemble the picture of R.G. Hawtree that adorns your blog…


  3. 3 Anthony T January 16, 2012 at 10:50 pm

    You’re wasting time and grey matter on Sumner. He is always going off on Krugman for some reason. I stopped reading him when he wrote a piece on why liquidity traps did not exist after Krugman wrote about it. Please turn your valuable intelligence towards the global economy.


  4. 4 Marcus Nunes January 17, 2012 at 2:18 am

    Scott forgot what he wrote in one of his very first posts:


  5. 5 Becky Hargrove January 17, 2012 at 2:50 am

    I’m going to re-read this post till it finally makes sense – no sleep tonight.


  6. 6 Kevin Donoghue January 17, 2012 at 5:51 am

    David, you’re a very patient man. I agree with most of your post but I quibble with this:

    “This is not your parent’s proof of the balanced-budget multiplier, in which consumption decisions are based only on current income without consideration of future income or expected tax liability. It’s a new proof.”

    Actually it’s not new. I don’t know where it originated, but certainly Paul Krugman and Brad DeLong both deployed this argument against the Lucas bridge-builder story, where in effect he said dY/dT has to be the same as dY/dG so the BBM=0.

    The main reason Simon Wren-Lewis deploys it is to make the point that opposition to fiscal expansion can’t be based solely on concerns about debt, since we see just as much opposition to a tax-financed increase in spending.


  7. 7 Scott Sumner January 17, 2012 at 6:56 am

    David, I have a new post up where I claim this proves I’m right.

    Et tu, Marcus? 🙂


  8. 8 nemi January 17, 2012 at 7:00 am

    I would agree that consumption smoothing increase the effect of fiscal policy given that the fiscal policy shorten the time it takes for a recovery – but I do not see how it can be true if e.g. fiscal policy do not have a effect on Y.

    In your scenarios, shouldn´t the consumption function without consumption smoothing be something like C(Y”shortrun”,T”shortrun”), and with consumptin smothening C(Y”longrun”,T”longrun”).

    Surely,dC/dT”shortrun” will be bigger for the first than the second, but should that not also be the case w.r.t. dC/dY”shortrun”?

    I.e, the new consumption function (with consumption smoothing) would rather stay as C = .5(Y – T) than turning to C = 10+.5(Y – T) for scenario 2′.

    PS: I firmly belive that fiscal policy would be effective, so I am asking beucase I do not understand.


  9. 9 John Hall January 17, 2012 at 7:43 am

    David, I think you have made an error.
    When you do the consumption smoothing, you need to adjust the formula so that before you add the taxes back it is consistent with the original equilibrium. In a world without government spending or taxes, the consumption smoothing equilibrium should equal the original one, if you really want to focus on the difference between them.
    So you would need to do is set up C=10+c(Y-T), and solve 10+cY+200=Y, when Y=400, the original equilibrium would have required c to equal 0.475.
    So then when you analyze G=100 and T=100, you get 10+0.475(Y-100)+150+100=Y => 212.5=Y(1-0.475) => Y=404.76, C=154.76, S=250 (the same saving you get in the last case).

    The above assumes that the adjustment to I is the same in both cases. However, it also shows an even smaller balanced budget multiplier of 0.05.


  10. 10 Barry January 17, 2012 at 8:48 am

    David: “I won’t bother with another encomium to Scott Sumner. But how many other bloggers are there who could touch off the sort of cyberspace fireworks triggered by his series of posts (this, this, this, this, this and this) about Paul Krugman and Simon Wren-Lewis and their criticism of Bob Lucas and John Cochrane? ”

    David, this is rather – well, dishonest. Just because Sumner can be spectacularly monetarist St Louisist wrong in an attention-getting manner, doesn’t mean that he’s a good economics blogger.


  11. 11 Benjamin Cole January 17, 2012 at 9:21 am

    Well, I hope we can present a Market Monetarist argument to the world, without endless diversions and contretemps.


  12. 12 Frank Restly January 17, 2012 at 9:36 am

    And this is why economics is in the Dark Ages. It completely ignores the role of finance – debt, interest rates, and equities – in essence it ignores contractual obligations of all types.

    When you start relating

    Nominal GDP = C (Personal Consumption Expenditures) + I (Business Investment) + G (Government Expenditures)


    National Income = Debt * (Real Interest Rate + Inflation Rate) + dD / dt (Change in Debt) + dEQ / dt (Change in Equity Valuation) + IL (Illiquidity Preference) * Debt + Taxes

    Then you are on to something. Note that taxes are a contractual transfer mechanism of sorts – you are obligated by law to pay taxes.

    National income falls when nominal interest rates are pushed to zero, when taxes are pushed to zero, when equity markets fall, and when illiquidity preference is low (liquidity preference is high).


  13. 13 David Glasner January 17, 2012 at 9:54 am

    Noah, It would be my pleasure. Feel free to contact me if you are ever in the DC area. There are actually at least two obvious characteristics that we share.

    Anthony, Thanks for the compliment. Krugman is a big boy, he can handle the attention. I don’t see why it’s a hanging offense to criticize Krugman on the liquidity trap. I have done it myself twice. See my posts Krugman and Sumner on the Zero-Interest Lower Bound: Some History of Thought and Krugman on Mr. Keynes and the Moderns.

    Marcus, Your knowledge of the Sumner oeuvre is quite remarkable.
    Becky, What a trooper you are!

    Kevin, Is “patient” by any chance a euphemism for some other adjective in the Donoghue lexicon? By “new” I meant compared to the original proof of the balance budget multiplier theorem, not that it had been recently stated for the first time.

    nemi, I am a bit confused. You are right that with consumption smoothing the change in consumption for a given change in taxes would be less than without consumption smoothing. There are many ways of changing the consumption function to reflect the effect of consumption smoothing I just chose a very simply one for illustrative purposes, not because it was derived from first principles. In doing so, I may have violated my own principle of not assuming changes in the model when they can be derived logically from some property of the model. John Hall below seems to think that I did. But you seem to say that the consumption function shouldn’t change at all. I don’t understand that.

    John, Thanks, good point. But I still need to think it through to make sure I understand it.

    Barry, Well, you are entitled to your opinion about, Scott, and I am to mine. My praise for Scott would only be dishonest if I didn’t believe what I wrote. And I assure you that I believe it entirely. Whether what I wrote was persuasive may be another matter, but that wasn’t really the point.


  14. 14 nemi January 17, 2012 at 1:03 pm

    Sorry – I got it wrong.
    I should think for two seconds before commenting.


  15. 15 Major_Freedom January 17, 2012 at 7:36 pm

    I don’t understand this fixation on goosing “spending” by government deficits.

    A higher nominal GDP through government deficits doesn’t mean the economy is being “stimulated” in the sense of leading to economic growth.

    Some incomes are consumptive, while other incomes are productive. It is possible for nominal GDP to rise and yet the economy shrinks in real terms, if a rise in consumption spending comes at the expense of investment spending.

    Since we cannot observe counterfactual worlds of what “could have happened”, single minded Keynesians and single minded Monetarists are going to be arguing at each other’s throats forever, debating what “could” have otherwise happened. Keynesians say the money would have just been sitting around, while Monetarists say the money would have been invested.

    The terms of the debate are all messed up.

    Even if nominal GDP is goosed by government deficits, it very well can come at the expense of productive investment spending. This is what Sumner is saying is possible, and yet you and so many other “No, all government spending comes from idle cash” ideologues simply deny it, and you’re falling over yourselves trying to manipulate stupid accounting tautologies all day long trying to refute Sumner on this incredibly obvious point.

    Just step back and think. If the government taxes people, then that means people have less money at their disposal. Agreed? OK, well then surely you must also agree that it is POSSIBLE that the people who are taxed, MAY have otherwise invested that money if they had control over their own money. Sure, they could have stuffed it under their mattresses too, but it’s a damn counterfactual for crying out loud. Nobody can say exactly what people would have done. If any of you deny that investment MAY have been sacrificed, then sorry, Sumner wins, because he’s clearly debating a bunch of blind moles who don’t know when they’re whacked. This is just basic verbal logic that the fixation on math and equations seems to confuse people over. Krugman ignorantly believes that it is verbal logic that leads people astray. But that’s just his positivist brainwashing. The OPPOSITE is the case. One sentence verbal logic wins:

    “If people are taxed, then they have less money at their disposal. Since money can be invested in principle, it means that it is possible that the taxpayers might have otherwise invested with it. Ergo, taxation MAY reduce investment.”


    At any rate, I have to ask why in the bleeding world is Sumner’s point about investment POSSIBLY being reduced on account of government taxation, how can that obvious point be challenged in any way by anyone who doesn’t have a hole in their head? It’s so incredibly obvious! You take my money, and boom, you don’t know what I would have done with it. That world is forever lost. But a possible world is me investing with it. Surely you cannot claim to know with 100% certainty that I would not have invested it. I mean I’ve heard dogmatic beliefs from people before, but that takes the cake. For it requires the person to be able to have knowledge of a world that doesn’t even exist. Are we economists or are we religious mystics with en eye to other dimensions?

    Please, David, for the love of everything holy, just concede Sumner’s painfully obvious point that taxation can POSSIBLY reduce investment. It’s not hard. Don’t worry, Keynesianism isn’t going to implode by making that concession. Yes, it requires you to view people as POSSIBLY non-hoarding forward looking abstainers from consumption. It’s so hard isn’t it? Government taxation and spending simply must have zero affect on investment, doesn’t it? Talk about dogmatic.


  16. 16 Mitch January 17, 2012 at 9:10 pm


    I have a bone to pick with your explanation here.

    You are using the term “equilibrium” to refer to a solution to the model, when in fact there is nothing dynamic in the equations you are discussing; they are just accounting identites – essentially just definitions of terms. One should distinguish between a “equilibrium” which refers to a static situation arising from a dynamic model, and a simple solution to a set of simultaneous equations with an ad hoc assumption that C = 1/2 Y or whatever. The solution you come to may or may not be an “equilibrium” in the sense that the system stays at that point.

    I think that this is an important point to keep in mind, because so many of economists seem to be thoroughly confused on this point. For example many seem to think that if they draw a supply curve and a demand curve, and note where the lines cross, that this is the place where the market must be at all times. However, they don’t seem to be very interested in the *dynamical* aspects of it. Suppose the market is *not* at that point. Suppose there is oversupply. What is the process by which the market comes back to clearing? If a price drop is needed, what is the *dynamics* of it?

    I said this in a comment on Krugman’s blog in response to the blog posting referencing you:

    “I find it amazing that so many economists seem to be unable to even conceive of a non-clearing market. Let’s state this: *In a recession* markets are not clearing, and there can be an oversupply. (Most notably, of course, there is an oversupply of labor, AKA unemployment.) Therefore, arguments based on the assumption that supply and demand are meeting are not going to work.

    “Therfore: (a) The government may be able to borrow without crowding out anyone else’s borrowing – there is an oversupply of funds to borrow. (b) The government can purchase without raising prices, because there is an oversupply of things to buy. (c) The government can hire people (or pay other people to do so) without raising wages because – wait for it – there is unemployment.”


  17. 17 David Glasner January 18, 2012 at 6:14 pm

    Scott, For some reason, the spam detector found your comments suspiciously spam-like. I wonder why. I had to rescue them myself from the spam folder. Why would you assume that ceteris paribus consumption smoothing would reduce investment? I reduced investment before consumption smoothing precisely to conform to the assumption of the exercise that we take BBM = 0 as our initial condition. This requires something happen to offset the increase in G and T to keep Y at 400. I chose for simplicity to reduce I by 50.

    You are right that you are in good company in making the gross mistake of treating E = Y and I = S as accounting identities. Keynes started that confusion and was properly put in his place by Hawtrey and Haberler and others. Nevertheless, that nonsensical proposition has taken on a life of its own despite the definitive and exhaustive refutation of the role of accounting identities by Richard Lipsey in his classic paper “The Foundations of the Theory of National Income” published exactly 40 years ago. Unfortunately, the lesson has still not been learned, and the notion that accounting identities have explanatory power continues to distort the teaching and, alas, sometimes the application of economic theory.

    Benjamin, You can’t expect people to agree all the time, even people who share the same basic outlook on economics and the economy. It is a sign of weakness not strength to be afraid of good-faith disagreements, even arguments. So my advice to you, Benjamin, is to lighten up.

    Frank, You obviously need a blog of your very own. What’s holding you back?

    Nemi, This is one big conversation. People don’t always think through everything they say before saying it. If they did there would be a lot of silence. How much fun would that be?

    Major_Freedom, And I don’t understand your fixation on not thinking through the implications of the models that we are working with. The point of this discussion is to understand the logic of a particular economic model and of an alternative to the model, not to genuflect before a particular moral or ideological policy imperative that some people have a prior commitment to. I was not advocating any particular policy, and I was not asserting that increasing taxes might reduce investment. You have no basis from the post that you are commenting on for drawing any conclusion about what my position is on taxes, so you have just wasted precious minutes of your own time and precious minutes of mine reading and responding to your entirely unnecessary outrage. Who knows what sort of productive activity was sacrificed by you and me as a result of your fevered comment?

    Mitch, You are right the simple model that I was working with was a one period model, so the solution was in the nature of what economists call “comparative statics” which is to compare two equilibria which differ only because a single parameter in the model has been changed. Given the numerical choice of parameters (e.g., the coefficient of Y in the consumption equation is ½), the solution of the model is an equilibrium with no tendency to change. Whether the model is any good is an entirely different question. Too much may have been left out of the model for one to be satisfied with the notion that any solution to the model would correspond to a plausible economic equilibrium. You are right that the notion of market clearing is a difficult one to apply and that drawing supply and demand curves as if they were real entities and identifying the point of intersection as something observable in the real world is problematic. I think that part of the problem lies in the fact that when we look at a supply and demand curve for a particular market, the implicit assumption is that all other markets are in equilibrium. It is then straightforward to analyze the particular market under consideration and draw appropriate conclusions based on that assumption. In situations of widespread unemployment, the implicit assumption underlying conventional microeconomic analysis that all markets but one are in equilibrium is clearly not appropriate, making conclusions of micro-level analysis less conclusive than we like to think.


  18. 18 Daniel Alexander January 18, 2012 at 7:04 pm

    Does graduate and post graduate study of economics revolve around reading and responding to each other’s blogs? 😉
    -an undergraduate economist.


  19. 19 Becky Hargrove January 19, 2012 at 8:26 am

    David, at least one commenter at Krugman’s above link thought yours was the definitive post. And under all the squabbling, surely some ‘rigor’ exists that is now better understood. However it is interesting that this long discussion stemmed from the potential effects of building a physical bridge, i.e. one that could be seen and touched. Interesting, because not long ago, there were several commenters hoping for bridge building of a slightly different sort: bridges between the schooled and ‘partially’ schooled for societal solutions. I now refer to such thoughts as ‘A Bridge Too Far’, not unlike that place where people had to go where they could be shot out of the water when the fog lifted, and wonder what the crazy people running around in the woods were really saying!

    Perhaps what I’m saying is there’s no need to give up on the bridge of societal hopes, it may just mean waiting a little longer before that can really be considered. (In the meantime civilization probably won’t be the worse for it if you get out a little more)


  20. 20 Scott Sumner January 19, 2012 at 7:31 pm

    David, Your span filter probably weeds out denials of a positive multiplier.

    The question of whether S=I is not like does E=MC2. It’s a definitional question. If all the textbooks now say S=I is an identity, then it is an identity. At least right now. Perhaps it wasn’t true in the 1920s, because the terms were defined differently. But right now saving is defined as simply the funds used on investment.

    For the same reason, one cannot debate whether GDI “actually” equals GDP, as they are defined to be equal. And the current account surplus is defined as national saving minus national investment. Again, it is an issue beyond dispute. Simply definitional.

    I await your post demolishing Karl Smith. 🙂


  21. 21 David Glasner January 19, 2012 at 8:13 pm

    Scott, Well then we showed the son of a gun who’s boss, didn’t we? You must read Lipsey’s paper. S=I is an equilibrium condition, not a definition. If you insist that it is a definition, you turn the Keynesian model into incoherent nonsense. It may be nonsense, but it’s not incoherent.


  22. 22 David Glasner January 20, 2012 at 8:38 am

    Daniel, Sorry, can’t help you with that one. My academic career ended well before the internet age. You should probably check with whatever graduate programs you are interested in to find out how they run things. But I would be surprised if they don’t expect you take basic theory and math courses, which aren’t that heavily blogged about.

    Becky, But we are only theorizing about a real bridge. As for getting out more, sorry, but I don’t think i can risk it. Too much is at stake.


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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. 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.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner


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