It’s tough to argue against an identity

I guess I shouldn’t have been surprised.  For three years conservatives have been coming over here and sneering that I was just trying to force people to spend more. Each time I patiently pointed out that I want more spending, but not more consumption.

Nevertheless, the last few days have been a real eye-opener.   The comment sections contained a torrent of attacks against my novel S=I claim.  Eventually people started quoted textbooks by Krugman and Mankiw, which also claimed it was an identity. But there was still a lot of grumbling, as there always is when you try to throw tautologies at people in an argument.  If it’s just a tautology, what difference can it make?  In this post I’d like to explain why it’s essential to think of saving as spending on capital goods, not as setting money aside.  And I’ll also show that even Nobel Prize winners can make elementary errors by forgetting this identity.  I’m going to rehash the Wren-Lewis/Krugman mistake, because I don’t think I explained it effectively in this post.  Here’s how Simon Wren-Lewis criticized Bob Lucas and John Cochrane’s claim that when the government builds a bridge using tax money, the balanced budget multiplier might be zero:

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.

But surely very clever people cannot make simple errors of this kind?

Then Paul Krugman cited the Wren-Lewis quotation with approval:

Yes indeed. A lot of people have been clutching their pearls over my (and Brad’s) simple statement that Lucas/Cochrane made simple, fail-an-undergrad-quiz-level, errors. To say that they did what they did is a “rant.” But the truth is that they did — and have refused to admit those errors, which is worse.

Undergraduate quiz?  He’s going to bitterly regret that snide remark.

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.  Checkmate in four.

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.  Checkmate in three.

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.  Checkmate in two.

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.  Checkmate in one.

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.  Checkmate.

I think Wren-Lewis and Krugman both made the same mistake as those angry Austrians that complained I was trying to goose up “spending”.  They momentarily forgot that saving is not money down a rat hole, but rather represents spending on capital goods.  They were so overconfident that anti-Keynesian arguments are bogus that they momentarily let down their guard, and employed a bogus argument themselves.

Of course it’s very possible that investment would not fall, it’s very possible that AD would rise by the amount of the spending on the bridge.  But you can’t get from here to there by employing a consumption smoothing argument against Cochrane.  After all, consumption smoothing is a part of the classical model, and the multiplier is zero in many versions of the classical model.  (Not all, there are classical models where wasteful expenditure makes the public poorer, and hence they work harder–Larry Sjaastad did a model like that way back in the 1970s.)

So Wren-Lewis and Krugman used the common sense notion that saving is money set aside and not “spent” and ended up making a simple error.  I used the idea that saving is nothing more than spending on capital goods and got the right answer.  Do you still think tautologies are useless?

Of course Nick Rowe has an even better idea, instead of obsessing over S=I, let’s drop saving completely out of business cycle theory.  After all when it looks like saving is depressing the economy, the real problem is money hoarding.  He’s right.  Saving, income, inflation, RGDP, interest rates; Nick and I could write a textbook that stripped all the inessentials out of macro.  Monetary policy controls M*V, and unexpected shocks to M*V causes fluctuations in hours worked because of sticky wages.  Replace the welfare cost of inflation with the welfare cost of fast NGDP growth.  Real wages become relative wages (W/NGDP per capita.)  Business cycle and “inflation” theory in 2 pages.  That’s not Occam’s razor, that’s Occam’s chainsaw!

There’s been a recent debate over etiquette in the blogosphere.  Tyler Cowen says we should try to be civil, and try to imagine the best argument the other side might be making.  Brad DeLong and Krugman insist that when the other side says something that you think looks foolish, you should call them ignorant.  I can’t imagine there being any serious question over who’s right, but in case there is consider the following.  Krugman recently bragged that he doesn’t read right-wing blogs.  This means that on the rare occasions when he makes a mistake he doesn’t find out, but rather keeps on repeating the mistake over and over again.  This allows conservatives who hate him to simply write him off.

I think conservatives are making a big mistake, as Krugman is brilliant—and you always want to be aware of the best arguments the other side has to offer.  But if Krugman were a bit more humble, and occasionally said he was wrong in attacking Cochrane, he’d have a much better change of convincing the other side.  So in an odd way I think both Krugman and DeLong, despite being incredibly bright and talented bloggers, are their own worst enemies.

And I think Chicago school economists made the same mistake in criticizing the Keynesian model–they simply assumed they could brush it away because for decades people had pretty much given up on fiscal stimulus.  Thus they underestimated the sophistication of modern “liquidity trap” arguments for fiscal stimulus.  In the end I don’t find those arguments convincing either, but I don’t think anyone reading this blog could deny that I’ve thought long and hard about the Krugman/DeLong/Thoma/Yglesias/Avent argument for stimulus.  I take their arguments very seriously indeed.

Now where the hell did I leave that f****** pearl necklace I was going to wear tonight . . .

Update: I see Paul Krugman has responded to this post, and of course completely distorted my argument.  I actually do understand the basic mechanical Keynesian model, believe it or not.  He also completely ignores the criticism I actually did make of the Wren-Lewis quotation that he endorsed.  I have a new post that responds in detail here.


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86 Responses to “It’s tough to argue against an identity”

  1. Gravatar of libfree libfree
    13. January 2012 at 12:45

    I’m pretty sure that Krugman wrote an entry not long ago where he claimed that liberals understand and can make the conservative argument but that conservatives don’t understand the liberal view. I’m pretty sure you could pass the Ideological Turing test Scott.

    Bryan Caplan has the relevant quotes.
    http://econlog.econlib.org/archives/2011/06/the_ideological.html

  2. Gravatar of Rajat Rajat
    13. January 2012 at 12:46

    “Replace the welfare cost of inflation with the welfare cost of fast NGDP growth.”
    Scott, you may have covered this in your post against ‘inflation’ last year, but if wages are sticky, why only recommend an NGP target of 5% (plus catchup)? Why not an NGDP target of 10%? This would reduce the risk of deflation even further. Is it because you think it would be even less palatable than 5% or is it because you think average inflation of 7-8%pa would be harmful?

  3. Gravatar of marcus nunes marcus nunes
    13. January 2012 at 13:06

    This is a longer paper by Wren-Lewis from which he based his arguments:
    http://www.economics.ox.ac.uk/members/simon.wren-lewis/docs/nier_final.pdf

  4. Gravatar of Ken Ken
    13. January 2012 at 13:07

    Great stuff. If you ever charge for this stuff, I’m signing up.

    One question (or set of related questions):

    To be clear (for the students out there like me), according to your definitions, when an individual hoards cash, they are NOT saving? In other words, putting money in the piggy bank is NOT a form of saving? Is that the standard definition? Or perhaps an individual CAN save this way, but in aggregate a society cannot save in this way? I’m guessing that has been my confusion (or one of many)…

  5. Gravatar of TravisA TravisA
    13. January 2012 at 13:21

    Finally, I understand your argument. Well done. You and Nick Rowe are doing yeoman’s work in educating us in economics. Thank you to you both.

  6. Gravatar of Kevin Donoghue Kevin Donoghue
    13. January 2012 at 13:32

    If the problem involves a tax-financed increase in G, wouldn’t it be a good idea to have taxes T (or a tax-rate t) appear explicitly in your exposition? It’s not clear to me why C falls. You refer to a reduction in after-tax income: but if C is a function of disposable income, G-T, and c is the marginal propensity to consume, dC = c.(dG-dT) = 0.

    You know that of course so evidently I’m not following your argument.

  7. Gravatar of Andrew C. Andrew C.
    13. January 2012 at 13:44

    I accidentally posted this in the earlier thread. I hope people don’t mind the double entry:

    I’m probably going to regret making this comment (I’m moving into broken-record territory), but this whole issue becomes extremely lucid when you use IS-LM. What Krugman/Wren-Lewis are saying is that people’s propensity to save is less than 1 so on net the government’s policy shifts the IS curve to the right. What happens to output, as Scott has said, depends on monetary policy. If the fed is targeting interest rates, then the LM curve is flat – so the balanced budget multiplier is greater than 0. If the fed targets the money supply then the LM curve is upward sloping and interest rates rise a little crowding out some investment, but the policy is still modestly expansionary. If the fed targets NGDP, then LM is vertical, and all this is a moot point.

  8. Gravatar of ssumner ssumner
    13. January 2012 at 14:05

    Thanks libfree.

    Rajat, Higher NGDP growth is a tax on capital, because it leads to high nominal returns on investments, and our investment income tax code is not indexed. That’s why the stock and bond markets did so poorly during the Great Inflation of 1966-81.)

    Thanks Marcus.

    Ken, Complicated question. If you take cash from someone else, you save more but they save less. The interesting question is what happens if the public as a whole hoards cash, and hence real cash balances rise.

    1. If cash is viewed as government debt, then the cash holder’s saving is exactly matched by government dissaving.

    2. If cash is viewed as a sort of paper gold, a capital asset that provides a flow of transactions services, then you can argue that more money hoarding means a bigger capital stock. The key is to be consistent in your assumptions.

    BTW, the yearly increase in real cash balances is generally pretty small. ERs now earn interest, and are definitely government debt. Bank accounts are debt, not capital.

    Thanks Travis A.

    Kevin, I should have been more explicit:

    C + I + G = C + S + T. Since we assume that delta G equals delta T (balanced budget multiplier), we can also assume that the change in after-tax income (delta C + S) is the change in private output (delta C + I).

    Note S and I are private saving and investment, so they need not be identical. But in this case the change in the two is identical because with the balanced budget multiplier assumption there is no change in government saving.

  9. Gravatar of ssumner ssumner
    13. January 2012 at 14:06

    Andrew, I find IS-LM to be very non-intuitive, but at first glance what you say sounds right to me.

  10. Gravatar of Steve Steve
    13. January 2012 at 14:07

    So Paul Krugman has a bridge to sell us. But if he had the Fed print the bridge, all would be fine.

    On a serious note, it’s important to remind laypersons that the “economist’s S” = I. Most people in business or consumer economics think of saving as money in the bank or under the mattress, i.e., money hoarding. They also think that money hoarding is morally virtuous and should be rewarded with above zero interest rates. So it’s really important for you preface your discussions with the reminder that money hoarding isn’t S.

  11. Gravatar of Simon Wren-Lewis Simon Wren-Lewis
    13. January 2012 at 14:10

    Your penultimate move: I did not forget that saving is the same thing as spending on capital goods, because it is not. Your final move: two mistakes here. You have output/income rising by 80, so after-tax income falls by 20, which is the same as the fall in planned consumption when income was expected to fall by 100, so you say no consumption smoothing and checkmate. First, consumption smoothing is about consumption plans, not outturns. Second, you are wrong to stop there. Consumers now change their plans, because they smooth: keeping proportions the same, they cut consumption by 4, not 20 and we iterate on. Anyone who has done first year macro will recognise the balanced budget multiplier. We get expansionary fiscal policy because of consumption smoothing.

  12. Gravatar of Master of None Master of None
    13. January 2012 at 14:16

    How about an expanded identity equation that explicitly includes money hoarding?

    C + I + money hoarding + G = AD + money hoarding = Real GDP = (nominal gross income + money hoarding)

    Is that right?

  13. Gravatar of Brian in Cleveland Brian in Cleveland
    13. January 2012 at 14:16

    Professor Sumner,

    Great post, I am a big fan of this blog (never commented before, so I apologize if I am way off base on anything here). Is it possible that there is a time lag element of the transition of S into I? For example, if my (and 1 million others’) taxes increase $100 in a month for the $100 million to fund the bridge, how immediate would the decrease in S (and hence, I) be felt in comparison to the benefits of the increase in G? What I am asking is doesn’t it take some time for the identity of S=I to fulfill itself? If 1 million of us deposit $100 into our savings accounts, won’t it take time for that money to be transitioned into I in the form of loans (for housing, in your example)? Maybe there is an S=I time smoothing effect? If so, does it matter in terms of positive GDP growth in the very short run that resulted from increasing G?

    Thanks again for all your insights. I am admittedly a fan of Paul Krugman as well, and I would thank you both for the great service you provide to your readers (non-economists like myself included).

  14. Gravatar of Kevin Donoghue Kevin Donoghue
    13. January 2012 at 14:26

    Sure Scott, but since disposable income is Y-T there’s no change there; hence no obvious reason for a change in C. As for I (and hence S, since we’re talking about realized outcomes here, not schedules), that has no reason to fall either.

    Now I’m certainly not saying that the balanced-budget multiplier can’t be zero or negative. (If unemployment is low I’d even say it must be.) But you need some behavioural assumptions to get that result. I’m not seeing what your assumptions are and you really seem to be saying you don’t need any.

    Perhaps your reply to Andrew is the clue? The central bank is assumed to sabotage the fiscal expansion? But neither Krugman nor Wren-Lewis would dispute that it can, so that’s a nothing-burger.

  15. Gravatar of Brett Sheckler Brett Sheckler
    13. January 2012 at 14:44

    Scott.

    I think what Andrew is arguing is that Paul and Brad are right, except in the event that the Fed chooses to row in the opposite direction.

    I will leave it to Paul (unlikely) or Brad (more likely) to defend their position in the terms you are arguing. I have to say, though, that it seems to me your argument is that it is not possible to expand AD through an net expansion of debt, and I find that argument impossible to swallow.

    Say I get sick of riding my bike in the rain so I go out and borrow $30k to buy a car. The banking system cuts a check and then turns around and deposits the check in the auto dealer’s account (we use the same bank). Voila, we just expanded C, AD, and GDP in year 1.

    As far as I can see, and as Andrew points out, the only way that is not the case is if the Fed is pursuing NGDP targeting (and are hitting their target) so they take action to counteract my expansion of my year-1 purchasing power.

  16. Gravatar of D R D R
    13. January 2012 at 15:12

    WRONG! WRONG! WRONG!

    You do not get to take the tax side of the argument exclusively. Where is the $100 of additional income resulting from the production?

    Just because taxes reduced disposable income by $100, does not mean a tax-financed bridge reduces disposable income by $100.

    You assumed a closed economy, so you didn’t import it. It must have been built domestically, and someone domestically got paid to build it.

  17. Gravatar of D R D R
    13. January 2012 at 15:28

    “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. Checkmate.”

    It’s only checkmate if the check cannot be removed. Proof by example doesn’t work unless you are exhaustive in your examples.

    Maybe C does not change, and neither does I. Then what? There is only “no consumption smoothing” because disposable income is unchanged. But GDP is still up $100 million.

  18. Gravatar of Andy Harless Andy Harless
    13. January 2012 at 15:35

    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.

    I don’t see how you get this.

    Start with a linearized consumption function

    C = a + b(Y-T)

    where b<1 because of consumption smoothing, or in your example b=.2 specifically.

    Now substitute into the closed-economy national income identity

    Y = a + b(Y-T) + I + G

    Now solve for Y

    Y = (a – bT + I + G) / (1 – b)

    Now hold I constant and increase G and T each by 100.

    Y increases by 100, which is exactly offset by the increase in T, so that Y-T is unchanged, and C is unchanged.

    So private after-tax income is unchanged, and there is, in aggregate, nothing to smooth.

    But individual households were smoothing. Some households received more after-tax income because they were hired to produce the additional 100 units of G, or because they were hired to produce consumer goods for those who received that income, or for those who were hired to produce those consumer goods, etc.. All of these households consumed only 20% of their extra net income. Everyone else received less after-tax income because their taxes were higher. They reduced their consumption by only 20% of their reduction in after-tax income. And the amount of additional consumption by the newly hired just offset the amount of reduced consumption by the newly taxed.

  19. Gravatar of D R D R
    13. January 2012 at 15:41

    Put another way, you cannot assume autonomous investment halfway through the analysis.

    If I is assumed fixed from the outset, and G is assumed to grow by $100 million, and taxes are assumed to grow by $100 million, then disposable income grows by the change in consumption. Therefore, consumption smoothing implies no fall in consumption!

  20. Gravatar of TheMoneyIllusion » Simon Wren-Lewis digs a deeper hole TheMoneyIllusion » Simon Wren-Lewis digs a deeper hole
    13. January 2012 at 15:45

    [...] Simon Wren-Lewis, Professor of Economics at Oxford, responds to my recent post with 5 arguments, none of which are persuasive: Your penultimate move: I did not forget that saving is the same thing as spending on capital goods, because it is not. [...]

  21. Gravatar of TravisA TravisA
    13. January 2012 at 16:50

    @Andy Harless: I think Scott is assuming that the economy is at maximum potential. If G increases, Y is unchanged, because the increase in G takes away resources from other areas of the economy. If I stays the same, the only place where the resources can come from is C.

  22. Gravatar of ssumner ssumner
    13. January 2012 at 20:10

    Steve, Yes, I should probably do that.

    Simon, Thanks for commenting. I have a new post that responds to your comment.

    Master of None, No, RGDP isn’t NGDP plus money hoarding. Money hoarding isn’t really involved in this dispute, except perhaps that in some models Keynesian stimulus assumes a velocity speed up.

    Brian, No, if it’s an identity there cannot be any time lag. When you save in a financial sense, someone else is borrowing, so there is no net change in national saving. Only when physical capital is produced does national saving go up.

    I realize this is counterintuitive, as it doesn’t at all seem that way at the individual level.

    Kevin, I don’t see why you assume no change in income. After tax income falls by 100–that’s a good reason for people to spend 100 less on consumer and capital goods; they have less money to spend.
    I could provide 100s of real world examples. Say interest rates rise and I falls. Or say say G goes up by 100 because the government takes over more of health care. Then private health care expenditures might fall by the amount of the tax increase. Obviously bridges seem less like C than health care, so it’s harder to make an intuitive argument. And I’d never deny that income might rise, you might not have 100% crowding out. But consumption smoothing has nothing to do with it, as it pretends that money saved simply disappears, whereas in reality S=I.

    As I said if the government wastes the money people will want to work harder, even in a classical model. So measured GDP will rise, but of course living standards will fall (WWII is an example). Not a strong argument for stimulus!

    Brett, you said;

    “I will leave it to Paul (unlikely) or Brad (more likely) to defend their position in the terms you are arguing. I have to say, though, that it seems to me your argument is that it is not possible to expand AD through an net expansion of debt, and I find that argument impossible to swallow.”

    Absolutely not. I never made that argument in my life. I’m saying Wren-Lewis is wrong, not Cochrane is right. Indeed I recently did a post showing that if you accept the basic Keynesian model, you can get higher NGDP from fiscal stimulus under either a constant money supply or a constant interest rate. But these arguments have nothing to do with consumption smoothing.

    You said;

    “As far as I can see, and as Andrew points out, the only way that is not the case is if the Fed is pursuing NGDP targeting (and are hitting their target) so they take action to counteract my expansion of my year-1 purchasing power.”

    I’m afraid this is wrong. If the Fed follows inflation targeting, or the Taylor Rule, or just about any plausible new Keynesian policy you get a zero multiplier. (at least in theory, obviously in the real world the number would differ depending on the monetary policy errors.) And I haven’t even gotten in to other arguments Cochrane could make:

    1. Crowding out
    2. Fear of future tax increases depressing animal spirits.
    3. Substitution of public goods for private goods.
    4. Higher taxes make the demand for currency rise, due to tax evasion. That’s deflationary BTW.
    5. etc.

    People need to realize that Keynesian economics is just a model. There’s really not that much empirical evidence for fiscal stimulus “working.”

    DR, Yes, the people who previously produced the 20 in C and 80 in I switched over and built the bridge. So total national income was unchanged and disposable income fell by 100.

    You said;

    “Maybe C does not change, and neither does I. Then what? There is only “no consumption smoothing” because disposable income is unchanged. But GDP is still up $100 million.”

    For the millionth time, I didn’t say fiscal stimulus doesn’t boost GDP, I said the consumption smoothing argument is nonsensical. It has nothing to do with the issue. It doesn’t “refute” Cochrane.

    Andy, Sure, You can simply assume the Keynesian model is right, but consumption smoothing played no role in your example. Make the MPC 90% instead of 20% and you get the same result. It’s nothing more that setting up a model with a balanced budget multiplier of one built in. But that’s what’s being debated. Cochrane denied the model, and Wren-Lewis responed in a way that was either completely wrong (most likely), or that was right by assumption, in which case consumption smoothing played to role.

    I am pretty sure almost everyone reading his post assumed he really meant to consider a case where aggregate C declined modestly because of consumption smoothing. Otherwise it makes as much sense as pulling out all the old Keynesian hydraulics and then saying “assuming the population is composed of redheads we can see that the balanced budget multiplier is one.” What do redheads have to do with it?

    DR, You said;

    “Put another way, you cannot assume autonomous investment halfway through the analysis.”

    Excuse me, he’s the one that assumed saving declined in response to the tax increase, because of “consumption smoothing”, not me. Blame him, not me.

    TravisA, No actually I’m not making that assumption. I can’t say whether Cochrane was.

  23. Gravatar of Rob Rob
    13. January 2012 at 20:15

    There is something I’m not quite getting that maybe you can clarify (perhaps I just didn’t read the post carefully enough)

    Both MMists and Keynesian have in common the view that the recession is caused by deficient AD, and at the root of that deficient AD is high cash balances being held.

    Surely when Simon Wren-Lewis talks about a tax increase not leading to a corresponding fall in spending he means that people will reduce their cash holdings. Is that not something that MMist would agree with ?

  24. Gravatar of D R D R
    13. January 2012 at 20:43

    Scott says:

    “Yes, the people who previously produced the 20 in C and 80 in I switched over and built the bridge. So total national income was unchanged and disposable income fell by 100.”

    That is one hidden assumption now exposed. I say instead that the people who built the bridge were previously watching American Idol. So total national income rose by 100 and disposable income was unchanged.

  25. Gravatar of D R D R
    13. January 2012 at 20:44

    Scott says:

    “Excuse me, he’s the one that assumed saving declined in response to the tax increase, because of “consumption smoothing”, not me. Blame him, not me.”

    First of all, that is not what he said. He said consumption declined in response to the tax increase. Big difference. Now, if consumption declined in response to the tax increase, than means that disposable income must have fallen in response to the tax increase. That in turn means that C+I must have fallen in response to the tax increase. That in turn means that I must not have grown more than C fell in response to the tax increase. But I may have increased, and therefore private savings may have increased.

    Second, the response to the tax increase is only half the story. What is the response to the building of the bridge? Just because C is assumed to fall in response to the tax increase doesn’t mean there is not an increase in C in response to the building of the bridge.

  26. Gravatar of ssumner ssumner
    14. January 2012 at 07:02

    Rob, You said;

    “Surely when Simon Wren-Lewis talks about a tax increase not leading to a corresponding fall in spending he means that people will reduce their cash holdings. Is that not something that MMist would agree with ?”

    Yup, that’s what he should have said. And if you read Cochrane’s longer paper on fiscal stimulus you quickly find similar statements. They aren’t that far apart.

    DR, You said;

    “That is one hidden assumption now exposed. I say instead that the people who built the bridge were previously watching American Idol. So total national income rose by 100 and disposable income was unchanged.”

    That might be right, it’s a pity Wren-Lewis didn’t explain why Cochrane’s view was wrong.

    You said;

    “First of all, that is not what he said. He said consumption declined in response to the tax increase. Big difference. Now, if consumption declined in response to the tax increase, than means that disposable income must have fallen in response to the tax increase. That in turn means that C+I must have fallen in response to the tax increase. That in turn means that I must not have grown more than C fell in response to the tax increase. But I may have increased, and therefore private savings may have increased.”

    You are still missing the point. He didn’t just say that consumption fell in response to the decline in after tax income, he said consumption smoothing occurred, which means it fell much much less than after-tax income fell. And that means private saving and investment fell much more than consumption.

  27. Gravatar of D R D R
    14. January 2012 at 09:21

    Scott,

    “That might be right”

    So, the argument, then, is not accounting identities at all, but whether there is unemployed labor which may be put to productive use.

  28. Gravatar of D R D R
    14. January 2012 at 09:37

    Scott,

    “You are still missing the point. He didn’t just say that consumption fell in response to the decline in after tax income, he said consumption smoothing occurred, which means it fell much much less than after-tax income fell. And that means private saving and investment fell much more than consumption.”

    I am sorry, but that is a most uncharitable reading. Here is the actual sentence… “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.” He is obviously writing about just the effect of the tax hike. How am I so sure? The sentence previous discusses the effect of the government expenditure. The sentence following begins “Put the two together and…” This is just not disputable.

    This does not mean that Wren-Lewis does not employ consumption smoothing in response to the building of the bridge as well.

    Unfortunately, I was also a bit sloppy in my last rundown as well. For that I apologize. Y-T=C+I-T for the tax hike. It is I-T which must fall along with C. If, for example, you say a rise in T of 100 induces C to fall by 20 and C+I-T to fall by 100, then C+I does not change. Thus, I rises by 20. Sure, consumption smoothing reduced consumption and private saving, but investment rose because public saving more than offset the fall in private saving.

    Again… that is just the tax hike.

    What if we include the G +100? If C and I are both unchanged, then Y rises by 100, and disposable income is unchanged. So, true, there is no *disposable* income to smooth, which is consistent with C remaining unchanged. But Y still rises by 100, so the overall multiplier is still 1.0. We get a bridge “for free” (because we are ignoring, for example, the increased labor)

  29. Gravatar of ssumner ssumner
    14. January 2012 at 10:01

    DR, If consumption didn’t fall by less than after tax income, then it would be literally possible for consumption smoothing to have occurred at all.

    You said;

    “Sure, consumption smoothing reduced consumption and private saving, but investment rose because public saving more than offset the fall in private saving.”

    How can public saving have risen? The entire debate concerns a balanced budget multiplier, which assumes public saving is constant. I just don’t get where you are coming from.

  30. Gravatar of D R D R
    14. January 2012 at 10:09

    Scott, this is all very very clear.

    You say we were talking about the balanced-budget multiplier. Which is true only up to a point. You took a statement by Wren-Lewis which referred quite clearly to the tax hike in isolation. I said, the tax cut in isolation led to an increase in investment.

    I then went on to discuss what happens when you include the government expenditure. Notice that I said that when you include the government expenditure (that is “balanced budget”) then investment is *unchanged*

    It’s not that difficult.

  31. Gravatar of D R D R
    14. January 2012 at 10:30

    Scott says:

    “If consumption didn’t fall by less than after tax income, then it would be literally possible for consumption smoothing to have occurred at all.”

    I assume there is an editing error here. In any case, I have no idea to what, specifically, this is a response. Please provide some context.

    Thanks.

  32. Gravatar of Es Es
    14. January 2012 at 11:55

    Comment on style, not arguments – dont let yourself turn into another arrogant Krugman, you can do bettter!

  33. Gravatar of D R D R
    14. January 2012 at 13:04

    Oops.

    Sumner makes an assumption leading to his declaration “Checkmate in two.” He said, “If taxes reduced disposable income by $100 million, then Wren-Lewis is arguing that consumption would only fall by $20 million.” That is, he assumes that disposable income is smoothed in consumption by a factor of five.

    That is fine, but *only* if by that he means “taxes, in isolation of the government expenditures.” If the expenditures raise income, and therefore disposable income, then on the whole, consumption may not fall by as much as $20 million.

    For example:
    C -10
    I -40
    G +100
    T +100

    so

    Y +50
    Yd -50
    Sp -40
    Sg +0
    S -40

    We still have taxes reducing disposable income by $100 million, but consumption fell by only $10 million.

    Sorry, Scott.

  34. Gravatar of D R D R
    14. January 2012 at 14:01

    The fact is, we arrange for any multiplier at all, even if we smooth consumption. If the multiplier is m, then…

    C +20*(m-1)
    I +80*(m-1)
    G +100
    T +100

    Y +100*m
    Yd +100*(m-1)
    Sp +80*(m-1)
    Sg +0
    S +80*(m-1)

    If I may summarize…

    1) Cochrane says m=0 (though not necessarily in this fashion)

    2) Sumner suggests that Wren-Lewis implies that m=0. I think this requires an unwarranted leap of logic, because m=0.5 works just fine. (I think m=1 better fits Wren-Lewis’ text, but I can afford to be generous to Sumner and have consumption fall overall.)

    3) Sumner says if m=1, then Yd does not change. I don’t see how this matters, as Y would still rise by 100.

  35. Gravatar of ssumner ssumner
    15. January 2012 at 07:10

    DR, You asked what this was in response to:

    “If consumption didn’t fall by less than after tax income, then it would be literally possible for consumption smoothing to have occurred at all.”

    I meant impossible, not possible. It was in response to my comment below and your disagreement:

    ““You are still missing the point. He didn’t just say that consumption fell in response to the decline in after tax income, he said consumption smoothing occurred, which means it fell much much less than after-tax income fell. And that means private saving and investment fell much more than consumption.”

    I am sorry, but that is a most uncharitable reading.”

    Es, Thanks for the suggestion. Is there anything here that’s objectionable? Unlike Krugman I don’t think I call those I disagree with idiots.

    Regarding your examples, I agree those could occur. But the burden of proof is on Wren-Lewis to show why the zero BBM can’t occur. He claims it can’t occur because of consumption smoothing, that’s flat out wrong. Consumption smoothing doesn’t get you a positive BBM, unless you already assume a positive BBM for some other reason.

  36. Gravatar of D R D R
    15. January 2012 at 07:54

    Scott,

    If that is what you are responding to, then you are not making sense in your response. To wit, your argument is as follows:

    a1) The private sector smooths consumption *overall*
    a2) Consumption falls overall

    If a1 and a2, then disposable income must fall *overall*.

    I ask, so what?

    The problem is manifold. One, you uncharitably read Wren-Lewis to say that consumption fell overall, and so even though “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.” clearly implies this is the effect of just the taxes, and not inclusive of the government spending, you choose to read it otherwise.

    Two, if you insist on this uncharitable reading, C-10, I-40, G+100, T+100 yields smoothed consumption and, contra Cochrane, a positive multiplier.

    Three, if you do not insist on this uncharitable reading, C+0 does not violate a1… it violates a2. There is no failure of accounting, and there is no failure of logic. It is true that there is no disposable income to smooth, but so what? That only matters if you make the uncharitable reading.

  37. Gravatar of D R D R
    15. January 2012 at 08:14

    Scott…

    “Regarding your examples, I agree those could occur. But the burden of proof is on Wren-Lewis to show why the zero BBM can’t occur. He claims it can’t occur because of consumption smoothing, that’s flat out wrong. Consumption smoothing doesn’t get you a positive BBM, unless you already assume a positive BBM for some other reason.”

    You cannot be serious. Cochrane claimed his was a proof that the BBM is 0. The burden of proof on Wren-Lewis is to show that a positive BBM CAN occur.

    The major hurdle is that we have no idea how Cochrane arrived at his results. There is no way to prove him wrong until those assumptions are laid out. Nor is there a way to argue for more plausible assumptions until Cochrane’s assumptions are known. Thus, Cochrane’s “proof” is mere assertion.

    Similarly, I understand your dissatisfaction with Wren-Lewis. I laid out how *any* assumed multiplier, along with consumption smoothing, is consistent with the accounting. I also laid out how a positive BBM along with consumption smoothing *and falling consumption* is still consistent with the accounting. These are all arguments showing weaknesses in Cochrane’s argument. (Of course, they are not disproving, because there is no proof to argue against.)

  38. Gravatar of DrJim DrJim
    15. January 2012 at 08:29

    The Keynesian S and I are not the same as the national income S and I. The IS curve represents equality of desired investment and desired savings and is an equilibrium condition, not an identity. The national income accounts include non-desired and unplanned components. For example, unplanned inventory accumulation due to an unexpected shortfall in demand is counted as investment in the national income accounts but is certainly not part of what a Keynesian, or a non-economist, would call desired investment. Econ 1 students and economists who don’t (want to) like Keynes routinely confuse the two definitions. But Keynes’ usage is the more natural; it is the national income usage that is unintuitive.

  39. Gravatar of Kevin Donoghue Kevin Donoghue
    15. January 2012 at 09:56

    Scott,

    To assume that a tax-financed bridge costing $100m reduces disposable income by $100m is tantamount to assuming a balanced-budget multiplier of zero. You’re setting up the chessboard to suit yourself. I could wipe the floor with Kasparov if he let me do that.

    D R is quite right about the burden of proof. Neither Krugman nor Wren-Lewis denies that there are models with a balanced-budget multiplier of zero. But that merely means that Keynesian models could be wrong, not that they are. Lucas and Cochrane are the ones accusing Keynesians of using “schlock economics” without presenting anything in the way of a coherent case. What are their critics supposed to do, politely request clarification and wait years for a reply?

    As for your “novel S=I claim” the best I can say is that it’s partly valid and partly novel. Sadly the set, {Points on which it is both valid and novel} = {the Null set}.

  40. Gravatar of Mayson Lancaster Mayson Lancaster
    15. January 2012 at 10:20

    Of course, in a liquidity trap like the present situation, when government spending rises by $100 billion, private sector spending does not fall by $100 million, but rises.

  41. Gravatar of Merijn Knibbe Merijn Knibbe
    15. January 2012 at 11:16

    My problem is with the ‘aggregate’ in ‘aggregate’ demand. Let’s look at the actors:

    * Households
    * Non-financial companies
    * Financial companies
    * The government
    * ‘Abroad’

    * All of these have their own kind of spending: consumption, investment, government spending (though this can be divided into consumption and investment spending) and ‘exports’.

    * In all these cases, this spending is financed by income plus change in net debt (at least, that’s what the national accounts and the flow of funds tell us, we actually do measure this)
    * But if I buy a car at 0% interest over 5 years (the present offer from Opel, another German car factory) this does not mean that Opel can buy less, as they lent me money. To the contrary – they lent me money (they do have a banking license, by the way) and they can actually buy more and invest more because they have lent me money (sorry, that’s the way money works), as, according to the rules of accounting (just check any textbook) their profits increase because their credit enables me to buy a car. Happens all the time.
    * Let’s classify this car as a consumer investment (just like a house).
    * That means that lending me money has increased production and income as well as saving (as well as debts, of course). And this hapens all the time. Of course I will have to pay back the debt. But production and income has increased, as money has been created which enabled saving as well as investment as well as an increase of income.

    And that’s the basic mistake of Cochrane. He misread Say. Opel is doing what Say told that suppliers do: selling people on credit when business is depressed, therewith increasing the flow of money. Remember: Say lived around 1800, when coins were in short supply and consumer credit and not cash was the lifeblood of the economy (just check any account from any baker or butcher or whatever)

    Now suppose that I resist Opels offer. The flow of money stalls. Wouldn’t it be nice when the government took its responsibility and kept the stream of money going? Remember, as Minsky stated – all economic units can create money, the problem is to get it accepted. When I buy an Opel on credit I’m in fact the one who creates this money… (money in the sense of the classics and the Post-Keynesians, that is, of course not money in the sense of the neo-classicals who finally should take a serious look at the counterparts of the M-1 and M-2 and M-3 data. And yes,I do know that M-3 is not estimated anymore in the USA)

  42. Gravatar of D R D R
    15. January 2012 at 13:17

    Jim,

    I’m not sure that they are different as such. I am not sure where the confusion there lies, but are you sure someone is not confusing the savings/investment schedules and quantities of savings/investment demanded?

  43. Gravatar of TheMoneyIllusion » Wren-Lewis seems to refute his own argument TheMoneyIllusion » Wren-Lewis seems to refute his own argument
    15. January 2012 at 13:33

    [...] a previous post I criticized Wren-Lewis’s claim that John Cochrane’s denial of a positive balanced [...]

  44. Gravatar of Greg Greg
    15. January 2012 at 15:05

    So: in a closed economy with full employment in which time does not exist (there is only one period in which things can happen), S = I.

    Thanks, Scott. Got it. But that is not what Cochrane, Wren-Lewis, Krugman, or DeLong were talking about.

  45. Gravatar of Alan Engel Alan Engel
    15. January 2012 at 17:26

    See Krugman’s response at http://krugman.blogs.nytimes.com/2012/01/15/the-method-of-comparative-statics-very-very-wonkish

  46. Gravatar of Callum Callum
    15. January 2012 at 17:27

    Looks like Krugman responded to your criticism. Sounds like there was some basic misunderstandings….

    http://krugman.blogs.nytimes.com/2012/01/15/the-method-of-comparative-statics-very-very-wonkish/

  47. Gravatar of The Method Of Comparative Statics (Very, Very Wonkish) | CATA NEWS The Method Of Comparative Statics (Very, Very Wonkish) | CATA NEWS
    15. January 2012 at 17:37

    [...] I read Scott Sumner’s claim that Simon Wren-Lewis and I are making basic errors, and at first I couldn’t figure out at all [...]

  48. Gravatar of Ignobilitor Ignobilitor
    15. January 2012 at 17:56

    Given that Krugman has effectively rebutted the gist of this piece, I’m guessing that’s the last we’ll hear from Mr. Sumner in this comment thread.

  49. Gravatar of karl smith karl smith
    15. January 2012 at 18:40

    Scott re: jan 13 20:10

    There you go bashing redheads again. I thought we had come to consensus on the auburn ;)

    http://www.auburnhaircolor.com/wp-content/uploads/2009/11/dark-auburn-hair-color-wr.jpg

  50. Gravatar of TheMoneyIllusion » It’s what they don’t say that is revealing TheMoneyIllusion » It’s what they don’t say that is revealing
    15. January 2012 at 19:16

    [...] the argument I actually made: Those readers who agree with Brad DeLong’s assertion that Krugman is never wrong must be [...]

  51. Gravatar of paineite paineite
    15. January 2012 at 19:57

    Here’s your reply from Krugman … in case you missed it (LOL):

    http://krugman.blogs.nytimes.com/2012/01/15/the-method-of-comparative-statics-very-very-wonkish/

  52. Gravatar of ssumner ssumner
    15. January 2012 at 20:06

    Everyone, I probably don’t have time to answer all the comments tonight, but let me just say that Krugman totally misrepresented my argument, and I spell that out in a new post. His entire post is beating a dead horse. I know all about the hydraulic Keynesian model he spells out in his post, and indeed said so in the post he was criticizing. Notice he didn’t quote from it, readers would have easily seen he was misrepresenting my argument. Indeed the entire critique of Wren-Lewis and him was was on one topic, and one topic only–consumption smoothing. It very revealing that he didn’t even address consumption smoothing in his reply. I’ll take that as tacit admission that I’m right and he and Wren-Lewis are flat out wrong.

    DR, You said;

    “One, you uncharitably read Wren-Lewis to say that consumption fell overall”

    I thought I was being very charitable. I assumed he wasn’t a complete idiot. Why would someone say Cochrane was wrong because there would be consumption smoothing unless he assumed there was . . . consumption smoothing. Or at least unless he assumed that if there was consumption smoothing, then Cochrane would have been wrong. But in fact consumption smoothing doesn’t move the ball one yard down the field. It has nothing to do with whether Cochrane is right or wrong. Again, I don’t care who’s right or wrong about fiscal stimulus, I am pointing out a completely illogical argument.

    You said;

    “Two, if you insist on this uncharitable reading, C-10, I-40, G+100, T+100 yields smoothed consumption and, contra Cochrane, a positive multiplier.”

    Of course it does, but you can get exactly the same result w/o consumption smoothing. Wren-Lewis is attempting this “aha, I caught you” argument. He’s basically saying, “Doesn’t Cochrane know that if after-tax income falls by $100 consumption will fall by much less?” Not in so many words, but that’s the clear implication of his argument to me.

    Another argument I just thought of is this. Even Keynesians admit that fiscal stimulus doesn’t work at full employment. But consumption smoothing does still occur at full employment. So something else has to be going on here, consumption smoothing can’t be the reason why the fiscal multiplier isn’t zero. It’s the standard Keynesian reasons. Did Keynes base his model on consumption smoothing?

    All your accounting examples mean nothing to me. I’ve said over and over again that it’s possible the balanced budget multiplier is positive, maybe even one. But it’s not positive because of consumption smoothing.

    Kevin, See my reply to DR, You are completely missing the point. Nobody wants to talk about how the consumption smoothing argument supposed disproves Cochrane. That’s the only issue I care about. It doesn’t disprove Cochrane, it has no bearing on the discussion. Would it help if I said I’m totally convinced that the BBM is precisely one? Could we then discuss the real issue?

    Even Wren-Lewis just admitted that S=I is an identity, after previously denying it. Even Krugman admits it. I have no fear of being proved wrong on that point.

    DrJim, OK, and how does that relate to anything I wrote? Have I ever denied anything you said? Believe it or not I’m not a complete moron. I don’t have to be addressed like a kindergardener.

    Mayson, And your point is???

    Merijn, Cochrane knows all that.

    Greg, Sorry to tell you this but both Krugman and Wren Lewis say S=I is an identity, that means it’s true whether you have full employment or not. Love your attitude however. I take it you are a Krugman fan.

    Callum, I doubt it’s a misunderstanding.

    Ignobiltor, WRONG.

    Karl Smith, Thanks for something pleasant after all these Krugman readers explaining the Keynesian cross to me.

  53. Gravatar of Michael Michael
    15. January 2012 at 20:11

    It’s been interesting watching this controversy since early this morning. And since early this morning, it’s been obvious (to me, anyway) that Scott, on the one hand, and Krugman and Wren-Lewis, on the other, have been using different operational definitions of the word “savings.” Scott has been using “savings” in such a way that it excludes what Nick Rowe terms “money hoarding.” Krugman and Wren-Lewis, on the other hand, have been using “savings” in such a way that it does include Rowe’s “money hoarding.” As a result, both sides in this controversy have been talking past each other; they’re actually much closer together than they’ve been thinking they are.

  54. Gravatar of D R D R
    15. January 2012 at 21:25

    Arrrrrgh. Fine. Let’s abstract this debate from any economics.

    Cochrane: “If P1 then Q and if P2 then Q. I say this because if P1 then A implies Q. What part of A do you dispute?”
    Wren-Lewis: “But Cochrane forgot B. If P2 then B and C implies not-Q…”
    Sumner: “B and D implies Q, so B is not an argument against Cochrane.”

    Perhaps not. But “If P2 then B and C implies not-Q” IS an argument against Cochrane, because Cochrane asserted that P2 implied Q.

    Why on earth is Sumner hung up on the totally irrelevant “forgot B” part of Wren-Lewis? Cochrane’s argument does in fact fail because if P2, then B and C imply not-Q.

  55. Gravatar of fausto412 fausto412
    15. January 2012 at 22:37

    “Well, I read Scott Sumner’s claim that Simon Wren-Lewis and I are making basic errors, and at first I couldn’t figure out at all what his problem is.”

    After reading it myself a couple of times. I had trouble figuring it out also.

  56. Gravatar of John Schultz John Schultz
    15. January 2012 at 22:58

    You stated the Keynesians’ key point, which was: “C fell by $20 million and investment was unchanged [while G increased by $100 million meaning GDP increased by $80B in the first year].”

    In the short run, the stimulus did stimulate the economy. That was their point and why they think the fresh water economists keep making howlers.

    “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. Checkmate.”

    Are you quibbling over the use of the exact terminology of “consumption smoothing” or what here? Krugman et al are arguing that (particularly in a liquidity trap) that fiscal stimulus can stimulate the economy in the year it occurs. By your own words, consumers are consuming $20M less per year “C fell by $20M”. Is that not consumption smoothing in response to the increased government spending?!!! I don’t see how you’ve refuted that point or checkmated them at all. What am I missing?

    Even if you think the assumption that investment is constant is completely unrealistic (it is), the slope of the line would likely be such that investment would not fall dollar for dollar to offset the increased govt. spending, thus short term stimulus works.

    Taking the debate up a level, I think the fresh water people are not actually arguing that govt. spending can’t stimulate in the immediate short term, but rather that in the long run the federal “stimulus” will turn out to be a wash at best because it will come at the expense of private sector growth. They seemingly reject the possibility that the economy can get stuck at an equilibrium of low output and that fiscal stimulus can kickstart the economy out of such an equilibrium up into a higher one where everyone is better off despite a ton of real world examples of both.

  57. Gravatar of D R D R
    16. January 2012 at 00:14

    Scott says:

    “He’s basically saying, ‘Doesn’t Cochrane know that if after-tax income falls by $100 consumption will fall by much less?’ Not in so many words, but that’s the clear implication of his argument to me.”

    I do see what you are saying here. Wren-Lewis did imply that investment fell by the amount consumption rose in response to the bridge-building. Wren-Lewis did NOT explain what happened to investment in response to the tax hike. Either…

    1) Wren-Lewis failed to fully spell out the additional hidden assumption (say, that the tax multiplier was only 0.5) or;

    2) by not specifying, he implicitly argued that there was no fall in investment resulting from the tax hike (in isolation)– an argument which is not consistent with consumption smoothing.

    I don’t see how the latter is the more charitable reading.

    On the other hand, I understand that the more charitable reading is that Wren-Lewis’ argument boils down to “the spending multiplier is larger than the tax multiplier, so the BBM is positive.” I also understand that once that much is assumed, consumption smoothing is irrelevant.

    But it still serves as a refutation of Cochrane, weak as it is. Cochrane says he proved that tax-financed government investment has a zero multiplier. But his proof never covered this case. He left it as mere assertion. With no assumptions beyond the description of that universe (that the change in G equals the change in T) any counterexample– no matter how unhinged–suffices to disprove that part of his case. So long as the counterexample is self-consistent and results in no change in government savings.

    Personally, I would have simply pointed out that he failed to complete his proof and leave it at that.

  58. Gravatar of John Schultz John Schultz
    16. January 2012 at 00:41

    Just as a follow on, in your analyses you use balanced budgets where the increase in G is matched *immediately* by an equal increase in T. Maybe such an assumption is true over the (very) long run, but Krugman et al aren’t arguing over the long run. They are arguing about the immediate (i.e. – within the first year or so) effects on output. So, in year one, G goes up by $100 M while T only goes up by (say) $5M. T going up by $5M will cause people to reduce their consumption in response by (say) an equal amount. Then the only remaining question is what happens to Investment?

    You seem to be poking the Keynesians in the eye for ignoring any impact on Investment or assuming that it is constant. In fact, you claim that you’ve checkmated them if they do assume Investment is fixed — although I still don’t understand why you think that’s a checkmate, other than a lame semantic argument that the idea of “consumption smoothing” has a specific meaning in the fresh water terminology (and by using it you’ve moved into their model and therefore can’t refute them with it) and isn’t talking about the reduction in consumption that people engage in in response to the higher taxes.

    Couldn’t private investment easily be (nearly) fixed when nominal rates are near 0% as they are now? In such a case, isn’t the government able to borrow nearly “for free” (in both the manna from heaven sense and the inexpensive borrowing senses) because it is putting resources to work that were being underutilized? That is, the economy is such that to get it back to full potential the nominal interest rates would need to be significantly negative but they can’t be because people (including banks — look at deposits on reserve with the FED) will simply prefer to hold money once nominal interest rates get too close to zero? In that case, the government borrowing isn’t crowding any private investment out at all. It is merely tapping into people who are marginally willing to exchange their no interest rate govt. debt (i.e. – govt. money) for low interest rate govt. debt (e.g. – T-bills).

    Getting back to the core of the argument though, I think there is a lot of talking past one another (or semantic disagreement on terminology). When Keynesians say the fiscal multiplier is 1.5 (or whatever) they are saying that if the government goes out and spends $100M this year then they expect total output to increase by $150M this year. They aren’t talking about the long run effect on output relative to the scenario where the money wasn’t spent by the government (although they would argue for positive multipliers in many important scenarios such as a liquidity trap / depressed economy), which I think is what most fresh water people are talking about when they assert that the fiscal multiplier is (less than) zero.

  59. Gravatar of Ben Ben
    16. January 2012 at 06:36

    As a non-economist (but math-savvy scientist) I’m sometimes confused by economists. Here the S=I “tautology” is puzzling, and it seems to underpin the logic of Scott’s argument so it can’t be simply ignored.

    What happens when a bank’s board of directors (in a free market) or the government (under regulation) requires a bank to increase its reserves? At least temporarily, it seems like S(t) > I(t), from which it follow that S=I is not an identity, but a statement that the long term averages must converge.

    Or is this a case where S has been redefined (e.g. Lewis Carroll’s Humpty Dumpty) to mean only what the economist wants it to mean, and not what the standard English definition?

  60. Gravatar of Min Min
    16. January 2012 at 06:40

    We have:

    (G – T) + (X – M) = S – i

    If S = I, this would be absurd, because we would simply have:

    (G – T} + (X – M) = 0

    or

    G – T = M – X

    So S = I is not an identity.

  61. Gravatar of Major_Freedom Major_Freedom
    16. January 2012 at 06:59

    “Nick and I could write a textbook that stripped all the inessentials out of macro. Monetary policy controls M*V, and unexpected shocks to M*V causes fluctuations in hours worked because of sticky wages. Replace the welfare cost of inflation with the welfare cost of fast NGDP growth. Real wages become relative wages (W/NGDP per capita.) Business cycle and “inflation” theory in 2 pages. That’s not Occam’s razor, that’s Occam’s chainsaw!”

    NGDP? Why in the world should anyone adhere to a policy model that chains people to their past through the constant threat from government that it will grow to whatever degree is necessary to prevent current spending from falling below past spending? What is so special about past spending that current spending cannot fall below it?

    What if people decide to increase their cash holdings to such a degree that they end up “hoarding” 99% of their nominal incomes, but consuming and spending in the same ratio as before? In a non-NGDP, free market world, this will lead to a fall in wage rates and prices, but at least the civilian population will continue to control most of the economy’s resources. But in Sumner’s NGDP model, such cash hoarding requires that the government take over the entire economy’s resources through its spending.

    NGDP policy, therefore, contains a blank check for unlimited government. It is a ticking communist bomb that will go off if people hold too much cash for too long. How much cash and how long? An arbitrary amount of cash for an arbitrary amount of time. In other words, whatever Sumner says.

    We’re supposed to accept that holding more cash is somehow a vote for more government spending and hence more government control over the economy, rather than what holding cash really is, which is just people wanting higher purchasing power. They would get in a non-NGDP world, but not in an NGDP world. In an NGDP world, they not only don’t get more purchasing power, they also don’t get to keep control over economic resources.

    Angry Austrians? I would be angry too if I was told to believe in a model that essentially tells people:

    “If you hold more money, then government will take over that much more of the economy. In theory this model calls for communism if you and others hold too much cash for too long. Thus, if you want to remain in control of your own economic lives, you must refrain from holding more cash than you held before. Your past is hereby your chain.”

  62. Gravatar of W. Peden W. Peden
    16. January 2012 at 07:29

    Major Freedom,

    Except that NGDP targeting doesn’t require that people have the same demand to hold money across time. Theoretically or practically. At all.

    And who is in favour of government expansion as a proportion of the economy? Not Scott Sumner or Nick Rowe, as far as I know. Perhaps they don’t understand their models…

  63. Gravatar of Major_Freedom Major_Freedom
    16. January 2012 at 07:45

    W Pedan,

    “Except that NGDP targeting doesn’t require that people have the same demand to hold money across time. Theoretically or practically. At all.”

    My argument also does not require that. My argument is that the model says people if people hold more money than they did in the past, then that would reduce NGDP, and because it reduces NGDP, the government is supposed to react by spending more and hence take more control over the economy.

    “And who is in favour of government expansion as a proportion of the economy? Not Scott Sumner or Nick Rowe, as far as I know. Perhaps they don’t understand their models…”

    I was considering the model only. I don’t know what amount of government is OK with Sumner, and is besides the point I am making anyway.

  64. Gravatar of W. Peden W. Peden
    16. January 2012 at 08:16

    Major Freedom,

    “My argument is that the model says people if people hold more money than they did in the past, then that would reduce NGDP, and because it reduces NGDP, the government is supposed to react by spending more and hence take more control over the economy.”

    No, that’s not part of the model. That would be an Old Keynesian approach. The model is based on the assumption that the private sector can always be the one to spend (even in a “liquidity trap”) and the Market Monetarist form of NGDP targeting is actively opposed to fiscal expansionism in a recession.

    “I was considering the model only. I don’t know what amount of government is OK with Sumner, and is besides the point I am making anyway.”

    So when you said-

    “What if people decide to increase their cash holdings to such a degree that they end up “hoarding” 99% of their nominal incomes, but consuming and spending in the same ratio as before? In a non-NGDP, free market world, this will lead to a fall in wage rates and prices, but at least the civilian population will continue to control most of the economy’s resources. But in Sumner’s NGDP model, such cash hoarding requires that the government take over the entire economy’s resources through its spending.”

    - what did you mean exactly? If people are hoarding <100% of their incomes, then there's no need for the government to expand at all (either proportionately or absolutely) since all the central bank has to do is loosen monetary policy to accomodate people's greater demand for money and prevent expenditure from falling.

    Incidentally, an Angry Austrian called F. A. Hayek was in favour of "maintaining expenditure" in a recession, which amounts to a kind of NGDP targeting. A more recent Angry Austrian, George Selgin, also favours a NGDP targeting as a least-bad-option for a central bank, based on a productivity norm. I'm not Angry, but I agree with the Austrians on a lot of issues and I also think that NGDP targeting is the best constraint to put on a central bank in most cases.

  65. Gravatar of 「比較静学の手法(超超オタク風)」 by Paul Krugman – 道草 「比較静学の手法(超超オタク風)」 by Paul Krugman – 道草
    16. January 2012 at 09:03

    [...]  さて、サイモン・レン-ルイスと僕が基礎的な間違いを犯しているというスコット・サムナーの主張を目にして、最初は彼が何を問題としているのか全く分からなかった。それからピンときた:彼はレン-ルイスと僕が比較静学をやっていることを理解していないんだと。 [...]

  66. Gravatar of Pat Pat
    16. January 2012 at 10:35

    To start, I bitterly note that the right-of-center response to Paul Krugman has become concern trolling. “He doesn’t read right-wing blogs! And he’s so mean to right-wingers! If he read my blog and was nicer to me, he’d be so much more influential.” First, he’s the leading public intellectual in the English-speaking world; I think he just might know what he’s doing. Second, you’re a right-winger, and he reads you, so you just might be misunderstanding his comments about not keeping up with the Powerlines of the world.

    On the substantive point, I believe your error is in your mate-in-three step, but I really can’t tell. But you deliberately move to a level of abstraction that makes it hard to see where, exactly, you and Krugman are differing in your respective interpretations. To do some concern trolling of my own (ahem), you might find yourself making more compelling points if you countered points with which you disagree on the same plane, rather than jumping to accounting identities instead of talking about the damn bridge.

  67. Gravatar of John Schultz John Schultz
    16. January 2012 at 10:59

    Re-reading your argument, it sounds like you are saying that you agree that fiscal stimulus can increase output, but that Wren-Lewis is wrong to say it is because consumers engage in consumption smoothing in response to higher taxes. Is that the gist of your gripe?

    In an immediately tax balanced stimulus (i.e. – dG = dT in year 0), assuming investment (savings) is constant, then consumption falls exactly by the amount that after tax income falls. So, no smoothing has occurred at all — that is, the consumption smoothing coefficient is 1 and only happens in year 0.

    Aggregate output may have increased, but it had nothing to do with consumption smoothing. Wren-Lewis essentially assumed or asserted aggregate output increased because investment (savings) was constant (or largely unaffected by changes in output) and that consumption declined by significantly less than the increase in G, but his assumption is exactly what is under debate. He assumed that he was correct and then made a wrong argument to show that he was correct.

    You might be correct that his particular argument doesn’t prove his conclusion, but his conclusion is almost certainly correct.

    I think the better way to reach his conclusion (which is what Krugman was really agreeing with, btw) is that if G increases by X at time t and T increases by X / 30 at time t (which eventually pays off the borrowed principal + interest), then it is likely that C drops by (at most) X / 30 and under many conditions (e.g. – liquidity trap) that I will fall by (far) less than X * 29 / 30 so the stimulus does increase output in the short run, which contradicts many of Cochrane’s statements that, for example, any increase in G must be matched by a dollar for dollar drop in C + I and that fiscal stimulus can’t work.

    To be fair, I doubt (all) the fresh water people believe that fiscal stimulus can’t work in the short term under any / every set of conditions (if they do, then they are more dense than I thought possible). But rather, over the long run, that the scenario in which the government stimulated will not lead to higher GDP than if they hadn’t stimulated. In effect, they reject the idea that an economy can get stuck in a depression that is “unwarranted” (i.e. – a depression not in response to a bubble popping that only persists until prices get back to equilibrium and markets clear) that government stimulus can help end.

  68. Gravatar of ssumner ssumner
    16. January 2012 at 12:25

    Michael, Nothing can rescue Wren-Lewis’s claim–see my new post.

    John, If C fell by 20 and I was stable then disposable income fell by 20 and there was no consumption smoothing–but the problem is far deeper than that, see my new post.

    DR, I think my newer post makes a stronger case for what he almost certainly was assuming. It was a simple error that I see as comparable to Cochrane’s. It doesn’t make him an axe murderer, but he was the one who trashed Cochrane’s reputation, does he not expect to be corrected on his own errors.

    John, Sure some of those outs are possible, but I addressed the argument as it was made. I could invent lots of outs for Cochrane as well.

    Ben, Reserves are usually treated as a government liability, so national saving and investment don’t increase. Trust me, it’s an identity.

    Min, Total global S=I, national or private may not equal. But this is closed economy, balanced budget debate.

    Major freedom, No, like you I favor small government.

    Pat, You said;

    “Second, you’re a right-winger, and he reads you,”

    Obviously not, unless you think he intentionally misrepresented my argument.

    John, You said;

    “You might be correct that his particular argument doesn’t prove his conclusion, but his conclusion is almost certainly correct.”

    That’s exactly my view of Cochrane, his argument is wrong but his conclusion is correct. I’m just trying to hold them to the same standard as they hold Cochrane. They trash him for making a false argument, why don’t they expect to be attacked under similar circumstances?

  69. Gravatar of Someone Someone
    16. January 2012 at 14:23

    Its trivial to argue against bullshit.

    “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. Checkmate in four.”

    You claim, that saving isn’t money saving, but capital investment. In that case, you CAN NOT assume, that any changes in after-tax income and C+I are identical. The taxes can be paid with money from the sack of money in the corner. The taxes don’t need to produce a fall in C+I at all. In the real world simply idle ressources are put to work and GDP rises.
    Not that this whole argument, has anything to do with what Paul Krugman has written, nor has Paul Krugman in his reply to Cochrane used any Keynesianism, but he used neoclassical theory, but your first assumption is already critically wrong.

  70. Gravatar of tmichl tmichl
    16. January 2012 at 14:42

    Scott,

    I’m sorry. I just can’t make heads or tails out of this. Can you just post a blog stating why YOU (not Cochrane or Lucas) think the multiplier is zero?

    I don’t see any evidence here that you understand the mistake Cochrane makes by arguing that a temporary fiscal stimulus must fail because of Ricardian Equivalence–that is just plain wrong on its own terms. But I’m willing to listen……

  71. Gravatar of Major_Freedom Major_Freedom
    16. January 2012 at 14:53

    W. Peden:

    “My argument is that the model says people if people hold more money than they did in the past, then that would reduce NGDP, and because it reduces NGDP, the government is supposed to react by spending more and hence take more control over the economy.”

    No, that’s not part of the model. That would be an Old Keynesian approach. The model is based on the assumption that the private sector can always be the one to spend (even in a “liquidity trap”) and the Market Monetarist form of NGDP targeting is actively opposed to fiscal expansionism in a recession.

    I consider the central bank to be a governmental entity. If the Fed is going to buy up assets in order to expand NGDP, then that is a governmental entity taking ownership of more assets in the market. If the Fed has to buy up mortgages, then that is the government owning more houses. If the Fed has to buy up derivatives, that is the government owning more exercisable claims to wealth. If the Fed has to buy up government debt, then that is an encouragement for the government to borrow and spend more on the fiscal side. If the Fed has to buy up stocks, bonds, etc, then that is the government owning more claims to wealth.

    “I was considering the model only. I don’t know what amount of government is OK with Sumner, and is besides the point I am making anyway.”

    So when you said-

    “What if people decide to increase their cash holdings to such a degree that they end up “hoarding” 99% of their nominal incomes, but consuming and spending in the same ratio as before? In a non-NGDP, free market world, this will lead to a fall in wage rates and prices, but at least the civilian population will continue to control most of the economy’s resources. But in Sumner’s NGDP model, such cash hoarding requires that the government take over the entire economy’s resources through its spending.”

    - what did you mean exactly? If people are hoarding <100% of their incomes, then there's no need for the government to expand at all (either proportionately or absolutely) since all the central bank has to do is loosen monetary policy to accomodate people's greater demand for money and prevent expenditure from falling.

    Loosen monetary policy by doing what exactly? Just giving free money to people? I thought the monetary NGDP model was about the Fed buying up assets in order to inflate. What if people increased their hoarding to such a degree that nominal NGDP will otherwise fall by 90%? The model calls for the Fed to buy up and become owners of whatever assets are necessary to reverse the drop in NGDP, which means the Fed could become owners of 90% of the economy, if people increase their cash holdings by enough. How is that not a model that permits communism if people hold too much cash for too long?

    Years into the future, people will, hopefully, look back at this silly model and ask “What were they thinking? They said communism is fine? It’s fine if people hold too much cash for too long? Really?”

    Incidentally, an Angry Austrian called F. A. Hayek was in favour of “maintaining expenditure” in a recession, which amounts to a kind of NGDP targeting. A more recent Angry Austrian, George Selgin, also favours a NGDP targeting as a least-bad-option for a central bank, based on a productivity norm. I’m not Angry, but I agree with the Austrians on a lot of issues and I also think that NGDP targeting is the best constraint to put on a central bank in most cases.

    Hayek was a muddleheaded social scientist, and Selgin doesn’t even consider himself Austrian.

    I think abolishing central banks and centrally planning aggregate spending is the best constraint in every case.

    I am Angry, and it’s because the NGDP model grants the government unlimited license to take over the economy on the silly basis that NGDP falls by too much according to some arbitrary percentage called “the magic of 5%”.

  72. Gravatar of Ben Ben
    16. January 2012 at 14:53

    Scott, I’m still trying to come to grips with S=I without having to simply trust someone. With a PhD in engineering I feel like I should be able to follow the basic math used in economic models.

    Are economists defining S so that it does not include holding cash? For example, if I take my paycheck and stuff it under my mattress, or if a bank holds cash without buying government bonds, where does that fall in econ accounting? We could call this holding (H), which is logically a subset of the total savings in the economy. My money in my mattress is “savings” in the conventional English definition as I can pull it out and use it at some later date, but my holding cash doesn’t allow anyone to invest. Thus, if savings is given the common English definition it would seem that I = S – H. Seems to me that S=I only if you prohibit people from holding (H=0) or you redefine S as the subset of savings that is used in investment, in which case it is a tautology simply by virtue of selective redefinition. Is there something I’m missing here?

  73. Gravatar of Major_Freedom Major_Freedom
    16. January 2012 at 14:58

    S. Sumner:

    “Major freedom, No, like you I favor small government.”

    Tomorrow, people have decided to increase their cash holdings to such a degree, that NGDP falls by 99%.

    The NGDP model calls for a governmental agency, the central bank, to go on a buying spree, buying up everything from treasuries, to derivatives, to stocks, bonds, and mortgages. NGDP is still under “target.” So the central bank starts buying cars and television sets and computers. The NGDP target is almost there. So the central bank buys up clothes, and food. NGDP target has been reached.

    Question: In this world, which you must agree is POSSIBLE, I must ask you whether you will reject the model, or reject the government taking over the economy. You can’t have both. You must pick one. Which will it be?

  74. Gravatar of hopkin hopkin
    16. January 2012 at 15:26

    Maybe you need to be an economist to understand that a given amount of saving always produces an equal amount of spending on capital goods, but I’m afraid I’m not and I don’t. I just observe corporate savings increasing and corporate investment falling, and wonder what you’re on about.

  75. Gravatar of hopkin hopkin
    16. January 2012 at 15:27

    Ben, I think you’ve hit the nail on the head.

  76. Gravatar of Vijay Vijay
    16. January 2012 at 19:16

    @Ben – this is where Keynesian definitions and explanations come handy. He says something to this effect. Its more or less accepted as an universal truth in Economics:
    A rational person wouldnt hold a lot of cash on hand as long as there is an incentive to keep it invested at a high interest rate. So, as long as the interest rate is good enough, a rational person would consider it prohibitive to hold a lot of money just for the heck of it. Ofcourse, money kept in hand for personal and emergency expense notwithstanding, his overall percentage of holdings with respect to his savings should be small enough to be ignored.

    But its a pertinet question though… particularly in a regime of ultra low interest rates when this money isnt really invested in any gainful way and is almost like its been thrown out of the money supply [money not being used is and not in supply is as good as being outside the supply. Doesnt help in the money velocity calc either] This should naturally lead to a lowering of GDP – a depressed economy. In simple words. No investment inspite of excess saving leads to a lowering of GDP. Atleast thats what the IS-LM model tells us.

    I’m sure Scott can do a better job of the explanation than me. Afterall, explanations of this kind are part of his day job.

    Keep up the good work, Scott. I ve been a long time reader of your blog… Right from the initial days of the blog when it used to be a lot less popular and had lot lesser people coming in. Always thought it was a special place to be in. Feel quite good to see this develop and get more interactons lately. Should start following the blog more closely now. Havent followed the blog as frequently as I would like, lately!

  77. Gravatar of RueTheDay RueTheDay
    17. January 2012 at 05:57

    I take issue with this statement:

    “it’s essential to think of saving as spending on capital goods, not as setting money aside”

    This is a holdover from classical economics where simple barter models literally had capital being saved out of current income. For example, a harvest yields 100 bushels of corn of which 10 bushels were saved as seed corn for next year. In this example, the act of savings literally is the same act as the act of investment.

    The genius of Keynes was in pointing out that the decision to abstain from current consumption is a separate decision from that to invest. It is a decision to not consume now, it is not necessarily a decision to consume more in the future (via capital investment). That is a second, separate decision. Taking this a step further, in a modern economy, capital is “produced” not “saved” – it’s a process that takes time and requires the creation of something different from what was saved. Then, taking this even a step further, as Minsky pointed out, before capital can be produced (real investment) it must be financed. Finance is the nexus of capitalism. If economics does not take into account the existence of money and the financial system, and simply assumes, ala a simple barter economy, that “savings is spending on capital goods”, it cannot hope to explain the business cycle, financial crises, persistent unemployment, etc.

  78. Gravatar of Greg King Greg King
    17. January 2012 at 06:52

    It is not that tough to argue against an identity. You just have to show it is false. Savings = spending on capital goods is the identity. Except that there is very obviously a lot of saving right now that is not spending on capital goods. The (historically largest ever) excess of savings is just sitting there right now.

  79. Gravatar of I Figured Out What Scott Sumner Is Talking About « Uneasy Money I Figured Out What Scott Sumner Is Talking About « Uneasy Money
    17. January 2012 at 08:41

    [...] 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 [...]

  80. Gravatar of ssumner ssumner
    17. January 2012 at 15:50

    Everyone, I have way too many old comments going back to previous posts to answer them all. Let’s move the action to the most recent post, where people finally seem to be accepting that I am right. I will read all comments, but won’t respond to stuff like whether S really equals I anymore. Read any intro text if you want to know why. If I miss an important question of yours, bring it to the new post after reading the comments that begin to accept my argument.

    Someone, That sack of cash is viewed as government debt.

    tmichl, Yes, the RE argument is stupid–I agree, but if you read Cochrane closely he’s not really making that argument, Check out footnote 2.

    I’ve done about 100 posts pointing out that in the standard NK model the fiscal multiplier is zero if the Fed inflation targets. It’s not a new idea.

    Ben, There’s several ways of dealing with cash, but the easiest is to view it as government debt. Then it’s government dissaving and nets out to zero aggregate saving.

    major, Good question. I’d increase the trend rate of inflation so we could avoid a takeover. I see that as the lesser of evils.

    Thanks Vijay,

    Ruetheday, I agree with Keynes that S=I.

  81. Gravatar of Major_Freedom Major_Freedom
    17. January 2012 at 18:30

    RueTheDay:

    “The genius of Keynes was in pointing out that the decision to abstain from current consumption is a separate decision from that to invest. It is a decision to not consume now, it is not necessarily a decision to consume more in the future (via capital investment).”

    If someone decides to consume less in the present, and they accumulate cash over time as a result, then that is a decision to consume less in the present and consume more in the future. If the cash accumulator really didn’t intend on consuming more in the future, then they would burn their money or throw it away. Holding the cash is evidence that they intend to consume more later on.

  82. Gravatar of Greg King Greg King
    17. January 2012 at 19:16

    Asserting S = I as an identity is an assertion, not a proof. And savings equals investment is at the very least PROVABLY false in the immediate term. Unless you use a very non-useful definition of investment. When you invest in something actually tends to matter in the real world.

  83. Gravatar of Eye of Siva » Eco-War Eye of Siva » Eco-War
    18. January 2012 at 01:23

    [...] Sumner wades in saying that it is tough to argue against an identity. With the example of a closed economy, he breaks down in four steps why Cochrane is right and [...]

  84. Gravatar of RueTheDay RueTheDay
    18. January 2012 at 07:51

    Major_Freedom – Accumulating cash is not necessarily a decision to consume more in the future. It could be a decision simply to hold cash as a precautionary balance, a hedge against unforseen events, such that one could simply be able to maintain consumption should such an unforseen event disrupt anticipated income inflows.

  85. Gravatar of Major_Freedom Major_Freedom
    18. January 2012 at 10:28

    RueTheDay:

    “Major_Freedom – Accumulating cash is not necessarily a decision to consume more in the future. It could be a decision simply to hold cash as a precautionary balance, a hedge against unforseen events, such that one could simply be able to maintain consumption should such an unforseen event disrupt anticipated income inflows.”

    When I said consume more in the future, you have to understand that to mean consume more “than would otherwise have been the case.” It’s not about consuming more relative to some past history. We don’t decide to invest or hold cash in order to act like robots and simply repeat the past. No, we decide to invest and hold cash so that we can consume more in the future than would have otherwise have been the case had we not invested or held cash, and simply consumed with it right away.

    Therefore, accumulating cash is in fact a decision to consume more in the future. If people didn’t want to consume more in the future, then they’d just throw their accumulating cash balances away.

    Holding cash as a precautionary balance, to hedge against unforeseen future events, etc is just another way of saying people want to be able to consume more in the future than they otherwise could if they didn’t accumulate that cash.

    I hold cash and make investments so that in the future I can consume more than I otherwise could had I not held more cash or made investments. I don’t do these things so that I can tell someone a story about what happens to the pattern of my consumption over time during my lifespan.

  86. Gravatar of ssumner ssumner
    19. January 2012 at 14:05

    Greg, Check any intro textbook, it’s an identity.

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