Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Friday, July 16, 2010

Krugman the Crude?

I love reading the K-man's blog. (A morning chuckle is always a good way to start the day.) Great title here: I'm Going to Haul Out the Next Guy Who Calls me "Crude" and Punch Him in the Kisser. In it you will find Krugman lamenting:

All through this debate, a recurring theme among anti-Keynesians has been that Keynesians like me or Brad are ignorant primitives who don’t know anything about modern macro. It’s really hard to see where that comes from, since I’ve done plenty of intertemporal optimizing in my time.

(Can't help but notice that he does not include his wing-man in that last sentence.)

This quote is rather revealing. What it reveals is the K-man has little idea what constitutes "modern" macro. There is, of course, no sin in this. Not everyone can devote most of everyday trying to advance the frontier of economic theory. Most people have real jobs. And, of course, just because one is not up-to-date on the entire body of macroeconomic research produced over the last 10-20 years (or so) does not mean that one might not contribute usefully to contemporary debate on theory and policy.

The K-man's sin (venial, rather than mortal) is an ego that does not permit him to admit that he's a little out of date on the theory front. What he labels "modern" macro is theory as it largely existed in 1980. A representative agent, a cash-in-advance constraint, no financial frictions (apart from CIA), and a sticky nominal price. Oh yes, and let's not forget intertemporal optimizing (as if this alone is what distinguishes the modern from the primitive).

We now have models that explicitly incorporate heterogeneity, financial frictions (the product of underlying commitment and private information problems), and search and matching frictions. Moreover, we have models of liquidity shortages-models in which government money and/or debt plays a socially useful role. More importantly, greater attention is being paid to matching a model's microstructure to microdata (ultimately, the only way to discriminate against competing theories with similar macroeconomic properties).

One lesson that emerges from this literature is how little we in fact know. The message is one of caution when faced with the real-world problem of formulating policy. Admittedly, this is not an attractive product for those who demand religion (a great many people, judging by the evidence). But then, we are supposed to be disinterested scientists--not the self-appointed "conscience" of any liberal or conservative.

Alright, enough of that. Now here is another good laugh -- the K-man accusing Bob Lucas of not understanding the implications of his own theory; see One More Time.

Here’s what we agree on: if consumers have perfect foresight, live forever, have perfect access to capital markets, etc., then they will take into account the expected future burden of taxes to pay for government spending. If the government introduces a new program that will spend $100 billion a year forever, then taxes must ultimately go up by the present-value equivalent of $100 billion forever. Assume that consumers want to reduce consumption by the same amount every year to offset this tax burden; then consumer spending will fall by $100 billion per year to compensate, wiping out any expansionary effect of the government spending.

But suppose that the increase in government spending is temporary, not permanent — that it will increase spending by $100 billion per year for only 1 or 2 years, not forever. This clearly implies a lower future tax burden than $100 billion a year forever, and therefore implies a fall in consumer spending of less than $100 billion per year. So the spending program IS expansionary in this case, EVEN IF you have full Ricardian equivalence.

Is that explanation clear enough to get through? Is there anybody out there?

Hey Paulo, here is a model for you. Let preferences be U(c+g)-v(n), so that the private sector views government spending as a perfect substitute for private spending. Assume lump-sum taxation and a fixed real wage w, so that the private sector budget constraint is c = wn - g. The effect of an increase in g on GDP here is zero. Embed this into a fully dynamic model and the result is the same (whether or not the change in g is temporary or not).

Conclusion: no, this is not enough of an explanation for me. You have to be more specific. The answer depends on an annoying set of details. Is this clear enough to get through? Probably not.


  1. Yeah, it IS difficult to resist commenting on Krugman, isn't it?

    David, would you walk me through the model please? I get that c is consumption and g is government spending and n must be hours worked because w is wages and consumption = wages * hours worked less what the government takes.

    But (if I'm right so far) I don't know what the function v() is, and I don't know why you are working with U() as Preferences.

    And if I understand enough to comment, then my comment is that your statement
    "The effect of an increase in g on GDP here is zero"
    is true if and only if one ignores deficit spending by g.

    If this comment is too stupid, then just delete it; I can take a hint! Thanks.


  2. Art: no problem at all. Let me be more explicit.

    The term -v(n) measures the disutility of labor. The formulation U(c+g) assumes that people view c and g as perfect substitutes. (You do not care if your child eats your packed lunch, or whether the lunch is provided at school by the government, to give an example).

    To see whether your claim is true or not, we can examine a 2-period economy.

    Let's assume an expenditure program (g1,g2) with g2=0. The question is then whether an increase in g1 will have different effects depending on how it is financed. Assume lump-sum taxes (t1,t2). The government's intertemporal budget constraint is:

    g1 = t1 + t2/R

    where R is the gross real rate of interest (take this as given, without loss of generality).

    The consumer wants to maximize:

    U(c1+g1)-v(n1) + b[U(c2)-v(n2)], where b is a discount factor. His budget constraint is:

    c1 + c2/R = w*n1 +w*n2/R - [t1 + t2/R]

    Next, write down the FOCs (taking g1 as given, of course). Forgive me for being cryptic, but you will get something like:

    MRS(c1+g1,c2) = R (1)
    MRS(c1+g1,n1) = w (2)
    MRS(c2,n2) = w (3)
    c1 + c2/R = w*n1 +w*n2/R - [t1 + t2/R]

    Next, invoke the govt budget constraint, so that:

    c1 + c2/R = w*n1 +w*n2/R - g1; or

    c1 + g1 + c2/R = w*n1 +w*n2/R (4)

    The system (1)-(4) determines the equilibrium c1,c2,n1,n2. This potentially depends on g1, but not on the timing of taxes (taxes appear nowhere in the four equations).

    So the question boils down to whether a change in g1, in this dynamic economy, has any effect at all (independent of how it is financed).

    The answer is that it does not (at least, I'm 99% sure). An increase in g1 here simply crowds out c1 one-for-one (think of the school lunch program example).

    Does this help? (And please correct me if I am wrong).

  3. Yep. Try another a concrete example. Suppose we all buy one loaf of bread per day, at $2. The government then taxes us $2 each, buys bread, and gives it to us. So we stop buying bread ourselves. Net effect zero. All that's happening is that the government is doing our shopping for us.

    You could run the same argument with investment. If the government builds a hospital that the private sector would otherwise have built, G goes up, I goes down, zero net effect on aggregate demand.

    These examples assume that government spending is a perfect substitute for private consumption or investment spending.

    (I remember David Laidler very briefly discussing this possibility in MA Macro 1977).

    The standard macro model implicitly assumes that government spending has no effect on the marginal utility of private consumption, or the marginal profitability of private investment.

    Of course, you can also make the exact opposite assumption, that government spending is a complement to private spending, which gives you an even bigger multiplier than the standard one.

    And with enough ingenuity, you can get a negative multiplier too: government spending is a complement to future consumption, so people save more now, so they can buy a car in 5 years time when the government completes building the new road for them to drive on.

    My benchmark assumption is that government spending has no effect on the marginal utility of private spending (which doesn't mean it has no effect on total utility). The real messy world could go either way from this benchmark.

  4. Another implicit assumption of the "standard benchmark" is that government spending does not earn any income (or help people themselves earn future income). If we assume government investment creates future income, that in itself upsets Ricardian equivalence. If government spending is profitable, it increases permanent disposable income (it is as if it decreases future taxes, rather than increasing them, as in RE).

    One ironical implication of this is that the best fiscal stimulus is a vulgarly materialistic one. Build infrastructure that earns cash, not beautiful new parks and sculptures.

  5. What about the cost of government taking my $2, then having someone go buy the bread, and then having a different someone deliver the bread to me? Seems like the extra "roundaboutness" needs to be accounted for.

  6. Sorry, above comment meant as a response to Nick Rowe.

  7. David. Thank you. I get most of what you say (except, of course, the cryptic part). But I see things here are moving faster than I can translate symbolic notation into English... I get that taxes t1 and t2 do not appear in the result, and this is very interesting.

    Nick's first concrete example -- "Suppose we all buy one loaf of bread per day, at $2. The government then taxes us $2 each, buys bread, and gives it to us. So we stop buying bread ourselves. Net effect zero" -- seems to be a concrete example of what I said previously: "The effect of an increase in g on GDP here is zero" is true if and only if one ignores deficit spending by g. If there are unemployed bakers and the government does a little deficit spending, the effect of this increase in g on GDP, I expect, is greater than zero.

    I understand that your "2-period economy," David, was an attempt to expand my snapshot and show that as a continuing process my thinking does not stand up. I'm still re-reading your comment. But I'm not arguing in favor of perennial deficits.

  8. Maybe Krugman's intention was clearer in his previous posts:

    Apparently, he precludes lump-sum taxation assumption.
    And he laments, "I don’t know how a trained economist can make something this simple so complicated …"

  9. Nick: Your first post is right on. It reinforces the point I am making: the details concerning the composition of G can matter.

    Nick: I think you are little off on your second post. RE holds even in a world with government investment. Remember, the proposition simply states that for a *given* program of government spending (consumption or investment), the timing of (lump sum) taxes does not matter. As for your last remark, I think you are right on (in fact, it is a standard result in the optimal dynamic public finance literature).

    Arthurian: Suppose we all buy $2 of bread per day for two periods. Now suppose that the government wants to give us $1 of bread today (not tomorrow). Where will it get the bread without taxing it? Simple: it can issue a bond. So I use $1 to buy the bond, the govt uses the $1 to buy a loaf, which it gives to me. Next period, the bond comes due. The government simply taxes me to make good on its bond payment. Whether the govt taxes me today or tomorrow does not matter. (And no, I am not arguing in favor of perennial deficits here!)

    himaginary: Thanks for the links. He is, however, very clear about his proposition in the link I cite (he says it is true even with lump sum taxation). As for his lament, what can I say? The world is so simple to the K-man. We must all be idiots for not seeing what the self-appointed one sees as obvious. Of course, I just presented an example that disproves his assertion. I'm sure, however, that he won't let that get in the way of him making more brash assertions in the future!

  10. I glanced through the model before going to bed. It seems like

    1. This conclusion only holds in a finite horizon model. The assumption that in G2 = 0 is critical. Do you know how it will change, if it is extended to infinite horizon? My guess tells me that it is either it will say that consumers will reduce consumption in the given period government spending rises, or does it state more that consumption will fall by an amount equal to the government spending over several periods. (As in consumers will treat such an increase as a fall to disposable income).

    It doesn't seem to me like it provides any conlcusion about whether the consumer is worse off as it says nothing about how the consumer values government services. I think Vancouverites rather enjoy the sky train. I also think that many of them rather enjoy public education, and subsidized education at SFU and UBC.

    3. This critique is one in general of a textbook lot of macro models, but it also seems like government spending is treated completely as if governments purchases non durable goods and they are equivalent to consumption. Which seems to me unrealistic.

    Government spending is often on infrastructure, which I think at least makes it similar to investment. For example, I do think its nearly impossible to quantify the value of mandatory universal public education in developed countries, as they guarantee a base quality to human capital. I also think is hard to put a value on a lot of communication infrastructure, transportation infrastructure, such as what the highway system has done for the united states. It seems to me that macro models have done a poor job capturing heterogeniety of government spending, as some government spending may fall more under the category of K than G.

    Though I'm someone who is unfamiliar with the literature.

    I'm also not saying that temporarily extension of unemployment benefits, does anything to stimulate economic growth.

  11. David,

    I haven't been able to visit your blog much recently but looking forward to catching up - you've been busy.

    I do have a few points to make about this post though. I think its important to go back to the original Lucas comments, quoted on Delong's page (

    Lucas said "But if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder... then it's just a wash.... [T]here's nothing to apply a multiplier to. (Laughs.) You apply a multiplier to the bridge builders, then you've got to apply the same multiplier with a minus sign to the people you taxed to build the bridge... taxing them later isn't going to help, we know that..."

    Krugman's argument is enough to show the fallacy in this line of reasoning. Is Krugman saying that taxation funded deficit spending will always result in increased GDP? No. He is saying that people who claim taxation funded government spending cannot possibly result in increased GDP are wrong. Lucas was the one making a universal statement, and it was enough for Krugman to find the exception.

    I also have a problem with your example. Your budget constraint doesn't allow income to vary with g because you assume fixed wages and a fixed number of workers. It is therefore not suprising that, in your model, income doesn't vary with g. This is not a result, but an assumption of your model.

    Krugman would readily admit that there are cases where increased g doesn't have much of an effect on income (ie, most of the time), but he certainly wouldn't assume it. Instead he would use a model where income is allowed to vary with g, and then come to the conclusion it won't move with g when resource constraints are binding (ie, not in the current situation).

    Look forward to hearing your thoughts.

  12. Patrick:

    First off, do you really believe that Bob Lucas does not get how a lump-sum taxed financed increase in g can stimulate output in even the simplest neoclassical model? C'mon now.

    Go and read Lucas' entire speech. The man is not a great public speaker (he is, I might add, an extremely nice and down-to-earth person). It was an awkward speech laced with a lot of loose language (very different from his academic papers). And so, one might charitably cut him some slack when interpreting his true meaning (unlike Crudeman and LeDong).

    If you read his talk, you'll see that he takes a broad swipe at the sloppy multiplier people. He goes on to say that the government should build a bridge if it is what the people want; we shouldn't do it just because Romer tells us that the multiplier is 3.0.

    Finally, I'm afraid that you are wrong concerning my example. I do not fix the number of workers. (n1,n2) can vary...preferences are given by U(c1,n1,c2,n2)...can u see this?

    If I had adopted Nick Rowe's preferred specification for preferences (g separable from c), then one would derive the standard result (that an increase in g increases GDP).

  13. David, right, regarding the number of workers not being fixed, that will teach me for jumping in without properly looking at the model.

    And Nick's comments are very helpful.

    But with regard to your defence of Lucas' comments, Lucas may have been speaking loosely, I don't know. But a lot of people use RE as the basis for their opposition to stimulus. And Krugman's comments (and, actually, your analysis) shows that the case is not so simple. In a way, from this perspective, you and Krugman actually agree (gasp...). You are both saying that, in the end, you need to go beyond RE to get an answer to this.

  14. Patrick:

    I cannot imagine any well-schooled economist using Ricardian Equivalence as an argument against fiscal stimulus.

    RE says that under a well-known set of assumptions, if we take the time-path (or stochastic process) for G as *given*, then how you finance it doesn't matter. RE has nothing to say about whether G is desirable or not.

    And if people are simply arguing for temporary tax cuts leaving G unchanged, RE simply says "go won't have much of an effect."

    If Krugman and I are in agreement on this matter, then so be it (but it makes me feel kind of

  15. David, I finally went and read a couple articles on RE, and that helped me "get" what you have been saying here. (My original comment was about deficit spending; your response was about taxes t1 and t2; RE relates them by saying "how you finance it doesn't matter," as you say.

    But aren't you splitting hairs in your last comment? If it really doesn't matter how you finance an increase in government spending, then clearly there can be no stimulus from that spending. If that's not an argument against fiscal stimulus, I don't know what is!

    But then, I'm neither an economist nor well-schooled...


  16. Art,

    Let G denote a government spending policy (think of G as entire time sequence of expenditures).

    The Ricardian Equivalence Theorem (RET) says that for a *given* spending policy G, how you finance it does not matter (you can tax today, or postpone taxes until tomorrow...these are equivalent ways to finance a given program).

    The easiest way to understand this is in terms of the government's intertemporal budget constraint, which is G = T, where T denotes a time sequence of taxes. For a given G, you have a given tax obligation T. Changing the timing of taxes does not change T, hence it does not change the disposable wealth of the household sector (W-T). Therefore, deficit financed tax-cuts should have no effect on consumer spending.

    Even if the RET holds, this does *not* imply that there is no stimulus (positive or negative) from changing the government's spending policy G. Clearly, increasing G will also increase T; and this will reduce household after-tax wealth. Whether changing G impacts on GDP depends on another set of assumptions; for example, whether or not the G is highly substitutable for private consumption/investment or not.

    By the way, one can use RET as an argument *for* fiscal stimulus in the form of a deficit-financed tax-cut. The way you would argue this is to say that RET asserts what's the harm in trying? Fiscal conservatives who rely on RET should not fret if they truly believe the theorem.

    Hope this the way, I have a free textbook you can download that has a chapter devoted to this question. I think you'll find it a relatively easy read and it goes into more detail. If you find it useful, you'll have to compensate me in the way of a beer, however! :)

  17. David: "Nick: I think you are little off on your second post. RE holds even in a world with government investment. Remember, the proposition simply states that for a *given* program of government spending (consumption or investment), the timing of (lump sum) taxes does not matter."

    Yep. I was sloppy in explaining what I was trying to say.

    Let me try again.

    Normally, a $1 increase in G implies a $1 increase in either present taxes, or in the present value of future taxes (and RE says it doesn't matter which of those latter two things happen, because the PV of disposable income falls by the same $1 in either case). So private C falls, and this will at least partly offset the effect on AD. But if the increase in G is in productive investment, that increases income for the government, or for people, it won't cause a $1 decline in the PV of disposable income. Conceivably, the PV of disposable income may even rise. So C may rise. And that's just in the "first round" effect.

  18. David,

    With regard to your comment that you can't imagine any well schooled economist using RE as an argument against stimulus, what about all those guys that Delong and Krugman have been complaining about?

    Like William Poole

    "Government spending can’t lead the way to sustained recovery, because its stimulating effect will be offset by anticipated higher taxes and the need to finance the deficit."

    or Fama (ok, I know he is a finance guy), but still..

    "...people must ignore the fact that the government will raise future taxes to pay back the debt. If you know your taxes will go up in the future, the right thing to do with a stimulus check is to buy government bonds so you can pay those higher taxes. Now the net effect of fiscal stimulus is exactly zero, except to raise future tax distortions. The classic arguments for fiscal stimulus presume that the government can systematically fool people."

    All Krugman and Delong are really doing in these cases is calling out people for presenting RE as if it were some sort of deal breaker for stimulus - something that you agree is not the case.

  19. Nick: OK, I see what you mean.


    Poole is not invoking RE in making this argument. He is assuming (quite rightly) that taxes are distortionary (and this violates the RE theorem). Increasing the debt today postpones the distortionary taxes needed to finance it.

    Fama is clearly invoking RE. But if he believes it, he shouldn't worry about higher deficits today.