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


Friday, December 30, 2011

On Paulo and Bobby, English and Math

I was once told by an English professor that Joseph Conrad preferred to write in English (his third language) because sentence meanings in that language often had a wonderful ambiguity that added an artistic flair to his prose.
 
Well, I'm not sure if that story is true. But I do know that it is easy to misinterpret what people mean when they try to communicate their economic theories in "plain" English. That is why academic economists, when speaking among themselves, prefer to communicate in a much more precise language--math.

For those among you who do not understand this language, I'm sorry. I'll do my best to translate into English as I go along. What I want to do here is provide a formal (mathematical) framework to evaluate the discussion on Ricardian equivalence these past few days (see my previous two posts).

Before I get started, I want to make a few things clear. I was not trying to defend Lucas' claim that G fully crowds out private spending. I am not a Republican (I am a Canadian). I agree with some of things that Krugman says (just take a look at some recent posts). I am annoyed that Krugman repeatedly attacks Lucas for "not understanding his own theory." Not only was that was a low blow, but that sort of talk just promotes a division that I do not think exists in the profession. Moreover, and more to the point of what motivated my original post, in delivering his low blow, Krugman presented his own muddled view of the role that Ricardian equivalence played in Lucas' argument.

So let me try to clear things up. Note that I do not speak for Lucas here. What follows is one possible interpretation of what he had in mind. More precisely, it is what came to my mind when I was trying to interpret the content of his speech.

The model I have in mind is a simple overlapping generations (OLG) economy. People live for two periods; they are "young" and then "old." The population is constant. For simplicity, the young do not care for consumption. Instead, everybody wants to postpone consumption to old age (this is not a critical assumption).

The young are endowed with a unit of labor that produces output y (the young supply this labor inelastically, so we may treat y as an endowment). The young also possess an storage technology; k units of investment today yields F(k,g) units of output tomorrow, where g denotes government investment spending. I assume that output F(k,g) is increasing in both k (private investment) and g (public investment). For simplicity, assume that all capital depreciates fully after it is used in production.

Consider the following two specifications of F(k,g):

PF1: F(k,g) = f(k+g)
PF2: F(k,g) = A(g)f(k)

In PF1, private and public capital are perfect substitutes in production. What this implies is that an increase in g lowers the marginal product of (the return to) private capital spending. In PF2, private and public investment are complements. What this implies is that an increase in g increases the marginal product of (the return to) private capital spending.

I believe, though I am  not sure, that Lucas had in mind specification PF1. At least, this is an assumption that is consistent with his conclusions. He would have come to a different conclusion if he believed PF2. Note: the choice of PF1 vs PF2 has nothing to do with Ricardian equivalence. 

Let me continue to describe my model economy. There is a government security that earns a gross real rate of return R. In the present economic climate, with nominal interest rates close to zero, R<1 is the inverse of the gross rate of inflation. I treat R here as a policy parameter.

The budget constraints for a young agent in this economy are given by:

k + m = y - t
c = F(k,g) + Rm - T


So here, a young person must take his after tax income (y-t) and make a portfolio allocation choice: how much to invest in private capital k and how much in government money/bonds m. In old age, the agent gets to consume the proceeds of his investments, minus his  future tax obligation T.

Next, we have to specify the government budget constraint. I consider two extreme cases.

GBC1: g = t + T/R
GBC2: g = (1-R)m

Under GBC1, I am assuming that the burden of financing g falls entirely on the young. This assumption (together with my use of lump-sum taxes) is going to generate a Ricardian equivalence result: the young are not going to care whether they are taxed now or later for g. (Note: Ricardian equivalence would not hold if I assume instead that the burden of finance falls on both the young and old--that is, if I assume that current g is financed by the current young and current old--in contrast, here I assume current g is financed by current young and future old).

Under GBC2, I assume that g is financed entirely through money creation (seigniorage revenue).

Finally, I consider two experiments:

E1: a permanent increase in g
E2: a temporary increase in g

OK, now let's investigate some of the properties of this simple model and see how it can be used to make sense of things.

Analysis

Case 1: PF1, GBC1, either E1 or E2

The key equation is the one that equates the marginal product of private capital investment to its opportunity cost:

[1] f'(k+g) = R

Result: An increase in g fully crowds out k (so future GDP remains unchanged). This is independent of whether the young are taxed now or later.

Does this conclusion rely on Ricardian equivalence? Well, yes and no (assuming distortionary tax finance would imply that an increase in g would decrease future GDP). Consider the next case.

Case 2: PF2, GBC1, either E1 or E2

The key equation now takes the form:

[2] A(g)f'(k) = R

Result: an increase in g stimulates k (so future GDP increases). This is independent of whether the young are taxed now or later.

This is the sense in which I believe Lucas' remarks have nothing to do with Ricardian equivalence (it has to do with his belief of PF1 over PF2). And indeed, what he literally says is "and taxing them later is not going to help." That is, it might even hurt--which can only be true if one departs from Ricardian equivalence (e.g., by assuming that the future tax hit will be distortionary). Again...words, words, words...we need an explicit model to decipher and evaluate what he really meant.

Aside: I often hear people say things like "Well, yes, if the increase in g is permanent, then it will fully crowd out. But this does not hold if the increase in g is temporary." My reply to this is: you are wrong. Take a look at the model above. It is possible for a permanent increase in g to increase GDP permanently. In particular, Cases 1 and 2 remain valid whether or not the increase in g is temporary or permanent (they hold for E1 and E2).

Case 3: PF1, GB2, E1

The key equation here is again given by [1]. A permanent increase in g is financed here by an inflation tax. Increasing g obviously requires increasing inflation (lowering R, the real return on government money). But if R is lowered, then condition [1] implies that k+g increases. That is, individuals substitute out of money and into capital (private or public). Consequently, if the government increases g permanently and finances it with money creation, output expands. (Note: this result need not be welfare improving. Do not confuse GDP with  economic welfare).

Case 4: PF1, GB2, E2

OK, so here we have a one-time increase in g financed by a one-time increase in the money supply. I think that this is what Lucas likely had in mind when he claimed that a money-financed increase in g stimulates.

The analysis here becomes a little more complicated because we have to do "out of steady state" analysis. Let me instead give you the intuition.

It is known that for OLG models, that money is not generally neutral (despite the fact that prices are completely flexible--indeed, I think that price flexibility is critical for the  non-neutrality result). In this model, a one-time increase in the money supply to finance a temporary increase in g will cause a surprise jump in the price level, which has the effect of reducing the purchasing power of the money brought into the period by the old. (If you are an Austrian, you will complain that the old have had their savings stolen by the surprise inflation policy). The effect is to divert purchasing power away from the old (who want to consume) toward the young (who would rather invest). This money-financed increase in g will stimulate; which is consistent with what Lucas said. Moreover, the result relies on a failure of Ricardian equivalence. (In a model with an infinitely-lived representative agent, the money-financed increase in g would have no effect at all, given PF1).

Conclusion

A reader of mine provided me with this quote (apparently, from Brad DeLong):
I learned this from Andy Abel and Olivier Blanchard before my eyes first opened: increases in government purchases are ineffective only if (a) "Ricardian Equivalence holds and (b) what the government buys (and distributes to households) is exactly what households would buy for themselves. RE by itself doesn't do it."

I think this is a nice way to summarize things. (Keep in mind that "ineffective" in the quote above means "no effect--whether good or bad.")

In conclusion, Lucas' remarks need not be interpreted as his theory relying on RE. Indeed, as I hope to have made clear above, his remarks, when taken together, require a departure from RE. The key assumption he makes, in my view (who really knows?) is the part (b) in DeLong's quote (my PF1). That part has nothing to do with RE.

Happy New Year, everyone!

Postscript Dec. 31, 2011
An economist that I admire once said this:
"...just talking plausibly about economics is not the same as having a real understanding; for that you need crisp, tightly argued models."
In case you missed it, Krugman takes a nice shot at me here: I Like Math. I like the cartoon! Moreover, I agree with what he says: "If you resort to math to justify what looks like a very foolish claim, and you can't find a way to express that justification in plain English, then something is wrong."

By "foolish," I presume he means "logically invalid" and not "empirically implausible." For those who speak the language of math and are familiar with OLG models, I have shown that there is a logic to the Lucas view as expressed in that speech. (I don't personally believe that the view is empirically plausible, but that is beside the point of my original post). I have shown that the logic implies a departure from RE; contrary to Krugman's claim. I have tried to express this logic in plain language here and here. And in keeping with the sentiment of the quote above (yes, by PK), I tried to re-express the logic in mathematical form to complement what I said earlier. If I have failed in any way, it is in my ability to communicate the idea in "plain" English. I am not as talented as Krugman in this regard. The logic of my argument, however, remains sound.

But I think it is now time to stop. Let me end by alerting you to an interesting take on the matter by Henrik Jensen: The Krugman Multiplier is Too Big. (He includes a link to a video of the speech by Lucas.)

Postscript Jan. 2, 2012

I should have linked up to this classic paper by Neil Wallace earlier than this, but better late than never: A Modigliani-Miller Theorem for Open Market Operations. As macroeconomists know, there is a strong connection between RE and MM (they are essentially the same proposition applied in different contexts). The Wallace paper asserts that open market operations "matter" only to the extent that some or all of the assumptions that underlie RE/MM are violated. Lucas believes that monetary policy matters. Ergo, his arguments (whatever they might be) cannot be based on RE alone.

Postscript Jan. 09, 2012

Well, I'm sure this one is going to fly under the radar, but I feel the need to record it here. It seems that Brad DeLong agrees with me (h/t Mark Thoma); see here. (Well, he doesn't mention me by name, but his elaboration squares with what I have been trying to say all along.)

Yes indeed, one may question whether the mix of publicly provided goods and services substitutes more or less well with privately supplied goods and services. It matters for whether how a change in G is likely to impact the economy. Ultimately, it is an empirical question. And it has nothing to do with RE. Krugman was wrong to question Lucas' understanding of his own theory. Instead, he could have legitimately questioned Lucas' parameter estimates governing the substitutability of private and public expenditure. But really now, I suppose that would have been a lot less fun.

Postscript Jan. 11, 2012

Krugman is like your neighbor's annoying little puppy that just won't stop gnawing at your feet. Scott Sumner weighs in here: Nobel Prizes for Alchemy?

73 comments:

  1. I'm reminded of Coddington's wisecrack about Clower's exposition of what Keynes 'must' have meant: this is not so much reading between the lines, as reading off the edge of the page. If Lucas had something like that in mind he should have said so. But all credit to you for taking the trouble and happy New Year to you too.

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  2. Haha, yes, that's a good one, Kevin. Are you suggesting that Lucas might have been clearer in his exposition? Yes, I agree. Would you want to approach him to his face and tell him he doesn't understand his own theory? I doubt it. Thanks for the New Year greetings!

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  3. A good addition would be to point out that it may be that A(g) is actually A(g,R), so that debt-financed fiscal stimulus is a lot more effective in a liquidity trap. If A'(g)>0 and A is not a function of R, then it seems to me that it's really just a case of inadequate public good provision. Would you agree?

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  4. David,

    That's a really good post and I agree that that's probably what Lucas had in mind.

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  5. "Would you want to approach him to his face and tell him he doesn't understand his own theory? I doubt it."

    No, my approach would be more along the lines of an earnest student seeking clarification. But that's to some extent a tactical choice. Similarly, if I was playing chess against a grandmaster I'd open 1. Nf3 rather than going for something hairy like the King's Gambit. I'd still lose of course, but I would probably hold out a bit longer. Krugman can afford the Bobby Fischer swagger: "The weakie has made a lemon and is busted", or words to that effect.

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  6. AdamP: thanks!

    Noah:

    Well, I suppose that "high-brow" theorists would take a dim view of assuming that an interest rate enters the production technology, but I agree that doing things this way might be capturing something that my current formulation misses. You may be interested in this piece by Larry Christiano, Eichenbaum and Rebelo:
    http://faculty.wcas.northwestern.edu/~yona/research/Multiplier-version12.pdf

    It is interesting to ask what the "optimal" level of G is in my model economy. I'm pretty sure that the condition would require that the marginal return on public investment equals the "natural" rate of interest (population growth, in this model).

    If A is not a function of R, then yes, it is just a case inadequate (or too much) public good provision.

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  7. BTW David,

    It's probably also worth you pointing out why a guy like Lucas would tend to believe in PF1 and not PF2.

    Presumably if there was no government supplied infrastructure, roads and stuff, then forming a government and having them build that stuff would be complementary to privat capital. So for very small stocks of government capital we'd have PF2.

    At some point though we reach a point where additional infrastructure is less helpful and perhaps even wasteful. Now PF1 obtains.

    A government that behaved optimally would invest until just about that point, so if in the past the government had behaved optimally then we should be in PF1.

    A guy like Lucas would always take as his baseline assumption that the government, at least on average over the long run, has been behaving optimally. That's why his baseline case would be PF1.

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  8. You can get quite interesting fiscal multipliers, either positive or negative, as big or as small as you want, by making just the right assumptions about whether current (and future) g is either a substitute or a complement for current or future k and/or c.

    For example, make current g a complement to future c, and a temporary increase in g will cause people to save more so they can consume more in future, and the fiscal multiplier is negative. "The government is building a new road, so I will stop eating restaurant meals and save my income so I can buy a car next year when the road is completed".

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  9. AdamP: Could be. It would be interesting to know what he really thinks. I guess we'll just have to ask him!

    Nick: Yep. That's partly why I get sometimes get annoyed with proposals to increase or decrease in some generic G as a desired policy. Surely, it matters what that G consists of and how it substitutes/complements private sector output.

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  10. I agree with Kevin. You develop an interesting model but to claim this is what Lucas had in mind is a real stretch. When most people talk about RE they have a much simpler version in mind in which it IS true that a permanent increase in G has no effect on AD but a temporary one does. I agree Lucas is not "most people" but if he had your sort of model in mind he might have said so.

    And is it really that hard to accept that a Nobel Prize winner can, in an informal set of remarks, say something sloppy? When Linius Pauling and Crick and Watson were racing to discover the structure of DNA Pauling came up with a paper which contained a basic chemical error – one that was clear to anyone who had read his own textbook. And Pauling won two unshared Nobel prizes in two separate fields.

    These guys are smart but they can say daft things just like the rest of us.

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  11. David,

    This is a nice outline, and very tractable. To me it looks like you've captured the essentials of Prof. Lucas' off-the-cuff remarks.

    My only critique is that one doesn't have to use symbolic logic to clearly communicate. However, if one uses verbal logic, one should employ it carefully and define all important terms up front. The master here is W.H. Hutt.

    It is very difficult to have a good detailed verbal blog post, because verbal logic is easily muddled. But it's also difficult to do one in symbolic logic because non-economists may think it's a sham. And, of course, Austrian economists think that symbolic logic isn't nuanced enough to capture all the neat stuff going on in human decision making. Ultimately, I have a great concern that policy debates are leaving journal articles and professional conferences and going to the blogs. I don't think this is a good trend, but I've been wrong before.

    In any event, Happy New Year! My best wishes for a productive 2012.

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  12. You don't actually have to strain so hard to guess or imagine which way Lucas meant his remarks, since they were followed by this:

    "Christina Romer — here’s what I think happened. It’s her first day on the job and somebody says, you’ve got to come up with a solution to this — in defense of this fiscal stimulus, which no one told her what it was going to be, and have it by Monday morning. So she scrambled and came up with these multipliers and now they’re kind of — I don’t know. So she scrambled and came up with these multipliers and now they’re kind of — I don’t know. So I don’t think anyone really believes. These models have never been discussed or debated in a way that that say — Ellen McGrattan was talking about the way economists use models this morning. These are kind of schlock economics."

    That gives at least a clue as to what he was getting at, enough to render all of the analysis above pretty much unecessary.

    It's also curious how a speech that contained this kind of cheap unwarranted accusation is the one you're defending while clearly being outraged by Krugman saying that Lucas's remarks altogether "betray a fundamental misunderstanding of his own theory". It's really not such a terrible thing to say; the person who made the remarks can clarify and say that he wasn't clear the first time (which you now say is the case) and take back or restate what he said. Again it's curious in the extreme why you've become so outraged over that statement that you actually agree with at least in a way, and not of accusing someone like Romer of "schlock economics". It's odd enough that you can perhaps imagine why people might assume you were a staunch Republican, since it would explain such a strong one-sidedness here.

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  13. Well, Conrad sure did a more bang-up job of communicating than that manifest in the thrust of Andalfatto's remarks, much less the sloppy speaker he defends; whether in language or mathematical symbols. All and all, if you can't communicate in the English language - assuming you possess the facility, that is - then you have nothing to say. Let's just leave it at that.

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  14. ParisNewYorker raises a point I admit I don't get, either. As I understand it your main problem with Krugman's post was his not reading Lucas favorably (though your point was much more elaborated, of course), as you don't really disagree on the technical question itself. Krugman can be critisized for this sort of thing, i.e. one-sided assessment of arguments and righteous ad-hominems, for almost every single post. But here? How can you ciritisize him for doing it once again, without acknowledging Lucas' (at least) equally derisive comments on Romer, calling him a gentlement instead in the comments (with regard to Krugman, though). Moreover, this is a stated reason why Krugman was annoyed with Lucas in the first place...

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  15. why would you use an OLG model to analyze Ricardian equivalence?!

    Has Lucas ever used OLG (I haven't read all his papers, but I don't seem to recall any OLG, except perhaps the Blanchard type model).

    In any case, Ricardian equivalence is about budget constraints in present value terms, together with no-Ponzi game conditions, and it's about distortions and deviations away from perfect markets. You should read Tobin on this.

    At any rate, why would you assume (ref. the quote you attribute to someone without formal evidence that that someone actually wrote it) that the government would redistribute the goods it purchases to households!? I doubt very much that this is what Lucas had in mind. And if he did, that's where he was wrong. Building bridges to nowhere or whatever is purchase of a public good, not of a private good.

    The sort of universal equivalence type of argument applied to government purchases has no relevance whatsoever to the fiscal packages implemented by the government Christy Romer was advising.

    But in this your intuition is correct: ever since the government bailouts of financial institutions I have donated less cash to bankers in need.

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  16. "academic economists, when speaking among themselves, prefer to communicate in a much more precise language--math."

    My colleagues talk like that all the time. But natural language is plenty "precise" - that is why, for instance, we have adjectives and adverbs. And in making mathematical models we leave such "incidental detail" (Schelling) out in order to distort reality. That is not more precise. More useful, maybe.

    In the end all your math is not "precise" enough to allow you to figure out which of the assumptions is doing the dirty work for Lucas.

    I am not a luddite. I just think the rhetoric and the reality don't match terribly well.

    Happy New Year.

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  17. If you want tounderstand why Krugman was soaggressive, youmight take him at his word. Clearly he feltt that Lucas smeared Romer and politeness was not in order.

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  18. Alfred Bostick is seriously out of his depth here.

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  19. "And the fact that people are leaping in to defend Lucas here tells you something."

    Indeed.

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  20. Like other commenters, I'm a little puzzled as to why we're spending all this effort to read between the lines of speakers who are still with us and have every opportunity to clarify their remarks themselves if they choose to. However, since that's what's afoot, let me return the favor you're doing Lucas and explain what I believe Krugman is really saying. I will attempt as best I can to express this mathematically.

    As I understand it, economists propose models (M) designed to explain data (D) in such a way as to produce a generally accurate picture of what's actually happening in the world. The goal is:

    M + D = F

    where F is, approximately, the facts -- what we see actually happening, like interest rates rising or falling and such. (Sorry, your site here isn't allowing me to do the wavy equal sign for approximation. My own model will be accordingly limited. But, onward.)

    Once we have a proven model, we can use it to decide upon policies (P):

    M -> P

    The problem is that rightist economists have a PREFERRED set of policies. Call this P(r). Of course, so do liberal/left economists; let's call this one P(k), with "k" standing for Keyenesian or Krugmanite, as you wish. What's been happening in recent years is that M(r), the models preferred on the right, when added to D, do not equal or approximate F. But M(k), the liberal / Keyesian models, do. Therefore, M -> P(r) doesn't hold; a correct M appears to imply P(k).

    Krugman has devoted tens of thousands of words over these last few years to chronicling the right's various responses to this. One popular one has been to deny or redefine D, replacing actual D with a right-preferred D(r): claims, for instance, that inflation is up even though it isn't. Similarly with F, which has given way on the right to a mythical F(r) -- a world in which, for instance, Spain was profligate before the crash, Ireland is doing well now, and, more to the immediate point, stimulus spending didn't help the U.S. economy. All of these are attempts to shore up the implausible view that, because P(r) MUST be the correct policies, the model we should be using is M(r):

    M = M(r)

    even though it's increasingly clear that

    M = M(k).

    What Krugman is saying about Lucas is that he has found yet another strategy for aligning M and M(r): simply redefine M(r) -- where "r" means both rightist and, for this purpose, Ricardian -- to be something other than it is. In other words, there is now a "Lucasian" M(r), which we'll call L(r). Your analysis above is an attempt to explicate and defend this special kind of Ricardian modeling.

    So here's where I think you're talking past Krugman. He doesn't mean that Lucas "doesn't understand" Ricardian equivalence in the sense that he fails to grasp the way M(r) would be explained in textbooks. He means that Lucas willfully insists that M(r) is really L(r), because his ultimate goal is to save P(r) against an F that refuses to point to that outcome. He is also unhappy that

    M(k) + D = F -> P(o)

    where P(o) is the set of policies advocated in the Obama administration by people like Christine Romer. So as a further rhetorical flourish, he insults Romer in the way you've mathematically tried to justify.

    Hope this helps. Happy new year.

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  21. Krugman's shot at Lucas was a pale shadow of Lucas' own low blow aimed at Christina Romer. Have you seen freshwater guys at conferences? They break out into giggles and otherwise act like drunken fraternity thugs if anyone dares to mention sticky prices or claims that government policy has any real impact. Your own credibility here is now completely shot.

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  22. Thank you, JeffersonSmith, for discovering the humor in this otherwise-lamentable affair.

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  23. Mr. Andolfatto’s attempt to rebuke Krugman is a pristine example of what is wrong with mainstream Anti-Keynesian Economics (Rational Expectations, Real Business Cycle, etc.) Lucas is caught making a logically faulty and confusing statement on something about which he is expected to have a very deep and intimate knowledge, and as consequence, should be able to use efficiently as a tool to explain reality. Then, one of his followers wants to convince us that what he said is so profound –remember, Lucas was supposed to explain reality- that, as the utterance of an oracle, it required an interpretation. One expects from the follower a plain English elucidation (like Krugman’s criticism) and what you get is a lot of math and more confusion. Abusing math and pretending to cover with it the fallacies contained in its models is how Rational Expectations and Real Business Cycle has gained “scientific credentials”. However, when the ultimate test for any real scientific theory, i.e. to explain reality, has shown up in the form of the present crisis, these mainstream schools of thought have not revealed any capacity whatsoever to explain it and to guide the actions to be taken. As a timely article in the last edition of The Economist implies, the blogosphere may expedite the demise of the barren orthodoxy since it permits the exposure of its fallacies in a way and for an audience that was oblivious of them before.

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  24. "I don't personally believe that the view is empirically plausible, but that is beside the point."

    No it is not freaking beside the point. When Lucas speaks the implication is that what he says contains a policy prescription. If he is just playing abstract games with no implications for real world policy no one should even be listening to him. There is work to be done by the grown-ups.

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  25. Is it a coincidence that once ParisNewYorker brought up the context that was really agitating Krugman -- Lucas' unwarranted slime (unwarranted by Andolfatto's own analysis) of Christina Romer -- a point that is picked up by Anonymous, Sander, and -- less charitably -- by Rich888, all of sudden Andolfatto is AWOL with clarificatory comments?

    David, as ParisNewYorker suggest, why not just call up Lucas and ask him to clarify what he was saying, with respect to both RET AND Christina Romer? The only math you'll need is his phone number.

    Or are you afraid to present your own analysis to his face, as you suggest Kevin might be?

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  26. It's toubling that our authority seems to arrive from stridently adjusting our shoe buckles.

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  27. The economics went over my head quite a while ago, but as for the plain English, you may want to revisit your blurb at the top of the page: "where I continue teach part time and supervise Ph.D. students."

    I assume you meant to say "where I continually teach part time..."

    (Apologies for the anonymous comment; no time to create a sign-in right now...)

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  28. Math can obfuscate as well as clarify, and all this pretty modeling serves only to hide a tautological argument. Stimulus is about increasing y, not k. Holding y constant renders the entire exercise moot.

    The analysis elaborates on the trivial topic of asset allocation in an economy that can't be stimulated - i.e. whether government spending is a wash because of Ricardian equivalence or another mechanism that equivalently makes stimulus fail.

    Rearranging the first consumer constraint, k + m + t = constant. This yields the entirely uninteresting conclusion that private investment increases to the extent that there is a combined decrease in government borrowing and current taxes - which based on the government balancing its books means a decrease in g or an increase in T.

    dg = dT is Ricardian equivalence, and implies dk = 0. dg > 0 and dT = 0 means an increase to the policy rate to increase m (at the expense of k), and is a straight crowding out result. In these and every other case, the only net moving part in the model - regardless of what policy levers are pulled - is the reallocation of tax burden between old and young and its consequence for asset allocation. Useless.

    The important question is whether dy/dg > 0. This blog analysis simply assumed it away, but it is the heart of the intuitive (and correct) interpretation by Krugman. OLG isn't really the best way to frame a transient phenomenon - as noted in the Case 4 analysis that reverted to intuition. But as best I can, consider dg as occuring in the current period, offset by dt = dg/2 in the current period and dT = dg/2 in the future period. d1y = dg/2 in the current period, washed out by dy2 = -dg/2 in the future...except that y2 has been increased by dF(k,g) = F(k,g+dg) - F(k,g) > 0. It's the same benefit as tax deferral in an IRA. That's the stimulus.

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  29. Not sure why you are bending over backwards for Lucas. If anyone has been divisive its been the Chicago School types dismissive of anyone who can't see the divine wisdom of new neoclassical economics.

    The trouble with math in isolation is that while it helps with analysis it requires a kind of critical mind to constantly challenge both the assumptions and definition of terms.

    You should read more Veblen as he was very much one who made fun of economics of his day. I grant to all the point that Veblen was a better critic that a founder of an alternative theory, though.

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  30. IANAE, but it seems Lucas owes an apology to Romer, no matter where he thinks he stands in economics.

    Perhaps he should reconsider his criteria for applying derision.

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  31. Anyone named "Jefferson Smith" should be expected to hit the nail on the head when it comes to explaining political economy-and he sure does.Thanks for the outburst of lucidity J.S.

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  32. I have been following this "online" discussion about RE. No need to say that I find Krugman’s behavior disgraceful and his latter reply today about your use of math simply staggering.

    I wanted to add my two cents, though, because I do not think DeLong's quote is right.

    There is a much simpler model where increases in g do not have any effect in output, where RE holds, where government does things that households do not like and that, in an admittedly totally subjective evaluation, I think it is perhaps closer to Bob's view of the world.

    Take an RBC model with GHH preferences and government expenditure financed through lump-sum taxes. This is a plain vanilla model that is taught in first year macro everywhere, starting at Princeton (of course Krugman has never bothered to talk with his colleagues in macro, so he may not know this). Government expenditure is fully thrown into water without yielding any utility (this is just to break DeLong’s point b)). Since GHH preferences imply there is no wealth effect, labor supply is given by

    MUL = MPL

    Once we have pin down labor supply with the previous equation, since capital and productivity are state variables, output is fully determined from the supply side (this is actually just a modern dynamic version of the "classical model" that Keynes describes in chapter 2 of the GT, oh! Wait a second! We are from Minnesota, we are not supposed to know anything about the GT, never mind then).

    Then, since y = c+i+g and y is determined in the supply side block of the model, any change in g would be undone by changes in c and i. Those changes come about through a change in the interest rate. That is, we have a full old-fashion crowding out but in an RBC model. In fact, output will fall in future periods because the fall of i will translate into lower k' (if we do not like this result, we can drop capital from the model).

    This result will be true even if we have a binding ZLB (for example because the discount factor is temporarily bigger than one) as long as prices as fully flexible (we are in an RBC world anyway). Now, instead of a change in the nominal interest rate (stuck at zero), we will have a change in the price path that delivers the same result.

    Then, in this simple model:

    1) Changes in g do not have any impact on y.

    2) RE holds.

    3) You can have a ZLB.

    4) DeLong's point B does not hold.

    It requires an epsilon more effort to describe a variation of this RBC model where monetary policy would affect output while keeping 1)-4) above. A simple (but by no means the only) way to get it through assumptions in the timing of the revealing of information (for instance, monetary policy is revealed after prices have been fixed but fiscal policy is revealed before).

    Conclusions:

    1) Lucas’ words were fully compatible with a rather standard RBC model. You may not like RBC models: ey, that is legit, but you cannot claim that Lucas does understand modern dynamic macro.

    2) Krugman, apparently, does not. He prefers to insult the rest of the profession rather than to attend Princeton’s macro seminars.

    3) To most commentators in this blog saying silly things about Chicago economics and stuff like that: you guys do not have a f@*& of what you are talking about. Have a minimum of modesty and keep your mouth closed.

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  33. Interesting attempt, but it obviously has nothing to do with what Lucas actually said. Lucas was talking about a real world economy, in recession and claimed "the only part of the stimulus package that's stimulating is the monetary part" and that "then taxing them later isn't going to help, we know that." That's just plainly wrong. There is no defending it.

    If someone builds a perfectly good barometer, and then hangs it on the wall, and tries to use it to tell time, is it not fair to question whether they understand the tool?

    As for your model, it's interesting, but it's really not that clear you understand it either. But I guess saying so means I'm also guilty of a low blow. Still, you say of case 4:

    "The effect is to divert purchasing power away from the old (who want to consume) toward the young (who would rather invest). This money-financed increase in g will stimulate; which is consistent with what Lucas said."

    Um, no. Shifting purchasing power from consumption to investment would not be a "stimulus".

    It is possible to have a full employment economy which is capital constrained, in which demand side stimulus would be crowded out, and where increasing investment would increase long term growth. But a model of such an economy would clearly have no relevance to analysis of a stimulus package in response to a financial crisis and recession.


    I'll also quibble with this:

    "In this model, a one-time increase in the money supply to finance a temporary increase in g will cause a surprise jump in the price level"

    How in the heck do you expect an increase in money to cause an increases in prices, by magic? Prices increase when demand for goods and services exceeds supply.

    But in your model, you have managed to create a fixed supply, and a consumption function with no sensitivity to current interest rates. Consumption is only by the old, out of past earnings. In your model, the additional money is simply held by the young as a substitute for bonds. So in this model, inflation would be the same regardless of whether G is financed by bonds or money.

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  34. By "foolish," I presume [Krugman] means "logically invalid" and not "empirically implausible."

    I think that's what he does mean. AFAICT he is pointing to this model as an example of how a model-builder can go wrong. He leaves finding the error(s) as an exercise for the reader. That's fair enough, his Princeton students pay hefty fees, but even they don't get worked solutions to all the exercises assigned.

    My first guess is that the problem resides in the way the taxes are levied. What does it mean to say the burden of financing g falls entirely on the young? Hardly that T=0. More likely that the young must pay the discounted value of their future taxes in advance rather than waiting. But then the (non-Ricardian) equivalence derives from the fact that $1 today equals $1 today. Isn't that a bit trivial?

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  35. Your benign interpretation of Lucas has the advantage of assuming that we live in a world of cavalier economists - despite the fact P Krugman (very unlike himself) steps out of line from time to time.
    But there can be other interpretations in this same cavalier world. For instance, Brad Delong's is that Lucas just jumped the gun in talking before thinking it through.
    Either way, this weird argument gave us the opportunity to confirm that Lucas has good blogger friends. That by itself is heartwarming in any circumstance.

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  36. Note: it would be most helpful for me if anonymous commentators would adopt a handle. Thank you.

    Anon Dec 31 12:53AM: I did not claim that this is what Lucas had in mind. I offered it as one possible interpretation of what he said. There are probably many other interpretations too, with logical validity. If so, then on what grounds does one publicly denounce the man as ignorant of his own theories? I cannot make things any clearer than this.

    Prof J: As it turns out, I have read Hutt (as an undergrad, no less). Thank you, and a Happy New Year to you too.

    ParisNewYorker: I have posted a link in my postscript that takes you to a video of Lucas’ speech. In my view, he was not taking a personal shot at Romer. He was describing the political reality of an economist suddenly being thrust in a real-world policymaking situation. I think that all of us would have to resort to some form of “schlock” economics at this point—economists do not have a single perfect model that would tell a policymaker what should be done.

    It’s odd enough that you can perhaps imagine why people might assume you were a staunch Republican, since it would explain such a strong one-sidedness here.”

    Yes, but given that I am not a Republican, what does this tell you about the strong one-sidedness here? And given that Lucas has publicly said that he voted for Obama in the last election, what does that tell you? I’m very interested to hear.

    Alfred W. Bostick: what did you say?

    Pat Toche: I used the OLG model for its analytical tractability. This is a blog, remember. Btw, it is a common misunderstanding that one cannot get RE in OLG models. Not true. I showed how in my post. Of course, non RE results are possible too. I don’t have to read Tobin on this; the OLG model is an environment with all the things you describe. My interpretation of Lucas is that government provided output substitutes more or less perfectly with privately provided output. I “assume” this on the basis of several remarks he made during his speech. Go listen to it (link available above).

    Jim Johnson: Yes, perhaps. And correct, the math is not a tool that can extract the true interpretation of what Lucas meant. But then again, neither can English, or any other language.

    Sander: Yes, I get that. I think that Krugman felt that Lucas insulted Romer. I viewed it as a slight against the entire profession. In any case, go see it for your self—a link to the video of his speech is available above. It seemed pretty innocuous to me. But, there you go.

    Jefferson Smith: Well done!

    Rich888: I cannot speak for those people who act like “drunken fraternity thugs” at conferences. I’m not sure what this observation has to do with Lucas. Go and take a look at the video of his talk.

    Anon Dec 31 11:07AM: Calm down and clear your head. Go listen to the video of his speech. Read the nature of my criticism carefully. Leave your preconceptions at the door. Feel free to disagree with me. But rather than just categorizing me as part of a “mainstream anti-Keynesian” group, explain to me what fault you have with the logic presented above.
    Absalon: Yes, it is freaking beside the point. Think about it.

    Billyblog: Hmm…an anonymous poster accusing me of cowardice? Why don’t you call me up and let us have a conversation to discuss the issue? Better yet, let’s go for a brew and talk about it.

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  37. Anon Dec 31 12:14PM

    Stimulus is about increasing y, not k. Holding y constant renders the whole exercise moot.

    In the simply model above, stimulus has the effect of increasing future GDP, not current GDP. That was just a simplifying assumption to get at the fact that infrastructure investment today can be expected to improve the future productive capacity of the economy. The analysis is robust to letting y vary.

    dg = dT is Ricaradian equivalence,…

    Um, no it is not. Go check with someone else, if you do not believe me.

    Anon Dec 31 4:48PM: Thanks for the analysis—I hadn’t thought of that. It has been duly noted in my head. As for you concluding point 3, I think that a lot of the “passion” that surrounds these types of discussions revolve around politics rather than economics. I wish we could separate the two, but it seems impossible on a forum like this.

    Acerimusdux: Yes, Lucas was talking about a real world economy. But all of us—you included—have a model economy in our heads when we try to predict and interpret the likely consequences of an intervention. I have shown that there is a logic to Lucas’ point of view. It may not be the logic he had in mind. It may not be empirically accurate. But this does not imply that he does not understand the implications of his own theory.

    As for “my” theory, trust me, I understand it perfectly well (it is not “my” theory; it is a standard OLG model). I did not complete the formal investigation because it was getting too technical for my blog. But I will be happy to send you the full analysis.

    You can say “um, no” all you want. We will get nowhere like this. Are you in the neighborhood? Come drop by and we can talk about it.

    How the heck do you expect an increase in money to cause an increase in prices, by magic?

    Are you suggesting that if the government started buying up goods and services, and did so by printing up new money, that this is likely to have no impact on the price-level? I’d be curious to know what sort of theory delivers this as a prediction. Moreover, I think we have plenty of empirical evidence that contradicts it.

    Yes, in my model, I make no distinction between money and bonds. We are in a liquidity trap. It is a point that Krugman makes frequently. Not sure what your problem is with this part of my model.

    Kevin Donoghue: You are correct, I meant that the young pay the discounted value of their tax obligation. The timing of taxes does not matter in this case—it is a Ricardian, not a non-Ricardian result. (If I had instead assumed distortionary taxation, it would have made things worse, not better). The non-Ricardian part comes in when I introduce the inflation tax.

    Antonio: I’m glad you find it heartwarming. It’s good to know that one has friends, no? Happy new year.

    Thanks for the comments, everyone. Looking forward to more good discussion in 2012. Happy New Year!

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  38. In analyzing any model, the default assumption is that the modeler can do the adding and subtracting part. True, you are sometime disappointed but if so you can then have the satisfaction of pinning the tail on the idiot.

    That given, the place to start is the assumptions, and there is a real doozy here
    " The model I have in mind is a simple overlapping generations (OLG) economy. People live for two periods; they are "young" and then "old." The population is constant. For simplicity, the young do not care for consumption. Instead, everybody wants to postpone consumption to old age (this is not a critical assumption)."

    Now Eli is not familiar with what world David Andolfatto inhabits, but it is clearly not this Earth. The young, almost all the young, do not have enough income to survive by themselves. They are, at first, spending their parent's income and taking out loans for such interesting activities as eating, education and buying a mansion or two until they hit middle age, when, if they are lucky, they have kids, get a slightly better job where they can start saving for retiremet, or increasingly not.

    The old, interestingly, are spending much of their income supporting their kids as a part of the ancient if I am broke and old, my kids will support me system, which, too often is broken.

    Given this quicksand base, it is not too surprising that the result points to what is happening on another planet

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  39. Have I got this right? You have constructed an elaborate model to prove that there may be a world - purely hypothetical since you don't believe some of these assumptions - where what Lucas said may still be true but without implying RE. Can this argument get any more pedantic? Esp since the model/cases you have described are ones with holes around the assumptions that would make them moot in real life. I actually don't think you believe Lucas had a world where his statement was not derived by RE. But it is true that there is a case to be made that what Lucas said can be true without implying RE - but a very stretched case indeed.

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  40. Sriram: Krugman was questioning Lucas' understanding of a theoretical question. How else would you have me address the issue, without being explicit with the theory? Btw, the model I used is not considered to be "elaborate" by the standards of the profession. It is, in fact, of the simple type we use as a teaching tool for undergraduates.

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  41. "Are you suggesting that if the government started buying up goods and services, and did so by printing up new money, that this is likely to have no impact on the price-level? I’d be curious to know what sort of theory delivers this as a prediction. Moreover, I think we have plenty of empirical evidence that contradicts it.

    Yes, in my model, I make no distinction between money and bonds. We are in a liquidity trap. It is a point that Krugman makes frequently. Not sure what your problem is with this part of my model. "

    David:

    I would agree that empirical evidence contradicts this. But I think the empirical evidence in a liquidity trap also contradicts PF1. What I am disagreeing with is your analysis above of the following two cases:

    Case 1: PF1, GBC1, E2
    Case 4: PF1, GBC2, E2

    If you are arguing that full crowding out occurs in Case 1 due to PF1, then shouldn't it also occur in Case 4?

    If you have full crowding out, you should have no net increase in demand for goods and services, so no change in the overall price level. My point is you can't get the change in prices without the increase in demand. But that won't happen if the money just sits in savings.

    I'm not sure why there has been so much confusion over what Lucas had in mind though, given how heavily he referenced Milton Friedman in that talk as the biggest influence on his thinking about this. To me, he was simply saying exactly what Friedman would have said, and said for example here:

    http://www.hoover.org/multimedia/uncommon-knowledge/27142

    (start about 2/3 the way down in response to: "Peter Robinson: There have been various fiscal stimulus plans proposed to get the economy back on track. Let me ask Milton Friedman what he makes of them.")

    This isn't exactly "Says law", that supply creates it's own demand. But the monetarist version of this (at least for those who believe in a strong form where money is essentially all that matters) seems to be a belief that money supply creates it's own demand.

    If you believe that money creates demand, then you can take the monetarist shortcut of assuming that inflation is monetary. But this would be in error if there is a liquidity trap and the money just sits there.

    I believe that Lucas recognized the possibility of a liquidity trap in the very short run, but he thought that additional money created by the Fed would get out into the economy before too long. Thus he argued:

    "I've already said I think what the Fed is now doing is going to be enough to get a reasonably quick recovery committed."

    despite acknowledging that:

    "This huge amount of reserves that Bernanke's put out there is almost all still in the banks."

    and:

    "I think people's cash balances are related to their spending behavior and it's got -- so if it's just sitting in banks, not affecting business or individual behavior, it wouldn't do anything I don't think."

    In short, I think he's was using a basic model that really didn't allow for the possibility of a liquidity trap. He didn't deny that it existed, but he seemed to be hopeful that it would go away by itself before very long. In part he believed that the Fed would not be constrained by the zero lower bound, and would somehow find ways to get this money out there into the real economy. I'm not sure there was a clearly thought out theory of how this would work.

    As for how I think things work in the real world, I believe monetary policy influences demand primarily through it's impact on interest rates (including a significant impact on asset prices and a "wealth effect" related to that). And money influences inflation through this influence on demand.

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  42. I wrote:

    "It’s odd enough that you can perhaps imagine why people might assume you were a staunch Republican, since it would explain such a strong one-sidedness here.”

    And you responded:

    "Yes, but given that I am not a Republican, what does this tell you about the strong one-sidedness here? And given that Lucas has publicly said that he voted for Obama in the last election, what does that tell you? I’m very interested to hear."

    Sure. Your surprisingly emphatic and clearly outraged response to what Krugman wrote seemed puzzling, so one guess as to why you had such a strong reaction could have to do with politics (many Republicans are fiercely critical of Paul Krugman and his views), thus some people might have made that assumption. Since you're not a Republican, as you say, then that would have been a wrong assumption. You might share the same political views as Republicans, and those might color your thinking about economics, there are many possibilities, so it's really not that important, at least in my opinion.

    Your question about what it explains that Lucas voted for Obama is easily answered, it would tend to indicate that Paul Krugman's comment about the strange comments that Lucas made were not based on whether he was a Republican or Democrat, but on the comments themselves. That seems pretty clear.

    Your doubling down, if you'll excuse the cliche, on how accusing someone of "schlock economics" is benign, while accusing someone of making "comments that betray a lack of comprehension" of something specific in economic theory are utterly outrageous and scandalous and warranted all this posting and all this defense of Lucas and outrage at Krugman just confirm my puzzlement at both your post and your comments here, but I do thank you for being honest and clear about it.

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  43. By the way, immediately following the "schlock economics" line in that video, Lucas goes on, referring here to Romer's paper about multipliers and the stimulus package:

    "I think it was a very naked rationalization for policies that were already decided"

    Lest there were any doubt about what he meant.

    So what you're saying is that there are no models for this, and anyone serving a President of the same party, out of political loyalty, would just make up some numbers so as to justify whatever policies his administration had already decided upon.

    I would be curious, to say the least, to hear what Romer would have to say in response to this. Just off the top of my head, the idea that she had no thoughts of her own, prior to this first day on the job with the White House, on these matters, would be a bit of a surprise.

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  44. Acerimusdux:

    PF1 is a specification of the economy's production function. The specification asserts that the government is no better than the private sector at creating capital (and no worse, either). This is a statement about technology. It has nothing to do with the liquidity trap, which refers to money and bonds earning the same rate of interest (so that open market swaps of the two objects have no real consequences).

    If you are arguing that full crowding out occurs in Case 1 due to PF1, then shouldn't it also occur in Case 4?

    No. The two cases differ in how the expenditure is financed. In the first case, the financing is borne "within" generations; in the second case, it is borne "across" generations. (These "generations" are metaphors for people with different consumption propensities). This is my whole point. The method of financing matters, even under PF1. That is why Krugman is wrong to claim that Lucas' argument relies on RE. It does not.

    Yes, if the Fed just created money to purchase zero interest Treasuries, the money just "sits there" as you say. But we are not talking about open market swaps of assets here. We are talking about using the new money to buy G (goods and services). This has nothing to do with the liquidity trap.

    Maybe I'll stop here and wait to see if I've cleared things up a bit.

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  45. ParisNewYorker:

    I do not want to defend anyone causing offense to any other. I'll leave it up to Lucas to decide if he needs to apologize to Romer. As for myself, it did not appear to be a personal insult, but I can see how it may have been taken that way.

    I think you miss a subtlety here. Krugman has insulted many people many times. He has used the same Lucas speech to insult Lucas earlier. (The insults garnered no reply from Lucas.) Isn't once enough? No, he continues to peck away. I am fine with that. Yes, it annoys me, but that's just the man's style. (He also has very many good posts, which is why I continue to read him.)

    But, when he comes out to insult Lucas, accusing him of not understanding his own theory (again), whilst demonstrating to the world that he himself appears a little hazy on the theory, well, then, this is when I decided to step in.

    The really sad part about all this is that there is considerable agreement among us. Krugman favors more infrastructure spending. I have written in earlier posts that I think this is also a good idea, given the low rates at which the US government can borrow, and given the reports of the state of our infrastructure. Lucas himself in his speech says he has nothing against building new infrastructure "if we want it and are willing to pay for it." I wish that a person of Krugman's stature would have spent his column space on emphasizing these similarities, rather than harping on bullshit. It would have been more productive.

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  46. David - by "elaborate" I meant for the economic blogging universe. I am not an economist myself and am in the enviable position of understanding what Paul and you are discussing from scratch with less bias than most economists. Seems like technically PK was wrong (though he did correct himself in a later post without admitting the flaw in his initial critique - you rarely catch PK admitting to his errors). And you do seem to be right to point out that Lucas may not have been getting confused about RE on the basis of that statement alone. But my gut feeling is that Lucas did demonstrate a mix-up (maybe inadvertently) of his understanding of RE, taxes and G spending when he made those comments. And I am sure Lucas realizes this given his pedigree but the debate has now gone on too far for him to admit to it. BTW - pls do read the absolute drivel written by John Cochrane on this issue. Your work is stellar in comparison.

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  47. David,

    I understand what you're saying and I just disagree. With all of it.

    I read Krugman's post, your post, and other responses such as this one:

    http://johnhcochrane.blogspot.com/2011/12/krugman-on-stimulus.html

    ..and in the end I don't see Krugman as fuzzy on the theory in the least, despite your claims. By the way, by your own rules, is that not terrible slander for you to say such a thing about Krugman not understanding economics? Is "Well, he started it" what excuses it when you engage in what you're characterizing as so awful and unacceptable when someone else engages in it?

    That seems pretty weak, I'm sorry, as does "well, this isn't the first time".

    On that point by the way, here's Brad DeLong today, detailing the many many times that people you're defending engaged in the sort of unprovoked "slander" that you're accusing Krugman of.

    http://delong.typepad.com/sdj/2012/01/hoisted-from-the-archives-yet-more-corruption-at-the-university-of-chicago.html

    I read what you have to say, I just find it not convincing.

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  48. ParisNewYorker:

    "The people I am defending?" I do not defending Cochrane, et. al.

    But in any case, this is probably a good place to leave it. I think we both understand each other and we can agree to disagree.

    I do appreciate your reasoned comments. Thanks.

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  49. "I am not an economist myself and am in the enviable position of understanding what Paul and you are discussing from scratch with less bias than most economists."

    No, you find yourself in the position of not understanding. Common problem for noneconomists.

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  50. "No, you find yourself in the position of not understanding. Common problem for noneconomists."

    The issue is that at the end of the day, economists are supposed to be the ones who steer the economy in the right direction by giving the right advice to government - if they build economic models it's not just to get a kick out of it.

    And noneconomists understand very well that economists messed up big time and that we have had a high unemployment rate for a very long time now. If you think that all is fine and that economists are awesome, think again.

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  51. By "the people you're defending" I was referring to this:

    "I think you miss a subtlety here. Krugman has insulted many people many times."

    Those people. Whoever you were referring to. That's a defense of them, as far as I can see.

    I'm happy to hear that you're not defending Cochrane. Honestly, some of these responses are amazing.

    I've been reading Paul Krugman for years, and I have never found anything of what you're describing. No criticism seemed overly harsh, none seemed terribly unjustified, and in fact, and I think you gather that this is my whole point here really, I find what's directed at him quite often to be not only overly harsh but often utterly ridiculous, as in Cochrane's. My own view is that it's politically driven and motivated, but that's a long and even more boring argument, and I agree, it was a bracing discussion and that's enough.

    Happy New Year.

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  52. Anonymous said, "Alfred Bostick is seriously out of his depth here." Anonymous has a point. But I was simply echoing Krugman's point, restating it somewhat more emphatically. I am impressed, though, by the obvious accomplishment and acumen of anyone who would be so bold as to claim that Krugman himself is likewise out of his depth here. Such a judgment could only issue from one carrying VERY SERIOUS creds. Still, I am happy to continue to swim along with Krugman, our heads out of the water, rather than sink to the depths with those drowning in error.

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  53. Okay, aside from everything else, saying "I'm not a Republican!" doesn't prove anything one way or another.

    Sure, you aren't a Republican. That's because you're a Canadian. What they're claiming is that you're a Harper Conservative. Same deal, different name.

    (And, sorry, but that Romer passage was not about how "good economists sometimes do schlock economics". It was an obnoxious, personal, derisive attack. It was worse than anything of Krugman's you've objected to. The fact that you are so ready to apologize for it speaks volumes... and nothing good within them.)

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  54. Anon above:

    I did not mean to imply that I had anything against Republicans. I just don't have any political affiliation of my own. I have good friends of all political stripes, here and in Canada.

    Oh, and one more thing. I feel sorry for you.

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  55. Dave-Why are you pimpin the defendant here? So unnecessary...

    Your blogs in last few weeks did hurt your own credibility more than they saved Lucas's.

    A one last humble advice: Stop posting more on this and just move on.

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  56. David:

    "PF1 is a specification of the economy's production function. The specification asserts that the government is no better than the private sector at creating capital (and no worse, either). This is a statement about technology. It has nothing to do with the liquidity trap, which refers to money and bonds earning the same rate of interest (so that open market swaps of the two objects have no real consequences)."

    Yes, but it asserts that production is a function of investment (g or k), which seems a foolish assumption to apply to an economy in a recession and liquidity trap.

    "No. The two cases differ in how the expenditure is financed. In the first case, the financing is borne "within" generations; in the second case, it is borne "across" generations. (These "generations" are metaphors for people with different consumption propensities). This is my whole point. The method of financing matters, even under PF1"

    I understand that the burden of the inflation tax might fall differently than the burden of direct taxation. And there are real world scenarios where this could produce interesting differences (though probably no real world scenarios where the entire tax burden would fall solely on those who would have spent the money anyway).

    But, if your model contains completely rational actors who will fully adjust to future taxation by offsetting current spending, why would they also not be perfectly rational with regard to the expected inflation tax, and thus adjust current spending to offset that as well?

    The way around this seems to be to create one group of actors who have no current consumption at all, and so cannot adjust current spending, and then to assume an instant price adjustment (even though prices shouldn't actually adjust until the liquidity trap is over). But even then, shouldn't the bond financing case then be the one in which RE fails, since the old in that case will not have to pay the future tax T, and thus have no reason to adjust to it?

    Other than that, I see no difference then in the impact of bond financing vs. money printing in the purchasing power of the young. With either form of financing, k shouldn't change. Y would increase as much as G, which would be offset by an increase in m (whether in money or bonds).

    It seems to me though, that you are suggesting in case 4 that the model would produce a shift from C to G (or K), but even if it did I think that should not increase Y. That is, unless you mean to suggest that output is not impacted by C? In that case, if your production function is really the only determinant of output, then your model is really a "Says law" model, in which supply really creates it's own demand.

    Or to put it another way, a production function cannot really tell you anything about output, unless you also assume an economy that is always operating at maximal output for existing technology. In other words, it's an economy that is not in a recession or liquidity trap.

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  57. Acer:

    Yes, but it asserts that production is a function of investment (g or k), which seems a foolish assumption to apply to an economy in a recession and liquidity trap.

    We usually think of technological capabilities for factor substitution are independent of financial conditions. Perhaps this is wrong, in your view. But it is standard.

    But, if your model contains completely rational actors who will fully adjust to future taxation by offsetting current spending, why would they also not be perfectly rational with regard to the expected inflation tax, and thus adjust current spending to offset that as well?

    Yes, the model actors are fully rational. But they are heterogeneous. And there are "frictions" that give rise to a role for government money/debt. Lump sum injections of cash, in this model, will have redistributional consequences (just as they would in the real world).

    Other than that, I see no difference then in the impact of bond financing vs. money printing in the purchasing power of the young. With either form of financing, k shouldn't change. Y would increase as much as G, which would be offset by an increase in m (whether in money or bonds).

    Well, yes, money and bonds are the same in my model. But what is critical are the two alternate methods of financing I assumed.

    Method 1: Create money to buy G in period t, then reverse the money injection by taxing people at date t+1 (these are the same people who received the money at t). This financing method delivers a RE result here.

    Method 2: Create money to buy G in period t, but do not reverse the money injection. In the model, this generates a price level effect, which has redistributional consequences. RE fails.

    It seems to me though, that you are suggesting in case 4 that the model would produce a shift from C to G (or K), but even if it did I think that should not increase Y. That is, unless you mean to suggest that output is not impacted by C? In that case, if your production function is really the only determinant of output, then your model is really a "Says law" model, in which supply really creates it's own demand.

    In my model, Y(t) is predetermined, but policy can influence Y(t+1). This is no big deal. I chose to treat Y(t) as predetermined just for expositional purposes.

    Are we getting closer?

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  58. David:

    "We usually think of technological capabilities for factor substitution are independent of financial conditions. Perhaps this is wrong, in your view. But it is standard."

    Yes, but a production function only defines an upper limit set by technological capability. Actual output can be anywhere below the curve. And in an actual recession, with significant unemployed labor and low capacity utilization, we know output *is* below that curve.

    In the long run, we might say that supplies of labor and resources seem to have fixed limits. So it might be reasonable then to consider that long run increases in potential output must come from changes in technology, or production efficiency. But this model really doesn't seem designed to deal with cases where actual output is below potential output.

    "In the model, this generates a price level effect, which has redistributional consequences. RE fails."

    OK, but I think in the real world, bonds financed by future taxes are also redistributional, just in different ways.

    "In my model, Y(t) is predetermined, but policy can influence Y(t+1). This is no big deal. I chose to treat Y(t) as predetermined just for expositional purposes.

    Are we getting closer?"

    Closer maybe, and I really appreciate your patience in explaining this model. But I need to be clearer on what you are using to determine Y(t+1)?

    If Y were a function of C+I+G, as it would be in Keynesian models, then it would make no sense to suggest that shifting purchasing power from consumption to investment would be a stimulus. It hasn't been made clear why G would increase Y any more than C would.

    It really seemed to me here though that you were suggesting a supply side only model, where changes in demand are not relevant. In your entire analysis above it seems you only consider effects of changes in the production function, which should only impact the supply curve. But in any model which allows for the possibility of unemployment, such changes could have no impact on actual output.

    What is the point of a consumption function though, if you aren't allowing consumption to impact output? If your production function is feeding a supply curve, and consideration is also being given to impacts on the demand curve, I don't think that was clear in the explanation.

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  59. Acer:

    Yes, but a production function only defines an upper limit set by technological capability. Actual output can be anywhere below the curve. And in an actual recession, with significant unemployed labor and low capacity utilization, we know output *is* below that curve.

    We "know" no such thing. The PPF cannot be observed. There may be other factors at play that inhibit the job search process (there is a whole literature that discusses the theory of equilibrium unemployment).

    But this model really doesn't seem designed to deal with cases where actual output is below potential output.

    I will have to disagree with you here. Please see this earlier post of mine:

    http://andolfatto.blogspot.com/2010/07/interpreting-recent-movements-in-money.html

    In that version of the model, fluctuations in expectations can cause fluctuations in output and investment around "potential."

    OK, but I think in the real world, bonds financed by future taxes are also redistributional, just in different ways.

    Fair enough.

    If Y were a function of C+I+G, as it would be in Keynesian models, then it would make no sense to suggest that shifting purchasing power from consumption to investment would be a stimulus. It hasn't been made clear why G would increase Y any more than C would.

    In the model I develop here, GDP(t) = y + f(k(t-1)+g(t-1)). Government purchases here are in the form of capital goods, instead of generic consumption as is typically assumed.

    The supply of output at date t is predetermined at GDP(t). A part of this is used to finance consumption (the old). The remainder is used to financed capital spending (private and public). Sacrificing consumption today for the purpose of increasing investment has no effect on current GDP in this model. But the higher level of investment means more capital tomorrow, hence more GDP tomorrow. That's how the stimulus works.

    I'm not sure of all this talk of supply and demand curves. That is partial equilibrium talk. The distinction is not so clear in general equilibrium. In the link I gave you above, for example, an "information shock" leading to an upward revision in the forecasted return to capital investment will look like an "aggregate demand" shock. Or it looks like a shock to the future production function. Whatever. The effect is to stimulate investment spending.

    I am happy to continue the discussion.

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  60. Postscript Jan. 2, 2012 is very thought-provoking.
    However, in "A Modigliani-Miller Theorem for Open Market Operations", Wallace assumes fixed fiscal policy. On the other hand, Lucas says fiscal policy is irrelevant to monetary effect. So, Lucas seems to be saying that monetary policy is effective whether fiscal policy is fixed or not. That is, he seems to be not considering MM.
    And, if "The G is so unimportant in the RET" as you said, RET seems to be also different from MM in this respect. Therefore, defense of Lucas based on equality of RET and MM appears to be unpersuasive.

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  61. David,

    Unfortunately I can't watch the video, so perhaps I'm misunderstanding what was said, but I see the lucas quote as basically saying that Romer lied for her politcal bosses. Krugman on the other hand is saying that Lucas's comments were boneheaded. Someone who lies for personal/political gain is probably a knave. Someone who makes a boneheaded comment may or may not be a fool. (who hasn't made boneheaded comments?) I think it pretty clear that Lucas's comments were significantly more damning of Romer than Krugman's were of Lucas. But perhaps you'd rather be thought a knave than a fool.

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  62. himaginary:

    So, Lucas seems to be saying that monetary policy is effective whether fiscal policy is fixed or not.

    If you listen to the whole video, you will see Lucas humbly admitting that he does not know for sure how to distinguish between monetary and fiscal policy. (An issue raised by some people earlier in the conference.)

    Creating money and injecting it lump-sum into the economy is not something a central bank can normally do. It is a fiscal operation in my books. Lucas is accustomed to calling it monetary policy. But what we label the action is irrelevant.

    The point is that Lucas believes that tax financed increase in G essentially has no effect, while a money financed increase in G does.

    Lucas also states that if the money were instead use "to purchase anything," it would have real effects. If these other objects include, for example, US treasuries, then for this to be true, the conditions that make MM/RE true must fail (or fiscal policy must not be held fixed in the Wallace sense).

    You may be right, however, that the link between MM and RE is not as tight as I make it out to be here. Let me think about it some more. Thanks for the good comment.

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  63. David:
    We "know" no such thing. The PPF cannot be observed. There may be other factors at play that inhibit the job search process (there is a whole literature that discusses the theory of equilibrium unemployment).

    We're in a recession and we know at least some of what caused it. It's not the "Great Vacation", for example. And if there were no demand side factors involved, you obviously wouldn't have inventory buildups. I think Lucas recognizes it's a recession, and recognizes we are below potential output. He talks about getting back to trend.

    I will have to disagree with you here. Please see this earlier post of mine:

    http://andolfatto.blogspot.com/2010/07/interpreting-recent-movements-in-money.html

    In that version of the model, fluctuations in expectations can cause fluctuations in output and investment around "potential."


    That's a another analysis which gives no thought to aggregate demand. As such, it isn't able to say much about those short term fluctuations, and I believe significant parts of the model (such as the price level equation) would be invalid in the midst of those fluctuations.

    The supply of output at date t is predetermined at GDP(t). A part of this is used to finance consumption (the old). The remainder is used to financed capital spending (private and public). Sacrificing consumption today for the purpose of increasing investment has no effect on current GDP in this model. But the higher level of investment means more capital tomorrow, hence more GDP tomorrow. That's how the stimulus works.

    I'm not sure of all this talk of supply and demand curves. That is partial equilibrium talk. The distinction is not so clear in general equilibrium.


    In microeconomics supply and demand is used for partial equilibrium. But I meant AS/AD here. I guess I thought that would be assumed.

    The model you are using looks like a version of a neoclassical growth model. This is derived from micro-economics, and still has some limitations when you try to do general equilibrium analysis with it. You can analyze what one equilibrium looks like vs. another equilibrium, assuming the economy does return to equilibrium after the shock. But I think you would be wrong about some of what happens when you are out of equilibrium.

    In micro, at the firm level, an individual firm is most often a price taker, and can often assume demand for a particular product at a given price. You can't as easily ignore aggregate demand at the macro level.

    In your model, I think you can't really assume that sacrificing consumption to increase investment will always increase future GDP. This should only be valid for that model if you have reason to assume that there is excess aggregate demand.

    Otherwise, wouldn't you maximize future GDP in this model by reducing consumption to zero? Wouldn't that result be self-evidently absurd?

    If you were analyzing a negative technology shock for example, it might be reasonable to assume that you started at equilibrium, output fell as a result of the shock (and not demand, in the initial period anyway), and thus you could analyze such a move to a new equilibrium through increased investment, because you have reason to assume you have excess demand you can reduce to get there.

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  64. Acer:

    One can certain draw straight lines through the data, call them "trends," and assume mean-reverting processes around such objects. Doing so does not, in itself, justify labeling measured deviations from (statistical) trend as evidence of one type of shock over another. What you say *may* be true; I just took issue with you claiming that you know for a fact what is true. Many interpretations are possible.

    How do you define "aggregate demand?" In the model I linked to, information (news) shocks cause fluctuations in investment demand with no contemporaneous effect on the supply of output. If I simulated the time-series from this model, you and most econometricians would likely identify these shocks as "aggregate demand" shocks.

    I do not know what "out of equilibrium" means. Equilibrium is a solution concept; a consistency requirement. One cannot simply look out in the world and say it is in "disequilibrium."

    In your model, I think you can't really assume that sacrificing consumption to increase investment will always increase future GDP. This should only be valid for that model if you have reason to assume that there is excess aggregate demand.

    Can you show me the evidence that suggests higher investment does not lead to higher GDP?
    (In the stochastic version of this model I pointed you to earlier, this is possible).

    Otherwise, wouldn't you maximize future GDP in this model by reducing consumption to zero? Wouldn't that result be self-evidently absurd?

    It would be absurd from a welfare perspective, but not from a technological perspective. The Soviets lived for many decades at close to subsistence consumption, while expanding capital rapidly.

    I'm not sure about the negative technology shock idea. I have more in mind a collapse in the confidence of exchange media as being central to the crisis. You may be interested in these notes:
    http://www.econ.sfu.ca/Seminars/SeminarPapers/AndolfattoDec2011.paperpdf.pdf

    On a related note, I saw a post you made to a Friedman interview that corresponded to the Lucas view of fiscal policy. Good link, thanks.

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  65. a good discussion about the models in people's heads, whether Krugman's or Kucas's,
    Of course they tell us nothing about the real world. I know if I add sodium and chlorine I get salt. No such knowledge exists in econ
    When will economics get around to studying the reality itself? Reality is not young and old generations or curves labeled IS and LM.
    Or maybe reality is just too complex.

    mr reality

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  66. Anonymous,

    Perhaps you might like to read this classic by Milton Friedman, on the Methodology of Positive Economics:

    http://www.ppge.ufrgs.br/GIACOMO/arquivos/eco02277/friedman-1966.pdf

    It is certainly not the last word on the subject, but having read it, I doubt that you would be inclined to post the same sort of message again.

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  67. I have read through you entire effort here and to be civil will hold my tongue.

    You wrote, "It is possible for a permanent increase in g to increase GDP permanently."

    I have asked this question before, in other ways, and you refuse to answer, so I will split it in two:

    Can a permanent increase in private debt increase GDP permanently?

    If the private debt are loans, funded by money created by commercial banks based on fractional reserve lending, does the result change.

    It is pretty plan to me that you are playing words games and not engaging a a serious conversation.

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  68. "Can a permanent increase in private debt increase GDP permanently?"

    This is perhaps the dumbest thing I've read today. Two babies died as a result of the stupidity expressed by John D.

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  69. There are many possible interpretations of the different states of the chemical compound H2O. Nonetheless, when I come across a small hard sample of it, that I can pick up in a solid block, and I put it on my tongue, and it feels very cold, I generally feel justified in calling it "ice".

    All I mean by out of equilibrium is that there is an imbalance between supply and demand, and when I look at real world economic data, and see capacity utilization fall below 70%, and see aggregate demand (defined as C+I+G) falling ahead of employment , I think I know in which direction that imbalance is.

    "It would be absurd from a welfare perspective, but not from a technological perspective. The Soviets lived for many decades at close to subsistence consumption, while expanding capital rapidly."

    And how did that work for them? I don't recall that GDP growth was particularly strong, though it's possible that contemporaneous accounts in Pravda would contradict my recollection.

    By my understanding, this model is concluding that increasing investment increases output, not as any result of the model, but because this is one of the basic starting assumptions of the model. And the model can assume this only because it also starts by assuming an economy already at full employment. Walras's law is a starting point. By introducing money as a good, you can begin to model aggregate demand shortfalls (in other goods) as an excess demand for money, but your production function can't model any of the dynamic effects of this, as it's still tied to long run assumptions of full employment.

    I'm not saying long term growth models can't be useful tools. I think guns are useful tools as well, but you still have to be careful what you point them at.

    (p.s. What you are saying about information shocks is interesting, but I'm not sure how that changes much. If bad "news" causes a drop in production, isn't this likely because some producers interpret the "news" as meaning there will be lower demand for their products?)

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  70. "All I mean by out of equilibrium is that there is an imbalance between supply and demand, and when I look at real world economic data, and see capacity utilization fall below 70%, and see aggregate demand (defined as C+I+G) falling ahead of employment , I think I know in which direction that imbalance is."

    Not out-of-equilibrium behavior at all, merely equilibrium in a relatively-undesirable state. Try to keep up.

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  71. "Not out-of-equilibrium behavior at all, merely equilibrium in a relatively-undesirable state. Try to keep up."

    Not in a neoclassical growth model. That undesirable state is not possible at equilibrium in that model. Which makes that model not very useful for analyzing the dynamics of this state.

    See how I actually used the term:

    "The model you are using looks like a version of a neoclassical growth model. This is derived from micro-economics, and still has some limitations when you try to do general equilibrium analysis with it. You can analyze what one equilibrium looks like vs. another equilibrium, assuming the economy does return to equilibrium after the shock. But I think you would be wrong about some of what happens when you are out of equilibrium.

    In micro, at the firm level, an individual firm is most often a price taker, and can often assume demand for a particular product at a given price. You can't as easily ignore aggregate demand at the macro level."

    What I'm saying shouldn't be that controversial. Pretty much every real world professional forecasting model, whether private firms, government, or international agencies, works by applying neoclassical assumptions in the long run (often for forecasts out 10 years or more), but relies heavily on Keynesian assumptions for any short to intermediate term forecasts.

    This is because it is assumed that in the long run the economy will tend towards full-employment equilibrium. Only then can you start talking about output being determined by production functions while ignoring aggregate demand (it's essentially a Say's law view; supply creates it's own demand).

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  72. If so many people (myself included) seem to find Mr. Krugman so annoying, why is he so widely read? He seems to me that he's become more of a celebrity than a great economist.

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  73. I was once told by an English professor that Joseph Conrad preferred to write in English (his third language) because sentence meanings in that language often had a wonderful ambiguity that added an artistic flair to his prose. China outsourcing

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