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

## Tuesday, December 27, 2011

### Does Krugman Understand Ricardian Equivalence? (Wonkish)

Suppose that the government wants to acquire the resources necessary to implement a new expenditure program G = {g1, g2, g3 ... }, where gt denotes government purchases of goods and services at date t.

Let us take G as given. To begin their evaluation of G, macroeconomists ask the following two questions. First, what are the likely macroeconomic consequences of implementing program G? Second, does the answer to first question depend on how G is financed? (Financing is assumed to take the form of taxes, deficits, and money creation, or some combination thereof).

The Ricardian Equivalence Theorem (RET) is a proposition that helps us answer the second question above. In particular, the RET lays out a set of conditions that must hold for the following proposition to hold: It does not matter how the government finances G

Whether the set of conditions holds in reality is a separate issue that need not concern us here. (You may be interested to read this article from the Economist on the subject page 1 and page 2). For now, let me emphasize what the RET does not say: The RET does not say that G does not matter (it says that the method of financing G does not matter).

The G is so unimportant in the RET, that it is useful to ignore it completely when teaching the theorem to students for the first time. That is, set G = {0, 0, 0 ...} and then ask whether it matters how G is financed. One way to finance such a program would be to cut taxes today and raise them tomorrow. Since G is fixed (at zero, in this case), this implies running a deficit today, which is matched by a surplus tomorrow. The RET states the conditions under which a deficit-financed tax cut like this does not matter.  A deficit today simply represents a higher future tax bill; and people really don't care whether they are kicked in the a\$\$ today or tomorrow--it's still an a\$\$-kicking.

What I have just described is the stuff of elementary macro textbooks. We should all understand now that the RET has nothing to do with G. In particular, we should all know enough never to write a column with the title: A Note on the Ricardian Equivalence Argument Against Stimulus.

The title of Krugman's post shows that it is he who does not understand the Ricardian proposition. There is no "Ricardian Equivalence argument against stimulus." Indeed---the proposition can be used to defend bond-financed stimulus. (In particular, if deficits do not matter, then why not bond finance?)

Now, perhaps you might want to entertain the idea that Paulo knows all this and only chose the title to mock that horrible Bob Lucas fellow. Could be. Except for the fact that Lucas makes no reference to the RET in his informal speech.

In fact--good lord, can it be true--it appears to me that Lucas is making distinctly non-Ricardian arguments in his assessment of fiscal policy. Take a closer look at the passage quoted by Krugman. First, Lucas asserts that a money-financed increase in G will be stimulative; but that the stimulus part comes from the manner in which the spending is financed.  (Because money can be thought of as zero-interest debt, this is virtually the same thing as saying that a deficit-financed increase in G will be stimulative.) Second, Lucas goes on to argue why he thinks a tax-financed increase in G will not be stimulative. In other words, his argument could be interpreted to be mean the method of finance matters. Needless to say, this is not a  Ricardian Equivalence argument against stimulus.

One may agree or disagree with what Lucas has to say on any given issue (certainly, I do at times). But to come out and publicly declare the man to be ignorant of high-school economics--repeatedly--and on the basis of an informal speech--from a fellow Nobel-prize winner--who is himself is guilty of the charge leveled against his own colleague in the profession---well---holy cow, I don't know what else to say.

PS. A couple of related blog posts on this subject:
Responding to Krugman on Ricardian Equivalence (Andrew Lilico, The Telegraph)
Ricardian Equivalence Redux (Stephen Williamson)

And in my defense:
On what is and is not an argument about Ricardian equivalence (Andrew Lilico)
Ricardian equivalence heat (Steve Williamson)
In PK's defense:
The great Ricardian equivalence throwdown! (Noahopinion)

Note: I am surprised that no one picked up on the following. If some "conservatives" are claiming that increasing G is "a wash" by whatever mechanism they have in mind, then does it not follow that increasing G further is innocuous? And indeed, decreasing G must be a wash too, if this is indeed what they believe.

1. excellent post!

2. Okay, I laughed hard at the title

(wonkish)

3. OK, Krugman doesn't understand RET (as defined), and Lucas comes out as non-RET. That's all good but not very germane to the main point, which is Lucas's argument for why a taxed-financed increase in G is non-stimulative. The Keynesian argument is that a tax on those who's spending is not constrained by income/wealth transferred to those who are (either through fiscal transfer, or preferably, employing the unemployed) increases the velocity of money. In short, the multiplier on spending is greater than the negative multiplier on taxing (in the short-term, at least; we can argue about the detrimental affects of such a policy in the long-term later) given the right policy. What is Lucas's rebuttal, other than "I don't believe that's true"?

4. Actually, that's one Keynesian argument against the government-spending-isn't-stimulative crowd.

The other's are
1. RET doesn't hold.
2. Even if RET holds, Lucas seems to agree with Krugman that debt-financed G is stimulative.

5. Anonymous @12:47 (can u pls adopt a handle next time, as per my instructions at top of page?)

In terms of what Lucas believes, I'm afraid I cannot speak for him. I certainly would not want to base my opinion of his thoughts solely on the what I have heard him say in an informal public speaking engagement.

Btw, one does not need to employ "Keynesian" theory to argue that fiscal stimulus in the form of G might be expansionary. The result can follow from a standard neoclassical model, for example.

6. Hi David,

I tried to post with a handle; it didn't take before.

What you say may be true, in which case, it's really hard to understand the logic of the folks who claim government spending isn't stimulative. What assumptions are they making?

7. Richard,

Well, for one thing, "stimulative" does not necessarily mean "welfare-improving." In Stalinist Russia, the official unemployment rate was always equal to zero, to take an extreme case.

Second, it could be that one acknowledges the stimulative properties of a particular fiscal action, but argue that empirically, the effects are very small.

Third, perhaps one believes that only spending in certain categories is stimulative and welfare-improving (e.g., bridges over bombs).

In terms of theory, one can get 100% crowding out (even if RET holds) in the case where G is viewed as a perfect substitute for C. That is, consider a utility function in the form of U(C+G). Think of government supplied school lunches, for example. Not likely to have much of an impact, because parents will just stop making an equal number of lunches.

8. "Rolnick: For example, by Paul Krugman in the New York Times and Lord Robert Skidelsky in the Economist and elsewhere. You were a visiting professor at Princeton in the spring of 2009. Along with Alan Blinder, Nobuhiro Kiyotaki and Chris Sims, you must have discussed these criticisms with Krugman at the Princeton macro seminar.

Sargent: Yes, I was at Princeton then and attended the macro seminar every week. Nobu, Chris, Alan and others also attended. There were interesting discussions of many aspects of the financial crisis. But the sense was surely not that modern macro needed to be reconstructed. On the contrary, seminar participants were in the business of using the tools of modern macro, especially rational expectations theorizing, to shed light on the financial crisis.

Rolnick: What was Paul Krugman’s opinion about those Princeton macro seminar presentations that advocated modern macro?

Sargent: He did not attend the macro seminar at Princeton when I was there.

Rolnick: Oh."

9. Ah, true, the welfare-improving argument (especially over the long-term) is the main valid critique that one can level against stimulus-spending (we'll have to see where China goes, for instance). I think the problem is that your side of the debate seems to have attracted a disproportionate number of those who can not reason after the 2008 crisis. For instance, this:
http://www.econjobrumors.com/topic/why-paul-krugman-hates-chicago-guys.
I went there (and your blog because I read Krugman's post (which seemed very cogent and reasonable) and was wondering what the other side was saying.
If you don't mind me copying and pasting, one guy wrote out my sentiments on that "debate":
"5959 seems to miss the point. Its your arguments aren't convincing. I know nothing about chrocane or his work. I can't name his department, and know nothing about his personality. If the criticisms here were basically an essay for an undergraduate class, the people with extensive posts defending krugman get an A and the people attacking him get D's. The reason is entirely to do with PK defenders actually substantiating their claims and giving a well formed coherent argument. The other side is Krugman Bad = because he refers old macro models. Or Krugman is bad because his policy prescription definitively entail X,Y,Z. At least krugman defenders also seem to present caveats and discuss under what conditions Krugman's conclusions hold.

Given that most of his writings have been times columns how are models even relevant to the discussion ? The PK defenders at least elaborated on topics relevant to the economic views Krugman present.

This thread makes economists who disdain paul krugman look like retards, when plenty of them have made some real contributions to the field. I would profess that most of paul krugman's views on economics aren't flawed under the conditions he proposes the world is in. If there is any reason that one disdains him it is for the fact that he often misrepresents views of the profession or discipline."

Crowding-out is an argument that Krugman addresses. I believe his retort would be that in a world where 100 kids don't get any lunch, providing 50 more government free lunches surely wouldn't lessen the number of lunches made by the private sector.

10. Richard,

What do you mean by "my side" of the debate?

To me, this is one of the main problem with the blogosphere. People just make assumptions about what others are saying without digging deeper.

To give you an idea of what I mean, see my post here where I agree with PK on the desirability of fiscal stimulus on infrastructure in the present climate:

http://andolfatto.blogspot.com/2011_11_01_archive.html

And indeed, you can see that PK agrees with a lot of what the "freshwater" school has produced.

I'm not sure I what to say about the sentiment expressed in that rumors post (I would have to read it to assess the arguments, many of which I am sure are terrible, which is a good reason not to go there for your economic diet). I do agree with the concluding sentence. That is a serious charge, and a legitimate one, in my view.

As for your concluding statement, yes, I know the argument of less than 100% crowding out. You asked me for a *theoretical* justification (the logic) for 100% crowding out. I gave one to you. The appropriate response should have been "thank you." ;)

11. Reading your post and Krugman's, it seems to me that you both correctly understand REIT and you both agree that it has nothing to say about the impact of government spending. (Isn't that the whole thrust of Krugman's post?)

Pity you don't like his title....but then, that's why he has his blog and you have yours.

12. Simon,

It does not appear to me that Krugman has a firm grasp on RET. In any case, in my view the main thrust of Krugman's piece is to mock Lucas for not understanding his own theory. This is not the first time he has done this, referencing the same old quote from one of Lucas' talks. Moreover, in that talk, Lucas clearly states that a money-financed increase in G will stimulate, while a tax-financed increase in G will not. Forget about whether you agree or disagree with this statement (I happen to disagree). Does the statement imply a belief in RET? Clearly not. Ergo, Krugman is wrong to disparage Lucas on these grounds. It shows that Krugman himself is confused. I'm not sure how you can disagree with what I just said, but feel free to give it a shot.

13. Congratulations, you've got yourself a Krugmalanche (or you will have if he fixes the broken link):

15. So I read the referenced material carefully, and while I see some of the points you're trying to make, I have to say broadly Krugman is exactly right, and you're just sort of diddling on the margins, hoping to poke holes in it but just looking like a partisan fool.

It's very clear that Lucas is anti- govt. spending on RET grounds, pure and simple, and would probably argue against some of what you said in this post himself. You're just trying to pull silly nuances out of your butt to degrade K's argument, but it's impossible to conclude anything other than K's main point is right on.

16. I'm a bit confused here. If Lucas says that 'if we do build the bridge by taking tax money away from somebody else, and [use] that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash. It has no first-starter effect' then it sounds like the same argument that is used to justify RE.

Perhaps instead of making the whole thing about RE, PK should have made it about the intuition behind RE. Still, it sounds like Lucas is taking the RE-type logic and applying it to a situation where it doesn't fit. If I raise taxes in the future to finance a bridge now, then it's not a 'wash'.

To then say that Lucas doesn't understand RE is beyond hyperbolic. Still, Lucas' argument sounds pretty wonky (not wonkish).

17. EconomistDelNorte: Since you have read the reference material "carefully," can you please point me to the passage where Lucas explicitly invokes the Ricardian proposition to defend his views?

Steve M: I never claimed to understand or defend Lucas' argument. Whatever argument he made, however, cannot in my view be based on RET. He argues that money financed increase in G stimulates, and that tax-financed increase in G does not. That's all I have to say.

18. "But, if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash. It has no first-starter effect. There’s no reason to expect any stimulation. And, in some sense, there’s nothing to apply a multiplier to. (Laughs.) You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge. And then taxing them later isn’t going to help, we know that."

Just need to revise the title of this post...to "I screwed up, shit happens!"

19. Lucas: "You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge. And then taxing them later isn’t going to help, we know that."

The claim that "taxing them later isn’t going to help" is invoking Ricardian equivalence AFAICT. Is there another way to read it?

20. "Moreover, in that talk, Lucas clearly states that a money-financed increase in G will stimulate, while a tax-financed increase in G will not. Forget about whether you agree or disagree with this statement (I happen to disagree). Does the statement imply a belief in RET? Clearly not."

But isn't this the sentence that implies Lucas relies on RE?

"And then taxing them later isn’t going to help, we know that."

don

21. Krugman has responded to your post. I suggest you read it. You have been flamed.

22. I saw this earlier and started searching the web for previous discussions on Ricardian Equivalence. You seem to make a solid argument in terms of math & economics, but when I look at the history trail, it's impossible for me not to see where Krugman is coming from.

You say that there is no Ricardian Equivalence argument against stimulus, but searching over the past few years quickly turned up an article written by Cochrane in which he states: "Robert Barro's Ricardian equivalence theorem was one nail in the coffin. This theorem says that stimulus cannot work because people know their taxes must rise in the future." Reading this article, I feel confident I am not taking him out of context, so it seems to me that he must fundamentally disagree with your explanation of RET. (http://www.economist.com/debate/days/view/283)

Further, while that was one of the most obvious examples, you can find numerous other discussions in various opinion columns regarding the question of stimulus in which the authors speak of RET as though it is an argument that government stimulus is always ineffective. (Google the terms "Ricardian" and "stimulus" with a date range from 2007-2010-ish). A very telling example is a post by Kevin Quinn who is frustrated that someone had added to Wikipedia the claim that "Ricardian equivalence states that a deficit-financed increase in government spending will not lead to an increase in aggregate demand." and that his students were being misled by it. (http://econospeak.blogspot.com/2008/12/world-wide-web-of-misinformation.html)

Based on my (admittedly brief) research, it certainly seems that the claim that RET implies that government stimulus is always ineffective was being gradually pushed into discussions about the stimulus as though it were obviously true.

Essentially, even if it is correct that Lucas is making a distinctly non-Ricardian argument, there is good reason to believe that he thinks his argument is supported by RET. And I think Krugman had a good reason to feel he needed to refute it.

23. You ought to read before you type. Sometimes it helps keep you from making an error that will now haunt you forever.

24. "And then taxing them later isn’t going to help, we know that."

And why do Lucas think that?

And is Krugman disrespectful for calling this nonsense?
I don´t think so. In fact, I think he is doing economics a favor.

25. @Nathan

I have not read the Cochrane article, but it sounds like pure gold.

26. @Nathan - it really was gold you found there.

Are these people realy as stupid as krugman make them out to be?

Cochrane seem to start the article by confusing growth theory with business cycle theory - but then go on with the claim that fiscal stimulus don´t work.

Cochrane:
"Why not? Most of all, modern economics gives very little reason to believe that fiscal stimulus will do much to raise output or lower unemployment. How can borrowing money from A and giving it to B do anything? Every dollar that B spends is a dollar that A does not spend.3 The basic Keynesian analysis of this question is simply wrong. Professional economists abandoned it 30 years ago when Bob Lucas, Tom Sargent and Ed Prescott pointed out its logical inconsistencies."

....

"Robert Barro's Ricardian equivalence theorem was one nail in the coffin. This theorem says that stimulus cannot work because people know their taxes must rise in the future. Now, one can argue with that result. Perhaps more people ignore the fact that taxes will go up than overestimate those tax increases. But once enlightened, we cannot ignore this central question. We cannot return to mechanically adding up today's consumption, investment and export demands, and prescribe the government demand necessary to attain some desired level of output. Every economist now knows that to get stimulus to work, at a minimum, government must fool people into forgetting about future taxes, an issue Keynes and Keynesians never thought of. It also raises the fascinating question of why our Keynesian government is so loudly announcing large and distortionary tax increases if it wants stimulus to work."

27. "The RET states the conditions under which a deficit-financed tax cut like this does not matter."

I can't parse this sentence and don't understand what it means. Are "conditions" a key aspect of RET (as implied by "...RET lays out a set of conditions that must hold...")? Or is the key aspect of RET simply the assertion that "It does not matter how the government finances G"?

28. rereading this stuff tonight...keep scratching my head at this... from you above.

"In fact--good lord, can it be true--it appears to me that Lucas is making distinctly non-Ricardian arguments in his assessment of fiscal policy. Take a closer look at the passage quoted by Krugman. First, Lucas asserts that a money-financed increase in G will be stimulative; but that the stimulus part comes from the manner in which the spending is financed. (Because money can be thought of as zero-interest debt, this is virtually the same thing as saying that a deficit-financed increase in G will be stimulative.) Second, Lucas goes on to argue why he thinks a tax-financed increase in G will not be stimulative. In other words, his argument could be interpreted to be mean the method of finance matters. Needless to say, this is not a Ricardian Equivalence argument against stimulus."

that's like saying "nothing to see here, just move along" as somebody is being robbed right in front of you.

it's like you define it for us above but fail to see that what Lucas said fits the profile you just described.

No he didn't say Ricardian Equivalence...but he defined it out in his talk...

"But, if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash. It has no first-starter effect. There’s no reason to expect any stimulation. And, in some sense, there’s nothing to apply a multiplier to. (Laughs.) You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge. And then taxing them later isn’t going to help, we know that."

can you see it? can you see it? if not then something is wrong with your reading comprehension.

29. Dr. Andolfatto,

I think you may misunderstand Lucas. It appears to me that he makes three claims:

1) a stimulus paid for by increasing the money supply (i.e. non-taxed stimulus) is same as monetary policy;

2) a current-tax-financed stimulus would just be a wash; and

3) a tax-financed stimulus by, quote, "...taxing them later isn't going to help, we know that" which IS surely Ricardian Equivalence... how else would we "know that?” Why else would it not help?

But, of course, RE only works under the assumptions of the RE model, 1) that capital markets are perfect, and 2) that consumers are infinitely lived (or else care about the utility of the next generation equally with their own). Neither of these assumptions hold in the real world.

Stimulus can work now, because high unemployment constrains the (expected) capital market by inducing uncertainty of future income. And, since people are not infinitely lived, future taxes are valued less than current government expenditures (i.e. personal discount rates are higher than government interest rate).

Jim G

30. Dear Mr Andolfatto,

In my undergraduate days, 'Ricardian equivalence' was always a chimerical concept in that, while seemingly simple, caused my professors to argue with each other without any hint of progress. It is heartening and depressing on different levels to find Nobel laureates accusing each other of misunderstanding it completely.

Your posts, along with Williamson's and Lilco's, spurred me to look back at the RET and examine it as carefully as I possibly could. Specifically, I found one of your points very provocatative: that Lucas, by acknowledging real effects from the choice of financing of public spending, was making a non-Ricardian argument.

31. Before anything, I want to thank you for inspiring me to nail down this table leg that I had left loose since college. I hope that my appreciation of your post sustains your sympathetic reading, including where I conclude that you are in fact mistaken.

If Krugman, Williamson, Lilco, and you were sitting around a table, I think you would all agree to begin your discussion with a clear statement of the RET. There is probably none better than the one famously given by Robert Barro in 1979, defining it as:

"the proposition that shifts between debt and tax finance for a given amount of public expenditure would no have no first-order effect on the real interest rate, volume of private investment, etc."

(This agrees with Ricardo's original description, where he compared financing a war with current taxes or a bond levy. He wrote that a lump sum tax and an annual levy with the same present value at a given interest rate are "precisely of the same value.")

The justification of RET is that, if the government faces an intertemporal budget constraint, then G for all time must equal T for all time. If consumers were perfectly rational, they would conclude that government deficits must be financed by future taxes equal in present value to the deficit. Reacting to anticipated future taxes as though they were a lump sum tax of the same present value, consumers would alter their private spending so as to cancel any potentially stimulative effect of the deficit. In other words, consumers determine their spending based on G, and so, when G does not change, neither does spending, no matter if G is financed via taxes or borrowing.

In Barro's definition, the only alternatives for funding public expenditure being compared are "debt and tax finance." In fact, after half an hour spent reading the first 30 hits for "Ricardian equivalence" in a Google search, I believe that there is consensus on this point: the "equivalence" in RET is meant to apply only to "debt and tax finance of public expenditure."

32. What is not included in Barro's definition as an alternative source of financing is expansion of the money supply (or "money creation").

If there is a theorem showing that, given some conditions, it does not matter whether G is financed through debt or tax OR monetary expansion, it is distinct from (and quite a bit more complicated than) the Ricardian Equivalence Theorem.

Yet you explicitly include monetary expansion as a source of government financing. You conclude that, since Lucas admits the potentially stimulative effect of "printing press" financing while denying it for debt financing, he must not be invoking the RET. However, in every description of the RET I could find, it is only a question of fiscal policy. Monetary policy is part the "ceteri" that have to be kept "paribus."

As a good Popperian, here is my explicit falsification criterion: I challenge you to find one citation of Ricardian equivalence that involves monetary policy in any way, explicitly or implicitly.

33. Admitting the potential of monetary stimulus, therefore, does not entail arguing against Ricardian equivalence. So was Lucas broaching Ricardian equivalence at all? To answer this question, we have to look specifically at what Lucas said regarding fiscal policy. To wit,

"You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge. And then taxing them later isn’t going to help, we know that."

How do we know that? That he is invoking Ricardian equivalence seems inescapable.

But is there even a "Ricardian Equivalence argument against stimulus?" Again, the RET posits the equivalence of debt vs. tax financing of G. If we think about this like non-economists for a second, it will appear as a somewhat bold proposition: While tax financing takes purchasing power out of consumers' hands immediately, debt financing leaves most of it there for 20 or 30 years. In order for equivalence to obtain, consumers would have to act exactly as if that purchasing power were out of their hands, i.e. by setting aside a lump sum at the outset equal in present value to the bond issue. If the "rainy day fund" consumers thereby run up is even slightly shy of that level, then the effect of debt financing is to move up spending from the future periods to the present one. That would be stimulative.

I think this "non-equivalence" is much likelier (for a variety of reasons, outlined in both Krugman and Williamson). However, if you believe that all the conditions of the RET are in effect, then you could argue that debt financed G would cause consumers to reduce their current spending to a degree exactly equal to a lump sum tax. That would be a (valid) Ricardian Equivalence argument against stimulus (or, more precisely, for its inefficacy).

34. So is this evidence that Lucas was misunderstanding Ricardian equivalence? It has to be said that he did not mention RET explicitly. On the other hand, what else could he have meant when he said, "And then taxing them later isn't going to help. We know that."?

What is more sure is that he is arguing that fiscal policy cannot be stimulative. He does explicitly argue that the timing of taxation does not "matter." That suggests that Lucas either believes that all of RET's assumptions hold, or that there is some entirely different mechanism for offsetting the ostensibly stimulative effects of deficit spending.

35. In conclusion,

1) Lucas' positions seem unlikely, though it's not entirely clear what place RET has in his arguments.

2) Krugman is right about the RET, but he is too hasty in characterising his opponents' positions (at least on the basis of the remarks quoted.)

3)By including "money creation" as an alternative form of government financing, you get Ricardian equivalence rather badly wrong.

In one very interesting sentence, you write that, since money can be thought of as interest-free debt, admitting the efficacy of monetary policy is "virtually" identical to admitting the efficacy of debt-financed government spending. Except for the weasel word "virtually," this is really a bold and genuinely radical position, and I applaud you for being so explicit with it. Among other things, if it were true, it would completely erase the distinction between fiscal and monetary policy.

However, such an erasure is untenable. If money can be thought of as "zero interest debt," then what about regular debt? If the government can issue both interest-bearing and interest-free debt, why would it ever issue interest-bearing debt? In the real world, the government's constraint on "money creation" is the fear of inflation, something that is never - ever - addressed as part of the issues surrounding Ricardian equivalence.

Debt and taxation are concepts that are applicable even to an economy without money. If there is a way to compare monetary expansion to the "real" forms of government financing, it belongs to a chapter, or maybe an entire book, separate from a discussion of Ricardian equivalence.

I know that you will not have time to respond to every post, now that your blog has been invaded by Krugmanites. That said, I have tried very hard to understand the different points of view and evaluate them fairly. I invite you to do the same now with my post and tell me whether you agree or where you think I am in error.

36. Not only is the attempted explication of the Ricardian Equivalence Theorem above incomprehensible, there appear to be a number of gratuitous, puerile snide asides (the title presumably mocking Prof. Krugman warnings in his weblog postings about technical, aka wonkish, commentary from him) that diminish the already poor explication.

When one reads Prof. Krugman's weblog postings, if nothing else, his writing and explication are crystal clear. Not only that, but he avoids juvenile put-downs when he disagrees with statements made by others, such as by Prof. Lucas.

So far as I can gather, the so-called equivalence theorem is irrelevant to intelligent policy setting. Perhaps useful to keep the concept inherent in the "theorem" in mind when thinking about what might be relevant to macro-economic theorizing and practice, but otherwise completely peripheral.

Its only current relevance appears to be to provide a rationale - without any factual basis of course - for extreme rightist politicians to argue against fiscal stimulus provided by a governmental entity, e.g. the USA federal government.

37. Babak,

I don't have Barro's text handy, but I believe the "condensed" intertemporal budget constaint includes only the present value of the stream of government spending. It does not include any of the means of financing the spending. This implies that fiscal policy can only induce a wealth effect on households if spending changes. Although most people think of RET with deficits in mind, it would seem to hold in the sense of "no wealth effect" for money financing as well.

38. Ouch, you got burned bad there.

39. How is this remotely 'wonkish'? Haha.

40. Your post is clear; Krugman's isn't. His writing is usually better than that. He still needs to unpack the variables more when describing RE stuff.

41. As far as I can tell, the fundamental mistake is believing that idle resources are free. They aren't, unless you're willing to let people starve. So the question becomes whether to pay them for doing nothing, or pay them for doing something useful.

Same argument goes for school lunches: there is no crowding out because your choice is between letting them starve or feeding them.

42. Kevin Donoghue and anonymous @ 3:07pm and @3:43: Please read Steve Williamson’s post and then ask me again.
http://newmonetarism.blogspot.com/2011/12/ricardian-equivalance-heat.html

Nathan: I just read the Economist article by Cochrane that you pointed to. Needless to say, I disagree with much of it. I can’t help but note that Cochrane never mentions whether the stimulus is in the form of a deficit-financed tax cut (in which case, RET applies), or an increase in G (in which case, RET does not apply). In any case, how something that Cochrane says gives PK license to disparage Lucas is beyond me.

West Coast Reader: Yes, the “conditions” are a key aspect of the Ricardian proposition. They include: the use of lump-sum taxes only (unrealistic), no borrowing constraints (unrealistic), infinite planning horizons (unrealistic), and so on.

Fausto412: I do not think I suffer from a lack of reading comprehension. Please read Steve Williamson post here and ask me again:
http://newmonetarism.blogspot.com/2011/12/ricardian-equivalance-heat.html

Jim G: A stimulus paid for by increasing the money supply is not a “non taxed” stimulus! In other parts of his speech, Lucas admits that there is a hazy line between monetary and fiscal policy. Read it. The money financed increase in G can be thought of as a fiscal stimulus. Certainly, seigniorage financing enters into formal statements of the theorem.

Babak: The Ricardian proposition, when formally stated, certainly does include the seigniorage tax.

Wendell Murray: Krugman avoids juvenile put downs. You mean, like the time he called Barro a “bonehead” for not understanding Keynesian theory? Give me a break, my good man.

43. So, Williamson agrees that the sentence "And then taxing them later isn’t going to help, we know that." is a reference to RE. To me, that is the only implicit asumption upon which Krugman could be attacked. If we accept it, it seems perfectly reasonable to infer that Lucas does not "understand" RE. The alternatives are 1)he made an off-the-cuff gaffe, notable only because of his stature in the profession, 2) he has some arguments to support the proposition that RE negates fiscal policy that he has not yet shared.

don

44. Um, David, the misunderstanding of Ricardian Equivalence lies in the fact that Lucas applies it to a situation where it doesn't apply:

"You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge. And then taxing them later isn’t going to help, we know that."

Krugman makes very clear why that comment is tantamount to a misunderstanding of RET in the post you inaptly responded to:

"Suppose that the family takes out a \$100,000 home loan (I know, it’s hard to find houses that cheap, but I just want a round number). If the house is newly built, that’s \$100,000 of spending that takes place in the economy. But the family has also taken on debt, and will presumably spend less because it knows that it has to pay off that debt.

But the debt won’t be paid off all at once — and there’s no reason to expect the family to cut its spending right now by \$100,000. Its annual mortgage payment will be something like \$6,000, so maybe you would expect a fall in spending by \$6000; that offsets only a small fraction of the debt-financed purchase."

In other words, Lucas is making real world pronostications ignoring that what he 'knows' is based on a theory that assumes things that are manifestly not true, like lump sum taxes. It's almost like he doesn't understand his own theory. hmmm....

As an aside, are you really trying to outsource your response to Krugman to Stephen Williamson. This Stephen Williamson? Say it ain't so.

45. Um, Majorajam...

Lucas seems to be claiming that the government spending multiplier is equal to the tax multiplier (balanced budget multiplier is zero) when the bridge is being finance by direct taxation. Moreover, it appears that the timing of this direct taxation is irrelevant (so this it the RET part of Lucas' claim).

However, Lucas also claims that money-financed increase in G (or any other purchase) will stimulate. This part of his statement is inconsistent with RET.

One might note that Lucas does not come out against additional infrastructure spending in his talk (notice how your hero failed to mention that part--he is more interested in mocking, in creating division, that he is in teaching).

Lucas never explicitly invokes RET in arguing against fiscal stimulus. He clearly has views that are at odds with PK. That is fine. PK should debate those views. But calling the man ignorant of his own theory---really? Hmmm...

And yes, Steve Williamson wrote a fine rebut today. I am willing to put his credentials up against yours any day.

46. @David Andolfatto

Firstly, I don't condone personal insults, especially Krugman's more recent attack against you which I feel was entirely unwarranted. I would post something about this on his blog, but due to the volume there I don't really have much expectation of being read. Also, though it annoys me, I understand that he has a real incentive to be inflammatory with his remarks.

It was this thought process which led me to google for the terms "Ricardian", "stimulus", and "tax", and then filter for results starting in 2008 and ending before Krugman's post (to exclude hits specifically related to this dicussion) in search of an answer. What I found was that the entire first page of results was opinion pieces discussing whether or not the claim that "RET implies that government stimulus is always ineffective" is true. The piece I linked by Cochrane was only a single example meant to explain the nature of my findings, although Cochrane was among the worst offenders as he made a similar claim on several occasions.

To summarize, I ended up concluding that Krugman was reasonably justified in describing Lucas's claim ("if we do build the bridge by taking tax money away from somebody else... then it’s just a wash... there’s no reason to expect any stimulation") as the RET argument against stimulus. The reason I feel he is justified is because nearly identical claims have been made by others over a period of several years, except those claims explicitly state that they are based on RET. Regardless of whether RET actually supports this claim, the notion that it does has become a part of public discussion, and so it is reasonable for Krugman to, upon seeing the claim, point out that RET does not in fact support it.

As evidence, a brief collection of quotes with sources follows, including those I mentioned previously. Note the strong similarity between Lucas's argument and the others. I have no doubt there are more examples out there, as I got tired after citing every result on the first page of Google hits. These quotes appear in a separate comment as I have gone over the comment size limit by more than 2x.

47. "Ricardian Equivalence suggests that government attempts to influence demand using fiscal policy will prove fruitless."
Wikipedia (anonymous author), December 2008, http://en.wikipedia.org/w/index.php?title=Ricardian_equivalence&oldid=257961588

"Robert Barro's Ricardian equivalence theorem was one nail in the coffin. This theorem says that stimulus cannot work because people know their taxes must rise in the future. Now, one can argue with that result."
John Cochrane, March 2009, http://www.economist.com/debate/days/view/283

"But, if we do build the bridge by taking tax money away from somebody else... then it's just a wash. ... There's no reason to expect any stimulation."
Robert Lucas, March 2009, http://www.cfr.org/economics/why-second-look-matters/p18996

"In economics, stimulus spending ran aground on Robert Barro’s Ricardian equivalence theorem. This theorem says that debt-financed spending can’t have any more effect than spending financed by raising taxes."
John Cochrane, September 2009, http://faculty.chicagobooth.edu/john.cochrane/research/Papers/krugman_response.htm
(Here he has some ground to stand on, but the article is about how government stimulus is ineffective, and his introductory sentence uses the phrase "ran aground" which seems to imply that RET is an argument against all stimulus.)

"Ed has asked me to deal specifically with the issue of Ricardian equivalence... it suggests that when a government tries to stimulate demand by increasing debt-financed government spending, demand remains unchanged."
Marshall Auerback, July 2010, http://www.creditwritedowns.com/2010/07/why-ricardian-equivalence-is-nonsense.html
(Note that this author is referring to the arguments of others without explicit citation; however, I still find it a worthwhile reference to describe the perceived state of discussion.)

"But how can the Ricardian trap be avoided, i.e. an outcome where the government stimulus fails to boost aggregate demand because economic agents expect future tax increases to pay for larger deficits and thereby increase savings?"
Justin Lin, February 2011, http://siteresources.worldbank.org/DEC/Resources/Beyond-Keynesianism-and-New-New-Normal-28Feb2011.pdf

"If one believes in Ricardian equivalence, the whole idea of a government stimulus flies out of thew window; people will recognize that a deficit now means higher taxes tomorrow and will adjust spending accordingly."
The Economist (anonymous author), June 2011, www.economist.com/blogs/buttonwood/2011/06/austerity-and-stimulus

"A main implication of their work is that permanent tax cuts have a lasting effect, but temporary tax cuts do little or nothing. Recipients of a temporary windfall reduce debt or save. The same is true of a one-time increase in spending."
Allan Meltzer, August 2011, http://www.economist.com/debate/days/view/737

"The debate on austerity versus stimulus... is in large part a debate about the validity of a property called Ricardian equivalence [which implies that] fiscal policy is therefore ineffective as a means of responding to economic dislocation."
John Kay, October 2011, http://ineteconomics.org/blog/inet/john-kay-map-not-territory-essay-state-economics

"Very few economists believe that Barro's strict version of Ricardian equivalence where stimulus spending has zero effect is correct. Nonetheless, his point is well taken."
Kerk Phillips, November 2011, http://www.deseretnews.com/article/700197922/What-does-an-economic-stimulus-do.html

48. Nathan:

You are a good man for wanting to find a way to cut Krugman some slack. Given his history, I do not think he deserves it, but I understand what you are saying.

Having said this however, I want you to think of this. If Krugman was really interested in starting a conversation on the matter, is insulting Lucas really the way to start? And to base the insult on an informal speech? And to do this repeatedly (this is not the first time he cites that one speech).

Hey, here's an idea: Why doesn't Krugman call Lucas? Why doesn't Krugman actually start attending macro seminars at Princeton?

In all my personal interactions with Lucas, I have never, ever, heard him slag Krugman or anyone else. Maybe he has, but I've never heard him. Lucas is a scholar and a gentleman. And his reward for this is to be slagged constantly by Krugman in the NYTs. My post was written mostly in response to this sad state of affairs. If Krugman wants to start slinging mud, I am prepared to get dirty with him.

49. A whinefest. How fun.

50. Wow David. My irony meter died before its charred remnants hit the ground. Krugman is a very bad boy for "failing to mention" that Lucas didn't explicitly argue against infrastructure spending after ignorantly and maliciously slandering Christina Romer for advocating it. But lets not talk about the latter bit- you're clearly less interested in mocking and creating division than you are in 'teaching'.

Also, Krugman is 'my hero'?? To me, this is one of the main problem with the blogosphere. People just make assumptions about what others are saying without digging deeper. In particular, your being wrong, and me having the temerity to point it out to you, doesn't make me an unabashed Krugman fan. Far from it.

As to the matter at hand, Lucas may have 'never explicitly invoked RET in arguing against fiscal stimulus', but that was clearly what he had in mind when he spoke the words Krugman quoted, and any argument to the contrary is dishonest. Ehem. And Krugman is dead accurate when he says that using the theory in these circumstances makes no sense.

Why on your man's heavenly earth would "the timing of the direct taxation be irrelevant" but the timing of consumption strictly prescribed? Perhaps yourself and Stephen Williamson, whose qualifications far surpass my own, can provide some clarification on that point.

When you don't, that will leave only two explanations: a) Lucas is willfully misrepresenting RET, or b) Lucas is ignorant of his own theory. I'll leave it to you whether Krugman's take on that question was ignorant or otherwise.

Lucas clearly has views that are at odds with PK, which is fine. But given that those views are based on either ignorance or a willful misreading of his own theory, are we meant to believe that decorum enjoins us from pointing out that truth. Really? Hmmm....

51. Majorassjam,

You take a gratuitous shot at Steve Williamson. You claim that Lucas is either willfully misrepresenting RET or is ignorant of his own theory. And you want me to...pat you on the back for that? Dishing it out (parroting PK) from behind your cloak of anonymity? Well done.

Perhaps yourself and Stephen Williamson, whose qualifications far surpass my own, can provide some clarification on that point.

Well, I can only assume that you have the qualifications ranking correct here. But providing clarification to the willfully blind is beyond even my power. Have a good day.

52. I didn't claim it, I showed it. And all your bluster can't hide the fact that you can't answer for your ignorance. Good day indeed.

53. Thanks for the link! However, you added an extra "o" to the name of my blog. "Noahpinion" makes a better pun than "Noahopinion"... ;)

54. Enjoy your blog. Part of the "Krugalanche" that found its way here.

FYI - The page numbers for your last publication seem out of whack.

55. @Nathan
Most of your quotes appear to be referring to the concept of deficit-financing stimulus. It is common to use the term "fiscal policy" to refer to how large a budget deficit or surplus the government runs. Similarly, when people talk of "fiscal stimulus" they often mean either increasing the deficit or even simply running one. So when most of the quotes you refer to say that Ricardian Equivalence claims that "fiscal policy" is ineffective, they are correctly characterising Ricardian Equivalence.

Older-fashioned (or, perhaps even now, stricter) economics discussions used the term "fiscal policy" to include the level of government spending, and "fiscal stimulus" to include increasing spending whilst increasing taxes by the same amount. One reason many of us tend not to use the terms in this way any more is that it is now highly contentious to claim that the economy will always be increased in size by increasing the level of government spending. Indeed, there are all kinds of reasons, both theoretical and empirical, for believing that that isn't so. (Above around 25% of GDP, economies tend to grow slower over the long-term, the higher is government spending. That doesn't, of course, mean that the government should spend only about 25% of GDP - after all, we get nice things from the extra spending, like helping the poor and the sick.)

Now it is possible there is some elision here. Some people, used to the older terminology, hear that Ricardian Equivalence says that "fiscal stimulus" doesn't work, and think that means that Ricardian Equivalence implies that increasing government spending doesn't provide a stimulus - when, of course, Ricardian Equivalence says no such thing.

Ths thing is, Krugman has been at the forefront of arguing that governments around the world ought, at present, to be running large deficits (i.e. attempting to provide "fiscal stimulus" in the first, deficit-based, form). To his case, standard orthodox Ricardian Equivalence is deadly. But when he argues about these matters, he often drifts into defending just increasing government spending - regardless of its current level. That way lies perdition.

56. I think Krugman wins this one.

Common ground:

Both Krugman and David agree that a non-permanent increase in G can be stimulative.

Example: say consumers usually have income of \$1 billion but this year their income falls to 900 million (due to recession). The government steps in and increases G by 100 million this year (and only this year), and then taxes the money back at the rate of 10 million per year for the next 10 years (ignoring time value of money).

Consumers can take advantage of this to smooth their income. Now instead of 900 million in income this year, and 1 billion in all future years, they might choose to have 1 billion this year and 990 million for the next 10 years - they have traded a dramatic fall in income this year, for a small fall in income spread over 10 years. Therefore, they can keep the kids in school, not sell the house etc.

Note that this doesn't have to be the case. As David says, if G is a perfect substitute for C, then it is conceivable that it will have no stimulus. Krugman would agree.

No problem.

Except that Lucas doesn't agree with this. He says that a tax-financed increase in G can't stimulate ("And then taxing them later isn’t going to help, we know that."). THat is a definite misunderstanding or RE - as we have seen above, a temporary stimulus can stimulate.

David then tries to argue that Lucas could not have been relying on RE because "Lucas clearly states that a money-financed increase in G will stimulate, while a tax-financed increase in G will not."

But Krugman points out that Lucas was really saying that a tax-financed in increase in G will not stimulate, and that if a money-financed increase in G does stimulate, its not because of G ("If the government builds a bridge, and then the Fed prints up some money to pay the bridge builders, that’s just a monetary policy. We don’t need the bridge to do that. We can print up the same amount of money and buy anything with it. So, the only part of the stimulus package that’s stimulating is the monetary part.")

So Lucas was really saying that neither a tax-financed or money-financed increase in G will stimulate.

It really does seem that Lucas doesn't understand RET.

57. @Majorajam
You say: >Lucas may have 'never explicitly invoked RET in arguing against fiscal stimulus', but that was clearly what he had in mind when he spoke the words Krugman quoted, and any argument to the contrary is dishonest.<
How was RET "clearly what he had in mind", given that he never invoked it and that what he actually talked about - namely the claim that the multiplier on taxes is the same as the multiplier on public spending - is nothing to do with RET?

Why would it be "dishonest" to say that Lucas wasn't invoking the RET if one honestly believed he wasn't (not a hard belief to come by, given that he doesn't invoke it and does invoke some other macro notions about multiplier effects, unrelated to the RET)?

Do you *actually* believe that Lucas *was* referring to the RET here? Can you offer any reason for anyone to think that would be true - other than your declaring it to be "clearly what he had in mind"?

58. This comment has been removed by the author.

59. Andrew, if you are able to explain how "taxing them later isn’t going to help, we know that" constitutes an argument about the relative magnitude of tax and spending multipliers, I'll be happy to take back my assertion about what Dr. Lucas did and did not 'clearly have in mind'

60. @Majorajam
Here's precisely what Lucas said (nearly three years ago, by the way, and Krugman has quoted it multiple times):
"But, if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash. It has no first-starter effect. There’s no reason to expect any stimulation. And, in some sense, there’s nothing to apply a multiplier to. (Laughs.) You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge. And then taxing them later isn’t going to help, we know that."
So Lucas' argument is:
a) If you tax some people and then spend some money on a bridge, "you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge"
b) You can't get out of the problem in (a) by taxing them later (because of RET).

So Lucas isn't arguing (he *obviously* isn't arguing) that spending on the bridge doesn't provide a stimulus on the basis of RET. He's arguing that spending on the bridge doesn't provide a stimulus because "you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge" - nothing to do with RET. All he says about RET is that, because of it, you can't wriggle out of his multiplier problem by taxing them later, because "taxing them later isn’t going to help, we know that".

Clear now?

If you still think that Lucas clearly had in mind the RET as his basis for saying building the bridge didn't provide a stimulus (incidentally, in the Q&A he said it could be a good idea to build the bridge, but not because of any stimulus but, rather, because we want a bridge and are prepared to pay for it) - if you still think that, then please explain why.

61. Andrew

You haven't answered Majorajam's question. How exactly does RET prevent you from wriggling out of the multiplier problem? In my example above, assume that the multiplier on G and T is the same - how does it lead to an outcome where G has no stimulus effect in the present year?

62. Following up on commentary here, it continues to strike me that this issue is much ado about nothing. The key issue, as I note above, is the use of normal academic kibbitzing about mostly marginally relevant issues such this as a basis for nefarious political policy setting or in the case of current Republican politicians for preventing any policy from being implemented that would reduce the unacceptably high level of unemployment in the USA and counter the accretion of wealth among smaller and smaller segments of the USA population.

Regarding the alleged comment from Prof. Krugman that Prof. Barro is a "bonehead" I have no knowledge of that. However, having read some of Prof. Barro's academic work, not to mention essays he has written for the WSJ, "bonehead" is not an inappropriate appellation for him. In any case that appellation is hardly juvenile as is much of the discussion in this thread of this weblog.

My recommendation, assuming Prof. Andolfatto wants to have a greater impact within webloghood, is to make greater effort to write clearly and concisely and to avoid the juvenile snideness. Perhaps fitting within segments of academia, but not appropriate for adults with an interest in facts and good quality of analysis.

63. @Andrew

I think I must be misunderstanding you. You say that the old meaning of "fiscal stimulus" is to increase both government spending and taxation, while the more common meaning is to increase government spending and run an increased deficit. Is that correct?

If we assume RET holds, then the effects of fiscal stimulus under either definition should be identical. Yet you seem to be saying that RET is an argument against one but not the other, which I don't understand.

What my quotations were supposed to demonstrate is new-ish literature with which a reader could be easily misled into believing that RET says something about the absolute effect of government expenditures, as opposed to the difference in effect between different ways of funding the same expenditure.

64. @Nathan,

No. When people talk of "fiscal policy" these days, they do not have in mind changes to the level of government expenditure at all. A pure fiscal policy keeps the level of government spending unchanged, and then we change the amount of the deficit by having more or less tax.

You keep failing to separate the concept of "fiscal stimulus" from that of increasing government spending. Increasing government spending is no part of "fiscal stimulus" in the modern sense. A pure fiscal stimulus would be an expansion in GDP created by a temporary tax cut.

Now, if we raise government spending but don't raise taxes, then we do two things at the same time: a) we increase government spending; b) we potentially provide a "fiscal stimulus" (by running a deficit).

Since, under RET, it doesn't matter how we fund spending, then no fiscal stimulus is provided by a temporary tax cut. (A permanent tax cut might have an effect - not a "fiscal stimulus", but an effect nonetheless - if households understand the permanence of the tax cut as indicating that public spending will be lower in the future.)

Similarly, funding increased government spending by increasing taxes has no different an effect from funding increased government spending by running a deficit.

Most of the references to RET negating stimulus that you quoted were saying that running a temporary deficit would not provide a fiscal stimulus.

I agree that it's easy to get mixed up here, though, because people certainly used commonly to talk of a "fiscal stimulus" in a way that included a temporary increase in output arising from a temporary increase in government spending - and some still do talk in that way. Not everyone talks in that way nowadays, though, because it's actually quite contentious whether a temporary increase in government spending *does* increase demand. (Not because RET says it doesn't - RET says no such thing - but for other reasons.)

65. @Patrick,

But in a world of Ricardian Equivalence, things wouldn't work as you described in your example. If households had an income of only \$900m that year, but \$1bn in all other years, then (assuming no discounting and infinitely-lived households) they would borrow \$100m and (if we're assuming no investment) consume (within epsilon of) \$1bn, perfectly smoothing consumption.

Lucas envisages a world in which the multiplier on tax is precisely the same as that on spending. So if we spend \$50m and thereby generate \$100m of output all up, then our \$50m of taxes destroys \$100m of output all up - no net stimulus. Now, I think it's pretty obvious that it isn't universally true that the multiplier on taxes is equal to that on spending (e.g. for countries running large deficits, such as a number of distressed Eurozone states at present, the multiplier on taxes is much larger than that on spending - that is a key reason why the IMF and OECD recommend that deficit rectification programmes should be 80% spending cuts and only 20% tax rises). But if we disagree with Lucas on this point, that's not because he has somehow misunderstood RET. It's because we disagree with him about taxation multipliers and public spending multipliers - the thing he himself invokes.

What purpose does it serve to ignore the argument Lucas actually offers, allege that he's trying to argue something else, and then say he's misunderstood that other argument? Why not, you know, try engaging with the argument he *actually* puts forward?

66. Andrew

You say that in a world of RE consumers would simply borrow the \$100 themselves. But, although they could do this, there is no reason to believe that they actually would do it, especially if government can borrow at a cheaper rate and consumers are trying to deleverage. So the world I describe is perfectly possible.

If, then, the world is as I describe in the example, I don't see how RE leads to no net stimulus, even if G and T multipliers are the same. Lets assume, as you do, multipliers on G and T of 2. The government spends \$50m in the current year, leading to \$100m in additional output in the current year. Now lets assume that the government raises taxes by \$5m for the subsequent 10 years, leading to a reduction in income of \$10m per year for 10 years. The net outcome is that in the current year we get an extra output of \$100m, and in the subsequent 10 years we get a reduction in output of \$10m per year.

So in the current year we get a very large stimulus, even though we assume the G and T multipliers are the same. Its true that we get decreases in output in subsequent years, but because they do not occur in the same year as the stimulus, they do not offset it in the way you describe.

If your logic were correct, then consumers wouldn't borrow either. On your logic, the \$100m they borrow would need to be paid back, so there would be no net benefit. You would ignore the fact that the repayments would be spread out in different time periods to the initial loan, just as you ignore the fact that the increased taxes occur in a different time period to the initial stimulus.

67. ps. Krugman made this point here:

http://krugman.blogs.nytimes.com/2011/03/10/ricardian-confusions-wonkish/

68. Andrew, see if you can spot the problem here:

"Lucas' argument is:
a) blah blah blah
b) You can't get out of a... because of RET.

So Lucas isn't arguing that spending on the bridge doesn't provide a stimulus on the basis of RET. QED"

Upon further review, I think you'll find the informal logic there less than watertight.

69. I don't think a speech whose transcript appears on the Council of Foreign Relations website can be considered an informal talk.

Similarly, everyone, including Wikipedia, seems to be using Ricardian Equivalence in the sense of "debt-financed government spending is equivalent to tax-financed government spending." Why would people be arguing about the assumptions underlying another theoretical economic result? They're arguing about whether stimulus can be effective!

70. @David Andolfatto,

If, instead of saying the RET "can" be stated to include "seigniorage tax," you actually made the effort to do so, you would realise the depth of your misunderstanding.

A "seigniorage tax" is the loss of purchasing power of currency. Nothing that anyone - not Krugman, not Lucas, not Williamson, and not even you - have said implies a change in purchasing power. You are implicitly assuming that a monetary expansion will decrease purchasing power, a proposition that is not at all clear (not to say absolutely false) when interest rates are at or near zero.

If you have something to say about economics, say it.

If you want to assert your authority in matters economic, you may burnish your ego, but at the price of becoming a public laughingstock.

No one gives you any extra points for being a staffer on at the St. Louis Fed. Your best hope for recognition is actually making economic arguments. Humbly.

71. @George

I'm very curious about Barro's argument. I would really appreciate it if you could look up the book. If you don't have it anywhere you can look up, can you try to work out the intuition behind including monetary expansion in with debt and taxation?

My hunch is that the RET implicitly or explicitly assumes stable prices, and, in a world with stable prices, monetary policy really does become equivalent to "seigniorage tax." But that would ignore monetary policy's most potent effects on incentives and expectations.

Full disclosure: this really is a hunch. I have not worked through Barro's theorem. But, for anyone who has, that really puts the onus on you to explain qualitatively how Ricardian equivalence applies in a world with variable money supply. It is my experience that economists who have "worked through theorems" are much better at making bold claims and recalling the mathematical gimmicks than remembering the assumptions and caveats.

72. Babak,

My, how brave we are behind the cloak! Well done.

Take a look at slide 7 here (lecture slides provided by Jesus himself, at Penn):

http://economics.sas.upenn.edu/~jesusfv/lecture5_olg_topics

73. Hi David:

Great post! My own take on all this mayhem:

http://blog.hjeconomics.dk/2011/12/31/the-krugman-multiplier-is-too-big/

Happy New Year,

Henrik Jensen

74. David,

I don't know what veil you're referring to, since I included my full name. Just to clear things up, let me assure you that the next time I'm in St Louis, I will make an appointment with your office to call you a puffed up, self-important functionary in person.

If we're through with your flimsy attempts at mockery, maybe we can get back to economics?

It seems from the link you chose to cite that you still don't understand that "seigniorage tax" occurs only when there is a decline in purchasing power by holders of currency. Monetary expansion by itself is not "seigniorage;" it must first lead to inflation for a "seigniorage tax" to result. However, there are many conditions (such as the ones we're currently living through) where expanding the money supply does not lead to inflation and hence doesn't result in a "seigniorage tax." Equating monetary expansion with seigniorage requires assumptions beyond those required by Ricardian equivalence.

If "seigniorage tax" is included in "formal statements" of Ricardian equivalence, that only means that a crucial theoretical and practical distinction is being elided in those "formal statements."

Below, I'm going to cut and paste every word of the slide you cited so that everyone can see that it does not prove anything close to what you think you're proving. (I'll note that making Powerpoint slides is not a substitute for thinking, and pointing to other people's Powerpoint slides is no substitute for understanding.)

Ricardian Equivalence
How should the government …nance a given stream of government
expenditures, say, for a war?
Two ways:
1 Tax current generations (as a tax or as seigniorage).
2 Issue government debt.
Which are the consequences of each option?
Ricardian equivalence: it makes no di¤erence.
We can call it the Modigliani-Miller theorem of public …finance.

75. Babak:

I will be happy to invite you to my office for a chat the next time you are in SL (and I am being serious).

I think that your statement to George says it all:

Full disclosure: this really is a hunch. I have not worked through Barro's theorem.

My recommendation would be for you to first go work through the theorem until you understand it thoroughly. As Jesus calls it in the slide I linked to, think of it as a Miller-Modigliani theorem for public finance (in case you are more familiar with that theorem). Moreover, the slide shows that when the theorem is discussed in classrooms, it includes seigniorage as a tax (contrary to what you were suggesting).

The seigniorage tax I modeled occurred in a zero nominal interest rate environment. A one-time expansion of the money supply to finance a one time increase in G leads (in the model) to a one-time increase in the price-level (not the inflation rate).

The key point is this: the effect of the money financed increase in G is expansionary only if we are living in a non-Ricardian world (given the assumption on the prevailing "substitutability" of government and private investment.

Am not sure why you have your knickers in such a knot.

76. if the Ricardian equivalence is true, why do we permit private debt (given that private debt is the source of our busts. See e.g., Keen (numerous article, book,blog, etc., and Mian and Sufi, here http://www.bloomberg.com/news/2011-11-17/how-household-debt-contributes-to-job-cuts-commentary-by-mian-and-sufi.html)?

As Keen shows, private debt leads to economic growth. Hows if public debt any different? (People have to pay back their private debts, as well, out of future consumption).

77. David:

I am perpetually surprised that professional economists have not taken the parable of "assuming the ladder" more to heart.

If what you're talking about is a government action to capture purchasing power from consumers, with no concomitant change in inflation, and in a zero interest rate environment, then you are talking about a lump sum tax. You can call this 'money creation,' but it bears no resemblance to actual monetary policy.

Since Lucas, whom Williamson called an "Old Monetarist," presumably believes in the stimulative effect of actual monetary policy, he was talking about a world with inflation and expectations, not to mention the phenomena of crowding out and (during a liquidity trap) of crowding in.

Many theories can elucidate why monetary expansion in such a world is stimulating. What I still can't see is what monetary policy has to do with what Ricardo was saying, or even Barro's clear exposition of RET. Monetary stimulus is "non-Ricardian" in the sense that Ricardo (and Barro) never thought their theorem had anything to do with it.

You are writing a blog presumably to hear responses to your work from non-specialists. Then when people write in, your go-to reaction is to pull rank which, I'm sorry to repeat, is genuinely hilarious given who you chose to start an argument with. Paul Krugman has presumably worked through Barro's theorem.

I know that, to a man with a hammer, everything looks like a nail. But if verbal reasoning (at the humble level presented in my posts) is not in your toolbelt, perhaps some doubts may be entertained about your ability to get the job done!

So what gets my "knickers in a knot" is a) the lazy resort to sexist cliches, and b) jumping to "theoremizing" as a way to avoid essential questions. If you build a model without having clarified what the disagreement is about, then you are more likely to _obscure_ the problem than to illuminate it.

The next time I am in St Louis, though, I will take you up on your invitation, if it still stands.

78. Anon Jan 1 3:59PM

Not quite sure what you are asking, but I looked at the link you provided me and it looks pretty interesting. Thanks.

Babak, yes, the invitation stands. Please give me some notice if you can. Thanks for your comments.

79. Prof. Andolfatto

I am still waiting for you to explain whether the alleged Ricardian equivalence applies to private debt?

If so, why do we permit private debt?

80. Anon:

The RE proposition states that under a set of conditions, the timing of government revenue does not matter. The government's income can arrive now or later (it can tax now or later). All that matters is the present value of the tax obligation.

There is an analogous result for private debt in the following sense. Under the same set of conditions for RE (where households are free to borrow and lend), the timing of a household's income over their lifetime is irrelevant. The household could have little income now and more in the future, or the other way around. All that matters is the present value of the income stream (wealth).

The RE result relies on (among other things) a perfect credit market. I'm not sure I understand your last question. We allow private debt because we believe that people should be allowed to borrow money and creditors should be allowed to lend it. I believe I am missing something in your questions?

81. Dear Professor Andolfatto:

As I read Lucas, Cochrane and others, they contend that Keynes is wrong about Gov't deficits being useful to deal with the Lesser Depression because taxpayers react to the borrowing by saving to pay future taxes (which is a silly assumption since we know since the 1980s that taxpayers just pay slightly greater amounts to K street lobbyists). This is offered as the Ricardian equivalence.

Keen and Mian and Sufi have separately documented that the Lesser Depression has been caused by excess private debt.

If excess private debt can be bad, and is of no value in promoting economic growth, why not get rid of it? In effect, isn't that the argument of the Ricardian equivalence. If debt is bad, it is bad for everyone. After all, you (the gov't) can go into debt as my agent, spending the money on exactly the same goods and services that I would buy myself.

Let me give a simple example.

Today, we let students borrow money to pay for taking your class. I assume you would say this is a good thing.

However, Lucas and Cochrane say that, if the gov't borrowed the money to pay for students to attend your class, that would be a bad thing, that is would neither result in future growth nor stimulate the economy, today.

To avoid the side issue of "crowding out," let's assume that the money the student or the gov't borrowed is a bank loan which created new money.

In sum, I strongly believe Lucas and Cochrane are just making it up as they go along. The assumption that they make---that people will save---is madness. People do a lot of different things when it comes to taxes, but bribery of Congress (did you see today's great cartoon about Congress) is a lot less expensive than savings and those who pay taxes now have a 40 year history of success behind them.

82. Blog War III - A summary of recent economic debate Krugman+DeLong etc vs. Fama+Cochrane etc. http://www.dpeon.com/english/25-blog-war-iii.html

83. Dear Professor Andolfatto

I have been waiting for a number of days for your answer to my question, above, about whether the Ricardian equivalence applies to private debt

If it doesn't and you haven't shown that it does, then it is obviously false and you should have started this discussion by saying the Ricardian equivalence is false.

If it does apply to private debt, then why do we permit private debt given that private debt bubbles causes recessions and depressions. See Keen, generally

84. Your ship has been sunk