Thursday, December 29, 2011

The Great Ricardian Equivalence Throwdown!

Y'all know I cannot resist wading into a good macro throwdown.

First, a summary of the action!!

This week's econ-blogosphere mayhem started when Paul Krugman wrote a post about the idea of Ricardian Equivalence (the idea that the timing of taxes doesn't matter), and why it doesn't imply that fiscal stimulus can't work. As an example of someone who does think that Ricardian Equivalence makes stimulus a non-starter, Krugman cited some remarks by uber-macroeconomist Robert Lucas:
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. 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's argument: Ricardian Equivalence says that the timing of taxes can't matter for the economy, not that the level of government spending can't matter.

Mark Thoma concurred: Ricardian Equivalence does not say that stimulus can't work, and Ricardian Equivalence is wrong anyway. But if it were right, it would only be an argument against tax-rebate stimulus, not against government-expenditure stimulus.

Then Krugman came under fire from David Andolfatto, who says that Lucas's statement was obviously not talking about Ricardian equivalence, and, hence, Krugman must not understand what Ricardian Equivalence is. Steve Williamson takes a somewhat less harsh line, saying that Krugman must not understand what Lucas was trying to say.

Krugman fired back, as did Andolfatto and Williamson. Much fun was had by all. I think I'm going to dub Andolfatto and Williamson the "Krugman-Teasing Brigade of St. Louis."

Update: Andolfatto has a new post on toy models that would get you dY/dG=0 (i.e., govt. spending doesn't affect output, i.e. Lucas' claim). It's a good post, but the toy models don't include prices, which are essential to many of the arguments for fiscal stimulus. Krugman challenges Andolfatto to explain the crux of his arguments without math.

Update: John Cochrane responds to Krugman, criticizing an example that Krugman used in his initial post. Along the way, Cochrane states that Ricardian Equivalence, by itself, implies that stimulus is ineffective. Mark Thoma convincingly refutes that latter statement, citing Robert Barro, the actual inventor of Ricardian Equivalence. DeLong argues against Cochrane's criticism of Krugman's example (and again here). Krugman also fires back at Cochrane. Karl Smith chimes in on the side of stimulus.

* * *

Now on to my (partially mistaken) contribution to the debate!

So allow me to wade in here. First of all, though it might not be clear from the heated exchange, Krugman, Andolfatto, Thoma, and Williamson all actually agree on the most important point! Ricardian Equivalence is about the timing of taxes, not about the effect of government spending. Hence, Ricardian Equivalence doesn't say whether or not government spending helps or hurts the economy. Everyone agrees about that!

Actually, this argument is about the second-order issue of what Bob Lucas was trying to say. So let me talk about that.

Lucas is restating Say's Law (Update: Actually, no! I made a mistake here; see below.). Say's Law says, basically, exactly what Lucas says: If you take money from Person A and give it to Person B, then total output (GDP) will be unchanged. This The idea that the effect of government spending is exactly canceled out by the effect of taxes is a very common argument for why stimulus can't work. Lucas is saying that A) Say's Law holds government spending cannot change output, and that B) you can't get around Say's Law that principle by taxing people in the future instead of today, because people are forward-looking and have rational expectations, so that the expectation of future taxation has the same effect as taxation in the present. That last part - the idea that expected future taxes have the same effect as present taxes - is Ricardian Equivalence.

So, Lucas is saying:
(Say's Law in the static case) + (Ricardian Equivalence) = (Say's Law in the dynamic case)
(dY/dG = 0 in the static case) + (Ricardian Equivalence) = (dY/dG = 0 in the dynamic case)

Now, it seems to me that IF you believe that Say's Law dY/dG = 0 holds in the static case (i.e., for tax-financed stimulus), and IF you believe in Ricardian Equivalence, it's reasonable to conclude that  Say's Law dY/dG = 0  holds for deficit-financed stimulus as well. The simplest interpretation of Lucas' statements is that he believes both.

Krugman thinks that Lucas thinks that Ricardian Equivalence implies that Say's Law dY/dG = 0 holds. Does Lucas think that? I don't think we can know, just from those short remarks.

But actually, I know of a pretty simple way to modify the Ricardian Equivalence Theorem so that it does imply Say's Law  dY/dG = 0. All you have to do is assume that government spending, G, is handed out to people as lump-sum transfers (either today or in the future), instead of used to make purchases. With this modification, G just becomes negative taxation. And since taxes in the Ricardian Equivalence model are non-distortionary, government spending would be non-distortionary too. The level of G would not affect output.

It may be that Lucas had such a model in mind. I often encounter the assumption, among economists and non-economists alike, that government spending consists purely of transfers. It is an explicit assumption in many models. It is not an assumption that, in my opinion, makes a lot of sense. But if Lucas was working with that assumption, then he could in fact start with Ricardian Equivalence and end up with Say's Law dY/dG = 0:

(Ricardian Equivalence) + (All govt. spending is nondistortionary transfers) = (Say's Law in the dynamic case)

(Ricardian Equivalence) + (All govt. spending is nondistortionary transfers) = (dY/dG = 0 in the dynamic case)

And Krugman would thus have read Lucas 100% correctly.

It's possible, though, that Krugman did read Lucas wrong, and that Lucas believes in the static version of Say's Law the ineffectiveness of government spending for other reasons entirely. In that case, Krugman should simply do a follow-up post called "Oh, and Say's Law is wrong too", because Say's Law is almost certainly wrong. (Even Say thought Say's Law was wrong!) "Lucas is wrong even if Ricardian Equivalence is right". Even if Krugman overestimated the degree to which Lucas was mentally extending the Ricardian Equivalence model, it's still true that Lucas' belief in Say's Law the ineffectiveness of government spending isn't something most macroeconomists would agree with.

I also think that Krugman's initial post was meant to say "Anyone who reads Lucas' remarks and comes away thinking that Ricardian Equivalence implies  Say's Law the ineffectiveness of government spending  is wrong." Which would also be a good point.

So basically, I score this throwdown: Krugman 2, Krugman-Teasing Brigade of St. Louis 1. On one hand, Ricardian Equivalence definitely does not imply Say's Law Lucas' claim, except in a special and unrealistic case (e.g. where all spending is just transfers). So nobody should try to overuse Ricardian Equivalence in this way! On the other hand, Krugman may or may not have overinterpreted the degree to which Lucas' belief in  Say's Law the ineffectiveness of government spending actually springs from his belief in Ricardian Equivalence. Who can know. But it's not a big deal. Because the big, important point is that, Ricardian Equivalence or no, Say's Law is just not right (Update: and from Say's Law not being right, it's only a short hop to what Lucas said being not right either), and Lucas was therefore making a very unorthodox and controversial claim.

Update: Smacked down by Brad DeLong! DeLong takes issue with two aspects of my post. The first is that I have mis-stated Say's Law:
I think Noah Smith is wrong here. Say's Law does not say that fiscal policy cannot affect spending but monetary policy can. Say's Law says that neither monetary nor fiscal policy can affect the level of spending because supply creates demand...
I agree that Lucas is wrong. But to say "Lucas believes in Say's Law" is, I think, not quite the right way to put it, for Lucas's statements are not consistent with Say's Law. 
Brad is correct. I stupidly and lazily copied the Lucas quote to my post and then considered it in isolation, forgetting that Lucas had said elsewhere in his remarks that monetary policy could be effective (a statement that is not consistent with Say's Law). So when I said "Say's Law" in the post above, I was completely wrong. Commenter TGGP actually pointed this out as well. Anyway, doh.

Brad also doesn't like that I am making claims about what Lucas "believes":
Noah Smith uses the phrase "X believes" as shorthand for "X's statements are consistent with a model in which". I think that is a misleading way to think about it... 
Now there is a sense in which this is a totally fruitless exercise: there is no point in trying to set out what the coherent model underlying somebody's thinking is when in fact there is no coherent model underlying their thinking.
I agree that we can't really know what model of the economy Lucas actually believes, or what probability weights he puts on various models. Or if he even had any formal model in mind at all when he made his remarks. I might be being too generous to Lucas - he might have just been tossing off incoherent statements without thinking of their implications, as DeLong says. Or I might be unfairly putting words in Lucas' mouth - he might actually have an underlying model in mind that is much more complex and has much more believable assumptions than the toy models Brad and I postulate (if so, Lucas should publish it).

It would have been more accurate for me to have said: "Lucas states that the level and type of government spending does not affect output, all other variables being equal. It is possible that Lucas arrived at this conclusion by using a slight modification of the assumptions that lead to the Ricardian Equivalence result, i.e. that Lucas was thinking about Ricardian Equivalence and simply assumed that government spending = transfers, and concluded that spending doesn't affect output. It is also possible that Lucas had some other model in mind, and if that is the case, then we just don't know what it is. Or it's possible that Lucas had no model in mind at all. But the statement that government spending can't affect output is not true in most models,  so whether Lucas' statement was motivated by a modified Barro-Ricardo type model is a bit of a moot point."

Update 2: Krugman also catches my mistake. He also describes Lucas' argument as "Ricardianoid", which I think is a good term for a model that starts with the Barro-Ricardo model and adds the assumption that government spending is pure transfer.


  1. just an observation about the oft-repeated lucas quote: no one need ever be taxed to pay for the bridge; the bonds can be rolled over far as i can determine, the cost of the interstate highway built in the 50s is still embedded in the debt today...

  2. I'm probably missing something here but the decomposition of the (Lucas) argument Say's Law + RE, troubles me.
    The part about Say's Law, in particular: stating that expanding G and raising T simultaneously is not very expansionary (I know he says not at all but...) doesn't strike me as Say's Law.

  3. Anonymous6:10 AM

    Aren't you making this too complicated and being a little too generous to Lucas?

    Ricardian Equivalence says: if G is constant and T is cut then this will have no effect on aggregate demand because when consumers take account of the present value of future taxes they realise their permanent income is unchanged. Hence they do not change consumption. So no component of aggregate demand changes.

    It is tempting but sloppy to think that the same applies in the reverse case where T is kept constant and G rises.

    It does apply if the rise in G is (known to be) permanent. In that case the present value of the future taxes required to pay the interest/principal on the bonds that now have to be issued reduces permanent income - and hence consumption - by the same amount as the increase in G. So aggregate demand is unaffected. One component goes up whilst another goes down by the same amount.

    But if the rise in G is temporary then the rise in future taxes reduces permanent income by less than the rise in G. For example, if the rise in G is 100 and for one period only then, with an interest rate of 5%, permanent income is reduced by 5 units because 100 units of (I'll assume infinite maturity) bonds are issued once and 5 units now have to be raised through taxation each period to pay the interest on them. So consumptions falls by 5 units whilst G increases by 100 units in the first period. So aggregate demand is stmulated in the first period at least.

    It seems to me a pefectly natural interpretation of Lucas's causal remarks is that he was sloppily moving from the first and second cases to the third. Which is what Krugman,as I read him, was alleging.

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  5. Minnesota Fed's interview with Robert Barro in 1985 ( in this regard is most confusing. Yes, Barro does say during the interview, "It's never part of Ricardian equivalence that the level of government expenditure doesn't matter." But the transcript of the interview leads in with this contradictory sentence, "Barro broke with tradition in 1974 with a powerful critique of Keynesian thought. Deficit spending won't stimulate an economy, he argued, since rational households will simply save more in anticipation of higher future taxes. "There will be no net-wealth effect," he wrote, "and, hence, no effect on aggregate demand or on interest rates of a marginal change in government debt." Did Barro change his position between 1974 and 2005? Who is misreading whom?

  6. exchemist11:08 AM

    So I knew that Ricardo was sceptical of Ricardian equivalence, I learnt that from Wikipedia.
    And now you tell me that Say didn't believe in the validity of Say's law.
    It's all very confusing.

  7. The usual story I've heard for how Say's Law is wrong comes from Nick Rowe, who says the reason is money. Say's Law would hold in a barter economy (but barter is so terrible we rarely resort to it even amid severe monetary dysfunction). Lucas seems to acknowledge that monetary stimulus could avoid the negative multiplier of taxation for government projects. So in that sense, he doesn't appear to believe in "Say's Law".

  8. @TGGP:

    You're right. What Lucas is really saying is just something that doesn't make a lot of sense.

  9. <sarcasm>But I thought Laffer disproved Ricardian Equivalence by showing that current borrowing could be paid for by future tax cuts.</sarcasm>

    Ricardian Equivalence says: if G is constant and T is cut then this will have no effect on aggregate demand because when consumers take account of the present value of future taxes they realise their permanent income is unchanged.

    There is a fundamental logical flaw here. Consumers are assuming that the only effect borrowing has on their permanent after-tax income is the change in their taxes. If we don't assume a priori that Ricardian Equivalence holds, then we have to allow for the possibility that borrowing and cutting taxes will affect economic growth, which will affect pre-tax incomes, and if you allow that then permanent income can change and the whole argument falls apart. Ricardian Equivalence is based on circular logic, as I've laid out here.

    As for Say's law, it seems to be based on the assumption that there is some physical constant determining the number of times a dollar is spent in a year. If you tax a dollar from someone who would have been slow to spend it (or borrow it, which will necessarily come from those who would have been slow to spend it) and spend it on someone who would be quicker to spend it, then spending will increase.

  10. Eric has a point here. See the comments on this post:

    Steve Williamson

  11. Steve:

    Sounds like an interesting model.

    With regards to the current controversy, I don't think anyone was arguing that Ricardian Equivalence itself has to hold. It's pretty clear that it doesn't, necessarily...the effect of the timing of taxes will depend on a lot of other stuff, e.g. the enforceability of debt contracts, like in your model.

  12. Noah,

    Lucas explicitly said something to the effect of 'we know the timing of the taxes doesn't matter' right? But if people only care about NAV, then there's no reason to expect them to offset the entire NAV of a tax increase with present savings.

    In other words, the assumptions of the RET manifestly don't hold in the real world where Lucas's proclamation was directed, therefore Lucas either doesn't understand the theory or is misrepresenting it, as per PK (the whole thing's a little like a physist claiming that 'we know' that it takes one drop of gasoline to drive from Sacramento to Bakersfield due to Newton's law of energy conservation).

    So all that said, shouldn't the score be something like N/A due to Andolfatto and Williamsons comprehensive whiffs en route to the field of play?

  13. Noah,

    But you can see why it's useful to start with Ricardian equivalence and work from there. I see how that works, and then I think: OK this won't work if there is some friction in private credit markets, e.g. people can run away from their debts. But a tax liability is a debt too, so what if people can run away from the government too? But maybe the government has greater powers of enforcement? But what if it's the Italian government trying to collect taxes in Sicily? That seems interesting.


  14. Steve,

    I agree, that is interesting! Have you read Jing Zhang's paper that combines limited enforceability with limited span of assets? She gets some very interesting's in a trade context, but could be applied elsewhere, I think.

  15. you can't get around Say's Law by taxing people in the future instead of today, because people are forward-looking and have rational expectations

    If Say's Law were not invalidated for other reasons, it would absolutely fall apart here.

    Have you ever heard anybody ponder what they would be doing with their money 5 or 10 years down the road if they didn't buy a big screen TV today?

    Does anyone ponder relative poverty in their old age vs taking a vacation now?

    To the extent that most people think about money at all, it's implicitly in terms of cash flow. Can I make the finance payments on this purchase and still afford to feed my cat? This is the real wold, which is apparently terra incognita to economists.

    Plus, rational expectations is the silliest idea to be taken seriously since chemists gave up on phlogiston. People act from the cerebral cortex at least as often as they act from the neocortex. This gives us wars and the herding instinct, makes bubbles and Ponzi schemes so exciting, and enables all sorts of wildly irrational behavior, like voting for Republicans or believing in Ricardian equivalence.


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  17. Right on Jazzbumpa.

    I love the fact that your comment is as equally no nonsense and lucid as it is likely to be ignored by the economists who frequent this blog. Modern economics is a chummy club where anyone with the temerity to advance human understanding of the real world is ostracized and the remainder prattle on about perfectly absurd theories that weren't even wrong 100 years ago.

    Speaking of which, of course RET is a great place for your average mainstream economist to start! It has neither theoretical nor empirical validity nor would the common sense available to non-economist laymen indicate it would, so nothing could be more appropriate. Never mind Keynesian uncertainty of eight decades ago. "The Keynesians" long ago abandoned such sensible ideas when they saw how cool the classicists looked scrawling PDEs on blackboards.

    Nevermind that uncertainty opens the door to the types of legitimations that dominate decision making in the real world. Nevermind how powerful the two dynamics are in the context of the massive agency problems of the real world.

    Nevermind the endless anecdotes that your average person could conjure to attest to the power of that vortex in the context of real world commercial and governmental institutions, e.g. the fact that organizing a price fixing conspiracy on one of the most important test markets in the world for deregulated wholesale electricity wasn't exactly in the interests of a wholesale electricity trader's long-term business plan didn't stop Enron from doing it, e.g. the fact that its not in private equity GPs long-term interest to screw over LPs hasn't stopped that epidemic, etc. etc.

    And what did happen when one mid 1990s Merril tech analysts suggested a midling upside for tech and internet stocks. Well, of course they found one with views more to their liking! Think he's an artist now- unless the money's run out. But at the time, I'm sure the powers that be were able to put together a very convincing PowerPoint!

    And while we're at it, never mind the same dynamic applies to individuals, e.g. in our capacity for things like procrastination, gambling, drug addition, etc. etc. etc. and on ad infinitum.

    No, but rational expectations is a GREAT jumping off point.

  18. Anonymous3:35 AM

    Say's Law is a total non-starter, which gives the argument to Krugman by default.

    There are many other perfectly good reasons to at least question the impact of stimulus, even in the context of a liquidity trap (the fragility of debt acquisition is a good starting point), as well as the problems with central planning (misallocation of capital).

    But nothing mentioned in this debate was of any use whatever.

  19. Ricardian equivalence doesn't hold up to reality:

  20. Noah said...

    " @TGGP:

    You're right. What Lucas is really saying is just something that doesn't make a lot of sense."

    Noah, from what I can follow Lucas' argument makes sense given Says' Law and Ricardian Equivalence, and not otherwise.

    In that case, either Lucas is using those two 'laws' (not honestly, because they don't work), or is just babbling.

    Which is it?

  21. well, it could be not so easy to stay in between of Nobel laureates while they're fighting each other...
    anyway I guess you got distracted by the whole "controversy" who took the form of "this guy don't understand his own doctrine, that guy to not understand the former, they don't read me properly and attack me" and so on... Personally I think this is part of the degeneration of economic profession...
    scientists should discuss models (once were called theories) not people...

  22. Mr. Violet -

    You are pining for an idealized world that does not exist - even in real science (which economics most emphatically is not.)

    Do you realize that Chemists have blood feuds with each other, and have come close to physical violence at international conferences over the nature of ionic properties in non-aqueous solvents?

    But, as to discussing models and not people, don't you think that when people mis-use and misrepresent models for some agenda-driven reason, they should be called out by people who know and understand?

    The degeneration of the economics profession, which you rightly decry, comes from two sources: 1) the joined-at-the-hip relationship with its other evil twin, politics; and 2) the fact that econ models have little to do with reality in gebeal, and when they differ most economists act as if it were reality that is wrong.

    Happy New Year!

  23. That's -

    . . . little to do with reality in general . . .

    not -

    . . . to do with reality in gebeal . . .


  24. "a special and unrealistic case...where all spending is just transfers"

    I think the issue is the extent to which government spending and private consumption are substitutes. We can probably all (even Lucas) agree that they are not perfect substitutes, so what Lucas says clearly isn't precisely right, but it's plausible that they are fairly close substitutes. (Maybe not all that plausible, but it doesn't surprise me, or seem wildly irrational on his part, that Lucas might believe that.) If what you care about is your overall standard of living, it might well be influenced similarly by both private and public goods. If you can spend time in a public park, you might be less inclined to buy a bigger television, and so on.

  25. Starts with model x and adds assumption y?

    This is not real economics, is it?

  26. The deconstruction of economics would be a worthy project: the exposure of assumptions, acknowledged and unacknowledged, with no empirical justification.

    Talk about a research program.

  27. 'In 1974, Robert J. Barro provided some theoretical foundation for Ricardo's hesitant speculation. . . Barro's model assumed the following:

    families act as infinitely lived dynasties because of intergenerational altruism[10]

    capital markets are perfect (i.e., all can borrow and lend at a single rate)

    the path of government expenditures is fixed." [Wikipedia]

    Words about words. Zero empirical content. Academic decadence.

  28. Anonymous1:22 PM

    If a retired gardener like Luke Lea thinks something, it must be true. Same goes for the equally-impressive Jazzbumpa. I thank the Flying Spaghetti Monster for all of their scientific contributions to economics, where would we be without such magnificant and life-altering papers?

    People, you're out of your depth trying to discuss economics. The sooner you realize it, the better of you and I will be.

  29. wood turtle3:52 PM

    Just where is that multiplier?;postID=5596687422013782558

    My non-economist view.

    Demand is always there, just not enough dough.

    Creating Manufacturing Supply expands into the Service sector.

    Manufacturing Supply has a Service to Manufacturing Labor component, and then Manufacturing workers generate Service consumption with their wages. More Service consumption leads to more Manufacturing Supply consumption, leading to more Service consumption, and so on, until an equilibrium is reached.

    In this model, Manufacturing multiplies into the Service sector, and Service does not multiply.

  30. Anonymous5:11 PM

    The fact that anyone is using Say's Law as the basis of anything is evidence of a lack of progress in economic theory