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.