Mankiw Followup

Earlier today, I blogged about Greg Mankiw’s calculation on the effects of capital tax cuts.

Following a tax cut, Mankiw computes the ratio of the long-run increase in wage payments to the short-run shortfall in government revenues, and, with reasonable assumptions, shows that this ratio has an astonishingly high value of 3/2.

I know how to make that ratio even higher.

The Mankiw Plan is: Cut capital taxes today and watch wages rise tomorrow. The Landsburg Plan is: Cut capital taxes tomorrow and watch wages rise the next day.

Under the Landsburg Plan, the short-run government revenue shortfall (today) is zero, while the long run increase in wages is positive. That gives me a ratio of infinity, which beats Mankiw’s 3/2 ratio by a factor of … infinity.

This is not meant to cast doubt on Mankiw’s result (which is entirely responsive and relevant to the current public debate he was addressing); it is meant to cast light on what’s driving it. When you cut taxes, government revenue falls by more in the long run than in the short run. The long run fall in revenue is what’s driving the wage growth (as I showed in my earlier post), and what drives the result is that the long run fall in revenue is greater than the short run fall. If you can drive down the short-run fall, you can drive up the ratio.

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20 Responses to “Mankiw Followup”


  1. 1 1 Bennett Haselton

    At the risk of ruining a joke by explaining it, are you just making a wonky joke about the fact that it’s silly to focus on “short-run” effects, because you can so easily cheat the measurement of “short-run” effects just by delaying the change slightly? Or is there some deeper point?

  2. 2 2 Will A

    The political issue is of course who gets the increase in wages. A tax cut that results in wages increasing wages only on those who are considered wealthy will be very unpopular.

    An EITC inversely tied to wage growth of those at lower income levels might be inefficient, but it would be a decent compromise. If the rising incomes lifts all boats, the EITC goes down and everyone is happy.

    If some boats don’t rise, the EITC increases and everyone is happy: lower incomes because they get more money; and higher wages because of their higher wages.

  3. 3 3 Rob Rawlings

    ‘When you cut taxes, government revenue falls by more in the long run than in the short run’

    Won’t there be some situations where (to reference the diagram from your earlier post) rectangle G will be bigger than rectangle C and hence revenue falls more in the short run than in the ling tun ?

  4. 4 4 Rob Rawlings

    ling tun = long run :)

  5. 5 5 Steve Landsburg

    Rob Rawlings:

    Won’t there be some situations where (to reference the diagram from your earlier post) rectangle G will be bigger than rectangle C and hence revenue falls more in the short run than in the long run ? Yes, and I said as much at the end of the blog post. In the paragraph you’re quoting I should (following Mankiw) have said that revenue typically falls more in the short run than in the long run, e.g. with Cobb-Douglas technology.

  6. 6 6 iceman

    By the day after tomorrow we’re all dead

    Just a little confused whether a) the SR loss in govt revenue is “in many circumstances” / “typically” an upper bound on the LR loss in govt revenue, suggesting the gain in wages is a multiple of either (with SR change being more easily measurable), or b) the whole result is based on LR loss in govt rev = gain in wages both of which exceed the SR loss in govt rev?

  7. 7 7 Bob Murphy

    Steve,

    I’m a little bit confused by all of this. And I *don’t* mean by the competing/complementary blog posts, rather, I mean that leading economists seem like they’ve just been presented with the notion of a corporate tax cut for the first time 3 weeks ago. How is it that big shots are arguing over something so basic?

    I feel like one of the bestselling textbook physicists just wrote a post saying, “Wow, it turns out, under certain assumptions (such as no air friction), that the mass of an object has nothing to do with its acceleration near the earth’s surface!”

    Then another physicist chimes in on his blog, “I spent all morning trying to understand this result, but I think I see it now…”

    I hope you understand, I’m not criticizing you or Mankiw. *I* hadn’t thought of any of this stuff before. But am I missing something? How can it be that the economics profession is grappling with the notion of, “How should we even conceptualize a corporate income tax cut?”

  8. 8 8 Steve Landsburg

    Bob Murphy: I think there are two answers.

    1) Economists have thought long and hard about natural questions like “how does a cut in capital taxes affect economic welfare?”. Politicians recently started asking a different question: When capital taxes are cut, what is the ratio of wage increases to government revenue losses? This is, to an economist, an unnatural and largely uninteresting question, and there’s no reason anybody should have thought about it before. Now that the politicians have brought it up, economists have answered it. There was a little initial confusion while everyone tried to figure out how to think about this strange question we’d never had any reason to think about before, but the confusion quickly dissipated. Nobody that I know of doubts that Mankiw’s calculation is correct, or that my post gives the correct intuition for it.

    It’s not uncommon for someone to ask a weird physics question that no physicist has ever had occasion to think about, and for the physicists to take a few days getting it right. (I’ve been the asker a few times in this scenario.)

    2) The tax code is very, very complicated. We have a pretty good idea of what happens when you cut capital taxes, or when you cut wage taxes. What we’re less sure of is this: If you cut corporate taxes, how will people restructure their affairs in order to take advantage of the new tax code, and in the end, when all is said and done, what will have happened to the rates at which capital and wages are now taxed? Answer: People will be very very clever, and it’s not reasonable for economists, especially economists who have no reason to be familiar with all the twists and turns of the federal tax code, to predict all that cleverness. Therefore we’re left guessing about what the adjustments will be.

    Those are my answers. But let me also add this: When you drop a pebble in a pond, it creates ripples. Those ripples are partly a solution to the usual two-dimensional linear wave equation and partly a result of nonlinear disturbances below the surface. I’ve been asking physicists for years whether the ripples we see are primarily the first or the second. I’ve gotten a lot of different answers, many of them backed up by a lot of math, and I’ve watched a lot of physicists argue with each other and reach no conclusion. So maybe your physics analogy is at least imperfect.

  9. 9 9 iceman

    shorter version of #6: do we think SR loss in govt rev is generally less than LR loss, or an upper bound? Because I seemed to get both takeaways from the various posts

  10. 10 10 Capt. J Parker

    Steve Landsberg in response to Bob Murphy said: “Politicians recently started asking a different question: When capital taxes are cut, what is the ratio of wage increases to government revenue losses? This is, to an economist, an unnatural and largely uninteresting question, and there’s no reason anybody should have thought about it before.”

    Really? The economic incidence of a tax or tax cut is an unnatural and uninteresting question to an economist? The effect of capital taxation on wages and tax revenue is an unnatural and uninteresting question to an economist? Supply side effects of tax policy are unnatural and uninteresting questions? Who wins and who loses as the result of a tax policy change is an uninteresting question?

  11. 11 11 Steve Landsburg

    Capt.JParker: Most of the things you’ve listed are very interesting to an economist, and economists have thought about them. That experience is why it only took a couple of days to answer the new question once it was asked.

    I assure you it’s very easy to come up with questions that physicists will need a few days to answer, even if the questions are about things that physicists know perfectly well how to think about. Why would you expect any different of economists?

    Tangentially, your mention of supply side effects is off-topic; the whole point is that this question has nothing to do with supply-side effects.

  12. 12 12 Bob Murphy

    Steve,

    Thanks for the answer. (And to reiterate to be extra-certain you got it: I am in no way saying you or Mankiw are being goofy here. I’m just trying to get a sense of the big picture because this debate seems surreal to me.)

    Two quick reactions:

    (1) I am out of the loop. Can you point me to something that shows it was a politician who asked about the impact on wages?

    (2) I don’t know what you mean when you say no one has challenged Mankiw; the whole reason I posted my comment, is that I’m amazed at the vitriol and disagreement here. DeLong and Krugman accuse Mankiw of using the wrong assumptions (small open economy, etc.) *and* of committing an algebra error, and then they end by saying this must be due to Mankiw’s politics, because there’s no way he could have honestly made such stupid mistakes.

    So this is kind of what I mean. I don’t imagine in physics that one Nobel laureate would accuse the other of an algebra mistake and say his dishonesty must be politically motivated, and then another awesome physicist from U of R says he doesn’t know of anyone who questions the original analysis.

    I hope I’m not missing something basic here, but do you see what I mean?

  13. 13 13 Steve Landsburg

    1) No, I can’t, but I’m aware that this question was all over the news for a couple of days before Mankiw’s post, and it’s not a question that any sensible economist would have asked in the first place — nor would it have been all over the news if it had been just an economist who was asking — so I’m quite sure this came out of the journalism-political complex one way or another.

    2) Regarding what you call “challenges” — I haven’t the stomach to read through DeLong or Krugman, both of whom would apparently rather impugn other people’s motives than have a conversation, but I am quite sure that if you asked a bunch of physicists to describe what would happen in some new physical situation they hadn’t thought about before, they’d initially disagree about what the reasonable assumptions are. E.g. Can we reasonably neglect friction here? Moreover, sometimes that disagreement will persist a very long time (see for example the long back and forths among physicists about my ripple question, where excellent physicists have been very sure of their assumptions and equally excellent physicists have been very sure of competing assumptions.) I’m quite sure that we all do agree on what conclusions follow from what assumptions, though again, when the problem is new, it might take us a day or two to get there.

    This is the first I’ve heard anyone mention an algebra error. There might be one, of course, but Mankiw and I both reached exactly the same conclusion via different routes (his calculus versus my geometry), and in neither case is the math particularly hard, so I’d be extremely surprised if there’s an algebra error here.

    As for the stuff you hear from Krugman and DeLong, don’t take it seriously. They’re both so full of spite and venom that it’s best to ignore them, which is too bad, because they both frequently have reasonable things to say. It’s just no longer worth it to dig those things out. I’m sure you can find two prominent physicists who are equally bonkers; they just get less media space.

  14. 14 14 Bob Murphy

    Steve,

    Usually when I profoundly disagree with you, it’s because you and I are talking about different things but we don’t realize it. I’m assuming something like that is happening here, but just in case you aren’t aware of the following, here goes:

    (1) It’s not just DeLong and Krugman. Larry Summers and Furman (past CEA chair I think?) are challenging the current CEA estimate. It’s not just Mankiw (and you) on the other side, but Casey Mulligan and John Cochrane have joined the battle. So this is a big fight among half a dozen sharp economists, some of whom have bestselling textbooks and/or Nobel prizes and/or were chairs of the CEA and/or were Treasury Secretary. If you want to see “Those guys are just being absurd” then it sounds like a no true Scotsman thing.

    (2) The CEA report that started all of this has all kinds of citations to the literature, talking about the impact of a corporate tax cut on wages.

    (3) Maybe you are saying the specific statistic of “how much do wages increase in response to a corporate tax cut in dollar terms.” But isn’t that what Mulligan is calling the “Furman ratio” in this post?

    So I can’t go along with your notion that this is some odd curiosity that a politician raised 4 days ago, and all respectable economists are in agreement on it, now that Mankiw has spoken. That’s not at all the impression I get.

  15. 15 15 Bob Murphy

    Steve,

    Last thing and I’ll drop it, I promise. I know you said Krugman is full of vitriol–and he is–but in this post, he has a diagram like yours, and claims that Mankiw’s result obviously cannot be correct.

    So we’ve got DeLong saying Mankiw’s calculus was wrong, and we’ve got Krugman verifying DeLong using a purely geometric argument.

    Are you guys talking about different things?

  16. 16 16 Steve Landsburg

    Bob Murphy: Mankiw and I are computing the ratio (Long Run Increase in Wages)/(Short Run Drop in Govt Revenues). Krugman is computing the ratio (Long Run Increase in Wages)/(Long Run Drop in Govt Revenues). So our denominators are different, and yes, we are computing different things.

    How very Krugmanesque to compute something different, get (of course) a different answer, and then conclude that whoever computed the first thing must be either incompetent or lying, and certainly evil in any event.

  17. 17 17 Steve Landsburg

    Bob Murphy: Don’t let this reply stop you from reading the reply above; that’s the important one.

    Let me mention another analogy: What is the integral of Sin(Log(Tan^2(x))? I am sure that no mathematician in the world has the answer at his fingertips. One might say: “But that’s ridiculous! Mathematicians think about sines and logs and tangents all the time!”. Sure, but that doesn’t mean they’ve thought about this particular combination of them.

    I’m not sure how much this is a response to you and how much to other commenters here or on your blog (I’ve forgotten who said what and am too pressed for time to check). But some — perhaps including you — have suggested that because economists are in the habit of thinking about wages, and about returns to capital, and about tax incidence, we should have had this answer at our fingertips. I think that’s a silly suggestion.

  18. 18 18 Bob Murphy

    Steve, thanks on all counts.

  19. 19 19 iceman

    Steve, Bob, any [actual] economist: Is there an economic rationale for having a non-zero corporate tax, other than it’s an opaque way to assess higher taxes on real people? I’ve asked this question unanswered for a while

  20. 20 20 Richard D.

    SL: “It’s not uncommon for someone to ask a weird physics question that no physicist has ever had occasion to think about, and for the physicists to take a few days getting it right.”

    Consider a rotating lawn sprinkler, with 3 arms. It sprays water clockwise,
    while rotating ccw. This is easily explained by Newton’s third law:
    action = reaction

    Now place the sprinkler underwater. Attach a vacuum pump to the hose
    (outside the pool), and suck water into the sprinkler arms. The water
    is pulled in ccw. Which direction does the sprinkler rotate?

  1. 1 Confused by the Confusion
  2. 2 In the Long Run, I Will Always Quibble With Krugman

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