Saturday, October 28, 2017

Corporate taxes and unscientific economists

I've been watching this ongoing "debate" among Brad DeLong, John Cochrane, and Greg Mankiw (and others, but to get started see here, here, here, and here). It started out with Mankiw putting up a "simple model" of how corporate tax cuts raise wages that he first left as an exercise to the reader, and then updated his post with a solution. The solution Mankiw finds is remarkably simple. In fact, it's too remarkably simple. And Mankiw shows some of the inklings of being an actual scientist when he says:
I must confess that I am amazed at how simply this turns out. In particular, I do not have much intuition for why, for example, the answer does not depend on the production function.
Cochrane isn't troubled, though:
The example is gorgeous, because all the production function parameters drop out. Usually you have to calibrate things like the parameter α [the production function exponent] and then argue about that.
The thing is that in this model, you should be at least a bit troubled [1]. The corporate tax base is equal to the marginal productivity of capital df/dk (based on the production function f(k)) multiplied by capital k i.e. k f'(k). Somehow the effect on wages of a corporate tax cut doesn't depend on how the corporate tax base is created?

But let's take this result at face value. So now we have a largely model-independent finding that to first order the effect of corporate tax cuts is increased wages. The scientific thing to do is not to continue arguing about the model, but to in fact compare the result to data. What should we expect? We should a large change in aggregate wages when there are changes in corporate tax rates — in either direction. Therefore the corporate tax increases in the 1993 tax law should have lead to falling wages, and the big cut in corporate tax rates in the 80s should have lead to even larger increase in wages. However, we see almost no sign of any big effects in the wage data:

The only large positive effect on wages seems to have come in the 70s during the demographic shift of women entering the workforce, and the only large negative effect is associated with the Great Recession. Every other fluctuation appears transient.

Now you may say: Hey, there are lots of other factors at play so you might not see the effect in wage data. This is the classic "chameleon model" of Paul Pfliederer: we trust the model enough to say it leads to big wage increases, but when they don't appear in the data we turn around and say it's just a toy model.

The bigger issue, however, is that because this is a model-independent finding at first order, we should see a large signal in the data. Any signal that is buried in noisy data or swamped by other effects is obviously not a model-independent finding at first order, but rather a model-dependent finding at sub-leading order.

This is where Cochrane and Mankiw are failing to be scientists. They're not "leaning over backwards" to check this result against various possibilities. They're not exhibiting "utter honesty". Could you imagine either Cochrane or Mankiw blogging about this if the result had come out the other way (i.e. zero or negative effect on wages)? It seems publication probability is quite dependent on the answer. Additionally, neither address [2] the blatant fact that both are pro-business Republicans (Mankiw served in a Republican administration, Cochrane is part of the Hoover institution), and that the result they came up with is remarkably good public relations for corporate tax cuts [3]. Cochrane is exhibiting an almost comical level of projection when he calls out liberal economists for being biased [4].

But the responses of DeLong [5] and Krugman are also unscientific: focusing on the mathematics and models instead of incorporating the broader evidence and comparing the result to data. They are providing some of the leaning over backwards that Cochrane and Mankiw should be engaged in, but overall are accepting the model put forward at face value despite it lacking any demonstrated empirical validity. In a sense, the first response should be that the model hasn't been empirically validated and so represents a mathematical flight of fancy. Instead they engage in Mankiw's and Cochrane's version of Freddy Krueger's dreamworld of the neoclassical growth model.

And this is the problem with economics — because what if Mankiw's and Cochrane's derivations and definitions of "static" analysis were mathematically and semantically correct? Would they just say I guess you're right — corporate tax cuts do raise wages. Probably not. They'd probably argue on some other tack, much like how Cochrane and Mankiw would argue on a different tack (in fact, probably every possible tack). This is what happens when models aren't compared to data and aren't rejected when the results are shown to be at best inconclusive.

Data is the great equalizer in science as far as models go. Without data, it's all just a bunch of mansplaining.


Update 10 Oct 2017: See John Cochrane's response below, as well as my reply. I also added some links I forgot to include and corrected a couple typos.



[1] In physics, you sometimes do obtain this kind of result, but the reason is usually topological (e.g. Berry phase, which was a fun experiment I did as an undergraduate) or due to universality.

[2] I freely admit I am effectively a Marxist at this point in my life, so I would likely be biased against corporate tax cuts being good for labor. However my argument above leaves open the possibility that corporate tax cuts do lead to higher wages, just not at leading order in a model-independent way.

[3] It's actually odd that corporations would push for corporate tax cuts if their leading effect was to raise wages (and not e.g. increase payouts to shareholders), all the while pushing against minimum wage increases.

[4] In fact, DeLong and Krugman are usually among the first to question "too good to be true" economic results from the left (even acquiring a reputation as "neoliberal shills" for it).

[5] At least DeLong points out that Mankiw should be troubled by the lack of dependence of the result on the production function.


  1. If you read my and Greg's post, you will see the question we address is whether it is POSSIBLE for a corporate tax cut to raise wages by more than it costs the government in revenue. Neither of us would take such a simple model to data. The point is not to estimate the wage changes of the Trump proposal, whatever it is. The point, clearly stated, is to establish a possibility result. For that you use the simplest possible model, as unrealistic as it is. Of course a real model needs depreciation, interest deduction, personal taxes, adjustment costs, and on and on. Reading before criticizing could save a lot of headaches, in particular most of Brad Delong's comments on everything.

    1. I did read them. The idea that this represents a "POSSIBLE" result is actually the problem. On exactly what basis is this a "POSSIBLE" result? The model itself hasn't been compared to data (which you've rationalized by it being too simple). Does it derive from a more complex model that has been compared to data? It's not presented that way. I'm 97% sure it does not because it's basically the Solow growth model and additionally there appear to be no models that get the data correct to a greater accuracy than my model result presented above.

      So I ask again: On exactly what basis is this a "POSSIBLE" result?

      The source of all possibility of describing reality (and therefore a fortiori policy) is empirical data. Without empirical data under its belt or in its genealogy, a model is just a math problem. It has zero validity. Zero. There is literally no other scientific field that would say it does. Economics is an aberration in this regard.

      You can't have toy models without first getting the empirical data right to some degree. Maybe it's 10%. Maybe it's 1%. Just some degree. This can't just be achieved by overfitting existing data either (unless it is then used to e.g. forecast).

      Given the accuracy of macroeconomic models, there should be no toy models in economics. No one should ever say they wouldn't "take such a simple model to data" in macro because there is no basis to formulate that simple model *except* on the explicit premise of comparing it to data. It's not like it's a simplification of some wildly successful macro model. (Which one is that?) As an aside, I have no idea where economists' concept of 'protecting' simple models from data comes from. It's not like the model is going to get hurt. If it's such a good model but looks ridiculous compared to data you should still show the comparison to data and argue why it's ok. Is it because economists already know their models will look ridiculous compared to data and just decided as a field not to talk about it? 'Obviously we're talking bollocks, but there's no need to actually come out and say it.' Is it just being patronizing of the public? 'If some layperson saw this, they'd think we have no idea what we're talking about, but it'd take years to explain it, so better just not show how the sausage gets made.' I don't get it.

      You can make toy models in physics. That's because relativity and quantum mechanics have been compared to data, therefore any model constructed using e.g. the quantum field theory framework automatically has the benefit of being consistent with empirical successes of relativity and quantum mechanics and therefore is well down the road of possible results.

      But there's no wildly accurate macro theory framework that lets us do this with corporate tax rate cuts (or really any policy choice). So whether or not any model, simple or complex, represents a "POSSIBLE" result is *entirely* dependent on data.

      Sure, the field's defense is that all** economists do things this way. They all** make up math problems and just assume they represent "POSSIBLE" results. And that is (unfortunately) very true. But it's cargo cult science. Just because all** economists do it doesn't make it scientifically valid. If all economists decided a p-value of 0.2 was just fine, would you go along with it too?

      **Let me put in the exception for econometric models like VARs, which are based mostly on data.

      So let me answer my question: there is no basis for this to be a "POSSIBLE" result. Claiming that it is "POSSIBLE" is unscientific. And as I said in my post, the fact that your result is basically model independent (plug in α = 0 and try to rationalize the result like any decent undergrad would on a homework problem) makes the lack of "leaning over backwards" (in Feynman's words) to reject it even more egregiously unscientific.

  2. Interesting read Jason. I'm surprised John commented. I'm even surprised he read your post. And I'll more surprised again if he responds to your response.

    What do you see as a plausible path for academic economics to make the changes you'd like to see? What would be the "game changer" or the "tipping point" in the field, or will it just be a gradual process (assuming it happens at all)? For example, will it be an undeniably successful model (or framework and associated models) which serve as a new gold standard against which other work is compared?

    1. In my second paragraph I realize I'm asking you to speculate.

    2. Here's a candidate scenario: a bunch of bored physicists discover a discipline (economics) that uses math and data, but seems to be somehow lacking in the scientific approach they're used to, so they decide to colonize it. =)

    3. For some reason, I don't see an "undeniably successful" framework of models or new paradigm doing it for a couple of reasons. First and foremost the lack of empirical success does not appear to have an effect, so why would positive results have an effect?

      Second, economics does seem to have a significant amount of philosophy built around the idea that you don't have to look at empirical data and there are a large number of people out there (including proponents of heterodox economics) who are perfectly willing to go along with this because their own theories probably wouldn't stand up to the scrutiny. I mean the von Mises crowd forswears even mathematics.

      Third, the field is male-dominated and therefore given to "male answer syndrome" (aka gender-dependent overconfidence bias) which generally gets in the way of any sort of progress. Impediments would range from economists looking at that "undeniably successful" framework and claiming to know what it's all about without knowing what it is, to continued reasoning using "stories" that fit the economist's preconceived notions.

      I imagine efforts like Susan Athey's to bring machine learning into econ might help (in particular, it puts data at the forefront -- and additionally, economists seem more amenable to colonization by new hip machine learning than physics which they seem to have some sort of complex about envying), but generally I am pessimistic about any sort of progress in a short period of time if for no other reason than progress rarely happens in a short period of time.

    4. Thanks Jason. I'll look up Susan Athey.

    5. You write:

      "First and foremost the lack of empirical success does not appear to have an effect, so why would positive results have an effect?"

      Well maybe the bar has been very low for empirical success for so long that nobody knows (or can imagine) anything different. An actually empirical success might raise the bar a bit. Of course everyone used to a low bar would hate that, but I can see that being a game changer. It might drag them kicking and screaming into a new empirical era. If it happens, it should be fun to watch! =)

      Re: male-dominated. But men love to humiliate each other, so if there's a way to beat the old school establishment over the head with an empirical hammer, it's hard to believe a red-blooded male wouldn't LOVE to be the one wielding the hammer. Once there's blood in the water, it'll be a feeding frenzy.

      Lol ... I think I set a new record for cliched metaphors in these last two comments.


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