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 . 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  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 . Cochrane is exhibiting an almost comical level of projection when he calls out liberal economists for being biased .
But the responses of DeLong  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.
 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.
 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.
 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.
 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).
 At least DeLong points out that Mankiw should be troubled by the lack of dependence of the result on the production function.