Corporate tax cuts, math, and intellectual swindles

John Cochrane writes,

Each dollar (per worker) of static tax losses raises wages by [more than one dollar] It’s always greater than one… A number greater than one does not mean you’re a moron, incapable of addition, a stooge of the corporate class, etc.

This is also a lovely little example for people who decry math in economics. At a verbal level, who knows? It seems plausible that a $1 tax cut could never raise wages by more than $1. Your head swims. A few lines of algebra later, and the argument is clear. You could never do this verbally.

For the other side of the controversy, see Mark Thoma.

Let me swindle you with the following example.

1. We have the GDP factory, with two workers, A and B.

2. Each worker faces a different tax rate on wages.

3. The pre-tax wage of worker A is fixed. It cannot change.

4. (a) Each worker stays fully employed. (b) That means that the ratio of the marginal product of worker A to the marginal product of worker B must remain constant.* (c) That means that the ratio of the after-tax wage of worker A to the after-tax wage of worker B must remain constant.

*That ratio is completely determined by the production function, which is given, and by the quantities used of the two workers, which are fixed at full employment.

OK, now we cut the tax rate for worker A. What happens to the pre-tax wage of worker B?

At the fixed pre-tax wage of worker A, the after-tax wage for worker A goes up. Because of 4(c), that means that the after-tax wage of worker B must go up. The only way that can happen is if the pre-tax wage of worker B goes up. And to get worker B’s after-tax wage to go up by, say $1, you have to raise worker B’s pre-tax wage by more than $1. So worker B gets a big raise.

Substitute “capital” for worker A, “the interest rate” for worker A’s wage, and the corporate income tax for worker A’s tax rate, and I think you have the story that everyone is talking about.

But this is a swindle. We have fixed both the quantity and price of worker A. Taking worker A to be capital, the fixed supply is plausible because you think “how can we instantly adjust the supply of capital?” The wage, er, interest rate is fixed because, well, we know that the world interest rate is given, right?

But it cannot be right. A fixed wage suggests a perfectly elastic supply. A fixed quantity suggests a perfectly inelastic supply. There is a contradiction between 3 and 4(a).

The larger issue is that the simple model of a GDP factory with two factors of production and full employment is just silly. And even though other models add enough complexity to require computers to solve, they are also just silly.

There are many types of capital, which is what creates all of the lobbying and infighting over corporate taxes to begin with. There are also many types of labor, which substitute for and complement with the various types of capital in different ways. Adjustment takes time, and not all types of capital and labor are continuously employed. Over time, there is innovation, some of which is exogenous and some of which is in response to the tax change. The supply of each type of capital and each type of labor is neither perfectly elastic nor perfectly inelastic (and certainly not both!).

The moral of the story, in my view, is that forecasting the impact of economic policy is not a science. We know that, but then people demand a forecast, and they turn to a CBO “score” as if it were the final word on the subject. I have a forthcoming essay on the mis-use of CBO scores.

8 thoughts on “Corporate tax cuts, math, and intellectual swindles

  1. Yep, projections are hard. History, if you choose to read it, is easy.

    Let me know when you find an example of corporate tax cuts leading to higher median wages, even if that is only correlation.

    Oh, and please do not use anything from the CEA to do this. Their history is not relevant to a discussion about reality.

    • “Oh, and please do not use anything from the CEA to do this. Their history is not relevant to a discussion about reality.”
      Well, at least you’re open about dismissing out of hand information from sources you disagree with. You and Paul Krugman have that going for you.

      “Let me know when you find an example of corporate tax cuts leading to higher median wages, even if that is only correlation.”
      First of all, correlation =/causation, and therefore lack of correlation =/= absence of causation, so “even just correlation” isn’t even the right thing to ask for. “Ceteris paribus” is rarely a feature of reality. Second of all, it’s overall compensation, not wages that we should be looking at. Non-monetary compensation has increased drastically in recent decades while wages have grown modestly; that’s an important confounding variable. It’s also a pretty easy challenge.

      Ireland lowered corporate taxes from 50% to 12.5% between 1987 and 2003; GDP growth accelerated, as did income. If you look at Canada’s historical unemployment rate (not wages, but equally relevant), it correlates clearly and negatively with after-tax profit margin (with the latter leading the former) (http://cme-mec.ca/_uploads/_media/5457sq3ke.pdf). Here’s a federal reserve paper that, looking at state corporate income tax, finds a significant negative effect on employment and income (https://www.federalreserve.gov/econresdata/feds/2016/files/2016006pap.pdf). Though curiously, they find that the negative impact of tax increases more significant than the positive impact of cuts. Here’s Desai, Foley, and Hines’s analysis of international wage and corporate tax data from 1989-2004 (http://www.people.hbs.edu/ffoley/labcapshr.pdf). There’s the research done by the Kansas city Fed (https://www.kansascityfed.org/Publicat/RegionalRWP/RRWP07-01.pdf). Here’s an analysis of data over 20 years in Germany (http://www.zew.de/en/publikationen/do-higher-corporate-taxes-reduce-wages-micro-evidence-from-germany-2/?cHash=f9c04d3d505906b54679428ec474fb37). Here’s one from 2006 by the CBO (https://cbo.gov/sites/default/files/cbofiles/ftpdocs/75xx/doc7503/2006-09.pdf). If you want to see more research, here’s a literature review by Hanson and Brannon (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3028135). There’s also Hassett and Mathur’s paper looking at wages in 65 nations over 25 years (http://www.aei.org/wp-content/uploads/2011/10/-a-spatial-model-of-corporate-tax-incidence_105326418078.pdf). (saved that for last figuring you’re least likely to read it)

      What would be more interesting, though, is how much corporate tax rate correlates with profit. How much of the benefit of corporate tax cuts goes to investors should, in theory, be measurable simply by looking at how much corporate profits increase as the tax rate declines. If you look at the historical variability of post-tax vs. pre-tax profit going, the former clearly varies much less than the latter over time.

      Long story short, yes, there is plenty of empirical evidence for an association between corporate tax rates and wages. That’s actually quite a soft ball.

      • Great work, Octavian.

        Tho I’m pretty sure that, like most ideologues, mere “facts” won’t change the minds of folk who already know the answer, and are smart enough to rationalize away or excuse any inconvenient facts.

        Tho I’d also support tax cuts even if median wage didn’t go up.

      • You got nothing in that pile of stuff you just threw against the wall.

        Not interested in silly “unemployment rates” in Canada, nor claims of income growth in Ireland(GDP, seriously?). How about you show some facts that actually back up the only interesting thoughts(non-monetary compensation increase would be nice, particularly if applied to just the working classes).

        Here some correlation for you.

        https://fred.stlouisfed.org/graph/?g=3p5

        Corporate taxes/GDP

        Let me know when you find the income increases for the working class that matches that trend. Cause I can sure show you the income increases of the Top of the income charts.

        And, spare me the non monetary increases that are not in actual dollar amounts by actual income levels, and are adjusted for the people that go in and out of those programs as opposed to making any of those people automatically getting those amounts on a constant basis.

        • On that vein as I head to the airport. Try to avoid the Medicare and/or health insurance transfers. Value is the same as it was in the 70s(more or less) and costs are obviously greater, so adding those numbers to people’s incomes is just an accounting gimmick, ass opposed ot an “income gain.”

          Particularly when 80% of those “gains” go to around 20% of the people.

          • Oh, and see if you can add in the income of DB plans, which are now almost impossible to find.

            “Employers with DB plans, however, face significant financial burdens. If contributions and investment returns are not enough to pay promised benefits, the employer is responsible for making up the difference. While DB plans are still the most common type of retirement plan among public-sector employees, these burdens help explain why DB pensions have become increasingly rare among private-sector employers over the past 30 years. For example, the 2013 National Compensation Survey found that only 19 percent of non-union, private-sector employees had access to DB plans – a sharp decline from the late 1990s.”

            https://bipartisanpolicy.org/blog/defined-benefit-plans-whered-they-go/

  2. Empirics can provide a complement to models. The problem with simplicity is that so many want even simpler models, chosen for the end they require, or use it as an argument for no model at all except a hidden one known only to themselves, because ignorance and BS is bliss and explaining and defending all too much work.

  3. This is incorrect: “The pre-tax wage of worker A is fixed. It cannot change.” It’s post-tax.
    Also this: “We have fixed both the quantity and price of worker A.” Quantity of A is the key thing that lowering the tax rate is supposed to change.
    Your point about GDP factory may still stand, but your math is off.

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