# Cutting the tax on corporate profits would probably reduce US national income

Paul Krugman has been explaining (very slowly and clearly) that if the US attracts foreign investment by cutting taxes on profits, then it will have to pay the foreign investors. The Tax Foundation appears not to have noticed that loans are not gifts.

This is the ultra-static effect of the cut in which its effects on behavior aren’t considered. Krugman went on to note that if there is a huge inflow of foreign cash (as promised by supporters of the bill) then there will be a huge increase in US payments to the foreigners. He calls this Leprechaun economics, because it is a very important reason that Irish GDP is much greater than their gross national income. He wrote

GDP is actually the wrong measure. If you’re going to be pulling in foreign capital, you’re going to be paying more investment income to foreigners; so gross national income – income accruing to domestic residents – is going to go up by less. And surely that’s the measure we care about.

and

There are really two bottom lines here. One is that the true growth impacts of Cut Cut Cut would be even more pathetic than the numbers you’ve been hearing. The other is that if you’re going to make international capital flows central to your arguments, you really need to think about the implications for future investment income.

Krugman raises a question

In fact, when you bear in mind the reduced taxes collected on foreign investors who are already here, GNI could actually go down, not up.

It is interesting. I think that somewhere he explains that the answer depends on another debated issue — the true incidence of taxes on profits. Enthusiasts for the tax cuts assert that, in the long run, all of the benefits will go to workers. People who look at data, estimate that about one quarter of the benefits of a reduction of taxes on profits go to workers

(before going on, there are no free lunches — the benefits are at the expense of the Treasury so other taxes will have to be raised or programs will be cut.)

This matters for the discussion of Gross National Income vs GDP, because roughly 35% of shares of US firms are owned by foreigners. So if the money goes to investors, 35% goes to foreigners. This is true both of the old foreign investment in the USA and the new investment attracted by the low taxes. After the jump I will try a lot of horrible pain ascii formulas attampting to answer Krugman’s question of whether a profits tax cut causes higher or lower domestic gross national income. The key parameters are the current tax rate, the incidence on workers, and the share of capital.

Doing the algebra, I conclude that unless more than half of the incidence of profits tax falls on labor, cutting the rate of taxes on profits below 35% reduces gross national income.

“Half” is embarrassingly close to a whole number, but it is what came out of the horrible algebra. Also 35% is coincidentally the current statutory rate. I regret the fact that messy calculations gave such a suspiciously simple result. I don’t totally trust my algebra and don’t think my effort added much to Krugman’s. The point is that, for plausible parameters, cutting the tax on capital income reduces US gross national income.

update:

thanks for comments. I didn’t explain the model well. I add a bit of explanation here. First it is assumed that tax reform doesn’t affect employment. In fact, it is standard to assume full employment in these models. This isn’t horribly silly at the moment. This means that total employment is equal to labor supply and can’t be changed by firms (who can compete with each other for the scarce workers).

However, increased capital does affect labor income by causing higher wages. The story is that it causes a higher marginal product of labor and higher labor demand for any given real wage. So there would be more demand for labor and the same supply, and so the price of labor (the real wage) would go up. This actually isn’t totally crazy. Real wages did go up in the late 90s and have otherwise stagnated since 1973.

end update:

Warning horrible horrible algebra after the jump

OK always following Krugman, I assume that capital is paid it’s marginal product. If there were no tax on capital income, then new foreign investment of deltaK would not change gross national income (GNI) because it would raise GDP by (detaK)r and also reduce net capital income by (deltaK)r where r is the marginal product of capital. However, if there is a tax tau on capital income, the IRS gets (deltaK)(tau)r so the inflow causes larger GNI.

Krugman notes that if the new statutory tax rate is 20%, then even ignoring loopholes and such, the increase in GNI due to the inflow is only 20% of the increase in GDP. But he also stresses the 35% of existing shares owned by foreigners and suggests that this might imply a reduction of US GNI due to a reduction in Tau. To find out, I need to use a model

First GDP is a standard cobb douglas function of capital and labor. I choose units so

1) GDP = Y = K^alpha L^(1-alpha) so the share of capital is alpha.

2) rK = (alpha)Y

3) WL = (1-alpha)Y

I will choose units of labor so L= 1

so W = WL = (1-alpha)Y

With Tau = 0.

4) GNI = Y – 0.35rK = Y(1-0.35alpha)

OK now imposing Tau will cause lower investment and change K down to K_tau and r up to r_tau. also investors will get (1-tau)(K_tau)r_tau

Workers will get wage (1-alpha)(K_tau)^alpha

Investors will get (1-tau)(K_tau r = (1-tau)alpha(K_tau)^alpha

Tax cut enthusiasts assume that K changes so much that (1-tau)r_tau doesn’t depend on tau. This is extreme.

Data suggests that the change in wages is one fourth the change in (1-tau)(r_tau)K_tau. I want to play with incidence as a parameter so I assume

5) d(W)/dtau = (beta)K_tau(d((1-tau)r_tau)/dtau)

Now I can do the algebra which depends on beta, alpha and tau. I am sometimes going to leave out the _tau of K_tau (sorry)

I want to figure out d(K_tau/d_tau) using equations 2, 3 and 5

6) (1-alpha)(alpha)K^(alpha-1) dK_tau/dtau =

[(alpha(alpha-1))(1-tau)K^(alpha-1)(dK_tau/dtau)- K_tau(alpha)K^(alpha-1)]beta

Oh look I can divide both sides by (alpha)K^(alpha-1) (which happens to be equal to r) so

7) (1-alpha)dK_tau/dtau = (beta)(alpha-1)(1-tau)dKtau/dtau – Ktau_a(beta)

8) (1-alpha)(1+beta(1-tau))dK_tau/dtau = – Ktau_a(beta)

9) dK_tau/dtau = -(K_tau)(beta/[(1-alpha)(1+beta(1-tau))])

Now I can calculate the effect of changing tau on GNI

10) d(GDP)/dtau = (alpha)K^(alpha-1)(dK/dtau)= (alpha)(K^alpha)(dK/dtau)/K

11) d(GNI)/dtau =

(alpha)(K^(alpha-1))(dK/dtau) – 0.35 (k_tau)d[(1-tau)r_tau]/dtau] – (1-tau)[(alpha)(K^(alpha-1)(dK/dtau)]

The two terms I subtract are the increased after tax payments on old capital an

d the new after tax payments on new capital.

12) d(GNI)/dtau = (tau)(alpha)(K^(alpha-1))(dK/dtau) – 0.35 (K_tau)d[(1-tau)r_tau]/dtau

r_tau = alpha(K^(alpha-1) so

13 d(GNI)/dtau = (tau)(alpha)(K^(alpha-1))(dK/dtau) + 0.35 (k_tau)alpha(K^(alpha-1) –

0.35(K_tau)(1-tau)(alpha-1)(alpha)(K^(alpha-2))(dK/dtau)

collecting terms

13) d(GNI)/dtau = [(tau + 0.35(1-tau)(1-alpha))((dK/dtau) + 0.35(K_tau)]alpha(K^(alpha-1)

plugging in dK/dtau

14)dGNI/dtau=

= [-(tau + 0.35(1-tau)(1-alpha))(K_tau)(beta/[(1-alpha)(1+beta(1-tau))]))+0.35(K_tau)]alpha(K^(alpha-1)

= [0.35 – [tau + 0.35(1-tau)(1-alpha)]beta/[(1-alpha)(1+beta(1-tau))](alpha)K_tau^alpha

The lower is beta, the better high tau looks. For beta = 0 (so no effect of taxes on investment) national income clearly increases in tau (of course it just means taxing money before sending it to foreigners). Beta = 1/3 is the empirical estimate. I will be kind to tax cutters and assume beta = 1.

For alpha = 1/3, and beta = 1 this is

15) d(GNI)/dtau = [0.35 – [tau + 0.35(1-tau)(2/3)]/[(2/3)(2-tau)](alpha)K_tau^alpha =

[0.35 – [tau + 0.35(1-tau)]/(2-tau)](alpha)K_tau^alpha =

= [0.35 – (0.35+0.65tau)/(2-tau)](alpha)K_tau^alpha

Which implies GNI is maximized at tau such that

0.35(2-tau) = 0.35 + 0.65tau

so tau = 0.35

Oh my that happens (by pure coincidence) to equal the current statutory rate (which by another pure coincidence happens to equal the fraction of shares own by foreigners).

The effective tax rate is lower than 35% and beta is less than 1 so cutting taxes on profits would reduce US gross national income.

Of course the math is so far above my pay grade I cannot see it from here, but this caught my eye:

” Enthusiasts for the tax cuts assert that, in the long run, all of the benefits will go to workers. People who look at data, estimate that about one quarter of the benefits of a reduction of taxes on profits go to workers.”

I am thinking that even the 1/4 thing is wrong. I do not doubt that the data is accurate, I think that there is just a correlation between the tax cuts and the gains by labor instead of a correlation.

Haven’t met many business owners in my lifetime that raise their workers salaries because they have more profits, though I have met some. At none of them were at the big corp level, but at the level where the owner knows almost everyone by name.

“ I do not doubt that the data is accurate, I think that there is just a correlation between the tax cuts and the gains by labor instead of a correlation.”

I am not sure what the above statement means.

My bad.

Should be

“ I do not doubt that the data is accurate, I think that there is just a correlation between the tax cuts and the gains by labor instead of a causation.”

The same sentence that Emichael noted also glared out at me.

My question is even more basic. Why should ANY of the tax cuts accrue to labor?

To the best of my knowledge private for profit enterprises aren’t known for being altruistic. Labor unions, having in the distant past some bargaining power (power of the cooperative strike). aren’t nearly as prevalent (outside of gov’t employment) now or as powerful so the source to coerce some proportion of the tax cuts out of private enterprise come from what source?

Longtooth,

I don’t think it is a question of whether or not any tax cuts SHOULD accrue to labor. The problem is that the tax cuts are being sold as a tool which WILL accrue to labor.

Jerry Critter,

Re-read the statement in context with the preceding one. “People who look at the data… ” in contrast to what “enthusiasts for the tax cut” assert (which is 100% accrue to labor)..

My question refers to why even a quarter of the cuts accrue to labor in the “reasonable case”.

I can see the mechanisms by which some proportion of the cuts accrue to labor but they all come down to the extra profits from the Cut, Cut, Cut Act get utilized in creating new business’s and expanding existing ones such that these new business’s and expansions of existing ones hire additional labor. The additional labor’s net income is then an accrual of some proportion of the tax cuts to labor.

But EPOP is currently at 60% and could conceivably be sustained as high as 62.5% (though I doubt that myself) So the added labor from expansion and new business’s can increase by max 2.5% of the proportion of the population’s employed labor.

So how does labor accrue 25% of the additional profits to capital from the cuts when labor can only grow by 2.5% at most ( or if you prefer extreme optimism a sustainable additional 3%) of the population when at the very outside only 50% of a business’ expense is labor income. Seems to me this mechanism can at most allow 1.25% to accrue to labor from the cuts (50% x 2.5% increase in labor as proportion of the population), and even that assumes 100% of the cuts are consumed in new business’s and expansions of existing ones… all domestically btw.

Dear Longtooth & EMichael

Yes the idea is that the tax cut will encourage firms to expand more than they otherwise would. That’s the mechanism. This means that the point is to encourage investment and expansion.

Yes again, it is assumed that this won’t cause higher employment which is limited by labor supply. This is always assumed in these models. under the current unusual conditions is actually a reasonable assumption.

The point is that, finally, the real wage is assumed to be determined by demand and supply. So an increase in demand for labor causes an increase wages even if it doesn’t cause an increase in employment. This is actually a semi reasonabe assumption. Feal wages have stagnated through decades of low labor demand except for during the late 90s when they increased (and also in 2015 and 2016 they increased some).

Now the practical point, which I think has been noted by all non hack economists who discuss the issue, is that if you want more investment, you should change the tax treatment of investment and not the treatment of capital which already exists. All the alleged gains from the tax bill come from expensiing investment (treating it as a cost and not taxing profits which are reinvested in physical capital). Cutting the tax rate matters only if reinvested profits are taxed.

The whole horrible math analysis is bending over backwards to avoid this elementary point. I noted thishere

http://angrybearblog.com/2017/11/the-right-way-to-reform-corporate-taxes.html

The question in the title of this post is not relevant to the debate. It assumes that reinvested profits continue to be taxed as they currently are. So aside from the horrible algebra, the post answers a question no one is really asking.

Oh one other thing. On corporations sharing wind falls with workers. It sounds implausible, but there is evidence that it happens. This is not in the model I considered.

1) the strange case of the tobacco products industry. This is an interesting industry (aside from killing people) because they received a Huge gift from the Federal Government in the 1960s — they were forbidden to advertize on TV. They had been sending huge sums of money to the networks in order to compete for the same slowly changing pool of nicotine addicts. When TV ads were banned, sales didn’t suddenly drop (addiction is like that). So they had huge profits. Wages in the sector went way up even compared to other wages (which were growing back then in the good old days). I learned this (and much else) from Larry Katz

Second, inventions. There is a survey of engineers and such describing important inventions. Firms with such inventions raise wages. So far it might be just they need smart workers to implement the invention. But also firms which compete with firms with important inventions cut wages (I mean they grow slowly). I learned this from the very smart John von Reenan.

It is assumed that managers don’t do this from the kindness of their hearts but rather, because if they don’t workers get very very angry.

Anway, these stories have nothing to do with the silly model or the silly arguments made by the Tax Foundation.

RW,

This ain’t the 60’s, but I understand the theory.

JimP,

There are more than 100,000 Americans alive today because of the waste of the ACA. Millions more living healthier lives and not suffering medical bankruptcies because the Dems wasted their chance with the ACA.

Better bring your A game in here if you are going to attack the ACA. There are actually people in here that know.

Yes . . .

Robert thanks for the explanation and theory supporting it.

However, in the 60’s Reagan’s tax cuts hadn’t happened yet so handing windfall profits to employees wasn’t nearly as big a loss as it is now — therefore I would discount the 60’s as having any historic empirical support of relevance since Reagan., (and besides that the Tobacco industry was in the mode of trying to change public perceptions so basically giving employees raises was large PR stunt as well).

The theory assumes constant full employment increase labor wages/salaries via supply/demand when the cuts induce investment in existing business growth in output or new business’s are created. But since constant full employment only exists intermittently, and is normally followed relatively soon by recession due to excessive investment in new production without sufficient new demand to cover it, then I fail to see why the theory uses full employment as a foundation.

At best full employment is a fraction of time

For the above reasons a 25% proportion of the tax cuts (as profit to producers) going to labor income wildly overstated, imo

Parenthetically, the economy’s growth is limited by demand for goods and services at affordable prices… much of what we afford is based o low cost imports rather than domestic production alone. Furthermore, current corporations are sitting on piles of cash and stock they bought back and haven’t invested it heavily in expanded production as a consequence. So why would greater profits be used to increase production unless demand were somehow stimulate in an economy where EPOP is still only now broaching 60%?

LT – “…the economy’s growth is limited by demand for goods and services at affordable prices.”

Yes, without an increase in demand, why would a business invest capital in expansion, either in more employees or facilities, even with an increased profits?

I am amazed and delighted that my pointless math post got so many comments almost all of which are also very smart.

@Longtooth

The tobacco fact is just one data point, so it doesn’t prove much. The invention fact is about the UK where workers have unions.

My honest impression is that the way to understand wages is to imagine it’s as if, even workers without a union could credibly threaten to recognize one as their exclusive bargaining agent. This is odd for the USA, because that threat it totally not credible (the laws which are supposed to protect the right to organize aren’t enforced at all).

This means that your point that we aren’t in the 60s anymore is very relevant. Corporate executives feared unions then. It mattered even in the South and even for Tobacco workers. I realize that my honest opinion is based on historical data and might not be relevant to the 21st century.

More generally the 25% (which I rounded up to 50% to be generous to GOPers) might be silly. I have read the number, but haven’t read the papers where it is estimated. I suspect that it is like the number that increased growth pays for *at most* about 25% of the cost of tax cuts. The key phrase there is “at most”. In order to prove Laffer totally demonstrably wrong, people grant him every imaginable concession. The find that, no matter what they assume, his claim is false. The the assumptions made for the sake of argument are taken to be known facts. The debate shifts to one where the overton window goes from total hacks like Laffer, Moore and Kudlow to sensible people who have made every possible concession for the sake of argument to the hacks.

Only very occasionally is there some mention of the facts that

1) tax cut enthusiasts also say deficits are terrible for growth and that effect is not considered in the relatively serious analysis of growth effects

2) The crude international data say that taxes are not (statistically significantly) bad for growth and deficits are terrible. Very crude correlation, but the claim that taxes are bad for growth has no empirical support (amazingly close to zero for something which has been studied so much).

3) It is assumed that something will be done to prevent default, but the fact that this something is likely to include tax increases and that this affects decisions is forgotten. In fact, the theory (used to justify cutting taxes on capital income) says that they should be reduced over time. In a simple model, they should be as high as possible so long as there is any reason to tax at all. The optimal policy is to tax capital as much as possible and build up a sovereign wealth fund large enough so income on it pays for all government spending. Somehow “will at some time in the future be zero (when there is no reason at all to tax as the government already has plenty of money) has become should be zero now. This is not an honest mistake.

This is explained here (pdf warning)

https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxyb2JlcnR3YWxkbWFubnxneDo3NmYxZDEzZWY1MjYyNzRm

The saint who translated my plain ascii to LaTex didn’t notice that I spell my name Waldmann.

5) Robert Rubin explains this here

https://www.washingtonpost.com/opinions/the-republican-tax-plans-five-worst-dangers/2017/11/15/b24029aa-ca2b-11e7-aa96-54417592cf72_story.html?hpid=hp_no-name_opinion-card-a%3Ahomepage%2Fstory&utm_term=.e81b8c0b4a1f

@Jim Pierson

Use the Wikipedia “The Economic Growth and Tax Relief Reconciliation Act of 2001 (Pub.L. 107–16, 115 Stat. 38, June 7, 2001) was a sweeping piece of tax legislation in the United States passed by the 107th Congress and signed by President George W. Bush.” I note that June 7 2001 was before November 5 2002. Your claim that Bush only got going after the mid term election is false. The GOP had massively slashed taxes “on the upper tail” (Bush’s words) by then. Yes they cut taxes on capital income again after the mid terms. But, in 2001, they showed no sign of letting the popular vote in 2000 influence their actions at all. None. Zero.

I think it is terribly naive to think that norms, traditions or customs have any influence on most Republicans. Maybe on 3 senators (which would be enough).