# Monopoly power and corporate taxes

There has been a fair amount of debate about corporate taxes in the econ blogosphere. The debate was framed early on by a cute little exercise on Greg Mankiw’s blog which was supposed to  show that, in a small-open economy with perfect competition, a 1 dollar cut in capital taxes raises wage income by more than 1 dollar.

Paul Krugman and others have rightly pointed out that Mankiw’s toy example, its cuteness notwithstanding, provides little to no insight into the real policy debate now going on in the US, because (i) the US is not a small open economy and (ii) there is evidence that much of corporate profits are monopoly rents rather than returns to capital, which casts doubt on the relevance of perfect competition models.

Indeed, there’s a new paper documenting that mark-ups (difference between price and marginal costs) have increased in practically every industry in recent decades. The paper has not yet gone through peer review, so it’s probably wise not to jump to conclusions from it. Nevertheless, it’s useful to think about potential implications.

One of the basic results in public finance is that taxes on rents produce no deadweight loss. So if corporate profits are just monopoly rents, we can tax them away at zero social cost. Right?

Wrong.

# “Self-financing” tax reforms: a simple formula

There is much talk these days about tax reforms, both in Austria and around world. Most political parties seem to agree that taxes on labor are too high and that cuts should be made. There is disagreement as to whether these tax cuts should be accompanied by cuts in government spending or increases in other taxes.

One recurrent issue in this debate is the extent to which tax cuts are “self-financing”. This usually comes from a vague notion that reducing tax rates has a “stimulating” effect on “growth” and “job creation”. Such “stimulus” makes the tax revenue increase thus offsetting some of the revenue loss due to the reduction in tax rates.

Although I usually take great pleasure in brutally debunking popular myths with my profound knowledge of Economic Science (insert resounding laughter here), let me say that I think that in this matter the vague notion of the layman is broadly correct.

Economics being a hard quantitative science, the careful economist always strives to replace broadly correct but vague notions with mathematically exact but only vaguely correct formulas. In this spirit, I offer a formula for calculating to which degree a cut in the marginal labor tax rate is “self-refinancing”.

We start from a definition: total tax revenue (T) is the tax rate (t) times income (Y):

$\displaystyle T = t\times Y.$

We treat t as both the average and marginal tax rate. In fancy language: income taxes are assumed to be linear. Not true, but (one hopes) true enough.

We want to know how T changes if t is reduced by a small amount dt. There are two effects, one direct, one indirect. The direct effect is to reduce T by an amount $\displaystyle Y dt$. The indirect effect comes from realizing that Y depends on labor input L which, in turn, depends on the tax rate. So therefore, if we reduce the tax rate by dt, labor supply rises by $\displaystyle n dt$, where n is the elasticity of labor supply. The increase in labor input raises output and thus income. Suppose the elasticity of output with respect to labor input is a. Then the total change in income is: $\displaystyle dY = (\alpha\times n)dt.$

The indirect effect is where “self-financing” comes from. Let us measure the self-refinancing effect of the tax cut by $\displaystyle X = t\times dY/Y,$ which is the indirect change in revenue measured in percent of income.

$\displaystyle X = (t\times\alpha\times n)dt.$ *

The self-financing share X is larger, the higher the initial tax rate, and the higher the two elasticities $\displaystyle \alpha$ and n.

How big is $\displaystyle \alpha$? Well, consider a Cobb-Douglas production function $\displaystyle Y=K^{1-\alpha}\times L^{\alpha}$, where K stands for other factors of production which we hold fixed for purposes of this exercise. The labor elasticity of output is $\displaystyle \alpha.$ It is well-known that under competitive conditions a is equal to the labor share of income. In Austria, as well as in most developed countries, this share is about 2/3. So let’s take that as our answer.

How big is n? That’s a tough one to measure. Theoretically, it depends on the labor-leisure preferences of households as well as on other „deep” parameters of the economy. The empirical evidence I have seen suggests that a 1 percent decrease in t increases L by less than 1, but more than 1/3 of a percent. Let’s take 1/2 as a guess.

Finally, what is t? In Austria the marginal income tax rate is close to 50%, the average rate is in the area of 30%.

Feeding these numbers to our formula we arrive at the following conclusion. The self-financing share of a tax cut is in the range between 10 and 17 percent. This means that a tax cut of 1 billion euros indirectly creates additional revenues between 100 and 170 million euros. That still leaves a hole in the public budget of at least 830 million euros, though.

*) The General Formula is:

$\displaystyle dT = Ydt + t\times\frac{dY}{dL}\frac{L}{Y}\times\frac{dL}{L}\frac{1}{dt}\times Y dt$

# Can robots pay taxes?

Bill Gates thinks robots should pay taxes. My first reaction was: Mr Gates obviously doesn’t know much economics. If he did, he would know that things do not pay taxes. Only people do.

Robots, so I thought, are machines. They don’t have an income of their own, they don’t consume stuff. The income they help produce goes to whoever owns the robot. If I own a robot, my willingness to let it (him? her?) work for a firm increases with the robot wage rate, the amount of money I receive per hour of work done by my robot. A tax on robot wages would shift the supply curve of robot labor up (or, if you prefer, to the left), increasing for each given amount of robot labor the wage rate employers must pay to get it. The gross robot wage increases, although probably by less than the tax rate, depending on how elastic the demand for robot labor is. Assuming that the demand elasticity is not infinite, the tax burden will be split between the robot owners and the employers of robots. So the robot tax would just be another form of a capital tax, which would partly be shifted to other factors of production, including human labor. In no real sense would it „tax robots“.

Now there are good reasons to believe that we are approaching the “technological singularity“, a scenario in which robots become smarter than humans. Some experts on artificial intelligence reckon we might be only 30 years away from that. I have exactly zero qualifications to judge the plausibility of that claim, but I don’t see any obvious reason why it couldn’t happen.

Suppose the singularity does happen. Then it seems quite ridiculous to assume that humans own robots. More likely, it would be the robots who own humans. Indeed, we can only hope the super-intelligent robots would treat us a little better than we are treating less intelligent life-forms now. Let’s assume, for the sake of argument, that humans will co-exist with the super robots as equals, at least for a while. Then robots would effectively become another class of people competing with us in the market place for jobs and goods. In such a world, robots are capable of bearing a tax in the sense that they would have to cut back on their consumption (whatever it is robots consume) when faced with a tax. But even in this, admittedly unlikely, scenario, it would be the case that humans feel some of the burden of the robot tax. This is because even super-intelligent robots will react to incentives. Why, given that they are super intelligent, they should react much better to incentives than homo sapiens with all its cognitive biases. If we tax their labor, they will supply less of it, which hurts humans.

So yes, robots could pay taxes. But only if they are intelligent and powerful enough to resist being held as slaves by humans, and not as intelligent and powerful as would allow them to enslave humans. Not a very likely scenario I guess.

PS: If you are curious what AI is currently capable of doing, here is some AI-produced poetry.

# Verteilt der österreichische Staat von oben nach unten oder umgekehrt?

Im heutigen wirtschaftspolitischen Kaffee ging es um die Frage, ob man den Bundesländern Steuerhoheit übertragen sollte oder nicht. Ich vertrat die Argumente dafür, Christian Lager die Gegenposition. Irgendwie kamen wir am Rande auf die Umverteilungswirkung der staatlichen Einnahmen und Ausgaben als Ganzes zu sprechen.

Ich habe im Zuge der Diskussion behauptet, die Umverteilungswirkungen wären vernachlässigbar und habe das damit begründet, dass wesentliche Teile der Staatsausgaben – besonders für die Unis, öffentliche Sicherheit und das Pensionssystem – eher von unten nach oben umverteilen als umgekehrt.

Eine Studie vom WIFO aus 2005 widerspricht mir. Die Studienautoren finden eine stark progressive Wirkung der staatlichen Ausgaben in Österreich. Sie schreiben:

„Wählt man Äquivalenzeinkommen als Bezugsgröße und gruppiert für das Jahr 2005 die Haushalte nach ihrem gewichteten Pro-Kopf-Bruttomarkteinkommen, so kommt der größte Teil der hier untersuchten öffentlichen Leistungen der unteren Einkommenshälfte zugute: dem ersten Drittel 43½%, dem mittleren rund 31½% und dem oberen 25%. […] Die relative Bedeutung dieser Leistungen bezogen auf das äquivalente oder Pro-Kopf-Bruttomarkteinkommen steigt im unteren Drittel auf 84% und sinkt im mittleren und oberen auf 29% bzw. 12%.“

Das ist ziemlich eindeutig.

Allerdings: In dieser Studie werden drei Bereiche außer Acht gelassen, nämlich Ausgaben für Kunst, Kultur und Sport, öffentliche Sicherheit (nach innen und außen) und das öffentliche Pensionssystem. Im Jahr 2014, betrugen die Ausgaben für diese Bereiche zusammen 52,8 Mrd. Euro, oder 30 Prozent der Gesamtausgaben.

Das sind genau jene Bereiche, die mit großer Wahrscheinlichkeit regressiv wirken, d.h. den oberen Einkommensschichten stärker zu Gute kommen als den unteren.

Die vom Staat finanzierten Opernhäuser und Sportereignisse werden vermutlich von den Reichen überproportional stark konsumiert. Die öffentliche Sicherheit wirkt mit Sicherheit regressiv weil erstens reiche Wohngegenden besser geschützt werden als ärmere (Die Polizei kommt schneller, wenn in Geidorf eingebrochen wird, als in Gries), und zweitens weil reiche Haushalte per Definition mehr zu schützen haben als arme.

Die regressive Wirkung des Pensionssystems kommt aus drei Gründen zustande: erstens sind die Pensionsbeiträge nach oben gedeckelt, zweitens arbeiten die Reichen kürzer weil sie aufgrund der längeren Ausbildungszeiten später ins Erwerbsleben eintreten, drittens leben die Reichen länger und beziehen daher länger Pensionen.

Natürlich müsste man in eine wirklich umfassende Analyse der Staatstätigkeiten auch noch auf die Verteilungswirkung von staatlichen Regulierungen zu sprechen kommen. Ich denke hier vor allem an die Mietpreisregulierung, die Eingriffe in die Landwirtschaft oder den Energiemarkt und natürlich die zahlreichen Arbeitsmarkregulierungen. Ich glaube, dass diese Eingriffe tendenziell die Armen schlechter stellen. Soweit ich weiß hat das für Österreich aber noch niemand umfassend unter die Lupe genommen.

Die Frage ist natürlich wie sich die Ergebnisse ändern, wenn man die genannten Bereiche in die WIFO-Analyse mit hineinnimmt. Ich vermute mal, dass immer noch eine leicht progressive Wirkung der Staatstätigkeit herauskommt. Aber es ist keineswegs klar und unstrittig, dass der österreichische Staat in Summe von oben nach unten verteilt.

# Can Redistribution Get Us Out of The Recession?

Another Guest Post by Max Gödl, enjoy!

One argument I frequently hear in discussions on macro policy is that income inequality is a big drag on our economy right now. The reason is that rich folks save a larger fraction of their income than poor folks. Hence redistributing income from the top to the bottom increases aggregate spending which “grows the economy”. Let’s do it!

My response to that is: woah, woah, woah!

First of all, when presented in this way the argument is a non sequitur. It’s pretty clear that the rich have a higher average propensity to save than the poor. But that does not imply that their marginal propensity to save is higher, too. And it’s the latter that counts: Redistribution from rich to poor increases aggregate consumption only if the poor spend a larger fraction out of additional income than the rich. (Nerds, think Keynesian consumption function: C = a + bY. C/Y decreases with income, but dC/dY doesn’t!)

Now it turns out that the evidence on the marginal propensities to save of different income groups is surprisingly inconclusive. It has been known for ages that the positive correlation between current income and saving rates typically found in cross-sectional data doesn’t tell us anything about the relationship between saving rates and permanent income. There is a pretty large (but pretty old) literature, beginning with Milton Friedman’s classic 1957 work, showing that the MPS does not vary systematically with permanent income. So if income is measured over longer periods, the rich seem to save the same fraction out of additional income as the poor.

A more recent study by Dynan, Skinner and Zeldes (pdf) produces evidence that the rich actually do have a somewhat higher MPS than the poor. According to one of their estimates, the MPS of the bottom quintile of the income distribution is 16 percentage points lower than the MPS of the top quintile. And that’s their most generous estimate! Dynan et al. use U.S. data and I couldn’t find a similar study for Europe. Nevertheless, let’s take this number and think this through. The share of the top quintile in aggregate income is roughly 40 percent in the European Union, while the share of the bottom quintile is below 10 percent. If we would take 10 percentage points away from the top and give it to the bottom, aggregate consumption would increase by only 1.6 percent of aggregate income. So even a massive redistribution would only have a modest expansionary effect.

Finally, the expansionary redistribution hypothesis has an awkward implication. If shifting income from top to bottom increases aggregate spending, doing the opposite must decrease it. Do those who want to tax the rich and feed the poor to stimulate the economy in recessions also want to tax the poor and feed the rich during the boom years when the economy is overheating? I very much doubt it. But it would seem to be the logical implication of their theory.

There may be a good case for higher taxes on the rich and higher transfers to the poor. But we shouldn’t expect redistribution to get out of the recession.