# Supply-side policies against global warming

Alas, it turns out that I was not the first to point out the perverse dynamic supply-side effects of a carbon tax! (Well, I never really believed I was the first anyway.)

Hans-Werner Sinn wrote a whole book about it. It is called the “Green Paradox“. And there is some academic literature on it, although surprisingly little. (For instance, this recent paper on the role of oil reserves and marginal extraction costs).

Sinn also wrote this paper in 2007 which confirms my hypothesis that a rising carbon tax makes resource owners extract more fossil fuels in the short run. But he does so in a much more sophisticated dynamic general equilibrium model. The paper helps to answer one important objections I received in private conversations.

My good friend (and Graz Economics alumnus) Michael Schwarz points out that oil extraction can’t just be turned on and off like a water tap. There are extraction costs! Yes, indeed, and Sinns paper addresses this point:

„If extraction costs are assumed, the problem of moving the economy in the wrong direction is mitigated, and with sufficiently strong extraction costs, current extraction may even move in the right direction.“

Sinn, HW. “Public policies against global warming: a supply side approach”, Int Tax Public Finance (2008), p. 21

But Sinn also points out:

„As marginal extraction costs are likely to be only a small fraction of the price of the extracted resource, the effect on the extraction path may be tiny. For instance, the average production costs of crude oil amounted to only about 15% of the average spot price in 2006.“

Sinn, HW. “Public policies against global warming: a supply side approach”, Int Tax Public Finance (2008), p. 20

Since oil extraction is a high fixed cost, small marginal cost industry, the average production costs overstate the marginal costs which are relevant for the extraction path.

Recent empirical research throws more doubt on the importance of extraction costs. Here is a quote from the paper by Heal and Schlenker linked to above:

Using data from a large proprietary database of field-level oil data, we show that carbon prices even as high as 200 dollars per ton of CO2 will only reduce cumulative emissions from oil by 4% as the supply curve is very steep for high oil prices and few reserves drop out.

Heal, GM and Schlenker,W, “Coase, Hotelling and Pigou: The Incidence of a Carbon Tax and Co2 Emissions” (July 2019). NBER Working Paper No. w26086

Sinn’s paper is interesting not just for its thorough analysis of the Green Paradox, but for suggesting a couple of alternative policies against global warming. The key to these policies is that they address the important point of the issue: the quantity of fossil fuels extracted.

Here are three of them:

1. Capping fossil fuel production: Basically, we need to tell the oil sheikhs very gently and politely that they need to stop extracting oil. For example, we could agree a fixed quota for annual oil and gas extraction. Since the oil sheikhs are intelligent people, they might be pursuaded to do that if we offer some development aid in exchange.
2. Emissions trading: We could set a global cap on carbon emissions and auction off carbon certificates to industries and households. The EU has already tried such a scheme, although the cap was probably too large and not enough industries were not included (e.g. airlines). The big advantage of emissions trading compared to a tax is that it directly addresses the quantity, not the price. The downside is that negotiating a global trading system opens up a huge can of worms: especially, which country gets how many certificates? How should the revenue be used, etc.
3. Sequestration and afforestation: Another way to solve the problem would be to de-link carbon emissions from fossil fuel consumption. Sequestration, i.e pumping the emitted CO2 back into the earth is one way (how feasible this is techniqually, I have no idea). Growing more trees which absorb CO2 naturally is another. Again, there could be international agreements to subsidize both these things.

I think all these policy proposals should get at least as much attention as the carbon tax. Why is nobody talking about them?

I should also point out that the issue is broader than the carbon tax. Any policy that merely tries to shift the demand curve for fossil fuels down will fail achieve the objective of decreasing greenhouse gas emissions unless it avoids the perverse effect on the fossil-fuel supply curve. Subsidizing e-mobility, putting tarrifs on international shipping, shaming people into avoiding airplanes, incentivizing the installation of solar panels and wind energy – all those things merely change the demand side.

I think the demand side is the wrong side. Let’s talk more about the supply side!

# Some unpleasant carbon tax economics

Every economist knows that a carbon tax is the correct solution to climate change. By correct I mean the solution that a perfectly informed, well-meaning dictator would choose.

But when I was recently brooding over some dynamic optimization problems, I made a discoverey that I haven’t seen anyone discuss. And I find it disturbing.

I’m going to develop the argument formally below, but I will give away the punchline. Brace for impact!

Theorem: A carbon tax that remains constant over time doesn’t change the extraction path of fossil fuel. A carbon tax that increases over time tilts the extraction path in such a way that more fossil fuel is extracted now, less later.

If this is obvious to you, you can stop reading and start freaking out. If you think that this must be wrong, I would like you to point out any error I made in the argument below.

Let’s start from the Hotelling rule which dictates how profit maximizing oil sheikhs exploit their resource over time:

P(1+r) = P’,

where P is today’s price for oil (or gas, or whatever), r is the real interest rate and a prime denotes future variables. The rule says that you want prices to rise over time at the rate of the real interest rate.

When I say P is the price for oil, I mean the price the oil sheikh gets. The price consumers pay is P(1+t) where t is the (ad-valorem) carbon tax.

Next we need to postulate a demand curve to translate the Hotelling rule, which is about the evolution of prices, into a rule about quantities. Let’s write the (inverse) demand curve as follows

P(1+t) = D(Q)

and let’s postulate that D is decreasing in Q. This should shock nobody: demand curves slope down.

I hope you agree with me that absolutely nothing about this is in any way controversial. But then you must agree with me that we can combine the Hotelling rule with the present and future demand curves to get the following equation:

D(Q)(1+r)/(1+t) = D(Q’)/(1+t’).

This, ladies and gentlemen, is the dynamic law of motion for fossil fuel consumption. It describes how the quantity of fossil fuel extracted from the ground evolves over time. Since everything that is extracted will be consumed in the end, it implies a time path of carbon emissions.

Now what can we deduce about that time path from this equation?

1. Hold the carbon tax constant over time by setting t=t’, and you will see that the equation reduces to
D(Q)(1+r) = D(Q’),
which is exactly the same equation that would hold if no carbon tax existed at all. It follows that with a time-invariant carbon tax, the sheiks will go on extracting oil and carbon emissions will continue at the exact same rate as if there were no carbon tax.
2. It gets worse.  Suppose the carbon tax increases over time, i.e. t<t’. The effect of this will be the same as if the real interest rate would increase: it will make fossil fuel prices rise at a faster rate. But how do sheikhs make the sure the price path is steeper? By extracting more today, thus lowering the price today, and less in the future, thus increasing the future price.

Quod erat demonstrandum!

Now, of course you can refine the argument. What if, for example, the carbon tax eventually becomes so high that even the most fanatical SUV lover will refuse to pump gas? I don’t think this changes the argument. All this means is that oil producers will tilt the extraction path even more towards the present.

After all, there is a fixed and finite reserve of fossil fuels in the ground. All a carbon tax can change is when it will be extracted and the price consumers will pay for it.

If my argument is correct, why exactly are we sure that a carbon tax is the correct solution to climate change?

Addendum: If you want to me more concrete, assume fossil fuel demand is iso-elastic with elasticity e. In this case it is almost trivial to derive the equilibrium quantity: If R is the current stock of oil reserves, the quantity extracted now is

Q = (1-1/s)R with s = [(1+r)(1+t’)/(1+t)]^e

Notice that the extraction share Q/R is increasing in s which is increasing in the ratio of future to present carbon taxes (1+t’)/(1+t).

# Sind Österreichs CO2-Steuern zu hoch?

In einem interessanten Artikel über CO2-Steuern macht Andreas Sator vom Standard eine wichtige Entdeckung:

Für die Höhe [der optimalen CO2-Steuer, Anm.] gibt es verschiedene Berechnungen, die von mindestens 35 Euro (Stiglitz-Bericht) über 60 Euro (IWF), mindestens 50 bis 100 Euro (Gernot Wagner) bis 180 Euro pro Tonne CO2 reichen (Umweltbundesamt). Schauen wir uns das an einem Beispiel an: einem Liter Benzin. Ein CO2-Preis von 100 Euro würde ihn um etwa 25 Cent teurer machen. Das ist nicht nichts, Schwankungen in dieser Höhe haben aber schon in der Vergangenheit nicht dazu geführt, dass Menschen ihre Autos massenweise in den Garagen gelassen hätten. Dazu kommt: Auf einen Liter Benzin sind jetzt schon 48,2 Cent Mineralölsteuer fällig – im Prinzip eine CO2-Steuer von fast 200 Euro.

Genau richtig! Österreich hat schon längst eine CO2-Steuer. Sie heißt Mineralölsteuer und beträgt 9,8 Cent pro Liter Heizöl, 39,7 Cent pro Liter Diesel und 48,2 Cent pro Liter Benzin. Wenn man diese Steuersätze durch den jeweiligen CO2-Ausstoß pro Liter dividiert und mit 1000 multipliziert erhält man die implizierte CO-Steuer in Euro pro Tonne. In nachstehender Tabelle habe ich das mal durchgerechnet: Im Durchschnitt wird jede Tonne CO2 durch die Mineralölsteuer mit 115 Euro besteuert.

 Steuersatz (Euro pro Liter) CO2-Ausstoß (Kilogramm pro Liter) implizite CO2-Steuer (Euro pro Tonne) optimaler Steuersatz (Euro pro Liter) Benzin 0,482 2,69 179,18 0,16 Diesel 0,397 2,91 136,43 0,17 Heizöl 0,098 3,17 30,91 0,19 Durchschnitt 0,326 2,92 115,51 0,18

In der letzten Spalte berechne ich den optimalen Steuersatz, wenn man die vom IWF empfohlenen 60 Euro pro Tonne als Basis für die sozialen Kosten von CO2 (Social Cost of Carbon) hernimmt. Diese Zahl stellt die geschätzten zusätzlichen Kosten des Klimawandels dar, die jede zusätzlich emittierte Tonne CO2 verursacht. Im Schnitt sollte man also Mineralöl mit 18 Cent pro Liter besteuern. Die derzeitigen CO2-Steuern sind mit 32,6 Cent pro Liter im Schnitt also fast ums Doppelte zu hoch!

Auch abgesehen von der durchschnittlichen Höhe, machen die Steuersätze aus klimapolitischer Sicht wenig Sinn: Benzin stößt weniger CO2 aus als Diesel und Heizöl, wird aber wesentlich höher besteuert. Das klimaschädlichste Heizöl trägt die geringste Steuerlast. Das ist nicht verwunderlich, weil die Mineralölsteuer ja nicht als CO2-Steuer konzipiert wurde.

Jetzt kann man natürlich trefflich darüber streiten, ob 60 Euro pro Tonne wirklich die gesamten sozialen Grenzkosten des CO2 abbildet. Ich bin hier kein Experte, möchte aber darauf hinweisen, dass Bill Nordhaus eine weit geringere Zahl angibt, und zwar 31 US-Dollar, und der hat schließlich den Nobelpreis dafür bekommen.

Bin gespannt, wie sich diese Entdeckung auf die Debatte um die “Ökologisierung” des Steuersystems auswirken wird. Meine Vorhersage: gar nicht.

# 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.