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).

Österreichs Klimastrategie ist viel zu konkret

Ökonomen kannten die Lösung für das Problem des Klimawandels als es ihn noch gar nicht gab. Im Jahr 1920 veröffentlichte Arthur Pigou sein Buch “The Economics of Welfare“, worin er erklärt wie man mit negativen Externalitäten umgeht: Man besteuert diejenigen, die die negative Externalität verursacht – und zwar möglichst so, dass durch die Steuer die privaten Kosten möglichst den sozialen Kosten angeglichen werden.

Der Klimawandel ist die Mutter aller Externalitätenprobleme. Unsere CO2-Emissionen hier und heute haben einen Effekt auf das globale Klima in der fernen Zukunft – und die Veränderungen im globalen Klima haben wiederum eine Reihe von komplexen, schwer vorhersehbaren und höchst unterschiedlichen Effekten auf Ökosysteme und unsere Gesellschaft.

Österreich hat sich mit den anderen Staaten dieser Welt im Pariser Abkommen dazu verpflichtet CO2-Emissionen zu reduzieren in der Hoffnung damit die globale Erwärmung auf 2 Grad gegenüber dem vorindustriellen Zeitalter zu begrenzen. So weit, so gut, obwohl man an der Effektivität und auch an der Sinnhaftigkeit des Abkommens zweifeln darf. Aber lassen wir diese Debatte beiseite und schauen wir uns lieber die neue „Klimastrategie” der österreichischen Bundesregierung an.

Was steht da drin? Im wesentlichen will die Regierung dass es in Zukunft keine Ölheizungen mehr gibt, dass möglichst viele Gebäude thermisch saniert werden, dass mehr mit Bahn und Rad und weniger mit Autos gefahren wird und wenn, dann mit Elektroautos.

An der Strategie wurde in den letzten Tagen viel kritisiert. Zu wenig konkret sei sie, die Finanzierung der vorgeschlagenen Maßnahmen sei unklar, die Zuständigkeiten seien nicht geregelt, usw.

In meinen Augen ist diese Kritik völlig verfehlt. Das wahre Problem ist: Die „Klimastrategie” ist viel zu konkret!

Es ist komplett unnötig, dass sich unsere Regierung Gedanken macht wie viele Ölheizungen es in Zukunft geben darf oder wie viele Solarpanels installiert werden müssen oder wie viele Elektroautos herumfahren sollen. Alles, was sie tun muss, ist eine Steuer für CO2-Emissionen einführen und dann dem Markt die Aufgabe überlassen herauszufinden, welche Heizungssysteme, welche Verkehrsmittel und welche Stromerzeugungsmethoden sinnvoll sind.

Natürlich gibt es wie bei jeder neuen Steuer administrative Herausforderungen: Wer genau soll die Steuer abführen? Wie genau wird die Steuer ermittelt? Wie geht man mit Importen und Exporten um? Aber ich bin mir sicher die braven Beamten des Finanzministeriums sind kreativ genug diese Probleme zu lösen, zumal sie auf die Hilfe von Umweltökonomen und Finanzwissenschaftlern zählen können. Schlaue Leute haben sich über all das schon Gedanken gemacht und Konzepte entwickelt. (Z.B. hier)

Es könnte so einfach sein.