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)

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.

On David D. Friedman’s view about climate change

This week David D. Friedman gave two talks at the University of Graz. The first has been on anarcho-capitalism and his proposal for a society organised without any form of public institution (cf. [1]). In his second talk Friedman argued why uncertainty in climate science denies any form of recommendation for climate mitigation and in particular for early action. In this blog post I will essentially focus on his second talk but give some conclusions why I think his proposal for anarcho-capitalism directly feeds into his ‘wait-and-see’ principle regarding climate change.

Argument I: What do we know – the bias of IPCC

What has been most striking to me was his argument regarding the credibility of climate change research. Currently the ‘best guess’ – to use his terminology – is represented by the Assessment Reports carried out by the Intergovernmental Panel on Climate Change (IPCC) which regularly publishes the latest state of knowledge. Friedman unhesitatingly dismissed the work of the climate science community because in his view the research is distorted towards negative externalities. But he even went further saying that climate science is biased due to the prejudice that climate change exclusively will trigger negative externalities. But as a matter of fact, this potential deficiency has led to increased attention by the scientific community in order to outweigh merits and demerits of a changing climate:

The IPCC research process [2]-[3] “multiple stages of review”

“comprehensive, objective and transparent assessment of the current state of knowledge”

“priority is given to peer-reviewed literature”

The IPCC selection of authors [3] authors are selected on the basis of their expertise [and their] detailed CVs”

“composition of author teams aims to reflect a range of scientific, technical and socio-economic views and backgrounds”

“author teams […] include a mix of authors from different regions and from developed and developing countries”

The IPCC AR5 report in figures [2] q.e.d.

Friedman did not even mention (least of all appreciate) this approach of doing peer-reviewed falsification analysis. Furthermore, he particularly challenged the robustness of climate models applied in the five assessment reports. Evidently, ALL MODELS ARE WRONG (see [4] for a nice recap “On mismatches between models and observations”). Friedman knows it, but everyone seriously doing research knows the deficiencies but also the merits of modelling. To continue, his argument was that the ex ante projections from the applied models in the first AR did not match with ex post empirical observations. Even if this argument would be correct (which is not, cf. [5, TFE.3, Figure 1, p. 64]) his claim regarding the misspecification of the AR1 models does not translate into the subliminal claim that improved models in AR2-5 are completely flawed.

To elaborate more on doing projection (not prediction) research by means of modelling, Friedman argued that in face of uncertainty we can never incorporate all potential effects (regardless of the challenge they are related to). The net effect of positive and negative externalities is unclear in the narrow approach of modelling. I totally agree on that but the implications of such a passive attitude towards the ability to actively follow a precautionary principle are devastating. If fate is the only determinant for future well-being, why are there so many efforts and vested interests in shaping its own prospects?

In the case of climate change the challenges ahead are higher by order of magnitudes especially since ‘tipping points’ can cause positive feedback effects additionally triggering forcing [6]. As Hansen [7] puts it: “wait and see and clean up the mess post facto, will not work […] because of inertial effects, warming already in the pipeline, and tipping points”. Hence, “[to avoid] the unmanageable and [to manage] the unavoidable” [8] certainly represents a more rational approach than Friedman’s proposal.

Argument II: From average homogeneity to heterogeneous distribution

Friedman then went on arguing that human species is not optimally adapted to weather conditions because humans are populated in various climate zones over the world. Obviously, there is a range of optimal or acceptable conditions but the point is that, again, passing lower or upper boundaries of this range can lead to severe impacts on humans [9]. A plausible response is migration as a form of adaptation which also Friedman highlighted. But in his argument he essentially disregards any influence to the adaptive capacity of individuals simply assuming homogeneity. He never mentioned one of the decisive points with regards to adaptive capacity which is: where are affected people located on the global cumulative curve of income and wealth.

Several times, Friedman pointed to the ‘marginal’ change of global average temperature, again neglecting the distribution of change among space and time. In its latest “Statement on the Status of the Global Climate” the World Meteorological Organisation documents that the global average temperature in 2016 has been 1.1°C above the pre-industrial level earmarking a novel record after the preceding record year of 2015 [10]. In Austria the temperature increase has even reached a 2°C increase in the same period investigated [11]. For some regions, the observed temperature increase is yet above this level [5, Figure SPM.1, p. 6]. And most strikingly is Friedman’s emphasis on ‘marginal’ or ‘slow’ change in temperatures. For the rate of increase since the beginning of the industrialization this is simply not true [5, Figure 5.7, p. 409].

The prospective impacts will vary in magnitude, direction, space and time [12-13]. But let’s focus a fortiori on a positive externality Friedman has been referring to. For the case of food security it is true that most crop yields could increase up to 20-30% [14]. But these numbers have been evaluated under controlled experiments in the laboratory. Where and when crop yield is expected to be increasing is again a question which Friedman did not further elaborate on. Additionally, there is evidence that the protein content of some crops decreases with higher temperatures [14]. Hence, distributional issues and implications are not within Friedman’s analytical approach. This is also reflected in his utilitarian and consequentialist view of the world: if the number of people dying from cold weather conditions decreases stronger due to global warming than the number of people dying from heat stress increases there is clearly a net benefit. Message to the individuals in the latter group: could you please stand up?

Argument III: Directed economic growth and path dependency

All the above makes the case for the complement of adaptation which is mitigation and in particular early action. It is true that at the moment many technological and behavioural changes complying with climate-neutrality are costly. But what Friedman essentially misses is that economic growth (and its associated benefits) not only has a rate but also a direction. For instance, the technologically driven cycle in the US originating in the ‘mission to the moon’ has been a political and social goal. Besides the development of rockets this mission-oriented approach has led to various kinds of state-funded offspring inventions and innovations ranging from telecommunication technologies, photovoltaics and so on [15].

Let me here bridge the gap back to Friedman’s first talk (and the blog post of Timon Scheuer) and then back again to climate change and the mission-oriented approach. In principle, his proposal for a stateless society – in which “private property, individual rights and voluntary co-operation” is solely brought about by bargaining between contract parties – is an interesting case to look at. In essence it is about completely decentralising the use of force or the threat of using force in order to enforce individual rights. A discussion of this proposal would fill several blog posts (again, cf. Timon Scheuer’s contribution). At the moment let me just argue that this proposal clearly feeds into his ‘wait and see’ principle. In his view, people are informed enough in order to react to changing social, economic and climate environments and, self-evidently, there exist ad hoc responses. But what about ‘tipping points’ and the associated irreversibility experienced post facto? Friedman’s anarcho-capitalist society reflected by self-interest at the micro scale and random walk at the macro scale is certainly not preparing in a way that the direction of change tackles the challenges ahead.


[1] Friedman, D.D., 1989. The machinery of freedom. Guide to radical capitalism. 2nd edition. Open source: [07.06.2017]





[6] Lenton, T. M., Held, H., Kriegler, E., Hall, J. W., Lucht, W., Rahmstorf, S., & Schellnhuber, H. J. (2008). Tipping elements in the Earth’s climate system. Proceedings of the national Academy of Sciences, 105(6), 1786-1793.

[7] Hansen, J., 2008. Tipping points. Perspective of a Climatologist. Available at:

[8] Scientific Expert Group on Climate Change, 2007. Confronting Climate Change: Avoiding the Unmanageable and Managing the Unavoidable, Report prepared for the United Nations Commission on Sustainable Development, eds Bierbaum RM, Holdren JP, MacCracken MC, Moss RH, Raven PH (Sigma Xi, Research Triangle Park, NC, and United Nations Foundation, Washington, DC.

[9] Parsons, K. (2014). Human thermal environments: the effects of hot, moderate, and cold environments on human health, comfort, and performance. Crc Press.

[10] WMO, 2017. WMO – World Meteorological Organization. Statement on the State of the Global Climate in 2016. WMO-No. 1189. Available at:

[11] APCC. 2014. Österreichischer Sachstandsbericht Klimawandel 2014 (AAR14): Synopse – Das Wichtigste in Kürze. Austrian Panel on Climate Change (APCC), Climate Change Centre Austria, Wien, Österreich.

[12] IPCC, 2014. Summary for policymakers. In: Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part A: Global and Sectoral Aspects. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Field, C.B., V.R. Barros, D.J. Dokken, K.J. Mach, M.D. Mastrandrea, T.E. Bilir, M. Chatterjee, K.L. Ebi, Y.O. Estrada, R.C. Genova, B. Girma, E.S. Kissel, A.N. Levy, S. MacCracken, P.R. Mastrandrea, and L.L. White (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 1-32.

[13] Zenghelis, D., 2015. 10. Decarbonisation: Innovation and the Economics of Climate Change. The Political Quarterly, 86: 172–190. doi:10.1111/1467-923X.12239

[14] Schmidhuber, J., & Tubiello, F. N. (2007). Global food security under climate change. Proceedings of the National Academy of Sciences, 104(50), 19703-19708. Available at: [07.06.2017]

[15] Mazzucato, M. (2013), “The Entrepreneurial State – Debunking Public vs. Private Sector Myths”, Anthem Press, ISBN 978-0-857282-52-1.