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!

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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).

No Deal Breakfast

Last evening sometime before supper, someone in my little family made a surprising proposal. They would rather have breakfast for supper than supper. This proposal seemed to have been made in jest, but was taken seriously enough that it was decided that there would be a vote on this issue. Before the vote, there would be a short phase of deliberation (and campaigning). The stay with supper group argued that with breakfast we would be foregoing healthy foreign food ingredients, but did not generally seem to make much of an effort to convince the breakfasteers. They seemed to be confident that such a proposal would never go through. The breakfast group mostly argued with clearly erroneous information about how much healthier breakfast would be.

Then surprisingly the breakfasteers won the vote. In fact, it turned out that the foreign food argument did not go down well with the breakfasteers at all. They would be quite happy to forego all this foreign food in fact. They never liked foreign food in the first place. Well the vote was actually close to fifty-fifty, and there was some debate whether we should vote again, perhaps after some more deliberation and campaigning. However, it was decided that voting on the same issue multiple times would be undemocratic and hence it was decided that we would have breakfast instead of supper.

Having made this firm decision, and only then, the question arose as to which kind of breakfast we should have. One of the breakfasteers was send to negotiate a good breakfast deal. After very long and tedious negotiations, a reasonable deal breakfast was close to being agreed upon. Some breakfasteers and some stay (with supper) supporters, however, did not like this deal. Some breakfasteers demanded a good deal breakfast and the stay supporters saw a new chance to possibly avoid breakfast altogether after all. There was one item in this deal, the early bedtime clause, that particularly annoyed most of the breakfasteers. Then voices were raised that even a no deal breakfast would be preferable over any deal with an early bedtime. Some argued that perhaps breakfast was not such a good idea in the first place. The breakfasteers then send a new negotiator that seemed to be prepared to accept a no deal breakfast in the hope of thus having a better bargaining position. But his efforts were then undermined by some breakfasteers having second thoughts about the now more likely seeming possibility of a no deal breakfast and pulled the negotiator back.

In the end we did not sleep last night and are still negotiating.

Towards a measure of welfare-relevant national output

Robert Barro says GDP overstates national income because it counts investment twice. 

Here is Scott Sumner explaining Barro’s point with an example:

Thus suppose Tesla builds a battery factory that costs $1 billion, which lasts for 20 years.  They hire workers and pay another $2 billion in wages over 20 years.  The batteries sell for a total of $3.3 billion, a profit margin of 10%.   In this example, $4.3 billion is added to GDP over the life of the factory—$1 investment and another $3.3 billion in consumer goods (batteries).   But there is actually only $3.3 billion worth of actual “goods” being produced; the $1 billion factory investment is an input.

As Scott Sumner points out, GDP isn’t meant to be a measure of national welfare, but of national output. This should always be kept in mind and should be pointed out whenever someone is using GDP per capita as a measure of welfare. But it’s clear that GDP, understood as national output, is really useful for many policy discussions.

That said, I was thinking about how to correct GDP to better measure that part of national output which is directly relevant to people’s wellbeing. And here’s what I would do: I would count all spending on consumption goods (private and public) as well as residential construction spending which is presently counted as „investment“. Following Barro’s critique I would not count spending on capital goods such as factories, machines, tools, and intellectual property which are only indirectly useful to consumers in so far as they help produce consumer goods in the future.

As for government consumption, I would suggest to apply a “waste correction” to take into account the fact that some of that consumption just isn’t useful to consumers. Spending billions of euros on a tunnel or an airport or a bridge which nobody has used yet or on a weapons system which (hopefully) will never be used, is to a large degree wasted money, although views will differ exactly how much of it is really wasted. At any rate, I think GDP should try to account for government waste.

So to sum up, I’d propose the following measure:

Welfare-relevant GDP
= Private consumption
+ Government consumption x (1 – waste ratio)
+ Investment in residential construction

Here’s what this would look like for Austria in 2018:


million euros, 2018
Private consumption199.459
Government consumption 74.295
      of which waste 14.859
Residential investment 17.232
Welfare-relevant GDP276.126
Conventional GDP386.063
Ratio: welfare-relevant 
/ conventionalGDP
71,5 %

In other words, conventional GDP overstates the supply of goods that are directly relevant for the welfare of households by almost 30%. I would like the welfare-relevant GDP measure to be used when comparing living-standard across countries or within countries across time. And I would like growth theory to focus on the growth of this measure.

(PS: What about exports and imports? Exports aren’t welfare-relevant for the home country, because those are goods consumed by foreigners. Imports are, of course, already included in measures of private and public spending measures. So there’s no need to add exports and subtract imports as done in conventional GDP.)

A quick game theoretic thought about the Brexit negotiations

In the last few days, I watched the British news a bit about Boris Johnson forming the new UK government. There was of course a lot of talk about the Brexit negotiations. I was a bit puzzled at one point about some of Boris Johnson’s statements. On the one hand there is a lot of talk about being prepared for a hard Brexit and on the other I also heard him say something like that “the chance of a hard Brexit is one in a million” a little while back. So why prepare for some contingency that you do not expect to happen under essentially any circumstances? Also you get the feeling that Boris Johnson, despite having said that, would not so much mind a hard Brexit. In this short post, I explore why all this might actually all make good game theoretic sense (and why perhaps, at least for this matter, his UK opponents should get on board with his strategy if they care about the UK unless, of course, they think they can still stop Brexit).

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Confirmed: Raising tariffs is shooting yourself in the foot

As everybody knows from Econ 101, protective tariffs are harmful for the country that imposes them. A protective tariff is a tax on imports that is so high as to make all imports fall to zero.

But there is an argument why a low tariff may be better than no tariff at all. The reason is that a large country (large compared to its trading partners) faces an upward-sloping supply curve for its imports such that a fall in import demand lowers the world-market price of imported goods. Hence, part of the cost of the increased tariff would fall on the rest of the world due to lower export prices (a fall in the terms of trade) while the country that imposed the tariff might win overall.

Whatever the theoretical merits and demerits of this argument, recent experience with tariff increases in the US (aka Trump’s Trade War) provides powerful evidence against it.

In a newly released paper, Amiti, Redding and Weinstein show that the tariffs imposed last year by the Trump administration had two main effects:

1) US prices of imported goods rose one-for-one with increases in tariff rates.

2) Import demand decreased substantially with an estimated price elasticity of 6 (i.e. 6 percent lower imports for every 1 percent of higher tariffs).

As a consequence of these two results the paper estimates the welfare costs of the Trade War to be about 6.9 billion dollars. While that is not a huge number compared to the total size of the US economy, keep in mind that we’re only talking about a marginal change of the average tariffs from 1.5 to about 3.25 percent. And remember that the welfare costs rise with the square of the applied tariff rate. So should tariffs go up more in the future, the welfare costs will be much bigger.

I regard this as decisive evidence that the optimum tariff is indeed zero. Note that finding No. 1 implies that American consumers are paying the full cost of the tariff increase, with no terms-of-trade effect on the rest of the world. If even the largest economy in the world cannot improve their terms of trade by increasing tariffs, then smaller economies have no hope of doing so either. Raising tariffs is indeed shooting yourself in the foot.

Moreover, this paper is also a triumph for simple textbook economics. The results of Trump’s tariffs are exactly what one would expect from the kind of supply-and-demand model taught in Econ 101. As Tyler Cowen points out, the complete pass-through of tariffs to consumer prices also implies that monopoly power is not a big issue in these markets. It’s good to know that the much-maligned perfect competition partial equilibrium models still gets some important things right.