Friday, October 26, 2012

Good graphs are general, or how a carbon tax is like drug legalisation

Stephen Gordon ably makes the case for market mechanisms over regulatory approaches to dealing with climate change. The deadweight costs of achieving any arbitrary level of greenhouse gas reduction are lower either under emissions trading or a carbon tax as compared to using regulations like "You must use Technology X" or "You may not use Technology Y.".*

Stephen illustrates with a couple of handy graphs. They're also graphs that I use in my Economics and Current Policy Issues class, but in an entirely different context.

Here's the welfare effect of a regulatory approach. Stephen writes:
Regulations essentially have the same effect of a technical setback: they oblige suppliers to undertake practices that increase the cost of production. This has the effect of shifting the supply curve up: Faced with higher costs, producers are going to raise the minimum price they’ll accept for any given quantity produced. This upward shift increases prices and reduces quantities produced, which is of course the policy goal. It also affects the producer and consumer surplus:

He then explains why the welfare loss is the entire green trapezoid, before illustrating the alternative approach:
Suppose now that instead of regulations, the government imposes a tax on the sale of the good. This also shifts up the supply curve, as producers will now require prices that offset the extra cost of the tax. The difference here is that government revenues are now introduced into the graph:

A good chunk of what was deadweight cost is now crunchy tasty tax revenue.

I use exactly the same graphs to illustrate the superiority of tax based approaches over drug prohibition in my Economics and Current Policy Issues course at Canterbury. Prohibition is a negative technology shock for producers involving real increases in production costs. The same consumption reduction can equivalently be achieved by a legalised system that uses taxes as consumption deterrent, and with a similar transformation of deadweight cost into tax revenue. You can make it more complicated by saying that the demand curve shifts out under legalisation and by noting that there are tax levels beyond which you induce black market providers to enter the system; I take these as suggesting you can't really have a retail price under legalisation that's above the current black market price. Whether we then have any substantial consumption increase is more of an empirical question; Portugal's experience suggests it not to be the case.

* I still put reasonable weight on that this may not be the best approach for New Zealand. If everyone in the world were doing carbon trading or carbon taxes, we'd want to as well. But, realistically, if New Zealand were to disappear into outer space tomorrow, it's pretty unclear that the entire abolition of New Zealand's net greenhouse gas emissions would do much on aggregate warming outcomes. Maybe we'd delay the onset of any particular level of GHG accumulation by a half day over a century. In that case, New Zealand could perhaps do better by picking high variance plays despite their lower expected mean. Pour money into biotech research for low GHG pastoral systems and give the resulting technology away to anybody who wants to use it. Lower expected returns, but if it pans out, it could reduce GHG emissions by a heck of a lot more than NZ could achieve on its own via domestic incremental reductions in carbon or methane emissions.


  1. Love it. To really ram home the point to the policy makers, you'd need to re-label "Producers'" in the first as "Drug Gang's" and "Law-Abiding Businesses'" in the second.

  2. The one thing left of these diagrams is the externality effect. Pigouvian taxes actually increase, rather than decrease welfare.

  3. Yes. For carbon, there's deadweight cost of overproduction. For drugs, I'm less convinced.

  4. This argument takes it as given that CO2 has a net negative externality. I have as yet seen no reason to be confident that that is true. The current climate was not designed for us, nor we for it, so there is no a priori reason to expect a climate a few degrees warmer to be worse (or better) for us. Humans, after all, currently prosper across a range of climates much larger than few degrees. It's true that change is presumptively costly, since we are optimized against current circumstances--but a few degrees in a century is very slow change.

    The alternative approach is to try to add up externalities, positive and negative. That's a very risky approach, given that both kinds exist, are large, and are uncertain. If you want the sum to be negative, you make generous estimates for the costs, skimpy estimates for the benefits, and probably miss a few benefits because you aren't looking for them--and conclude that you have objective evidence that the net externality is negative. If you want the opposite result, reverse the procedure.

    I first encountered this problem some forty years ago in the context of population policy, where almost everyone (except Julian Simon) thought the net externalities were negative, they had no good reason for that belief, and the predictions they made turned out to be wildly wrong.

  5. There's actually very little we can do about pastoral systems or farming with respect to CO2 or methane. Nothing; almost everyone seems to ignore the point that animals and agriculture don't produce methane, bacteria do. And those bacteria do with or without agriculture.

    Sure, agriculture can change the patterns a bit, but not in a globally significant way, the key would be how to stop the long term leaching of carbon from soils through overuse. Biochar for example is one way to reintroduce carbon to soils in a beneficial way. So low GHG is completely the wrong focus, although it is no doubt where the money is and so where the research and propaganda efforts go. Classic public choice theory and almosy entirely wasteful.

  6. I remain completely unconvinced that carbon is in fact a problem... its all about climate 'models'... where oh where is the theory???

  7. You'll note that it's comparing a carbon tax with other regulatory interventions that achieve comparable levels of abatement. Of the two, the tax is less damaging, unless we move to a political economy argument where lower compliance costs abet more regulation.

    I have pretty much no worries about outcomes under median warming estimates. But the fat tails of the distribution are worrying.

  8. I'll entirely defer to scientists on the science here; I could be very wrong. I had thought there were promising leads on re-engineering the bugs in sheep and cow guts to produce less methane.

  9. I agree that, if one wants to reduce CO2 output, a carbon tax makes more sense than direct regulation--but that isn't an argument for a carbon tax unless one wants to reduce CO2.

    You write: "I have pretty much no worries about outcomes under median warming estimates. But the fat tails of the distribution are worrying."

    You might consider the other tail of the distribution--the one where it is preventing global warming that leads to catastrophe. We are, after all, in an interglacial, it's lasted a fair while, and we don't know with any confidence what causes an interglacial to end. One obvious possibility is that global warming is preventing the next glaciation.

    I'm not sure if any of the low probability/high cost outcomes in the other direction matches half a mile of ice over the present locations of London and Chicago. And that is, more or less, the typical condition of the globe during the current ice age.

  10. Basically, anyone who objects to NZ being warmer by several degrees is nuts. We would be warmer, healthier, richer, remove the second most common reason for moving to Australia and be a better destination for tourism and long term migration.

    Frankly, its almost obscene that we should not consider warming as a benefit to us regardless of what happens in the rest of the world.. when you consider the rest of the world wouldn't give a hoot if we turned into a snowball.

    The costs of adjusting to increased warmth are almost certainly much cheaper than trying to decrease it.


  11. 1. Agree that ice age is scarier than any plausible warming scenarios.
    2. The probability of bad warming still seems sufficiently large relative to the probability of another ice age to make it the worse expected outcome, no?

    To what evidence would you point suggesting that I should be more worried about a new ice age's emergence than bad warming?

  12. Granted, unless it does odd stuff to precipitation. Otherwise, agree, though the cities will need to move a bit inland. And Canada would do well. But I do put weight on "what happens everywhere" rather than just here.


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