Duality and Uncertainty: Lessons from the carbon market

The Great Recession has hit the European carbon market hard. With output down, the demand for allowances is down, and so is the price. As recently as the start of this year, emissions allowances were trading at €14/t CO2. But last week the price was below €7. This is gloomy news for those who want the carbon price to incentivize innovation in low carbon technology. For example, David Hone, Climate Change Advisor for Shell, is one of many who have been advocating that the Union set aside a number of allowances in order to support the price. Earlier this week that proposal moved a step closer to becoming a reality with a favorable vote by the European Parliament’s Environment Committee. The price of carbon subsequently jumped up by 30% on Tuesday on the news.

I bring up this news because I think it highlights a weakness in the economic debate about the best means to the end of pricing emissions. The argument revolves around whether or not the government should set the price of emissions, and let companies choose the quantity of emissions, or whether the government should set the quantity of emissions it will allow, and let the market set the price. The former is a carbon tax, the latter is a cap-and-trade system. In a world of certainty, where the cost of abatement by companies is well known, the two are equivalent. When the government sets the price (tax level), it knows the quantity of emissions that companies will choose. Alternatively, when the government sets the cap, it knows the price that will emerge in the market. That’s duality.

But, in a world of uncertainty, where the government doesn’t have a precise fix on companies’ costs of abatement, the two are no longer equivalent. That same duality doesn’t hold. The classic paper on the problem is by Martin Weitzman. He lays out the conditions under which controlling the price is preferred to controlling the quantity, and vica-versa.

This issue has gotten a lot of attention by economists studying how best to reduce greenhouse gas emissions. Many economists are convinced that the special nature of the greenhouse gas problem—that it is a stock pollutant—argues for fixing the price and not the quantity. That logic is faulty, so that the choice can go either way depending upon one’s assessment of key parameters. For more detail, see my paper on the subject, coauthored with my colleague Luca Taschini at the LSE.

All of that is theory, however. In the world of theory, the assumptions hold, so that a cap-and-trade system involves a fixed quantity. Now back to the real world. This week’s action by the European legislators is a reminder that in the long-run the government can always revise the number it controls, whether that’s a price or a quantity. When the government sets a cap, it isn’t fixed forever in stone. If the cap yields a price that’s too low, then the cap may get revised downward so as to produce a higher price. Similarly, if the government were to set a tax rate and the resulting abatement was insufficient, it could raise the rate.

I don’t mean to say that there’s no difference between control via price or quantity. The original Weitzman insights are certainly relevant, as are the insights of the subsequent literature. But sometimes analysts make too much of the distinction. In the short-run it will be impossible for the government to quickly, easily and precisely fine tune its control. So whether it starts by setting a price or a quantity will matter. But it’s just in the short-run. In the long-run, it will tinker with the control to get the combination of price and quantity that it wants. The duality between price and quantity is re-established, even in the face of uncertainty.

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