Tuesday, September 18, 2012

Discount rates and the social cost of carbon

Joanna Foster at the New York Times Green Blog discusses how discount rates affect estimates of the social cost of carbon---the "price" we all would have to pay for emissions to bring them down to an efficient level.  A new study suggests we should use a lower discount rate, which indicates much higher carbon prices.  Michael Greenstone, who led a study by the President's CEA, seemed to think the rate his study used was just fine.

A little background:  There are many assumptions that go into estimating the social cost of carbon.  We need to think about impacts of climate change on sea level rise, agriculture, coral reefs, fisheries, recreation, human health and on and on, each of which is controversial in its own right.  But the biggest overarching assumption is, by far, the choice of discount rate, which coverts projected future benefits and costs into today's dollars.
 The starting point for thinking about discount rates is to look at real interest rates, which equal nominal rates minus expected inflation.  In theory, real rates should be tied, first and foremost, to projected economic growth.  The idea is that the richer we become, the less we will value additional wealth, and so the more we'd prefer a dollar today when we are relatively poorer over a dollar tomorrow when we expect to be relatively richer.

So, if we expect our offspring to be much richer than we are, we should use a higher discount rate and a much lower price of carbon, because our descendents will be able to absorb the costs climate change much more easily than we can afford preventing the change. If we expect little growth, the discount rate should be lower, the price of carbon emissions would be higher, and we should work harder now to reduce emissions.

Using data to project long-run real interest rates is difficult because we don't have particularly good measures in history, since nominal rates combine expectations about inflation and future real rates.  But since the late 1990s, we can observe long-run real rates on inflation-indexed treasury bills. These rates are now at the lowest in history, and if we had inflation-indexed bonds going back to the 1960s, today might still be the lowest.  From FRED, here's the available history of 5, 10 and 30-year inflation indexed bonds.

The old saw in economics is that baseline real growth is on the order of 2 percent per year.  That rate also roughly matches the data for 10-year rates prior to crisis.  Since then, however, real rates have steadily declined and are now firmly negative for 5-year and 10-year rates, while the 30-year rate is at about 1/2 %.

I see two ways to interpret these data.  One is that this is just what happens in a really bad recession, and in the long run we'll pull out of this and get back to 2% real rates.  Another is that expectations about growth have become a lot more dismal.  After all, the 30-year rates mostly cover a period well beyond current business-cycle considerations, and even these are relatively tiny 1/2%.

(Incidentally, the sharp decline at the end, especially for the 5-year, was the intended effect of Fed's recent action)

My guess is that the combination of these two things like  explain the low rates: this is still a bad recession and expectations about the long-run future have declined as well.

Anyhow, to the extent that we believe long-run rates are down because expectations for long-run growth are down, and that these rates are accurate reflections of the future, I'd say the discount rates used in pricing carbon emissions are probably too high.

The question is, where's the rethink in policy analysis given rates have fallen so much in recent years?

Consider:  the 30-year rate above, at 1/2%, is smaller than any rate being considered.  And that doesn't take risk premiums or uncertainty into account, and both of these theoretically push the rate lower.  The risk premium is negative because investments in curbing emissions will pay off most if climate change turns out to be worse than expected.   Weitzman has a nice piece showing why discount rate uncertainty means we should err on the low side.

Given the data, and the basic reasoning here, I was disappointed to see Greenstone brush off the issue so casually. It's the critical question and one that should be continually revisited.

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