Leonhardt gets Stern’s discount rate wrong

Aaaaarrrrgh! Why is it that when the debate over discount rates and climate

change finally makes it into David

Leonhardt’s NYT column, he gets it completely wrong?

The Stern Review assumed that a dollar of economic damage prevented a century

from now (adjusted for inflation) is roughly as valuable as a dollar spent

reducing emissions today.

This is not true. This is wrong.

John Quiggin has an invaluable backgrounder

on all this, but basically Stern’s choice of discount rate (eta = 1) means that

he adjusts for income, not for inflation. Global income presently is

about $7,000 per person, and global income in 2100 will be about $100,000 per

person, according to Stern’s projections. Using his discount rate and other

assumptions, a dollar of economic damage prevented a century from now is roughly

as valuable as 7 cents spent reducing emissions today. (In fact, it’s

less than that, because Stern adds another discount rate, called delta, on top

of eta.)

Leonhardt says that "spending a dollar on carbon reduction today to avoid

a dollar’s worth of economic damage in 2107 doesn’t make sense"

– but this is a straw man, since Stern never comes close to saying that

we should do such a thing. Leonhardt also spends a lot of time on the academic

qualifications of Stern’s opponents, but neglects to mention that Stern himself,

a former chief economist of the World Bank, is actually a real expert on discount

rates, and understands them much better than most economists do.

Leonhardt says that Stern is "right for the wrong reasons", and says

that "technically, Sir Nicholas’s opponents win the debate."

The problem is that this is a very high-level and complex debate, which is not

at all easy to follow. Leonhardt, with his talk of inflation, has shown that

he is not up to following it. This is no great failing, since I’m not up to

following it either, and most economists I know also can’t follow it. But if

you can’t follow the argument, you certainly shouldn’t be declaring winners.

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13 Responses to Leonhardt gets Stern’s discount rate wrong

  1. Will says:

    “In fact, it’s less than that, because Stern adds another discount rate, called delta, on top of eta.”

    “Adding delta” would increase the value of consumption today versus a 100 years from no. So 7 cents to is too small, not too big.

    Stern’s assumptions lead to an interest rate of 1.4%. Put about a quarter (not 7 cents) in the bank today and keep it there for 100 years at that interest rate and you’d get a dollar at the end of the period.

    You’re point still stands, Stern doesn’t assume a dollar today is equal in value to a dollar a 100 years from now.

    However, Stern assumes a near-zero delta which means, controlling for the fact future generations will be richer, consumption today is worth the same as consumption tomorrow. Of the two preference parameters, Stern’s choice of a near-zero beta is the most controversial. Stern agrees with Ramsey when over 80 year ago he said, “it is assumed that we do not discount later enjoyments in comparison with earlier ones, a practice which is ethically indefensible and arises merely from the weakness of the imagination.”

    Stern’s critics object to this sentiment because it seems people DO prefer consumption today rather than later. Do people act unethically when they take a dollar today rather than tomorrow?

    I think this was the conflict Mr. Leonhardt was trying to relate. In my reading, he did that satisfactorily.

  2. Felix says:

    Are you saying that Leonhardt is right for the wrong reasons? :-)

    Leonhardt ultimately agrees with Stern, which means that I ultimately agree with Leonhardt. But the problem is that Leonhardt makes it far too easy to disagree with Stern. If you use a much higher delta, then all manner of weirdness happens with regard even to your own future happiness, let alone that of your children and grandchildren.

  3. Michael E Sullivan says:

    John Quiggin had a a while back on crooked timber about why a near zero discount rate across generations is not in conflict with people’s revealed preference about discount rates.

    Also, I’ve been watching this debate and feeling much like felix in that I could spot obvious distortions and misstatements like Leonhardt’s but couldn’t really get a handle around the differences between the people who actually understand what’s going on. Then I read a paper by Martin Weitzman, linked by Greg Mankiw a couple weeks ago (the link is now broken, or I’d post it). It’s technically demanding, but not so much that I couldn’t follow it with undergraduate math.

    If you, or other math savvy readers, want to understand this debate better that paper is a great feast of information on the expected utility paradigm that Stern and Nordhaus are using.

  4. Michael E. Sullivan says:

    Update: John Q has I mentioned earlier.

  5. eman says:

    interesting discussion. obviously there was a big miscom that happened here. i will use this as a sample when i

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