On Krugman's toy climate model

Today paul Krugman posted a 5-page snippet about a toy climate model.

I have no problems with Krugman's little model and I expect few will--this is just a classic investment model applied to climate change.  Putting a price a carbon amounts to investing in carbon abatement.  The optimal policy maximizes the returns on that investment.

So, what's the optimal policy?  Should price start low and steadily increase or start high? That's hard to tell.  The big pieces, not so surprisingly, are

a) What are the potential returns on the investment of curbing carbon emissions?

b) How should those returns be discounted to the present?

I've posted before that I think the discount rate should be lower than for most kinds of capital (like rate typical of stock market returns) because investments in curbing climate change are an insurance policy--they pay off most in if climate change turns out to be a truly bad thing.  That means the risk premium is negative.  Ken Arrow made this point as have many others (even Lind, when writing about energy policy in his famous book on discounting).  Nordhaus thinks we should use a discount rate similar to that used on wall street.  I think that's wrong in a big way for pretty clear reasons.

I also think Weitzman's point about uncertain discount rates has some real salience: if we don't know which discount rate to use then we should err on the down side, big time.

With regard to (a) I think we're still flying blind, and will likely remain that way indefinitely.  But I think we are naive to think that the benefits of climate change might outweigh the costs, if only because changing climates causes serious costs of transition.  In addition, we're likely to see mass extinctions that will have hard-to-predict broader ecological consequences that are unlikely to be good.  So, I think it's fair to say that the effects of climate change have a negative expected value with a very large variance.

I don't know what this means about whether the price path of carbon should be increasing or decreasing.  But I think I'd feel a little more comfortable with our prospects if there a price--any price--on carbon.


  1. The insurance issue is crucial. Here's how I put it on Krugman's site:

    A big reason to reduce the discount rate to the level Stern uses, or really much lower, is not just something intergenerational, it's the classic risk-expected return trade off in finance.

    The lower the risk, the lower the expected return you should settle for. With insurance, where the investment is even better than zero risk – it's risk decreasing, it can make sense to settle for a negative return, a negative discount rate. And people do it all the time when they buy fire insurance for their homes.

    So certainly the discount rate for fire insurance on your planet should be even more negative than the discount rate for fire insurance on your home. A NEGATIVE discount rate actually makes sense here, not just a low one.

    End Quote

    I would also note that models that consider the returns on the investment of curbing carbon emissions it's very important to consider not just primary and direct benefits, but also secondary ones.

    These investments will greatly decrease oil funds going to terrorists and some of the worst authoritarian regimes in the world. There's strong evidence that harmful behavior of these regimes is highly correlated with the price of oil.

    In addition, investment in technologies like solar, nuclear, wind, electric cars, etc. will result in learning that will advance many other fields outside of alternative energy, thereby increasing GDP in a secondary, indirect way.

  2. I agree with you completely but I expect that rising concentrations are likely to yield rising damages, and I think that must imply that marginal abatement costs should be rising over time, no matter how uncertain I am about the appropriate rate of increase.


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