Tuesday, April 21, 2009

Discounting and the Scientific Consensus

Climate change is real. The consequences are going to be costly. Clearly, something must be done. That's usually where the cost benefit analysis stops in the public debate over climate change. The implicit suggestion is that it is worth a substantial chunk of our creative energies and a large fraction of our national wealth to solve the problem of climate change.

For the science of climate change, Nobel Peace Prizes have been awarded. For the votes of climate change, campaign promises have been made. Heck, even actors on the television show, 24, have a series of public service announcements that vaguely warn of the dangers of climate change. All of this is taking place based on a scientific consensus that climate change is real, and that 50 to 100 years from now, there will be costly consequences.

In the face of this overwhelming consensus, it is useful to ask how costly climate change will be. There are studies pushing in this direction, but given that the most substantial costs of climate change are projected to occur 50 years or so from now, even the most precisely estimated costs deserve our scrutiny. Important questions do not go away (even with perfect foresight and no uncertainty). In particular, this post addresses the question:

How much is it worth to avert a billion dollar catastrophe that we know will happen 50 years from now?
No one has a perfect answer about how to weight these future costs against current demands on our resources, but there are clearly some wrong approaches. In particular, we should not treat a billion dollars in the year 2059 the same as a billion dollars in 2009. Nevertheless, I fear that our scientific consensus exaggerates the costs of climate change by making this mistake.

To see why a billion dollars is not worth a billion dollars whenever it is owed, think of putting some amount of money in a 50-year certificate of deposit that will pay a billion dollars at maturity. It is clear you would not have to set aside one billion dollars today. In fact, a bank would be happy to give you a three percent interest rate if they knew they had access to your money for 50 years. They would do this because they know there are better uses for your money (i.e., investments with a better return than three percent).

To see what effect this has on cost estimates, it helps to take a concrete example where we have perfect foresight and no uncertainty about future costs. Suppose we also know the following facts with certainty:
  • In 2059, there will certainly be an environmental catastrophe that costs one billion dollars (in today's dollars) to clean up after the fact.
  • A savings account gets three percent real return per year for every year between now and 2059.
If we set aside $228 million dollars today [$1 billion / (1.03^50)] , the account will mature in 2059 with one billion dollars -- enough to cover the expense of the catastrophe. This means that $228 million is the real cost of a billion dollar expense 50 years into the future.

$228 million may sound like a lot of money, but it is nearly five times less than the original number. Merely neglecting the fact that our current resources have alternative uses, therefore, leads to an overstatement of costs by a factor of five. What can we cost forecasts for the year 2100? In that case, a billion dollars is only worth $67 million [$1 billion / (1.03^91)]. Forgetting to discount in this setting overstates the costs by a factor of nearly 15!

To be fair, economists have yet to agree on the exact interest rate for these calculations. Some economists advocate using the historical return to capital investment (~8 percent) as the discount rate. Others are less conservative, using rates closer to two or three percent.

One thing is for sure -- zero percent is the wrong rate to use. Using no interest rate can vastly overstate future costs (even in a world where the right interest rate is small). If we look far enough into the future, our scientific consensus could be off by a factor of 10, and with the numbers they're throwing around, that's no small change.

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