Discounting

Were there any peeping Toms in Island Bay last Wednesday they would have been in for a shock. At 7.21pm, towards the eastern edge of the suburb, a man could have been spotted leaping from the bath, and running naked into the lounge shouting 'I've found it!'. Which was a bit of an undue claim, as it happens, as I hadn't found anything. I'd just finally got my head around the concept of discounting as it relates to climate change. All this was thanks to a very handy paper from Geoffrey Heal of Columbia University [pdf]. Heal's paper also explains how William Nordhaus is able to get such counter-intuitive results from his economic models as to whether or not we should do anything about climate change. Nordhaus, while admitting that climate change is real and serious, argues that the economics of the matter suggest that we do little. Nordhaus's models have been used by people like Bjorn Lomberg to suggest that we should turn a blind eye to the issue and by others to 'prove' that the Stern Review on climate change is wrong.

My recommendation is that you read Heal's paper yourself to get an understanding of all this. What follows is just my own attempt to crystalise my learning by trying to explain it. I may get it wrong.

Discounting is a tool that economists use to help us weigh costs and benefits across time.

There are several important components to any discounting equation.

The first of these is the pure rate of time preference, which is a function that reflects, in Heal's words, "the rate at which we discount the welfare of future people just because they are in
the future".

A rate of zero will mean that we discount their welfare not at all. Rates greater than zero will suggest that we place less value on their lives. Stern chose a pure rate of time preference slightly higher than zero to take into account the fact that there is a slight chance that there may be no future generations (if, for example, the Earth is hit by an asteroid). If you choose rates much higher than Stern's you are essentially saying that the lives of people living in the future are less valuable than those living at present. Discriminating across time in other words. Like all forms of discrimination, discrimination across time is hard to defend in any ethical sense. Yet a surprising number of people who call for little action on climate change on economic grounds are doing so because they make use of models with high pure rates of time preference. Their argument is, in effect, that, we shouldn't take action now because your grandchildren don't matter as much as you do. Seriously.

The next important component is simply the degree to which you think consumption will increase between now and the day of reckoning. This seems simple enough, yet as Heal points out most economic models of climate change are based on a simple consumption function that uses a single consumption good. In reality we consume many goods, and there are important ones of which our consumption may decrease, despite increasing overall consumption. Goods (services) related to natural capital may, in particular, decrease as a result of climate change. And these are some of the goods most important to our wellbeing. The models, in other words, are a bit fuzzy on the stuff that matters. They're also fuzzy on distributional issues (i.e. who does the consuming - rich or poor).

The third important component to our equation is the impact of consumption on utility (wellbeing). Perhaps one of the most sensible assumptions that one can make in economics is diminishing marginal utility. That is, the more we have, the less the next unit of consumption will contribute to our wellbeing. So when discounting a number is included into the equation to reflect the fact that future changes in consumption will be less important than current ones because we'll be richer then (and diminishing marginal utility would suggest that a change in consumption of value x will have an impact of y on wellbeing now but less than y in the future when x is greater). One thing to note is that Partha Dasgupta takes Stern to task for under assuming diminishing marginal utility. I'm not sure Dasgupta is right to do this but that's a post for another day. Another point to note is that there are also distributional issues at play. Most regimes for addressing climate change are structured so that wealthier nations bear the brunt of the costs. On the other hand if we do nothing it may be the poorest who are hit hardest - so therefore diminishing marginal utility could be inserted into a model in a manner opposite to the way it is used at present. Meaning that it would increase the case for action rather than decrease it.

Now, where was I? Oh, that's right, so what's the matter with Nordhaus's model. In a nutshell he calculates the pure rate of time preference from the observed rate of return on capital. Heal details all the problems with this but the most glaring one to me is simply that Nordhaus is confusing 'is' with 'ought'. Which is just so wrong in this instance it isn't funny. There are also all sorts of other problems including the way risk is managed and the assumptions needed to even consider deriving discounting from the rate of return to capital but you're better reading them from Heal's mouth than mine. I gotta run now...dinner needs to be cooked...but in the meantime remember this one thing:

Nordhaus's work like so much in economics brings with it the veneer of certainty that comes with numbers and maths. But underneath the surface is a much less clear world - one of philosophy. At the very least this ought undermine the tone of certainty with which people appeal to Nordhaus when they argue against action on climate change. But I also think it's worse than that. I think Nordhaus gets the philosophy horribly wrong. As far as dicsounting goes, we ought to discount Nordhaus.

[Update: added a bit more under diminishing marginal utility.]