Scientific American and Climate Change II: Discounting


This continues the prior post.

John Broome, in his cover article for the most recent Scientific American, tries to help us think though how to compare current economic costs of emitting less carbon dioxide with the economic benefits such mitigation is projected to provide to future generations. In plain English, when somebody tells us that we should give up $X of economic consumption today in order to save ourselves $Y of global warming-driven losses in the future, how do we decide if this is a good deal, even if we accept X and Y?

There is a common-sense element to this. As we all know from everyday life, normally I would rather have a dollar today than the promise of a dollar a year from now. I “discount” the promise. Roughly speaking, the amount of cash I would be willing to take today in lieu of that promised dollar is termed its “present value,” and the percentage lower I am willing to accept today is called the “discount rate.”

In the global warming debate, however, we are discussing how to compare costs over at least the next several decades with benefits that are projected to obtain over the next several hundred years. When decisions are made on the timescale of centuries, discounting can have counterintuitively large effects: Consider that if the legendary sellers of Manhattan Island had put $28 in an account with a 4 percent real interest rate in 1626, they would have enough money in the bank today to buy back all of the land in Manhattan. Albert Einstein supposedly said that “the most powerful force in the universe is compound interest” – and this mathematical reality is central to the correct evaluation of plans to address the risk of climate change.

Broome provides a chart showing that a promise of a $1 trillion benefit 100 years from now has a present value of $247 billion if we use a 1.4-percent discount rate, and $2.5 billion if we use a discount rate of 6 percent. That is, the lower discount rate leads us to value this future benefit 100 times more than the higher discount rate.

I hope this makes it obvious why there is a fierce battle in the nerdier end of the global-warming debate to control the discount rate assumption. Broome did not select his example discount rates arbitrarily. The “Stern Review,” produced by the British government last year, is cited frequently as demonstrating that the world should begin immediate, aggressive emissions abatement, and it used a 1.4-percent discount rate. William Nordhaus, a Yale professor widely considered to be the world’s leading expert on this kind of integrated environmental-economic assessment, advocated a 6-percent discount rate.

Broome poses the question, then, as: What discount rate should we use? As I’ll explain, I think this is a poor question, and the far more useful question is the more direct one: Would I trade the projected near-term costs of some specific proposed policy for the projected long-term benefits that it promises?

Here’s why.

If you ask me whether a given discount rate makes sense, I will immediately start to consider the decisions that it would imply under a wide variety of test cases. The rate that under a wide variety of relevant cases advocates the trade-offs between costs and benefits over time that strike me as correct (or fair or ethical or whatever) is the one I will support.

Consider the Stern Review assumption of a very low discount rate. To demonstrate just how unrealistic that assumption is, Nordhaus asks us to imagine a scenario in which global warming would lead to zero costs between now and the year 2200, at which point global economic growth would be permanently reduced by 0.1 percent – in other words, that economic output starting in 2200 would be 99.9 percent of what it would have been had there been no global warming. Under this scenario, how much should we be willing to pay today as a lump sum to avoid this cost? Using the assumptions of the Stern Review, Nordhaus points out, we would pay about $30 trillion, which is more than half of the world’s entire annual economic output. Thanks, but no thanks.

Interestingly, in his pointers to further reading, Broome completely loads the dice on this, the central issue of his article. Last May, Nordhaus wrote a massive, and massively influential, reply to the Stern Review. Stern and Nordhaus had a famous debate on this exact question at Yale. Where does Broome point his readers?: to Nordhaus’s 15 year-old paper on the general question of economic analysis of warming. Broome is obviously current on the debate, as he also points readers to Weitzman’s much more sophisticated attempt to raise the present value of future costs by adopting a non-standard utility functional form.

But the whole debate about rates (and in Weitzman’s case, functional forms) strikes me as formalism run amok. When it comes time to consider whether I support a specific policy, I would want to see the data on projected costs and benefits by time period in order to come to a decision, rather than rely on the single-number estimate of net benefits created by any discounting (or, more generally, utility) function. The primary practical use for these discounting / utility functions in global warming analysis is to have a function that allows integrated environment-economics models to search a wide space of possible policies automatically with a commonly applied set of explicit assumptions without requiring human intervention to consider each model run. When it comes time to look at the policies that the model says are best, I would always want to see the actual data by time period for a variety of “good” scenarios to determine what policy I think makes sense.

Think of these models as being like a Google search. With infinite time and patience, I could review every document on the Web, but I have only finite time. The Google PageRank algorithm imperfectly, but usefully, narrows down the number of documents I need to review; usually, however, I don’t use the “I Feel Lucky” button, and certainly would not in a case where my life depended on it.

Why, in fact, should I believe that there is any discounting function relevant to global warming that exists in closed form? I have a set of preferences for comparing current to future scenarios of projected costs vs. benefits. Much of the knowledge that informs this set of preferences is tacit and/or contingent on elements of the scenarios that I didn’t list comprehensively in advance, but react to as I am presented with specific scenarios. This is of particular practical importance in a case like global warming which operates across a scope — centuries of time across the globe – in which many of the embedded assumptions that I use when making discounting assumptions in day-to-day life will likely be violated. If an economist can’t find a function that encompasses these, I’m not necessarily irrational; the economist just can’t model my beliefs in a way that he finds convenient. The discounting function is merely a heuristic, not some straightjacket that I have agreed to be bound by just because I haven’t disputed its assumptions.

When we consider this in these common-sense terms, and remember that the IPCC’s expected case is that a much richer world will lose about 3 percent of its income more than a century from now, you have to do some pretty fancy footwork with discount rates to get me super-excited about accepting big costs today to avoid this. 

Jim Manzi is the CEO of an applied artificial-intelligence software company.


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