Discounting the future, yet again

Felix Salmon gnashes his teeth at yet another incorrect report on discounting and the Stern review, by David Leonhardt in the New York Times.

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.

Salmon is right, both about the Leonhardt piece and, unfortunately, about the limited understanding of discounting issues on the part of economists in general.

Leonhardt’s error follows a column by Hal Varian which, while not strictly wrong, was ambiguous enough to lend itself to this misreading. And the same error has been made by lots of Internet commentators who have enough economics that I would have expected them to know better.

But even economists who avoid the obvious error of confusing the pure rate of time preference with the money discount rate, as Leonhardt has done, have been badly confused about this question, being led astray by a presumption that the money discount rate has to be fairly high. There are a number of reasons for this.

First, standard practice in benefit-cost analysis is to use high discount rates, often as high as 8 or 10 per cent, and this seems to work reasonably well (by no means perfectly) in terms of selecting good projects and rejecting bad ones. But this is a paradigm case of “being right for the wrong reasons”. In a typical project evaluation, the project’s proponents (in the case of infrastructure, usually engineers) have a lot of influence over the projections on which cash flows are based, and they tend to be biased upwards (mostly by ignoring things that might go wrong). By contrast, economists usually get to choose the discount rate, and they almost always go for a high rate. If an economically correct discount rate is applied to cash flow estimates with a pervasive optimism bias, too many projects will pass the test. But using a high discount rate offsets, on average, the bias in cash flow projections. This is far from a perfect approach, but it’s hard to implement a better one. However, it leads you badly astray in the case of climate change, where the big risks of unforeseen bad outcomes arise with the do-nothing option.

Second, there’s a belief that market rates of discount are high and that we should follow the market. The problem here is that the premise as false at least for the obvious choice of market rate, namely the real rate of interest on high grade bonds, which has averaged about 1 or two per cent. This is much lower than the rate of return to equity, which seems to be what most economists have in mind (at this point we need to start thinking about the equity premium). But, on the face of it, the bond rate is the appropriate rate for discounting riskless flows of either cash or utility. The best way to deal with risk is not to use a risk-adjusted cash rate to convert risky cash flows into certainty equivalents using expected utility or some more general model.

Third, it’s commonly assumed that individuals display high rates of time preference, and therefore so should society. In fact, individual behaviour on this score is inconsistent, with some decisions implying unreasonably high rates of time preference and others low or negative rates. More importantly, the putative fact that individuals have high rates of time preferences implies almost nothing about the social rate of time preference, for a couple of reasons. First, individuals are mortal whereas (except for a small probability of nuclear annihilation and similar disasters) society is not. To quote Richard Tol and his co-authors in 2006 paper in Environmental Science and Policy*

The PRTP is the ‘utility discount rate’,which reflects our time preference for utility. Estimates of utility discount rates for individuals are almost always positive – an estimate of 1.5% is considered plausible for the UK for instance (HMTreasury, 2003) – for the simple reason that humans prefer good things to come earlier rather than later. Given the inevitability of death for individuals, a preference for benefits to accrue earlier rather than later is entirely sensible. At the social level, however, the arguments are more nuanced, and indeed whether or not the PRTP should be equal zero has been debated by philosophers and economists for decades. Cline (2004), for example, proposes to use a zero PRTP in evaluating climate change policies. Reasonable ethical considerations suggest using a zero PRTP—a positive PRTP involves placing a lower weight on the welfare of future generations, which is impartial and contrary to intergenerational equity. However, there are also persuasive arguments for employing a very small positive PRTP.”

We can sharpen this up a bit by observing that the average annual mortality probability for adults is around 1.5 per cent, suggesting that this factor alone is sufficient to explain positive time preference.

A more fundamental problem is that individual time preference is relevant to optimal individual consumption profiles, but not to the equitable distribution of resources between different age cohorts. I doubt that many gen X-ers (certainly not the esteemed Paul Watson) will agree that, having been born earlier, baby boomers like myself are entitled to a higher weight in social welfare calculations. But there is no other coherent basis for using a positive social rate of time preference. You can’t discriminate between generations without discriminating between people who are alive at the same time.

You can read my general summary of the issues here

Note: I’ve been a bit mischievous in a couple of places above. The phrase “right for the wrong reason” is quoted by Leonhardt, and comes from Marty Weitzman’s excellent review of Stern, where he observes that Stern tends to overweight known risks as a way of dealing with unknown ones. I’m just making the point that this kind of offsetting bias is widely prevalent, and is incorporated in the unexamined assumptions of most economists on discounting.

Also, while I’ve quoted Richard Tol in support of Stern’s position (as indeed Stern did) he’s strongly criticised Stern and (on my blog) has repeatedly denounced the idea that a zero social rate of time preference could ever be appropriate. He has also claimed that the correct rate for both individuals and society is between 2 and 4 per cent, whereas the quote above suggests 1.5 per cent for individuals and either zero or “a very small positive rate” for society. I’ll leave it to Tol to reconcile these positions; I’m happy to endorse the passage I’ve quoted.

* Discounting and the social cost of carbon: a closer look at uncertainty by Jiehan Guo, Cameron J. Hepburn, Richard S.J. Tol and David Anthoff, Environmental Science & Policy, 9(3): 205-216