Discounting the future, yet again

by John Q on February 24, 2007

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



Michael E. Sullivan 02.24.07 at 2:43 pm

I don’t really have much substantive to say in response, but I want to thank you for what you’ve written on this in the last year. Between your thoughts, and the Weitzman paper you link, I’m finally beginning to understand this vital debate.

Now that I get the expected utility paradigm Stern is using, I’m in 100% agreement with your take on the discounting.

I’m seriously troubled by the gaps in the model, even to the point of wanting to work on modeling the problem of thick tails what that should imply for EU calculations, though I doubt I have the chops for it (let alone the time, not being an academic who could consider it my job).

Anyway, anyone with undergrad math and stat who likes wrestling with this stuff (like me) can make it through Weitzman’s paper, and it’s the fullest explanation I’ve read of what’s going on here.


Alex 02.24.07 at 8:45 pm

If one thinks the present value of climate mitigation in the future should be low, for internal consistency you should be indifferent to a high rate of inheritance tax.


aaron 02.24.07 at 10:51 pm

Who in their right mind would accept a 1-2% rate of return. If my memory serves, in our financial engineering classes the risk-free rate of return is generally accepted to be ~5%.

I haven’t heard an argument that would lead me to accept any discount rate lower than GDP growth. The best that I’ve heard yet is that the last couple of hundred years have been an anomaly. But if that’s the case, and we should expect growth to revert to previous low levels, then AGW should be the least of our concerns.


aaron 02.24.07 at 10:53 pm

(granted 5% was back in 1998, things may have changed)


John Quiggin 02.25.07 at 12:15 am

In fact, your memory doesn’t serve, Aaron. US interest rates in 1998 were the same as they are now. .

Stern’s method gives a discount rate that is just above the projected real rate of per capita growth.


aaron 02.25.07 at 1:35 am

I’ll have to dig into my notes sometime, I’m pretty sure 5% was used as a good estimate for rfr. I think there are calculations, rather than using the current bond rate.


aaron 02.25.07 at 1:49 am

Of course the proper thing to do is use the expected growth rate, especially considering that we are looking at highly improbable events.


radek 02.25.07 at 2:45 am

You can’t discriminate between generations without discriminating between people who are alive at the same time.

But the Diamond impossibility result states that you cannot not discriminate between generations. Zero time preferance still discriminates, just in a different way.

Anyway, this point has been made before.

I find the Weitzman “right for the wrong reasons” argument much more convincing, so I agree with the policy recommendations even while still frowning at the zero rate of time preferance.


Lord Acton 02.25.07 at 3:08 am

Personally, even one penny spent today, to
prevent $100 of environmental damage 100 years
from now, is wasted.

And I would argue that most acturial tables
would support the statement that none of us
current posters will be around 100 years from
now, so as to even care.

However, I would be the last to oppose the
right of any of you to spend as much of your
money as you see fit to avoid ecological damage
in the future.

Since I take public transit to work, I’m already
doing MY share :-}


John Quiggin 02.25.07 at 4:51 am

Radek, I didn’t claim the argument was new, but I haven’t seen it before. Can you point to a good source.

The Diamond impossibility theorem isn’t relevant, I think, since the argument I’m making has nothing to do with infinite time horizons. It would work fine with two periods and three generations.


Will 02.25.07 at 7:06 am

I think John’s substantive point regarding time preferences is that marginal benefits are discounted over time at the individual level because individuals fear they may die before they can consume in the future, but this reasoning doesn’t follow for the everlasting society, thus society shouldn’t have time preferences.

But we should think carefully about what we mean buy ‘consume’. What is the thing that’s providing us the marginal benefits, today and tomorrow? What is the thing that we’d be giving up today in exchange for it in the future?

That I value the marginal benefit of eating today higher than my marginal benefit from eating tomorrow (i.e. I’ve discounted my marginal benefit) seems to follow from my fear of death in the next 24 hours. I might not get the chance to eat tomorrow.

That I value the marginal benefits of ‘consuming’ new knowledge today, on the other hand, doesn’t follow from my fear of death. Knowing something today means I can know more things tomorrow. I have a time preference for learning today versus tomorrow because my consumption of learning today determines my consumption of learning tomorrow.

(The assumption of time separability has precluded my example, but it shouldn’t preclude it from the discussion… We, society, do and should have time preferences independent of our individual fears of death.)


Cranky Observer 02.25.07 at 7:35 pm

> 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.

In my experience of large-scale cost/benefit analyses, neither engineers nor economists have much to do with being the proponents of or setting the goals for the project – that inevitably occurs in the political realm (whether corporate or electoral politics). Both economists and engineers are technicians who are called in long after those with the political power have made the decisions, and are just proxies for the final struggle between the politicians.



Akshay 02.25.07 at 8:36 pm

The Weitzman piece really *is* excellent! I love it when people far more intelligent then myself help me rationalize my gut feelings. A big applause for:

– showing that discount rates dominate CBA’s
– acknowledging the key role of uncertainty
– emphasizing that natural beauty is a source of “utility”
– arguing that attitudes towards catastrophes, which *might* befall humanity and *will* befall the non-human world, will dominate the decision making
– calling for more insight into the last bullet

I think this takes us pretty close to a summary of the main issues from the perspective of (generalized) (expected) utilitarianism. Of course, non-utilitarian approaches have a lot to contribute too.


radek 02.26.07 at 1:37 am

John, maybe I’m missing something but the following sounds like an infinite horizon type argument:

First, individuals are mortal whereas (except for a small probability of nuclear annihilation and similar disasters) society is not.

As far as the source, I just meant that some of this came up in the previous discussions.

Good write up, btw, mind if I share it with my students (discounting came up in class the other day and the range of opinions was WIDE)?


Kevin 02.26.07 at 9:07 pm

There’s a more important misunderstanding being made in these comments: a SW function discounts utility, not dollars. Assume $1m real dollars of damage will occur in year 2107, with 2% annual real per capita growth. The discount rate incorporates 1) pure time preference, with which 0 (or .01 to account for the possibility of an extinction-level event) AND 2) differentials in marginal utility. We can agree (for a variety of reasons) with a 0 rate of social time preference, while still discounting the future at, say, p=.02. In this case, we’re only willing to pay 138000 real dollars to alleviate that future damage.

(This example makes some assumptions about the link between income growth and the utility curve, but the point is evident no matter how you slice it. As for Diamond, in this case we only see the weight we put on future problems go to zero because the income (and therefore marginal utility, given the “more is better” clause) goes to infinity.)


pinus 02.27.07 at 2:38 am

I agree with kevin. We have income growth and technological progress. The real return on capital is about 2-3% in the long run. This is what we should use as the discount rate.

Having said this, I have to add that there is still space for environmental protection even at this discount rate. We should just beware of self-punishing actions which could be consequences of public hype rather than sober reasoning.


John Quiggin 02.27.07 at 2:47 am

Radek, the distinction between individual and social mortality is obviously relevant over the (finite) period from now until 2100 central to the current debate. Virtually everyone in a position to make savings decisions today will be dead in 2100, but we can reasonably hope that society will still be around. Feel free to share my writeup with your students.

Kevin, this distinction is indeed the crucial one.

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