The battle over discounting

The new episode in the war between economics and folk economics

As a highschooler, I sucked at physics. That’s despite all the topics being supremely cool; thermodynamics, optics, electricity, I found them all super exciting, yet, when it came to working out an actual numerical problem, I sucked super hard. The thing I probably sucked the most at in physics was mechanics. The mechanics problems looked a little bit like this: 

Two objects are headed for each other on a flat terrain with masses X kg and Y kg and constant speeds V km/h and W km/h. They’re on a direct collision course and after they hit, they will continue moving backwards along their current trajectory. What will be their speeds after collision? Assume no friction.

First, less importantly for my story, I proclaim right away that this type of problem is super easy and should have caused no difficulty for high-school me. Shame on 15-year-old Peter. Yet I assign at least 50% of the blame of me sucking at physics on my two teachers who just couldn’t be bothered to actually teach this properly.

Second, and more to the point, this “Assume no friction” annoyed the crap out of me. On one hand, it bothered me intellectually. We all know friction exists, why are we pretending it isn’t? It took me some time to appreciate assumptions of convenience and by now, I, in keeping with the cult of economic theorists, have become a master of this. The second reason was that I sucked at physics and I just wanted a reason not to have to do the actual exercise. 

Why do I bring this up?

It is because not long ago on April 25, 2022, I attended an informal talk at the Theoretical and Experimental Ecology Station (Station d’Ecologie Théorique et Expérimentale) of the French National Centre for Scientific Research (CNRS) where a smart, cool, and friendly ecologist expressed the opinion that economists ought to “assume no discounting” in their models because that would help save the planet from climate change.

That, and some other parts of her talk, triggered me a bit and hence this blog post. The post itself is a sequel/spin-off/soft reboot of my earlier post, titled 'You're being too hard on economics' but it is meant to be self-contained so don't go anywhere just yet.

Disclaimers, trigger warnings, and so on: This is not a scientific ‘perspectives’ article. This a personal opinion on a personal blog whose editorial standards are only slightly higher than those of MDPI journals’ special editions. Second, some people may read this and think I’m overexplaining things. Some people may think I’m not explaining thigs in enough detail. Then again, some people might think I’m explaining everything perfectly. My apology is offered to the first two camps and a modest nod is given towards the third one. Third, although no offense is intended, some offense might yet be caused. Again, my apology is offered. If you’re a philosopher or an ecologist or have a positive predispotion towards these and if you know you’re sensitive, read this with a stress ball in hand. Also, discounting has a lot to do with death, so I'm gonna talk about that as well. Read on only if you're braced.

Let’s get going.

My first meeting with Longtermism: philosophy is still a thing

Between my two postdoc contracts in Grenoble and Toulouse there was a gap of six months due to the academic calendar and some inflexible French research contract nonsense. I spent that time in blissful unemployment (it turns out French unemployment benefits are super generous) hiking in the Alps and occasionally doing some research with my first postdoc advisor (I was allowed to retain my office in Grenoble). But before I resigned myself to relative scientific idleness I had attempted to get a visiting position somewhere to pass the time.

Enter Oxford University’s Global Priorities Institute. The Institute had just rejected my application for a proper postdoc contract (good decision on their part, they’d have hated me) but they kind of enjoyed my portfolio and offered me a fellowship. This gave me the opportunity to interact with cool people doing some cool research at the intersection of economics and philosophy (as it would turn out, it was much more philosophy than economics at that point). COVID made any physical visit impossible which was a huge shame, but we hung out online, gave and attended some talks, and played some board games. Overall, it was a nice experience that, if ever so briefly, exposed me to some new ideas and people. I got a glimpse into how the ideas of decision theory and game theory are making waves in philosophy which was both pleasurable and informative.

They were using some concepts that were well-known to me (they seemed to have found a use for expected utility maximization, nice!), some others were familiar but were under a different name (they rebranded the term ‘ambiguity’ as ‘cluelessness’ for some reason), and yet others that I thought I recognized but were somehow strange. Longtermism fell under the latter category; it uses the terminology and tools of the theory of time preference but at the same time argues that we… shouldn’t have time preferences? Or that they ought to be sort of irrelevant? It’s hard for me to get a grasp on it.

Longtermism is a branch of moral philosophy that prioritizes improving the far future. How far? Unclear. Perhaps thousands of years for future humans, perhaps millions of years for future trans-humans, perhaps billions for future… whatevers. I assume the scope ends sometime before 10^100 or so years from now because after that, things should be pretty uniformly dark for a while. Longtermism began in 2017 in the philosophy departments of Oxbridge and in that short time between then and now it attracted a fair amount of proponents and critics. I don’t consider myself either, nor do I consider myself qualified to summarize or review it, so I’ll just link the wiki here and let the reader educate themselves based on demand.

The way Longtermism relates to economic models, is advocating for a zero (not ‘close to zero’, zero) discount factor to be used by economic modelers and planners. What is a discount factor?

Discounting is the name of a family of economic methods by which economic agents compare payoffs happening at different points in time. A common assumption is that future payoffs of equal size are worth less than present ones. By far the most common method is called exponential discounting that assumes a special structure for these comparisons. It uses a single parameter called the discount factor which I denote by δ. Then, the story goes, the value of 100 euros received today is equal to the value of 100(1+δ) euros received one year from today, 100(1+δ)^2 euros received two years from today, and so on. There are other discounting methods that might be more realistic representations of how people make intertemporal decisions, but exponential is the most widely used one, probably because it's got nice mathematical properties that are super handy when one is trying to build economic models.

Where does δ come from? Supposedly, this is a personal characteristic of the decision maker(s) receiving the payoffs and making decisions. You might be impatient and have a high δ or patient and have a low δ.

Longtermism argues that we should all be infinitely patient and have δ=0, basically telling us to stop using discounting of any kind. Its proponents argue that the value of 1 (year of) life lost ought to be independent of whether the loss takes place now or a thousand years from now, and so should it be with 100 euros lost. Or 100 gazillion euros of GDP.

To understand the motivation behind Longtermism, I reference a GPI fellow’s paper on Longtermism vs Robust Temporalism (the direction arguing for the use of positive discount rates) which leads with the following thought experiment (edited for brevity).

“You’re trapped inside a bunker. This bunker houses two nuclear missile launchers. One missile is programmed to fire in five days’ time, towards a town with a population of 5,000. The second missile is programmed fire in 70 years’ time towards a town which, by that time will have a population of 6,000. The missiles, if not deactivated, will wipe out the target towns entirely. For whatever reason, you’re able to deactivate only one of the two missiles. Which should you deactivate?”

It seems clear that unless we make a moral argument as to why present lives are more important than future ones, you ought to deactivate the second missile irrespective of the time difference and the lives-saved-difference (so long as both are positive between the second and first missiles), and thus the implied “moral discount rate” of lives saved ought to be zero.

We’ll get back on this.

My second meeting: ecologist goes on the offensive against neoclassical economics

The second meeting is the one described above. The reason it triggered me was because, unlike the Longtermism of philosophers, which I kind of took as intellectual self-gratification, that, by its nature, is meant to be innocuous at worst and though-provoking at best, this one was neither. This appeared to come as part of a general call for economists to change their way of thinking. To do better. To be better. For the future, for society, for the planet.

The talk led with the following list of assumptions that, according to the speaker, neoclassical economists make: 1, a positive discount rate; 2, substitutability; 3, that the Earth’s resources are infinite; 4, that the Earth’s biosphere is too big for humanity to pollute. The talk alleged that neoclassical economics ought to be replaced by “steady-state economics” that, in the speaker’s opinion, correctly, assumes 1, no discounting; 2, no substitutability; 3, that the Earth’s resources are finite; 4, that it is well within our capabilities to fuck up the Earth’s biosphere permanently and irreversibly.

Now, I must absolutely concede that of the latter list, 3 and 4 are important truths that, for far too long were either ignored or outright denied by far too many. Some of them, undoubtedly, were economists, very likely, even neoclassical economists. And, before I dig into 1 and 2, I also concede that the context in which these two were introduced was on point. For 1, if we’re aiming for a stable ecosystem, it’s not enough to stave off a set of species’ extinction in the short term, it has to be a long-term, sustainable solution: avoiding extinction for, say, 100 years is not good enough. For 2, it was that one species cannot be substituted by another in terms of the niche it occupies within the ecosystem. I’m fully on board with the messages within these very narrow contexts.

Yet, I take a major objection as to the actual details and how the messages were presented. The low-hanging fruit is the speaker's take on neoclassical economics. Neoclassical economics, as a school of thought, makes two and only two assumptions:

1. Economic agents follow incentives by maximizing an objective function (utility or profits).

2. Economic agents are perfectly informed.

Importantly, neoclassical economists don’t assert that these two hold true in real life. This is neoclassical economics after all, which, despite ‘neo’ being in the name, is actually approaching 90 years of age and, in many ways, it shows. This is the economics equivalent of “Assume no friction”: assumptions that are made for tractability, convenience, and for didactic purposes. 1 is defensible (perhaps even necessary for us to begin describing an ‘economic agent’), 2 is admittedly a simplification at best and is often relaxed in one way or another. It turns out that neoclassical models work even when economic agents aren’t perfectly informed (some of the time).

Specific models based on neoclassical thinking will have other assumptions. But assumptions of specific models are not meant to be taken out of context; just imagine me asserting that theoretical biology assumes ‘no sexual selection’ because I’ve once seen a model of a haploid population. The school of thought as a whole, what makes neoclassical economics truly ‘neoclassical’, assumes no more and no less than these two.

Now let me focus specifically on the “assume no discounting” part, which deserves to be unpacked because I now see it a recurrent point of attack on economic thinking.

Why “assume no discounting” isn't the same as “assume no friction”

First let’s discuss the motivations behind discounting, staying within the exponential method of discounting. In case of financial assets, this sort of understood by the layman: If the annual “risk-free” return on my investments is r and I have 100 euros now, I will have 100(1+r) euros one year from now. Or, if I want to have 100 euros in my pocket exactly one year from now, I need to make an investment of 100/(1+r) euros now. This is known as the present value of 100 future euros. To invoke an example close to life, if you have 100,000 euros in savings, then, first of all, good for you, especially if you’re the same age as me, and second of all, if the rate of inflation is 10% and you don't get interest on your savings, those savings will be worth 90,909 euros next year (as in, you’ll be able to purchase the similar amount of stuff one year from now that you’d be able to today with 90,909 euros).

Now, notice that nothing in the first story guarantees that r is positive; indeed, we’ve seen cases where returns on some “risk-free” investments was (close to) zero or even negative. Yet, in pretty much all financial markets, one will see investment options that are “risk-free” and yet have a positive return.

So why does “the market” seem to think that future euros are worth less than present euros? And it is here that we arrive to the fundamentals of neoclassical economics. Neoclassical economics imagines “the market” as the aggregation of economic agents. These agents bring their assets to “the market” then exchange them as their preferences compel them. So, if “the market” has positive interest rates, it is because individuals prefer present payments to future ones. Note the ‘if’: neoclassicals do not make an assumption on whether “the market” or individuals should behave this way or that way, they only say that these should align in some sense.

'But Peter', the strawman ‘folk economist’ might cry out triumphantly, 'This is circular logic! Individuals discount because “the market” has positive interest rates and “the market” has positive interest rates because individuals discount!'

No. Well, sort of no. The way I make sense of it is that both sides of the financial market is populated with economic agents with given preferences. Depending on whether bargaining power lies on the supply side or the demand side of future bonds or stocks, individuals on both sides can act as price setters or price takers as the market ebbs and flows. Nevertheless, I do acknowledge that the chicken-and-egg story holds some ground here. But it’s not like the actual chicken and the egg would suddenly realize the paradox of their existence and just disappear from the material world because of that. The same forces that produced both the chicken and the egg produced us as well, and with us, produced the drive to discount that is reflected in both our personal choices and our financial markets.

This drive has everything to do with the uncertainty of the future. Even if we assume away inflation for a thought experiment, if you promise to give me 100 euros today vs one year from now, I will trust and therefore value the former promise more. Maybe you change your mind or maybe by that point you’ll be unable to deliver because you die of COVID or Putin nukes your place of residence. The longer the time difference between the promise and delivery, the less I can trust it and thus the less it is worth.

Death isn’t the only source of uncertainty but it’s certainly the most dramatic and, well, eternal one. In fact, death is so closely connected to intertemporal preferences that, given any stream of monetary payoffs c(t) where t=1,2,…, evaluating the utility of this payoff stream through exponential discounting with rate δ actually equals the expected total payoff with a death rate of δ after any given period. Death is also something that, unlike some other sources of uncertainty, we can’t really solve. Yet I can almost hear my other strawman, a longtermist, argue that we’re just selfish. Who cares if I die, what money I have, what consumption utility I could have attained, my descendants can still enjoy with the assets that I leave behind.

Now, even if this were something that I would be likely to be persuaded by, this argument is completely fucked over by the simple fact that we’re not just consumers of goods and services that result in utility, we’re their producers as well. Dead people don’t produce. Whatever human capital they accumulated that they haven't fully passed on future generations, whatever services they would have been able to render, whatever love and affection they could have been bestowed on others is, unfortunately, lost.

Now, you might be able to tackle some sources of uncertainty in the economy (or, if you want to philosophize, you can assume it away like the ‘two missiles’ example tries to do) to the point where people’s discount factors go much closer to zero than they are now. But, unless you cure death, you're not likely to eliminate the reasons why the drive for discounting has evolved.

One might point out that the call isn't for economists to stop using individual discount factors, but social discount factors; the ones we use to evaluate damages to the economy occurring in different times. If humanity fucks up the ecosystem at year Y, it doesn’t really matter what the GDPs of the years between 2022 and Y are. So, when you’re investigating the possible consequences of a certain set of economic policies and your report finds great prosperity for Y minus 2022 years, then a sudden, catastrophic, and irrecoverable loss in year Y, the bottom line shouldn’t be positive no matter what Y is.

And on the surface, this one again sounds reasonable (although implementing it under more realistic dilemmas is highly paternalistic and not something that a democratic society of discounters is likely to, or indeed should, swallow). But again-again, for this to make any practical sense, one has to know what will happen in the next Y minus 2022 years with certainty. To give you an idea as to how close we are to predictions like that, here’s a projection of Australian yearly GDP growth from 2018.

Those cones around black projection line indicate the size of uncertainty we’re talking about. Projecting as far as two years and already we’re back to predicting that “with 90% probability, Australia’s GDP will grow somewhere between 0% and 5% (the highest growth rate Australia’s economy has had for like 40 years)”. In other words, the prediction is absolutely meaningless; it has the same value as something like “I will end my contract with the Toulouse School of Economics some time between 2022 and the year 2122 with high probability”.

And guess what: even the useless prediction about Aussie GDP was wrong! Australia’s economy actually shrunk in 2020 (thanks COVID)! So how far are we from eliminating uncertainty in economic predictions? Pretty far. It’s not even the failure of economics (or if you think it is, read the prequel) it’s just the power of compound standard deviation.

Conclusions

Discounting of any kind goes hand in hand with uncertainty about the future. Examples that seek to show that discounting is “not good” (immoral and/or dangerously shortsighted) assume away uncertainty in the weirdest of ways. In the bunker-missile case it is that we know for sure what loss of life will occur from the second missile in 70 years (like, holy shit, a lot can happen in 70 years… 70 years ago there were no nuclear missiles, 70 years before that weren’t even combustion engines, 70 years before that no steam engines…).

As for ecologists, I can’t really speak to their motivations as to why some of them call on economists to stop discounting, but I can theorize based on what I’ve seen. The underlying assumption seems to be that we face a choice between continued economic growth in the short run followed by an ecological catastrophe or immediate degrowth and sustainable living. Under this dilemma, indeed, a zero social discount factor would commit us to the second option. Yet, the evidence this is based on is horrible not decisive. In my reading, committing to sustained degrowth would not only invite massive global instability (hello, 10,000 nuclear warheads!), it would actually limit our available assets needed transition to green energy. But that’s another story.

Whatever the fate of the planet, calling on economists to stop discounting isn’t just a misunderstanding of what discounting is, it is a misunderstanding of what economics is supposed to do: take individual preferences as the primitives of our models and see where the night takes us. I would even argue that there is some confusion interesting debate as to what models of complex systems are supposed to be like and what they’re meant to do but again, beyond the scope of today’s post.

So… how do we improve communication between economists and other scientists? If those other scientists subscribe to 'folk economic' ideas, I honestly don't think that's a goal worth achieving. We're only gonna get frustrated with each other without accomplishing anything of any use to anyone. Folk economics' subscribers tend to have pre-set ideas about how economics works that are both predictably wrong and extremely hard to get rid of. However, I have excellent experience discussing with non-economists who have never subscribed or successfully unsubscribed from these ideas. Here is my list of four folk economic assumptions that need revising and what, in my humble yet stubborn opinion, ought to replace them.

I’m beyond excited to see the conversation that will unfold if we can get more scientists unsubscribed from folk economics.

May 15, 2022.

Comments and questions should be addressed to peter.bayer7@gmail.com.

Some links:

Longtermism vs Robust Temporalism paper titled 'Time discounting, consistency and special obligations: a defence of Robust Temporalism' by Harry Lloyd.

https://philpapers.org/archive/LLOTDC.pdf

The criticism of Longermism from a much more different angle, treating it as much more consequential and sinister than I did. Allegedly, Longtermist think tanks received 50 billion in funding (holy shit!).

https://aeon.co/essays/why-longtermism-is-the-worlds-most-dangerous-secular-credo

‘Folk Economics’ by Paul Rubin.

https://www.jstor.org/stable/1061637?seq=1

Find Waldo (or Peter) on the 2021 GPI fellows’ list.

https://www.forethought.org/the-new-cohort-2021