Hyperbolic discounting: Why we procrastinate

Mar 25 JDN 2458203

Lately I’ve been so occupied by Trump and politics and various ideas from environmentalists that I haven’t really written much about the cognitive economics that was originally planned to be the core of this blog. So, I thought that this week I would take a step out of the political fray and go back to those core topics.

Why do we procrastinate? Why do we overeat? Why do we fail to exercise? It’s quite mysterious, from the perspective of neoclassical economic theory. We know these things are bad for us in the long run, and yet we do them anyway.

The reason has to do with the way our brains deal with time. We value the future less than the present—but that’s not actually the problem. The problem is that we do so inconsistently.

A perfectly-rational neoclassical agent would use time-consistent discounting; what this means is that the effect of a given time interval won’t change or vary based on the stakes. If having $100 in 2019 is as good as having $110 in 2020, then having $1000 in 2019 is as good as having $1100 in 2020; and if I ask you in 2019, you’ll still agree that having $100 in 2019 is as good as having $1100 in 2020. A perfectly-rational individual would have a certain discount rate (in this case, 10% per year), and would apply it consistently at all times on all things.

This is of course not how human beings behave at all.

A much more likely pattern is that you would agree, in 2018, that having $100 in 2019 is as good as having $110 in 2020 (a discount rate of 10%). But then if I wait until 2019, and then offer you the choice between $100 immediately and $120 in a year, you’ll probably take the $100 immediately—even though a year ago, you told me you wouldn’t. Your discount rate rose from 10% to at least 20% in the intervening time.

The leading model in cognitive economics right now to explain this is called hyperbolic discounting. The precise functional form of a hyperbola has been called into question by recent research, but the general pattern is definitely right: We act as though time matters a great deal when discussing time intervals that are close to us, but treat time as unimportant when discussing time intervals that are far away.

How does this explain procrastination and other failures of self-control over time? Let’s try an example.

Let’s say that you have a project you need to finish by the end of the day Friday, which has a benefit to you, received on Saturday, that I will arbitrarily scale at 1000 utilons.

Then, let’s say it’s Monday. You have five days to work on it, and each day of work costs you 100 utilons. If you work all five days, the project will get done.

If you skip a day of work, you will need to work so much harder that one of the following days your cost of work will be 300 utilons instead of 100. If you skip two days, you’ll have to pay 300 utilons twice. And if you skip three or more days, the project will not be finished and it will all be for naught.

If you don’t discount time at all (which, over a week, is probably close to optimal), the answer is obvious: Work all five days. Pay 100+100+100+100+100 = 500, receive 1000. Net benefit: 500.

But even if you discount time, as long as you do so consistently, you still wouldn’t procrastinate.

Let’s say your discount rate is extremely high (maybe you’re dying or something), so that each day is only worth 80% as much as the previous. Benefit that’s worth 1 on Monday is worth 0.8 if it comes on Tuesday, 0.64 if it comes on Wednesday, 0.512 if it comes on Thursday, 0.4096 if it comes on Friday,a and 0.32768 if it comes on Saturday. Then instead of paying 100+100+100+100+100 to get 1000, you’re paying 100+80+64+51+41=336 to get 328. It’s not worth doing the project; you should just enjoy your last few days on Earth. That’s not procrastinating; that’s rationally choosing not to undertake a project that isn’t worthwhile under your circumstances.

Procrastinating would look more like this: You skip the first two days, then work 100 the third day, then work 300 each of the last two days, finishing the project. If you didn’t discount at all, you would pay 100+300+300=700 to get 1000, so your net benefit has been reduced to 300.

There’s no consistent discount rate that would make this rational. If it was worth giving up 200 on Thursday and Friday to get 100 on Monday and Tuesday, you must be discounting at least 26% per day. But if you’re discounting that much, you shouldn’t bother with the project at all.

There is however an inconsistent discounting by which it makes perfect sense. Suppose that instead of consistently discounting some percentage each day, psychologically it feels like this: The value is the inverse of the length of time (that’s what it means to be hyperbolic). So the same amount of benefit on Monday which is worth 1 is only worth 1/2 if it comes on Tuesday, 1/3 if on Wednesday, 1/4 if on Thursday, and 1/5 if on Friday.

So, when thinking about your weekly schedule, you realize that by pushing back Monday’s work to Thursday, you can gain 100 today at a cost of only 200/4 = 50, since Thursday is 4 days away. And by pushing back Tuesday’s work to Friday, you can gain 100/2=50 today at a cost of only 200/5=40. So now it makes perfect sense to have fun on Monday and Tuesday, start working on Wednesday, and cram the biggest work into Thursday and Friday. And yes, it still makes sense to do the project, because 1000/6 = 166 is more than the 100/3+200/4+200/5 = 123 it will cost to do the work.

But now think about what happens when you come to Wednesday. The work today costs 100. The work on Thursday costs 200/2 = 100. The work on Friday costs 200/3 = 66. The benefit of completing the project will be 1000/4 = 250. So you are paying 100+100+66=266 to get a benefit of only 250. It’s not worth it anymore! You’ve changed your mind. So you don’t work Wednesday.

At that point, it’s too late, so you don’t work Thursday, you don’t work Friday, and the project doesn’t get done. You have procrastinated away the benefits you could have gotten from doing this project. If only you could have done the work on Monday and Tuesday, then on Wednesday it would have been worthwhile to continue: 100/1+100/2+100/3 = 183 is less than the benefit of 250.

What went wrong? The key event was the preference reversal: While on Monday you preferred having fun on Monday and working on Thursday to working on both days, when the time came you changed your mind. Someone with time-consistent discounting would never do that; they would either prefer one or the other, and never change their mind.

One way to think about this is to imagine future versions of yourself as different people, who agree with you on most things, but not on everything. They’re like friends or family; you want the best for them, but you don’t always see eye-to-eye.

Generally we find that our future selves are less rational about choices than we are. To be clear, this doesn’t mean that we’re all declining in rationality over time. Rather, it comes from the fact that future decisions are inherently closer to our future selves than they are to our current selves, and the closer a decision gets the more likely we are to use irrational time discounting.

This is why it’s useful to plan and make commitments. If starting on Monday you committed yourself to working every single day, you’d get the project done on time and everything would work out fine. Better yet, if you committed yourself last week to starting work on Monday, you wouldn’t even feel conflicted; you would be entirely willing to pay a cost of 100/8+100/9+100/10+100/11+100/12=51 to get a benefit of 1000/13=77. So you could set up some sort of scheme where you tell your friends ahead of time that you can’t go out that week, or you turn off access to social media sites (there are apps that will do this for you), or you set up a donation to an “anti-charity” you don’t like that will trigger if you fail to complete the project on time (there are websites to do that for you).

There is even a simpler way: Make a promise to yourself. This one can be tricky to follow through on, but if you can train yourself to do it, it is extraordinarily powerful and doesn’t come with the additional costs that a lot of other commitment devices involve. If you can really make yourself feel as bad about breaking a promise to yourself as you would about breaking a promise to someone else, then you can dramatically increase your own self-control with very little cost. The challenge lies in actually cultivating that sort of attitude, and then in following through with making only promises you can keep and actually keeping them. This, too, can be a delicate balance; it is dangerous to over-commit to promises to yourself and feel too much pain when you fail to meet them.
But given the strong correlations between self-control and long-term success, trying to train yourself to be a little better at it can provide enormous benefits.
If you ever get around to it, that is.

The World Development Report is on cognitive economics this year!

JDN 2457013 EST 21:01.

On a personal note, I can now proudly report that I have successfully defended my thesis “Corruption, ‘the Inequality Trap’, and ‘the 1% of the 1%’ “, and I now have completed a master’s degree in economics. I’m back home in Michigan for the holidays (hence my use of Eastern Standard Time), and then, well… I’m not entirely sure. I have a gap of about six months before PhD programs start. I have a number of job applications out, but unless I get a really good offer (such as the position at the International Food Policy Research Institute in DC) I think I may just stay in Michigan for awhile and work on my own projects, particularly publishing two of my books (my nonfiction magnum opus, The Mathematics of Tears and Joy, and my first novel, First Contact) and making some progress on a couple of research papers—ideally publishing one of them as well. But the future for me right now is quite uncertain, and that is now my major source of stress. Ironically I’d probably be less stressed if I were working full-time, because I would have a clear direction and sense of purpose. If I could have any job in the world, it would be a hard choice between a professorship at UC Berkeley or a research position at the World Bank.

Which brings me to the topic of today’s post: The people who do my dream job have just released a report showing that they basically agree with me on how it should be done.

If you have some extra time, please take a look at the World Bank World Development Report. They put one out each year, and it provides a rigorous and thorough (236 pages) but quite readable summary of the most important issues in the world economy today. It’s not exactly light summer reading, but nor is it the usual morass of arcane jargon. If you like my blog, you can probably follow most of the World Development Report. If you don’t have time to read the whole thing, you can at least skim through all the sidebars and figures to get a general sense of what it’s all about. Much of the report is written in the form of personal vignettes that make the general principles more vivid; but these are not mere anecdotes, for the report rigorously cites an enormous volume of empirical research.

The title of the 2015 report? “Mind, Society, and Behavior”. In other words, cognitive economics. The world’s foremost international economic institution has just endorsed cognitive economics and rejected neoclassical economics, and their report on the subject provides a brilliant introduction to the subject replete with direct applications to international development.

For someone like me who lives and breathes cognitive economics, the report is pure joy. It’s all there, from anchoring heuristic to social proof, corruption to discrimination. The report is broadly divided into three parts.

Part 1 explains the theory and evidence of cognitive economics, subdivided into “thinking automatically” (heuristics), “thinking socially” (social cognition), and “thinking with mental models” (bounded rationality). (If I wrote it I’d also include sections on the tribal paradigm and narrative, but of course I’ll have to publish that stuff in the actual research literature first.) Anyway the report is so amazing as it is I really can’t complain. It includes some truly brilliant deorbits on neoclassical economics, such as this one from page 47: ” In other words, the canonical model of human behavior is not supported in any society that has been studied.”

Part 2 uses cognitive economic theory to analyze and improve policy. This is the core of the report, with chapters on poverty, childhood, finance, productivity, ethnography, health, and climate change. So many different policies are analyzed I’m not sure I can summarize them with any justice, but a few particularly stuck out: First, the high cognitive demands of poverty can basically explain the whole observed difference in IQ between rich and poor people—so contrary to the right-wing belief that people are poor because they are stupid, in fact people seem stupid because they are poor. Simplifying the procedures for participation in social welfare programs (which is desperately needed, I say with a stack of incomplete Medicaid paperwork on my table—even I find these packets confusing, and I have a master’s degree in economics) not only increases their uptake but also makes people more satisfied with them—and of course a basic income could simplify social welfare programs enormously. “Are you a US citizen? Is it the first of the month? Congratulations, here’s $670.” Another finding that I found particularly noteworthy is that productivity is in many cases enhanced by unconditional gifts more than it is by incentives that are conditional on behavior—which goes against the very core of neoclassical economic theory. (It also gives us yet another item on the enormous list of benefits of a basic income: Far from reducing work incentives by the income effect, an unconditional basic income, as a shared gift from your society, may well motivate you even more than the same payment as a wage.)

Part 3 is a particularly bold addition: It turns the tables and applies cognitive economics to economists themselves, showing that human irrationality is by no means limited to idiots or even to poor people (as the report discusses in chapter 4, there are certain biases that poor people exhibit more—but there are also some they exhibit less.); all human beings are limited by the same basic constraints, and economists are human beings. We like to think of ourselves as infallibly rational, but we are nothing of the sort. Even after years of studying cognitive economics I still sometimes catch myself making mistakes based on heuristics, particularly when I’m stressed or tired. As a long-term example, I have a number of vague notions of entrepreneurial projects I’d like to do, but none for which I have been able to muster the effort and confidence to actually seek loans or investors. Rationally, I should either commit or abandon them, yet cannot quite bring myself to do either. And then of course I’ve never met anyone who didn’t procrastinate to some extent, and actually those of us who are especially smart often seem especially prone—though we often adopt the strategy of “active procrastination”, in which you end up doing something else useful when procrastinating (my apartment becomes cleanest when I have an important project to work on), or purposefully choose to work under pressure because we are more effective that way.

And the World Bank pulled no punches here, showing experiments on World Bank economists clearly demonstrating confirmation bias, sunk-cost fallacy, and what the report calls “home team advantage”, more commonly called ingroup-outgroup bias—which is basically a form of the much more general principle that I call the tribal paradigm.

If there is one flaw in the report, it’s that it’s quite long and fairly exhausting to read, which means that many people won’t even try and many who do won’t make it all the way through. (The fact that it doesn’t seem to be available in hard copy makes it worse; it’s exhausting to read lengthy texts online.) We only have so much attention and processing power to devote to a task, after all—which is kind of the whole point, really.