Episode 8: Time Discounting and Time Preference


What is the nature of time? Oh how I love Carl Sagan. But we’re not talking about spacetime, rather, we’re talking about humantime. Or how humans value time.

How humans perceive time is a tricky question, and one that I am not going to answer today. Too much unknown and unexplored psychology and not enough behavioral economics. Maybe how humans perceive time is a more interesting question, I’m not sure.

But what is easier to measure is how much you are willing to be paid to wait. In that way you can put a value on how much it is worth to get something sooner. This will be my first post in a series on time and what economists call time discounting.

Time discounting as an economic concept is pretty simple. I can pay $6 to get an online order to me today, or $5 to receive it tomorrow. There’s a discount if I wait.

In later posts I’m going to dig into some of the specific research that gives some concrete numbers on time discounting. But today I am going to stick with the theoretical.

Just like you can make a choice between things, you can make a choice to give or get something between times. The technical term for this is “intertemporal choices”. In “Time Discounting and Time Preference: A Critical Review” by Frederick, Loewenstein and O’Donoghue they define intertemporal choices as decisions involving tradeoffs among costs and benefits, that occur at different times. Choice means choice, intertemporal means between times.

How have economists dealt with this problem in the past? Like the rest of economics, the answer is they did so by oversimplifying the situation. Let’s start with the idea of discount utility because it’s very straightforward. Mind journey!

It’s a nice crisp fall day and you know what time of year it is… Pumpkin latte season! Your favorite. As you walk into your neighborhood coffee shop you can smell the strong aroma of nutmeg and pumpkin pie spice drift over you. You check the big board menu for ideas but let’s be honest; you’re getting your first pumpkin latte of the year and you’re really excited about it.

After waiting your turn in line, you give your order to the barista. At checkout you’re asked if you would like your order right now, or tomorrow. “Say what?” you ask. “Well, we’re giving you a choice. We can give you your order now, or you can choose to pick it up tomorrow. It’s the same price, and you have to pay now regardless of your choice”.

Ummm… You’re getting that latte right then and there. It’d be silly to wait until tomorrow! But what if they gave you a discount off your bill, say, $1 to wait until tomorrow. Or $2. At some point they can bribe you enough to wait.

That’s what is called your discount utility: the amount of value (utility) that you derive from getting your latte that instant.

Further, let’s assume you’re willing to take $1 to wait one day. The assumption in the old economics world is that time preferences are linear. Therefore, if you would take $1 to wait one day, then you would accept $2 to wait two days.

There are many psychology research studies that suggest that the discount utility model of time is wrong, and, in fact, in “Time Discounting and Time Preference: A Critical Review”, they painstakingly look at academic evidence for the traditional view of discount utility. And conclude that the old model has little empirical support.

“Economics has always been both an art and a science” says the paper’s authors. And that is a statement this author also agrees with. Simple discount utility is far too simple to accurately model human behavior.

This idea is only the tip of the iceberg.  There is research that shows that dopamine is released in anticipation of a reward, not when a reward is actually received (CITE), so sometimes it’s more fun and addictive to be forced to wait.

Here’s a video where Sapolsky goes through this research: http://library.fora.tv/2011/02/15/Robert_Sapolsky_Are_Humans_Just_Another_Primate

Humans certainly don’t value time linearly, and there are a lot of behavioral science papers about that I’ll be discussing later in this series. Briefly, making me wait one week is going to be expensive. But making me wait 10 weeks is not going to be 10x as expensive. It’s at least not linear.

And then there are the other wonderful human traits of scheming, plotting, planning, investing, gratification, and being lazy. There are a lot of competing factors about how we value time.

Frederick, Loewenstein and O’Donoghue encourage economists to abandon using the fundamental idea of discount utility altogether since it doesn’t seem to line up with what is happening in human heads. I quote from the paper:

“In sum, we believe that economists’ understanding of intertemporal choices will progress most rapidly by continuing to import insights from psychology, by relinquishing the assumption that the key to understanding intertemporal choices is finding the right discount rate (or even the right discount function), and by readopting the view that intertemporal choices reflect many distinct considerations and often involve the interplay of several competing motives.”

Sorry for the long, complicated paragraph, but I feel it is a great summary. Use insights from psychology. Stop trying to find a magical discount formula. Accept the messiness and strangeness of human decision making.

That’s great you may say, but if not discount utility, then what?

There is a competing way to define time discounting in economics and it’s called hyperbolic discounting. Pardon the name. But it’s a general understanding that human discounting is not time-consistent. Humans probably don’t even perceive time linearly, or consistently; much less value it that way. Its value is random and weird, just like humans.

Sure, there might be patterns that behavioral economists can find, but humans just don’t value or devalue things in linear, simple ways. It’s messy.

Again, I plan on talking about more specifics about how behavioral economists should think about humans and how we value time. But for now I just wanted to cover the big idea of even thinking about how to measure the value of time using economics.

In sum, if you are working on anything that involves time passing, don’t assume that there will be a lot of rational consistency in how people value waiting.

Frederick, S., Loewenstein, G., & O’Donoghue, T. (2002). Time Discounting and Time Preference: A Critical Review. Journal of Economic Literature40(2), 351-401. doi:10.1257/002205102320161311

Fiorello: Fiorillo C. D., Tobler P. N., Schultz W. (2003). Discrete coding of reward probability and uncertainty by dopamine neurons. Science 299, 1898–1902 10.1126/science.1077349 [PubMed] [Cross Ref] (dopamine anticipation)

Episode 6: Using the idea of “utility” to calculate “value”

Economics gets a bad reputation for being wrong about things, or only measuring things in terms of dollars or GDP (gross domestic product).

But most of these “bad raps” are simply because people don’t understand what economics is, and what it is actually capable of.

When I talk about “economics”, I’m not talking about Adam Smith (Wealth of Nations), or Marx, or anything before the 1950’s really. Those guys were philosophers. They looked at the world, thought about things, and then made sweeping guesses about how the world worked.

They get credit for sometimes being right, but just because Aristotle philosophized that there must be some small finite particle because you couldn’t cut things in half forever, it doesn’t mean he discovered the quark!

We wouldn’t call Aristotle a nuclear physicist and we shouldn’t call Adam Smith an economist. Hard science research and philosophy are fundamentally different fields. The biggest difference? A lot of math. Statistics. Econometrics. Linear Algebra. Adam Smith drew some lines on a chart; it’s philosophy.

Modern Economics only really came into its own in the late 1940’s or 1950’s, with the Milton Friedman generation. That makes the science maybe 70 years old at most! And that’s nothing. Modern physics got started in maybe the very late 1800’s, so imagine the difference between what we knew about physics in 1970 (which was a lot, we had nuclear power, etc…), compared to today. It’s a whole different level of sophistication and understanding.

Economics has come a long way, but it is a much newer field and simply hasn’t had time to fully blossom. It also helps your field if the largest nations on earth is pouring billions into research to make weapons to blow other nations up (ahem physics, computing, chemistry, etc…). So you have to forgive the field of economics for being a little bit behind.

With that lengthy precursor; how then does economics calculate value?

When economists try and figure out which decisions people will take, they have to compare apples to apples. There are a few ways to do this. The oldest trick is money, or money equivalents. Would you prefer a massage or a hamburger? Idk. So I instead ask how much would you pay for one or the other.

Just give each a “value” in dollars and compare, poof. Now we’re cooking.

The evolution of this method of comparing values is the idea of “utility”. Instead of money, you figure out how much something is “worth” to a human, or the utility the human gets.

For example, when your spouse cooks you breakfast that has an inherent value. But because it is not a financial transaction there is no financial transaction where money changes hands; so you must turn to the level of “utility” (happiness essentially) the breakfast provides you.

The main way to measure this is still in dollars (money) instead of “units of utility”; which has little meaning. The best way to measure what a spouse cooked breakfast is worth is usually to illicit how much you would pay for someone else to make that same meal for you. But there are lots of different ways to calculate utility.

The main point is that utility more accurately represents human decision-making because humans make decisions in abstract ways.

We don’t boil everything down into dollars (money) and compare the two values every time we make a decision. And once you get into behavioral economics utility amounts become even more important.

This is because the traditional economic assumption was that humans try to maximize their utility. The axiom, or assumption we take to be true is that we are rational, we want what’s best, so we maximize our utility. If there is a simple way to make $5 we’ll do it because that’s more than $0.

But, of course, there are many many times when that doesn’t happen! Just read the rest of these blog posts. That’s behavioral economics.

The answer is of course that we’re just measuring utility wrong. Traditional economics MISSES critical variables. Mind journey time! Think of a paperclip on a beach.

You are walking down the street with 3 of your closest friends in high school. It’s the suburbs so not a lot is going on.

It’s a tree-lined street, and farther down the street there are kids learning how to bike on a training bike. The sun is out, and birds are singing. It’s a very nice day.

On the ground off to the side of the sidewalk, you spot a crinkled $5 bill. Dirty, but totally spendable. You note “Oh! Look it’s $5!”, the friend walking on your left turns to you and says “Ew, that’s covered in dirt, you weren’t really going to pick that up, were you? It could be poop!”

You glance at your other friend to your left, and then to the friend to your right. All of them are staring at you with one eye raised and a grimace of slight disgust on their face.

Classical economics says you pick up the $5 because your utility of $5 is greater than $0, but of course you don’t pick up the free money. There is a hidden cost that traditional economic theories miss, which is the “social utility”. There is a social cost to your friends thinking you’re weird. Or poor. Or dirty. And that can be insanely powerful, more than a free $5 powerful.

It’s not that economics is broken or doesn’t work; it’s just that often it isn’t advanced enough to correctly calculate all the variables appropriately.

The first MAJOR behavioral economic papers in the 1970’s and 1980’s were all about different ways to calculate utility. There’s transactional utility, social utility, discounted utility, etc… etc… etc… It’s all just trying to reframe what humans are weighing when making their decisions. Some of it is because of fear of loss, or laziness, or social pressures.

I’ll probably devote an entire other blog post just to Kahneman and Tversky’s seminal, groundbreaking, famous-making paper “Prospect Theory: An Analysis of Decision under Risk” from 1979. There’s a reason those two are really considered the grandfathers of the behavioral sciences, especially behavioral economics. This is one of a few famous papers that really defined the genre.

In sum, their whole point was that economists were doing it wrong! It’s not about linear choices or straight classic rational decision making. And I quote from that paper: “people normally perceive outcomes as gains and losses, rather than as final states of wealth or welfare.”

So sure, your final state after you pick up the $5 is +$5 but that’s not the calculation you go through. You feel the loss of your social status, you weigh that decision not as finite, but in the moment. It’s complicated and messy, and human.

And that’s hard to measure; but discovering the Higgs Boson was hard too. It just takes time and refinement. Maybe a few Nobel Prizes, and a few billions of dollars for a huge research facility (CERN Particle Accelerator but for Behavioral Econ) would go a long way.

So I’m positive about the future of the field. And the concept of utility is an important one, and one you should understand. So that’s a brief primer on it.

Btw, I have attached a picture of what real full-fledged economics looks from the original Prospect Theory paper from 1979. The good news is that later papers are… more concise and have more fun field work, although the economic models are more complicated.

This segment is not from some crazy appendix by the way, but from the heart of the paper, perhaps outlining one of the more important points, which is the concavity of u (utility). So just in case you were worried about what you were missing…

Also… this is a formula for the value of different prospects. Economics is so fun!

Don’t worry, they clarify this nicely later in plain English. I’d go through it, but I’ll save it for the post about Prospect Theory.