The Meaning of Milestones

We often give milestones more significance than they objectively have

Koen Smets

May 10, 2018·6 min read

Do you have a mortgage? If you live in Northwestern Europe, you probably do. According to Eurostat, more than half the population in the Nordic countries, the Benelux and, at a stretch, the UK and Ireland, live in their own home and are repaying a mortgage for the privilege. In the USA, more than 35% of homes are owner-occupied with a mortgage — a slightly different measure, but considering household size, quite similar.

If so, you may occasionally be thinking about the day that your loan will be paid off. At long last you will be free of the lender’s shackles, and you will be able to call every single brick, every rooftile, every door handle your own. Not only will you feel wealthier with a house that is paid off, you will also be able to actually save all the money that went back into the lender’s coffers. A highly symbolic moment, for sure. But how much substance is there to this?

A roof as a milestone

Home ownership is an emotive affair: the security of a roof over your head is, well, priceless. But economically, there is no real difference between renting a house, and borrowing the money to buy a house. Picture two pairs of identical twins: Anna and Alice, and Bob and Ben. Anna is married to Bob, and Alice to Ben. They move into adjacent semi-detached houses, but while Anna and Bob rent their house, Alice and Ben take out a mortgage to buy theirs (for, say, £243,500). Or, as we can reframe it, they rent the money to buy their house. For that is what renting means: you obtain the right to use an asset (a house or a sum of money), pay a monthly fee (the rent or the interest), and give it back to the owner at the end of the term.

Alice and Ben make capital repayments throughout the term, while Anna and Bob make identical payments in a savings account. Although the buyers start with an asset (the house) balanced by a liability (the loan), and the renters with neither, the two couples’ net wealth increases in very much the same way. Over time, Alice and Ben reduce their liability, and Anna and Bob build up an asset (their savings).

The day Alice and Ben make their last mortgage payment, Anna and Bob have accumulated exactly the amount of the loan in their savings account. But they are unlikely to experience having saved £243,500 as a milestone in the same way as their neighbours (and siblings). One house may be a clear, round number, but £243,500 is very much an arbitrary amount. If Anna and Bob continue to save (and there is no reason why they should suddenly stop at this amount), the specific point in time that Alice and Ben pay off their mortgage makes no difference to them. And neither does it for Alice and Ben. The monthly amount they used to repay the loan added exactly as much to their wealth as the same amount going into their savings account now the loan is paid off. There is no financial discontinuity for either.

We see such arbitrary symbolism in the financial markets too. A Google search for ‘Dow Jones 20000’ produces over 2 million hits. ‘Dow Jones 21000’ yields just 276,000 results, and ‘Dow Jones 21443’ a mere handful. And yet, there is nothing inherently relevant about round numbers, as this somewhat sarcastic tweet from Gerald Ashley indicates:

Clocks, cards and charities

That doesn’t mean symbolism does not affect us, though. A study by Eric Allen of the University of Southern California and colleagues looked at nearly 10 million marathon finishing times. You would expect these times pretty much to follow quite a smooth, normal-like distribution. Instead, the researchers found significant bunching just before round times (3 hours, 3.5 hours etc). For example, there were around 100,000 finishers in each of the minutes before the 3:58, 3:59, and 4:00 marks, compared to around just 70,000 finishers in the 4:00, 4:01, and 4:02 bins. This is no coincidence. When the authors looked at the proportion of runners speeding up in the last 2.195 km, they discovered that approximately 30% of runners increase their speed. However, that fraction increased to almost 40% for runners who were on target to finish at a round number.

This is an example of a so-called reference-dependent preference: it is because runners strongly prefer to finish with a time of 3:59:59 compared to a time of 4:00:01 that they notch up the pace. Such symbolic milestones are also used in loyalty schemes and by charities.

Hairdressers and coffee shops, among many others, often give their customers a card which is stamped with every purchase. The milestone to strive for is that of a completed card in order to obtain a discount or a free coffee or haircut. (This is not at all new, of course. I remember the colourful stamps our local grocer used to hand out every time we bought something, when I was little. I was sometimes allowed to help stick them in a little booklet which, when it was full, my mother then swapped for some money back.)

What is interesting is that our effort increases when the goal becomes more clearly within reach. The goal-gradient hypothesis is a concept linked to behaviourism, first formulated by Clark Hull, a psychologist at Yale University in 1932, when he discovered that rats ran faster when they were getting closer to the food used to reward them in experiments. Likewise, marathon runners turn out to accelerate when a ‘good’ time is within their grasp, and indeed donors are more likely to give (or give more) when a charitable goal appears within reach, as Cynthia Cryder from Washington University in St Louis and her colleagues found. They say this is partly because donors get a heightened sense of personal impact from their late-stage effort, more than from donations earlier in the campaign.

The fact that we seem to be more motivated as we get closer to a milestone is further supported by another intriguing observation, described in a study by Ran Kivets from Columbia University and colleagues. They set up a reward programme experiment at a café on the university campus, involving 108 customers in two conditions. The control condition was a conventional, “buy 10, get the 11thfree” arrangement, while the treatment condition required 12 stamps, but with two bonus stamps already on the card. In both cases, the customer needed 10 stamps to complete the card. However, there was a difference in behaviour: the customers with the conventional reward card took on average 15.6 days to complete their card, but those in the experimental 12-stamp group completed it in 12.7 days, nearly 20% faster. This phenomenon is known as illusionary goal progress: we believe we are closer to a milestone when we’ve already made some progress towards it.

Milestones are by and large symbolic. Their precise position is often arbitrary and almost always dependent on arbitrary measures (1093 yards, 1 foot and 10.06 inches is only a milestone if you express that distance as 1 kilometre). Yet they can be significant in providing focus and motivation — for others… or for ourselves.

Originally published at koenfucius.wordpress.com on May 10, 2018.

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