Time Discounting

Time Discounting

“Time discounting” is the term used to describe the human tendency to discount future costs and benefits. It makes economic sense; a cost paid in a year is not the same as a cost paid today, because that money could be invested and earn interest during the year. Similarly, a benefit accrued in a year is worth less than a benefit accrued today.

Way back in 1937, economist Paul Samuelson proposed a discounted-utility model to explain this all. Basically, something is worth more today than it is in the future. It’s worth more to you to have a house today than it is to get it in ten years, because you’ll have ten more years’ enjoyment of the house. Money is worth more today than it is years from now; that’s why a bank is willing to pay you to store it with them.

The discounted utility model assumes that things are discounted according to some rate. There’s a mathematical formula for calculating which is worth more–$100 today or $120 in twelve months–based on interest rates. Today, for example, the discount rate is 6.25%, meaning that $100 today is worth the same as $106.25 in twelve months. But of course, people are much more complicated than that.

There is, for example, a magnitude effect: smaller amounts are discounted more than larger ones. In one experiment, 51 subjects were asked to choose between an amount of money today or a greater amount in a year. The results would make any banker shake his head in wonder. People didn’t care whether they received $15 today or $60 in twelve months. At the same time, they were indifferent to receiving $250 today or $350 in twelve months, and $3,000 today or $4,000 in twelve months. If you do the math, that implies a discount rate of 139%, 34%, and 29%–all held simultaneously by subjects, depending on the initial dollar amount.

This holds true for losses as well,52 although gains are discounted more than losses. In other words, someone might be indifferent to $250 today or $350 in twelve months, but would much prefer a $250 penalty today to a $350 penalty in twelve months. Notice how time discounting interacts with prospect theory here.

Also, preferences between different delayed rewards can flip, depending on the time between the decision and the two rewards. Someone might prefer $100 today to $110 tomorrow, but also prefer $110 in 31 days to $100 in thirty days.

Framing effects show up in time discounting, too. You can frame something either as an acceleration or a delay from a base reference point, and that makes a big difference. In one experiment,53 subjects who expected to receive a VCR in twelve months would pay an average of $54 to receive it immediately, but subjects who expected to receive the VCR immediately demanded an average $126 discount to delay receipt for a year. This holds true for losses as well: people demand more to expedite payments than they would pay to delay them.54

Reading through the literature, it sometimes seems that discounted utility theory is full of nuances, complications, and contradictions. Time discounting is more pronounced in young people, people who are in emotional states–fear is certainly an example of this–and people who are distracted. But clearly there is some mental discounting going on; it’s just not anywhere near linear, and not easily formularized.