# Time Preference Puzzles

Last week I saw Charles Courtemanche present an interesting paper about how people react to changes in food prices. Turns out the impatient people and those who might have trouble with commitment (to diets for example) are quicker to buy more food when the prices drop. The paper had some issues so I wouldn’t immediately go betting the farm on the results, but it used some measures of how people think about time that got me thinking.

The National Longitudinal Survey of Youth (1979 cohort) interviewed individuals age 14-22 in 1979 and continued to interview them every year until 1994 and every two years after that. It includes great data on schooling, employment, income, fertility, marriage, and cognitive skills. In 2006, they added two particularly interesting questions. First, they asked about trade-offs between getting money today versus one year later:

Suppose you have won a prize of $1000, which you can claim immediately. How- ever, you have the alternative of waiting one year to claim the prize. If you do wait, you will receive more than$1000. What is the smallest amount of money in addition to the $1000 you would have to receive one year from now to convince you to wait rather than claim the prize now? Based on this question, it’s easy to compute an annual discount rate; i.e., how much an individual values the present over the past. If someone says they would be indifferent between$1000 today and $1100 a year from now, then their discount rate would be 1100/1000, or about 0.91. That is, a dollar today is only worth 91 cents a year from now. In Courtemanche’s paper, they report that the average discount factor of respondents based on the first question is 0.59. That is, on average, people report indifference between$1000 today and $1684 a year from now. This is far far lower than any revealed preference measure I’ve ever seen. For example, in Keane and Wolpin’s classic 1997 paper, they estimate that the discount factor is 0.9367, based on career choices of young men in the same data set. Rust and Phelan’s 1997 paper reports an estimate of the discount factor of 0.98 based on retirement decisions of low income older men in another data set. And then there’s the fact that if people really did discount the future at a really high rate, why would they ever invest their money in assets that return 5-10%? Strange. It turns out people sometimes report different annual discount rates depending on how long they have to wait–that is, they are inconsistent about how much they discount the future. You can get at the extent of this inconsistency by looking at answers to a second (very similar) question that was added to the NLSY in 2006: Suppose you have won a prize of$1000, which you can claim immediately. How- ever, you can choose to wait one month to claim the prize. If you do wait, you will receive more than $1000. What is the smallest amount of money in addition to the$1000 you would have to receive one month from now to convince you to wait rather than claim the prize now?

You could compute an annual discount rate from this question too, and for many (most?) people it will be lower, because we think that people are “present-biased.” That is, as soon as they have to wait at all, there is a penalty. The average discount rate in the data based on this question is indeed lower: 0.28. Quasi-hyperbolic discounting formalizes the idea of present bias by saying that individuals discount future payments that are t periods away by β δt where β is the measure of present bias and δ is the “pure” measure of time preference.

The average estimates reported in the Courtemanche paper are 0.80 for β and 0.75 for δ. I don’t have much intuition for what these numbers should be, but Fang and Sliverman’s 2009 paper (published in International Economic Review) uses the NLSY 1979 to estimate them based on labor supply and welfare take-up decisions of single mothers. They get a very different number for β (0.34) and a kind of close one for δ (0.88). You can look at the glass as half-empty or half-full.

Personally, I find this inconsistency in estimates of people’s time inconsistency somewhat disturbing. It makes me wonder what would happen if the NLSY added a third question where the time people had to wait was even shorter. Like a day instead of month. This would give us another estimate of β. If it was very close to 0.28, I’d feel better about the theory of hyperbolic discounting. Perhaps these experiments have already been done in the lab? We’ve now reached the limits of my knowledge of this area.