Should We Take Everything from the Old to Give to the Young?

The strange implications of social discount rates

The social discount rate is the constant governing how we should treat present and future consumption as a society. If it is 0%, we would be indifferent between consumption now and consumption later; if it is higher, then we would require more and more future consumption to counterbalance foregone consumption in the present day. This is of extreme importance for problems like climate change; in order to mitigate future damages, we need to regulate emissions at the cost of present consumption.

The market interest rate is the rate at which we personally discount our consumption. We are willing to invest if and only if it pays above a certain rate – say, 6%. We can decompose the interest rate r into the few components – the pure rate of time preference delta, plus our coefficient of relative risk aversion eta times expected future growth g. A good rule of thumb is that each of these is equal to around 2. (You can see Martin Weitzman’s review of the Stern report for more on this). The social discount rate can also be decomposed into these components, but we would generally say that society should be risk neutral, or have a coefficient of relative risk aversion of 0. Let’s save arguments over how risk-averse society should be for later.

Many people have made arguments that the social discount rate should be lower than the market interest rate. People are free to discount their own consumption at a higher rate, but this should not affect how our society should view the future. They won’t live to see it, so their selfishness shouldn’t be allowed to harm future generations. Such arguments run into a pretty serious problem though, as Maya Eden argues in the article “Some Cross-Sectional Implications of the Social Discount Rate”. Specifically, if we have a market interest rate of 6%, and a social discount rate of 1.5%, we would be fine with taking one dollar from a 70 year old to give a bit more than ten cents to a 20 year old.

The logic behind this is to realize that every transfer across people can also be thought of as a transfer across time. The social discount rate governs how much we care about consumption that occurs in different time periods, while the interest rate governs how much we care about our own consumption. Suppose the social discount rate is 0. We would be indifferent between a dollar to a 20 year old today, and a dollar to a 20 year old in 2045. However, the 20 year old would not be indifferent – they would benefit more from having had that dollar earlier in their life. Thus, it would greatly increase utility by transferring a dollar from an older person to a younger person, bounded only by people not being able to consume before they are alive. The cause of this is the difference between market and social discount rate. If they were the same, then we have no reason to do these transfers.

If this is so, it makes it very difficult to support our present governmental priorities. The primary activity of the government is transferring from young people to old people. Medicare and Social Security account for 35% of the budget, and the elderly are often the benefits of other programs as well. At the same time, we support action against climate change, which is something that is made cost effective largely if we value future consumption at a rate lower than the rate we would accept for delaying our own future consumption. Again, Weitzman’s review (cited earlier) is an extremely clear overview of the math; the numbers have changed (for better!) since, but the direction has not.

What I am unconvinced of are the origins of our consumption discounting. Why is it that we care about future consumption less? I think the reasons why do not speak positively of us, and are also not representative of the underlying construct.

First, I think it isn’t clear that we are an “agent”. We are, rather, numerous people, which we like, but not as much as we like ourselves now. When we behave irresponsibly now, we are in some sense harming someone who isn’t us. We are not the same person as we were in the past. We do care, a bit, but imperfectly. Thus, society can and should force us to save more and behave more the benefit of our future selves, and a higher market interest rate is a sign of nothing more than selfishness.

Second, I think the premium we pay for delaying our consumption is a function both of our pure time preference, but other things besides. I think we should get into how we measure time preferences. The paper “Measuring Time Preferences” was of great help in writing this, for obvious reasons. The simplest way is just to get people in a laboratory, and see how much people need to delay receiving money or treats or similar.

It’s not clear, however, that preferences for money now represent anything other than credit constraints. Suppose that people have decreasing marginal utility of money in each time period – they obviously prefer more money to less, but with a discount rate of 0 they optimize their consumption by consuming the same amount in each period. If someone expects to receive a payout in the future, they will borrow against it to smooth their consumption. If they cannot fully borrow, then they trade off between present and future consumption at a discounted rate – but this doesn’t represent anything deep about their preferences. Worse, we don’t know how close or far we are from the true parameter. Studies just assume that consumption is hand to mouth, which might be a reasonable assumption if it’s the literal marshmallow experiment, but probably isn’t otherwise.

We should also note that the real interest rate equation given earlier – r = delta + eta*g – is actually abstracting away from the risk of not ever receiving the money. Let’s grant that the US government is not going to default, though the probability it might surely exists. We still have to account for the possibility that someone will die, or become less able to enjoy money as they are getting older. This risk is asymmetric, and so our personal discount rate isn’t saying anything about how much we care about consumption over time per se.

Alternatively, we can infer discount rates from purchasing behavior. People buy durable goods in order to receive a flow of future benefits, and people can purchase more efficient goods at higher cost now, in order to save on future expenses. The original study with this approach is Hausman (1979), who studied air conditioning units; similar work has been done on automobiles and fuel-efficiency, as in Busse, Zettelmeyer, and Knittel (2013).

In any case, we probably can’t speak of people having “a” discount rate – it’s context dependent. Thus, I think we can be safe having a low social discount rate, because the “real” real interest rate is considerably lower than it appears.