By Mark Buchanan
July 28 (Bloomberg) -- What is the value of time? This
question was once a matter for philosophers such as Plato or
Aristotle. Today economists claim to know the answer. The
future, they say, is “discounted” because the value of having
something or some amount of cash is greater than the value of
having that same thing or amount of money a year from now.
How much so? Well, if you can put $96 today into an
investment earning 4 percent interest, it will be worth almost
$100 in a year. So $100 a year from now is worth only $96 today.
This way of thinking about future assets can make a big
difference if we look at things more complicated than cash,
especially if we try to assess their value many, many years into
the future.
Pretend, for example, that we want to see if it is worth
creating a costly marine sanctuary that could take many years to
establish and even longer to effectively protect a population of
endangered salmon or cod. The costs of the sanctuary come mainly
in the first years -- the expense of setting it up and policing
it, as well as perhaps millions of dollars a year in lost
fishing revenue. The most important benefits, on the other hand,
may come in the distant future. Even if the fish population
might increase 100-fold, creating a sustainable fishing industry
500 years from now that is far more valuable than today’s,
economists would discount the advantages coming in those distant
years almost to nothing.
Discounting 4 percent for 500 years in a row means dividing
the future value by a number close to 500 million. So those
future benefits contribute virtually zero in the calculation to
determine if eventual benefits justify the upfront costs.

Calculating a Payoff

This so-called exponential discounting -- reducing the value
of something by a fixed percentage for each unit of time -- is
standard practice in economics. It comes into play whenever
people consider investing for long-term payoff, whether by
building railroads for high-speed trains or reining in carbon
emissions to preserve the climate. And it discounts the distant
future especially drastically. This is why economists and others
often squabble over the right annual percentage to use -- should
it be 5 percent, 7 percent, 1 percent? Change this a little, and
values change a lot.
Some economists and philosophers have even argued that in
cases of environmental preservation 0 percent is the only
ethically defensible number. That is, no discounting at all. But
this debate over percentages may actually be a distraction from
a more serious problem with the formulas used in discounting.
That’s the message of a recent paper written jointly by John
Geanakoplos, an economist at Yale University, and Doyne Farmer,
a physicist at the Santa Fe Institute, in New Mexico. They argue
that economic discounting as currently practiced is logically
incorrect and, as a result, the cost/benefit analyses done by
such authorities as the International Panel on Climate Change
and the U.S. Environmental Protection Agency may drastically
undervalue the future.
Economists like exponential discounting because it seems
“rational”; in particular, it discounts equal periods of time
equally. The standard analysis also assumes that the discount
rate remains constant. That assumption is rather peculiar,
Geanakoplos and Farmer point out, given that interest rates
bounce up and down all the time -- and the interest rate at any
moment should be closely linked to the discount rate, to reflect
how cash investments gain value through time.
Revising the assumption of a never-changing discount rate
leads to results totally at odds with current economic practice,
Geanakoplos and Farmer have shown. To understand their argument,
consider the next half-century. Year by year, the true discount
rate (which no one knows precisely) will probably fluctuate in
some complicated way, following one of many possible up-and-down
paths. Since we don’t know the future, to determine the
effective discount rate for the 50-year period, we should
average over all possibilities.

Counting the Paths

That’s simple enough, but here is where things get
interesting: In calculating this average, some paths turn out to
contribute far more than others. In particular, paths that
descend into relatively low rates and stay there for many years
have a disproportionate effect -- a path at 1 percent for 50
years, for instance, counts 20 times as much as a path running
along at 7 percent. Change 50 to 500 years, and the difference
becomes 10 trillion times.
This demonstrates how simple thinking about the future can
lead to terrific mistakes. When something fluctuates, we often
suppose we can use the average rate over time. And sometimes
this works. The amount of food you will eat over 20 years, for
example, will be roughly equal to 20 times what you ate last
year, because your appetite doesn’t fluctuate that much. But
averaging to get a true effective discount rate isn’t so easy.
Some of the paths of fluctuation -- the lower paths -- carry
extraordinary weight, and hence dominate the outcome.
Not surprisingly, Geanakoplos and Farmer find that the
correct formulas for discounting over long periods don’t follow
the textbook exponential form. The math is tricky (I’ve put some
discussion of the technical stuff on my blog. But the
consequences are not. Using a standard model from finance for
interest rate movements (with an average rate of 4 percent), the
authors show that, for the first 100 years or so, their correct
form of discounting gives results that are similar to those that
come from traditional calculations. But at 500 years the
standard exponential discounts the future not just a little too
strongly, but a million times too strongly. And it gets worse
after that.
Going back to the example of the marine sanctuary, and using
the Geanakoplos-Farmer formula, you find that the present value
of benefits 500 years from now gets multiplied millions of times
compared with the standard analysis. A thriving marine ecosystem
in the future, linked with a much larger fishing industry, might
well be worth investing in today.
In effect, today’s standard economic methods make the
distant future count for almost nothing. And those who always
thought this seemed hopelessly naïve turn out to be right.
The important point, Geanakoplos and Farmer emphasize, is
that everything about discounting depends on what assumptions
you make about how variables fluctuate with time. A fixed
interest rate doesn’t work. And neither does the strong
exponential discounting to which it leads -- even though most
economists continue to use it.
This is a prime example of what John Maynard Keynes meant
when he said the ideas of economists “are more powerful than is
commonly understood.” Economists calculating the value of the
future to perform cost-benefit analyses that influence how we
take care of our world have been making some astronomically
large mistakes.

(Mark Buchanan, a theoretical physicist and the author of
“The Social Atom,” is a Bloomberg View columnist. The opinions
expressed are his own.)