Comments on Discounting Grandchildren and Spotted Owls

Comments on Chris Robinson’s “Discounting Grandchildren
and Spotted Owls”

Sherman Hanna, Professor, The Ohio State University

Robinson summarizes discounting as a positive and normative process,
quickly dispensing with discounting for inflation, he focuses on discounting
for time preference and risk. He provides an example of discounting of
a future disaster that might take place 200 years in the future. The disaster
would, if it occurred, cause damages equal to one trillion Canadian dollars.
I will interpret this as U.S. dollars, since in the future a Canadian dollar
might go the way of the ruble. First of all, with a 5% discount rate, the
present value would be very low, and by the standard method, we would not
invest more today than the expected present value of the costs. If we were
not certain that the event would take place, the expected present value
would be even lower, thus limiting the amount we would be willing to spend
to prevent the possible disaster.

I agree that political structures around the world are not set up to
deal with uncertain distant disasters – for instance, if a large asteroid
hit the earth in 100 years, the results might be even more catastrophic.
What’s worse, it could happen next year. How much should we be willing
to spend on a Star Wars program to save the earth?


The Expected Utility Approach
There is a method in economics for accounting for such possibilities, assuming
that we give future generations some weight – expected utility models.
Let us consider a two period model. Should I be willing to make a sacrifice
today to protect against a small risk of a big loss? If I am risk neutral,
the answer would be NO unless the expected value of the loss were smaller
than the sacrifice today. However, if the risk included the possibility
of zero or very low consumption in the second period, the answer could
be YES, if my utility function were at least as risk averse as the natural
log utility function. Consider the following example:

Assume that income in period 1 = Y and income in period 2 will either
= 3*Y or zero.

Should you save any money out of your period 1 income if you face an
interest rate=0?

For instance, assume that your income in period 1 is $10,000, and that
there is a 99% chance that in period 2 your income will be $30,000, and
a 1% chance that you would have an income of zero. If your lifetime utility
= U(C1) + EU(C2) and U=Ln(C), then you should save $146 out of year 1 income,
so that your consumption in period 2 would either equal $30,146 or $146.
If, however, you had a relative risk aversion level of 6 and a constant
relative risk aversion utility function, then you would save $3,170 out
of your period 1 income, and your period 2 consumption would either equal
$33,170 or $3,170. If you have extremely high risk aversion, you might
save over 40% of your period 1 income to protect against the 1% chance
that your period 2 income will equal zero.

Therefore, a standard economic approach is available to analyze the
type of problem Robinson discusses. Of course, there is the question of
whether we will value future generations. If we do, however, the expected
utility approach can provide reasonable answers, if we frame the question
appropriately, just as a normative life cycle model can help us consider
how much to save for an uncertain old age. However, we should consider
several variations on Robinson’s examples:

a. Actions we should take to prevent truly irreversible changes that
may lead to disaster.

b. Actions we might take to prevent possible disasters, but for which
delay is possible, although possibly expensive.

I believe that Robinson poses the environmental issue in a way similar
to Pascal’s wager in Pensées

“If God does not exist, one will lose nothing by believing in him, while
if he does exist, one will lose everything by not believing.”

Just as Pascal’s argument is not a compelling argument for believing
in God, I do not think that posing an extreme scenario provides a compelling
argument for not discounting the future.  I did provide a simple example
of providing for the future even with no discounting.  But consider
an extension of my example.  A 25 year old is considering whether
or not to start saving for retirement.  Discounting the future may
be appropriate, to allow for the possibility that she may not be alive
at age 90, etc.  The real rate of return on investments is important,
as it will affect the optimal amount of savings at each age.  However,
delay in starting to save is not fatal, and may even be rational, if she
is confident that real earnings will increase.  For some environmental
issues, we face a similar concept.  We will be richer in the future
– I am confident of that, just as I am confident of the fact that humans
are better off today on the average than they were 100 years ago and 200
years ago.

Who should make the sacrifice today to make people have a better environment
100 years from now – Us?   Our children?  Our grandchildren? 
Our great-grandchildren?  This is a question that economics can help
provide an answer for, as it depends on projections of real per capita
growth, and technological progress.  If our children will be richer
than we are, then their sacrifice will be relatively less than our sacrifice
for a given investment.  If you asked whether the people of South
Korea should have made a particular sacrifice in 1960 or 1970 or 1995,
surely it is relevant that real per capita income increased almost tenfold
between 1960 and 1995.


Is Growth an Illusion?
Robinson implies that real growth is an illusion and that sustainable growth
is not possible. However, citing as evidence of this proposition a book
by the Erlichs is not very convincing to me, partly because of Paul Erlich’s
well publicized loss to the late Julian Simon about the price of raw materials:

In 1980, the year after the tenth Earth Day, Ehrlich and two associates
wagered with me about future prices of raw materials. We would assess the
trend in $1000 worth of copper, chrome, nickel, tin, and tungsten for ten
years. I would win if resources grew more abundant, and they would win
if resources became scarcer. At settling time in 1990, the year after the
twentieth Earth Week, they sent me a check for $576.07.

Simon also noted that:

In 1970 Paul Ehrlich wrote, “If I were a gambler, I would take even
money that England will not exist in the year 2000.”

In dismissing Ehrlich as a source, I do not mean to imply that we should
not worry about future environmental problems. However, if you want to
convince others, you should not only quote friendly sources, but quote
opposing sources and deal directly with the opposing arguments. The writings
of Julian Simon on the environment provide a good starting point. (See
the links at the bottom of this paper.)

More documentation is needed for the assertion that real growth is an
illusion. To convince me of that assertion, first you would have to convince
me not only that official statistics on national income and other social
indicators are flawed, but that some alternative system of accounting for
human welfare is more reliable. I have not seen anything that would convince
me that an alternative system is both valid and reliable. Therefore, I
am left with the belief that in the past 200 years there has been a general
trend toward improvements in the human condition, not only in terms of
real per capita income, but in terms of human health, life expectancy,
education, water quality, and air quality. The fact that gasoline is as
cheap as it has ever been does not help the cause of pessimism.

Therefore, what is left to be done in improving discounting to help the
environment? The answer is not to have a zero discount rate, but I agree
that a low social discount rate is appropriate. Defining appropriate social
utility functions would help deal with the problem of uncertainty and distant
costs. I think that part of the issue of counting the “votes” of future
generations is already underway. In the United States and I assume many
other countries, the children of finance professors are being indoctrinated
in the religion of the environment. Most people accept the concept of recycling,
even if they may need selfish incentives to get them to take action. However,
activists must go beyond “preaching to the choir” if they want to change
the method of analyses of future risks – they must directly analyze the
Appendix I: Do Only Capitalists Over-Discount the Environment?
Consider what was written 150 years ago:

The bourgeoisie, during its rule of scarce one hundred years, has created
more massive and more colossal productive forces than have all preceding
generations together. Subjection of nature’s forces to man, machinery,
application of chemistry to industry and agriculture, steam navigation,
railways, electric telegraphs, clearing of whole continents for cultivation,
canalization of rivers, whole populations conjured out of the ground –
what earlier century had even a presentiment that such productive forces
slumbered in the lap of social labor?

Karl Marx and Frederick Engels, Manifesto of the Communist Party, 1848

It is not only capitalistic economists and finance professors who might
not value nature highly enough — obviously most who have followed Marxist
thought in the past 150 years believed that capitalism was capable of tremendous
economic growth, and just as obviously, some communist countries went further
than free enterprise countries in degrading the environment.  Therefore,
I would suggest that the villain is not necessarily the discounting method
used in finance.


Appendix II: Related links

Sierra Club


Resources for the Future


Cato Institute

Brief overview by Julian Simon

Simon’s views on Human Progress


Simon’s views on conservation and inducing guilt about ‘waste’

Simon: The amazing theory of raw-material scarcity:


Simon’s views on why resource forecasts are so often wrong:


Simon’s proposals on analyzing altruism, binding commitments, etc.


Simon’s views on Earth Day after 20 years:


Manifesto of the Communist Party, 1848