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 ON DISCOUNT RATES IN THE COST-BENEFIT ANALYSIS OF CLIMATE CHANGE
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                    Edmund Tweedy Flanigan
                            2011

[I am grateful to Patrick Connolly, Simon Feldman, and especially to
John Broome  and  David Miller for comments on  an  earlier draft of
this paper. A version of  this paper made  up Chapter  4  of my 2011
M.Phil. thesis (Department of Politics, University of Oxford).]

## Introduction

There  has  been much  discussion  lately  about the  selection  of
an  appropriate  discount  rate  in the  cost-benefit  analysis  of
climate  change. This  is the  rate at  which the  value of  future
stuff - commodities, harms, benefits - is weighed against the value
of present stuff.   To  'discount'  in cost-benefit  analysis is to
select a  positive discount  rate, thereby devaluing  future stuff.
A  number  of  factors  determine what  rate  is  appropriate,  and
theorizing about these factors has led eminent economists to select
very  different discount  rates  for the  cost-benefit analysis  of
climate change. This  seemingly small matter is  of great practical
importance. Nicholas Stern and  William Nordhaus are two economists
who make sharply divergent recommendations  for action based on the
results  of  their  respective  analyses;  the  divergence  is  due
primarily to differences in the discount rate used.[1]

Philosophers  appear  to  stand  largely against  the  practice  of
discounting,  which  is  also  called   'discounting  the  future.'
They oppose  it on  ethical grounds. Different  philosophers oppose
the practice in different ways. Most commonly, philosophers tend to
oppose the incorporation of what  is called a 'pure  time  discount
rate' or   a  'rate of   pure  time  preference' into  the  overall
discount rate. This  is discounting future stuff  simply because it
comes in the future.

I  stand with  most philosophers  in  thinking the  practice to  be
misguided, at  least as it  is commonly construed.  Nevertheless, I
also think that philosophers and economists are, as John Broome has
said, in important respects talking at cross-purposes on the matter
(see Broome 1992, 1994). Discounting  is not quite so objectionable
as writing  by philosophers may make  it seem. I think  much of the
disagreement  arises  from differing  views  about  the purpose  of
cost-benefit analysis.

I will argue  here for that claim. I begin  by giving a preliminary
account of what I take to  be the purpose of cost-benefit analysis.
This is, perhaps surprisingly,  quite difficult to do. Cost-benefit
analysis is ultimately a way of weighing harms and benefits,[2] but
it's  hard to  specify exactly  what  counts  as a  harm  and  what
counts as  a benefit in a  way that is both  precise and consistent
with  economic  practice. Since  cost-benefit  analysis  is not  my
primary  subject here,  I  give a  loose  characterization. I  also
introduce the idea of an analysis-given reason, which is the reason
for action produced by a cost-benefit analysis. How forcefully that
reason counts in  favor of a plan of action  depends on two things:
(1) whether the analysis  accurately evaluates and aggregates harms
and benefits,  and (2) whether  the conception of harm  and benefit
adopted  by the  analysis captures  enough  of the  goods and  bads
associated with the plan being  considered (or maybe just enough of
the important ones).

Discounting is  done with respect to  time. There are at  least two
very good  reasons for discounting; these  have to do with  the way
that economists use  prices to approximate the values  of harms and
benefits. I  describe these  reasons. Next,  I describe  some other
reasons that are commonly given  for discounting. These reasons are
ethical and  political ones, and they  have nothing to do  with the
price  evaluation method  that supports  the first  two discounting
practices. They  have to  do with the  force of  the analysis-given
reason. I suggest that these should be considered separately.

This  sets  up  my  discussion of 'pure time discounting.' I review
an argument recently given for the practice by the economist Martin
Weitzman. While the motivation for  the argument seems to come from
the  method of  economic cost-benefit  analysis, its  justification
appears to  be moral or  political. I  consider the merits  of this
justification.

This  leads  me to  turn,  finally,  to  one political  reason  for
discounting  that  I think  is  especially  important. It  has  not
received  enough  attention.  The  reason is  that  nations,  whose
responsibility  it  is  to   enact  climate  policy,  have  special
obligations to their citizens. These special obligations may extend
to future citizens. As such,  I'll consider  some arguments for and
against  including  future  citizens  among those  people  to  whom
nations owe special obligations.

One further  point before beginning.  There is  quite a lot  to say
about discounting, and I will not  attempt to say anywhere near all
of it. Some of  what will go unsaid here is  of great importance to
the economic analysis of climate change.  A few of these issues are
(a)  hyperbolic  and  gamma discounting,[3]  (b)  implausibly  high
implied  savings  rates  of  low discount  rates,[4]  and  (c)  the
appropriate formalization of discounting formulas.[5] These matters
are, in my view, better left  to economists, who have the expertise
necessary to  really address them.  I don't  think my  omission  of
them here will have any adverse effects on the arguments I offer.

## Cost-Benefit Analysis

The conventional view of cost-benefit analysis is that it is a tool
to assess  the value of  a possible plan  of action (see  Dreze and
Stern 1987, Broome 2000).[6] When a  person, or a group of persons,
wants to know whether to undertake  some plan, one way of beginning
to answer that question is to ask how good or bad the plan is. That
is, we can  evaluate the plan. Oftentimes a plan  will have various
bad consequences associated  with it; call these harms. If  it is a
plan  we  are seriously  considering,  it  probably has  some  good
consequences  associated  with it  as  well;  call these  benefits.
Cost-benefit  analysis  is  the  adding  up  and   weighing  -  the
aggregation  -  of the harms and benefits of a plan of  action as a
method of evaluating it.[7]

Why do we  want to assess the value  of a plan of action?  We do so
because if the plan is a good one, in the sense that it will result
in more benefits than  harms, it may be that it  is one that should
be undertaken.  If, on balance, a  plan will result in  a net harm,
this  fact may  be  said to  count  against the  plan;  and if,  by
contrast,  the  plan  will  result  in a  net  benefit,  this  fact
may  be  said to  count  in  the  plan's  favor. In   this   sense,
cost-benefit analysis  aims at  producing a practical  reason. Call
the reason generated by the  cost-benefit analysis of some plan the
analysis-given reason for or against that plan.

The analysis-given reason is a  derivative reason. It is derivative
of some of the reasons linked to  the harms and benefits of a plan.
Each benefit  counts in favor  of a plan and  is thus a  reason for
undertaking the plan; and conversely,  each harm counts against the
plan and is  thus a reason not to undertake  the plan. The weighing
of these harms and benefits in  the analysis is also an aggregation
of reasons associated with each.  But the analysis-given reason may
not  be derivative  of  all the  reasons linked  to  the harms  and
benefits associated  with a  plan; indeed  it is  typically not.[8]
How  large  the  slice  of  reasons is  that  is  captured  by  the
analysis-given reason depends on how  ambitious the analysis is and
how good its methods are. This  may seem opaque. What I mean should
become clearer shortly.

Whether  the  analysis-given  reason  produced  by  a  cost-benefit
analysis counts  strongly in favor  of or against the  plan depends
mostly on two factors. The first  is how accurate the evaluation of
the harms  and benefits of a  plan is. This depends  on whether the
estimates  made by  the  analysis of  the value  of  each harm  and
benefit reflect the true values of those harms and benefits (Broome
2000, p. 954).  Because of this,  a cost-benefit analysis  needs  a
theory of value.  The second factor is how  well the analysis-given
reason captures the entire set of  reasons for or against the plan.
If  it  captures  only  a  small slice  of  those  reasons,  or  if
the  reasons it  does  capture are  unimportant  reasons, then  the
analysis-given  reason may  not do  much to  guide us  practically.
Because of this,  a cost-benefit analysis needs to have  an idea of
the set of reasons it aims to capture.

This  second  factor is  of  special  importance. It  is  important
because what  reasons are  captured by  a cost-benefit  analysis is
determined  at least  in  part  by the  specification  of harm  and
benefit that  it employs; that is,  by which of the  bads and goods
associated  with  a  plan  are aggregated  by  the  analysis.  This
specification is  constrained in two directions.  It is constrained
first by the  ambitions of the analysis.  The cost-benefit analysis
of climate  change is particularly  ambitious. Judging at  least by
the  analyses of  the Stern  Review (2007)  and the  Garnaut Report
(2008), the cost-benefit analysis of climate change aims to provide
a strong analysis-given reason for action. It thus needs to adopt a
fairly wide specification of what  counts as harms and benefits, so
that it can  account for harms to the  environment, harms resulting
from premature deaths, and so on.

The  specification  is  constrained   second  by  the  demands  and
possibilities of  its methods. Economic cost-benefit  analysis uses
the market price  method of evaluation (see  Broome 1994, p.  133).
This  method uses  market prices - or  estimated market  prices for
stuff that is not traded-to value harms and benefits.   Because the
price of  a  benefit is a ranking of that benefit's value to people
compared  to other  benefits, the  price  that people  pay (or  are
willing to pay) to avoid a harm  or receive a benefit does not give
a value to  that harm or benefit that is  independent of the values
of other harms and benefits. Cost-benefit analyses using the market
price method of evaluation are thus  committed to the full range of
specifications of  harm and benefit associated  with market prices,
and they may  be committed to not weighing harms  and benefits that
cannot be priced.

For  a  cost-benefit  analysis  as ambitious  as  the  cost-benefit
analysis  of  climate  change,   this  makes  things  very  tricky.
When  weighing the  harms  and benefits  associated with  premature
deaths and  population change,  for instance,  the theory  of value
underpinning the analysis  needs to be more  explicitly worked out.
This is  because we need  to know how  bad it is  if a life  is cut
short, and  whether it is good  or bad if certain  people come into
existence rather than  others. In an ambitious analysis  it is also
more difficult to  see how strong the analysis-given  reason is for
action, since  it is  more difficult  to tell  what portion  of the
reasons for  or against the  proposed plan of action  the evaluated
harms  and  benefits capture.  For  instance,  it  is hard  to  say
whether  the prices  it assigns  to certain  benefits (such  as the
non-destruction of certain species) reflect attitudes about matters
of  justice.  If  so,  we  need to  know  whether  those  attitudes
are  correct. If  not, matters  of  justice need  to be  considered
exogenously  when evaluating  the  strength  of the  analysis-given
reason.

## Value in the Future

Cost-benefit  analysis  weighs  harms  and benefits  that  come  at
different times.  Most such  analyses, as practiced  by economists,
adopt a rate of discount. As I  have said, using a discount rate is
a way of  counting future harms and benefits for  less than similar
harms and benefits in the present.

This should seem surprising. Harms  and benefits are differences in
goodness. But whether something is  good, or bad, seems independent
of timing. A harm is no less a  harm if it takes place now, at some
time in  the future,  or at some  time in the  past. Call  this the
time-insensitivity  of harms.  Benefits,  too,  are insensitive  to
timing  in  this  way.  Similarly,  we could  say  that  harms  and
benefits are subject-insensitive and location-insensitive. They are
subject-insensitive because  a harm  is just as  bad no  matter who
endures it, just  as a benefit is  just as good. A harm  is just as
bad for me as  it is for you; and as to the  kind of harms that can
be endured by  both humans and other animals, those  harms are just
as bad no matter whether they are  endured by a human or an animal,
a  person  or  a  non-person.[9]  The  argument  is  the  same  for
location-insensitivity. How bad  or good a harm or  benefit is does
not  depend on  where  it  is endured  or  received.  I take  these
features to be part of the meaning of harm and benefit.

There is thus a moral  presumption against discounting. How can the
practice be  justified? I will now  very briefly survey two  of the
ways in  which it  can be, since  it is important  to get  clear on
exactly what the  justification is in these cases.  These two cases
represent  extremely  common  practices  in  economic  cost-benefit
analyses.

### Discounting Prices

Discounting can  be justified when  it is applied to  certain harms
and benefits  within the  market price  method of  evaluation. This
method is, as  John Broome and Joseph Stiglitz have  said, a way of
using  "reasonable shortcuts" to  approximate  the  aggregation  of
harms and benefits I described  above (Broome 1994, Stiglitz 1983).
The  central  feature  of  this  method  is  that  it  uses  market
prices  -  a 'money  metric'  -  to give  a value ranking  of harms
and benefits. The  prices, however, are not prices  of benefits but
rather prices  of commodities  that count  as benefits.  Because of
certain facts about economies (namely,  the growth of economies and
the difference in the value of money at different times), prices at
different  times  need  to  be  adjusted if  they  are  to  form  a
reasonable  basis for  accurate comparisons  of value.  A commodity
with some price X  in the present may not have the  same value as a
commodity priced at X in the past or the future.

Consider a  simple example,  which  I've taken  from Broome (1994).
Suppose that  the price  of a bottle  of wine is  $5. With  $100, I
could buy twenty bottles of  wine. Alternatively, I could save that
money and earn interest on it.  Say the interest rate for saving is
10% and the price of wine a year from now rises to $5.25. By saving
the  money and  earning interest  on  it (bringing  my holdings  to
$110), I could buy twenty-one bottles a year from now. The interest
rate of the  wine is 5%, which is reflected  in its price increase.
Call the  wine I can buy  now present wine  and the wine I  can buy
next year  future wine. Present  wine and  future wine have  both a
present and  future price. If I  want to compare their  value using
the market  price method  of evaluation,  I need  to choose  a time
index. Presently,  I can  buy twenty bottles  of present  wine. How
much future wine can I buy now? Twenty-one bottles. That is because
future  wine is  worth five  percent less  in present  prices. This
example  can be  generalized,  since most  commodities behave  this
way.[10] The present prices of  future commodities are usually less
than the present  prices of present commodities.  This represents a
justified reason for discounting the value of future commodities.

Another justified  reason for  discounting within the  market price
evaluation  method is  because of  the law  of decreasing  marginal
value.   Many commodities  are  less valuable  to  people  'at  the
margin'.  In other  words, the value to a person  of  an additional
unit of some commodity depends on  how many units of that commodity
the person  already has: the more  of it had, the  less valuable an
additional  unit. My  tenth orange  is less  of a  benefit than  my
second;  a restauranteur's ten thousandth dollar less of  a benefit
than her first;   a family's fourth home bathroom less of a benefit
than its  second; and so on.  Additional stuff counts as  less of a
benefit to those  who have more stuff to begin  with. (The converse
is true  as well. A  family losing one  of its four  home bathrooms
counts as  less of a harm  than a family losing  its only bathroom,
etc.) Since economies grow, people in the future will be better off
in the sense that they will have more commodities. Many benefits to
them  will  thus  be  less  valuable.  In  general,  then,  we  can
justifiably discount  the value of  stuff that will be  received by
people in the  future as long as those people  will have more stuff
to begin with.

The thing that's  important about  these reasons for discounting is
that  they're  methods  of correcting  the price of  commodities at
different  times so  as  to reflect  the fact  that  the harms  and
benefits brought  about by them count  for the same no  matter when
they're endured or received.  This supports the  time-insensitivity
of harms  and benefits. There  can thus be reasons  for discounting
within the market  price method of evaluation that  are not reasons
for discounting  generally.[11] That is,  there can be  reasons for
discounting price  valuations that are not  reasons for discounting
harms and benefits.

### Discounting Harms and Benefits

Neither   of   the   immediately   preceding   justifications   for
discounting,  then, justify  discounting harms  and benefits.  They
justify discounting prices. Are there other reasons for discounting
harms and benefits?  Some have been proposed. I'll discuss three of
these now.

#### Risk and Uncertainty

The further into the  future we look, the less likely  we are to be
correct about what benefits will or  will not come about. There are
lots  of factors  that may  prevent the  realization of  a benefit.
Storms might cause delays in construction  that raise the cost of a
construction project.  Natural disasters may have  similar but much
more  severe  effects.  In  the cost-benefit  analysis  of  climate
change, we need  to account for the possibility  that humanity will
not survive far into the future.  In all of these cases, unforeseen
events  prevent the  realization  of  a benefit,  so  in adding  up
expected  future  benefits, we  might  discount  them due  to  this
uncertainty. The same goes, mutatis mutandis, for harms.

I  can think  of just  one justification  for discounting  expected
future harms and benefits in  this way. This justification requires
us to assume that the likelihood of each (of every) future harm and
benefit  occurring decreases  uniformly with  time. If  an expected
benefit  has an  85% chance  of  occurring  at time  t1  and  a 65%
chance of  occurring at time t2,  then  they  should not  be valued
equally; a good  cost-benefit analysis should take  account of this
difference. Thus,  the appropriate  rate of  discount for  risk and
uncertainty  would be  the  rate  according to  time  at which  the
expectancy of each future harm and benefit decreases.

But  of course  there is  no single  rate at  which the  expectancy
of  future  harms and  benefits  decreases.  Different events,  and
therefore different expected harms and  benefits, are more and less
likely  to  occur  in  the  future, and  the  rate  at  which  that
likelihood changes with time is similarly differential.

Consider:  If  a  benefit  occasions every 'heads'  in  a series of
coin  tosses extending  into  the future,  the  likelihood of  that
benefit occurring remains 50% as far  into the future as the series
of coin tosses  does. This is a very different  kind of uncertainty
from  the kind  that  accounts  for harms  due  to certain  natural
disasters that  are, let's  say,  50% likely  to occur  every  four
years. To discount both of  these kinds of uncertainty according to
a single rate would be to commit a serious error.

Moreover, economists have  a mechanism for accounting  for risk and
uncertainty  that  is  a  much  finer  implement  than  a  discount
rate.  It is  called expected  utility theory,[12]  and it  weights
individual future harms and  benefits according to their likelihood
of  occurring.  It works,  more  or  less,  like this.  Instead  of
aggregating future harms and benefits,  which there is an epistemic
barrier to doing accurately, in practice what we do is to aggregate
expected harms and benefits. If Plan A has a 90% chance of bringing
about some  benefit and Plan B  has a 95% chance  of bringing about
the same benefit, then Plan B  has a greater expected benefit. That
fact ought to  count in favor of Plan B  in a cost-benefit analysis
comparing the  two. Expected utility  theory is the right  tool for
this job; a discount rate is not.[13]

#### Future People Will Be Better Off

I mentioned  just above  that one good  reason for  discounting the
future  within the  market price  method of  evaluation is  that if
future people will have more  stuff, additional stuff that comes to
these people will  count as less of  a benefit. This is  due to the
law of  decreasing marginal  value. But  there is  another argument
that says  harms and benefits  themselves count for less  to people
who  are better  off. This  argument is  similar but  distinct, and
worth considering on its own.

It  is  widely held  that  it  is  either  usually or  always  more
important to  benefit people who  are worse off. Conversely,  it is
widely held that  it is either usually or always  more important to
avoid harming people  who are worse off. John  Rawls held something
like this  view; prioritarians certainly  hold this view;  and most
egalitarians presumably  hold this  view, if only  derivatively. We
might think that,  if we hold this view, and  if future people will
be  better  off,  we  have  reason to  discount  future  harms  and
benefits.

This is a good argument, but  some care is warranted here. There is
an ambiguity  when  we  speak  of  harms being  'worse' or benefits
being   'better'  under   certain   circumstances  or  for  certain
people. Take a harm, such as the infliction of some amount of pain,
and consider  it as befalling two  people: a poor child  and a rich
adult. In one sense,  we could say that the harm  to the poor child
is worse than the harm to  the poor adult, either because the child
is a child  (and harms to children are worse),  because she is poor
(and  harms to  the  poor are  worse), or  both.  But each  endures
the  same  amount  of  pain,  so  in  another  sense  the  harm  is
just  as bad  for each.  When  I say  that harms  and benefits  are
subject-insensitive, I mean that in this latter way. Another way of
formulating this would be to say that  a harm or a benefit qua harm
or benefit is just as bad or good no matter who endures it.

To avoid this ambiguity,  I will say that a harm  is never worse to
one person or another, but that  it can be less important. The same
goes for benefits. According to this  way of speaking, if we say we
should discount  harms or  benefits because  future people  will be
better off, what we must mean is  that a harm or benefit that comes
to someone  who is better off  is less important; that  is, that it
counts for  less as a reason  for or against adopting  some plan of
action.

This may well be a good  reason for discounting harms and benefits.
If it is,  it is because (a) the ethical  view about the importance
of  benefitting people  who are  worse off  is the  right one,  and
because (b) enough future people will  indeed be better off, and in
a way that bears a good correlation to time. The first of these two
justifications has to do with  ethics; the second concerns a matter
of empirical fact.

It  should  be clear  that  this  reason  for discounting  is  very
different  from the  reasons  discussed in  the preceding  section.
Those were reasons for discounting prices; they operated within the
price  method  of  evaluation  as  a  way of  making that  method's
evaluations accurate.  This reason represents  a view about  how to
weigh certain kinds  of harms and benefits as  they are aggregated.
It is a way of giving greater force to the analysis-given reason by
weighing  harms and  benefits in  a  way that  better captures  the
reasons associated with them. It  is an explicitly ethical view for
discounting,  and it  should  be  considered on  its  merits as  an
ethical  view.  It  should  be  considered  separately  from  price
discounting reasons.

#### Self-Interest and Special Ties

There  is a  third argument  we might  take to  justify discounting
future harms and benefits that  I think is especially important. It
is the  argument from  special ties.  Special ties  are obligations
that we have  to ourselves or to certain other  people because of a
relationship  that  exists between  us.  We  have special  ties  to
ourselves  because we  each  have  a special  interest  in our  own
wellbeing.  We have  special  ties to  our  families, friends,  and
fellow  citizens  because  we  have a  special  interest  in  their
wellbeing. These interests are different  from the interests I have
in  everyone's  doing  well  or  being free  from suffering;  those
interests are not special.

The  argument claims  that since  we have  these special  ties, and
since these special ties drop off in the future, we should discount
future harms and benefits.[14] As above,  this is not a claim about
harms being any less bad or  benefits being any less good to future
people.  Rather,  it's the claim that harming or benefitting future
people is less important.  Since  it's less important, the  reasons
generated by  future harms and benefits  count for less as  part of
the analysis-given reason.

The same argument  could be given in political  terms: Nations will
be the actors undertaking climate policy. A nation has special ties
to its own citizens. So nations  should discount harms that come to
non-citizens, including to future people.

One thing to notice about this  argument is that whether it affects
the  force of  the analysis-given  reason  depends on  just who  is
considering  the reason.  That is,  it makes  cost-benefit analysis
agent-relative.  Imagine a  cost-benefit  analyst  who gives  extra
weight to benefits that  will come to her own family.  If it is the
cost-benefit  analyst who  is considering  undertaking the  plan of
action being evaluated, this way  of weighing will indeed capture a
fuller  set of  reasons  for  or against  the  plan.  For her,  the
analysis-given reason  will have greater  force than it  would have
had otherwise.  But if it  is someone  else who is  considering the
plan of action,  the cost-benefit analyst will have  made an error.
For  the analysis  will  have failed  to  accurately represent  the
importance of the  harms and benefits being aggregated,  as it will
have given undue extra weight to certain benefits.

Discounting for special ties, then, can  be tricky, since it may be
unclear  which agent-relative  reasons should  be incorporated  and
what their  strength is against  other reasons. One  plausible view
would  be that  since the  business of  cost-benefit analysis  is a
'pure' evaluation,  it  should  take  account of  no agent-relative
reasons to weigh some harms  and benefits differently. Special ties
are  agent-relative,  so on  this  view  it  would be  improper  to
discount (or otherwise  give special weight to)  harms and benefits
that  will be  received  by those  to whom  we  have special  ties.
Another plausible view,  however, says that the agent  for whom the
analysis-given reason  is meant  to count  should be  considered as
part of the analysis, precisely by giving extra weight to harms and
benefits  that will  be received  by those  to whom  the agent  has
special  ties. These  are not  compatible  views, so  they must  be
chosen between.

As I  said, I think  this argument  is especially important,  and I
will say more about it soon. Now, however, I just want to reiterate
a point: this reason, like the reason from the argument that future
people will  be better off,  represents a  view about how  to weigh
future harms and benefits as they are aggregated. It is a view that
is,  depending on  its formulation,  ethical or  political, and  it
should be considered on its merits as such a view. It too should be
considered separately from price discounting reasons.

There are other, similar arguments  for discounting that I will not
continue to go through now.[15] I  have gone through these three to
bring out my central  claim in the first part of  this paper. It is
that  there are  reasons for  discounting within  the market  price
method  of  evaluation  and  reasons for  discounting  outside  it.
The  reasons  within  the  method  have to  do  with  the  accuracy
of  the  evaluation  given  the  method  of  economic  cost-benefit
analysis.  They are  excellent reasons,  and correspond  in precise
ways with time. The reasons  outside the method are very different.
When  they do  justify discounting,  they justify  it in  ways that
recommend different  rates of discount.  The grounds for  this kind
of  justification  are  ethical  and political,  and  are  ways  of
altering the force of the analysis-given reason. While an ambitious
cost-benefit analysis  should take account of  these reasons, since
it aims to produce an  analysis-given reason with great force, they
need to be considered separately  and on their own merits. Grouping
both kinds  of reason  under the heading  'discounting' invites
confusion.

## Pure Time Discounting

We are now in a position  to assess an argument given very recently
by Martin Weitzman  (2007). He argues for what is  called a rate of
pure time  preference. Such a  rate is sometimes  incorporated into
the  discount  rate. I  said  earlier  that pure  time  discounting
devalues future  harms and benefits  just because they come  in the
future. Though this  is how the practice is  commonly described, it
should be clear  by  now that that cannot be  exactly right.  Let's
get clearer on what it means. Consider two possible interpretations
of the practice.[16]

1. Future harms and benefits  are discounted because they count for
  less. They count for less just  because they come in the future.

2. Future harms  and benefits  are discounted  because  they  count
  for less. They  count for  less for  some reason(s) which corre-
  late(s) with time.

I  think  the only  plausible  interpretation  is the  second.  (1)
contradicts the time insensitivity of harms and benefits. It offers
a poor justification, since timing as such does not affect how much
a harm  or benefit  counts for.  So we should  expect a  reason why
future harms and benefits should  count for less. Many philosophers
have pointed  this out. While  philosophers who point this  out are
not  wrong to  do so,  some take  the unwarranted  further step  of
rejecting pure  time discounting on that  basis.   It's unwarranted
because   there's  a  better  interpretation  of  the practice.  We
should address that interpretation.[17]    With that in mind, let's
turn to Weitzman.

Weitzman's focus is the discount  rate  selected  by Nicholas Stern
in the  Stern Review. Stern  discounts mostly just for  the reasons
that  correct  prices in  the  market  price  method; that  is,  he
discounts for growth. The rate of discount he uses is significantly
lower than  observed market  interest rates. Since  market interest
rates reflect revealed preferences about the value of future stuff,
Weitzman objects to the  discrepancy. It is inappropriate, Weitzman
writes, to select a low discount rate

 . . . by relying  mostly on  a  priori  philosopher-king  ethical
 judgments  about the  immorality of  treating future  generations
 differently from  the  current  generation-instead  of  trying to
 back out what possibly more representative members of society . .
 . might be  revealing from their behavior is  their implicit rate
 of  pure time  preference. An  enormously important  part of  the
 "discipline" of  economics  is supposed  to  be  that  economists
 understand the difference between  their own personal preferences
 for apples over oranges and  the preferences of others for apples
 over oranges. Inferring society's revealed preference value . . .
 is  not  an   easy  task  in  any  event  (here  for purposes  of
 long-term discounting, no less), but at least a good-faith effort
 at such an inference might  have gone some way towards convincing
 the public that the economists  doing the studies are not drawing
 on conclusions primarily from  imposing their own value judgments
 on the rest of the world. (2007, p. 712)

There's a  lot  going  on  in this argument,  and I  won't  try  to
address all of it.[18] The main claim seems to me to be that rather
than make ethical  or political judgments about  the discount rate,
we  should  try to  discover  the  rate  at which  people  actually
discount the value of future  stuff in their day-to-day lives. This
could  mean trying  to  infer a  discount rate  from  the way  that
individuals value harms  and benefits that will come  in the future
in their own lives. This claim  is sometimes argued for. But in the
cost-benefit  analysis of  climate  change, we  are thinking  about
discounting across generations; that  is, we are discounting across
lives, not  within them.  Alternatively, then,  the claim  might be
that  we should  try  and  discover at  what  rate people  actually
discount across  generations. This  latter claim  looks to  be what
Weitzman has in mind.

Why  would  we  care  what  'representative  members  of   society'
reveal  to be  their implicit  rate  of pure  time preference  with
regard  to intergenerational  projects? If  we were  considering an
intragenerational project, one  justification might seem appealing.
It is  that it is  important to  respect the attitudes  that people
have toward  their future wellbeing,  since they have the  right to
count future harms  and benefits for less, even at  an overall harm
to themselves. So it only matters whether people prefer benefits to
come  sooner and  harms to  come later,  not whether  people should
prefer them that way. We must respect the autonomy of individuals.

This  argument   could  be  extended  to   cover  intergenerational
projects.  If  we can  discover  the  rate  at which  people  value
harms  and benefits  that will  be received  by their  children and
grandchildren,  we should  respect  those valuations  even if  they
appear to be morally unjustified.

But  to   argue  from  respect   for   people's   autonomy   is  to
misunderstand the purpose of cost-benefit analysis. As I have said,
the conventional view is that it  is a tool for evaluating plans of
action. It  produces an  analysis-given reason  for or  against the
plan  that  reflects this  evaluation.  People  should be  free  to
respond  to, disregard,  or otherwise  react to  the analysis-given
reason,  but the  analysis itself  need not  take into  account how
they  are  likely to  react.[19]  Indeed,  to  do  so would  be  to
view  cost-benefit analysis  not as  an  evaluative tool  but as  a
decision-making procedure - a preference aggregator.  But it is not
one. Rather,  an agent should  take the analysis-given  reason into
account as  part of  its decision-making  procedure. If  this seems
unclear,  consider a  parallel.  Suppose a  government  asks for  a
report on the security dangers posed by a rogue nation. Key members
of the  government are  hawkish, so  they are  likely to  give more
weight  to reasons  for military  action.  It is  obvious that  the
report should not  take into account the political  leanings of the
members  of the  government. That  is because  the report  has been
asked  to give  an  evaluation  of a  threat.  After receiving  the
report, the government  should then be free to weigh  the advice of
the report as  part of its policy decision, or  to disregard it. To
incorporate  the political  leanings of  the members  of government
into  the  evaluation  would  be  to turn  the  evaluation  into  a
decision-making procedure, which it is not.

Besides,  the   intergenerational  variant   of  the   argument  is
problematic on  its own terms.  It seems  doubtful at best  that it
would  be morally  permissible for  people to  consistently benefit
themselves  at  the expense  of  their  children or  grandchildren,
living or future.  This is because while people  typically have the
right to make  poor decisions that affect themselves,  they are not
permitted to  do so when  those decisions adversely  affect others.
Autonomy  is no  grounds for  including the  rate at  which present
people value harms and benefits to  future generations as part of a
cost-benefit analysis. We have no  right of autonomy to bring harms
to future people.  If we should value harms and  benefits that come
to future  people for less,  it is not because  we have a  right of
autonomy to do so.

## Future Generations and National Ties

So should the  cost-benefit analysis, as an  evaluation, give harms
and  benefits  equal  weight  no matter  what  generation  will  be
affected? To think so would be to endorse the

 intergenerational neutrality thesis, which  says that we ought to
 remain neutral between  harms and benefits to  present and future
 generations.

I'm  not sure  that  the  intergenerational  neutrality  thesis  is
true. I can  think of several considerations that  suggest it might
not be and some others that may suggest it is. These considerations
have  to  do  with  discounting  for what I called   'special ties'
above.  Discounting for  this  reason  is to  adopt  the view  that
cost-benefit analysis should account for agent-relative differences
in the value of harms and benefits to different people.

One reason to doubt the  intergenerational neutrality thesis has to
do with a special feature of what we could call the

 individual neutrality thesis, which says  that we ought to remain
 neutral between  harms and benefits  that will come  at different
 times in our own lives.

Consider first that many people think  that we have special ties to
ourselves.  These people think that each person has  "one supremely
rational ultimate aim":  that her life  go, on balance,  as well as
possible  (Parfit 1984,  p. 4) - or  something similar.[20]   These
people  think that  this interest  generates normative  reasons for
action; they think that each should act  in such a way as to ensure
that her life go as well as possible.

Does  this view  contradict  or support  the individual  neutrality
thesis? It supports  it. It demands that I  assess possible actions
from the  point of  view of  my entire life,  rather than  from the
present  point of  view  or through what we could  call  a  'myopic
lens'    (giving   extra    weight   to    the    nearer   future).
Since, on this view, my one supremely rational ultimate aim is that
my entire life go as well  as possible, any preference for one time
in my  life over another  can only be  derivative; that is,  it can
only  matter  insofar  as  preferring my  wellbeing  at  some  time
is  instrumental to  the  overall  wellbeing of  my  life. In  this
sense, individual  self-interest view requires that  we support the
individual neutrality thesis. It requires that we remain rationally
neutral between the wellbeing of our present and future selves.

Now  consider that  there is  no plausible  direct parallel  of the
individual  self-interest  view  to support  the  intergenerational
neutrality thesis. Such a parallel  would recommend, from the point
of view  of humanity (i.e. all  generations), that we  as  humanity
act with  the supremely rational  aim that things go,  for humanity
itself,  as  well  as  possible. The  humanity  self-interest  view
would  entail  that we  should  remain  rationally neutral  between
the  welfare  of  generations;  that   is,  it  would  endorse  the
intergenerational neutrality thesis. But the humanity self-interest
view is untenable. Humanity cannot act as humanity, nor is it clear
that humanity has  robust interests. I know of no  one who endorses
the humanity self-interest view, and I know of no reason why anyone
should.

Nevertheless,   there  may   be   a  different   special  ties   or
'self-interest'   view    that   supports   the   intergenerational
neutrality thesis. It  is a self-interest view that  I believe many
people endorse. It is the

 national  self-interest view,  which says  that nations  have one
 supremely rational interest: that things  go, for that nation, as
 well as possible.

Does this view support the intergenerational neutrality thesis? The
answer is that it depends. It  depends on the nature of the special
ties  that nations  have.  It  is possible  that  the  nature of  a
nation's  special  ties  depends  on  the  correct  view about  the
identity of nations through time. On one view of this kind, nations
have special ties only to the people who make it up at a time; that
is,  only to  present  people. This  first view  is  the view  that
nations  do  not  have  an identity  that  persists  through  time.
On  another  such  view,  nations  have  a  special  obligation  to
these people,  but that obligation  extends through time  to future
generations.  This second  view is  the view  that nations  do have
identity through time.

On the first view, nations do  not exist above and apart from those
people who currently count among its members. Though the membership
of a nation may change through  time, referring to some nation at a
time is  just the same as  referring to a list  of people - namely,
those  people who  are  members  of the  nation.  The only  special
obligations that nations have are to a particular set of people who
all exist  at a time. The  special obligation the nation  has is to
the  interests or  wellbeing of  these  people. On  this view,  any
regard  that  a  nation  has  for  future  people  must  be  simply
derivative of an interest that present people have in the wellbeing
of future people (e.g. their  children and grandchildren). That is,
of course, if present people indeed  have an actual interest in the
wellbeing of these future people  at all. The special obligation of
nations to act as the caretakers  of the interests of future people
on this view is thus a very shallow one. This view does not endorse
the  intergenerational  neutrality  thesis. It  endorses  something
weaker, such as the  claim that we ought to give  as much weight to
the  wellbeing  of  future  generations  as  is  reflected  in  the
interests of present people.

I am not  inclined to endorse the  first view, but I do  not have a
decisive argument to  give against it. The second view  seems to me
the right  view  about the  nature of nations'  identities  through
time. On this  view, a nation is a collection  of people, and since
nations persist  through time (and indeed  across generations), the
collection of people  that make up a nation must  include people at
all of  those times.  Thus, the constituency  of a  nation includes
present and future people.

This  view of  the nature  of nations  means that  if nations  have
special ties, they are to people  who exist at different times. The
national self-interest  view demands  that a nation  remain neutral
between its present and future interests. I take it that this means
a nation must remain neutral  between the interests or wellbeing of
the people who constitute it in the present and the future. It thus
endorses a  particular variant of the  intergenerational neutrality
thesis. It says that a nation should remain neutral between its own
present and future generations.

This view raises a further  question about the identity of nations.
Certainly, the character of nations  changes through time. This has
something to do with the nature  of the people who are its citizens
and also something  to do with the institutions that  govern it. We
could hold different  views about the extent to  which this matters
for the identity of a nation  through time, and further views about
how  this  affects the  special  ties  that  a  nation has  to  its
citizens.  One plausible  view  is  that while  a  nation may  have
identity through time  despite a changing character, at  time t the
only special  ties it has  are to citizens  of the nation  when its
character is  sufficiently similar to  its character at t,  or that
the strength  of the  special ties  decreases at  temporal distance
from t. This view seems supported by historical cases. While France
may have existed for a very long time, it seems odd to say that the
people  fighting  in  the  Gallic  Wars had  any  special  ties  to
present-day  citizens of  France.  Another plausible  view is  that
while some  continuity of  character is  a necessary  condition for
continued  identity of  a  nation through  time,  only identity  is
required  to generate  special  ties.  A nation  on  this view  has
special ties to all of its  past, present, and future citizens, and
thus to  past, present,  and future  generations. This  view claims
that the Gauls  indeed had special ties to  the present-day French.
It might explain  the apparent oddity of that claim  by saying that
since  the Gauls  would not  have  known that  their history  would
extend  so  far into  the  future,  much  less anything  about  the
interests or wellbeing of the future citizens of their nation, they
did not have reasons to take these future people into account.[21]

While I  am inclined to  endorse the latter  view, I do  not really
know which of these views is right. There are interesting parallels
to  questions  about personal  identity,  but  I suspect  that  our
intuitions about  national identity are  much less robust  than our
intuitions  about  personal  identity.  It may  therefore  be  very
difficult  to argue  for a  position about  national identity  from
these parallels. Indeed, the question of special ties of nationhood
may come apart  significantly from the question of  the identity of
nations through  time; it may thus  be a mistake to  argue from the
latter to  the former. Which  of these views we  endorse determines
which future generations we think  nations have special ties to. If
we discount for special ties,  holding one view rather than another
makes a serious difference.

There  may be  other self-interest  views  that support  or do  not
support some variety of  the intergenerational neutrality thesis. I
won't search for  them here.  Because nations  are  the agents that
are able  to take the  action required  to mitigate the  effects of
climate change,  the national self-interest  view is the  one worth
reckoning  with. But  as  I  have argued,  there  are  a number  of
plausible ways to interpret the  national self-interest view. If we
hold a view that does not  give nations special ties to generations
in the further future, that may justify a higher discount rate.

Whether  any   special  ties  justify  discounting   also  depends,
as  I  noted,  on  whether  cost-benefit  analysis  should  account
for  agent-relative  valuations  of  harms  and  benefits.  Whether
agent-relative reasons  are truly normative  is a rather  large and
difficult question  for moral  philosophy in general.  Thomas Nagel
asks,

 For the purposes of ethics, should we identify with the detached,
 impersonal will that  chooses total outcomes, and  act on reasons
 that are determined  accordingly? Or is this a denial  of what we
 are really  doing and an avoidance  of the full range  of reasons
 that apply to creatures like us? (Nagel 1986, p. 185)

This is,  as he says, a  true philosophical dilemma. So  is welfare
economics, and particularly cost-benefit  analysis, the right place
to take  a stand  on it?  Perhaps not, but  then again  perhaps the
choice  is  forced.  If  we include  agent-relative  valuations  in
cost-benefit analysis and are right to do so, then we will increase
the force of  the analysis-given reason. But if we  are wrong to do
so, the analysis-given  reason will be weakened since  it will have
weighed  some harms  and  benefits  wrongly. If  we  choose not  to
include  agent-relative valuations  in  cost-benefit analysis,  the
risks are  the same but in  the opposite direction.   I  don't know
which view should be  adopted. Whether cost-benefit analysis should
account for agent-relative valuations seems to me an open question.

## Conclusion

Harms and benefits are just as bad whether they occur now or in the
future,  whether they  occur  to  one person  or  another. This  is
because harms and benefits are differences in goodness. That a plan
will occasion a harm counts against the plan; that it will occasion
a benefit counts in  its favor. In deciding what to  do, we need to
add up and weigh harms and benefits.  This is what is meant when we
say  that the  purpose of  cost-benefit analysis  is to  evaluate a
plan  of action.  This evaluation  produces what  I have  called an
analysis-given reason.

I have argued, however, that there are a number of grounds on which
we  might count  future harms  and benefits  for less  than present
ones. Some  of these are  not very controversial:  economic growth,
or, that future people will be better off, gives reason to discount
the future  value of certain  goods. These grounds  for discounting
have  to do  with  the  way that  economists  use  prices to  value
commodities that count as harms or benefits. Specifically, they are
ways of correcting prices so that they accurately reflect value.

But  there  are  other  reasons   for  discounting  that  are  more
controversial. They aim to increase the force of the analysis-given
reason by changing the way in which certain harms and benefits that
come in  the future are weighed  against harms and benefits  in the
present. One such  reason came from special  ties, or self-interest
views. These views may give reason  to think that a harm or benefit
received by a  future person may count for less  than the same harm
or benefit to a present person. Whether this is the case depends on
the particular self-interest view adopted.

The cost-benefit  analysis of  climate change recommends  action by
nations, which  could recommend adopting  a discount rate  based on
the national self-interest view. This view gives nations putatively
normative  reasons  for  acting  in  the  interests  of  their  own
citizens.  I  argued for  an  interpretation  of the  national-self
interest  view that  supports  a version  of the  intergenerational
neutrality  thesis.   That  version  says  that   a  nation  should
remain  neutral between  its  own present  and future  generations.
However,  I  did not  have  a  decisive  argument against  a  rival
interpretation  of the  national self-interest  view that  does not
support any version of the intergenerational neutrality thesis, nor
against  an interpretation  that  supports a  weak  version of  the
intergenerational  neutrality  thesis.  Whether  nations  ought  to
support the thesis thus depends on  the right view about the nature
of the special ties nations  have to their members; namely, whether
they have a  strong obligation to their future  members. The issues
here are  very complex  and do not  appear to  have straightforward
answers.  That  makes  discounting  for  special  ties  related  to
nationhood a very difficult task.

We might think that it is immaterial whether any self-interest view
supports  the intergenerational  neutrality thesis  since we  could
think that  self-interest views do  not give normative  reasons for
action; we could  reject agent-relativity as a  source of normative
reasons. The intergenerational neutrality  thesis is certainly true
from  an  impartial  perspective  -  Sidgwick's  'point of  view of
the  Universe'  or   Nagel's  'view  from  nowhere'   -   since  an
impartial perspective does not  admit of self-interested reasons of
any  kind. I  am  sympathetic to  this  view, but  I  know of  many
people who  support a national self-interest  view. Indeed, nations
themselves certainly support it. As I have said, I regard this as a
serious dilemma to which there is as yet no clear answer.

I end  therefore with  a pragmatic question.  Cost-benefit analyses
produce analysis-given  reasons, which are reasons  for action. But
more than that, they are  usually tasked with producing reasons for
someone.  In  the case  of  the  cost-benefit analysis  of  climate
change, that someone is nations. If  the analysis is to be true, we
may  well  think  it  should adopt  an  impartial  perspective  and
endorse the intergenerational neutrality  thesis. This is to reject
discounting for special  ties; this is to  deny that agent-relative
reasons are  normative. This  is the  view I  tend toward.  On this
view, the  discount rate  should be very  low. But  normativity may
admit of agent-relative reasons,  and anyway nations certainly take
account of  their own agent-relative  reasons for action. So  if we
want  the analysis  to  be  accepted, we  may  well  think that  it
should adopt  some more partial  perspective, such as  the national
self-interest view. On this view, the  discount rate may or may not
be very  low. Whether it  is or not depends  on which is  the right
view of national self-interest.

Since it  is true on any  accounting that climate change  will have
some very bad  effects, perhaps, as the saying goes,  we should not
let the perfect  stand in the way  of the good. Our  efforts may be
best  spent  by arguing  for  the  interpretation of  the  national
self-interest view  that supports the  intergenerational neutrality
thesis,  rather than  by arguing  against self-interested  views in
cost-benefit analysis altogether.

## References

Kenneth  Arrow.   Discounting,  morality,   and  gaming.   In  Paul
R.   Portney  and   John  P.   Weyant,  editors,   Discounting  and
Intergenerational Equity,  chapter 2, pages 13-22.  Resources for
the Future, Washington, 1999.

Wilfred Beckerman and Cameron Hepburn.  Ethics of the discount rate
in  the stern  review on  the  economics of  climate change.  World
Economics, 8(1), 2007.

Robin Boadway and Neil Bruce. Welfare Economics. Blackwell, Oxford,
1984.

John Broome. Utility. Economics & Philosophy, 7:1-12, 1991.

John  Broome. Counting  the  Cost of  Global  Warming. White  Horse
Press, 1992.

John Broome. Discounting the future. Philosophy and Public Affairs,
23(2):128- 156, 1994.

John Broome.  Cost-benefit analysis and population.  The Journal of
Legal Studies, 29(2):953-970, June 2000.

Tyler Cowen.  Caring about the  distant future: Why it  matters and
what it means. The University  of Chicago Law Review, 74(1):5-40,
2007.

Partha  Dasgupta. Commentary:  The  stern  review's economics  of
climate change.  National Institute Economic  Review, 199(4):4-7,
2007.

Partha  Dasgupta  and  Eric   Maskin.  Uncertainty  and  hyperbolic
discounting. The American Economic Review, 95(4):1290-1299, 2005.

Jean Dreze and Nicholas Stern. The theory of cost-benefit analysis.
In  Alan J.  Auerback and  Martin Feldstein,  editors, Handbook  of
Public Economics, volume 2, pages 909-989. North-Holland, 1987.

S. Frederick, G.  O. Lowenstein, and T.  Donoghue. Time discounting
and  time  preference:  A  critical  review.  Journal  of  Economic
Literature, 40:351-401, 2002.

Ross  Garnaut. The  Garnaut  Climate Change  Review: Final  Report.
Cambridge UP, Cambridge, 2008                                     .

Thomas Nagel. The View From Nowhere. Oxford UP, Oxford, 1986.

William  Nordhaus.  A   review  of  the  "stern   review  on  the
economics  of climate  change". Journal  of Economic  Literature,
45(3):686-702, September 2007.

Derek Parfit. Reasons and Persons. Oxford UP, Oxford, 1984.

Derek Parfit. On What Matters: Volume 1. Oxford UP, Oxford, 2011.

Frank Ramsey.  A mathematical  theory of saving.  Economic Journal,
38:543-559, 1928.

Nicholas Stern. The Economics of  Climate Change: The Stern Review.
Cambridge UP, Cambridge, January 2007                             .

Joseph Stiglitz. The rate of discount for benefit-cost analysis and
theory of the second best. SSRN eLibrary, 1983.

Martin L. Weitzman. Why the far-distant future should be discounted
at its lowest possible rate. Journal of Environmental Economics and
Management, 36:201-208, 1998.

Martin  L.  Weitzman.  A  review  of "the  Stern  Review  on  the
economics  of climate  change". Journal  of Economic  Literature,
45(3):703-724, September 2007.

## Notes

[1]  Stern  uses  a  discount rate  of  1.4%;  Nordhaus  recommends
something in  the range of  3-5%. Stern recommends  strong action
now to  mitigate the  effects of  climate change,  whereas Nordhaus
recommends a  more slowly ramped-up response.  These differences in
policy  prescription are  due to  the  differences in  view on  the
discount rate. See Nordhaus (2007).

[2] I  use the  term 'harm' rather  than 'cost'  to reflect
common philosophical practice. 'Benefit,' of course, is used by
both philosophers and economists.

[3] See  Cowen (2007,  p. 12), Weitzman  (1998), and  Dasgupta and
Maskin (2005).

[4] See Arrow (1999) and Dasgupta (2007).

[5] By this  I mean the appropriate way  to incorporate discounting
into the  economic cost-benefit  model. Economists  tend to  use an
equation from Frank  Ramsey's (1928) growth model.  I concur with
Beckerman and  Hepburn (2007,  pp. 194-195), who think  parts of
that formalization  are "overworked" and "not  rich enough to
separate the  key ethical  elements relevant to  climate change."
For this reason, I have decided not to discuss discounting in terms
of the Ramsey discounting equation, which some readers might expect
to see given prominent treatment.

[6]  One  welfare  economics  textbook says  right  at  its  outset
that the  entire discipline  "can be  viewed as  an investigation
of  methods  of  obtaining   a  social  ordering"-a  betterness
ranking-"over  alternative  possible  states  of  the  world"
(Boadway and Bruce 1984, p. 1; original italics).

[7] This may  seem an unusual conception of harm  and benefit. Many
take  harms and  benefits to  be  differences in  the wellbeing  of
particular  persons. This  conception  is much  broader than  that,
though it includes  it. I discuss the narrower  conception of harms
and benefits to people in a note later in the paper.

[8] Beckerman and Hepburn (2007,  p. 188) correctly point out that
"the standard  welfare economic approach  has no  room . .  . for
ethical dimensions  concerning the processes by  which outcomes are
reached." We  should thus not  expect a cost-benefit  analysis to
capture any  procedural reasons  for or  against a  plan, including
those having  to do with  "rights, justice and  freedoms." This
limitation is very important, and is  one example of a way in which
the analysis-given reason fails to  capture the full set of reasons
for or against a plan.

[9] It  may be thought that  a harm is  less bad when endured  by a
person who deserves  to be harmed. This may be  true, but it trades
on a different sense of 'good'  and 'bad' than the one I am
using.  I would  say that  while a  harm is  as bad  no matter  who
endures it,  causing it may be  less wrong (or indeed  not wrong at
all)  if  it  is  deserved.  This seems  to  me  a  very  plausible
distinction.

[10] Some  commodities have  interest rates that  are zero  or very
near zero. The value of these commodities should not be discounted.
Many  of these  commodities,  like Derek  Parfit's  example of  a
beautiful  stretch  of  countryside  (1984, p. 483),  need  to  be
accounted for in the cost-benefit analysis of climate change, which
means  that  this kind  of  price  adjustment discounting  in  that
analysis needs to be done with special care.

[11]  There  are other  reasons  unrelated  to  time (and  thus  to
discounting) for correcting price valuations that reflect different
kinds of insensitivity  of harms and benefits. Here is  one that is
very important to the cost-benefit  analysis of climate change. One
plausible way of valuing the harm represented by loss of life is to
find out how much people are  willing to pay to insure their lives.
But people  in rich  countries are  willing to  pay much  more than
people in poor countries. This does not reflect a difference in the
value  of lives  between rich  and  poor countries;  it reflects  a
difference  in the  value of  money. This  difference of  valuation
needs to be corrected for precisely  because the badness of loss of
life does not depend  on the value of money to  a person whose life
is lost.

[12] I don't want to spend time talking about 'utility' here.
For a  discussion of that term  as it's used in  the market price
method  (and indeed  in  welfare economics  generally), see  Broome
(1991). For an analog in ethics, see expectabilism in Parfit's On
What Matters (2011, p. 106).

[13] Savvy readers  will know that the risk of  human extinction is
sometimes  factored  into the  discount  rate  of the  cost-benefit
analysis of climate change rather than accounted for using expected
utility  theory.  This practice,  which  I  don't understand,  is
adopted  in  the  Stern  Review.  Stern  recognizes  that  this  is
disputable; see Stern  (2007, p. 663 fn8). See  also Broome (1992,
p. 102) for support on this point.

[14] John Broome has pointed out  to me that this argument could be
right  about  the  nature  of  our special  ties  but  wrong  about
discounting. Suppose  benefits to  grandchildren count for  half as
much  as benefits  to  children.  If a  person  has  twice as  many
grandchildren as children, the  aggregate importance of benefits is
constant across  these two generations,  thus failing to  support a
rate  of discount.  I do  not wish  to discuss  issues relating  to
population size here, but this is a point well-worth noting.

[15] One that  merits mention even though I do  not want to address
it here is that  we may not in fact benefit  or harm certain future
people at all; namely, those particular people whose very existence
is owed  to the  policy options being  evaluated by  a cost-benefit
analysis. This is  what Derek Parfit (1984)  calls the non-identity
problem. There are different views on the extent to which this is a
problem  for cost-benefit  analysis,  though I  cannot  think of  a
reason why it would justify a rate of discount.

[16]  The practice  does indeed  warrant 'interpretation.'  See
Stern (2007, p. 664) and Frederick et al. (2002).

[17] Beckerman  and Hepburn (2007) seem  to have this in  mind when
they  suggest we  should consider  agent-relative ethical  theories
when selecting a rate of pure time preference.

[18] For some  considerations that call into question  the value of
revealed  preferences in  this context,  see Beckerman  and Hepburn
(2007, pp. 202-205).

[19] This  is different from  saying that  we should or  should not
take agent-relative reasons into  account in cost-benefit analysis,
which  I have  suggested is  an  open question.  The argument  from
autonomy says that people should be  free to respond or not respond
to the analysis-given reason. This seems  right to me, but does not
bear on the cost-benefit analysis itself.

[20] Parfit, of course, argues against this view.

[21]  This raises  another  interesting  question. If  cost-benefit
analyses  are  to  take   account  of  agent-relative  reasons,  as
the   argument  for   discounting   for   special  ties   suggests,
then  the  cost-benefit  analysis  of  climate  change-generating
an  analysis-given  reason  for   a  nation-should  consider  the
possibility that  the nation  will not exist  far into  the future.
This  is distinct  from considering  the possibility  that humanity
itself will not exist far into  the future, which, as I've noted,
the Stern Review does.