Climate Change Policy: What Do the Models Tell Us?

 
Journal of Economic Literature 2013, 51(3), 860–872
http://dx.doi.org/10.1257/jel.51.3.860

                  Climate Change Policy:
                What Do the Models Tell Us?                                                                    †

                                               Robert S. Pindyck*

     Very little. A plethora of integrated assessment models (IAMs) have been constructed
     and used to estimate the social cost of carbon (SCC) and evaluate alternative
     abatement policies. These models have crucial flaws that make them close to useless
     as tools for policy analysis: certain inputs (e.g., the discount rate) are arbitrary, but
     have huge effects on the SCC estimates the models produce; the models’ descriptions
     of the impact of climate change are completely ad hoc, with no theoretical or empirical
     foundation; and the models can tell us nothing about the most important driver of the
     SCC, the possibility of a catastrophic climate outcome. IAM-based analyses of climate
     policy create a perception of knowledge and precision, but that perception is illusory
     and misleading. (  JEL C51, Q54, Q58)

                   1.    Introduction                                  limiting carbon emissions, and is the focus of
                                                                       policy-oriented research on climate change.

T    here is almost no disagreement among
     economists that the full cost to society
of burning a ton of carbon is greater than its
                                                                          So how large is the SCC? Here there is
                                                                       plenty of disagreement. Some argue that cli-
                                                                       mate change will be moderate, will occur in
private cost. Burning carbon has an exter-                             the distant future, and will have only a small
nal cost because it produces CO2 and other                             impact on the economies of most countries.
greenhouse gases (GHGs) that accumulate                                This would imply that the SCC is small, per-
in the atmosphere, and will eventually result                          haps only around $10 per ton of CO2. Others
in unwanted climate change—higher global                               argue that without an immediate and stringent
temperatures, greater climate variability, and                         GHG abatement policy, there is a reasonable
possibly increases in sea levels. This external                        chance of substantial temperature increases
cost is referred to as the social cost of carbon                       that might have a catastrophic economic
(SCC). It is the basis for taxing or otherwise                         impact. If so, it would suggest that the SCC is
                                                                       large, perhaps as high as $200 per ton of CO2.1
   * Massachusetts Institute of Technology. My thanks to
Millie Huang for her excellent research assistance, and
to Janet Currie, Christian Gollier, Chris Knittel, Charles                1 The SCC is sometimes expressed in terms of dollars
Kolstad, Bob Litterman, and Richard Schmalensee for                    per ton of carbon. A ton of CO2 contains 0.2727 tons of
helpful comments and suggestions.                                      carbon, so an SCC of $10 per ton of CO2 is equivalent to
   †
     Go to http://dx.doi.org/10.1257/jel.51.3.860 to visit the         $36.67 per ton of carbon. The SCC numbers I present in
article page and view author disclosure statement(s).                  this paper are always in terms of dollars per ton of CO2.

                                                                 860
Pindyck: Climate Change Policy: What Do the Models Tell Us?                              861

   Might we narrow this range of disagree-               damage. Instead, the raison d’etre of these
ment over the size of the SCC by carefully               models has been their use as a policy tool.
quantifying the relationships between GHG                The idea is that by simulating the models, we
emissions and atmospheric GHG concentra-                 can obtain reliable estimates of the SCC and
tions, between changes in GHG concentra-                 evaluate alternative climate policies.
tions and changes in temperature (and other                 Indeed, a U.S. Government Interagency
measures of climate change), and between                 Working Group has tried to do just that. It
higher temperatures and measures of wel-                 ran simulations of three different IAMs, with
fare such as output and per capita consump-              a range of parameter values, discount rates,
tion? In other words, might we obtain better             and assumptions regarding GHG emissions,
estimates of the SCC by building and simu-               to estimate the SCC.3 Of course, different
lating integrated assessment models (IAMs),              input assumptions resulted in different SCC
i.e., models that “integrate” a description of           estimates, but the Working Group settled
GHG emissions and their impact on temper-                on a base case or “average” estimate of $21
ature (a climate science model) with projec-             per ton, which was recently updated to $33
tions of abatement costs and a description of            per ton.4 Other IAMs have been developed
how changes in climate affect output, con-               and likewise used to estimate the SCC. As
sumption, and other economic variables (an               with the Working Group, those estimates
economic model).                                         vary considerably depending on the input
   Building such models is exactly what some             assumptions for any one IAM, and also vary
economists interested in climate change pol-             across IAMs.
icy have done. One of the first such models                 Given all of the effort that has gone into
was developed by William Nordhaus over                   developing and using IAMs, have they helped
twenty years ago.2 That model was an early               us resolve the wide disagreement over the
attempt to integrate the climate science and             size of the SCC? Is the U.S. government
economic aspects of the impact of GHG                    estimate of $21 per ton (or the updated esti-
emissions, and it helped economists under-               mate of $33 per ton) a reliable or otherwise
stand the basic mechanisms involved. Even                useful number? What have these IAMs (and
if one felt that parts of the model were overly          related models) told us? I will argue that the
simple and lacked empirical support, the                 answer is very little. As I discuss below, the
work achieved a common goal of economic                  models are so deeply flawed as to be close to
modeling: elucidating the dynamic relation-              useless as tools for policy analysis. Worse yet,
ships among key variables, and the implica-
tions of those relationships, in a coherent
                                                             3 The three IAMS were DICE (Dynamic Integrated
and convincing way. Since then, the develop-
                                                         Climate and Economy), PAGE (Policy Analysis of the
ment and use of IAMs has become a growth                 Greenhouse Effect), and FUND (Climate Framework for
industry. (It even has its own journal, The              Uncertainty, Distribution, and Negotiation). For descrip-
Integrated Assessment Journal.) The models               tions of the models, see Nordhaus (2008), Hope (2006),
                                                         and Tol (2002a, 2002b).
have become larger and more complex, but                     4 See Interagency Working Group on Social Cost of
unfortunately have not done much to better               Carbon (2010). For an illuminating and very readable dis-
elucidate the pathways by which GHG emis-                cussion of the Working Group’s methodology, the models
                                                         it used, and the assumptions regarding parameters, GHG
sions eventually lead to higher temperatures,            emissions, and other inputs, see Greenstone, Kopits, and
which in turn cause (quantifiable) economic              Wolverton (2011). The updated study used new versions
                                                         of the DICE, PAGE, and FUND models, and arrived at
                                                         a new “average” estimate of $33 per ton for the SCC. See
                                                         Interagency Working Group on Social Cost of Carbon
  2   See, for example, Nordhaus (1991, 1993a, 1993b).   (2013).
862               Journal of Economic Literature, Vol. LI (September 2013)

their use suggests a level of knowledge and          GDP, again under BAU and alternative
precision that is simply illusory, and can be        abatement scenarios, and on an aggre-
highly misleading.                                   gate or regionally disaggregated basis.
   The next section provides a brief overview
of the IAM approach, with a focus on the          2. Projections of future atmospheric CO2e
arbitrary nature of the choice of social wel-         concentrations resulting from past, cur-
fare function and the values of its parameters.       rent, and future CO2e emissions. (This
Using the three models that the Interagency           is part of the climate science side of an
Working Group chose for its assessment of             IAM.)
the SCC as examples, I then discuss two
important parts of IAMS where the uncer-          3. 
                                                     Projections of average global (or
tainties are greatest and our knowledge is           regional) temperature changes—and
weakest—the response of temperature to an            possibly other measures of climate
increase in atmospheric CO2, and the eco-            change such as temperature and rain-
nomic impact of higher temperatures. I then          fall variability, hurricane frequency, and
explain why an evaluation of the SCC must            sea level increases—likely to result over
include the possibility of a catastrophic out-       time from higher CO2e concentrations.
come, why IAMs can tell us nothing about             (This is also part of the climate science
such outcomes, and how an alternative and            side of an IAM.)
simpler approach is likely to be more illumi-
nating. As mentioned above, the number of         4. 
                                                     Projections of the economic impact,
IAMs in existence is large and growing. My           usually expressed in terms of lost GDP
objective is not to survey the range of IAMs         and consumption, resulting from higher
or the IAM-related literature, but rather to         temperatures. (This is the most specu-
explain why climate change policy can be             lative element of the analysis, in part
better analyzed without the use of IAMs.             because of uncertainty over adaptation
                                                     to climate change.) “Economic impact”
                                                     includes both direct economic impacts
      2.   Integrated Assessment Models
                                                     as well as any other adverse effects of
  Most economic analyses of climate change           climate change, such as social, politi-
policy have six elements, each of which can          cal, and medical impacts, which under
be global in nature or disaggregated on a            various assumptions are monetized and
regional basis. In an IAM-based analysis,            included as part of lost GDP.
each of these elements is either part of the
model (determined endogenously), or else is       5. Estimates of the cost of abating GHG
an exogenous input to the model. These six            emissions by various amounts, both now
elements can be summarized as follows:                and throughout the future. This in turn
                                                      requires projections of technological
 1. Projections of future emissions of a CO2         change that might reduce future abate-
     equivalent (CO2e) composite (or indi-            ment costs.
     vidual GHGs) under “business as usual”
     (BAU) and one or more abatement              6. Assumptions about social utility and the
     scenarios. Projections of emissions in           rate of time preference, so that lost con-
     turn require projections of both GDP             sumption from expenditures on abate-
     growth and “carbon intensity,” i.e., the         ment can be valued and weighed against
     amount of CO2e released per dollar of            future gains in consumption from the
Pindyck: Climate Change Policy: What Do the Models Tell Us?                                   863

      reductions in warming that abatement                    can give wildly different estimates of the
      would bring about.                                      SCC and the optimal amount of abatement.
                                                              You might think that some input choices
   These elements are incorporated in the                     are more reasonable or defensible than oth-
work of Nordhaus (2008), Stern (2007),                        ers, but no, “reasonable” is very much in
and others who evaluate abatement poli-                       the eye of the modeler. Thus these models
cies though the use of IAMs that project                      can be used to obtain almost any result one
emissions, CO2e concentrations, tempera-                      desires.7
ture change, economic impact, and costs                          There are two types of inputs that lend
of abatement. Interestingly, however,                         themselves to arbitrary choices. The first
Nordhaus (2008), Stern (2007), and oth-                       is the social welfare (utility) function and
ers come to strikingly different conclusions                  related parameters needed to value and
regarding optimal abatement policy and the                    compare current and future gains and losses
implied SCC. Nordhaus (2008) finds that                       from abatement. The second is the set of
optimal abatement should initially be very                    functional forms and related parameters that
limited, consistent with an SCC around $20                    determine the response of temperature to
or less, while Stern (2007) concludes that                    changing CO2e concentrations and (espe-
an immediate and drastic cut in emissions                     cially) the economic impact of rising temper-
is called for, consistent with an SCC above                   atures. I discuss the social welfare function
$200.5 Why the huge difference? Because                       here, and leave the functional forms and
the inputs that go into the models are so                     related parameters to later when I discuss
different. Had Stern used the Nordhaus                        the “guts” of these models.
assumptions regarding discount rates,
                                                              2.2 The Social Welfare Function
abatement costs, parameters affecting tem-
perature change, and the function deter-                         Most models use a simple framework for
mining economic impact, he would have                         valuing lost consumption at different points
also found the SCC to be low. Likewise, if                    in time: time-additive, constant relative risk
Nordhaus had used the Stern assumptions,                      aversion (CRRA) utility, so that social wel-
he would have obtained a much higher                          fare is
SCC.6
                                                              (1) 	W = ​ _1  ​ ​​ ​ ​∫​  ∞
                                                                                 0 0​  ​         t​  ​
2.1 What Goes In and What Comes Out                                                         ​C​  1−η  ​e−δt
                                                                                                        ​ ​dt,
                                                                         1−η
  And here we see a major problem with
IAM-based climate policy analysis: the
modeler has a great deal of freedom in                        where η is the index of relative risk aver-
choosing functional forms, parameter val-                     sion (IRRA) and δ is the rate of time pref-
ues, and other inputs, and different choices                  erence. Future consumption is unknown,
                                                              so I included the expectation operator ,
   5 In an updated study, Nordhaus (2011) estimates the       although most IAMs are deterministic in
SCC to be $12 per ton of CO2.                                 nature. Uncertainty, if incorporated at all,
   6 Nordhaus (2007), Weitzman (2007), Mendelsohn
                                                              is usually analyzed by running Monte Carlo
(2008), and others argue (and I would agree) that the Stern
study (which used a version of the PAGE model) makes          simulations in which probability distributions
assumptions about temperature change, economic impact,
abatement costs, and discount rates that are generally
outside the consensus range. But see Stern (2008) for a
detailed (and very readable) explanation and defense of         7 A colleague of mine once said “I can make a model tie
these assumptions.                                            my shoe laces.”
864                    Journal of Economic Literature, Vol. LI (September 2013)

are attached to one or more ­parameters.8                     (or care) that their policy decisions reflect
Equation (1) might be applied to the United                   the values of voters. As a policy parameter,
States (as in the Interagency Working Group                   the rate of time preference might be posi-
study), to the entire world, or to different                  tive, zero, or even negative.10 The problem
regions of the world.                                         is that if we can’t pin down δ, an IAM can’t
   I will put aside the question of how mean-                 tell us much; any given IAM will give a wide
ingful equation (1) is as a welfare measure,                  range of values for the SCC, depending on
and focus instead on the two critical param-                  the chosen value of δ.
eters, δ and η. We can begin by asking what is                   What about η, the IRRA? The SCC that
the “correct” value for the rate of time pref-                comes out of almost any IAM is also very
erence, δ? This parameter is crucial because                  sensitive to this parameter. Generally, a
the effects of climate change occur over very                 higher value of η will imply a lower value
long time horizons (50 to 200 years), so a                    of the SCC.11 So what value for η should be
value of δ above 2 percent would make it hard                 used for climate policy? Here, too, econo-
to justify even a very moderate abatement                     mists disagree. The macroeconomics and
policy. Financial data reflecting investor                    finance literatures suggest that a reasonable
behavior and macroeconomic data reflecting                    range is from about 1.5 to at least 4. As a
consumer and firm behavior suggest that δ is                  policy parameter, however, we might con-
in the range of 2 to 5 percent. While a rate                  sider the fact that η also reflects aversion to
in this range might reflect the preferences                   consumption inequality (in this case across
of investors and consumers, should it also                    generations), suggesting a reasonable range
reflect intergenerational preferences and                     of about 1 to 3.12 Either way, we are left with
thus apply to time horizons greater than fifty                a wide range of reasonable values, so that any
years? Some economists (e.g., Stern 2008                      given IAM can give a wide range of values
and Heal 2009) have argued that on ethical                    for the SCC.
grounds δ should be zero for such horizons,                      Disagreement over δ and η boils down to
i.e., that it is unethical to discount the wel-               disagreement over the discount rate used to
fare of future generations relative to our own
welfare. But why is it unethical? Putting aside                   10 Why negative? One could argue, perhaps based on
their personal views, economists have little                  altruism or a belief that human character is improving over
to say about that question.9 I would argue                    time, that the welfare of our great-grandchildren should be
that the rate of time preference is a policy                  valued more highly than our own.
                                                                  11 The larger is η, the faster the marginal utility of con-
parameter, i.e., it reflects the choices of pol-              sumption declines as consumption grows. Since consump-
icy makers, who might or might not believe                    tion is expected to grow, the value of additional future
                                                              consumption is smaller the larger is η. But η also measures
                                                              risk aversion; if future consumption is uncertain, a larger
   8 A recent exception is Cai, Judd, and Lontzek (2013),     η makes future welfare smaller, raising the value of addi-
who developed a stochastic dynamic programming version        tional future consumption. Most models show that unless
of the Nordhaus DICE model. Also, Kelly and Kolstad           risk aversion is extreme (e.g., η is above 4), the first effect
(1999) show how Bayesian learning can affect policy in a      dominates, so an increase in η (say from 1 to 4) will reduce
model with uncertainty.                                       the benefits from an abatement policy. See Pindyck (2012)
   9 Suppose John and Jane both have the same incomes.        for examples.
John saves 10 percent of his income every year in order to        12 If a future generation is expected to have twice the
help finance the college educations of his (yet-to-be-born)   consumption as the current generation, the marginal util-
grandchildren, while Jane prefers to spend all of her dis-    ity of consumption for the future generation is 1/2  η as
posable income on sports cars, boats, and expensive wines.    large as for the current generation, and would be weighted
Does John’s concern for his grandchildren make him more       accordingly in any welfare calculation. Values of η above
ethical than Jane? Many people might say yes, but that        3 or 4 imply a relatively very small weight for the future
answer would be based on their personal values rather than    generation, so one could argue that a smaller value is more
economic principles.                                          appropriate.
Pindyck: Climate Change Policy: What Do the Models Tell Us?                           865

put gains and losses of future consumption                   translates increases in the CO2e concentra-
(as opposed to utility) in present value terms.              tion to increases in temperature, a mecha-
In the simplest (deterministic) Ramsey                       nism that is referred to as climate sensitivity.
framework, that discount rate is R = δ + ηg,                 The second translates higher temperatures
where g is the real per capita growth rate of                to reductions in GDP and consumption, i.e.,
consumption, which historically has been                     the damage function.
around 1.5 to 2 percent per annum, at least
                                                             3.1 Climate Sensitivity
for the United States. Stern (2007), citing
ethical arguments, sets δ ≈ 0 and η = 1 , so                    Climate sensitivity is defined as the tem-
that R is small and the estimated SCC is very                perature increase that would eventually result
large. By comparison, Nordhaus (2008) tries                  from an anthropomorphic doubling of the
to match market data, and sets δ = 1.5 per-                  atmospheric CO2e concentration. The word
cent and η = 2, so that R ≈ 5.5 percent and                  “eventually” means after the world’s climate
the estimated SCC is far smaller.13 Should                   system reaches a new equilibrium following
the discount rate be based on “ethical”                      the doubling of the CO2e concentration, a
arguments or market data? And what ethi-                     period of time in the vicinity of fifty years.
cal arguments and what market data? The                      For some of the simpler IAMs, climate sensi-
members of the Interagency Working Group                     tivity takes the form of a single parameter; for
got out of this morass by focusing on a mid-                 larger and more complicated models, it might
dle-of-the-road discount rate of 3 percent,                  involve several equations that describe the
without taking a stand on whether this is the                dynamic response of temperature to changes
“correct” rate.                                              in the CO2e concentration. Either way, it can
                                                             be boiled down to a number that says how
                                                             much the temperature will eventually rise if
           3.   The Guts of the Models
                                                             the CO2e concentration were to double. And
   Let’s assume for the moment that econo-                   either way, we can ask how much we know
mists could agree on the “correct” value for                 or don’t know about that number. This is an
the discount rate R. Let’s also assume that                  important question because climate sensi-
they (along with climate scientists) could also              tivity is an exogenous input into each of the
agree on the rate of emissions under BAU                     three IAMs used by the Interagency Working
and one or more abatement scenarios, as                      Group to estimate the SCC.
well as the resulting time path for the atmo-                   Here is the problem: the physical mech-
spheric CO2e concentration. Could we then                    anisms that determine climate sensitiv-
use one or more IAMs to produce a reliable                   ity involve crucial feedback loops, and the
estimate of the SCC? The answer is no, but                   parameter values that determine the strength
to see why, we must look at the insides of the               (and even the sign) of those feedback loops
models. For some of the larger models, the                   are largely unknown, and for the foresee-
“guts” contain many equations and can seem                   able future may even be unknowable. This is
intimidating. But in fact, there are only two                not a shortcoming of climate science; on the
key organs that we need to dissect. The first                contrary, climate scientists have made enor-
                                                             mous progress in understanding the physical
   13 Uncertainty over consumption growth or over the        mechanisms involved in climate change. But
discount rate itself can reduce R, and depending on the      part of that progress is a clearer realization
type of uncertainty, lead to a time-varying R. See Gollier   that there are limits (at least currently) to our
(2013) for an excellent treatment of the effects of uncer-
tainty on the discount rate. Weitzman (2013) shows how       ability to pin down the strength of the key
the discount rate could decline over time.                   feedback loops.
866                    Journal of Economic Literature, Vol. LI (September 2013)

   The Intergovernmental Panel on Climate                    ΔT.” Thus the actual climate sensitivity is
Change (2007) (IPCC) surveyed twenty-two                     given by
peer-reviewed published studies of climate
                                                                                                     ​λ0​ ​
sensitivity and estimated that they implied                  (2) 	                            λ = ​ _        ​,
an expected value of 2.5º C to 3.0º C for cli-                                                      1−f
mate sensitivity.14 Each of the individual
studies included a probability distribution                  where f (0 ≤  f ≤ 1) is the total feedback fac-
for climate sensitivity, and by putting the dis-             tor (which in a more complete and complex
tributions in a standardized form, the IPCC                  model would incorporate several feedback
created a graph that showed all of the dis-                  effects).
tributions in a summary form. A number of                         Unfortunately, we don’t know the value
studies—including the Interagency Working                    of f. Roe and Baker point out that if we
Group study—used the IPCC’s results to                       knew the mean   _    and standard deviation of f,
infer and calibrate a single distribution for                denoted by f ​​ and ​σf​​respectively, and if ​σf​​ is
climate sensitivity, which in turn could be                  small, then the standard deviation    _           of λ would
used to run alternative simulations of one or                be proportional to σ   ​ ​f​   /(1 − ​f ​​)2​ ​. Thus uncer-
more IAMs.15                                                 tainty over λ is greatly magnified by uncer-
   Averaging across the standardized distri-                 tainty over f, and becomes very large if f is
butions summarized by the IPCC suggests                      close to 1. Likewise, if the true value of f is
that the 95th percentile is about 7º C, i.e.,                close to 1, climate sensitivity would be huge.
there is roughly a 5 percent probability that                     As an illustrative exercise, Roe and Baker
the true climate sensitivity is above 7º C. But              assume _ that f is normally distributed (with
this implies more knowledge than we prob-                    mean f ​​ and standard deviation ​                  σf​​), and
ably have. This is easiest to see in the rela-               derive the resulting distribution for λ,_ cli-
tively simple climate model developed by                     mate sensitivity. Given their choice of f ​​ and​
Roe and Baker (2007). Using their notation,                  σ​f​ , the resulting median and 95th percentile
let ​λ0​ ​be climate sensitivity in the absence of           are close to the corresponding numbers that
any feedback effects, i.e., absent feedback                  come from averaging across the standardized
effects, a doubling of the atmospheric CO2e                  distributions summarized by the IPCC.16
concentration would lead to an increase in                        The Interagency Working Group cali-
radiative forcing that would in turn cause a                 brated the Roe–Baker distribution to fit
temperature increase of Δ​T​0​  = ​λ0​ ​º C. But as          the composite IPCC numbers more closely,
Roe and Baker explain, the initial tempera-                  and then applied that distribution to each
ture increase Δ​T​0​“induces changes in the                  of the three IAMs as a way of analyzing the
underlying processes . . . which modify the
effective forcing, which, in turn, m      ­ odifies             16 The     Roe–Baker distribution is given by:

                                                                                                                [ (                            )]
                                                                                                                                  _
                                                                       _                                                       1 − ​f ​ − 1/z
                                                                                                                                                 2
                                                                g (λ; f ​​ , ​σf​​, θ) = ​ _        1_  ​  exp ​ − ​ _
                                                                                                                     1 ​ ​​ _
                                                                                                                            ​        ​σf​ ​   ​ ​  ​,
   14 The IPCC also provides a detailed and readable
                                                                                           ​σf​​  ​ 2π ​ ​z​ ​
                                                                                                  √        2         2                   ​
                                                                                                                                          _
overview of the physical mechanisms involved in climate      where z = λ + θ. The parameter values are f ​​= 0.797,​
change, and the state of our knowledge regarding those       σ​f​= 0.0441, θ = 2.13. This distribution is fat-tailed, i.e.,
mechanisms.                                                  declines to zero more slowly than exponentially. Weitzman
   15 Newbold and Daigneault (2009) and Pindyck (2012)       (2009) has shown that parameter uncertainty can lead to a
(who fit a gamma distribution to the IPCC’s summary          fat-tailed distribution for climate sensitivity, and that this
graph) used the distribution to infer the implications of    implies a relatively high probability of a catastrophic out-
uncertainty over climate sensitivity for abatement policy.   come, which in turn suggests that the value of abatement
But as discussed below, they probably underestimated the     is high. Pindyck (2011a) shows that a fat-tailed distribution
extent of the uncertainty.                                   by itself need not imply a high value of abatement.
Pindyck: Climate Change Policy: What Do the Models Tell Us?                                                             867

s­ensitivity of their SCC estimates to uncer-          loss functions is based on any economic (or
 tainty over climate sensitivity.                      other) theory. Nor are the loss functions that
    Given the limited available information,           appear in other IAMs. They are just arbi-
 the Interagency Working Group did the best            trary functions, made up to describe how
 it could. But it is likely that they—like oth-        GDP goes down when T goes up.
 ers who have used IAMs to analyze climate                The loss functions in PAGE and FUND,
 change policy—have understated our uncer-             the other two models used by the Interagency
 tainty over climate sensitivity. We don’t know        Working Group, are more complex but
 whether the feedback factor f is in fact nor-         equally arbitrary. In those models, losses
mally distributed (nor do we know its mean             are calculated for individual regions and (in
and standard deviation). Roe and Baker simply          the case of FUND) individual sectors, such
assumed a normal distribution. In fact, in an          as agriculture and forestry. But there is no
accompanying article in the journal Science,           pretense that the equations are based on any
Allen and Frame (2007) argued that climate             theory. When describing the sectoral impacts
sensitivity is in the realm of the “unknowable.”       in FUND, Tol (2002b) introduces equations
                                                       with the words “The assumed model is:”
3.2 The Damage Function
                                                       (e.g., pages 137–39, emphasis mine), and at
   When assessing climate sensitivity, we at           times acknowledges that “The model used
least have scientific results to rely on, and can      here is therefore ad hoc” (142).
argue coherently about the probability dis-               The problem is not that IAM developers
tribution that is most consistent with those           were negligent and ignored economic the-
results. When it comes to the damage func-             ory; there is no economic theory that can tell
tion, however, we know almost nothing, so              us what L(T ) should look like. If anything,
developers of IAMs can do little more than             we would expect T to affect the growth rate
make up functional forms and corresponding             of GDP, and not the level. Why? First, some
parameter values. And that is pretty much              effects of warming will be permanent; e.g.,
what they have done.                                   destruction of ecosystems and deaths from
   Most IAMs (including the three that were            weather extremes. A growth rate effect
used by the Interagency Working Group to               allows warming to have a permanent impact.
estimate the SCC) relate the temperature               Second, the resources needed to counter the
increase T to GDP through a “loss func-                impact of warming will reduce those avail-
tion” L(T ), with L(0) = 1 and ​       L′​(T) < 0.     able for R&D and capital investment, reduc-
Thus GDP at time t is GD​Pt​​= L(​Tt​​)GD​P​  ′t​,​    ing growth.17 Third, there is some empirical
where GD​P​  ′t​​  is what GDP would be if             support for a growth rate effect. Using data
there were no warming. For example, the
Nordhaus (2008) DICE model uses the fol-
lowing inverse-quadratic loss function:                   17 Adaptation to rising temperatures is equivalent to
                                                       the cost of increasingly strict emission standards, which,
(3) 	 L = 1/[1 + ​π1​ ​  T + ​π2​ ​(T​)2​ ​].          as Stokey (1998) has shown with an endogenous growth
                                                       model, reduces the rate of return on capital and low-
                                                       ers the growth rate. To see this, suppose total capital
Weitzman (2009) suggested the exponential-             K = ​Kp​ ​+ ​Ka​ ​(T), with K          ​ ​  a′ ​(​  T ) > 0, where K ​ p​ ​ is directly pro-
quadratic loss function:                               ductive capital and K              ​ a​ ​(T ) is capital needed for adaptation
                                                       to the temperature increase T (e.g., stronger retaining
(4) 	          L(T) = exp[−β (T​)2​ ​],                walls and pumps to counter flooding, more air condi-
                                                       tioning and insulation, etc.). If all capital depreciates at
                                                                    ​​  ˙ p​ ​= ​ K​
                                                       rate ​δK​ ​, K​            ˙ − ​​ K​​
                                                                                         ˙ a​= I − ​δK​ ​K − ​K​  a′ ​(​  T )​ T​
                                                                                                                               ˙ , so the rate of
which allows for greater losses when T is              growth of ​K​p​is reduced. See Brock and Taylor (2010) and
large. But remember that neither of these              Fankhauser and Tol (2005) for related analyses.
868                    Journal of Economic Literature, Vol. LI (September 2013)

on temperatures and precipitation over fifty                   we are looking at temperature increases of 2
years for a panel of 136 countries, Dell,                      or 3º C, because there is a rough consensus
Jones, and Olken (2012) have shown that                        (perhaps completely wrong) that damages
higher temperatures reduce GDP growth                          will be small at those levels of warming. The
rates but not levels. Likewise, using data for                 problem is that these damage functions tell
147 countries during 1950 to 2007, Bansal                      us nothing about what to expect if tempera-
and Ochoa (2011, 2012) show that increases                     ture increases are larger, e.g., 5º C or more.19
in temperature have a negative impact on                       Putting T = 5 or T = 7 into equation (3) or
economic growth.18                                             (4) is a completely meaningless exercise. And
   Let’s put the issue of growth rate versus                   yet that is exactly what is being done when
level aside and assume that the loss function                  IAMs are used to analyze climate policy.
of eqn. (3) is a credible description of the                      I do not want to give the impression that
economic impact of higher temperatures.                        economists know nothing about the impact
Then the question is how to determine the                      of climate change. On the contrary, consider-
values of the parameters π   ​ 1​ ​and ​π2​ ​. Theory          able work has been done on specific aspects
can’t help us, nor is data available that could                of that impact, especially with respect to
be used to estimate or even roughly cali-                      agriculture. One of the earliest studies of
brate the parameters. As a result, the choice                  agricultural impacts, including adapta-
of values for these parameters is essentially                  tion, is Mendelsohn, Nordhaus, and Shaw
guesswork. The usual approach is to select                     (1994); more recent ones include Deschenes
values such that L(T ) for T in the range of                   and Greenstone (2007) and Schlenker and
2º C to 4º C is consistent with common wis-                    Roberts (2009). A recent study that focuses
dom regarding the damages that are likely to                   on the impact of climate change on mortal-
occur for small to moderate increases in tem-                  ity, and our ability to adapt, is Deschenes and
perature. Most modelers choose parameters                      Greenstone (2011). And recent studies that
so that L(1) is close to 1 (i.e., no loss), L(2)               use or discuss the use of detailed weather
is around 0.99 or 0.98, and L(3) or L(4) is                    data include Dell, Jones, and Olken (2012)
around 0.98 to 0.96. Sometimes these num-                      and Auffhammer et al. (2013). These are just
bers are justified by referring to the IPCC                    a few examples; the literature is large and
or related summary studies. For example,                       growing.
Nordhaus (2008) points out that the 2007                          Statistical studies of this sort will surely
IPCC report states that “global mean losses                    improve our knowledge of how climate
could be 1–5 percent GDP for 4º C of warm-                     change might affect the economy, or at least
ing” (51). But where did the IPCC get those                    some sectors of the economy. But the data
numbers? From its own survey of several                        used in these studies are limited to relatively
IAMs. Yes, it’s a bit circular.                                short time periods and small fluctuations in
   The bottom line here is that the damage                     temperature and other weather variables—
functions used in most IAMs are completely                     the data do not, for example, describe what
made up, with no theoretical or empirical
foundation. That might not matter much if
                                                                  19 Some modelers are aware of this problem. Nordhaus
                                                               (2008) states: “The damage functions continue to be a
                                                               major source of modeling uncertainty in the DICE model”
   18 See Pindyck (2011b, 2012) for further discussion and     (51). To get a sense of the wide range of damage numbers
an analysis of the policy implications of a growth rate ver-   that come from different models, even for T = 2 or 3º C,
sus level effect. Note that a climate-induced catastrophe,     see table 1 of Tol (2012). Stern (2013) argues that IAM
on the other hand, could reduce both the growth rate and       damage functions ignore a variety of potential climate
level of GDP.                                                  impacts, including possibly catastrophic ones.
Pindyck: Climate Change Policy: What Do the Models Tell Us?                  869

has happened over twenty or fifty years fol-      (2013a), the problem is that the possibility of
lowing a 5º C increase in mean tempera-           a catastrophic outcome is an essential driver
ture. Thus these studies cannot enable us         of the SCC. Thus we are left in the dark;
to specify and calibrate damage functions of      IAMs cannot tell us anything about cata-
the sort used in IAMs. In fact, those damage      strophic outcomes, and thus cannot provide
functions have little or nothing to do with the   meaningful estimates of the SCC.
detailed econometric studies related to agri-        It is difficult to see how our knowledge of
cultural and other specific impacts.              the economic impact of rising temperatures
                                                  is likely to improve in the coming years.
                                                  More than temperature change itself, eco-
        4.   Catastrophic Outcomes
                                                  nomic impact may be in the realm of the
   Another major problem with using IAMs          “unknowable.” If so, it would make little
to assess climate change policy is that the       sense to try to use an IAM-based analysis to
models ignore the possibility of a cata-          evaluate a stringent abatement policy. The
strophic climate outcome. The kind of out-        case for stringent abatement would have to
come I am referring to is not simply a very       be based on the (small) likelihood of a cata-
large increase in temperature, but rather         strophic outcome in which climate change is
a very large economic effect, in terms of a       sufficiently extreme to cause a very substan-
decline in human welfare, from whatever cli-      tial drop in welfare.
mate change occurs. That such outcomes are
                                                  4.2 What to Do?
ignored is not surprising; IAMs have nothing
to tell us about them. As I explained, IAM           So how can we bring economic analysis
damage functions, which anyway are ad hoc,        to bear on the policy implications of possi-
are calibrated to give small damages for small    ble catastrophic outcomes? Given how little
temperature increases, and can say nothing        we know, a detailed and complex modeling
meaningful about the kinds of damages we          exercise is unlikely to be helpful. (Even if we
should expect for temperature increases of        believed the model accurately represented
5º C or more.                                     the relevant physical and economic relation-
                                                  ships, we would have to come to agreement
4.1 Analysis of Catastrophic Outcomes
                                                  on the discount rate and other key parame-
   For climate scientists, a “catastrophe” usu-   ters.) Probably something simpler is needed.
ally takes the form of a high temperature out-    Perhaps the best we can do is come up with
come, e.g., a 7º C or 8º C increase by 2100.      rough, subjective estimates of the probability
Putting aside the difficulty of estimating the    of a climate change sufficiently large to have
probability of that outcome, what matters in      a catastrophic impact, and then some distri-
the end is not the temperature increase itself,   bution for the size of that impact (in terms,
but rather its impact. Would that impact be       say, of a reduction in GDP or the effective
“catastrophic,” and might a smaller (and          capital stock).
more likely) temperature increase be suffi-          The problem is analogous to assessing the
cient to have a catastrophic impact?              world’s greatest catastrophic risk during the
   Why do we need to worry about large tem-       Cold War—the possibility of a U.S.–Soviet
perature increases and their impact? Because      thermonuclear exchange. How likely was
even if a large temperature outcome has           such an event? There were no data or models
low probability, if the economic impact of        that could yield reliable estimates, so analy-
that change is very large, it can push up the     ses had to be based on the plausible, i.e., on
SCC considerably. As discussed in Pindyck         events that could reasonably be expected to
870                Journal of Economic Literature, Vol. LI (September 2013)

play out, even with low probability. Assessing   unknown. When it comes to the impact of
the range of potential impacts of a thermo-      climate change, we know even less. IAM
nuclear exchange had to be done in much          damage functions are completely made up,
the same way. Such analyses were useful          with no theoretical or empirical foundation.
because they helped evaluate the potential       They simply reflect common beliefs (which
benefits of arms control agreements.             might be wrong) regarding the impact of 2º C
   The same approach might be used to assess     or 3º C of warming, and can tell us nothing
climate change catastrophes. First, consider     about what might happen if the tempera-
a plausible range of catastrophic outcomes       ture increases by 5º C or more. And yet those
(under, for example, BAU), as measured by        damage functions are taken seriously when
percentage declines in the stock of produc-      IAMs are used to analyze climate policy.
tive capital (thereby reducing future GDP).      Finally, IAMs tell us nothing about the like-
Next, what are plausible probabilities?          lihood and nature of catastrophic outcomes,
Here, “plausible” would mean acceptable          but it is just such outcomes that matter most
to a range of economists and climate scien-      for climate change policy. Probably the best
tists. Given these plausible outcomes and        we can do at this point is come up with plau-
probabilities, one can calculate the present     sible estimates for probabilities and possible
value of the benefits from averting those out-   impacts of catastrophic outcomes. Doing
comes, or reducing the probabilities of their    otherwise is to delude ourselves.
occurrence. The benefits will depend on             My criticism of IAMs should not be taken
preference parameters, but if they are suffi-    to imply that, because we know so little, noth-
ciently large and robust to reasonable ranges    ing should be done about climate change
for those parameters, it would support a         right now, and instead we should wait until
stringent abatement policy. Of course this       we learn more. Quite the contrary. One can
approach does not carry the perceived preci-     think of a GHG abatement policy as a form
sion that comes from an IAM-based analysis,      of insurance: society would be paying for a
but that perceived precision is illusory. To     guarantee that a low-probability catastrophe
the extent that we are dealing with unknow-      will not occur (or is less likely). As I have
able quantities, it may be that the best we      argued elsewhere, even though we don’t
can do is rely on the “plausible.”               have a good estimate of the SCC, it would
                                                 make sense to take the Interagency Working
                                                 Group’s $21 (or updated $33) number as a
              5.   Conclusions
                                                 rough and politically acceptable starting
   I have argued that IAMs are of little or      point and impose a carbon tax (or equivalent
no value for evaluating alternative climate      policy) of that amount.20 This would help to
change policies and estimating the SCC.          establish that there is a social cost of carbon,
On the contrary, an IAM-based analysis sug-      and that social cost must be internalized in
gests a level of knowledge and precision that    the prices that consumers and firms pay.
is nonexistent, and allows the modeler to        (Yes, most economists already understand
obtain almost any desired result because key     this, but politicians and the public are a dif-
inputs can be chosen arbitrarily.                ferent matter.) Later, as we learn more about
   As I have explained, the physical mecha-      the true size of the SCC, the carbon tax could
nisms that determine climate sensitiv-           be increased or decreased accordingly.
ity involve crucial feedback loops, and
the parameter values that determine the            20 See Pindyck (2013b). Litterman (2013) and National
strength of those feedback loops are largely     Research Council (2011) come to a similar conclusion.
Pindyck: Climate Change Policy: What Do the Models Tell Us?                            871

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