What Does it Take to Control Global Temperatures?
A toolbox for testing and estimating the impact of economic
policies on climate.
Guillaume Chevillon∗

Takamitsu Kurita

ESSEC Business School

Kyoto Sangyo University

FranceJapan

April 16, 2024

Abstract
This paper tests the feasibility and estimates the cost of climate control through economic policies. It provides a toolbox for a statistical historical assessment of a Stochastic
Integrated Model of Climate and the Economy, and its use in (possibly counterfactual) policy
analysis. Recognizing that stabilization requires supressing a trend, we use an integratedcointegrated Vector Autoregressive Model estimated using a newly compiled dataset ranging
between years A.D. 1000-2008, extending previous results on Control Theory in nonstationary systems. We test statistically whether, and quantify to what extent, carbon abatement
policies can effectively stabilize or reduce global temperatures. Our formal test of policy
feasibility shows that carbon abatement can have a significant long run impact and policies
can render temperatures stationary around a chosen long run mean. In a counterfactual
empirical illustration of the possibilities of our modeling strategy, we show that the cost ofcarbon abatement for a retrospective policy aiming to keep global temperatures close to their
1900 historical level is about 75% of the observed 2008 level of world GDP, a cost equivalent
to reverting to levels of output historically observed in the mid 1960s. This constitutes ameasure of the putative opportunity cost of the lack of investment in carbon abatement
technologies.
Keywords: Vector Autoregression, Cointegration, Control theory, Carbon abatement, Climate change, Counterfactual analysis, Integrated Assessment Models.

∗The authors thank participants to the EC2 conference in Aarhus, the IAAE at King’s College, London, the ISF
in Oxford, the Climate Econometrics online seminar, the SNDE at UCF, Orlando, the Barcelona Summer Forum,and the IWEEE at Bolzano for helpful comments and suggestions. They are in particular grateful to Jennifer
Castle, Frank Diebold, Luca Fanelli, David Hendry, Robert Kaufmann, Frank Kleibergen, Andrew Martinez,
Sophocles Mavroeidis, Zack Miller, John Muellbauer, Barbara Rossi and Glenn Rudebusch.

1

1Introduction

This article presents a novel approach to testing the feasibility and evaluating the costs associatedwith global temperature control by drawing on historical data on the interaction between climate
and the economy spanning over a thousand years. Our primary objective is to rely on empiricallyestimated relationships, acknowledging the criticism raised by Pindyck (2013) towards models
that solely rely on theoretical assumptions, calibrations, or simulations, as they may create a“misleading perception of knowledge and precision”. In pursuit of our objective, we construct a
dataset and employ a new econometric methodology relying on stable long-run interactions totest the hypothesis of temperature controllability and evaluate its cost through counterfactual
policy analysis.
Our approach relies on a model inspired by Stochastic Dynamic Integrated Models of Climate
and the Economy (SDICE) proposed by Nordhaus (2017) that has become one of the main
Integrated Assessment Models (IAMs) of climate and the economy. This model is often assessed
through simulations and scenario analyses in order to evaluate the cost of carbon abatement
policies required to achieve some specific temperature control objectives. The lack of historicalcarbon abatement policies, at least until the recent decades, renders empirical studies of the
SDICE models limited. This is one issue we tackle using long historical time series dating backto AD 1000, i.e., prior to natural experiment that the industrial revolution constitutes. This
allows us to prove, through a statistical test, that policies whose objectives focus on temperature
control are empirically feasible.
The industrial revolution having accelerated the upward trend in economic activity, Greenhouse gas (GHG) emissions and temperatures, we recognize that temperature control requires
suppressing the upward stochastic trend to render temperatures stable around a long run mean.
For this we draw on the abundant literature studying the dynamic interactions between climate
variables and human activity through an integrated-cointegrated Vector Autoregressive (VAR)
model (see, inter alia, Stern and Kaufmann, 2014, and Chang et al., 2020). We study thismodeling strategy in light of work on nonstationary Control Theory developed by Johansen andJuselius (2001, JJ01 henceforth) who find cointegration properties to be the determining factor.
We show that the effect of the control policy is to augment the VAR(p) into a VARMA(p, 1)
that reflects additional cointegration relations.
Hence, we assess within a cointegrated VAR model what policies are feasible to render “climate” variables stationary around a stated objective while retaining economic progress. We
focus on very long series (despite the unavoidable mismeasurements) to capture long-run equilibria that are invariant to changes in policy, i.e., that are immune to the Lucas (1976) critique.
Our empirical model can be used as a toolbox for evaluating the statistical feasibility and costof policies. In an empirical application, we propose a formal test that carbon abatement or
technology investment are capable of achieving temperature control. We entertain the counter2

factual question whether a centralized authority could have implemented, in the 20th century,a policy aiming to maintain global temperatures at the level of 1900. We assess its cost using
two distinct indirect examples, either (i) via a costing of the lack of carbon abatement policy,
using a reduction of output and consumption as controls; or (ii) through the increased wealththat a costless reduction of the carbon content of production technology would generate. The
estimated cost of the lack of abatement policy amounts to about 75% of the 2008 global level of
output (equivalent to forestalling growth since the 1960s) together with a reduction of 45% in
consumption. Investment in carbon neutral technology would by contrast achieve its objective
and be profitable as long as it costs less than 50% of 2008 global GDP and 75% of consumption.
Both policies show that, under the condition that the stated temperature control is achieved, thehuge magnitude of investment in mitigating technologies that is required and is more profitable
than a degrowth alternative. We state in the title that our analysis provides a toolbox as ourmodel and methodology can be applied to other policies and choices of controls that climate
scientists may prefer.
The rest of this study consists of four sections. Section 2 reviews the SDICE model, thedatabase we consolidate, and its framing in a cointegrated VAR system. Section 4 discusses thecontrol theory of JJ01 and develops some of the results needed for a counterfactual analysis.
Section 4 then assesses empirically the controllability of temperature through carbon abatement
policies and performs some counterfactual costing analyses. Details, further explanations andempirical results are provided in an online Supplementary Appendix.

2

A linearized SDICE Model

We propose an empirical model for the climate-economy nexus and estimate over a thousand
years. We introduce a log-linearized SDICE that has been sufficiently streamlined so it can shedlight on long-run equilibria estimated later in the paper. There exist a multiplicity of IAM models
but most of them can been seen as refinements or extensions of the main equations we consider
here (see, e.g., Barnett et al., 2022, and Hänsel et al., 2022, for analyses of the uncertainty
surrounding the models). By construction, log-linearization removes the nonlinearities that are
inherent in the discussion surrounding possible future tipping points but these can easily be
introduced through additional local trends.
We consider here a simplified version of the SDICE model of Nordhaus (2017) as studied,inter alia., in Ikefuji et al. (2020), see Figure 1 for a presentation of its general principles. The
key feature is that the model introduces a negative feedback loop from climate to the economy.
At each period t, human economic activity combines various production factors (such as labor
force and capital) to generate real Gross Domestic Product (GDP, or world output), Yt . This
production generates externalities in the form of greenhouse gas (GHG) emissions – Carbon
dioxide (CO2 ) in particular. Humans may decide to mitigate these externalities via abatement,3

i.e. investment that reduces the emission producing (brown) content of economic activity. We
simplify the model and only present the log-linearized version of that in Ikefuji et al. (2020), withlower case letters representing logarithms, see the Supplementary Appendix for more details.
Total CO2 emissions consist of anthropogenic emissions (caused by human activity) andother – exogenous – types e0t . Total emissions et then result fromet = σt − µt + yt + e0t ,(1)where σt is the emissions-to-output ratio for CO2 and µt is the abatement fraction for CO2 .
Regarding the presence of CO2 in the atmosphere, the SDICE specifies that its concentration
mt accumulates through interactions with shallow and lower oceans. The lack of long historicalseries on the carbon contents of oceans, mt can be seen as following a Markov state-spaceprocess with two hidden layers (latent variables). This amounts to specifying that mt follows an
autoregressive model with distributed lags of et , here an ARDL(4,4), A (L) mt = B (L) et ,where
L denotes the lag operator such that Lmt = mt−1 and A (·) , B (·) are polynomials of degree 4.
Now atmospheric temperatures, ht , themselves relate dynamically to atmospheric gas concentrations, ocean temperatures, as well as extraneous radiative forcing, ft0 , which in log form
0
can be written as an equation linking ht+1 − a1 mt+1 − ft+1
to the lagged value of that expression
together with ht and ht−1 . Finally, we consider the impact of climate on economic growth:
the fraction of GDP not spent on abatement is consumed, ct , or invested, it , along the budget
constraint: yt − ωt − ξht = c̃t , where c̃t = ct + it , and the logarithm of the cost of abatement,ωt , satisfies ωt = ψt + θµt .with θ > 1 so the cost of abatement increases faster than abatement
itself. Parameter ξ represents damage induced by warming: it closes the feedback loop fromclimate to the economy shown in Figure 1. Considering ψt constant over the historical sample(but not over the future under tipping point scenarios), we identify ωt to θµt below.
The model presented above can be expressed in terms of six endogenous variables (yt , c̃t , mt ,ht , µt , σt ) and two exogenous e0t , ft0 . This leads (removing constant terms and introducing two
lag polynomials D (·) and G (·)) to the following equations:
Economy-Climate nexus: A (L) mt = B (L) σt − µt + yt + e0t ,Carbon-Temperature: D (L) ht = G (L) a1 mt + ft0 ,Damage loop:

yt = c̃t + θµt + ξht .

(2a)
(2b)
(2c)

The SDICE model is typically solved by the Central Planner who sets the policy variables:level of abatement, µt , or its cost ωt , and carbon content of technology σt to achieve a welfare
objective in terms of c̃t .1 We consider this objective from an empirical perspective below through1

By specifying a production function for yt as a function of labor and capital, as well as a utility function, thecentral planner may consider the tradeoff between consumption and leisure. We abstain from it for simplification.

4

1st Cointegration relation
Human economic
production (GDP)++Consumption and
Investment that emit
CO2

Investment on
mitigating technology+

2nd Cointegration relation
CO2 in oceans––

Radiative Forcing
in atmosphere+
Temperature of oceans

Temperature of
atmosphere

Physical model for carbon & temperature

Economic-Climate nexus

Figure 1: Principle of SDICE Model. The solved out empirical model finds two long term
equilibria ( ‘cointegration relations’) corresponding to (i) the economic-climate nexus and (ii) thephysical equilibria between global temperatures and radiative forcings linked to concentrationsof carbon in the atmosphere and the oceans.
the concept of controllability, where we ask whether and what policies can generate a stableequilibrium between economic activity and climate.

3

An Empirical Model for Climate and the Economy

The dynamic model described above can be assessed using historical empirical evidence througha cointegrated vector autoregressive model (CVAR) developed by Johansen (1988), i.e., a modelfor the dynamic interactions and long run equilibria between climate of and the economy. For
this we first construct a new dataset compiling and extending various sources over the second
millennium AD.
Constructing a long dataset. The data were obtained and reconstructed from various
sources that are presented in the Supplementary Appendix, and whose online links and interpolation details are provided in separate code file (Data Preparation). The data is presented
in Figure ??: it comprises measures of economic activity (real world output and consumption)
as well as variables describing temperature anomalies, carbon concentrations in the atmosphere,radiative forcings of non-anthropogenic origin (solar, volcanic...). We consolidate this data at5the annual frequency, dating back to year 1000 AD.
It is obvious that the data we consider must necessarily be subject to mismeasurement as we
consider global variables over extended periods of time. Yet, following Duffy and Hendry (2017),
we expect that this mismeasurement does not affect inference on the presence of cointegration.
In Figure ??, we see that all variables except radiative forcings of volcanic origin exhibit upward
trends towards the end of the sample.
The Cointegrated VAR approach. We perform a cointegration analysis within a VAR(8)model for the four variables Xt = (yt , ct , mt , ht ) measured as log GDP and log consumption, log
CO2 atmospheric concentration and actual (non-logged) temperature anomalies. The impactof the Industrial Revolution is captured by a broken linear trend that starts in 1800 (thatis restricted to the cointegrating space). We prefer to model long term population patterns
through this trend for statistical reasons, as conditioning on the actual data impacts estimator
distributions in a non-standard way. For technical reasons, we also need to include the change
in the broken trend, i.e., a step dummy starting in 1800. Solving the model for concentrations
and radiative forcings as proxies for emissions allows to extend the data set to cover the years
1000-2008. Our analysis leads to focusing on Xt , with radiative forcings of volcanic origin, ftV olentering as unrestricted exogenous regressors.
The cointegrated model writes as∆Xt = τ + α β 0 Xt−1 + δ1 t1{t≥1800}
+

7
X



(3)

V ol
Γi ∆Xt−i + γ 0 ∆ft−1+ δ0 1{t≥1800} + t ,i=1

where β 0 Xt−1 captures the two long run equilibria taking the form of “cointegration” relations
are stationary although the individual variables are not.
In the empirical model, the data indicates the presence of two stochastic trends, and two
cointegration relations. Based on the SDICE model, we make the following assumption on thecommon stochastic trends.
Assumption 1 (S) The sources of nonstationarity in the empirical system come from two latent common stochastic trends:(i) a measure of the carbon content of technology progress, which in the model amounts to thelogarithm of emissions-to-output ratio of CO2 , σt ;(ii) a wealth effect that combines global population and capital accumulation through investment, it .
Remark 1 We could alternatively interpret a linear combination of them as wealth and technology of green (carbon free) and brown (carbon intensive) origin and impact noting that these6are not orthogonal in the sample.
Assumption S helps us identify the two stable (i.e. stationary) long run cointegration relations(see the Supplementary Appendix for a description of the estimated model) as
c1,t = yt − 1.54ct − .81ht − .036t × 1{t≥1800} ,c2,t = ht − 4.12mt .
We interpret them with the help of the SDICE model.
1. The first equation, c1,t , corresponds to an interaction between temperature and humanactivity. In the SDICE, this corresponds to equation (2c). The broken trend grows at anannual rate of 3.6%, corresponding to the long run growth rate of population, total factor
productivity and capital intensity over the industrial era (for the latter, see Baumol, 1986
and references therein).
2. The second cointegrating relation, c2,t , corresponds to the interplay between CO2 concentrations in the atmosphere and temperature, as in equation (2b).
3. The data does not support equation (2a) as a cointegration relation. This is in line with
Assumption S.(i) that includes the nonstationary σt .
The second cointegration relation does not involves human activity although the technology
mix has strong evolved over the millennium. Yet, yt is close to significant in this equation so
we might have preferred to retain it. In Smil (2017, in his last table on page 458) who reports
estimates of per capita annual consumption of primary energy, these have only started increasing
by an order of magnitude when countries started their industrial revolution (the estimates are
explicitly uncertain). Hence, it is likely that the technology mix, prior to 1800, has not modified
much the elasticity of temperature to CO2 emissions, yet given the ensuing changes, we preferto leave human activity outside this equation, to reflect only physical equilibria. For robustness,
we reestimated the model starting in AD 1750, and found the estimates to be very similar, witha test of overidentifying restrictions that has a p-value of 0.41.
In the model above, 100% green growth is feasible if a downward trend in σt is achieved,
tending towards −∞ so actual carbon content Σt = exp (σt ) is driven to zero. This constitutes
an alternative to reducing growth altogether. In practice, given the current technologies, acombination of green investment and restrained brown growth is required in our model to achieve
stability in temperature, let alone the counterfactual analysis we perform below.
Comparison with estimates in the literature. To assess the plausibility of our estimatedmodel, we compare its implications with meta analyses based on the existing literature. The
7

long run impact of climate change on the economy has been considered nonlinear so calibrated
parameter uncertainty is an important issue. The table below summarizes the results for threemain indicators used in the climate-economy literature (see the Appendix for derivations andexplanations).
Ranges in Literature∗

Temperature damage on GDP, ξ
200 year temperature increase due to CO2
GDP loss due to CO2 , γ[.68, 1.34][.7, 2.1]†[.27, 10.4]†

Our results (s.e.).81 (.40)
1.35 (.66)
4.25 (.38)∗ Nordhaus & Moffat (2017); † Hassler, Krusell & Olovsson (2018).

Overall, these results (with reported standard errors) show that our estimates are very muchin the low to mid-range of those reported in the literature, so we are confident that our analysis
neither severely underestimate nor overestimate the relative impacts of climate and the economy.

4

Control theory in a cointegrated system

We now review the non-stationary control theory derived by JJ01 and show how it can beused to understand the issue of climate control through carbon abatement, reinterpreting theobjective of the policy as suppressing the stochastic trend in temperature through use of cointegration properties. For the sake of expositional simplicity, setting k = 1 in (3) and removing
deterministic terms reduces the model to∆Xt = α β 0 Xt−1 − µ + t ,(4)

and its Granger-Johansen moving average representation is
Xt = CPt

j=1 j + C (L) t + A0 ,(5)

where the long-run impact matrix C governs the nonstationary stochastic trends of the system:
it latter plays a key role in the theory of controllability. In the expression above, C (L) t
represents a stationary series, A0 depends upon the initial values and µ such that β 0 A0 = µ. It
follows from β 0 C = 0 that β 0 Xt − µ = β 0 C (L) t is stationary so β are cointegration vectors. The
long-run expected value of Xt is defined as X∞ = limτ →∞ E (Xτ |X0 ) = CX0 + α (β 0 α)−1 µ. We
now consider a Control Theory derived from Preston and Pagan (1982, Chapter 4, and Section
5.8 in particular) and adapted to the nonstationary context as follows.
Definition 1 The Control Policy consists in two selection matrices (a, b), an objective b∗ anda contemporaneous control rule ν (·) such that, in the system (4),8(i) Policy controls a0 Xt can be changed by intervention using control rule ν (Xt ) :ctr : a0 Xtctr = a0 Xt + a0 ν (Xt ) ;(ii) The objective is the desired value b∗ of a targeted combination of variables, b0 Xt . It isdefined as the long-run conditional expectation
newb∗ = lim E b0 Xt+h
|Xtctr ,h→∞

new is the ecosystem outcome for X
where b0 Xt+1
t+1 (now made stationary) given by expression (4)when the control has been applied to Xt .
new =We assume in this paper that the policy objective is to control temperature so that b0 Xt+1∗
hnew
t+1 and this process becomes stationary around a mean b .
The control policy defined above is explicitly written as a new equation to the system, onethat necessitates the “authority” that implements it must be able to modify a0 Xt via a0 ν (Xt ) .
This may require extra controls that are outside the system but interact with it, though forsimplicity here we disregard this possibility. Indeed, our aim is not to assess how to implementa policy, but whether it can be effective.
With continuous monitoring and control, the procedure delineated above works as follows(for a policy that starts at time t = 0)
X0 → X0ctr = X0 + ν (X0 ) → X1new = Ip + αβ 0 X0ctr − α0 µ + ε1 → X1ctr = X1new + ν (X1 ) → ....
{z
}
|
{z
}
|
|
{z
}
(Policy)(Ecosystem)(Policy)where we define the projector onto the space spanned by a as a = a (a0 a)−1 .
Invariance. Success of the above approach relies on the notion of invariance of the system(4) to interventions of the type a0 Xt → a0 Xtctr so that we can assume that the potential outcome
is generated through mechanism (4) that is not affected by interventions. For invariance, we
require here that parameters remain unaffected by the introduction of the new policy so we can
new = X ctr + α β 0 X ctr − µ + 
be assured that Xt+1
t+1 .
t
t
This relates to the notion of “super-exogeneity” proposed by Engle, Hendry and Richard(1983), and studied by Pretis (2021) in the context of climate. Yet, super-exogeneity is about
invariance of conditional equations, while we consider here a system approach. While invariancecannot be ascertained with certainty, we follow in the Supplementary Appendix two approaches
to ensure it constitutes a plausible assumption. These rely on (i) estimating the model using
extra long historical data to capture stable relations pre- and post-industrial revolution, treating
the latter as an historical “natural expirement” in climate change; and (ii) using statistical tests
9

used in the context of super-exogeneity, inter alia by Castle et al., (2017).
Policy Impact. A question raised by JJ01 is that of controllability of b0 Xt via a0 Xt . Since the
new , the choice of controls
objective is formulated in terms of a conditional expectation for b0 Xt+h
new is indeed stationary around b∗ . In the cointegrated
and policy rule must ensure that b0 Xt+h
VAR(1), JJ01 show that


−1 
new
Xtctr = b0 C [Xt + ν (Xt )] + α β 0 αb∗ = b0 lim E Xt+hµ ,h→∞so that the condition for controllability writes as follows.
Condition 1 (Controllability, C) The Policy objective is achievable using the chosen controlsif
det b0 Ca 6= 0.
(6)where C is the matrix measuring the long run impact of the stochastic trends in the GrangerJohansen moving average representation (5).
Notice that Controllability is a property of the system (under invariance) for the targetedvariables and chosen controls. It does not depend on the actual rule ν (Xt ) . JJ01 show that if
Controllability applies, then a linear rule is possible:



−1 
ν (Xt ) = a b0 Ca−1b∗ − b0 Xt + b0 α β 0 α{z}|policy discrepancy 
β 0 Xt − µ  .
| {z }(7)

system discrepancy

The rule consists of a weighted average of b∗ − b0 Xt , a “policy” discrepancy between the desired
objective and the current value at t, and β 0 Xt − µ is a “system” deviation from the steady state
at t. Policy becomes, here, fully endogenous and does not constitute an exogenous shock, as isoften modelled in economics via structural VARs. The reason for the effectiveness of the policy,
and hence the channel through which it operates, relies on ν (Xt ) generating an extra linear
cointegration relation. The new augmented system writes,


new
∆Xt+1
= α β 0 Xtnew − µ + Ip + αβ 0 ν (Xtnew ) + εt+1 .

(8)

Following the most recent literature on treatments in time series and macroeconometrics, the policy controls and objective above define a Direct Potential Outcome System in the sense of Rambachan and Shephard (2021). In there framework, the policy consists in an assignment Wt+1 =new = −αµ+(I + αβ 0 ) X new +(I + αβ 0 ) Wν (Xtnew ) that is uncorrelated with εt+1 so Xt+1
t+1 +εt+1
tconstitutes a “Non-anticipating Potential Outcome” (see the Supplementary Appendix for a discussion of our framework and theirs).
10

In the context of a VAR(1) dynamic system, it can be shown that ν (Xtnew ) = a (κ0 Xtnew − κ0 ) =aκ0 εt , so the impact of the policy is to augment the VAR(1) into a VARMA(1, 1) :


new
Xt+1
= −αµ + I + αβ 0 Xtnew + εt+1 + I + αβ 0 aκ0 εt .

(9)This results also holds for higher order VAR(p) dynamics that are modified into VARMA(p, 1)(for a careful choice of policy parameters among those that achieve the stated objective, see JJ01,
Theorem 6). Equation (9) shows that the policy can be identified in practice for its parametersaκ0 through a Structural VARMA or VMA and associated response functions. This is not ourobjective here though, since our aim is to study the impact of implementing a given policy.
Testing for Climate Controllability. Our first question is whether economic activity, yt or
ct , can be used as an instrument for a policy that aims to control temperature. Based on theanalysis above which can be extended to cover k > 1, this amounts to testing the significanceof the element in the long run C matrix corresponding to equation (6). In the empirical model,
the estimated Ĉ, which is reported in the Supplementary Appendix, shows that coefficient for
the long run impact of yt on temperature is 1.56, with a highly significant t-statistic of 3.33.
The matrix estimate and corresponding t-statistics show that the null of non controllabilityof temperature ht by policy controls yt or ct , i.e. b0 Ca = 0 for either variable in equation (6),or a linear combination thereof, can safely be rejected at conventional levels. This shows thatcarbon abatement can achieve its purpose of controlling temperature, i.e. rendering it stationaryaround a chosen mean. The levels of significance indicate that any linear combination of yt andct can also be used as a policy. Note that direct capture of carbon dioxide in the atmosphere,
provided the technology develops sufficiently fast, would also achieve its objective.

5

Counterfactual Policy Analysis

Now that we have established that a policy of carbon abatement is capable of controlling global
temperatures, the natural follow-up question is at what cost. To this end, this section considers
the retrospective and prospective costs of a policy. For this, we design, and then simulate basedon the empirical model, a counterfactual path for the endogenous variables.
Policy design. We now consider JJ01’s analysis from the perspective of the policy makerand econometrician who aim to perform a historical counterfactual analysis. We assume thatthe policy is actioned by a central authority, which may represent international coordination,or might be fictitious. For instance, a counterfactual analysis that may be of interest consists
in deriving the development path that would have arisen if mitigating policies had been put inplace through carbon abatement at some point in the past.

11

The methodology and model above allow for a variety of policy objectives and instruments.
Here, we consider retrospective policies that would have aimed to control global temperatures
to render them stationary around a long run mean equal to their 1900 level (assuming ht wereobserved then), i.e. stable over the 20th century at 0.7◦ C below their 2008 level. Naturally, theensuing cost depends on the timing of the policy initiation as well as on the choice of controls.
We contemplate two distinct policies that provide different approaches to measuring theopportunity cost of inaction on green investment.
1. One that mixes investment and consumption, with more weight accrued to the latter (since
our model does not specify the increase in abatement effectiveness that would have arisen
from higher investment on mitigating technologies – yet this can be easily embedded via
specific assumptions). Our baseline choice for the control is a0 Xt = yt + ct /2 with target
b0 Xt = ht . The weights are arbitrary but the modeler has the flexibility to consider policiesof their choice, as our study provides a toolbox that is adaptable.
2. Another that targets the same object through a reduction of the carbon content of technology, σt , in equation (2a), assuming that it can be put in place to control emissions andconcentrations a0 Xt = mt directly. This amounts, for a given level of economic activity,
to reducing emissions and, possibly, to capturing atmospheric CO2 . Notwithstanding theactual cost of developing these technological solutions – which is assumed to be zero in abaseline scenario, but could be introduced as a fraction of yt or c̃t – such a policy would
restrain the economic damage caused by increasing temperatures, hence increasing yt andc̃t . As we do not model the cost of such a reduction, the ensuing impact on yt and ct canhelp the policy maker assess what costs they are willing to endure for a specific objective.
Policy 1: Cost of inaction on abatement technologies. Assuming an authority has
modified at will both world GDP and consumption to achieve its objective, Figure 3 reports
the resulting dynamics, where to avoid a sudden shock in the early 20th century, we introduce
the policy progressively. We also include a forecast over the first half of the 21st century, bothas obtained unconditionally from the empirical model and with a policy that aims to maintainthe same temperature level. We also produce the bootstrap mean prediction and associatedconfidence intervals, restricting ourselves to using residuals post 1900.
Temperature control is achieved in this exercise via stabilizing atmospheric carbon concentrations to a level about 20% below that of 2008. The ensuing cost in terms of foregone GDP
in 2008 is about 75% so the observed counterfactual GDP in 2008 would have been that which
we have known in the 1960s (the uncertainty is large), i.e., a cost of about 40 years of growth.
The cost in terms of world consumption is 45% of the 2008 level, foregoing the growth observed
since the mid-1970s. When looking at the bootstrap distributions (at each step forecasting thenext period using 500 bootstrap samples), we see that the historical sequence of shocks imposed
12that most of the gains, in the counterfactual experiments, where obtained in the second half ofthe 20th century.
In order to assess the cost of inaction in the face of climate change, we also perform acomplementary analysis where the objective in terms of temperature control remains the same,but the policy only starts in 1950. Corresponding counterfactual outcomes are presented in the
Supplementary Appendix. The ensuing cost becomes 90% of the GDP of 2008, i.e. essentiallyno growth since 1950. In terms of consumption, the counterfactual stands at 75% below theobserve level of 2008, i.e. an additional 20% reduction to the baseline scenario.
Projecting our experiment over the 21st century in either policy, we see that the efforts will
have to be sustained, reinforcing abatement policies. Clearly, these projections are contingent
on specific assumptions over the forecast period and nonlinearities due to major climate change(see, e.g., Diebold et al., 2022, and Lenton et al., 2019).
Policy 2: Reducing the carbon content of technology Assuming the technological improvement is available freely but activated progressively to reach a reduction in 20% of atmospheric CO2 concentrations, the resulting gain in economic activity is potentially massive:
Figure 3 shows that the bootstrap interval ranges from −3% to +160%, with a mean gain of+50%, and where the realized policy is at the upper bound. Similar values hold for c̃t , with awider bootstrap range and higher mean.

6

Conclusions

This paper assesses the feasibility and quantifies the cost of carbon abatement policies using
long series of economic and climate data compiled for the second millennium AD. By means ofa cointegrated VAR modeling strategy that matches a simple linearized SDICE model, we test
whether and show how a policy that aims to render temperatures stationary around a given
long run mean can be achieved. In an empirical application, we tested that carbon abatement is
indeed significantly capable of such a policy. We assessed its counterfactual cost, if a centralized
authority had been able to implement such a policy in the 20th centuries in order to maintainthe temperature level (observed ex post) in 1900. The estimated cost of the policy leads to a
reduction of about 75% of the 2008 world level of output (equivalent to foregoing growth since
historical levels of the 1960s) together with a reduction in about 45% in global consumption.
These costs are assessed under the assumption of a constant carbon content of technology, sothey show the opportunity cost of the lack of investment in mitigating technologies.
The analysis in this paper constitutes an exercise where we deliberately chose simple policy
controls, but economically meaningful alternatives are also possible (say the discounted wealthrather than spot GDP and consumption). Indeed we see the collected data, model and results
above as a toolbox for policy analysis where refinements on possible projected scenarios and13

Panel (b): Atmospheric Concentrations (m t in logs)

Panel (a): Economic activity (in logs)
5.0

yt

7.5

ct

CO2

CH4

N2O

7.0
2.5
6.5
0.0

6.0

0

350

700

1050

1400

1750

0

2100

Panel (c): Temperature anomalies

350

700

1050

1400

1750

2100

1050

1400

1750

2100

Panel (d): Forcings f t
01

Volcanic
GHGs
Solar
Volc_AOD

0-5
Berkeley
Reconstructed

-1

0

350

700

Hegerl
TAman

1050

1400

1750

2100

0

350

700

Figure 2: Data series obtained from various sources. All references and explanations are theSupplementary Appendix.

yt
Forecasts
Boot. mean
Forecast error band

7.5

y tnew
Forecasts_new
Boot. bands25.0

h t (Target)
Boot. meanh tnew
Boot. bands

10.0

y tctr
Forecasts_new
Boot. bands

2

7.5

1

-75%

1

2.5

-1

~c
t
Boot. mean

2000

2050

~cnew
t
Boot. bands

1900
6.25

0.7°C

0

0.0
1950

h tnew
Boot. bands

5.0

+50%

1900

h t (Target)
Boot. med.

+160%

0.7°C

0

2.5

yt
Forecasts
Boot. mean
Forecast error band1950
mtBoot. mean

2000

2050

1900

m tnew
Boot. bands

10.0

1950
~c
t
Boot. med.

2000

2050

~cnew
t
Boot. bands

-1
1900
6.2

1950
mt
Boot. med.

2000

2050

m tnew
Boot. bands

6
6.00

7.5
6.0

-45%

4

+180%

-20%

5.75

5.0

5.50

1900

1950

2000

2050

1900

-12%

5.8

+75%

2

2.5
1950

2000

2050

1900

Panel (a)

1950

2000

2050

1900

1950

2000

2050

Panel (b)Figure 3: Counterfactual cost of a policy starting in 1900 aiming at controling global temperatures and rendering them stationary around a long run mean equal to their 1900 level (as it is
known now). Panel (a): the control is yt + c̃t /2. Panel (b): the control is mt .

14

abatement policies need to be assessed. This constitutes one step into statistical analyses of thefeasibility of temperature control, and cost assessment of such policies.

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