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What Does it Take to Control Global Temperatures? A toolbox for testing and estimating the impact of economic policies on climate.
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This article presents a novel approach to testing the feasibility and evaluating the costs associated with 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 empirically estimated relationships, acknowledging the criticism raised by Pindyck (2013\nocite{Pind13}) towards models that solely rely on theoretical assumptions, calibrations, or simulations, as they may create a \textquotedblleft misleading perception of knowledge and precision\textquotedblright. In pursuit of our objective, we construct a dataset and employ a new econometric methodology relying on stable long-run interactions to test 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\nocite{Nord2017}) that have become one of the main Integrated Assessment Models (IAMs) of climate and the economy. These models are often assessed through simulations and scenario analyses that evaluate the cost of carbon abatement policies required to achieve some specific objectives of temperature control. The lack of historical carbon 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 back to AD\ 1000, i.e., before the 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\nocite{SterKauf14}, and Chang et al., 2020\nocite{Chan20}). We study this modeling strategy in light of work on nonstationary Control Theory developed by Johansen and Juselius (2001,\nocite{JohaJuse01} 2024\nocite{JohaJuse24}, JJ henceforth) who find cointegration properties to be the determining factor.\ We show that the effect of the control policy is to augment the VAR$\left( p\right) $ into a VARMA$\left( p,1\right) $, alternatively written as an SVAR$\left( p\right) $ with\ recoverable excess shocks that reflect additional, policy generated, cointegration relations.
Hence, we assess within a cointegrated VAR model what policies are feasible to render \textquotedblleft climate\textquotedblright\ 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. Their stability prior to and through the industrial revolution constitutes a gauge that these equilibria are immune to the Lucas (1976\nocite{lucas1976macro}) critique. Our empirical model can be used as a toolbox for evaluating the statistical feasibility and cost of 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 counterfactual 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 $\left( i\right) $ via a costing of the lack of carbon abatement policy, using a reduction of output and consumption as controls; or $\left( ii\right) $ through the increased wealth that 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 self-sustainable 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, the huge 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 our model and methodology can be applied to other policies and choices of controls that climate scientists and economists may prefer.
The rest of this study consists of five sections that we have kept deliberately short for clarity of the exposition; details, further explanations and empirical results are provided in an online Supplementary Appendix. Section 2 briefly reviews\ our choice for the SDICE\ model, then Section 3 the database we consolidate, and its empirical framing in a cointegrated VAR\ system. Section 4 discusses the control theory of JJ and develops some of the results needed for a counterfactual analysis. Section 5 then assesses empirically the controllability of temperature through carbon abatement policies and performs some counterfactual analyses of its cost. Section 6 concludes.
We propose an empirical model for the climate-economy nexus and estimate it over a thousand years. We introduce a log-linearized SDICE\ that has been sufficiently streamlined so it can shed light 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\nocite{BBH22}, and H{\"{a}}nsel et al., 2022,\nocite{CPC22} 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 (see, e.g., Kim et al., 2020, for an application to climate data\nocite{KOEP20}).
We consider here a simplified version of the SDICE\ model of Nordhaus (2017) as studied, inter alia., in Ikefuji et al. (2020\nocite{ikefuji2020expected}), see Figure (ref) 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),\ $Y_{t}.$ This production generates externalities in the form of greenhouse gas (GHG) emissions -- Carbon dioxide (CO$_{2}$) in particular. Humans may decide to mitigate these externalities via abatement, 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\nocite{ikefuji2020expected}), with lower case letters representing logarithms, see the Supplementary Appendix for more details.
Total CO$_{2}$ emissions consist of anthropogenic emissions (caused by human activity) and other -- exogenous -- types $e_{t}^{0}$. Total emissions $e_{t}$ then result from
where $\sigma_{t}$ is the emissions-to-output ratio for CO$_{2}$ and $\mu_{t}$ is the abatement fraction for CO$_{2}.$ Regarding the presence of CO$_{2}$ in the atmosphere, the SDICE specifies that its concentration $m_{t}$ accumulates through interactions with shallow and lower oceans. Thus, $m_{t}$ can be seen as following a Markov state-space process with two hidden layers (latent variables). The lack of long historical series on the carbon contents of oceans leads us to using the reduced form model for $m_{t}$ which follows an autoregressive model with distributed lags of $e_{t},$ here an ARDL(4,4), $A\left( L\right) m_{t}=B\left( L\right) e_{t},$where $L$ denotes the lag operator such that $Lm_{t}=m_{t-1}$ and $A\left( \cdot\right) ,$ $B\left( \cdot\right) $ are polynomials of degree 4 (we allow for more flexibility in the empirical study).
Now atmospheric temperatures, $h_{t}$ (or their anomalies in lieu of their logarithm) themselves relate dynamically to atmospheric gas concentrations, ocean temperatures, as well as extraneous radiative forcing, $f_{t}^{0}$. This can be written in log form as an equation linking $h_{t+1}-a_{1} m_{t+1}-f_{t+1}^{0}$ to the lagged value of that expression together with $h_{t}$ and $h_{t-1}$. Finally, we consider the impact of climate on economic growth: the fraction of GDP not spent on abatement is consumed, $c_{t},$ or invested, $i_{t},$ along the budget constraint: $y_{t}-\omega_{t}-\xi h_{t}=\tilde{c}_{t},$ where $\tilde{c}_{t}=c_{t}+i_{t},$ and the logarithm of the cost of abatement, $\omega_{t},$ satisfies $\omega_{t}=\psi_{t}+\theta \mu_{t}.$with $\theta>1$ so the cost of abatement increases faster than abatement itself. Parameter $\xi$ represents damage induced by warming: it closes the feedback loop from climate to the economy shown in Figure (ref). Considering $\psi_{t}$ constant over the historical sample (but not necessarily in the future, if we consider tipping point scenarios), we identify $\omega_{t}$ to $\theta\mu_{t}$ below.
The model presented above can be expressed in terms of six endogenous variables $( y_{t}, \allowbreak\tilde{c}_{t}, \allowbreak m_{t}, \allowbreak h_{t}, \allowbreak\mu_{t}, \allowbreak\sigma_{t}) $ and two exogenous $\left( e_{t}^{0},f_{t}^{0}\right) .$ This leads (removing constant terms and introducing two lag polynomials $D\left( \cdot\right) $ and $G\left( \cdot\right) $) to the following equations:
where $\beta^{\prime}X_{t-1}$ captures the two long run equilibria taking the form of \textquotedblleft cointegration\textquotedblright\ relations that are stationary although the individual variables themselves 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 the common stochastic trends.
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
We interpret them with the help of the SDICE model.
The second cointegration relation does not involves human activity although the technology mix has strong evolved over the millennium. Yet, $y_{t}$ 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\nocite{Smil2017}) 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 prefer to 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, with a 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 $\sigma_{t}$ is achieved, tending towards $-\infty$ so actual carbon content $\Sigma_{t}=\exp\left( \sigma_{t}\right) $ is driven to zero. This constitutes an alternative to reducing growth altogether. In practice, given the current technologies, a combination of green investment and restrained brown growth is required in our model to achieve stability in temperature, see the counterfactual analysis we perform below.
\paragraph{Comparison with estimates in the literature.}
To assess the plausibility of our estimated model, we compare its implications with meta analyses based on the existing literature. The 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 three main indicators used in the climate-economy literature (see the Appendix for derivations and explanations).
Overall, these results (with reported standard errors) show that our estimates are very much in the low to mid-range of those reported in the literature, so we are confident that our analysis neither severely underestimates nor overestimates the relative impacts of climate and the economy.
We now review the non-stationary control theory derived by JJ and show how it can be used to understand the issue of climate control through carbon abatement, reinterpreting the objective 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 ((ref)) and removing deterministic terms reduces the model to
and its Granger-Johansen moving average representation is
where the long-run impact matrix $C$ governs the nonstationary stochastic trends driving the nonstationary system: it plays a key role below in the theory of controllability. In the expression above, $C\left( L\right) \epsilon_{t}$ represents a stationary series, $A_{0}\ $depends upon the initial values and $\mu$ such that $\beta^{\prime}A_{0}=\mu$. It follows from $\beta^{\prime}C=0$ that $\beta^{\prime}X_{t}-\mu=\beta^{\prime}C\left( L\right) \epsilon_{t}$ is stationary so $\beta$ are cointegration vectors. The long-run expected value of $X_{t}$ is defined as $X_{\infty}=\lim _{\tau\rightarrow\infty}\mathsf{E}\left( X_{\tau}\left\vert X_{0}\right. \right) =CX_{0}+\alpha\left( \beta^{\prime}\alpha\right) ^{-1}\mu.$ We now consider a Control Theory derived from Preston and Pagan (1982, Chapter 4, and Section 5.8 in particular\nocite{pagan1982theory}) and adapted to the nonstationary context as follows.
We assume in this paper that the policy objective is to control temperature so that $b^{\prime}X_{t+1}^{new}=h_{t+1}^{new}$ and this process becomes stationary around a mean $b^{\ast}$.
The control policy defined above is explicitly written as a new equation to the system, one which requires that the \textquotedblleft authority\textquotedblright\ that implements it must be able to modify $a^{\prime}X_{t}$ via $a^{\prime}\nu\left( X_{t}\right) .$ This may require extra controls that are outside the system but interact with it, though for simplicity here we disregard this possibility. Indeed, our aim is not to assess how to implement a 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 $t=0$) \[ \color{black}X_{0}\color{blue}\rightarrow\underset{\color{blue}(\text{Policy} )}{\underbrace{X_{0}^{ctr}=X_{0}+\nu\left( X_{0}\right) }} \color{red}\rightarrow\underset{\color{red}(\text{Ecosystem})}{\underbrace {X_{1}^{new}=\left( I_{p}+\alpha\beta^{\prime}\right) X_{0}^{ctr} -\alpha^{\prime}\mu+\varepsilon_{1}}}\color{blue}\rightarrow\underset {\color{blue}(\text{Policy})}{\underbrace{X_{1}^{ctr}=X_{1}^{new}+\nu\left( X_{1}\right) }}\color{red}\rightarrow.... \]
\paragraph{Invariance.}
Success of the above approach relies on the notion of invariance of the system ((ref)) to interventions of the type $a^{\prime}X_{t}\rightarrow a^{\prime}X_{t}^{ctr}$ so that we can assume that the potential outcome is generated through mechanism ((ref)) that is not affected by interventions.\ For invariance, we hence require here that parameters remain unaffected by the introduction of the new policy so we can be assured that $X_{t+1}^{new}=X_{t}^{ctr}+\alpha\left( \beta^{\prime}X_{t}^{ctr}-\mu\right) +\epsilon_{t+1}$.
This relates to the notion of \textquotedblleft super-exogeneity\textquotedblright\ proposed by Engle, Hendry and Richard (1983\nocite{engle1983exogeneity}), and studied by Pretis (2021\nocite{PRETIS21}) in the context of climate. Yet, super-exogeneity is about invariance of conditional equations, while we consider here a system approach. While invariance cannot 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 \textquotedblleft natural expirement\textquotedblright\ in climate change; and $(ii)$ using statistical tests used in the context of super-exogeneity, inter alia by Castle et al., (2017\nocite{CHM17}).\
\paragraph{Policy Impact.}
A question\ raised by JJ is that of controllability of $b^{\prime}X_{t}$ via $a^{\prime}X_{t}.$ Since the objective is formulated in terms of a conditional expectation for $b^{\prime}X_{t+h}^{new}$, the choice of controls and policy rule must ensure that $b^{\prime}X_{t+h}^{new}$ is indeed stationary around $b^{\ast}.$ In the cointegrated VAR(1), JJ show that \[ b^{\ast}=b^{\prime}\underset{h\rightarrow\infty}{\lim}\mathsf{E}\left( X_{t+h}^{new}\left\vert X_{t}^{ctr}\right. \right) =b^{\prime}\left( C\left[ X_{t}+\nu\left( X_{t}\right) \right] +\alpha\left( \beta^{\prime }\alpha\right) ^{-1}\mu\right) , \] so that the condition for controllability writes as follows.
Notice that Controllability is a property of the system (under invariance) for the targeted variables and chosen controls. It does not depend on the actual rule $\nu\left( X_{t}\right) .$ JJ show that if Controllability applies, then a linear rule achieves it:
where we define the projector onto the space spanned by $a$ as $\overline {a}=a\left( a^{\prime}a\right) ^{-1}.$ The rule consists of a weighted average of $b^{\ast}-b^{\prime}X_{t}$, a \textquotedblleft policy\textquotedblright\ discrepancy between the desired objective and the current value at $t,$ and $\beta^{\prime}X_{t}-\mu$ is a \textquotedblleft system\textquotedblright\ deviation from the steady state at $t.\ $Policy becomes, here, fully endogenous and does not constitute an exogenous shock, as is often modelled in economics via structural VARs (more on this below). The reason for the effectiveness of the policy, and hence the channel through which it operates, relies on $\nu\left( X_{t}\right) $ being stationary and generating an extra linear cointegration relation. The new augmented system writes,
In the context of a VAR$\left( 1\right) $ dynamic system, it can be shown that $\nu\left( X_{t}^{new}\right) =\overline{a}\kappa^{\prime} \varepsilon_{t},$ so the impact of the policy is to augment the \color{blue}VAR$\left( 1\right) $ \color{black}into a \color{red}VARMA$\left( 1,1\right) \color{black}:$
\color{black} This results also holds for higher order VAR$\left( p\right) $ dynamics that are modified into VARMA$\left( p,1\right) $ (for a careful choice of policy parameters among those that achieve the stated objective, see JJ, Theorem 6).\ Equation ((ref)) shows that the policy can be identified in practice for its parameters $\overline{a}\kappa^{\prime}$ through a Structural VARMA or VMA and associated response function. 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\nocite{rambashep21}). In their framework, the policy consists in an assignment made at time $t+1$, $W_{t+1}=\nu\left( X_{t}^{new}\right) $ that is uncorrelated with $\varepsilon_{t+1}$ so \[ X_{t+1}^{new}=-\alpha\mu+\left( I+\alpha\beta^{\prime}\right) X_{t} ^{new}+\left( I+\alpha\beta^{\prime}\right) W_{t+1}+\varepsilon_{t+1} \] constitutes a \textquotedblleftNon-anticipating Potential Outcome \textquotedblright\ (see the Supplementary Appendix for a discussion of their framework and ours). Alternatively, an SVAR representation exists where the assignment $W_{t+1}$ constitutes an \textquotedblleft excess shock\textquotedblright\ (see Pagan and Robinson, 2022\nocite{PaganRobinson2022}) that is chosen, orthogonally to $\varepsilon _{t+1}$, to coincide with $\overline{a}\kappa^{\prime}\varepsilon_{t}.$ Since $\overline{a}\kappa^{\prime}$ is chosen to add a stationary relation in the system, the MA term in equation ((ref)) is invertible and $W_{t+1}$ recoverable from past observations (Chahrour and Jurado, 2022\nocite{ChahJura22}). Such an analysis does not consitute our objective here though, since our aim is to study the impact of implementing a given policy. Yet, we retain the Rambachan and Shephard interpretation that the process observed after the introduction of the sustained control policy is $X_{t}^{new},$ not $X_{t}^{ctr}$ as may seem to result from the definition above.
\paragraph{Testing for Climate Controllability.}
Our first question is whether economic activity, say $y_{t}$, $c_{t}$ or $m_{t},$ can be used as an instrument for a policy that aims to control temperature. Based on the analysis above which can be readily extended to cover $k>1$, this amounts to testing the significance of the element in the long run $C$ matrix that enters Condition C.
The matrix estimate and corresponding $t$-statistics show that the null of non controllability of temperature $h_{t}$ -- i.e. $b^{\prime}Ca=0$ in equation ((ref)) -- by each of the potential policy controls $y_{t}$, $c_{t}$ or $m_{t}$ (or a linear combination thereof) can safely be rejected at conventional levels. This shows that carbon abatement can achieve its purpose of controlling temperature, i.e. rendering it stationary around a chosen mean. Such policies can amount to carbon mitigation through economic adaptation (controls $y_{t}$ and $c_{t}$), or via direct capture of carbon dioxide in the atmosphere (control $m_{t}$), provided the technology develops sufficiently fast. Alternative choices of policies can be introduced through the various equations of the model (see, e.g., Policy\ 2\ below).
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 using the empirical model, a counterfactual path for the endogenous variables.
\paragraph{Policy design.}
We now consider JJ's analysis from the perspective of the policy maker who aims to perform a historical counterfactual analysis. We assume that the 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 in place through carbon abatement at some point in the past.
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 and to render them stationary around a long run mean equal to their 1900 level (assuming $h_{t}$ were observed then), i.e. stable over the 20th century at 0.7$ {{}^\circ} $C below their 2008 level. Naturally, the ensuing 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 the opportunity cost of inaction on green investment.
\paragraph{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 (ref), Panel $\left( a\right) $, 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, both as obtained unconditionally from the empirical model and with a policy that aims to maintain the same temperature level. We also produce the bootstrap mean prediction and associated confidence 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 the next period using 500 bootstrap samples), we see that the historical sequence of shocks imposed that most of the gains, in the counterfactual experiments, where obtained in the second half of the 20th century.
In order to assess the cost of inaction in the face of climate change, we also perform a complementary 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. essentially no growth since 1950. In terms of consumption, the counterfactual stands at 75%\ below the observe 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., 2023,\nocite{Dieb23} and Lenton et al., 2019\nocite{lenton2019climate}).
\paragraph{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 CO$_{2}$ concentrations, the resulting gain in economic activity is potentially massive: Figure (ref), Panel $\left( b\right) ,$ 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 $\tilde{c}_{t},$ with a wider bootstrap range and higher mean (+75%). These positive gains show that there exists a rationale for massive self-financing investment in \textquotedblleft green\textquotedblright \ technologies.\ Uncertainty is also high here, yet much less so than via Policy 1.
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 of a 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 test that carbon abatement is indeed significantly capable of such a policy. We assess its counterfactual cost, if a centralized authority had been able to implement such a policy over the 20th century to maintain the globe's temperature at its level of 1900 (observed ex post). These costs are first assessed under the assumption of a constant carbon content of technology, so they show the opportunity cost of the lack of investment in mitigating technologies. This is corroborated by a complementary counterfactual policy where carbon emissions and concentrations are directly controlable through technology, showing the massive extent to which technological investment is self-sustainable.
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 wealth rather than spot GDP and consumption) at the cost of additional assumptions. Indeed we see the collected data, model and results above as a toolbox for policy analysis where refinements on possible projected scenarios and abatement policies need to be assessed. This constitutes one step further into statistical analyses of the feasibility of temperature control, and cost assessments of such policies.
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