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date: 18 April 2024

The Role of Uncertainty in Controlling Climate Changefree

The Role of Uncertainty in Controlling Climate Changefree

  • Yongyang CaiYongyang CaiDepartment of Agricultural, Environmental and Development Economics, The Ohio State University


Integrated assessment models (IAMs) of the climate and economy aim to analyze the impact and efficacy of policies that aim to control climate change, such as carbon taxes and subsidies. A major characteristic of IAMs is that their geophysical sector determines the mean surface temperature increase over the preindustrial level, which in turn determines the damage function. Most of the existing IAMs assume that all of the future information is known. However, there are significant uncertainties in the climate and economic system, including parameter uncertainty, model uncertainty, climate tipping risks, and economic risks. For example, climate sensitivity, a well-known parameter that measures how much the equilibrium temperature will change if the atmospheric carbon concentration doubles, can range from below 1 to more than 10 in the literature. Climate damages are also uncertain. Some researchers assume that climate damages are proportional to instantaneous output, while others assume that climate damages have a more persistent impact on economic growth. The spatial distribution of climate damages is also uncertain. Climate tipping risks represent (nearly) irreversible climate events that may lead to significant changes in the climate system, such as the Greenland ice sheet collapse, while the conditions, probability of tipping, duration, and associated damage are also uncertain. Technological progress in carbon capture and storage, adaptation, renewable energy, and energy efficiency are uncertain as well. Future international cooperation and implementation of international agreements in controlling climate change may vary over time, possibly due to economic risks, natural disasters, or social conflict. In the face of these uncertainties, policy makers have to provide a decision that considers important factors such as risk aversion, inequality aversion, and sustainability of the economy and ecosystem. Solving this problem may require richer and more realistic models than standard IAMs and advanced computational methods. The recent literature has shown that these uncertainties can be incorporated into IAMs and may change optimal climate policies significantly.


  • Econometrics, Experimental and Quantitative Methods
  • Environmental, Agricultural, and Natural Resources Economics
  • Public Economics and Policy

Uncertainty and Climate Policy

It has been widely recognized that anthropogenic greenhouse gas emissions have been distorting the planet’s energy balance, resulting in global warming, sea level rise, and more frequent extreme weather, with industrial carbon emissions constituting the major component of greenhouse gas emissions.1 These emissions then influence economic well-being via a damage function. Integrated assessment models (IAMs) combine the climate and the economy, as well as the interactions between them, to analyze which policies are more efficient in controlling climate change. DICE (Dynamic Integrated Climate-Economy model; Nordhaus, 2008, 2017) is a representative IAM. Most existing IAMs assume that the climate and economic systems as well as interactions between them are deterministic, and that economic agents are myopic. However, there are significant uncertainties in these systems and their interactions, and these uncertainties may play an essential role in determining optimal policy. For example, the dismal theorem of Weitzman (2009) shows that the risk premium could be infinite for unboundedly distributed uncertainties.2 Pindyck (2013, 2017) criticizes IAMs as being crucially flawed and fundamentally misleading, but Heal (2017) argues that

IAMs can play a role in providing qualitative understanding of how complex systems behave, but are not accurate enough to provide quantitative insights. Arguments in favor of action on climate issues have to be based on aversion to risk and ambiguity and the need to avoid a small but positive risk of a disastrous outcome. (p. 1046)

However, a policy maker often has to make a quantitative decision, such as the size of a carbon tax, in the face of this uncertainty. Moreover, because carbon emissions have long-lasting impacts on temperature, the “wait and see” approach may not make sense given that changes in the climate system may be irreversible. For example, Steffen et al. (2018) point out the risk that if the earth system crosses a planetary threshold then continued warming could occur even as human emissions are reduced, preventing climate stabilization.

Moreover, once an ice sheet collapses, it is irreversible for millennia (Intergovernmental Panel on Climate Change [IPCC], 2013). Metcalf and Stock (2017) argue that policy makers need a numerical value for the social cost of carbon (SCC) for U.S. regulatory policy evaluation and implementation, and that producing a credible numerical value requires sophisticated computer models, such as IAMs.3 Brock and Hansen (2018) stress:

Defenses for policies that combat climate damage externalities induced by human activity need not require precise knowledge of the magnitude or timing of the potential adverse impacts. . . . Waiting for precise knowledge of the eventual consequences of continued or expanded human induced CO2 emissions could make mitigation or adaptation extremely costly. (pp. 51–52)

Goulder (2020) calls for urgent and stronger policy action to address global climate change.4

This article focuses on recent work on the role of uncertainty in controlling climate change. The broad perspective of uncertainty applied in this review includes parameter uncertainty, risk, model uncertainty, scenario uncertainty, policy uncertainty, ambiguity, and misspecification. The article focuses on the first five types of uncertainty and methods for making decisions in the face of these uncertainties (see Brock & Hansen, 2018, for a more complete survey about ambiguity and misspecification). Moreover, the article focuses on reviewing discrete-time stochastic IAMs (see Brock & Xepapadeas, 2018, for discussion of continuous-time IAMs).

The rest of the article is organized as follows. It begins with a discussion of parameter uncertainty and how to deal with it, focusing on uncertainty in the discount rate, climate sensitivity, and damage function. This discussion is followed by a review of economic and climate risks and methods for handling them. The review then goes on to discuss model uncertainty, scenario uncertainty, ambiguity and misspecification, as well as policy uncertainty. Finally, a conclusion and issues for further research are presented.

Parameter Uncertainty

Parameters in IAMs are estimated from historical data, expert opinions, survey data, and projections for future scenarios. Their values are often uncertain because no model can replicate the real world, historical data may have errors, expert opinions and survey data are subjective, and projections for future scenarios may not be close to what will actually happen. These uncertain parameters are assumed to have fixed and unchanged values over time, but their exact values are unknown. In some cases, knowledge of the exact values can be expressed by some probability distributions, which are referred to as belief distributions. In this review, parameter uncertainty represents only the cases in which an uncertain parameter has an unknown true value that is unchanged over time, in order to distinguish from risk representing the cases with different realization over time and simulation. If an uncertain parameter’s true values have a linear time trend, then it can be decomposed into two parameters: intercept and slope, both of which can have parameter uncertainty. Similarly an uncertain parameter with a nonlinear time trend true values can be decomposed into multiple parameters which can have parameter uncertainty.5

The most well-known and debated uncertain parameters in IAMs include the discount rate, climate sensitivity (also known as “equilibrium climate sensitivity”), and parameters in climate damage functions. These parameters can change optimal solutions significantly but are still hard to pin down. Other uncertain parameters include economic growth, the intertemporal elasticity of substitution, and risk aversion.6

Discount Rate

Economic analysis often uses two types of discount rates: a utility discount rate that represents the rate at which utility is discounted and a consumption discount rate that represents the rate at which consumption is discounted.7 These two discount rates can be connected by the famous Ramsey rule and are discussed in a large number of papers (e.g., Arrow et al., 2013, 2014; Drupp, Freeman, Groom, & Nesje, 2018; Frederick, Loewenstein, & O’Donoghue, 2002; Gollier, 2012; Heal, 2017; Weitzman, 2001).

Interagency Working Group [IWG] (2010) employs three consumption discount rates (2.5, 3, and 5%) to compute the SCC. Nordhaus (2008) uses a utility discount rate of 1.5%, which is calibrated together with the intertemporal elasticity of substitution to match the estimated growth of consumption. For ethical reasons, Stern (2007) sets a utility discount rate of 0.1% and finds that the SCC will be significantly higher.

Climate Sensitivity and Transient Climate Response

Climate sensitivity, also known as equilibrium climate sensitivity (ECS), is a parameter that measures the long-run increase in atmospheric temperature (in degrees Celsius) if the atmospheric carbon concentration doubles. A typical value of climate sensitivity used in the literature is 3°C, which is considered to be the median of the distribution of climate sensitivity. The IPCC (2007) suggests the likely range (i.e., with a 66% probability) of climate sensitivity is [2.0, 4.5], but a later report (IPCC, 2013) expands the likely range to [1.5, 4.5] (the same as given by Jule Charney in 1979) in light of recent research, demonstrating that it is challenging to narrow the envelope of parameter uncertainty of climate sensitivity with additional research. Meinshausen et al. (2009) plot 19 probability density distributions of climate sensitivity, representing a wide variety of climate modeling approaches, observational data, and statistical methodologies in the literature. The range of the ECS value is from below 1 to more than 10, and some distributions are skewed to the left while others are skewed to the right.

Instead of climate sensitivity, some climate scientists suggest using a more stable measurement called transient climate response to emissions (TCRE) to simplify modeling the climate system. The TCRE scheme assumes that contemporaneous atmospheric temperature increase is nearly linearly proportional to cumulative carbon emissions. Therefore, atmospheric temperature can be obtained with only one state variable: cumulative emissions. In contrast, the climate system modeled using climate sensitivity is often complicated and requires many state variables.8 With the simplification of the TCRE scheme, economists have also employed it in their models, including Brock and Xepapadeas (2017), Anderson, Brock, and Sanstad (2018), and van der Ploeg (2018). Dietz and Venmans (2019) use a continuous-time IAM with the TCRE scheme and find that the optimal carbon price should start relatively high and grow relatively fast. However, the value of TCRE is still uncertain and highly correlated to ECS. MacDougall, Swart, and Knutti (2016) estimate the mean value of TCRE as 1.72°C (that is, if there are an additional one trillion tonnes of carbon emissions, then the mean atmospheric temperature increases 1.72 °C), and its 5–95% percentile range as [0.88, 2.52], while IPCC (2013) reports its likely range as [0.8, 2.5].

Damage Function

The specification of the damage function, which measures the damage from global warming, has been debated extensively. The most common damage function is a quadratic function of the temperature increase, specified by Professor William Nordhaus in his DICE/RICE models (Nordhaus, 2008, 2010, 2017). It assumes that temperature increases reduce instantaneous economic output in a ratio represented by the damage function. However, Weitzman (2012) points out that the quadratic function results in implausibly low damage at high temperatures, and thus suggests adding one high-exponent term to the damage function so that 50% of output is lost if the temperature increase is 6 °C. Dietz and Stern (2015) find that the modification of Weitzman (2012) leads to a much higher SCC. Diaz and Moore (2017) review and synthesize the limitations of the damage functions.

Sterner and Persson (2008, p. 72) argue that “it is exactly the nonmarket effects of climate change that are the most worrisome.” These include (p. 71) “biodiversity and ecosystem loss; effects on human well-being (human amenity, loss of lives, and air pollution); impacts from natural disasters, such as extreme weather events, droughts, hurricanes or floods (Manne, Mendelsohn, & Richels, 1995); as well as socially contingent consequences, such as migration and risk for conflicts,” many of which have been presented in the Stern review (Stern, 2007). The nonmarket amenities and aggregate consumption can be combined with a utility function with a constant elasticity of substitution kernel, which leads to a much higher SCC (Cai, Judd, Lenton, Lontzek, & Narita, 2015; Sterner & Persson, 2008). That is, explicitly including the nonmarket amenities in the utility function allows for relative price changes and then leads to very different results, as compared with implicitly including the nonmarket amenities as the equivalent loss in consumption of market goods.

Besides the climate damage to instantaneous output and nonmarket goods, researchers also find that climate change can reduce economic growth. For example, Dell, Jones, and Olken (2012) find a reduction in economic growth of approximately 1.3% for a 1°C increase in global temperatures. In the face of the damage to economic growth, the SCC will be significantly higher (Dietz & Stern, 2015; Moore & Diaz, 2015).9 Some recent empirical works on estimating climate impacts include Burke, Hsiang, and Miguel (2015a, 2015b), Burke, Dykema, Lobell, Miguel, and Satyanath (2015), Carleton and Hsiang (2016), Costinot, Donaldson, and Smith (2016), Hsiang et al. (2017), Schauberger et al. (2017), Burke, Davis, and Diffenbaugh (2018), Chen and Mueller (2018), Fan, Fisher-Vanden, and Klaiber (2018), Schlenker and Auffhammer (2018), Zhang, Deschenes, Meng, and Zhang (2018), Diffenbaugh and Burke (2019), Duffy et al. (2019), Hsiang, Oliva, and Walker (2019), and Mach et al. (2019). For example, Burke et al. (2015b) find that overall economic productivity is nonlinear in temperature, and then estimate that in 2100 “unmitigated climate change will make 77% of countries poorer in per capita terms than they would be without climate change,” and their estimate of damage in global GDP is much larger than those from major IAMs including DICE (Nordhaus, 2008, p. 237).

Dealing with Parameter Uncertainty

The most common way to deal with parameter uncertainty is through sensitivity analysis; that is, choosing a different value of the uncertain parameter and checking its impact on the solution to see if results are qualitatively robust. If there are multiple uncertain parameters, then doing sensitivity analysis over each uncertain parameter might not be enough, as a combination of multiple uncertain parameters may produce nontrivial results. Thus, a global sensitivity analysis—going through a number of combinations of multiple uncertain parameters—should be conducted. For example, Cai, Judd, and Lontzek (2017) and Cai and Lontzek (2019) use global sensitivity analysis in a dynamic stochastic integrated framework of climate and economy (DSICE) to study the impact of the intertemporal elasticity of substitution (IES) and risk aversion on the SCC in the face of long-run economic growth risk. They find that a larger degree of risk aversion increases the SCC if the IES is small, but decreases the SCC if the IES is large, which can be reconciled using the impact of economic growth. However, in the face of climate tipping risk, a larger degree of risk aversion always increases the SCC regardless of the size of the IES. It may be too time-consuming to run global sensitivity analysis if tensor grids for uncertain parameters are used. Uncertainty quantification can be applied to address this issue: choose a small set of nodes (e.g., a sparse grid) for uncertain parameters, then apply an approximation method to estimate solutions over the whole domain of uncertain parameters (see Harenberg, Marelli, Sudret, & Winschel, 2019, for a detailed discussion).

Sensitivity analysis methods provide the lower and upper bounds of the solutions and the qualitative robustness of solutions, but it is often challenging to provide one specific quantitative value (e.g., the SCC) for use in decision-making, as policy makers do not know which values of uncertain parameters are correct. However, if policy makers have a belief distribution for possible values of the uncertain parameters, then it is possible to give a quantitatively robust solution. For example, Cai and Sanstad (2016) use an expected cost minimization method to find a robust mitigation pathway in the face of research and development (R&D) technology uncertainty. Some researchers use a Monte Carlo method: They draw samples of the uncertain parameters from the belief distributions, solve the deterministic model with each sampled realization of the uncertain parameters, and use the average over the solutions as an approximate solution in the face of uncertainty.10 While this Monte Carlo analysis may be helpful in some cases, it may also lead to very biased solutions (see Cai, 2019; Crost & Traeger, 2013; Lemoine & Rudik, 2017, for detailed discussions).

If policy makers have belief distributions of uncertain parameters, they may collect more data over time to update their belief distributions by shrinking the range of uncertain parameters or reducing the variances of these distributions. This process is called Bayesian learning. Note that any sampled realization of the uncertain parameters in simulated solutions should be their fixed true values, so the true values have to be assumed before simulation in order to study the impact of learning under the assumed true values. Bayesian learning has been applied in climate change economics in Kelly and Kolstad (1999a), Keller, Bolker, and Bradford (2004), Leach (2007), Kelly and Tan (2015), Hwang, Reynes, and Tol (2017), Gerlagh and Liski (2018), and Rudik (2020), among others. Since Bayesian learning depends on the frequency of new data collection, in dynamic models it depends on the size of the time steps. With annual time steps belief distributions can be updated every year, but with decadal time steps belief distributions can be updated only every decade. Thus, the size of the time steps should be chosen reasonably to be consistent with the frequency of real data collection.11 In addition, Bayesian learning ignores the possibility of active learning through R&D (see Goulder & Mathai, 2000), so it may provide biased results.

In the face of parameter uncertainty without belief distributions, decision makers may have to provide only one robust solution instead of many solutions from (global) sensitivity analysis. This robust decision-making problem can be solved using a robust decision-making method, such as the max-min method or the min-max regret method (Anthoff & Tol, 2014; Cai & Sanstad, 2016; Iverson, 2012, 2013). See Cai (2019) for a detailed discussion.


There are many risks in economic and climate systems, where “risks” refer to random variables with probability distributions that are known or dependent on state or control variables at each time period but could be time-varying. Unlike parameter uncertainty, where the true value of an uncertain parameter is unchanged over time, risks are assumed to be realized with possibly different values over time and simulation, and a different simulation could lead to a different time-varying path. Risks in the economic system can happen in technology, productivity, health and mortality, R&D, and international cooperation and noncooperation, as well as in many other areas. Risks in the climate system include the frequency and damage of extreme weather and regime-switching of the climate system (often called climate-tipping risks). In particular, fat-tailed uncertainty in catastrophic climate change is the most worrisome (Weitzman, 2011).

Economic Risks

The economic system of an IAM often assumes that output is proportional to total factor productivity (TFP), At, and business cycle models assume that At is a stochastic process. For example, Fischer and Springborn (2011) use a dynamic stochastic general equilibrium (DSGE) model with ln(At+1)=ρln(At)+εt, where εt is an i.i.d. shock that is normally distributed with mean zero, to compare the performance of three instruments in achieving an exogenous and fixed level of expected emissions reduction: a carbon tax, emissions cap-and-trade (i.e., an exogenous limit on aggregate emissions), and an emission intensity target (i.e., an exogenous limit on emissions per unit of aggregate output). They find that the intensity target scheme produces higher mean values and lower welfare costs than the other two policies, and compared to the no-policy case, volatility of the main macroeconomic variables decreases under the carbon tax policy but increases under the cap-and-trade instrument. Heutel (2012) also uses the same form of At in his DSGE model, but focuses on comparing the optimal emissions tax rate and the optimal emissions quota. He finds that they both decrease during recessions, and during economic expansions a price effect from costlier abatement dominates an income effect of greater demand for clean air. Fischer and Heutel (2013) survey some related work using real business cycle models with environmental policy and induced technological progress.

Annicchiarico and Di Dio (2015) formulate a New-Keynesian-type DSGE model to study the role of different environmental policy regimes in economic fluctuations, in the presence of nominal rigidities and accounting for two additional sources of uncertainty: public consumption shocks and monetary policy shocks. They find that in the presence of nominal rigidities, a cap-and-trade scheme is likely to dampen the response of the main macroeconomic variables to shocks, an intensity target makes macroeconomic variables more volatile, and a carbon tax policy tends to have slightly higher mean welfare and lower volatility than the cap-and-trade scheme, as long as the degree of price stickiness is not too high. However if prices adjust very slowly, the cap-and-trade policy will have higher mean welfare. Karydas and Xepapadeas (2019) include transition risks of climate policy (i.e., the risks associated with carbon-intensive assets, which may become stranded due to stringent climate policies) in their dynamic asset pricing framework with rare disasters related to climate change, and show that transition risks substantially lower the participation of carbon-intensive assets in the market portfolio.

Jensen and Traeger (2014), Cai et al. (2017), and Cai and Lontzek (2019) also build DSGE models assuming that TFP, At, is a Markov process but is extended to be a long-run risk (Bansal & Yaron, 2004) that includes persistence of shocks. That is, they assume At=A˜tζt, where A˜t is an exogenous deterministic trend of TFP from DICE and ζt is a shock with


where χt represents the persistence of the shock, ωζ,t,ωχ,ti.i.d.N(0,1), and σ, r, and ς are parameters. Moreover, the papers incorporate a recursive utility function (Epstein & Zin, 1989) with two preference parameters: the IES and relative risk aversion. However, the DSICE model of Cai et al. (2017) and Cai and Lontzek (2019) is a stochastic extension of the full DICE model (Nordhaus, 2008), and its parameters for the long-run risk on growth are calibrated with historical consumption growth data, whereas Jensen and Traeger (2014) use a reduced form model without empirical validation for the calibration of their long-run risk (see Cai et al., 2017; Cai & Lontzek, 2019, for a more detailed discussion). Moreover, Cai et al. (2017) and Cai and Lontzek (2019) discretize ζtand χtto be Markov chains with a large number of time-varying values, while Jensen and Traeger (2014) do not. The discretization is to avoid existence issues caused by the unbounded normal distributions of ωζ,t and ωχ,t, and to avoid excessive dependence on extreme tail events (as the risk premium could be infinite for unboundedly distributed uncertainties; Weitzman, 2009). Cai et al. (2017) and Cai and Lontzek (2019) find that in the presence of long-run risk on growth, the SCC itself is a stochastic process with a wide range of possible values and the recursive utility’s preference parameters have a nontrivial impact on the SCC in 2005. If the IES is large (not less than 0.9 in their numerical examples), then a larger risk aversion implies a smaller SCC; if IES is small (not larger than 0.7 in their numerical examples), then a larger risk aversion implies a larger SCC; and if risk aversion is small (not larger than 5), then the SCC increases with the IES.12

Climate Risks

One major type of climate risk is a “climate tipping risk,” which refers to risks that can qualitatively alter the state or development of the climate system if a large-scale component of the earth system (the “tipping element”) passes a critical threshold (the “tipping point”). Some examples of tipping elements include the Greenland ice sheet, the Antarctic ice sheet, and the Amazon rainforest. A climate tipping risk is often represented by an irreversible climate process, called a “tipping process,” which is often a Markov chain.13

Lemoine and Traeger (2014) study the impact of tipping points on climate policy, where their tipping point is an instantaneous, irreversible increase in climate sensitivity (from 3°C to 4, 5, or 6°C) or an instantaneous, irreversible weakening of carbon sinks (by 25, 50, or 75%). However, Lontzek, Cai, Judd, and Lenton (2015) point out that such a tipping point is not scientifically plausible because “positive feedbacks are never instantaneously switched on—instead they may get progressively stronger as temperature increases—so an instantaneous ‘tipping’ formulation is qualitatively wrong.” Climate scientists point out that the duration of a climate element tipping to a new state is unknown and can last from a decade to even millennia (Lenton & Ciscar, 2013). There is no widespread belief in the scientific community that the entire Greenland ice sheet will melt within one year and cause an instant global sea level rise of six meters.

Lemoine and Traeger (2014) assume that a tipping point cannot occur when the contemporaneous temperature is below last period’s temperature.14 However, this assumption violates the consensus in climate science and completely ignores recent findings that suggest climate tipping might already have occurred, despite the last two decades, in which global warming had a short decreasing trend. For example, there is already scientific evidence that major ice sheets are losing mass at an accelerating rate (Khan et al., 2014). The Greenland ice sheet’s mass loss is estimated to be contributing ~0.7 mm/year to sea level rise (Csatho et al., 2014), and Joughin, Smith, and Medley (2014) argue that the collapse of the West Antarctic ice sheet is already underway. Moreover, a real temperature path always rises and falls frequently, so the tipping probabilities assumed by Lemoine and Traeger will also frequently fluctuate between nonzero and zero, which is implausible. Furthermore, Lemoine and Traeger (2014) assume that the tipping probability only depends on the positive change between this year’s and next year’s temperature. Hence, no matter how low the current year’s temperature is, as long as it increases, the tipping probability will be nonzero. Moreover, no matter how high the current year’s temperature is, if next year’s temperature does not increase, then the tipping probability is zero. Thus, the decision maker’s mitigation efforts and optimal climate policy will be based on distorted incentives.

In addition, the hazard rate in Lemoine and Traeger (2014) is not based on a calibration in part because climate scientists do not know when or at which level of global warming a tipping point will occur (Kriegler, Hall, Held, Dawson, & Schellnhuber, 2009; Lenton et al., 2008). Lemoine and Traeger (2014), however, assume that a tipping point will occur if temperatures reach 4.27°C above preindustrial levels. When one aggregates the implied probabilities from expert elicitation by Kriegler et al. (2009), one finds that tipping is more likely than not in a 4–8°C long-term warming scenario, but still not certain.

In contrast, Cai et al. (2017) and Cai and Lontzek (2019) use an alternative approach to investigate the impact on the SCC from climate tipping risks. Their tipping point process incorporates basic features of how climate scientists think about climate tipping points, such as a stochastic formulation of the physical process of triggering the tipping point and a transition time of tipping impacts with uncertain duration and long-run impact size. Their hazard rate formulation treats the physical process of the tipping point as stochastic with tipping probabilities that depend on the contemporaneous temperature itself, so a higher temperature will always have a higher tipping probability. Their hazard rate is calibrated according to beliefs expressed in expert elicitation studies, where the experts based their probability statements partly on the earth’s history, partly on fundamental understanding, and partly on future model projections (Lenton et al., 2008). Cai et al. (2017) and Cai and Lontzek (2019) model their tipping process as a five-stage sequential process with each stage having a stochastic duration. Thus, not only do they model the long transition of climate tipping, as postulated by climate scientists, but they also account for these scientists’ lack of knowledge and imperfect information regarding the length of the transition process. Their multiple-stage approach to modeling the representative tipping element can produce lengths of transition in accordance with scientific beliefs. Cai et al. (2017) and Cai and Lontzek (2019) also account for the additional uncertainty about the long-run impact of climate tipping on the economy, which, according to climate scientists, is the biggest uncertainty.

Cai et al. (2017) and Cai and Lontzek (2019) find that under recursive utility and climate tipping risks, a higher IES or risk aversion always implies a higher SCC in 2005. If a tipping event has not happened, then the SCC is significantly higher than in a deterministic model, but it will jump down significantly and immediately once the tipping event happens, even though the post-tipping damage has just started to unfold and may take many years to reach its maximum level. This pattern appears because the incentive to prevent or delay the tipping event has disappeared if it has been triggered.

The DSICE framework has also been applied with several variants. Lontzek et al. (2015) use it to investigate the impact of a tipping risk with a continuous tipping damage path under separable utility, and find that the optimal carbon tax in 2005 increases by around 50% even with conservative assumptions about the rate and impacts of a stochastic tipping event. Moreover, the effective discount rate for the costs of stochastic climate tipping is much lower than the discount rate for deterministic climate damages. Cai et al. (2015) use the DSICE framework to study the impact of environmental tipping risk on market and nonmarket goods and services, and find that even if a tipping risk only has nonmarket impacts, it could substantially increase the optimal carbon tax in 2005. Cai, Lenton, and Lontzek (2016) extend DSICE to incorporate five major interacting climate tipping risks (Atlantic meridional overturning circulation, disintegration of the Greenland ice sheet, collapse of the West Antarctic ice sheet, dieback of the Amazon rainforest, and shift to a more persistent El Niño regime) simultaneously in their model. They find that doing so increases the SCC in 2005 by nearly eightfold, and passing a tipping point may abruptly increase the SCC if it increases the likelihood of other tipping events. Note that if there is only one tipping risk, then passing its tipping point will abruptly decrease the SCC, as shown in Lontzek et al. (2015), Cai et al. (2015), and Cai and Lontzek (2019).

Diaz and Keller (2016) find that the threat of the West Antarctic ice sheet disintegration implies little motivation for additional mitigation. Nordhaus (2019) finds that the risk of Greenland ice sheet disintegration makes a small contribution to the overall social cost of climate change. These findings are consistent with Cai et al. (2016) in the case without interactions between tipping events (see Cai et al., 2016, fig. 3). But Cai et al. (2016) also show that in the case with interactions between tipping events, if the Greenland ice sheet tips first, it leads to the most stringent emissions control because the likelihood of the presumably most-damaging event (Atlantic meridional overturning circulation collapse) significantly increases. Anthoff, Estrada, and Tol (2016) apply the Climate Framework for Uncertainty, Negotiation and Distribution (FUND) model to study the impact of potential slowdown of the thermohaline circulation (i.e., Atlantic meridional overturning circulation), a vast system of currents across all four oceans. They find that the change in human welfare associated with a slowdown of the thermohaline circulation is modest if its potential to reduce both ocean heat and carbon uptake is considered but its other effects, such as ocean acidification and possibly more extreme weathers, are ignored.15

Cai et al. (2019) construct a numerical dynamic stochastic two-region model, DIRESCU, which separates the world into the North and the Tropic-South regions with their own economic and climate systems and includes interactions between regions. They also consider a global climate tipping risk, global sea level rise, and regional adaptation, and find that carbon taxes increase significantly in both regions to curb or delay the occurrence of climate tipping and sea level rise in both cooperative and noncooperative worlds, while regional adaptation reduces carbon taxes significantly.

There is also theoretical analysis for pricing carbon in the face of climate tipping. For example, van der Ploeg and de Zeeuw (2016) build a simple stylized North-South model of the global economy to investigate how differences between regions in terms of their vulnerability to climate change and their stage of development affect cooperative and noncooperative responses, both to curb the risk of a calamity and accumulate precautionary capital to facilitate consumption smoothing. Van der Ploeg and de Zeeuw (2018) find that if the mean lag for the impact of the catastrophe from climate tipping is long enough, the saving response will be negative because the precautionary return in the Keynes–Ramsey rule becomes negative.

Dealing with Risks

A typical dynamic stochastic IAM can be written as


where E is the expectation operator over all random variables εt for all time t, xt is a vector of state variables (such as capital, oil stock, carbon concentration in the atmosphere, and global average atmospheric temperature), at is a vector of control variables (also called action or decision variables, such as consumption and emission mitigation rates), β is the discount factor, T is the terminal time (could be infinite), ut is a utility function, VT is the terminal value function (when T=, this term disappears), ft is a vector of functions representing transition laws of state variables, and Dt(xt) is a feasible set of the control variables and depends on the state variables at each time t. When the transition law of the j-th state variable is deterministic, xt+1,j=gt,j(xt,at), it is still denoted as xt+1,j=ft,j(xt,at,εt)=gt,j(xt,at)+0ε for convenience. The model (3) can also be transformed to the following Bellman equation (Bellman, 1957):


for t=0,1,,T1, where Et is the expectation operator over εt conditional on time-t information (xt,at), and Vt is the value function at time t.

In economics, consumption ct is often a decision variable (one element of at), and a typical utility function is a power function:


for γ>0 and γ1, where γ=1 is the special case of logarithmic utility:


For a deterministic dynamic model, γ is the inverse of intertemporal elasticity of substitution (IES). For a stochastic model, γ is also the relative risk aversion parameter. To disentangle the IES from risk aversion, recursive utility (Epstein & Zin, 1989) has been employed in IAMs (e.g., Cai et al., 2016; Cai & Lontzek, 2019; Cai et al., 2019; Jensen & Traeger, 2014). The corresponding Bellman equation is




with ψ and γ as the IES and the risk aversion parameter, respectively.

The most common method to solve the (time-varying) Bellman equation is value function iteration (VFI). When some state variables are continuous, value functions Vt have to be approximated. An efficient approximation method is to use complete Chebyshev polynomials (over multi-dimensional continuous state variables) and associated Chebyshev nodes. It is essential for approximation errors to be small, and the errors of the solution should always be checked, otherwise the numerical solution could be far away from the true solution.

For example, assume that VFI is employed to solve an infinite-horizon stationary problem, where the true value function V satisfies the Bellman equation V=Γ(V), where Γ is the Bellman operator. Starting with an initial guess V0, VFI solves Vt=Γ(Vt1) for t=1,2, until it converges under a stopping criterion: ||VtVt1||<ε, where ε is a small positive number and is a norm operator over functions. Since Vt cannot be solved at all states if some state variables are continuous, numerically Vt is solved at approximation nodes xj and then values Vt(xj) are used to construct an approximation of Vt at all states. Let the value function at iteration t be approximated by a linear combination of basis functions, denoted V, and numerical VFI converges under a stopping criterion: V^tV^t1<ε. This convergence does not guarantee that V^t is a good approximation to the true value function V, as numerical VFI computes (Γ(V^t1))(xj) and then uses the values (Γ(V^t1))(xj) to approximate Γ(V^t1) with V^t; that is V^tΓ(V^t1). In fact, numerical VFI may converge under the stopping criterion with any degree of approximation (such as linear or quadratic polynomial approximation). Therefore, if the approximation error, V^tΓ(V^t1), is large, then the converged solution V^t may be far away from the true solution. In addition, even if a high-degree Chebyshev polynomial is used in approximation, a loose stopping criterion may also lead to large errors in the solution. For example, Cai (2019) points out that the stopping criterion of VFI used in Lemoine and Traeger (2014) is problematic, so the numerical solution of Lemoine and Traeger (2014) may have large errors.16

However, the Bellman equation (4) or (5) only applies to a social planner’s problem, where the social planner makes all decisions including reallocating resources among different regions or countries (with some costs), while these regions/countries are completely cooperative. In the real world, the regions/countries may be noncooperative, which leads to a (time-varying) dynamic stochastic game. Cai et al. (2019) introduce a new time-backward iterative method to solve a system of Bellman equations and then find a feedback Nash equilibrium numerically.

In many cases, it is challenging to employ VFI if there are kinks in value functions or if the number of state variables is large. Cai, Judd, and Steinbuks (2017) introduce a nonlinear certainty equivalent approximation method to solve infinite-horizon stationary problems in the form (3). Cai, Steinbuks, Judd, Jaegermeyr, and Hertel (2020) then extend it to solve (finite/infinite) nonstationary problems. See Cai (2019) for a discussion about other computational methods.

Model Uncertainty and Scenario Uncertainty

IAMs and scenarios are developed to analyze climate policies and estimate future pathways of temperature, but no model can replicate the real world completely and no scenario can predict a realized future pathway perfectly. For tractability, every model or scenario has to make some simplifying assumptions, particularly in mathematical representations of economic and climate systems. Different assumptions then lead to different models or scenarios.

In the words of Albert Einstein, “Everything should be made as simple as possible, but not simpler.” Economists often adopt the first half of the sentence and ignore the second half, using oversimplified models, particularly for IAMs, as climate models are often too complicated to be applied in IAMs for economic analysis. Moreover, there is large uncertainty in future temperature projections from climate models, as well as in future economic systems. It is often hard to judge which model or scenario is better, but policy makers have to make their decisions in the face of the model or scenario uncertainty. In some simple cases, model or scenario uncertainty can be represented as a special case of parameter uncertainty. For example, Goulder and Mathai (2000) compare two models for carbon abatement knowledge accumulation: induced technical change versus autonomous technical change. But these two energy models can be connected with one single parameter: if the parameter’s value is 0, then it represents the case of autonomous change, otherwise induced.

There are many IAMs in the literature, which can be divided into two broad categories: policy optimization IAMs and policy evaluation IAMs. Policy optimization IAMs include a damage function mapping temperature increases to economic damages, allowing the optimal policy to be found using cost-benefit or cost-effectiveness analysis, so policy optimization models are also called cost-benefit IAMs. Examples of policy optimization IAMs include DICE (Nordhaus, 2008, 2017), FUND (Anthoff & Tol, 2013), PAGE (Hope, 2011), WITCH (Bosetti, Carraro, Galeotti, Massetti, & Tavoni, 2006), MERGE (Manne & Richels, 2005), RICE (Nordhaus, 2010), NICE (Dennig, Budolfson, Fleurbaey, Siebert, & Socolow, 2015), DSICE (Cai et al., 2017; Cai & Lontzek, 2019), and DIRESCU (Cai et al., 2019).17 These policy optimization IAMs are the main tools for calculating the SCC. For example, DICE, FUND, and PAGE have been used by the IWG (2010) to calculate the SCC under different consumption discount rates.

Since policy optimization IAMs can only use a simple climate system for computational tractability, some researchers developed policy evaluation IAMs that assume that emissions or mitigation policies are exogenous and have no feedback to the economy.18 Policy evaluation IAMs focus on quantifying future developmental pathways and provide detailed information on the complex processes in the carbon cycle, climate systems, land use, or other related systems (sometimes economic systems), so they are also called process-based IAMs or simulation IAMs. Examples of policy evaluation IAMs include GCAM (Calvin et al., 2019), IMAGE (Stehfest et al., 2014), MESSAGE (Huppmann et al., 2019), AIM/CGE (Fujimori, Masui, & Matsuoka, 2017), REMIND (Luderer et al., 2015), and IGSM (Chen et al., 2016).19 These policy evaluation IAMs have been used to explore different pathways for staying within climate policy targets, for example, limiting global mean temperature increase below 1.5 or 2 °C. See Kelly and Kolstad (1999b) and Weyant (2017) for more detailed discussions on policy optimization IAMs and policy evaluation IAMs.

IAMs often assume some exogenous paths, such as population and technology paths, but these are often uncertain so these models have scenario uncertainty. For example, policy evaluation IAMs often rely on exogenous emission scenarios, but there are four representative concentration pathways (RCPs) of greenhouse gas concentrations (Meinshausen et al., 2011): RCP2.6, RCP4.5, RCP6, and RCP8.5, and they all have wide ranges in 2100. O’Neill et al. (2014) describe five Shared Socio-Economic Pathways (SSPs) covering a wide range of projected population, income, and temperature in 2100.

A different model or scenario provides a different optimal policy. Usually policy makers do not know which model or scenario is more reliable, and it is challenging to assign a belief distribution over the models or scenarios. But they often have to choose only one policy. One way is to do a multimodel or multiscenario comparison to find robust results from the models. For example, Kim et al. (2017) analyze a set of simulations to assess the impact of climate change on global forests under two emissions scenarios: a business-as-usual reference scenario analogous to the RCP8.5 scenario, and a greenhouse gas mitigation scenario, which is between the RCP2.6 and RCP4.5 scenarios. Gillingham et al. (2018) compare six models: DICE, FUND, GCAM, MERGE, IGSM, and WITCH. But in many cases, different models or scenarios may lead to significantly different solutions, so it is not possible to extract a robust policy from a multimodel or multiscenario comparison.

A robust decision-making method, such as the max-min method or the min-max regret method (Anthoff & Tol, 2014; Cai & Sanstad, 2016; Iverson, 2012, 2013), is a tool used to solve this problem in the face of model uncertainty. For example, Cai, Golub, and Hertel (2017) apply the min-max regret method to study robust decisions of agricultural research and development in the face of uncertain SSP scenarios in population, income, and temperature. Rezai and van der Ploeg (2017) derive max-min, max-max, and min-max regret policies to deal with climate model uncertainty (among DICE, FUND, and PAGE) and climate skepticism. If a distribution for model uncertainty can be given, then model uncertainty aversion can be incorporated. For example, Berger, Emmerling, and Tavoni (2017) study the impact of model uncertainty aversion on optimal mitigation policy under catastrophic climate risks.

Ambiguity and Misspecification

If an uncertain parameter does not have a belief distribution, it is ambiguous on its value, and approaches for dealing with parameter uncertainty can be applied to address the ambiguity. If there are many models (or scenarios) but there is no belief distribution across the models (or scenarios), the robust decision-making methods discussed in the previous section can address the ambiguity on the choice of models (or scenarios). An ambiguity-averse individual would rather choose an alternative with a known probability distribution over one where the probabilities are unknown. Thus, this review discusses only ambiguity and misspecification on probability distributions.

A stochastic IAM often assumes that the probability distribution functional form of a risk or shock is given with parameters estimated from historical data, future projections, survey data, or expert opinions. For example, researchers often assume that TFP is a lag-1 autoregression process and its shock has a normal distribution with mean zero and an estimated standard deviation. However, estimated parameters have standard errors, implying that the true probability distribution is uncertain. Sometimes even the functional form of the probability distribution may be misspecified. For example, researchers provide many different belief distributions for the climate sensitivity parameter (IPCC, 2013), but it is unclear which particular one should be applied in IAMs.

In the face of the probability ambiguity (i.e., deep uncertainty) and misspecification, Hansen and Sargent (2008) introduce a robust control framework with risk and ambiguity aversion, which is applied by Athanassoglou and Xepapadeas (2012) for an analytical pollution control problem. Millner, Dietz, and Heal (2013) study climate mitigation policy with ambiguity aversion and find that the value of emissions abatement increases as ambiguity aversion increases. Anderson et al. (2018) conduct an empirically disciplined robustness analysis for the size of the set of perturbations from their baseline model of economic growth dynamics and climate dynamics. Rudik (2020) incorporates the robust control framework to include learning on climate damage.20 Baker, Bosetti, and Salo (2020) introduce a Robust Portfolio Decision Analysis approach to help identify robust individual investments into clean energy technology R&D portfolios with deep uncertainty. Barnett, Brock, and Hansen (2020) investigate risk, ambiguity, and misspecification with continuous-time models and corresponding pricing methods to assess what sources of uncertainty matter the most for the SCC. Berger and Bosetti (2020) find that policy makers are generally ambiguity averse.

Policy Uncertainty

The preceding sections have focused on modeling and climate policy analysis on pricing carbon in the face of uncertainty in the literature. The models may provide quantitative estimates on the SCC, which is often essential for regulatory policy evaluation and implementation, but they often do not explicitly include climate policy instruments to control emissions. In the literature, many climate policies have been suggested, some of which have even been used globally, but there is no consensus on what mix is best or how these policies interact. This section discusses policy uncertainty in choice and efficiency of climate policy instruments, innovation, geoengineering, and adaptation.

Climate Policy Instruments

There are many climate policy instruments, including carbon taxation, cap-and-trade, intensity- based targets, and subsidies (for renewable energy, research for new clean technology, emission reductions, etc.). Each instrument has its advantages and disadvantages. For example, a carbon tax gives a direct price on carbon emissions so companies can adjust their emissions based on cost-benefit analysis, but there is uncertainty in its effect on total emissions in the real world. A cap-and-trade scheme issues a number of emission allowances for the market to auction and trade, so it provides direct control over future emissions and it would be more straightforward to control temperature increase under some threshold (e.g., 2 or 1.5°C), but it is hard to estimate its economic cost. An intensity-based target scheme requires emissions per unit of economic activity (e.g., output) to not exceed given targets, so it may be appealing to developing economies, but there is uncertainty in aggregate emissions and economic costs. Subsidies to renewable energy can help renewable energy firms to improve their market shares and competitivity with fossil fuel energy firms, but there is uncertainty in its effect on controlling total emissions. Carbon tax is the most popularly debated policy, and it is often estimated to be equal to the SCC if it is not explicitly modeled (as in Baldwin, Cai, & Kuralbayeva, 2020), and if emissions control has not reached its limit (Cai et al., 2017; Cai & Lontzek, 2019). However, it could be challenging to politically pass a carbon tax policy in some countries (such as the United States). Instead, the cap-and-trade scheme may be implemented at a regional level. For example, there are currently cap-and-trade programs like the European Union Emissions Trading Schedule, the Regional Greenhouse Gas Initiative, and the California cap-and-trade program, although these programs require careful design to make them effective.

Policy comparisons among the climate policy instruments have been conducted in the literature. For example, Goulder and Parry (2008) review many instrument choices in climate policy with different evaluation criteria, including economic efficiency and cost-effectiveness, distribution of benefits or costs (across income groups, ethnic groups, regions, generations, etc.), ability to address uncertainties, and political feasibility. Fischer and Springborn (2011) compare carbon tax, cap-and-trade, and intensity-based targets in a DSGE model with stochastic productivity. Heutel (2012) compares the optimal emissions tax rate and the optimal emissions quota. Drouet, Bosetti, and Tavoni (2015) discuss selection of climate policies under uncertainties. Goulder, Hafstead, and Williams (2016) argue that under plausible conditions a more conventional form of regulation, a clean energy standard, is more cost-effective than emissions pricing such as carbon taxation or cap-and-trade. Meckling, Sterner, and Wagner (2017) investigate the combination and sequence of policies to avoid environmental, economic, and political dead ends in decarbonizing energy systems. Rozenberg, Vogt-Schilb, and Hallegatte (2020) compare the impact of mandates (for new power plants, buildings, and appliances), feebates (programs that tax energy-inefficient equipment and subsidize energy-efficient equipment), energy efficiency standards, and carbon pricing in a simple model with clean and polluting capital, irreversible investment, and a climate constraint. They find that carbon prices are efficient but can cause stranded assets, while feebates and mandates do not create stranded assets. Baldwin et al. (2020) compare a carbon tax with a subsidy for renewable energy using a DSGE model, which is based on the full DICE model but adds renewable and nonrenewable energy sectors as well as a government that decides the optimal dynamic carbon tax or subsidy. They find that a carbon tax is more efficient under a stringent climate target, while a subsidy is more efficient under a mild climate target.

Economides and Xepapadeas (2018) build a New Keynesian DSGE model to explore how and to what extent monetary policy should be adjusted under conditions of climate change. Barrage (2020) characterizes and quantifies optimal carbon taxes in a dynamic general equilibrium climate–economy model with distortionary fiscal policy, and finds that optimal carbon tax schedules are 8–24% lower when there are distortionary taxes, compared to the setting with lump-sum taxes considered in the literature. Hafstead and Williams (2020) examine the role for tax adjustment mechanisms, which automatically adjust the carbon tax rate based on the level of actual emissions relative to a legislated target, and the trade-offs of alternative designs. They show that tax adjustment mechanisms in carbon tax design can substantially reduce emissions uncertainty. Kalkuhl, Steckel, and Edenhofer (2020) find that the time-consistent policy is the “all-or-nothing” policy with either a zero carbon tax or a prohibitive carbon tax that leads to zero fossil investments, and it is the lobbying power of owners of fixed factors (land and fossil resources), rather than fiscal revenue considerations or the lobbying power of renewable or fossil energy firms, that determines which of the two outcomes (all or nothing) is chosen. Van der Ploeg and Rezai (2020) allow for immediate or delayed carbon taxes and renewable subsidies that will cause discrete jumps in the present valuation of physical and natural capital, and then investigate how the legislative “risk” of tipping into policy action affects the time at which the fossil era ends, the profitability of existing capital, and the green paradox effects (Sinn, 2008).


The adoption of a regulatory policy to limit emissions may be the necessary first step toward creating a market for low-carbon technologies. But it should also be complemented by policies that specifically address the technology innovation and development pipeline. Environmentally friendly technologies to limit emissions are divided into three categories: fossil fuel augmenting, alternative energy augmenting, and offset technologies (i.e., carbon geoengineering). Fossil fuel augmenting technologies improve the efficiency of fossil fuel use by allowing more output per unit of fuel (e.g., hybrid or electric cars substitute petroleum for electricity). Alternative energy augmenting technologies such as solar panels or wind power generation utilize alternative, nonemitting energy sources. Offset technologies directly reduce carbon pollution, either at the point of emission via carbon capture by electricity generators or by a distinct process that sequesters carbon from the atmosphere (e.g., afforestation).

Acemoglu, Aghion, Bursztyn, and Hemous (2012) show that sustainable growth can be achieved with temporary taxes or subsidies that redirect innovation toward clean input, and that the use of an exhaustible dirty resource helps the switch to clean innovation under laissez-faire. Gans (2012) shows that a tighter emissions cap will reduce fossil fuel usage, which will diminish incentives to improve fossil fuel efficiencies, but more stringent climate change policy may not increase incentives to adopt and develop technologies that augment alternative energy sources and will likely increase innovation in abatement technologies. Acemoglu, Akcigit, Hanley, and Kerr (2016) develop a microeconomic model of endogenous growth where clean and dirty technologies compete in production and innovation. They characterize the optimal policy path that makes heavy use of research subsidies as well as carbon taxes. Fried (2018) finds that a carbon tax induces large changes in innovation, and the innovation response increases the policy’s effectiveness in reducing emissions. Gillingham and Stock (2018) review the costs of various technologies and actions aimed at reducing greenhouse gas emissions. McCollum et al. (2018) find that to meet the “well below 2°C” target of the Paris Agreement, low-carbon investments should overtake fossil investments globally by around 2025.


Climate engineering is viewed as a way to control climate change. It can be split into two broad categories: solar geoengineering and carbon geoengineering. Solar geoengineering, also known as solar radiation management, is a technology that reflects a small fraction of sunlight back into space or increases the amount of solar radiation that escapes back into space to cool the planet. Carbon geoengineering, often also called carbon dioxide removal, removes carbon dioxide from the atmosphere via afforestation, bio-energy with carbon capture and sequestration, and direct carbon removal and storage.

Tavoni, Sohngen, and Bosetti (2007) show that forestry is a determinant abatement option that could lead to significantly lower policy costs. Avoiding deforestation in countries with abundant tropical forests can crowd out some of the traditional abatement in the energy sector and lessen induced technological change in clean technologies. Heutel, Moreno-Cruz, and Shayegh (2016, 2018) and Keith, Wagner, and Zabel (2017) investigate the use of solar geoengineering as a substitute for emissions abatement to reduce the atmospheric carbon burden. Favero, Mendelsohn, and Sohngen (2017) recommend using forests to mitigate greenhouse gases by storing carbon and supplying woody biomass for burning in power plants with carbon capture and storage. Griscom et al. (2017) estimate natural climate solutions including conservation, restoration, and improved land management actions that increase carbon storage and avoid greenhouse gas emissions across global forests, wetlands, grasslands, and agricultural lands. Proctor, Hsiang, Burney, Burke, and Schlenker (2018) estimate the global agricultural effects of solar radiation management for managing global temperatures by scattering sunlight back to space. Abatayo, Bosetti, Casari, Ghidoni, and Tavoni (2020) study the governance of solar geoengineering using a laboratory experiment, and find that too much geoengineering can occur, leading to considerable economic losses and increased inequality between countries.


Adaptation has little control on climate change, so it is outside the scope of this review. However, a brief review of recent research work on adaptation shows its critical role in climate policy analysis. For instance, Barreca, Clay, Deschenes, Greenstone, and Shapiro (2016) examine the evolution of the temperature-mortality relationship in the United States to identify potentially useful adaptations, and find that residential air conditioning contributes a substantial fraction of the welfare gains. Burke and Emerick (2016) exploit large variation in recent temperatures and precipitation trends to identify adaptation to climate change in U.S. agriculture. They find that longer-run adaptations appear to have mitigated less than half—and more likely none—of the large negative short-run impacts of extreme heat on productivity. Cai, Feng, Oppenheimer, and Pytlikova (2016) find a positive and statistically significant relationship between temperature and international outmigration only in the most agriculture-dependent countries. Chen and Mueller (2018) find that coastal soil salinity has direct effects on internal and international migration in Bangladesh even after controlling for income losses. Gopalakrishnan, Landry, and Smith (2018) analyze coastal climate change adaptation in the face of sea level rise, ocean warming and acidification, and increased storminess, and conclude that adaptation will require governance coordination across multiple levels. Massetti and Mendelsohn (2018) examine methods for measuring climate adaptation using the empirical evidence. Cai et al. (2019) find that low-latitude regions will implement stronger adaptation than high-latitude regions, and adaptation can significantly reduce the optimal regional carbon tax.

Conclusion and Future Research

This article provides a review of state-of-the-art work on different types of uncertainty in controlling climate change: parameter uncertainty, risk, model uncertainty, scenario uncertainty, policy uncertainty, ambiguity, and misspecification. Uncertainty often plays an essential role in models and can change results significantly. With advanced computational methods and hardware, it becomes possible to analyze policies in more complex and realistic IAMs with uncertainty.

With advances in understanding the physical science of climate change and the economic system, there are a number of potential future studies that can incorporate uncertainty in climate change economics. Burke et al. (2016) discuss some research opportunities in climate change economics, particularly in three areas: SCC refinement, policy evaluation, and evaluation of climate impact and policy choices in developing countries. Incorporating uncertainty into related research may generate interesting results. Other research opportunities include richer and more realistic representations of the economic and climate systems as well as policies with uncertainty: spatial disaggregation as in Krusell and Smith (2017), disaggregation of intertemporal agents (overlapping generations) as in Kotlikoff, Kubler, Polbin, Sachs, and Scheidegger (2019), disaggregation of sectors (e.g., adding the green finance sectors), disaggregation of heterogeneous agents, integration with other systems (e.g., the water system), and more realistic international trade and international agreements in climate policies. It will be interesting to incorporate uncertainty in research work on IAMs with climate impact on income inequality, regional inequality, social conflict, human health and ecosystems, and migration. As suggested by Irwin, Gopalakrishnan, and Randall (2016), it will also be important for future work to evaluate sustainability and resilience in the face of uncertainty and climate change.

Disclosure Statement

The author is not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.


I acknowledge support from the National Science Foundation grants SES-1463644 and SES- 1739909, and the U.S. Department of Agriculture NIFA-AFRI grant 2018-68002-2793. I would like to thank William Brock, Kenneth Judd, Thomas Lontzek, Brent Sohngen, Anastasios Xepapadeas, and anonymous reviewers for their helpful comments. I thank the editorial committee, especially Brent Sohngen, for the invitation to write this article.

Further Reading

  • Burke, M., Hsiang, S. M., & Miguel, E. (2015). Global non-linear effect of temperature on economic production. Nature, 527(7577), 235–239.
  • Cai, Y. (2019). Computational methods in environmental and resource economics. Annual Review of Resource Economics, 11, 59–82.
  • Cai, Y., & Lontzek, T. S. (2019). The social cost of carbon with economic and climate risks. Journal of Political Economy, 6, 2684–2734.
  • Intergovernmental Panel on Climate Change. (2013). Climate change 2013: The physical science basis. New York, NY: Cambridge University Press.
  • Nordhaus, W. D. (2008). A question of balance: Weighing the options on global warming policies. New Haven, CT: Yale University Press.
  • Pindyck, R. S. (2013). Climate change policy: What do the models tell us? Journal of Economic Literature, 51(3), 860–872.
  • Stern, N. H. (2007). The economics of climate change: The Stern review. Cambridge, UK: Cambridge University Press.
  • Weitzman, M. L. (2011). Fat-tailed uncertainty in the economics of catastrophic climate change. Review of Environmental Economics and Policy, 5(2), 275–292.


  • Abatayo, A. L., Bosetti, V., Casari, M., Ghidoni, R., & Tavoni, M. (2020). Solar geoengineering may lead to excessive cooling and high strategic uncertainty. Proceedings of the National Academy of Sciences, 117(24), 13393–13398.
  • Acemoglu, D., Aghion, P., Bursztyn, L., & Hemous, D. (2012). The environment and directed technical change. American Economic Review, 102(1), 131–166.
  • Acemoglu, D., Akcigit, U., Hanley, D., & Kerr, W. (2016). Transition to clean technology. Journal of Political Economy, 124(1), 52–104.
  • Ackerman, F., Stanton, E. A., & Bueno, R. (2010). Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE. Ecological Economics, 69(8), 1657–1665.
  • Anderson, E. W., Brock, W., & Sanstad, A. H. (2018). Robust consumption and energy decisions. In V. V. Chari & R. Litterman (Eds.), Climate change economics: The role of uncertainty and risk. Wiley.
  • Annicchiarico, B., & Di Dio, F. (2015). Environmental policy and macroeconomic dynamics in a new Keynesian model. Journal of Environmental Economics and Management, 69, 1–21.
  • Anthoff, D., Estrada, F., & Tol, R. S. J. (2016). Shutting down the thermohaline circulation. American Economic Review: Papers and Proceedings, 106(5), 602–606.
  • Anthoff, D., & Tol, R. (2013). The uncertainty about the social cost of carbon: A decomposition analysis using FUND. Climatic Change, 117(3), 515–530.
  • Anthoff, D., & Tol, R. (2014). Climate policy under fat-tailed risk: An application of FUND. Annals of Operations Research, 220(1), 223–237.
  • Arrow, K., Cropper, M., Gollier, C., Groom, B., Heal, G., Newell, R., . . . Weitzman, M. (2013). Determining benefits and costs for future generations. Science, 341(6144), 349–350.
  • Arrow, K., Cropper, M., Gollier, C., Groom, B., Heal, G., Newell, R., . . . Weitzman, M. (2014). Should governments use a declining discount rate in project analysis? Review of Environmental Economics and Policy, 8(2), 145–163.
  • Athanassoglou, S., & Xepapadeas, A. (2012). Pollution control with uncertain stock dynamics: When, and how, to be precautious. Journal of Environmental Economics and Management, 63(3), 304–320.
  • Baker, E., Bosetti, V., & Salo, A. (2020). Robust portfolio decision analysis: An application to the energy research and development portfolio problem. European Journal of Operational Research, 284(3), 1107–1120.
  • Baldwin, E., Cai, Y., & Kuralbayeva, K. (2020). To build or not to build? Capital stocks and climate policy. Journal of Environmental Economics and Management, 100, 102235.
  • Bansal, R., Kiku, D., & Ochoa, M. (2019). Climate change risk. Advance online publication
  • Bansal, R., Ochoa, M., & Kiku, D. (2018). Climate change and growth risks. In V. V. Chari & R. Litterman (Eds.), Climate change economics: The role of uncertainty and risk. Wiley.
  • Bansal, R., & Yaron, A. (2004). Risks for the long run: A potential resolution of asset pricing puzzles. Journal of Finance, 59(4), 1481–1509.
  • Barnett, M., Brock, W. A., & Hansen, L. P. (2020). Pricing uncertainty induced by climate change. Review of Financial Studies, 33(3), 1024–1066.
  • Barrage, L. (2020). Optimal dynamic carbon taxes in a climate-economy model with distortionary fiscal policy. Review of Economic Studies, 87(1), 1–39.
  • Barreca, A., Clay, K., Deschenes, O., Greenstone, M., & Shapiro, J. S. (2016). Adapting to climate change: The remarkable decline in the US temperature-mortality relationship over the twentieth century. Journal of Political Economy, 124(1), 105–159.
  • Bellman, R. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.
  • Berger, L., & Bosetti, V. (2020). Are policymakers ambiguity averse? Economic Journal, 130(626), 331–355.
  • Berger, L., Emmerling, J., & Tavoni, M. (2017). Managing catastrophic climate risks under model uncertainty aversion. Management Science, 63(3), 749–765.
  • Bosetti, V., Carraro, C., Galeotti, M., Massetti, E., & Tavoni, M. (2006). WITCH: A world induced technical change hybrid model. Energy Journal, 27, 13–37.
  • Brock, W. A., & Hansen, L. P. (2018). Wrestling with uncertainty in climate economic models. In In V. V. Chari & R. Litterman (Eds.), Climate change economics: The role of uncertainty and risk. Wiley.
  • Brock, W., & Xepapadeas, A. (2017). Climate change policy under polar amplification. European Economic Review, 99, 93–112.
  • Brock, W. A., & Xepapadeas, A. (2018). Modeling coupled climate, ecosystems, and economic systems. In P. Dasgupta, K. Pattanayak, & V. K. Smith (Eds.), Handbook of environmental economics (Vol. 4, pp. 1–60). Elsevier.
  • Brock, W., & Xepapadeas, A. (2019). Regional climate change policy under positive feedbacks and strategic interactions. Environmental and Resource Economics, 72(1), 51–75.
  • Burke, M., Craxton, M., Kolstad, C. D., Onda, C., Allcott, H., Baker, E., . . . Tol, R. S. J. (2016). Opportunities for advances in climate change economics. Science, 352(6283), 292–293.
  • Burke, M., Davis, W. M., & Diffenbaugh, N. S. (2018). Large potential reduction in economic damages under UN mitigation targets. Nature, 557(7706), 549.
  • Burke, M., Dykema, J., Lobell, D. B., Miguel, E., & Satyanath, S. (2015). Incorporating climate uncertainty into estimates of climate change impacts. Review of Economics and Statistics, 97(2), 461–471.
  • Burke, M., & Emerick, K. (2016). Adaptation to climate change: Evidence from US agriculture. American Economic Journal: Economic Policy, 8(3), 106–140.
  • Burke, M., Hsiang, S., & Miguel, E. (2015a). Climate and conflict. Annual Review of Economics, 7(1), 577–617.
  • Burke, M., Hsiang, S., & Miguel, E. (2015b). Global non-linear effect of temperature on economic production. Nature, 527(7577), 235–239.
  • Cai, R., Feng, S., Oppenheimer, M., & Pytlikova, M. (2016). Climate variability and international migration: The importance of the agricultural linkage. Journal of Environmental Economics and Management, 79, 135–151.
  • Cai, Y. (2019). Computational methods in environmental and resource economics. Annual Review of Resource Economics, 11, 59–82.
  • Cai, Y., Brock, W., Xepapadeas, A., & Judd, K. L. (2019). Climate policy under spatial heat transport: Cooperative and noncooperative regional outcomes. arXiv Working Paper 1909.04009.
  • Cai, Y., Golub, A. A., & Hertel, T. W. (2017). Agricultural research spending must increase in light of future uncertainties. Food Policy, 70, 71–83.
  • Cai, Y., Judd, K. L., Lenton, T. M., Lontzek, T. S., & Narita, D. (2015). Environmental tipping points significantly affect the cost-benefit assessment of climate policies. Proceedings of the National Academy of Sciences, 112(15), 4606–4611.
  • Cai, Y., Judd, K. L., & Lontzek, T. S. (2012). Open science is necessary. Nature Climate Change, 2(5), 299.
  • Cai, Y., Judd, K. L., & Lontzek, T. S. (2017). The social cost of carbon with economic and climate risks. Working Paper 18113. Stanford, CA: Hoover Institution, Stanford University.
  • Cai, Y., Judd, K. L., & Steinbuks, J. (2017). A nonlinear certainty equivalent approximation method for dynamic stochastic problems. Quantitative Economics, 8(1), 117–147.
  • Cai, Y., Lenton, T. M., & Lontzek, T. S. (2016). Risk of multiple interacting tipping points should encourage rapid CO2 emission reduction. Nature Climate Change, 6(5), 520–525.
  • Cai, Y., & Lontzek, T. S. (2019). The social cost of carbon with economic and climate risks. Journal of Political Economy, 6, 2684–2734.
  • Cai, Y., & Sanstad, A. H. (2016). Model uncertainty and energy technology policy: The example of induced technical change. Computers and Operations Research, 66, 362–373.
  • Cai, Y., Steinbuks, J., Judd, K. L., Jaegermeyr, J., & Hertel, T. W. (2020). Modeling uncertainty in large natural resource allocation problems. Working Paper 9159. Washington, DC: World Bank.
  • Calvin, K., Patel, P., Clarke, L., Asrar, G., Bond-Lamberty, B., Cui, R. Y., . . . Wise, M. (2019). GCAM v5.1: Representing the linkages between energy, water, land, climate, and economic systems. Geoscientific Model Development, 12(2), 677–698.
  • Carleton, T. A., & Hsiang, S. M. (2016). Social and economic impacts of climate. Science, 353(6304).
  • Chari, V. V. (2018). The role of uncertainty and risk in climate change economics (Federal Reserve Bank of Minneapolis Staff Report).
  • Chen, J., & Mueller, V. (2018). Coastal climate change, soil salinity and human migration in Bangladesh. Nature Climate Change, 8(11), 981–985.
  • Chen, Y., Henry, H., Paltsev, S., Reilly, J. M., Morris, J. F., & Babiker, M. H. (2016). Long-term economic modeling for climate change assessment. Economic Modelling, 52, 867–883.
  • Costinot, A., Donaldson, D., & Smith, C. (2016). Evolving comparative advantage and the impact of climate change in agricultural markets: Evidence from 1.7 million fields around the world. Journal of Political Economy, 124(1), 205–248.
  • Crost, B., & Traeger, C. P. (2013). Optimal climate policy: Uncertainty versus Monte Carlo. Economics Letters, 120(3), 552–558.
  • Csatho, B. M., Schenk, A. F., van der Veen, C. J., Babonis, G., Duncan, K., Rezvanbehbahani, S., . . . van Angelen, J. H. (2014). Laser altimetry reveals complex pattern of Greenland ice sheet dynamics. Proceedings of the National Academy of Sciences, 111(52), 18478–18483.
  • Daniel, K. D., Litterman, R. B., & Wagner, G. (2018). Applying asset pricing theory to calibrate the price of climate risk. In V. V. Chari & R. Litterman (Eds.), Climate change economics: The role of uncertainty and risk. Wiley.
  • Dell, M., Jones, B. F., & Olken, B. A. (2012). Temperature shocks and economic growth: Evidence from the last half century. American Economic Journal: Macroeconomics, 4(3), 66–95.
  • Dennig, F., Budolfson, M. B., Fleurbaey, M., Siebert, A., & Socolow, R. H. (2015). Inequality, climate impacts on the future poor, and carbon prices. Proceedings of the National Academy of Sciences, 112(52), 15827–15832.
  • Diaz, D., & Keller, K. (2016). A potential disintegration of the West Antarctic ice sheet: Implications for economic analyses of climate policy. American Economic Review: Papers and Proceedings, 106(5), 607–611.
  • Diaz, D., & Moore, F. (2017). Quantifying the economic risks of climate change. Nature Climate Change, 7(11), 774–782.
  • Dietz, S., & Fankhauser, S. (2010). Environmental prices, uncertainty, and learning. Oxford Review of Economic Policy, 26(2), 270–284.
  • Dietz, S., & Stern, N. (2015). Endogenous growth, convexity of damage and climate risk: How Nordhaus’ framework supports deep cuts in carbon emissions. Economic Journal, 125(583), 574–620.
  • Dietz, S., & Venmans, F. (2019). Cumulative carbon emissions and economic policy: In search of general principles. Journal of Environmental Economics and Management, 96, 108–129.
  • Diffenbaugh, N. S., & Burke, M. (2019). Global warming has increased global economic inequality. Proceedings of the National Academy of Sciences, 116(20), 9808–9813.
  • Ditlevsen, P. D., & Johnsen, S. J. (2010). Tipping points: Early warning and wishful thinking. Geophysical Research Letters, 37, L19703.
  • Drouet, L., Bosetti, V., & Tavoni, M. (2015). Selection of climate policies under the uncertainties in the Fifth Assessment Report of the IPCC. Nature Climate Change, 5(10), 937–940.
  • Drupp, M. A., Freeman, M. C., Groom, B., & Nesje, F. (2018). Discounting disentangled. American Economic Journal: Economic Policy, 10(4), 109–134.
  • Duffy, P. B., Field, C. B., Diffenbaugh, N. S., Doney, S. C., Dutton, Z., Goodman, S., . . . Williams, P. (2019). Strengthened scientific support for the endangerment finding for atmospheric greenhouse gases. Science, 363(6427), eaat5982.
  • Economides, G., & Xepapadeas, A. (2018). Monetary policy under climate change. SSRN Scholarly Paper ID 3200266.
  • Epstein, L. G., & Zin, S. E. (1989). Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework. Econometrica, 57(4), 937–969.
  • Fan, Q., Fisher-Vanden, K., & Klaiber, H. A. (2018). Climate change, migration, and regional economic impacts in the United States. Journal of the Association of Environmental and Resource Economists, 5(3), 643–671.
  • Farmer, J. D., Hepburn, C., Mealy, P., & Teytelboym, A. (2015). A third wave in the economics of climate change. Environmental and Resource Economics, 62(2), 329–357.
  • Favero, A., Daigneault, A., & Sohngen, B. (2020). Forests: Carbon sequestration, biomass energy, or both? Science Advances, 6, eaay6792.
  • Favero, A., Mendelsohn, R., & Sohngen, B. (2017). Using forests for climate mitigation: Sequester carbon or produce woody biomass? Climatic Change, 144(2), 195–206.
  • Fischer, C., & Heutel, G. (2013). Environmental macroeconomics: Environmental policy, business cycles, and directed technical change. Annual Review of Resource Economics, 5(1), 197–210.
  • Fischer, C., & Springborn, M. (2011). Emissions targets and the real business cycle: Intensity targets versus caps or taxes. Journal of Environmental Economics and Management, 62(3), 352–366.
  • Frederick, S., Loewenstein, G., & O’Donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature, 40(2), 351–401.
  • Fried, S. (2018). Climate policy and innovation: A quantitative macroeconomic analysis. American Economic Journal: Macroeconomics, 10(1), 90–118.
  • Fujimori, S., Masui, T., & Matsuoka, Y. (2017). AIM/CGE V2.0 model formula. In S. Fujimori, M. Kainuma, & T. Masui (Eds.), Post-2020 climate action: Global and Asian perspectives (pp. 201–303). Singapore: Springer.
  • Gans, J. S. (2012). Innovation and climate change policy. American Economic Journal: Economic Policy, 4(4), 125–145.
  • Gerlagh, R., & Liski, M. (2018). Carbon prices for the next hundred years. Economic Journal, 128(609), 728–757.
  • Ghil, M., & Lucarini, V. (2019). The physics of climate variability and climate change. arXiv Working Paper 1910.00583.
  • Gillingham, K., Nordhaus, W., Anthoff, D., Blanford, G., Bosetti, V., Christensen, P., . . . Reilly, J. (2018). Modeling uncertainty in integrated assessment of climate change: A multimodel comparison. Journal of the Association of Environmental and Resource Economists, 5(4), 791–826.
  • Gillingham, K., & Stock, J. H. (2018). The cost of reducing greenhouse gas emissions. Journal of Economic Perspectives, 32(4), 53–72.
  • Gollier, C. (2012). Pricing the planet’s future: The economics of discounting in an uncertain world. Princeton, NJ: Princeton University Press.
  • Golosov, M., Hassler, J., Krusell, P., & Tsyvinski, A. (2014). Optimal taxes on fossil fuel in general equilibrium. Econometrica, 82(1), 41–88.
  • Gopalakrishnan, S., Landry, C. E., & Smith, M. D. (2018). Climate change adaptation in coastal environments: Modeling challenges for resource and environmental economists. Review of Environmental Economics and Policy, 12(1), 48–68.
  • Goulder, L. H. (2020). Timing is everything: How economists can better address the urgency of stronger climate policy. Review of Environmental Economics and Policy, 14(1), 143–156.
  • Goulder, L. H., Hafstead, M. A. C., & Williams, R. C., III. (2016). General equilibrium impacts of a federal clean energy standard. American Economic Journal: Economic Policy, 8(2), 186–218.
  • Goulder, L. H., & Mathai, K. (2000). Optimal CO2 abatement in the presence of induced technological change. Journal of Environmental Economics and Management, 39(1), 1–38.
  • Goulder, L. H., & Parry, I. W. H. (2008). Instrument choice in environmental policy. Review of Environmental Economics and Policy, 2(2), 152–174.
  • Griscom, B. W., Adams, J., Ellis, P. W., Houghton, R. A., Lomax, G., Miteva, D. A., . . . Fargione, J. (2017). Natural climate solutions. Proceedings of the National Academy of Sciences, 114(44), 11645–11650.
  • Hafstead, M. A. C., & Williams, R. C. (2020). Designing and evaluating a U.S. carbon tax adjustment mechanism to reduce emissions uncertainty. Review of Environmental Economics and Policy, 14(1), 95–113.
  • Hansen, L. P., & Sargent, T. (2008). Robustness. Princeton, NJ: Princeton University Press.
  • Harenberg, D., Marelli, S., Sudret, B., & Winschel, V. (2019). Uncertainty quantification and global sensitivity analysis for economic models. Quantitative Economics, 10(1), 1–41.
  • Heal, G. (2017). The economics of the climate. Journal of Economic Literature, 55(3), 1046–1063.
  • Heal, G., & Park, J. (2016). Reflections: Temperature stress and the direct impact of climate change—A review of an emerging literature. Review of Environmental Economics and Policy, 10(2), 347–362.
  • Heutel, G. (2012). How should environmental policy respond to business cycles? Optimal policy under persistent productivity shocks. Review of Economic Dynamics, 15(2), 244–264.
  • Heutel, G., Moreno-Cruz, J., & Shayegh, S. (2016). Climate tipping points and solar geoengineering. Journal of Economic Behavior & Organization, 132, 19–45.
  • Heutel, G., Moreno-Cruz, J., & Shayegh, S. (2018). Solar geoengineering, uncertainty, and the price of carbon. Journal of Environmental Economics and Management, 87(2), 24–41.
  • Hope, C. (2011). The PAGE09 integrated assessment model: A technical description. Working Paper 4/2011. Cambridge, UK: Judge Business School, Cambridge University.
  • Hsiang, S., & Kopp, R. E. (2018). An economist’s guide to climate change science. Journal of Economic Perspectives, 32(4), 3–32.
  • Hsiang, S., Kopp, R., Jina, A., Rising, J., Delgado, M., Mohan, S., . . . Houser, T. (2017). Estimating economic damage from climate change in the United States. Science, 356(6345), 1362–1369.
  • Hsiang, S., Oliva, P., & Walker, R. (2019). The distribution of environmental damages. Review of Environmental Economics and Policy, 13(1), 83–103.
  • Huppmann, D., Gidden, M., Fricko, O., Kolp, P., Orthofer, C., Pimmer, M., . . . Krey, V. (2019). The MESSAGE integrated assessment model and the ix modeling platform (ixmp): An open framework for integrated and cross-cutting analysis of energy, climate, the environment, and sustainable development. Environmental Modelling and Software, 112, 143–156.
  • Hwang, I.-C., Reynes, F., & Tol, R. S. J. (2017). The effect of learning on climate policy under fat-tailed risk. Resource and Energy Economics, 48, 1–18.
  • Interagency Working Group on Social Cost of Carbon. (2010). Social cost of carbon for regulatory impact analysis under Executive Order 12866 (Technical Report, US Government).
  • Intergovernmental Panel on Climate Change. (2007). Climate change 2007: The physical science basis. New York, NY: Cambridge University Press.
  • Intergovernmental Panel on Climate Change. (2013). Climate change 2013: The physical science basis. New York, NY: Cambridge University Press.
  • Irwin, E. G., Gopalakrishnan, S., & Randall, A. (2016). Welfare, wealth, and sustainability. Annual Review of Resource Economics, 8(1), 77–98.
  • Iverson, T. (2012). Communicating trade-offs amid controversial science: Decision support for climate policy. Ecological Economics, 77, 74–90.
  • Iverson, T. (2013). Minimax regret discounting. Journal of Environmental Economics and Management, 66(3), 598–608.
  • Jaakkola, N., & van der Ploeg, F. (2019). Non-cooperative and cooperative climate policies with anticipated breakthrough technology. Journal of Environmental Economics and Management, 97, 42–66.
  • Jensen, S., & Traeger, C. (2014). Optimal climate change mitigation under longterm growth uncertainty: Stochastic integrated assessment and analytic findings. European Economic Review, 69, 104–125.
  • Joughin, I., Smith, B. E., & Medley, B. (2014). Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science, 344(6185), 735–738.
  • Judd, K. L. (1998). Numerical methods in economics. Cambridge, MA: MIT Press.
  • Kalkuhl, M., Steckel, J. C., & Edenhofer, O. (2020). All or nothing: Climate policy when assets can become stranded. Journal of Environmental Economics and Management, 100, 102214.
  • Karydas, C., & Xepapadeas, A. (2019). Pricing climate change risks: CAPM with rare disasters and stochastic probabilities. SSRN Scholarly Paper ID 3324499.
  • Keith, D. W., Wagner, G., & Zabel, C. L. (2017). Solar geoengineering reduces atmospheric carbon burden. Nature Climate Change, 7(9), 617–619.
  • Keller, K., Bolker, B. M., & Bradford, D. F. (2004). Uncertain climate thresholds and optimal economic growth. Journal of Environmental Economics and Management, 48(1), 723–741.
  • Kelly, D. L., & Kolstad, C. D. (1999a). Bayesian learning, growth, and pollution. Journal of Economic Dynamics and Control, 23, 491–518.
  • Kelly, D. L., & Kolstad, C. D. (1999b). Integrated assessment models for climate change control. In H. Folmer & T. Tietenberg (Eds.), International yearbook of environmental and resource economics 1999/2000: A survey of current issues (pp. 171–197). Cheltenham, UK: Edward Elgar.
  • Kelly, D. L., & Tan, Z. (2015). Learning and climate feedbacks: Optimal climate insurance and fat tails. Journal of Environmental Economics and Management, 72, 98–122.
  • Khan, S. A., Kjar, K. H., Bevis, M., Bamber, J. L., Wahr, J., Kjeldsen, K. K., . . . Muresan, I. S. (2014). Sustained mass loss of the northeast Greenland ice sheet triggered by regional warming. Nature Climate Change, 4(4), 292–299.
  • Kim, J. B., Monier, E., Sohngen, B., Pitts, G. S., Drapek, R., McFarland, J., . . . Cole, J. (2017). Assessing climate change impacts, benefits of mitigation, and uncertainties on major global forest regions under multiple socioeconomic and emissions scenarios. Environmental Research Letters, 12(4), 045001.
  • Knutti, R., Rugenstein, M. A. A., & Hegerl, G. C. (2017). Beyond equilibrium climate sensitivity. Nature Geoscience, 10(10), 727–736.
  • Kolstad, C. D. (1996). Learning and stock effects in environmental regulation: The case of greenhouse gas emissions. Journal of Environmental Economics and Management, 31(1), 1–18.
  • Kotlikoff, L. J., Kubler, F., Polbin, A., Sachs, J. D., & Scheidegger, S. (2019). Making carbon taxation a generational win win. Working Paper 25760. Cambridge, MA: National Bureau of Economic Research.
  • Kriegler, E., Hall, J. W., Held, H., Dawson, R., & Schellnhuber, H. J. (2009). Imprecise probability assessment of tipping points in the climate system. Proceedings of the National Academy of Sciences, 106(13), 5041–5046.
  • Krusell, P., & Smith, A. (2017). Climate change around the world. memo.
  • Leach, A. J. (2007). The climate change learning curve. Journal of Economic Dynamics and Control, 31(5), 1728–1752.
  • Lemoine, D., & Rudik, I. (2017). Managing climate change under uncertainty: Recursive integrated assessment at an inflection point. Annual Review of Resource Economics, 9(1), 117–142.
  • Lemoine, D., & Traeger, C. (2014). Watch your step: Optimal policy in a tipping climate. American Economic Journal: Economic Policy, 6(1), 137–166.
  • Lenton, T. M., & Ciscar, J.-C. (2013). Integrating tipping points into climate impact assessments. Climatic Change, 117(3), 585–597.
  • Lenton, T. M., Held, H., Kriegler, E., Hall, J. W., Lucht, W., Rahmstorf, S., & Schellnhuber, H. J. (2008). Tipping elements in the earth’s climate system. Proceedings of the National Academy of Sciences, 105(6), 1786–1793.
  • Lontzek, T. S., Cai, Y., Judd, K. L., & Lenton, T. M. (2015). Stochastic integrated assessment of climate tipping points indicates the need for strict climate policy. Nature Climate Change, 5(5), 441–444.
  • Luderer, G., Leimbach, M., Bauer, N., Kriegler, E., Baumstark, L., Bertram, C., . . . Strefler, J. (2015). Description of the REMIND model (Version 1.6). SSRN Scholarly Paper ID 2697070.
  • MacDougall, A. H., & Friedlingstein, P. (2015). The origin and limits of the near proportionality between climate warming and cumulative CO2 emissions. Journal of Climate, 28(10), 4217–4230.
  • MacDougall, A. H., Swart, N. C., & Knutti, R. (2016). The uncertainty in the transient climate response to cumulative CO2 emissions arising from the uncertainty in physical climate parameters. Journal of Climate, 30(2), 813–827.
  • Mach, K. J., Kraan, C. M., Adger, W. N., Buhaug, H., Burke, M., Fearon, J. D., . . . von Uexkull, N. (2019). Climate as a risk factor for armed conflict. Nature, 571(7764), 193–197.
  • Manne, A., Mendelsohn, R., & Richels, R. (1995). MERGE: A model for evaluating regional and global effects of GHG reduction policies. Energy Policy, 23(1), 17–34.
  • Manne, A. S., & Richels, R. G. (2005). MERGE: An integrated assessment model for global climate change. In R. Loulou, J.-P. Waaub, & G. Zaccour (Eds.), Energy and environment (pp. 175–189). New York, NY: Springer-Verlag.
  • Massetti, E., & Mendelsohn, R. (2018). Measuring climate adaptation: Methods and evidence. Review of Environmental Economics and Policy, 12(2), 324–341.
  • Matthews, H. D., Gillett, N. P., Stott, P. A., & Zickfeld, K. (2009). The proportionality of global warming to cumulative carbon emissions. Nature, 459(7248), 829–832.
  • McCollum, D. L., Zhou, W., Bertram, C., de Boer, H.-S., Bosetti, V., Busch, S., . . . Riahi, K. (2018). Energy investment needs for fulfilling the Paris Agreement and achieving the Sustainable Development Goals. Nature Energy, 3(7), 589–599.
  • Meckling, J., Sterner, T., & Wagner, G. (2017). Policy sequencing toward decarbonization. Nature Energy, 2(12), 918–922.
  • Meinshausen, M., Hare, W., Frieler, K., Meinshausen, N., Raper, S. C. B., Knutti, R., Frame, D. J., & Allen, M. R. (2009). Greenhouse-gas emission targets for limiting global warming to 2°C. Nature, 458(7242), 1158–1162.
  • Meinshausen, M., Smith, S. J., Calvin, K., Daniel, J. S., Kainuma, M. L. T., Lamarque, J.-F., . . . van Vuuren, D. P. P. (2011). The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Climatic Change, 109, 213–241.
  • Metcalf, G. E., & Stock, J. H. (2017). Integrated assessment models and the social cost of carbon: A review and assessment of U.S. experience. Review of Environmental Economics and Policy, 11(1), 80–99.
  • Millner, A., Dietz, S., & Heal, G. (2013). Scientific ambiguity and climate policy. Environmental and Resource Economics, 55(1), 21–46.
  • Moore, F. C., & Diaz, D. B. (2015). Temperature impacts on economic growth warrant stringent mitigation policy. Nature Climate Change, 5(2), 127–131.
  • New, M., & Hulme, M. (2000). Representing uncertainty in climate change scenarios: A Monte-Carlo approach. Integrated Assessment, 1(3), 203–213.
  • Nordhaus, W. D. (1994). Expert opinion on climatic change. American Scientist, 82(1), 45–51.
  • Nordhaus, W. D. (2008). A question of balance: Weighing the options on global warming policies. New Haven, CT: Yale University Press.
  • Nordhaus, W. D. (2010). Economic aspects of global warming in a post-Copenhagen environment. Proceedings of the National Academy of Sciences, 107(26), 11721–11726.
  • Nordhaus, W. D. (2017). Revisiting the social cost of carbon. Proceedings of the National Academy of Sciences of the United States of America, 114(7), 1518–1523.
  • Nordhaus, W. D. (2019). Economics of the disintegration of the Greenland ice sheet. Proceedings of the National Academy of Sciences, 116(25), 12261–12269.
  • Nordhaus, W. D., & Boyer, J. (2000). Warming the world: Economic models of global warming. Cambridge, MA: MIT Press.
  • O’Neill, B. C., Kriegler, E., Riahi, K., Ebi, K. L., Hallegatte, S., Carter, T. R., . . . van Vuuren, D. P. (2014). A new scenario framework for climate change research: The concept of shared socioeconomic pathways. Climatic Change, 122(3), 387–400.
  • Pindyck, R. S. (2013). Climate change policy: What do the models tell us? Journal of Economic Literature, 51(3), 860–872.
  • Pindyck, R. S. (2017). The use and misuse of models for climate policy. Review of Environmental Economics and Policy, 11(1), 100–114.
  • Proctor, J., Hsiang, S., Burney, J., Burke, M., & Schlenker, W. (2018). Estimating global agricultural effects of geoengineering using volcanic eruptions. Nature, 560(7719), 480–483.
  • Rezai, A., & van der Ploeg, F. (2017). Climate policies under climate model uncertainty: Max-min and min-max regret. Energy Economics, 68, 4–16.
  • Rozenberg, J., Vogt-Schilb, A., & Hallegatte, S. (2020). Instrument choice and stranded assets in the transition to clean capital. Journal of Environmental Economics and Management, 100, 102183.
  • Rudik, I. (2020). Optimal climate policy when damages are unknown. American Economic Journal: Economic Policy, 12(2), 340–373.
  • Schauberger, B., Archontoulis, S., Arneth, A., Balkovic, J., Ciais, P., Deryng, D., . . . Frieler, K. (2017). Consistent negative response of US crops to high temperatures in observations and crop models. Nature Communications, 8(1), 1–9.
  • Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V., . . . Sugihara, G. (2009). Early warning signals for critical transitions. Nature, 461(7260), 53–59.
  • Schlenker, W., & Auffhammer, M. (2018). The cost of a warming climate. Nature, 557(7706), 498–499.
  • Sinn, H.-W. (2008). Public policies against global warming: A supply side approach. International Tax and Public Finance, 15(4), 360–394.
  • Sohngen, B., & Mendelsohn, R. (2003). An optimal control model of forest carbon sequestration. American Journal of Agricultural Economics, 85(2), 448–457.
  • Steffen, W., Rockstrom, J., Richardson, K., Lenton, T. M., Folke, C., Liverman, D., . . . Schellnhuber, H.-J. (2018). Trajectories of the earth system in the Anthropocene. Proceedings of the National Academy of Sciences, 115(33), 8252–8259.
  • Stehfest, E., van Vuuren, D., Kram, T., Bouwman, L., Alkemade, R., Bakkenes, M., . . . Prins, A. (2014). Integrated assessment of global environmental change with IMAGE 3.0: Model description and policy applications. The Hague, The Netherlands: PBL Netherlands Environmental Assessment Agency.
  • Stern, N. H. (2007). The economics of climate change: The Stern review. Cambridge, UK: Cambridge University Press.
  • Sterner, T., & Persson, U. M. (2008). An even Sterner review: Introducing relative prices into the discounting debate. Review of Environmental Economics and Policy, 2(1), 61–76.
  • Tavoni, M., Sohngen, B., & Bosetti, V. (2007). Forestry and the carbon market response to stabilize climate. Energy Policy, 35(11), 5346–5353.
  • van der Ploeg, F. (2018). The safe carbon budget. Climatic Change, 147(1), 47–59.
  • van der Ploeg, F., & de Zeeuw, A. (2016). Non-cooperative and cooperative responses to climate catastrophes in the global economy: A north–south perspective. Environmental and Resource Economics, 65(3), 519–540.
  • van der Ploeg, F., & de Zeeuw, A. (2018). Climate tipping and economic growth: Precautionary capital and the price of carbon. Journal of the European Economic Association, 16(5), 1577–1617.
  • van der Ploeg, F., & Rezai, A. (2020). The risk of policy tipping and stranded carbon assets. Journal of Environmental Economics and Management, 100, 102258.
  • Weitzman, M. L. (2001). Gamma discounting. American Economic Review, 91(1), 260–271.
  • Weitzman, M. L. (2009). On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics, 91, 1–19.
  • Weitzman, M. L. (2011). Fat-tailed uncertainty in the economics of catastrophic climate change. Review of Environmental Economics and Policy, 5(2), 275–292.
  • Weitzman, M. L. (2012). GHG targets as insurance against catastrophic climate damages. Journal of Public Economic Theory, 14(2), 221–244.
  • Weyant, J. (2017). Some contributions of integrated assessment models of global climate change. Review of Environmental Economics and Policy, 11(1), 115–137.
  • Zhang, P., Deschenes, O., Meng, K., & Zhang, J. (2018). Temperature effects on productivity and factor reallocation: Evidence from a half million Chinese manufacturing plants. Journal of Environmental Economics and Management, 88, 1–17.


  • 1. See Hsiang and Kopp (2018) for an introduction to the physical science of climate change for economists.

  • 2. See Chari (2018) for a discussion about uncertainty and risk in climate change.

  • 3. Dietz and Fankhauser (2010) suggest that when facing an emission quantity target (e.g., determined through the Paris Agreement for keeping a globally average atmospheric temperature increase this century well below 2°C over the preindustrial level), the marginal abatement cost (i.e., the shadow price of the target constraint), rather than the SCC, will often provide more consistent and robust prices for achieving the target.

  • 4. Kolstad (1996) suggests that with the tension between postponing control until more is known versus acting now before irreversible climate change takes place, a temporary carbon tax may dominate a permanent one because a temporary tax may induce increased flexibility to future uncertainty.

  • 5. In fact, a time varying path would not be called a parameter.

  • 6. See e.g., Gillingham et al. (2018), Cai, Judd, and Lontzek (2018), and Cai and Lontzek (2019) for investigations on the impact of these uncertain parameters.

  • 7. “Utility discount rate” has other names, such as the pure rate of time preference. “Consumption discount rate” also has other names, including the social rate of time preference and the social discount rate.

  • 8. For example, DICE uses five state variables for the climate system: carbon concentration in the atmosphere, carbon concentration in the upper ocean, carbon concentration in the deep ocean, atmospheric temperature, and oceanic temperature. See Matthews, Gillett, Stott, and Zickfeld (2009), MacDougall and Friedlingstein (2015), and Knutti, Rugenstein, and Hegerl (2017) for further details.

  • 9. See Heal and Park (2016) for a review of the climate impact on output levels and growth rates.

  • 10. See e.g., New and Hulme (2000), Nordhaus (2008), Ackerman, Stanton, and Bueno (2010), and Anthoff and Tol (2013).

  • 11. In dynamic programming models, the frequency of policy updates in the real world should also be taken into account with the choice of the time step size. For example, climate policies might not update annually, while consumption decisions could be more frequent, so an IAM with annual time steps may be more suitable than those with decadal time steps or continuous time. See Cai, Judd, and Lontzek (2012) for an example in which a solution with decadal time steps is significantly different from one with annual time steps.

  • 12. Asset pricing theory has also been applied to estimate the SCC in the face of risks. For example, Bansal, Ochoa, and Kiku (2018) and Daniel, Litterman, and Wagner (2018) explore the implications of risk preferences for the SCC and optimal abatement policies. Bansal, Kiku, and Ochoa (2019) show that the long-run temperature elasticity of equity valuations is significantly negative and that long-run temperature fluctuations carry a positive risk premium in equity markets.

  • 13. See e.g., Lenton et al. (2008), Kriegler et al. (2009), Scheffer et al. (2009), Ditlevsen and Johnsen (2010), and Ghil and Lucarini (2019) for discussions about the physics and early warning of climate tipping points.

  • 14. Footnote 5 of Lemoine and Traeger (2014) states: “In our climate application, the decision maker keeps track of the greatest historic temperature.” However, given their model equations and code, that statement is wrong. The decision maker keeps track of the last-period temperature.

  • 15. Nordhaus (1994) and Nordhaus and Boyer (2000) suggest that a collapse of the thermohaline circulation might result in a 25–30% reduction in GDP.

  • 16. See Judd (1998) and Cai (2019) for details about computational methods and error checking.

  • 17. There are also many reduced form IAMs (e.g., Brock & Xepapadeas, 2019; Golosov, Hassler, Krusell, & Tsyvinski, 2014; Jaakkola & van der Ploeg, 2019), but they are mainly used for theoretical or qualitative analysis. This review focuses on quantitative analysis for climate policies.

  • 18. With advances in computational methods and hardware, IAMs are moving forward by including more and more sectors as well as more complicated climate systems. For example, Favero, Daigneault, and Sohngen (2020) apply the dynamic global timber model (Sohngen & Mendelsohn, 2003) with more than 200 managed and natural forest ecosystems across 16 world regions to assess the role of Bioenergy with Carbon Capture and Storage in climate mitigation and also on economic outcomes, such as timber prices. Cai et al. (2019) study cooperative and noncooperative climate policy with their dynamic stochastic IAM, DIRESCU, which incorporates a more complicated climate system with heat and moisture transfer between low latitude and high latitude regions.

  • 19. In addition, agent-based models have been employed in IAMs; see Farmer, Hepburn, Mealy, and Teytelboym (2015) for a review.

  • 20. See Brock and Hansen (2018) for a review on research challenges in climate economics that focuses on three types of uncertainty: risk, ambiguity, and misspecification.