Quantifying uncertainty about global and regional economic impacts of climate change
QQuantifying uncertainty about global and regionaleconomic impacts of climate change
Jenny Bjordal , Trude Storelvmo and Anthony A. Smith, Jr. Nord University, Bodø, Norway Department of Economics, Yale University, New Haven, USA * e-mail: [email protected] Abstract
The economic impacts of climate change are highly uncertain. Two of themost important uncertainties are the sensitivity of the climate system and theso-called damage functions, which relate climate change to economic damagesand benefits. Despite broad awareness of these uncertainties, it is unclear whichof them is most important, both on the global as well as the regional level. Herewe apply different damage functions to data from climate models with vastlydifferent climate sensitivities, and find that uncertainty in both climate sensitiv-ity and economic damage per degree of warming are of similar importance forthe global economic impact. Increasing the climate sensitivity or the sensitivityof the damage function both increases the economic damages globally. Yet, atthe country-level the effect varies depending on the initial temperature as wellas how much the country warms. Our findings emphasise the importance ofincluding these uncertainties in estimates of future economic impacts, as theyboth are vital for the resulting impacts and thus policy implications.
Future projections of the economic impacts of climate change are highly uncertain. Onthe climate side, the most important uncertainty is how sensitive the climate system isto increasing amounts of greenhouse gases. On the economic side, the most importantuncertainty is the relationship between climate change and economic impacts, oftenexpressed in models by so-called damage functions. But which of these uncertainties ismost important when assessing the economics impacts of future climate change?A standard measure of how sensitive the climate is to greenhouse gas emissions is the1 a r X i v : . [ phy s i c s . a o - ph ] F e b quilibrium climate sensitivity (ECS) (IPCC, 2013). This is how much the global meansurface air temperature will eventually increase when the amount of atmospheric CO is doubled. For decades the estimated range for ECS has been 1.5-4.5 ◦ C (IPCC, 2013;Charney et al., 1979). However, among the newest generation of climate models, thereare several models with ECS above 5 ◦ C (e.g. Zelinka et al., 2020). Since economic im-pacts of climate change are currently mostly calculated from temperature (van Vuurenet al., 2012), it is important to understand the implications of this uncertainty.In economics, integrated assessment models (IAMs) for climate and economy are es-sential tools for simulating the economic impacts of climate change (see e.g. Nordhaus,1992; Ackerman et al., 2009; Weyant, 2017). These models link climate and the econ-omy by expressing changes in economic productivity (also called economic damages orbenefits) as a function of the climate state, often represented by surface air tempera-ture. So far, most damage functions have been applied to the global mean temperature(Nordhaus, 2018; Weitzman, 2012) or to the temperature of large regions (Nordhausand Yang, 1996; Hope, 2011; Anthoff and Tol, 2014), and therefore cannot tell us howindividual countries or smaller regions will be impacted. The damage function is alsoan aspect of IAMs that has been criticised for being particularly uncertain (see e.g.Ackerman et al., 2009; Weitzman, 2010; Howard and Sterner, 2017; Diaz and Moore,2017), yet it is a crucial part of assessing the impacts of climate change.Hassler et al. (2018) have previously found, using an IAM, that the importance ofuncertainty in climate sensitivity and sensitivity in damage functions are of similarmagnitude globally. Here, we aim to compare these two uncertainties using a differentmethod, which also allows us to investigating their importance at the regional andcountry level.We investigate the global and regional economic impacts of climate change by con-structing regional damage functions that aggregate up to the global damages fromalready existing global damage functions. Our approach builds on the method usedby Zheng et al. (2020), by applying a damage function to climate model data, butour focus is on future projections dominated by greenhouse gas emissions, rather thanaerosols. Additionally, we span the range of ECS and damage function uncertaintiesby using a low and a high climate sensitivity model, as well as a relatively insensitiveand a relatively sensitive damage function.
We used data from a high-sensitivity model, the Community Earth System Model ver-sion 2 (CESM2, ECS=5.3 ◦ C)(Danabasoglu et al., 2020), and a low sensitivity model,2he Norwegian Earth System Model (NorESM2, ECS=2.5 ◦ C)(Seland et al., 2020).Both participate in the 6th phase of the Coupled Model Intercomparison Project(CMIP6) (Eyring et al., 2015), and together the two models span most of the ECSinterval of 1.8–5.6 K found in CMIP6 (Zelinka et al., 2020).Specifically, the climate model data used were the surface air temperatures from thefour future emission scenarios used in CMIP6 (Riahi et al., 2017; O ' Neill et al., 2016),called shared socioeconomic pathways (SSPs). Since the scenarios go from 2015 to2100, we also used the last years from runs with historical emission, because our baseyear here is year 2000. The scenarios are named using two numbers, where the firstrefers to the narrative (evolution of society and natural systems) (O’Neill et al., 2014),and the second refer to the radiative forcing at the end of the century (Moss et al.,2010). Generally, lower (higher) numbers refer to lower (higher) emissions, and thusa lower (higher) temperature increase. A short summary of the scenarios are given intable 1.Scenario Narrative 2100 Forcing Pathway ofname (W/m ) forcingSSP1-2.6 Sustainability 2.6 Peak and decline(Low challenges tomitigation and adaptation)SSP2-4.5 Middle of the Road 4.5 Stabilising(Medium challenges tomitigation and adaptation)SSP3-7.0 Regional Rivalry 7.0 Rising(High challenges tomitigation and adaptation)SSP5-8.5 Fossil-fueled Development 8.5 Rising(High challenges to mitigation,low challenges to adaptation) Table 1:
Summary of the four future scenarios employed in this study. The nar-rative is what kind of world the scenario reflects, with indication of the mitigationand adaption challenges. The 2100 forcing gives the radiative imbalance at the endof the century under the scenario, and the pathway explains how the forcing evolvesthroughout the century. .2 Damage functions and economic impacts Integrated assessment models typically incorporate global (or aggregate) economicdamages from global warming as a reduction in global total factor productivity (TFP),a measure of the productivity of a set of factors of production (such as physical capitaland labour) taken as a whole. These damages can therefore be expressed as a fractionof global GDP, holding fixed productive inputs such as capital and labour, that varieswith ∆ T t , the change in the global surface air temperature in year t from the pre-industrial temperature.That fraction, π (∆ T t ), is typically represented by an increasing convex function withthe following functional form (see e.g. Dietz and Stern, 2015): π (∆ T t ) = φ (∆ T t ) φ (∆ T t ) , (1)where φ is a coefficient chosen to match estimates of aggregate damages from globalwarming. A change in the global temperature from T t to T would therefore leadto a percentage change in global TFP (and hence global GDP, holding inputs fixed)given by D ( T t ) = (cid:18) φ ( T t − T ) φ ( T − T ) − (cid:19) , (2)where T , T and T t is the global mean surface air temperature in years 2000,1850 (pre-industrial), and year t , respectively.The damage function developed by Nordhaus (Nordhaus, 1992, 2018) is one of themost commonly used damage functions and sets φ = 0 . ◦ C )(see blue line in figure 1). Like many other damage functions, the Nordhaus damagefunction is only based on estimates of damages up to 3 ◦ C (Tol, 2011; Stern, 2013),and is strictly speaking not valid for temperature increases beyond that. However, itis often extrapolated to higher temperature changes, and it is also criticised for beingtoo optimistic, in that it may underestimate damages at large temperature increases(Stern, 2013; Revesz et al., 2014). We therefore use this as our low sensitivity damagefunction.Another, more sensitive damage function, is the one estimated by Howard and Sterner(2017), which sets φ = 0 . ◦ C warming, the difference in productivity betweenthe two functions is less than 1%, but as we approach 6 ◦ C warming the difference ismore than 17%, ranging from -9.3% with the Nordhaus function to -26.5% with theHoward & Sterner function. 4 p r o d u c t i v i t y ( % ) NordhausHoward & Sterner
Figure 1:
Global productivity change. The percentage change in productivity againsttemperature changes from pre-industrial for the Nordhaus (blue) and the Howard &Sterner (orange) damage function.
In order to study how global warming affects regional economies, we constructed func-tions that capture how regional productivity varies with regional, rather than theglobal, surface air temperature. These functions are chosen so that the sum of re-gional variations across the globe matches estimates of global damages stemming fromglobal warming. The full details on the calculations of the regional damage functionis given in the appendix.To operationalize the regional productivity function H , we used an inverse U -shaped5unction that depends on four parameters: H ( T it ) = (cid:40) (1 − b ) e − κ + ( T it − T ∗ ) + b if T it ≥ T ∗ (1 − b ) e − κ − ( T it − T ∗ ) + b if T it < T ∗ , (3)where T it is the temperature in region i at time t , T ∗ is the optimal temperature(given in ◦ C) at which H attains its maximum of 1, and κ + and κ − determine thesteepness of the decline on either side of the optimal temperature. The lower bound b is set to 0.02. The remaining three parameters of the function H are chosen so thatthe aggregate damages from global warming implied by it match those delivered bythe aggregate damage function D in equation 2 at three different global temperaturechanges ranging from 1 to 5 ◦ C, noting that the temperature in any particular regiondepends on the global temperature via a statistical downscaling model derived fromruns of CESM2 and NorESM2 (see the appendix for details). We used the downhillsimplex equation to solve these three nonlinear equations in the three unknowns T ∗ , κ + , and κ − . The resulting functions are shown in figure 2 (and the parameters canbe found in supplementary table 1). Note that the three parameters are unique foreach climate model–damage function combination. And the resulting regional damagescompared to the global damages are shown in supplementary figures 7 and 8. As seenin the figures, the regional damage functions are not prefect fits for the global damagefunctions. But considering the large uncertainties for these functions, the resultingregional damage functions seem reasonable enough for our purpose. After constructing the regional damage functions, we applied them to the climatemodel data. First, we calculated the annual spatial temperatures and re-gridded itto fit our 1 ◦ × ◦ population and GDP data grid. Then we calculated the fraction ofoptimum productivity for each year with the regional damage function.The 2000 temperature was calculated from a historical run, using the years 1996-2004.We used this to calculate the relative change in optimum productivity from 2000.Which was finally used to calculate the relative change in productivity. Our results show that global warming decreases the global economic productivity, butthe size of these economic damages is highly dependent on the sensitivity of both theclimate and the damage function (see fig. 3). Both changing to a more sensitive cli-mate model and a more sensitive damage function increases the damages. Also, the6
Temperature (°C) F r a c t i o n o f o p t i m u m p r o d u c t i v i t y NorESM2 NordhausT*=13.04CESM2 NordhausT*=14.29NorESM2 Howard & SternerT*=13.16CESM2 Howard & SternerT*=11.60
Figure 2:
Regional damage functions for the four climate model–damage functioncombinations. Showing the fraction of optimum productivity against temperature,where fraction is one at the optimum temperature T ∗ . differences between models and damage functions grow as we reach higher tempera-tures, as seen from both the increasing distance between the lines with time in eachSSP scenario, and the larger distance between lines in the higher emissions scenarios.While the range in productivity due to the two damage functions shown here is slightlylarger than that of the two climate models, the results indicate that the span of dam-ages due to uncertainty in climate sensitivity and uncertainty associated with damagefunctions are of a similar magnitude globally, supporting previous work (Hassler et al.,7018). p r o d u c t i v i t y ( % ) SSP1-2.6NorESM2 Nordhaus (low - low)CESM2 Nordhaus (high - low)NorESM2 Howard & Sterner (low - high)CESM2 Howard & Sterner (high - high)
SSP2-4.5
Year p r o d u c t i v i t y ( % ) SSP3-7.0
Year
SSP5-8.5
SSP1-2.6 SSP2-4.5 SSP3-7.0 SSP5-8.520151050 p r o d u c t i v i t y ( % ) Years 2091-2100NorESM2 NordhausCESM2 NordhausNorESM2 Howard & SternerCESM2 Howard & Sterner(a) (b)(c) (d)(e)
Figure 3:
Percentage change in global productivity from year 2000 for the four SSPs.The line is the 5-year moving average, while the dots show each individual year’sglobal productivity change from year 2000 for the four climate model–damage functioncombinations for SSP1-2.6 (a), SSP2-4.5 (b), SSP3-7.0 (c) and SSP5-8.5 (d). e, Thechange between the end of the century (years 2091-2100) and 2000 (1996-2004). .2 Regional economic impacts However, the global estimates of economic impacts of climate change hide a lot ofheterogeneity at the regional level. Regionally, our calculations predict decreasingproductivity for most of the globe, except in the northern high latitudes and theTibetan Plateau (fig. 4). Figure 4 a,b,d,e shows how the fraction of the optimumproductivity has changed from year 2000 to the end of the century in the SSP5-8.5 scenario for the four climate model–damage function combinations. The otherscenarios have the same main patterns but of smaller magnitude (see supplementaryfigures 1-3). While the area with increased productivity (green) might seem vast, muchof the area has a small population and economy, and thus does not contribute muchto the global productivity.
NorESM Nordhaus CESM Nordhaus NorESM - CESM Nordhaus
NorESM Howard & Sterner CESM Howard & Sterner NorESM - CESM Howard & Sterner ° ° ° W ° ° E ° ° NorESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° CESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° NorESM - CESM Nordhaus - Howard & Sterner p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) (a) (b) (c)(d) (e) (f)(g) (h) (i) Figure 4:
Spatial distribution of change in optimum productivity for SSP5-8.5.a,b,d,e Percentage change in optimum productivity at the end of the century (2091-2100) from year 2000 (1996-2004) for the four climate model–damage function com-binations for SSP5-8.5. c,f,g,h,i The differences in productivity change between thecombinations.
Also, changing between climate models and/or damage functions has different effectsin different areas. If we start with the low–low combination (low climate sensitivity -low sensitivity damage function), going to a high sensitivity in either climate model(high–low, fig. 4 c) or damage function (low–high, fig. 4 g) increases the productivityin cold areas, and decreases the productivity in warm areas. But if we start witheither the high sensitivity climate model (high–low) or damage function (low–high),9nd move to the high–high combination (fig. 4 f and h, respectively) the productivitydecreases almost everywhere.This can be understood from the different temperature increases between models, andthe different optimum temperatures and slopes of the regional damage functions (seefigure 2 and supplementary table 1 for details). When going from the low–low to thelow–high combination we have the same warming and approximately the same opti-mum temperature. The larger increase in productivity in the cold regions and decreasein the warm regions is thus due to the steeper slopes of the damage function, makingthe regions move faster toward or away from the optimum temperature. If we insteadmove from the low–low to the high–low combination we still have a similar optimumtemperature and steeper slopes. Additionally, this effect is strengthened by the highertemperature increase. In the other case, starting from the low–high or the high–lowcombination and going to the high–high combination, we have a different situation.Now the slopes are not changing much, but the optimum temperature is lower for thehigh–high combination. This means that fewer regions have the potential to increasetheir productivity, and more regions will cross over the optimum temperature andstart decreasing their productivity. Additionally, the baseline temperature differencebetween the models plays a part when changing model.
On the country level, as indicated by figure 4, it is the countries with a cool climate thatbenefit, while the warm countries suffer damages. Figure 5 shows how the temperatureand productivity change from 2000 to the end of the century for each country in eachclimate model–damage function combination for SSP5-8.5 (for the other SSPs seesupplementary figures 4-6). Like the global average, the country-level average takesinto account each country’s economic activity, measured in gross domestic product(GDP) (indicated by size of circle), and population in year 2000. The colour of thecircles show the population-weighted temperature in year 2000. Again, the same threefactors that explain figure 4 are important for each country’s change in productivity,as well as the countries’ distribution of population and economic activity. We see thatmost countries will experience economic impacts that are very different from the globalaverage (black dot).Some examples of how countries may be impacted in each scenario and climate model–damage function combination are shown in fig. 6. The United States, the biggestcountry-level economy, nicely follows what we saw for the global productivity (fig. 3 e),while other countries show very different responses. Russia is one of the countries thatbenefit from climate change independent of scenario and combination, while India andSudan clearly see economic damages under all circumstances. However, these countriesdo not follow the same increase in effect with increasing sensitivity as seen globally10 p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndia Sudan
NorESM2 and Nordhaus
United StatesRussiaGermany India Sudan
CESM2 and Nordhaus temperature (°C) p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndia Sudan
NorESM2 and Howard & Sterner temperature (°C)
United StatesRussiaGermany India Sudan
CESM2 and Howard & Sterner
GDP ($)10 t e m p e r a t u r e ( ° C ) (a) (b)(c) (d) Figure 5:
Country-level temperature and productivity change. Showing the four cli-mate model–damage function combinations’ productivity change at end of the cen-tury (2091-2100) from year 2000 (1996-2004) against population-weighted temperaturechange for SSP5-8.5. Each country’s dot is coloured based on the year 2000 population-weighted temperature, and the size indicates the GDP in year 2000. The black dot isthe global average (and does not indicate temperature or GDP). and for the United States. On the regional level it is not clear that increasing theclimate sensitivity and/or sensitivity of the damage function increases the economicimpacts.Another interesting group of countries is the one with relatively small impacts that lieclose to the zero line in figure 5. Germany (fig. 6 c) is a nice example of these, andwe see that whether the country will see benefits or damages due to climate changedepends on both the scenario and the climate model–damage function combination.This is because Germany has a temperature lower than, yet close to, the optimaltemperature (10.0 ◦ C in NorESM2, 10.4 ◦ C in CESM2) in year 2000. As the climatewarms, as decided by both the scenario and the climate model, Germany might crossthe optimum temperature. When crossing the optimum temperature, the productivity11 p r o d u c t i v i t y ( % ) United States p r o d u c t i v i t y ( % ) Russia p r o d u c t i v i t y ( % ) Germany p r o d u c t i v i t y ( % ) India
SSP1-2.6 SSP2-4.5 SSP3-7.0 SSP5-8.56040200 p r o d u c t i v i t y ( % ) Sudan
NorESM2 NordhausCESM2 Nordhaus NorESM2 Howard & SternerCESM2 Howard & Sterner (a)(b)(c)(d)(e)
Figure 6:
Country-level productivity change. Showing the percentage change in pro-ductivity at the end of the century (2091-2100) from year 2000 (1996-2004) for thefour climate model–damage function combinations and the four future SSP scenariosfor five selected countries.
Our results show how the large uncertainties in climate sensitivity and damage func-tions result in large uncertainties in economic impacts. This points out how importantit is to include uncertainty estimates when calculating economic impacts of climatechange. Particularly, this is important when using estimates of economic impacts forpolicy purposes, like for example the US government does (Auffhammer, 2018). Thestudy also points out how different the economic impacts of climate change can bebetween regions. Especially, we see how the regional uncertainty in economic impactscan be very different from the global.In a full economic model, the economic impacts will feed back on the emissions. Witheconomic damages, consumption will decrease, and consequently the emissions (andthus the warming) will be lower (and visa versa for economic benefits). In our work,future emissions are already set by the SSP scenarios, and this climate-economy feed-back is therefore not included. However, the study still gives important insights intothe relative importance of the climate sensitivity and sensitivity of the damage func-tion. Both of these are important for the size of the climate-economy feedback, andthis could be a step towards assessing the feedback’s uncertainty.Our calculations are based on the assumption that the population growth is constant intime and space, and the actual future population growth and migration could thereforeresult in a different future global productivity. If, for example, people living in lessproductive areas move northward into more productive areas, the global productivitywould decrease less with warming. Such migration to more productive areas are indeedexpected, and even simulated in some models (Conte et al., 2020).An important remaining question is how good of a proxy temperature is for climatechange. In the damage functions employed here, it is assumed that the global temper-ature represents global climate change well. This is probably a reasonable assumption,but it might not hold as well when we construct regional damage functions that lookat regional temperature. Changes in other climate variables, like rainfall, sea levelrise or extreme events, do not necessarily have the same distribution patterns as tem-perature change (IPCC, 2013). Sea-level rise, for example, should only affect regionswith a coast line, but when temperature is the only input to the damage function, theinherent damages from sea-level rise in the global damage function will be distributeddepending on temperature in the regional function. Thus the impacts of climate change13hat do not follow the temperature distribution could be wrongly distributed.In our study, we have used damage functions that calculate the impact of climatechange on the economic output rather than on the economic growth rate. Yet, thisis an area of some debate (see e.g. Moore and Diaz, 2015; Burke et al., 2015). Sinceeven a small change in the growth rate could lead to large economic impacts in thelong run, such damage functions could be even more sensitive than the high sensitivitydamage function employed here.
We have found that the uncertainties in climate sensitivity and damage functions areof similar magnitude globally, but differ a lot regionally. What is clear from thisstudy is that progress toward reliable assessments of economic damages due to climatechange will require both more constrained estimates of the climate sensitivity andimproved damage functions. Especially, this is important when economic models areused for policy purposes (see e.g. Burke et al., 2016; Hassler et al., 2018). We see thatthe global productivity tells us little about what will happen regionally or in a givencountry. The regional productivity could also be more impacted by changes that arenot as well represented by the annual mean surface air temperature, such as rainfallor extreme events. A focus on constructing regional damage functions will thereforebe important. 14 cknowledgements
This work was supported by the Norwegian Research Council through grant 281071.We acknowledge the World Climate Research Programme, which, through its Work-ing Group on Coupled Modelling, coordinated and promoted CMIP6. We thank theclimate modelling groups for producing and making available their model output, theEarth System Grid Federation (ESGF) for archiving the data and providing access,and the multiple funding agencies who support CMIP6 and ESGF.
Competing Interests statement
The authors declare no competing interests.
Data availability
All NorESM2 and CESM2 simulation output is available through the Earth SystemGrid Federation’s (ESGF) CMIP6 search interface ( https://esgf-node.llnl.gov/search/cmip6/ ) under ‘source ID’
NorESM2-LM and
CESM2 , respectively, and ‘ex-periment ID’ historical , ssp126 , ssp245 , ssp370 and ssp585 .Population and GDP data from the Geographically based Economic data (G-Econ)site, version 2.11 (Nordhaus et al., 2006), is no longer available on the web site, but isavailable from the authors on request. References
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Nature Climate Change (3), 220–224.doi:10.1038/s41558-020-0699-y. 19 upplementary MaterialAppendix To look at regional differences in productivity stemming from global warming, weneeded a regional function mapping regional surface air temperatures into regionalproductivity. Following Krusell and Smith, Jr. (2020), we constructed such a functionso that regional variations in productivity, when summed across all regions, match theglobal changes in productivity delivered by the aggregate damage function (equation2).To do this, we used a simple economic model of regional GDP: Y it = K αit L − αit , (4)where, in region (or grid-cell) i in year t , Y it is GDP, K it is the physical capital stock,and L it is the effective supply of labour, measured in so-called “efficiency units” whichcapture how productive workers are. The coefficients α and 1 − α are the shares ofincome (GDP) going to capital and labour, respectively. We assume further that theeffective supply of labour evolves according to: L it = A it H ( T it ) N it , (5)where, in region i in year t , N it is the population and A it H ( T it ) is the number of effi-ciency units per person. Population is assumed to grow at rate n . The first componentof the number of efficiency units, A it , does not depend on regional temperature and isassumed to grow at rate g . The second component of the number of efficiency units, H ( T it ), does depend on regional temperature: it captures on how changes in regionaltemperature, T it , affect the regional productivity of labour. The function H govern-ing this component of regional productivity has an inverse U -shape and is boundedbetween 0 and 1.Finally, we assume that at any point in time capital is freely mobile across regionsso that the marginal product of capital (i.e., the extra amount of GDP generated byan incremental amount of additional capital) is equated across regions. Consequently,regional capital-to-labour ratios, K it /L it , are also equalised, implying in turn thatglobal GDP in year t , Y t ≡ (cid:80) Mi =1 Y it , where M is the number of regions, has a simpleexpression: Y t = K αt (cid:32) M (cid:88) i =1 L it (cid:33) − α , (6)1here K t ≡ (cid:80) Mi =1 K it is the global capital stock. Substituting equation (5) intoequation (6) yields an expression for global GDP in year t depends explicitly on theset of regional temperatures: Y t = K αt (cid:32) M (cid:88) i =1 ((1 + g )(1 + n )) t − A i, N i, H ( T it ) (cid:33) − α . (7)To derive an analogous expression for global GDP that depends only on the globaltemperature, we used a statistical downscaling model that relates regional temperatureto global temperature: T it = T i, + γ i ( T t − T ) . (8)To obtain the region-specific responsiveness coefficients γ i , we proceeded in three steps.First, we calculated the global temperature change from pre-industrial to year 2000,which is our reference year. Second, we calculated the temperatures in year 2000 foreach grid cell ( T i, ). Here we used surface air temperature from three historical runsby the climate model, and calculated the average of these three runs using the nineyears around 2000 (1996-2004). Finally, we calculated how each grid cell’s tempera-ture changes relative to the global temperature, the responsiveness coefficients ( γ i ).These we calculated by using five different model runs: historical, SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5. For each run, the difference between the first and thelast five years was calculated, and each grid cell’s change was divided by the globaltemperature change. The average of these five coefficients was then used as the fi-nal set of responsiveness coefficients for each of the two models (e.i. NorESM2 andCESM2).Armed with the statistical downscaling model in equation (8), equation (7) can nowbe rewritten: Y t = S t G ( T t ) K αt (9)where S t ≡ [(1 + g )(1 + n )) t − ] − α , G ( T t ) ≡ (cid:16)(cid:80) Mi =1 a i N i, H ( T i, + γ i ( T t − T )) H ( T i, ) (cid:17) − α ,and a i, ≡ A i, H ( T i, ) is efficiency units per person in region i in 2000. Givena regional productivity function H (in our case equation 3), a change in the globaltemperature from T t to T would lead to a percentage change in global GDP (againholding inputs fixed) equal to: d ( T t ) ≡ (cid:18) G ( T ) G ( T t ) − (cid:19) . (10) Krusell and Smith, Jr. (2020) show that even when capital markets are closed completely optimalaccumulation of capital in each region leads the marginal product of capital to be approximatelyequalised across regions. Thus the assumption of free capital mobility underlying the formulas in thispaper appears to be an innocuous one. H (equation 3) so that the two “damage functions”, D ( T t )and d ( T t ), the first taken from existing estimates of global damages from climatechange and the second derived from the simple economic model of regional damagesfrom climate change outlined here, agree for different values of the global temperature T t .Regional population and GDP data for the year 2000 are taken from the G-Econdatabase, version 2.11 (Nordhaus et al., 2006). The a i, are chosen by solving thefollowing two equations for K i, and a i, in each region: K αi, ( a i, N i, ) − α = Y i, αK α − i, ( a i, N i, ) − α = r. The first of these equations ensures that regional GDP in year 2000 equals its valuein the data and the second of these equations imposes that the marginal product ofcapital in each region is equated to a common rate of return r (net of depreciation),here set to 2.53%. Capital’s share of income, α , is set to 0.36.Damage function Model T ∗ κ − κ + Nordhaus NorESM2 13.0 0.00267 0.00127Nordhaus CESM2 14.3 0.00522 0.00367Howard & Sterner NorESM2 13.2 0.00476 0.00453Howard & Sterner CESM2 11.6 0.00420 0.00434
Supplementary Table 1:
The parameter values found for the four climate model–damage function combinations. NorESM Nordhaus CESM Nordhaus NorESM - CESM Nordhaus
NorESM Howard & Sterner CESM Howard & Sterner NorESM - CESM Howard & Sterner ° ° ° W ° ° E ° ° NorESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° CESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° NorESM - CESM Nordhaus - Howard & Sterner p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) (a) (b) (c)(d) (e) (f)(g) (h) (i) Supplementary Figure 1:
Country-level temperature and productivity change forSSP1-2.6. Showing the four climate model–damage function combinations’ produc-tivity change at end of the century (2091-2100) from year 2000 (1996-2004) againstpopulation-weighted temperature change for SSP1-2.6. Each country’s dot is colouredbased on the year 2000 population-weighted temperature, and the size indicates the GDPin year 2000. The black dot is the global average (and does not indicate temperatureor GDP). NorESM Nordhaus CESM Nordhaus NorESM - CESM Nordhaus
NorESM Howard & Sterner CESM Howard & Sterner NorESM - CESM Howard & Sterner ° ° ° W ° ° E ° ° NorESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° CESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° NorESM - CESM Nordhaus - Howard & Sterner p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) (a) (b) (c)(d) (e) (f)(g) (h) (i) Supplementary Figure 2:
Country-level temperature and productivity change forSSP2-4.5. Same as figure 1, but for SSP2-4.5.
NorESM Nordhaus CESM Nordhaus NorESM - CESM Nordhaus
NorESM Howard & Sterner CESM Howard & Sterner NorESM - CESM Howard & Sterner ° ° ° W ° ° E ° ° NorESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° CESM Nordhaus - Howard & Sterner ° ° ° W ° ° E ° ° NorESM - CESM Nordhaus - Howard & Sterner p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) D i ff e r e n c e i n p r o d u c t i v i t y ( f r a c t i o n ) (a) (b) (c)(d) (e) (f)(g) (h) (i) Supplementary Figure 3:
Country-level temperature and productivity change forSSP3-7.0. Same as figure 1, but for SSP3-7.0. p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndiaSudan
NorESM2 and Nordhaus
United StatesRussiaGermanyIndiaSudan
CESM2 and Nordhaus temperature (°C) p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndiaSudan
NorESM2 and Howard & Sterner temperature (°C)
United StatesRussiaGermanyIndiaSudan
CESM2 and Howard & Sterner
GDP ($)10 t e m p e r a t u r e ( ° C ) (a) (b)(c) (d) Supplementary Figure 4:
Country-level temperature and productivity change forSSP1-2.6. Showing the four climate model–damage function combinations’ produc-tivity change at end of the century (2091-2100) from year 2000 (1996-2004) againstpopulation-weighted temperature change for SSP1-2.6. Each country’s dot is colouredbased on the year 2000 population-weighted temperature, and the size indicates the GDPin year 2000. The black dot is the global average (and does not indicate temperatureor GDP). p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndia Sudan
NorESM2 and Nordhaus
United StatesRussiaGermany India Sudan
CESM2 and Nordhaus temperature (°C) p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndia Sudan
NorESM2 and Howard & Sterner temperature (°C)
United StatesRussiaGermany India Sudan
CESM2 and Howard & Sterner
GDP ($)10 t e m p e r a t u r e ( ° C ) (a) (b)(c) (d) Supplementary Figure 5:
Country-level temperature and productivity change forSSP2-4.5. Same as figure 4, but for SSP2-4.5. p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndia Sudan
NorESM2 and Nordhaus
United StatesRussiaGermanyIndia Sudan
CESM2 and Nordhaus temperature (°C) p r o d u c t i v i t y ( % ) United StatesRussiaGermanyIndia Sudan
NorESM2 and Howard & Sterner temperature (°C)
United StatesRussiaGermanyIndia Sudan
CESM2 and Howard & Sterner
GDP ($)10 t e m p e r a t u r e ( ° C ) (a) (b)(c) (d) Supplementary Figure 6:
Country-level temperature and productivity change forSSP3-7.0. Same as figure 4, but for SSP3-7.0. D a m a g e s ( % ) NorESM2Nordhaus
GlobalRegionalHistoricalSSP1-2.6SSP2-4.5SSP3-7.0SSP5-8.5 15 16 17 18 19 20024681012
CESM2Nordhaus D a m a g e s ( % ) NorESM2Howard & Sterner
15 16 17 18 19 20Global temperature (°C)010203040
CESM2Howard & Sterner(a) (b)(c) (d)
Supplementary Figure 7:
Global and regional damages plotted against temperature.Each year from historical run and the SSP scenarios are plotted for both the global (line)and the regional (dots), for the four climate model damage function combinations.
000 2020 2040 2060 2080 210001234 D a m a g e s ( % ) NorESM2Nordhaus
GlobalRegionalHistoricalSSP1-2.6SSP2-4.5SSP3-7.0SSP5-8.5 2000 2020 2040 2060 2080 2100024681012
CESM2Nordhaus D a m a g e s ( % ) NorESM2Howard & Sterner
CESM2Howard & Sterner(a) (b)(c) (d)
Supplementary Figure 8: