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Global warming has increased global economic inequality

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Abstract

Understanding the causes of economic inequality is critical for achieving equitable economic development. To investigate whether global warming has affected the recent evolution of inequality, we combine counterfactual historical temperature trajectories from a suite of global climate models with extensively replicated empirical evidence of the relationship between historical temperature fluctuations and economic growth. Together, these allow us to generate probabilistic country-level estimates of the influence of anthropogenic climate forcing on historical economic output. We find very high likelihood that anthropogenic climate forcing has increased economic inequality between countries. For example, per capita gross domestic product (GDP) has been reduced 17–31% at the poorest four deciles of the population-weighted country-level per capita GDP distribution, yielding a ratio between the top and bottom deciles that is 25% larger than in a world without global warming. As a result, although between-country inequality has decreased over the past half century, there is ∼90% likelihood that global warming has slowed that decrease. The primary driver is the parabolic relationship between temperature and economic growth, with warming increasing growth in cool countries and decreasing growth in warm countries. Although there is uncertainty in whether historical warming has benefited some temperate, rich countries, for most poor countries there is >90% likelihood that per capita GDP is lower today than if global warming had not occurred. Thus, our results show that, in addition to not sharing equally in the direct benefits of fossil fuel use, many poor countries have been significantly harmed by the warming arising from wealthy countries’ energy consumption.
Global warming has increased global
economic inequality
Noah S. Diffenbaugh
a,b,1
and Marshall Burke
a,c,d
a
Department of Earth System Science, Stanford University, Stanford, CA 94305;
b
Woods Institute for the Environment, Stanford University, Stanford, CA 94305;
c
Center on Food Security and the Environment, Stanford University, Stanford, CA 94305; and
d
Environment and EnergyEconomics, NationalBureau of Economic
Research, Cambridge, MA 02138
Edited by Ottmar Edenhofer, Potsdam Institute for Climate Impact Research, Potsdam, Germany, and accepted by Editorial Board Member Hans J.
Schellnhuber March 22, 2019 (received for review September 16, 2018)
Understanding the causes of economic inequality is critical for
achieving equitable economic development. To investigate whether
global warming has affected the recent evolution of inequality, we
combine counterfactual historical temperature trajectories from a suite
of global climate models with extensively replicated empirical evi-
dence of the relationship between historical temperature fluctuations
and economic growth. Together, these allow us to generate proba-
bilistic country-level estimates of the influence of anthropogenic
climate forcing on historical economic output. We find very high
likelihood that anthropogenic climate forcing has increased economic
inequality between countries. For example, per capita gross domestic
product (GDP) has been reduced 1731% at the poorest four deciles of
the population-weighted country-level per capita GDP distribution,
yielding a ratio between the top and bottom deciles that is 25% larger
than in a world without global warming. As a result, although
between-country inequality has decreased over the past half century,
there is 90% likelihood that global warming has slowed that de-
crease. The primary driver is the parabolic relationship between tem-
perature and economic growth, with warming increasing growth in
cool countries and decreasing growth in warm countries. Although
there is uncertainty in whether historical warming has benefited some
temperate, rich countries, for most poor countries there is >90% likeli-
hood that per capita GDP is lower today than if global warming had
not occurred. Thus, our results show that, in addition to not sharing
equally in the direct benefits of fossil fuel use, many poor countries
have been significantly harmed by the warming arising from wealthy
countriesenergy consumption.
economic inequality
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global warming
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climate change attribution
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CMIP5
Detection of impacts caused by historical global warming has
increased substantially in the past decade, including docu-
mented impacts on agriculture, human health, and ecosystems (1).
Quantifying these historical impacts is critical for understanding
the costs and benefits of global warming, and for designing and
evaluating climate mitigation and adaptation measures (1).
The impact of historical warming on economic inequality is of
particular concern (2). There is growing evidence that poorer
countries or individuals are more negatively affected by a changing
climate, either because they lack the resources for climate protection
(3) or because they tend to reside in warmer regions where additional
warming would be detrimental to both productivity and health (46).
Furthermore, given that wealthy countries have been responsible for
the vast majority of historical greenhouse gas emissions, any clear
evidence of inequality in the impacts of the associated climate change
raises critical questions of international justice.
More broadly, measuring and understanding the past and
present evolution of global economic inequality is an area of
active research and policy interest, with ongoing disagreement
about the nature and causes of observed inequality trends (7
10). Quantifying any climatic influence on these trends thus has
implications beyond climate risk management.
Recent research has identified pathways by which changes in
climate can affect the fundamental building blocks of economic
production (11, 12). Empirical work has included sector-specific
analyses of agriculture, labor productivity, and human health (12),
as well as analyses of aggregate indicators such as gross domestic
product (GDP) (4, 13). A key insight is the nonlinear response of
many outcomes to temperature change, with the coolest regions
often benefitting in warm years, and warmer regions being
harmed. As a result, empirical evidence combined with projections
of future climate change suggests that, although some wealthy
countries in cooler regions could benefit from additional warming,
most poor countries are likely to suffer (4, 14).
Efforts to apply empirical approaches to explicitly quantify the
spatial pattern of aggregate impacts have primarily focused on
future climate change (46, 14), with quantification of historical
impacts being limited to specific economic sectors and outcomes
(e.g., ref. 1), or to global GDP (12). Likewise, although a number of
researchers have noted that the most robust regional warming has
generally occurred in lower-latitude regions that are currently rel-
atively poor (e.g., refs. 1519), these analyses have not attempted to
quantify the distributional impacts of historical temperature change.
Here, we build on past work linking economic growth and
fluctuations in temperature (4, 14) to quantify the impact of
historical anthropogenic climate forcing on the global distribu-
tion of country-level per capita GDP (Materials and Methods and
Fig. 1). We use the Historical and Natural climate model simu-
lations from the Coupled Model Intercomparison Project
(CMIP5) (20) to quantify the temperature trajectory of different
countries in the absence of anthropogenic forcing. We then com-
bine these counterfactual country-level temperature trajectories
Significance
We find that global warming has very likely exacerbated global
economic inequality, including 25% increase in population-
weighted between-country inequality over the past half cen-
tury. This increase results from the impact of warming on
annual economic growth, which over the course of decades
has accumulated robust and substantial declines in economic
output in hotter, poorer countriesand increases in many
cooler, wealthier countriesrelative to a world without an-
thropogenic warming. Thus, the global warming caused by
fossil fuel use has likely exacerbated the economic inequality
associated with historical disparities in energy consumption.
Our results suggest that low-carbon energy sources have the
potential to provide a substantial secondary development
benefit, in addition to the primary benefits of increased
energy access.
Author contributions: N.S.D. and M.B. designed research, performed research, contrib-
uted new reagents/analytic tools, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. O.E. is a guest editor invited by the Editorial Board.
This open access article is distributed under Creative Commons Attribution-NonCommercial-
NoDeriv atives Lic ense 4.0 (CC BY-NC-N D).
1
To whom correspondence should be addressed. Email: diffenbaugh@stanford.edu.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1816020116/-/DCSupplemental.
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with empirically derived nonlinear temperatureGDP response func-
tions to calculate the counterfactual per capita GDP of individual
countries over the past half century. Finally, we use those counter-
factual country-level economic trajectories to calculate the impact of
historical anthropogenic forcing on population-weighted country-
level economic inequality, accounting for both uncertainty in the
relationship between temperature and economic growth and uncer-
tainty in the climate response to historical forcing.
Results
The estimated parabolic relationship between temperature and
economic growth means that long-term warming will generally
increase growth in cool countries and decrease growth in warm
countries (Fig. 1). For example, for cooler countries such as
Norway, warming moves the country-mean temperature closer to
the empirical optimum (Fig. 1B), resulting in cumulative economic
benefits (Fig. 1C). In contrast, for warm countries such as India,
warming moves the country-mean temperature further from the
optimum (Fig. 1B), resulting in cumulative losses (Fig. 1D).
As a result, anthropogenic climate forcing has decreased eco-
nomic growth of countries in the low latitudes and increased eco-
nomic growth of countries in the high latitudes (Fig. 2). The median
losses exceed 25% for the 19612010 period (relative to a world
without anthropogenic forcing) over large swaths of the tropics and
subtropics (Fig. 2A), where most countries exhibit very high likeli-
hood of negative impacts (Fig. 2 Cand D), including >99% likeli-
hood (SI Appendix,TableS1). The median gains can be at least as
large in the high latitudes, where many countries exhibit >90%
likelihood of positive impacts. Many countries in the middle lati-
tudes exhibit median impacts smaller than ±10%, along with greater
uncertainty in the sign of the response (particularly in the northern
hemisphere). Thus, the global-scale pattern is of cool countries
benefitting and warm countries suffering, with temperate countries
exhibiting the greatest uncertainty.
Although this global pattern could be expected from the con-
cave structure of the empirical temperaturegrowth relationship
(Fig. 1B), such an outcome is not determined for historical climate
forcing, because internal climate variability creates uncertainty in
the sign and magnitude of regional temperature change (e.g., refs.
21 and 22). However, because the mean temperature response is
positive across all land areas (Fig. 1A), and because the differences
in temperature change between countries (Fig. 1A)aresmall
compared with the range of country-mean temperatures (Fig. 1B),
the median economic response is that countries that are currently
warmer than the median optimum have experienced losses, while
countries that are currently colder than the median optimum have
experienced benefits (Fig. 3A).
Consistent with the strong spatial correlation between tempera-
tureandGDP(23),wefindapositive relationship between current
GDP and impact from historical warming, with lower per capita
GDP generally associated with more negative impacts (Fig. 3B).
Furthermore, at a given level of wealth, warmer countries have
tended to experience more negative impacts, while cooler countries
have tended to experience less negativeor in some cases more
positiveimpacts. Because the majority of the worldswarmest
countries are poor (Fig. 3 Aand B), the majority of large negative
impacts have been concentrated in poor countries (Fig. 3 Aand
B). Likewise, because the majority of the worlds richest countries
are temperate or cool, the median likelihood is that the majority
of rich countries have benefited.
Consistent with the strong relationship between wealth, energy
consumption, and CO
2
emissions (2426), we also find a positive
relationship between per capita cumulative emissions and impact
from historical global warming (Fig. 3Cand SI Appendix,Fig.S1).
For example, over the 19612010 period, all 18 of the countries
whose historical cumulative emissions are less than 10 ton CO
2
per
capita have suffered negative economic impacts, with a median
impact of 27% (relative to a world without anthropogenic forcing)
(Fig. 3C). Likewise, of the 36 countries whose historical emissions
are between 10 and 100 ton CO
2
per capita, 34 (94%) have suffered
negative economic impacts, with a median impact of 24%. In
contrast, of the 19 countries whose historical emissions exceed 300
ton CO
2
per capita, 14 (74%) have benefited from global warming,
with a median benefit across those 14 countries of +13%.
The net effect of these economic impacts is that country-level
inequality has very likely increased as a result of global warming
(Fig. 4). For example, the ratio between the top and bottom
population-weighted deciles [a common measure of economic
inequality (9)] has become 25% larger (5th to 95th range of 6%
to +114%) during the 19612010 period compared with a world
change in temperature from
anthropogenic forcing
˚C
0 0.4 0.8 1.2 1.6
−0.15
−0.10
−0.05
0.00
mean temperature (°C)
change in ln[GDP per capita (USD)]
Observed temperature
Natural temperature
NOR
DEU
CHN AUS
MEX
BRA
USA
SDN
IND
0102030
AB
1960 1970 1980 1990 2000 2010
Norway (NOR)
1960 1970 1980 1990 2000 2010
0
+10
1960 1970 1980 1990 2000 2010
India (IND)
1960 1970 1980 1990 2000 2010
0
+10
growth rate (%)
% change in
GDP per capita
0
CD
GCM range of cumulative impact
GCM median
GCM range of cumulative impact
GCM median
GCM range of impact
on growth rate
actual growth rate
GCM range of impact
on growth rate
actual growth rate
Quantifying the country-level economic impact of historical global warming
+100
0
+100
Fig. 1. Response of temperature and per capita GDP
to global warming. (A) The ensemble-mean differ-
ence in annual temperature between the CMIP5
Historical and Natural forcing experiments during
the IPCCs historical baseline period (19862005). (B)
The annual temperature for selected countries from
historical observations [black; calculated as in Burke
et al. (14)] and the world without anthropogenic
climate forcing (gray). Overlaid on the country-level
temperatures are the response functions containing
the 10th (red), 50th (orange), and 90th (yellow)
percentile temperature optima, calculated across the
1,000 temperature optima generated by the boot-
strap replication of the regression. The full distribu-
tion of temperature optima from ref. 14 is shown in
the gray box; as in ref. 14, darker red colors indicate
cooler temperature optima and thus greater likeli-
hood of negative impacts from warming. (Cand D)
The impact of anthropogenic climate forcing on an-
nual economic growth rate, and accumulated impact
on per capita GDP, for Norway and India.
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without global warming, with 90% likelihood that the ratio has
increased (Fig. 4C). Likewise, the ratio between the top and bottom
population-weighted quintiles [another common measure (9)] has
become 45% larger (5th to 95th range of +10% to +99%), with
99% likelihood that the ratio has increased. As a result, although
overall between-country inequality has decreased substantially over
thepasthalfcentury(Fig.4A,refs.9and10),itisvery likely(27)
that global warming has slowed that decrease (Fig. 4 Aand C).
The increase in inequality between countries has resulted
primarily from warming-induced penalties in poor countries,
along with warming-induced benefits in some rich countries
(Figs. 2A,3B, and 4B). We find that the poorest half of the
population-weighted country-level economic distribution has
become relatively more poor over the 19612010 period, in-
cluding a median impact of 17% at the poorest decile, and
30% to 31% at the next three poorest deciles (Fig. 4B). In
contrast, the top half of the population-weighted country-level
economic distribution has likely suffered much lessand has a
much higher likelihood of having benefitedthan the bottom
half of the distribution (Fig. 4B).
Discussion
Although some canonical uncertainties in quantifying future economic
impacts are largely removed when focusing on the historical period
such as future discounting uncertainty (e.g., refs. 14, 28, and 29) and
the limits of accounting for future changes that fall well outside of
historical experience (14)other uncertainties must be considered.
For example, uncertainty in the exact magnitude of the tem-
perature optimum creates uncertainty in the sign of the historical
climate impact in some countries (Fig. 2Cand SI Appendix,
Table S1). However, the sign of the impact on inequality is ro-
bust (Fig. 4C), primarily because the mean temperature of so
many poor countries lies in the extreme warm tail of uncertainty
in the optimum (Fig. 3 Aand B). For these countries, it is very
likely(27) that historical warming has reduced economic growth
and lowered per capita GDP (Fig. 2Cand SI Appendix,TableS1).
As a result, although uncertainty in the magnitude of the response of
regional temperature to historical forcing creates uncertainty in the
magnitude of impact at a given decile of the country-level economic
distribution (Fig. 4B), the sign of the impact on the lower deciles
(Fig. 4B)and therefore on inequality (Fig. 4C)is robust.
from 1991−2010from 1961−2010
percent change in GDP per capita
from 1991−2010
from 1961−2010
AB
0 +20 +40-20-40
CD
0.90.50.1 0.70.3
probability of economic damage
Country-level economic impact of historical global warming
Fig. 2. Country-level economic response to global
warming. (A) The median impact on country-level
per capita GDP across the >20,000 realizations of
the world without anthropogenic forcing, calculated
for each country over the 19612010 period. (B)Asin
A, but for the 19912010 period. Differences in the
presence/absence of countries between the 1961
2010 and 19912010 periods reflect differences in
the availability of country-level economic data. Dif-
ferences in the magnitude of country-level values
between the 19612010 and 19912010 periods re-
flect the influence of accumulation time on the net
accumulated economic impact. (Cand D) The prob-
ability that historical anthropogenic forcing has
resulted in economic damage, calculated as the
percentage of the >20,000 realizations that show a
decrease in per capita GDP relative to the counter-
factual world without anthropogenic forcing.
−25
0
+25
+50
+75
510152025 0204060 0123
% change in GDP per capita (1961-2010)
log10(total ton CO2 per capita)2010 GDP per capita
(1000 USD)
mean temperature (˚C)
−25
0
+25
+50
+75
mean temperature (˚C)
210 2028
temp.
optimum
ABC
Relationship between the economic impact of historical global warming
and temperature, wealth, and cumulative carbon emissions
log10(GDP per capita)
234
20 40 60
GDP (103 USD)
Fig. 3. Relationship between economic impact of
global warming and country-level temperature, GDP,
and cumulative CO
2
emissions. (A)Therelationship
between country-level mean annual temperature and
median economic impact of anthropogenic forcing
over the 19612010 period. The orange line shows the
median temperature optimum reported by Burke
et al. (14), and the orange envelope shows the 595%
range. (B) The relationship between per capita GDP in
2010 and median economic impact of historical an-
thropogenic forcing over the 19612010 period. (C)
The relationship between cumulative emissions over
the 19612010 period (calculated from ref. 32) and
median economic impact of historical anthropogenic
forcing over the 19612010 period. (AC)Graystrip
plots show the density of points along the xand y
axes. The black regression line and gray envelope
show the 95% confidence interval of a locally
weighted regression (loess).
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The sign of the inequality impact is also robust to the inclusion
of lagged responses (SI Appendix,TableS2). Lagged responses can
compensate the growth effects of temperature fluctuations, leading
to decreases in both the growth benefit in cool countries and the
growth penalty in warm countries (4). These lagged responses re-
duce the calculated magnitude and probability of warming-induced
increases in economic inequality. However, even with a 5-y lag, there
is still 66% likelihood that historical warming has increased country-
level inequality.
The availability of socioeconomic data also creates uncer-
tainty. Because growth effects cumulate, the length of time over
which economic impacts are evaluated can meaningfully affect
results (4, 12, 14). However, data availability creates an inherent
tradeoff between evaluating fewer countries over a longer period
and evaluating more countries over a shorter period. We repeat
our primary analysis using a larger, shorter sample. Overall, the
pattern of impact is robust, but the cumulative magnitude is larger
over the longer period (Figs. 2 and 3 and SI Appendix,Fig.S1). This
expansion over longer periods suggests that the full impact of
warming since the Industrial Revolution has been even greater than
the impact calculated over the past half century.
Our approach to quantifying the impact of global warming on
economic inequality is also limited by its reliance on country-
level relationships between temperature and economic growth.
Our analysis focuses on country-level data because their wide
availability (in both space and time) allows us to use empirical
relationships to quantify how historical temperature changes
have affected economic outcomes around the world. The impact
of climate change on the evolution of within-country inequality is
a critical question (e.g., ref. 2), but would require either strong
assumptions about how within-country income distributions re-
spond to aggregate shocks at the country level, or comprehensive
subnational data on incomes (which are currently unavailable for
most country-years around the world). Although our population
weighting provides some indication of global-scale individual-
level inequality (9), documenting the impact of global warming
on within-country inequality remains an important challenge.
Many countries in our sample have experienced rapid urbaniza-
tion and economic development for reasons unrelated to climate,
and such trends could plausibly alter how economies respond to
subsequent climate change. Because past work did not find statis-
tically significant evidence that higher incomes reduce temperature
sensitivities (4), we do not attempt to model this moderating effect
here. However, if increasing urbanization or economic development
has reduced the temperature sensitivity of economies over our study
period, this effect will be implicitly included in our estimated impact
of temperature on GDP growth and inequalitythat is, we have
estimated the effect of temperature on growth for economies that
are rapidly urbanizing. Explicitly quantifying the role of these
moderating influences is an important avenue for future work, as it
will be critical for understanding how future climate change will
affect the level and distribution of global income.
Trade between countries has likely already influenced the im-
pacts of global warming on population-weighted inequality. First, a
large part of the reduction in historical inequality during our sample
period has been due to the unprecedented growth in incomes in
East Asia [and particularly China (9, 10)], much of which was built
on critical trading relationships with high-income countries. In
−75
−50
−25
0
+25
+50
+75
+100
10 20 30 40 50 60 70 80 90
population−weighted country-level
per capita GDP (percentile)
percent change in GDP per captia
(1961-2010)
density of 1000 regression
bootstraps x 21 climate models
median bootstrap for
each climate model
−17 −30 −30 −31 +5 +5 +4 −11 +0
median impact (% change)
richest
poorest
1%
99%
95%
5%
90%
50%
10%
33%
67%
−20
0
+20
+40
+60
+80
+100
+120
+140
+160
percent change in ratio of population-
weighted percentiles of GDP per capita
90:10
ratio
80:20
ratio
A
90:10 ratio of population-weighted
percentiles of GDP per capita
1960 1970 1980 1990 2000 2010
Impact of anthropogenic global warming on economic inequality
1%
5%
33%
50%
67%
95%
99%
historical observations
(1961-2010)
counterfactual without anthropogenic forcing
(1000 regression bootstraps x 21 climate models)
50
150
100
BC
Fig. 4. Impact of global warming on country-level
inequality over the past half century. (A) The ratio
between the population-weighted 90th percentile
and 10th percentile country-level per capita GDP for
the historical observed time series and each of
the >20,000 realizations of the world without an-
thropogenic forcing. (B) The density of the >20,000
realizations at each decile of the population-
weighted country-level per capita GDP distribution.
(C) The distribution across the >20,000 realizations of
percent change in population-weighted 90:10 and
80:20 percentile ratios in the year 2010, relative to
the present ratio. Calculations include only those
countries that have continuous socioeconomic data
from 1961 through 2010 (n=86).
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a no-trade counterfactual, China would likely grow much less rap-
idly. Thus, because of Chinas large population and small sensitivity
to historical warming (Fig. 2), repeating our analysis in a no-trade
counterfactual would likely result in smaller reductions in per capita
GDP in the lower deciles of the population-weighted income dis-
tribution (Fig. 4B). However, trade can also serve as a buffer against
climate shocks, particularly in poor countries (e.g., ref. 30). Thus,
the economic impacts of global warmingwhich has substantially
increased the occurrence of extremes (e.g., ref. 21)would likely
have been even greater in poor countries in a no-trade counterfactual,
amplifying the impact on between-country inequality.
Conclusions
It has been frequently observed that wealthy countries have
benefited disproportionately from the activities that have caused
global warming, while poor countries suffer disproportionately
from the impacts (e.g., refs. 16, 17, 19, 25, and 26). Our results
show that, in addition to the direct benefits of fossil fuel use, many
wealthy countries have likely been made even more wealthy by the
resulting global warming. Likewise, not only have poor countries
not shared in the full benefits of energy consumption, but many
have already been made poorer (in relative terms) by the energy
consumption of wealthy countries. Given the magnitude of the
warming-induced growth penalties that poor countries have al-
ready suffered, expansion of low-carbon energy sources can be
expected to provide a substantial secondary development benefit
(by curbing future warming-induced growth penalties), in addition
to the primary benefits of increased energy access.
Materials and Methods
Climate Model Experiments. We compare the Historical and Natural climate
model simulations from the CMIP5 archive (20). As in Burke et al. (14), we analyze
the subselection of CMIP5 realizations analyzed by the Intergovernmental Panel
on Climate Change (IPCC) (31). For the Natural experiment, this includes one
realization each from 21 of the participating global climate models, which are
paired with the 21 corresponding Historical realizations. Note that although the
socioeconomic data are available through 2010, the CMIP5 experimental protocol
for the Historical and Natural experiments ends in 2005. Thus, as in Burke et al.
(14), we use the IPCCs 20-y historical baseline period (19862005) as the baseline
period for climate model bias correction.
For each country, we create 21 counterfactual historical temperature
timeseries T
NoAnthro
, which remove the influence of anthropogenic forcing
simulated by each of the 21 climate models. Our approach to creating the
counterfactual timeseries follows the widely applied delta methodof
climate model bias correction, in which the model-simulated change in the
mean is applied to the observed timeseries. For each country c, we first
calculate the observed country-level population-weighted mean annual
temperature timeseries T
Obs
for the 19612010 time period covered by the
socioeconomic data, following Burke et al. (14). Then, for each country cand
climate model m, we calculate the difference in country-level population-
weighted mean temperature between the Historical and Natural CMIP5
simulations, both for the 20-y period centered on the beginning of the so-
cioeconomic data (19511970), and for the 20-y historical baseline period
used by the IPCC (19862005). We then linearize the difference between the
Historical and Natural simulations over the 19612010 period, such that the
difference in 1961 is equal to the difference in the Historical and Natural
means during the 20-y period centered on 1961 (19511970), and the dif-
ference in 2010 is equal to the difference in the Historical and Natural means
during the IPCCs 20-y baseline period (19862005). Finally, for each year tin
the 19612010 observed temperature timeseries, we add the linearized
Natural minus Historical difference ΔTfor that year:
TNoAnthro½t=TObs ½t+ΔT½t.
This process generates, for each country, an ensemble of 21 counterfactual
timeseries T
NoAnthro
. This 21-member ensemble reflects a combination of
uncertainty in the climate response to external forcings and uncertainty
arising from internal climate system variability, but removes biases in the
climate model simulation of the absolute temperature magnitude and of
the interannual temperature variability. [The T
NoAnthro
timeseries corre-
sponds to the counterfactual timeseries used in Diffenbaugh et al. (21) to
calculate the contribution of the observed trend to the extreme event
magnitude, except that in this case the magnitude of the counterfactual
trend is calculated from the CMIP5 Natural forcing simulation.]
Impact of Historical Temperature Change on Economic Growth. Burke et al.
(4, 14) used historical data to quantify the empirical relationship between
variations in country-level temperature and country-level annual growth in
per capita GDP, allowing for the marginal effect of annual temperature
deviations to vary nonlinearly as a function of country-level mean temper-
ature. As described in detail in Burke et al. (4, 14), the equation for the panel
fixed-effects model is as follows:
ΔlogðYitÞ=β1Tit +β2T2
it +λ1Pit +λ2P2
it +μi+υt+θ1it+θ2it2+«it,
where Y
it
is per capita GDP in country iin year t,Tis the average temper-
ature in year t,Pis the average precipitation in year t,μ
i
are country-fixed
effects, υ
t
are year-fixed effects, and θ
1i
t+θ
2i
t
2
are country-specific linear
and quadratic time trends.
In the current study, we repeat the primary regression calculation de-
scribed in Burke et al. (14), using historical data from 1961 to 2010, and
bootstrapping with replacement to estimate a separate response function
for each of 1,000 resamples, which we denote f
b
. The uncertainty in the
magnitude of the temperature optimum (Fig. 1B) creates uncertainty in
exactly which countries are likely to benefit or be penalized at different
levels of warming, and is the largest source of uncertainty in the response of
GDP growth to elevated levels of global climate forcing (14).
We quantify the uncertainty in economic damages arising from uncertainty in
the temperature optimum (e.g., Figs. 2 and 4 and SI Appendix, Table S1), as well
as the uncertainty arising from lagged responses to temperature fluctuations
(SI Appendix, Table S2). We also explore additional aspects of the relationship
between temperature and GDP growth. For example, we find that historical
temperature fluctuations explain on average 8.6% of the overall variation in
country-level annual income growth fluctuations during our study period (SI
Appendix,Fig.S2). Likewise, given the shape of the temperaturegrowth re-
sponse function (Fig. 1B), temperature fluctuations around a stable mean will
induce a negative trend in per capita GDP. However, we find that the magnitude
of this effect is small compared with the impact of long-term warming (SI Ap-
pendix,Fig.S3).
Whereas Burke et al. (4, 14) projected economic impacts under future
emissions scenarios, we calculate the accumulated economic impacts of
historical temperature change. For each country cin each year t, we compare
economic growth under historical observed temperatures (T
Obs
) with pre-
dicted growth under counterfactual temperatures (T
NoAnthro
). We repeat this
comparison for each climate model mand each bootstrap j, yielding more
than 20,000 realizations of the impact of anthropogenic forcing on eco-
nomic growth in each country.
We first initialize the analysis in each country with the observed per capita GDP
from the starting year t=0 of the socioeconomic data (e.g., GDPcap
Obs
[1961]).
Then, for each year tand using the temperaturegrowth response func-
tions festimated above, we calculate the difference in growth rate be-
tween the observed temperature and the counterfactual temperature
(Fig. 1 Cand D):
ΔGrowth½t=fðTNoAnthro½tÞ fðTObs ½tÞ.
We then add that difference ΔGrowth[t] to the actual observed growth rate
Growth
Obs
[t] to calculate the counterfactual growth rate Growth
NoAnthro
[t]:
GrowthNoAnthro½t=GrowthObs ½t+ΔGrowth½t.
We then multiply this counterfactual growth Growth
NoAnthro
[t] by the accumu-
lated counterfactual per capita GDP in the previous year (GDPcap
NoAnthro
[t1])
to calculate current-year counterfactual per capita GDP:
GDPcapNoAnthro½t=GDPcapNoAnthro ½t1
+ðGDPcapNoAnthro½t1
*
GrowthNoAnthro½tÞ.
We repeat this process through the last year of the socioeconomic data
(2010), for each country in the GDP dataset.
Finally, we calculate the percent difference between the actual observed per
capita GDP (GDPcap
Obs
) and the per capita GDP calculated for the counterfactual
temperature timeseries (GDPcap
NoAnthro
) in the last year of the socioeconomic
data (2010):
ΔGDPcap =½ðGDPcapObs½2010GDPcapNoAnthro ½2010Þ=
GDPcapNoAnthro½2010 ×100%.
For each country c, we calculate GDPcap
NoAnthro
and ΔGDPcap for each of the
1,000 bootstrapped response functions f
b
, applied to the counterfactual
temperature timeseries T
NoAnthro
from each of the 21 global climate models
Diffenbaugh and Burke PNAS Latest Articles
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SUSTAINABILITY
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(thus yielding more than 20,000 values of GDPcap
NoAnthro
and ΔGDPcap for
each country).
Our primary analysis is focused on quantifying the impacts that historical
global warming has had during the full period for which socioeconomic data
are available (19612010). However, because the socioeconomic data do not
extend to 1961 for a large number of countries, we repeat our analysis for the
19912010 period. For all analyses that start in 1961, we analyze only those
countries that have continuous socioeconomic data from 1961 through 2010
(n=86); for all analyses that start in 1991, we analyze only those countries that
have continuous socioeconomic data from 1991 through 2010 (n=151). Ob-
served and estimated counterfactual temperatures and growth rates are the
same for the years that overlap between the two periods, but growth rates are
cumulated over 30 more years in the longer period, yielding larger (in absolute
value) impacts on economic outcomes by the end of the period (Fig. 2).
Quantifying the Impact of Historical Global Warming on Economic Inequality. A
number of measures of economic inequality have been developed (9). Given the
limited availability of long timeseries of subnational economic data, investiga-
tions of changes in global inequality often rely on country-level metrics (e.g., refs.
9 and 10). However, when using country-level metrics, weighting by country-
level population is critical to accurately capture trends in global inequality (9).
We measure global economic inequality using the ratio of the top and
bottom decile (90:10 ratio) and top and bottom quintile (80:20 ratio)of
the population-weighted country-level per capita GDP distribution. Both
metrics are included among eight of the most popularindexes of income
inequality identified by Sala-i-Martin (9). According to Sala-i-Martin (9), The
top-20-perce nt-to-bottom-20-percent is the ratio of the income of the person
located at the top twentieth centile divided by the income of the corre-
sponding person at the bottom twentieth centile. A similar definition applies
to the top-10-percent-to-bottom-10-percent ratio.Because of the lack of
availability of long timeseries of subnational economic data, we calculate
these ratios using the respective percentiles of the population-weighted em-
pirical CDF of country-level per capita GDP values (SI Appendix,Fig.S4).
We first calculate the percent difference in per capita GDP for each decile
of the population-weighted country-level GDP distribution. To do so, we
calculate the deciles of country-level population-weighted per capita GDP,
using the countries in the 19612010 dataset. For each year tin the observed
country-level per capita GDP dataset (GDPcap
Obs
), we calculate the pth
percentile population-weighted GDP as the country-level per capita GDP
below which the sum of the country-level populations represents ppercent
of the total population of countries in the 19612010 dataset (SI Appendix,
Fig. S4). For example, we calculate the 10th percentile population-weighted
GDP as the country-level per capita GDP for which the total population of
countries with lower per capita GDP is 10% of the total population of
countries in the 19612010 dataset, and so on for each decile.
Next, we calculate the deciles of country-level population-weighted per capita
GDP in each year tof each bootstrap jand climate model mof the counterfactual
world without anthropogenic climate forcing (GDPcap
NoAnthro
). Then, for the year
2010 in each bootstrap jand climate model m, we calculate the percent difference
between the observed population-weighted decile value and the counterfactual
population-weighted decile value (as described for ΔGDPcap above). For the
differences in each population-weighted decile, we calculate the density distri-
bution across all 1,000 bootstrap regressions from all 21 climate models, as well as
the median value across the 1,000 bootstrap regressions for each climate model.
Finally, we quantify the between-country population-weighted economic
inequality GDPcapHigh:Low as the ratio between the higher percentile (e.g.,
90th) and lower percentile (e.g., 10th) population-weighted per capita GDP. We
first calculate GDPcapHigh:Low in each year tof the observations (GDPcapHigh:
Low
Obs
),andineachyeartof the counterfactual world without anthropogenic
climate forcing (GDPcapHigh:Low
NoAnthro
). Then, for each bootstrap jand cli-
mate model m, we calculate the percent difference between the observed
population-weighted inequality GDPcapHigh:Low
Obs
and the counterfactual
population-weighted inequality GDPcapHigh:Low
NoAnthro
in the year 2010:
ΔGDPcapHigh:Low =½ðGDPcapHigh:LowObs½2010
GDPcapHigh:LowNoAnthro ½2010Þ=
GDPcapHigh:LowNoAnthro ½2010 ×100%.
ACKNOWLEDGMENTS. We thank the editor and two anonymous reviewers
for insightful and constructive feedback. We acknowledge the World Climate
Research Programmes Working Group on Coupled Modelling (which is re-
sponsible for CMIP), the climate modeling groups for producing and making
available their model output, and the Department of Energys Program f or
Climate Model Diagnosis and Intercomparison for access to the CMIP5 data.
Computational facilities were provided by the Center for Computational Earth
and Environmental Science and Stanford Research Computing Center at Stan-
ford University. We acknowledge funding support from Stanford University.
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www.pnas.org/cgi/doi/10.1073/pnas.1816020116 Diffenbaugh and Burke
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Atmospheric <span classCombining double low line"inline-formula">CO2 concentration is measured directly and its growth rate (<span classCombining double low line"inline-formula"> G ATM ) is computed from the annual changes in concentration. The ocean <span classCombining double low line"inline-formula">CO2 sink (<span classCombining double low line"inline-formula"> S OCEAN ) and terrestrial <span classCombining double low line"inline-formula">CO2 sink (<span classCombining double low line"inline-formula"> S LAND ) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (<span classCombining double low line"inline-formula"> B IM ), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as <span classCombining double low line"inline-formula">±1 σ . For the last decade available (2008-2017), <span classCombining double low line"inline-formula"> E FF was <span classCombining double low line"inline-formula">9.4±0.5 GtC yr<span classCombining double low line"inline-formula">ĝ'1 , <span classCombining double low line"inline-formula"> E LUC <span classCombining double low line"inline-formula">1.5±0.7 GtC yr<span classCombining double low line"inline-formula">ĝ'1 , <span classCombining double low line"inline-formula"> G ATM <span classCombining double low line"inline-formula">4.7±0.02 GtC yr<span classCombining double low line"inline-formula">ĝ'1 , <span classCombining double low line"inline-formula"> S OCEAN <span classCombining double low line"inline-formula">2.4±0.5 GtC yr<span classCombining double low line"inline-formula">ĝ'1 , and <span classCombining double low line"inline-formula"> S LAND <span classCombining double low line"inline-formula">3.2±0.8 GtC yr<span classCombining double low line"inline-formula">ĝ'1 , with a budget imbalance <span classCombining double low line"inline-formula"> B IM of 0.5 GtC yr<span classCombining double low line"inline-formula">ĝ'1 indicating overestimated emissions and/or underestimated sinks. For the year 2017 alone, the growth in <span classCombining double low line"inline-formula"> E FF was about 1.6 % and emissions increased to <span classCombining double low line"inline-formula">9.9±0.5 GtC yr<span classCombining double low line"inline-formula">ĝ'1 . 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