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Estimating economic damage from climate change in the United States


Abstract and Figures

Estimates of climate change damage are central to the design of climate policies. Here, we develop a flexible architecture for computing damages that integrates climate science, econometric analyses, and process models. We use this approach to construct spatially explicit, probabilistic, and empirically derived estimates of economic damage in the United States from climate change. The combined value of market and nonmarket damage across analyzed sectors—agriculture, crime, coastal storms, energy, human mortality, and labor—increases quadratically in global mean temperature, costing roughly 1.2% of gross domestic product per +1°C on average. Importantly, risk is distributed unequally across locations, generating a large transfer of value northward and westward that increases economic inequality. By the late 21st century, the poorest third of counties are projected to experience damages between 2 and 20% of county income (90% chance) under business-as-usual emissions (Representative Concentration Pathway 8.5).
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Solomon Hsiang1,2,3, Robert Kopp3,4, Amir Jina3,5 , James Rising1,3, Michael Delgado3,6, Shashank
Mohan3,6, D.J. Rasmussen7, Robert Muir-Wood8, Paul Wilson8, Michael Oppenheimer7, Kate Larsen3,6,
and Trevor Houser3,6
1University of California, Berkeley
2National Bureau of Economic Research
3The Climate Impact Lab
4Rutgers University
5University of Chicago
6Rhodium Group
7Princeton University
8Risk Management Solutions
Forthcoming in Science
Equal contribution.
Corresponding author: Global Policy Laboratory, Goldman School of Public Policy, 2607 Hearst Ave, Berkeley, CA,
94720. Email:
Corresponding author: Dept. of Earth & Planetary Sciences, 610 Taylor Rd, Piscataway, NJ, 08854. Email:
Estimates of climate change damage are central to the design of climate policies. Here we develop
a flexible architecture for computing damages that integrates climate science, econometric analyses,
and process models. We use this approach to construct spatially-explicit, probabilistic, and empir-
ically derived estimates of economic damage in the United States from climate change. The com-
bined value of market and non-market damage across analyzed sectors—agriculture, crime, coastal
storms, energy, human mortality, and labor—increases quadratically in global mean temperature, cost-
ing roughly 1.2%GDP/+1C on average. Importantly, risk is distributed unequally across locations,
generating a large transfer of value northward and westward that increases economic inequality. By
late twenty-first century, the poorest third of counties are projected to experience damages between
2-20% of county income (90% chance) under business-as-usual (RCP8.5).
Economically rational management of the global climate requires that the costs of reducing greenhouse
gas emissions be weighed against the benefits of doing so (or, conversely, the costs of not doing so). A
vast literature has considered this problem, developing, among other insights, our understanding of the
optimal timing of investments (1), the role of uncertainty (2), the importance of future adaptation (3), and
trade (4), and the potentially large impact of unanticipated tipping points (5, 6). Integrated assessment
models that value the benefits of greenhouse gas abatement are used by governments to estimate the social
cost of climate change (7, 8), which in turn informs the design of greenhouse gas policies. However, the
estimated benefits of greenhouse gas abatement—or conversely, the “damages” from climate change—
are conceptually and computationally challenging to construct. Because of this difficulty, prior analyses
have relied on rough estimates, theorized effects, or limited process modeling at continental scales or
larger (9, 10, 11), with no systematic calibration to observed human-climate linkages (12). Since the
original development of these models, methodological innovations (13) coupled with data availability
and computing power have fueled rapid growth in a spatially-resolved, empirical understanding of these
relationships (14). Yet integrated assessments of climate change and their calculation of the social cost
of carbon do not reflect these advances (15, 16, 17).
Here we develop an integrated architecture to compute potential economic damages from climate
change based on empirical evidence, which we apply to the context of the United States (US). Our
risk-based approach is grounded in empirical longitudinal analyses of nonlinear, sector-specific impacts,
supplemented with detailed energy system, inundation, and cyclone models. Built upon a calibrated
distribution of downscaled climate models, this approach is probabilistic and highly resolved across ge-
ographic space while taking into account the spatial and sectoral covariance of impacts in each possible
future. Our framework is designed to continuously integrate new empirical findings and new climate
model projections as the supporting subfields of research advance in the future. When applied to the US
economy, this approach provides probabilistic and empirically derived “damage function,” linking global
mean surface temperature (GMST) to market and non-market costs in the US, built up from empirical
analyses using micro-level data.
System Architecture
We developed the Spatial Empirical Adaptive Global-to-Local Assessment System (SEAGLAS) to dy-
namically integrate and synthesize research outputs across multiple fields in near-real time. We use SEA-
GLAS to construct probabilistic, county-level impact estimates that are benchmarked to GMST changes.
See the Supplementary Online Materials (SOM, Section A) for additional details (18).
County-level projections of daily temperature and precipitation are constructed and sampled follow-
ing a three-step process that simultaneously captures the probability distribution of climate responses to
forcing, spatiotemporal structures within each climate realization, and spatiotemporal autocorrelation of
weather (19): (1) For each forcing pathway considered (Representative Concentration Pathways [RCP]
2.6, 4.5, and 8.5; ref. (20)), a probability distribution for GMST change is constructed based on an esti-
mated distribution of equilibrium climate sensitivity, historical observations, and a simple climate model
(SCM) (19). (2) The joint spatio-temporal distribution of monthly temperature and precipitation is con-
structed from a broad range of global climate models (GCMs), statistically downscaled from the CMIP5
archive (21) and assigned a probability of realization such that the distribution of 21st century GMST
change mirrors the distribution from the SCM. Tails of the distribution beyond the range present in the
CMIP5 archive are represented by ‘model surrogates’, constructed by scaling patterns from CMIP5 mod-
els using the GMST projections from the SCM. Together, we refer to the union of monthly-resolution
GCM and model surrogate output as the set of climate realizations that are each weighted to reflect a
single probability distribution (Figure 1A). These weights are used when we compute damage probabil-
ity distributions for specific RCP scenarios. (3) We then construct a set of ten daily projections for each
climate realization by superimposing daily weather residuals relative to monthly climatologies that are
resampled in yearly blocks from the period 1981–2010. (Figure 1B).
A distribution of empirically grounded economic impacts are computed for each joint realization of
county-level, daily temperature and precipitation: (4) econometrically-derived dose-response functions
(13) estimating the nonlinear effects of temperature, rainfall, and CO2on agriculture (22, 23), mortality
(24, 25), crime (26, 27), labor (28), and energy demand (24) are constructed via Bayesian distributed
meta-analysis (29) (e.g. Figure 1C-H, see SOM B-C). Following the approach and criteria laid out in ref
(30), we only employ studies that are nationally representative, spatially disaggregated, and account for
temporal displacement and unobserved heterogeneity across locations; along with the additional criteria
that studies statistically identify marginal distortions in the distribution of experienced daily temperatures
(13, 14). (5) Econometric uncertainty are accounted for by resampling from the 26 posterior functions in
(4). (6) County-level daily projections from (3) are mapped onto the distribution of possible responses
from (5) to construct 3,143 county-level joint distributions for 15 impacts across 29,000 possible states of
the world during 2000–2099 (SOM D-E), although for display purposes we primarily summarize 2080-
2099 impacts here.
A parallel approach is necessary to estimate energy demand changes and coastal impacts: (7) Energy
demand estimated in (4) is used as a partial calibration for the NEMS energy system model (31) (SOM
G). NEMS is then run with different weather realizations to estimate energy supply costs. (8) Cyclone
exposure is simulated via analytical wind field models (32) that force a storm surge model (33), with
cyclogenesis and storm tracks generated via either (i) semi-parametrically resampling historical activity
(34) or (ii) resampling from projected storm tracks and intensities (35) (SOM H). (9) Inundation from
localized probabilistic sea level rise projections (36) interacting with storm surge and wind exposure in
(8) are mapped onto a database of all coastal properties maintained by maintained by Risk Management
Solutions, where engineering models predict damage (SOM H).
Finally, economic impacts are aggregated and indexed against GMST in their corresponding cli-
mate realization to construct multi-dimensional probabilistic damage functions suitable for application
in integrated assessment modeling: (10) Direct impacts from (6), (7), and (9) are aggregated across
space or time within a sector. Monetizing the value of non-market impacts (deaths and crime) using
willingness-to-pay or accounting estimates (37,38), impacts across all sectors are aggregated to compute
total damages (I-J).
Importantly, for clarity, our approach holds the scale and structure of the US population and economy
fixed at values observed in 2012, since current values are well understood and widely agreed on. Vari-
ous prior analyses (e.g. (39)) note that natural demographic change and economic growth may dominate
climate change effects in overall magnitude, although such comparisons are not our focus here. Because
we compute impacts using scale-free intensive measures (e.g., percentage changes), future expansion of
the economy or population does not affect our county-level estimates, and our aggregate results will be
unbiased so long as this expansion is balanced across space. If such expansion is not balanced across
space, then our aggregated results will require a second-order adjustment with a sign that depends on
the spatial covariance of changes in climate exposure and changes in economic or population structure,
as shown in ref. (40). In prior work (41), we demonstrated how results for some direct impacts might
change if future rates of adaptation to climate mirror historical patterns and rates. The paucity of exist-
ing quantitative studies on adaptation prevents us from currently applying this approach to all sectors,
although such additions are expected in future work.
Distribution of costs and benefits
Standard approaches to valuing climate damage describe average impacts for large regions (e.g., “North
America”) or the entire globe as a whole. Yet examining county-level impacts reveals major redistributive
impacts of climate change on some sectors that are not captured by regional or global averages. Figures
2 and S2 display the median impact from 2080-2099 climate changes in RCP8.5, a trajectory consistent
with fossil-fuel-intensive economic growth, for each county. In cases where responses to temperature
are nonlinear (e.g. Figure 1C, E, H), the current climate of counties affects whether additional warm-
ing generates benefits, has limited effect, or imposes costs. For example, warming reduces mortality in
cold northern counties and elevates it in hot southern counties (Figure 2B). Sectors with roughly linear
responses, such as violent crime (Figure 1G), have more uniform effects across locations (Figure 2H).
Atlantic coast counties suffer the largest losses from cyclone intensification and mean sea level (MSL)
rise (Figure 2F). In general (except for crime and some coastal damages), southern and midwestern pop-
ulations suffer the largest losses, while northern and western populations have smaller or even negative
damages, the latter amounting to net gains from projected climate changes.
Combining impacts across sectors reveals that warming causes a net transfer of value from Southern,
Central, and Mid-Atlantic regions towards the Pacific Northwest, the Great Lakes Region, and New
England (Figure 2I). In some counties, median losses exceed 20% of Gross County Product (GCP), with
median gains sometimes exceeding 10% of GCP. Because losses are largest in regions that are already
poorer on average, climate change tends to increase pre-existing inequality in the US. Nationally averaged
effects, used in prior assessments, do not capture this subnational restructuring of the US economy.
Nationally aggregated sectoral impacts
We recover sector-specific damages as a function of GMST change by aggregating county-level impacts
within each state of the world defined by an RCP scenario, climate realization, resampled weather, and
econometrically derived parameter estimate (SOM D-E). The distribution of sectoral impacts is compared
to GMST change in each realization in Figure 3 (SOM J). Although several sectors exhibit micro-level
responses that are highly nonlinear with respect to county temperature (e.g. Figure 1C), aggregated
damages exhibit less extreme curvature with respect to GMST change, as was hypothesized and derived
in ref (42).
Average yields in agriculture decline with rising GMST, but higher CO2concentrations offset much of
the loss for the coolest climate realizations in each of the three RCP scenarios. Accounting for estimated
effects of CO2fertilization (SOM B) and precipitation, warming still dominates, reducing national yields
9.1(±0.6) %/C (Figure 3A). Because effects of CO2are highly uncertain and not derived using the
same criteria as other effects, we evaluate the sensitivity of these projections by computing losses without
CO2fertilization (Figure 3B) and find that temperature and rainfall changes alone would be expected to
reduce yields 12.1(±0.7) %/C (see also FiguresS11-S12 and Tables S10-S11).
Rising mortality in hot locations more than offsets reductions in cool regions, so annual national
mortality rates rise 5.4(±0.5) deaths per 100,000/C (Figure 3C). For lower GMST changes, this is
driven by mortality between ages 1-44, and by infant mortality and ages 45 for larger GMST increases
(Figure S13 and Table S12).
Electricity demand rises on net for all GMST changes, roughy 5.3 (±0.14)%/C, because rising
demand from hot days more than offsets falling demand on cool days (Figure 3D and Table S13). Because
total costs in the energy sector are computed using NEMS, demand is not statistically resampled as other
sectors are (see SOM G).
Total hours of labor supplied declines 0.11 (±0.004) %/C in GMST for low-risk workers, who
are predominantly not exposed to outdoor temperatures, and 0.53 (±0.01) %/C for high-risk workers
who are exposed (23% of employed workers, in sectors such as construction, mining, agriculture, and
manufacturing) (Figure 3E-F and Table S14).
Property crime increases as the number of cold days–which suppress property crime rates (Figure
S4)–falls but then flattens for higher levels of warming because hot days do not affect property crime
rates. Violent crime rates increase linearly at a relatively precise 0.88 (±0.04) %/C in GMST (Figure
3G-H and Table S15).
Coastal impacts are driven by the amplification of tropical cyclone and extratropical cyclone storm
tides by local MSL and by the alteration of the frequency, distribution, and intensity of these cyclones
(SOM H). Rising MSL increases the storm tide height and floodplain during cyclones: Figure 4A-D
illustrates how 1-in-100 year floodplains evolve over time due to MSL rise (RCP8.5) with and without
projected changes in cyclones for two major coastal cities. Coastal impacts are distributed highly un-
equally, with acute impacts for eastern coastal states with topographically low cities; MSL rise alone
raises expected direct annual economic damage 0.6-1.3% of state GDP for South Carolina, Louisiana
and Florida in the median case, and 0.7-2.3% for the 95th percentile of MSL rise (Figure 4E, RCP8.5).
Nationally, MSL rise would increase annual expected storm damages roughly 0.0014% GDP per cm if
capital and storm frequency remain fixed (Figure 4F). Accounting for the projected alteration of the TC
distribution roughly doubles the damage from MSL rise, the two combined costing an estimated addi-
tional 0.5 (±0.2)% of GDP annually in 2100 when aggregated nationally (Figure 4G).
At the county level, conditional upon RCP, uncertainty in direct damages is driven by climate uncertainty
(both in GMST and in the expected spatiotemporal distribution of changes conditional on GMST), by
within-month weather exposure, and in statistical assumptions and sampling used to derive dose-response
functions, as well as by uncertainty generated by the interaction of these factors. Figure 2A-G displays
county-level uncertainty in the impact on each sector by indicating the level of agreement among 11,000
projections on the overall sign of impacts in each county. Notably, process models (e.g. NEMS) and other
variables, such as baseline work hours or the VSL, contain uncertainty that remains uncharacterized.
Aggregating results nationally, we decompose uncertainty into contributions from climate, within-
month weather, and dose-response relationships by resampling each individually while holding the oth-
ers fixed (43), recovering how these variances combine to produce the total variance across projections
(Figure S6-S7). In general, climate uncertainty dominates, contributing 41–104% of the total variance
by end of century, with econometric uncertainty in low-risk labor (88% of total variance) being the only
exception. Within-month weather uncertainty has a negligible effect on 20-year averages. The interaction
between climate and dose-response uncertainty also contributes to the total variance (negatively in some
cases), because impact functions are nonlinear (SOM F).
Economy-wide damage
Nationally aggregated damage
Impacts across sectors can be aggregated into a single measure of overall economic damage if suitable
values can be assigned to each impact category. For non-market costs, we use current US Environmental
Protection Agency values for the value of a statistical life (37) and published estimates for the cost of
crime (38), which we combine with current average market valuations of market impacts (see SOM I).
Summing across impacts, we estimate the conditional distribution of total direct damages as a function
of global mean temperature change (Figure 5A), finding that expected annual losses increase by 0.6%
GDP per 1C at +1C of warming GMST, to 1.7% GDP per 1C at +5C GMST (see SOM J). This
response is well approximated by a quadratic function (Figure S14) that is highly statistically significant
for changes above 1C(p<0.001) (Table S16). Combined uncertainty in aggregate impacts grows with
warming, so the likely range of losses (5-95th quantiles) at 1.5C of warming spans 0.1-1.7%GDP,
4C warming spans 1.5-5.6%GDP, and 8C warming spans 6.4-15.7% GDP annually (grey band, Figure
5A). Approximating this damage function with a linear form suggests losses of 1.2% GDP per 1C on
average in our sample of scenarios (Table S16).
The greatest direct cost for GMST changes larger than 2.5C is the burden of excess mortality, with
sizable but smaller contributions from changes in labor supply, energy demand, and agricultural produc-
tion (Figure 5B). Coastal storm impacts are also sizable but do not scale strongly with GMST because
projections of global MSL are dependent upon RCP but are not explicitly calculated as functions of
GMST (36), causing the coastal storm contribution to the slope of the damage function to be relatively
muted. It is possible to use alternative approaches to valuing mortality in which the loss of lives for
older and/or low-income individuals are assigned lower value than those of younger and/or high-income
individuals (44), an adjustment that would alter damages differently for different levels of warming based
on the age and income profile of affected individuals (e.g. Figure S13). Here, we focus on the approach
legally adopted by the US government for environmental cost-benefit analysis, in which the lives of all
individuals are valued equally (37). Because the VSL parameter is influential, challenging to measure
empirically, and may evolve in the future, its influence on damages is an important area for future inves-
Risk and inequity of local damages
Climate change increases the unpredictability and between-county inequality of future economic out-
comes, effects that may alter the valuation of climate damages beyond their nationally averaged expected
costs (45). Figure 5C displays the probability distribution of damage under RCP 8.5 as a fraction of
county income, ordering counties by their current income per capita. Median damages are systematically
larger in low income counties, increasing by 0.93% of county income (95% CI=0.85-1.01) on average
for each reduction in current income decile. In the richest third of counties, the average very likely range
(90% credible interval, determined as the average of 5th and 95th percentile values across counties) for
damages is 1.2-6.8% of county income (negative damages are benefits); whereas for the poorest third
of counties the average range is 2.0-19.6% of county income. These differences are more extreme for the
richest 5% and poorest 5% of counties, with average intervals for damage of 1.1-4.2% and 5.5-27.8%,
We note that it is possible to adjust the aggregate damage function in Figure 5A to capture societal
aversion to both the risk and inequality in Figure 5C. In SOM K, we demonstrate one approach to con-
structing such inequality-neutral, certainty-equivalent damage functions. Depending on the parameters
used to value risk and inequality, accounting for these factors may dramatically influence society’s val-
uation of damages in a manner similar to the large influence of discount rates on the valuation of future
damages (46). This finding highlights risk and inequality valuation as critical areas for future research.
Our results provide a probabilistic, national damage function based on spatially disaggregated, empirical,
longitudinal analyses of climate impacts and available global climate models–but it will not be the last.
Because we use stringent selection criteria for empirical studies, there are multiple known sectors of the
US economy for which no suitable studies exist and were thus omitted from this analysis (e.g., impacts
of morbidity (47), worker productivity (48), or biodiversity loss (49)). The SEAGLAS architecture is
constructed around the idea that rigorous future studies will quantify climate impacts in these “missing
sectors” and thus should be included in future assessments. Our approach therefore allows for updating
based on new econometric results or climate model projections, and our results should be interpreted as
current best estimates that will be dynamically adjusted as research in the community advances.
We stress that the results presented here are projections relative to a counterfactual baseline economic
trajectory that is unknown and will evolve based on numerous factors unrelated to climate change. As
constructed, knowledge of this baseline trend is not essential to constructing the relative first-order impact
imposed by climate change.
We should expect that populations will adapt to climate change in numerous ways (14). Some actions,
such as use of air conditioning (25), likely limit the impact of climatic exposure, while other actions, such
as social conflict (30), likely exacerbate impacts. Because the empirical results we utilize describe how
populations have actually responded to climatic conditions in the past, our damage estimates capture
numerous forms of adaptation to the extent that populations have previously employed them (50). For
example, if farmers have been adjusting their planting conditions based on observable rainfall, the effect
of these adjustments will be captured by our results. Although, if there are trends in adaptive behaviors,
previously unobserved adaptation “tipping points,” or qualitative gains in adaptation-related technologies,
then our findings may require adjustment. In previous work we demonstrated how to employ empirical
approaches to project trends in adaptive behaviors and recompute impacts in some sectors (41), but
sufficient data do not yet exist to estimate these effects in all the sectors we cover here. Yet in cases
where sufficient data do exist to simulate these adaptations, the net effect of this correction is small in
magnitude relative to the large uncertainty that is introduced by such adjustments (41), a result of the
high uncertainty in current estimates for trends in adaptation (25, 51).
As mentioned above, populations may move across space in response to altered climate conditions.
This response will not alter our local projections, but it will cause our estimates to over- or under-predict
nationally aggregated impacts, depending on the spatial covariance between population changes and local
economic losses caused by climate change. This adjustment will tend to be second order relative to the
direct effect of climate change (13); nonetheless, accounting for this adjustment is an area for future
Another possible adjustment that may occur in response to climate damages is for the economy to
reallocate non-labor resources, partially shifting the locations of economic activity, in order to cope with
these changes. We consider the extent to which this response might alter the direct economic damages
that we characterize above by developing a computable general equilibrium (CGE) model that reallocates
capital across locations and industries in response to the capital and productivity losses described above
during each period of a century-long integration (SOM L). Theoretically, it is possible for these reallo-
cations to reduce damages, as production migrates away from adverse climates, or for them to increase
damages, as losses in one location alter economic decisions in other locations and/or later periods by
influencing markets via prices. We simulate the trajectory of the future economy under each RCP8.5
climate realization, imposing our computed direct damages each period. When direct damages are im-
posed on only one sector at a time, the total end-of-century economic loss may be larger or smaller than
the corresponding direct damages estimate, depending on the sector and climate realization (Figure 5D).
Note that market costs of mortality computed with this approach are dramatically lower than non-market
costs described above because the foregone earnings in the market equilibrium are much smaller than the
VSL used to compute direct damages. Overall, in a complete simulation where national markets are si-
multaneously forced by direct damages in all sectors, net market losses in general equilibrium tend to be
larger than direct damages by 50% (mortality is excluded from both). These simulations are relatively
coarse approximations of the complex national economy and do not capture international trade effects,
but they suggest that the spatial reallocation of economic activity within the US may not easily mitigate
the economic damage from climate change.
Our results are “bottom-up” micro-founded estimates of US damages, although parallel analyses have
employed “top-down” macro-level approaches that estimate how overall productivity measures (such as
GDP) directly respond to temperature or cyclone changes without knowledge of the underlying mech-
anisms generating those losses. This alternative approach can be compared to our estimates of market
losses only, as they will not account for non-market valuations. Our market estimates are for a 1.0-3.0%
loss of annual national average GDP under RCP8.5 at end-of-century. Prior top-down county-level anal-
ysis of productivity estimates that national output would decline 1.2-3.1% after twenty years of exposure
to RCP8.5 temperatures at end-of-century (52). In top-down global analyses of all countries, the 10.3%
intensification of average US tropical cyclone exposure in emissions scenario A1B (roughly comparable
to RCP8.5) (35) is estimated to reduce GDP 0.09% per year (53) (not accounting for MSL rise) and the
cumulative effect of linear national warming by an additional 1C over 75 years is estimated to reduce
GDP 2.9% (2080-2099 average) (42). In comparison, we estimate losses to cyclone intensification are
0.07% of annual GDP per 1C in global mean temperature change and economy-wide direct damages
are 1.2% of annual GDP per year per 1C. Overall, such comparisons suggest top-down and bottom-up
empirical estimates are beginning to converge, although some important differences—in accounting pro-
cedures as well as recovered magnitudes and temporal structure—remain. Future investigation should
reconcile these differences.
Here we have focused on the US economy, although the bulk of the economic damage from climate
change will be borne outside of the US (42), and impacts outside the US will have indirect effects on the
US through trade, migration, and possibly other channels. In ongoing work, we are expanding SEAGLAS
to cover the global economy and to account for additional sectors, such as social conflict (30), in order
to construct a global damage function that is essential to estimating the global social cost of carbon and
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This research was funded by grants from the National Science Foundation, the US Department of En-
ergy, Skoll Global Threats Fund, and a nonpartisan grant awarded jointly by Bloomberg Philanthropies,
the Office of Hank Paulson, and Next Generation. The methodology and results presented represent the
views of the authors and are fully independent of the granting organizations. We thank Max Auffham-
mer, Malte Meinshausen, Kerry Emanuel, Joshua Graff Zivin, Olivier Deschenes, Justin McGrath, Lars
Lefgren, Matthew Neidell, Matthew Ranson, Michael Roberts, Alastair Norris, Karandeep Chadha, Ali-
son Dobbin, Alexandra Guerrero, Linda Schick and Wolfram Schlenker for providing data and additional
analysis; Marshall Burke, William Fisk, Nicholas Stern, William Nordhaus, Tony Broccoli, Matthew
Huber, Tom Rutherford, Jonathan Buzan, Karen Fisher-Vanden, Miles Light, David Lobell, Michael
Greenstone, Katharine Hayhoe, Geoffrey Heal, Douglas Holt-Eakin, Jonathan Samet, Andrew Schreiber,
Wolfram Schlenker, Joseph Shapiro, Michael Spence, Larry Linden, Linda Mearns, Sean Ringstead,
Gary Yohe, and seminar participants at Duke, MIT, Stanford, the University of Chicago, and the NBER
for important discussions and advice; Joseph Delgado and Sergey Shevtchenko for invaluable technical
assistance. Rhodium Group is a private economic research company that conducts independent research
for clients in the public, private and philanthropic sector. Risk Management Solutions is a catastrophe risk
modeling company that provides hazard modeling services to financial institutions and public agencies.
The analysis contained in this research article was conducted independently of any commercial work and
was not influenced by clients of either organization. Data and code used in this analysis can be obtained at
Supplementary Online Materials
Supplementary materials include additional details of data and methods, Figures S1-S17, Tables S1-S27,
and References (53-91).
local mean surface
temperature anomaly (˚C)
Jul 03 Jul 10 Jul 17 Jul 24 Jul 31
25 30 35
New York City, July 2090, monthly avg: 30.3°C
daily avg. temp. (°C)
2080-2099 Global mean temperature anomaly (ºC)
Simulation date
10 0 10 20 30
Mortality rate
(per 100k)
10 0 10 20 30
Max daily temperature (ºC)
Avg daily temperature (ºC)
Mortality (45-64 yrs old)
Electricity demand
10 0 10 20 30 40
Crime rate (%)
Max daily temperature (ºC)
Violent crime
0 10 20 30 40
log annual yield
24 hr temperature (ºC) Seasonal precipitation (m)
00.5 1 1.5
log annual yield
Maize yield Maize yield
0 10 20 30
Minutes per day
Max daily temperature (ºC)
Labor supply (high risk)
Probability Density
Figure 1: Recombining prior research results as composite inputs to SEAGLAS. (A) 44 climate
models (outlined maps) and model surrogates (dimmed maps) are weighted so the distribution of the
2080–2099 GMST anomaly exhibited by weighted models matches the probability distribution of esti-
mated GMST responses (blue-grey line) under RCP8.5. Analogous display for precipitation in Figure
S1. (B) Example of ten months of daily residuals in New York City block resampled from historical
observations at the same location and superimposed on monthly mean projections for a single model
(GFDL-CM3) and scenario (RCP8.5) drawn from (A). (C-H) Examples of composite (posterior) county-
level dose-response functions derived from nonlinear Bayesian meta-analysis of empirical studies based
on selection criteria in (30). Median estimate is black, central 95% credible interval is blue-grey. To con-
struct probabilistic impact projections, responses for each category are independently resampled from
each distribution of possible response functions and combined with resampled climate realizations, as in
(A), and weather realizations, as in (B). Estimated causal effect of (C) 24 hr temperature and (D) seasonal
rainfall on maize yields; (E) daily average temperature on all-cause mortality 45-64 yr old population;
(F) daily maximum temperature on daily labor supply in “high-risk” industries exposed to outdoor tem-
peratures; daily maximum temperature on daily (G) violent crime rates and (H) electricity demand. All
sources are detailed in SOM B. 21
Figure 2: Spatial distributions of projected damages. County-level median values for average 2080-
2099 RCP8.5 impacts using median dose-response functions. Impact changes are changes relative to
counterfactual “no additional climate change” trajectories. Color indicates magnitude of impact in me-
dian projection, outline color indicates level of agreement across projections (thin white outline: inner
66% of projections disagree in sign; no outline: 83% of projections agree in sign; black outline: 95%
agree in sign; thick white outline: state borders; maps without outlines shown in Figure S2). Negative
damages indicate economic gains. (A) Percent change in yields, area-weighted average for maize, wheat,
soybeans, and cotton. (B) Changes in all-cause mortality rates, across all age groups. (C) Change in
electricity demand. (D) Change in labor supply of full-time equivalent workers for low risk jobs where
workers are minimally exposed to outdoor temperature. (E) Same as (D) except for high risk jobs where
workers are heavily exposed to outdoor temperatures. (F) Change in damages from coastal storms. (G)
Changes in violent crime rates. (H) Changes in property crime rates. (I) Median total direct economic
damage across all sectors (A)-(H).
% change, average 2080-2099
1Low-risk Labor
1High-risk Labor
8Violent Crime
Temperature change (oC)
2080-2099 relative to 1980-2010
% change, average 2080-2099
2Property Crime
Change in deaths /100,k, average 2080-2099
120 Mortality
2080-2099 relative to 1851-1900 2080-2099 relative to 1851-1900
40 Agricultural Yields
without CO2 fertilization
% change, average 2080-2099
40 Agricultural Yields
% change, average 2080-2099
50 Electricity Demand
Temperature change (oC)
2080-2099 relative to 1980-2010
Figure 3: Probabilistic national aggregate damage functions by sector. Dot-whiskers indicate the
distribution of direct damages in 2080-2099 (averaged) for multiple realizations of each combination
of climate models and scenario projection (dot=median, dark line=inner 66% credible interval, medium
line=inner 90%, light line=inner 95%). Green are RCP2.6, yellow from RCP4.5, red from RCP8.5.
Distributions are located on the horizontal axis according to GMST change realized in each model-
scenario combination (blue axis is change relative to pre-industrial). Black lines are restricted cubic
spline regressions through median values and grey shaded regions are bounded (above and below) by
restricted cubic spline regressions through the 5th and 95th quantiles of each distribution, all of which
are restricted to intercept the origin. (A) Total agricultural impact accounting for temperature, rainfall,
and CO2fertilization (CO2concentration is uniform within each RCP, causing discontinuities across
scenarios), (B) without CO2effect. (C) All-cause mortality for all ages. (D) Electricity demand used
in process model, which does not resample statistical uncertainty (see SOM G). Labor supply for (E)
low-risk and (F) high-risk worker groups. (G) Property crime rates and (H) violent crime rates.
Damages (% of Gross State Product)
Current storm activity
Plus median MSL rise
Plus 1-in-20 MSL rise
Plus 1-in-100 MSL rise
Texas New York S. Carolina Louisiana Florida
Fy = 0.0008x2 + 0.2297x
0 50 100 150 200
Change in expected annual storm damages
(% of Gross Domestic Product)
Global mean sea level rise (cm)
2010 2030 2050 2070 2090
Damages (% of Gross Domestic Product)
Projected storms
Historical storms
Historical storms
historical sea level
y = 5.36×10-6x2 + 0.00154x
Figure 4: Economic costs of sea level rise interacting with cyclones. (A) Example 100-year floodplain
in Miami, FL under median sea level rise for RCP8.5, assuming no change in tropical cyclone activity.
(B) Same, but accounting for projected changes in tropical cyclone activity. (C) Same as (A) but for New
York, NY. (D) Same as (B) but for New York, NY. (E) Annual average direct property damages from
tropical cyclones and extratropical cyclones in five most affected states, assuming installed infrastructure
and cyclone activity is held fixed at current levels. Bars indicate capital losses under current sea level,
median, 95th-percentile and 99.5th-percentile sea level rise in RCP8.5 in 2100. (F) Nationally aggregated
additional annual damages above historical vs. global mean sea level rise holding storm frequency fixed.
(G) Annual average direct property damages nationally aggregated in RCP8.5 assuming historical and
projected tropical cyclone activity with mean sea level rise in both cases. Historical storm damage is
dashed line.
Figure 5: Estimates of total direct economic damage from climate change. (A) Total direct dam-
age to US economy, summed across all assessed sectors, as a function of global mean temperature
change. Dot-whisker markers as in Figure 3. Black line is quadratic regression through all simula-
tions (damage =0.283 GMST +0.146 GM ST 2), shaded region is bounded by quantile
regressions through 5th and 95th percentiles. Alternative polynomial forms and statistical uncertainty
reported in Figure S14 and Tables S16-S17. (B) Contributions to median estimate of aggregate damage
by impact category. (Note coastal impacts do not scale with temperature.) (C) Probability distribution
damage in each of 3,143 US counties as fraction of county income, ordered by current county income.
Dots=median, dark whiskers=inner 66% credible interval, light whiskers=inner 90%. (D) Distributions
of GDP loss compared to direct damages when CGE model is forced by direct damages each period.
Black line=median (labeled), boxes=IQ range, dots=outliers. Energy, Ag., Labor, and Mortality indicate
comparisons when model is forced by damages only in the specified sector and GDP losses are compared
to direct damages in that sector under the same forcing. (Note CGE mortality only affects GDP through
lost earnings but direct mortality damages in (A)-(C) account for non-market VSL.) All indicates ratio
of total costs (excluding mortality for consistency) in complete simulations where all sectors in CGE are
forced by direct damages simultaneously. 25
Supplementary Materials
“Estimating Economic Damage in the United States
from Climate Change”
Solomon Hsiang, Robert Kopp, Amir Jina, James Rising, Michael Delgado,
Shashank Mohan, D.J. Rasmussen, Robert Muir-Wood, Paul Wilson,
Michael Oppenheimer, Kate Larsen and Trevor Houser
Table of Contents
A Materials and Methods Overview 2
B Micro-founding climate impacts with econometric results 6
C Meta-analysis approach 17
D Applying climate projections to econometric dose-response functions 20
E Probabilistic and aggregated econometrically-derived impacts 25
F Decomposition of uncertainty for econometrically-derived impacts 30
G Energy impact modeling 37
H Coastal impact calculations 42
I Valuation of direct damages by sector 50
J Damage function calculation 52
K Valuing risk and inequality for total direct damages 66
L Evaluation and comparison of CGE model results 69
Authors’ Note: This analysis builds on the technical analysis developed in our 2015 book “Economic
Risks of Climate Change” (41) which in turn built on the proposed research program described in the
2013 conference paper “Empirically calibrating damage functions and considering stochasticity when
integrated assessment models are used as decision tools” by Kopp, Hsiang and Oppenheimer (15). The
work presented in the current Research Article represents new analysis and results that were not contained
in either earlier text and which ultimately operationalizes the goals we outlined in the 2013 conference
A Materials and Methods Overview
Climate model integration Probabilistic projections of daily temperature and precipitation were pro-
duced with the Surrogate/Model Mixed Ensemble (SMME) method (19, 41), which employs probabilis-
tic projections of GMST change produced using a simple climate model (SCM) to weight the gridded
temperature/precipitation projections from a multi-model ensemble of downscaled GCM output, and em-
ploys linear pattern scaling (54) to produce ‘model surrogates’ that cover portions of the SCM-derived
GMST probability distribution not present in the GCM ensemble (spatial patterns of temperature shown
in Figure 1A, precipitation shown in Figure S1). SCM temperature projections were produced using the
MAGICC6 (55, 56), forced with Representative Concentration Pathway emissions (20) and with equi-
librium climate sensitivity calibrated to match the assessment of ref. (57). The multi-model downscaled
GCM ensemble (58) was produced using the Bias-Correction/Statistical Disaggregation method of GCMs
participating in the Coupled Model Intercomparison Project (CMIP) Phase 5 project (21). In contrast to
traditional pattern scaling, pattern scaling as employed in SMME to capture tails not represented in
the CMIP5 archive retains unforced climate variability, which can substantially influence year-to-year
weather. To produce station-level projections, model and model surrogate projections are anomalized
with respect to their own historical records and then are added to observed temperature and precipita-
tion normals (1981-2010) at stations from the Global Historical Climatology Network (GHCN) (59).
Monthly averages are temporally disaggregated into daily realizations using historical weather variabil-
ity (60). Each county is assigned station-level projections that are nearest its geographic centroid.
precipitation percent change (%)
2080-2099 Global mean temperature anomaly (ºC)
-30% 30%0%-15% 15%
Supplementary Figure S1: Distribution of Surrogate/Model Mixed Ensemble of precipitation projec-
tions as function of GMST anomaly. 44 climate models (solid maps) and model surrogates (dimmed
maps) are weighted so the distribution of the 2080–2099 GMST anomaly exhibited by weighted models
matches the probability distribution of estimated GMST response (blue-grey line) under RCP8.5. Anal-
ogous display for temperature in Figure 1A.
Econometrically-derived impact integration Fifteen impacts are calculated using twenty-six dose-
response functions from empirical econometric analyses that met specific methodological and sample
criteria, in some cases with additional analyses from personal communication with authors (details in
SOM B). Dose-responses functions are conditional probability distributions, p(I|Tavg,T
min,P), for
an impact Iand daily mean (Tavg ), maximum (Tmax), and minimum (Tmin ) temperatures and precipitation
(P). In cases where multiple estimates are available, we combine them for each set of conditioning
variables values using hierarchical Bayesian modeling (61). We developed an collaborative online tool
for this meta-analysis technique ( to crowdsource future empirical
analyses, facilitating updates to these results. See Sections B-C.
Projection calculation Impacts are calculated from the dose-response functions at the county-level
for each year and reported as changes from 2012. In each RCP scenario, Monte Carlo (MC) sampling
is used to account for uncertainty in climate realization uncertainty (RCP2.6: 29 climate realizations,
Supplementary Figure S2: Spatial distributions of projected median damages by sector. Same as
Figure 2 in main text for median projections, but without significance levels indicated. County-level
median values for average 2080-2099 RCP8.5 impacts using median dose-response functions. Impact
changes are changes relative to counterfactual “no additional climate change” trajectories. Color indicates
magnitude of impact in median projection. Negative damages indicate economic gains. (A) Percent
change in yields, area-weighted average for maize, wheat, soybeans, and cotton. (B) Changes in all-
cause mortality rates, across all age groups. (C) Change in electricity demand. (D) Change in labor
supply of full-time equivalent workers for low risk jobs where workers are minimally exposed to outdoor
temperature. (E) Same as (D) except for high risk jobs where workers are heavily exposed to outdoor
temperatures. (F) Change in damages from coastal storms. (G) Changes in violent crime rates. (H)
Changes in property crime rates. (I) Median total direct economic damage across all sectors (A)-(H).
RCP4.5: 43, RCP8.5: 44), within-month weather uncertainty (10 draws), and econometric uncertainty
(25 quantiles). Thus, we calculate 116 10 25 = 29,000 possible values for each of the 15 impacts
in each of 3,143 counties in each year 2000–2099 (distributions of end-of-century impacts in counties
shown in Figure 2 and median projections shown in Figure S2). State and national impacts are weighted
averages over counties. Impact distributions are computed as empirical distribution functions. See SOM
Uncertainty decomposition Within RCP8.5, the climate realization, within-month weather draw, and
dose-response function quantile are sources of uncertainty. We calculate the variance across impacts,
varying each of these three individually and holding the others at a baseline. The interaction component
in Figure S6 is the total variance minus the sum of the remaining variances. Mathematical derivations are
in Section F.
Energy impacts The direct costs and benefits of climate-driven change in energy demand were as-
sessed using RHG-NEMS, a version of the National Energy Modeling System (NEMS), developed by the
U.S. Energy Information Administration (62), maintained by the Rhodium Group (RHG). RHG-NEMS
is a detailed, multi-sector, bottom-up model of U.S. energy supply and demand linking residential, com-
mercial, and industrial demand, electricity and primary energy supply, and macroeconomic feedbacks,
among other factors. Because of the complexity and run time of RHG-NEMS, we used representative
climate scenarios to construct region-specific response functions linking energy expenditures to changes
in climate. These impact functions were applied to compute county-level heating degree-day and cooling
degree-day data and were then aggregated using spatially-explicit energy expenditure data (63, 64). See
Section G.
Coastal impacts Damages from MSL interacting with cyclones are computed using the Risk Man-
agement Solutions (RMS) North Atlantic Hurricane Model and U.S. Winter Storm Model. Stochastic
spatial Markov models semi-parametrically fitted to historical storm tract data (34) are used to construct
a large ensemble of storm tracks, including genesis and lysis. For tropical cyclones, analytical wind
field profiles (32) are used to compute 10-meter, three-second peak gusts on a variable resolution grid
for each storm. Wind and pressure fields, over the lifetime of the storm, are used to force the MIKE 21
hydrodynamic model system (33) to estimate storm surges and wave impacts. Damages from both wind
fields and storm surges are estimated based on engineering-based models of vulnerability calibrated to
historical statistical relationships between exposure and historical damage, where the location, elevation,
and value of exposed assets are drawn from a proprietary RMS data base of all individual buildings along
the Atlantic Coast. Impacts of MSL are simulated by imposing MSL projections derived from ref. (36)
and differencing storm losses from simulations without MSL. Changes in hurricane frequency and inten-
sity are accounted for by adjusting the rate of storm genesis and intensification to match distributions of
tropical cyclone projections from ref. (35) for RCP8.5 and (65) for RCP4.5, and then differencing losses
from baseline simulations. See Section H.
Aggregate damage function construction Total damages in each sector and each daily projection are
valued and aggregated nationally. Each of these aggregate outcomes are then indexed against GMST
in the corresponding climate realization. OLS or quantile regressions are used to characterize the joint
distribution of aggregate impact realizations and GMST across the three RCPs. The procedure is simi-
larly implemented for total direct damages to compute the aggregate economy-wide damage function. It
is then possible to adjust this damage function to account for social valuations of risk and inequality. See
Sections I-K.
Dynamic computable general equilibrium modeling Temporal dynamics and general equilibrium ef-
fects of direct damages were modeled using a dynamic recursive computable general equilibrium (CGE)
model, the RHG Model of the U.S. Economy (MUSE) (41). The model is calibrated using 2011 so-
cial accounting matrices (66) and solves for market-clearing prices and quantities simultaneously at the
NCA-region level for multiple production sectors, households, and government agents. The model tracks
investment by region and sector and tracks changes in productivity, age-specific population, and capital
stock by vintage, region, and sector over time. Energy expenditure and labor productivity impacts are
implemented as changes in input factor productivity for producers and consumers using these goods.
Agricultural yield impacts are represented as changes in the output productivity of the relevant agricul-
tural goods, after storage is accounted for using an empirical auto-regressive model. Coastal damages
are represented as reductions in vintaged capital stock and mortality affects the time series of population
projection for the age cohorts in which deaths (or reductions in deaths) occur. See Section L.
B Micro-founding climate impacts with econometric results
We develop empirical, micro-founded sector-specific damage functions for a number of sectors seen to be
economically important. These comprise agriculture, crime, health, labor, and electricity demand. Within
each sector, we draw on statistical studies that robustly account for a number of potential confounding
factors when trying to identify the impacts of climate. Numerous high-quality and insightful studies are
omitted from our analysis because they did not meet all of our criteria, although many studies were used
to confirm the validity reported findings of the selected studies. Notably, however, we have designed
our approach to be dynamically inclusive in the long-run by building a system for crowd-sourced meta-
analysis and collaboration. Incorporating each study took considerable effort, often requiring new data,
efforts on the part of the original authors and ourselves to rerun analyses, and extensive discussions to
ensure an accurate interpretation of results. In this process, we are indebted to the authors of the analyzed
We applied the following criteria in assessing studies:
1. Nationally representative. We required that studies be conducted at national level or be drawn
from a representative random sample of the entire US. This was of particular relevance to health
studies. For example, many studies that we considered performed detailed time-series analysis of
single or multiple cities (e.g., (67); (68)). While these were high-quality studies, inclusion would
have required either a weighting scheme based on city populations or an assumption of national
2. Analyze recent time-periods in US history. As we are concerned with potential effects of adap-
tation, we preferred studies that identified effects as close to the present as possible.
3. Robust to unobserved factors that differ across spatial units (jurisdictions, counties, or states).
We placed an emphasis on studies that were able to control for unobservable differences between
spatial units of analysis with the inclusion of fixed effects. This required the use of longitudinal or
panel data, as cross-sectional comparisons between could suffer from omitted variable bias.
4. Identify responses to high-frequency (daily or weekly) climate variables. The importance of
using high-frequency data to estimate climate impacts is demonstrated by all papers included,
building on early work by (50), and in one case finding large effects by considering sub-daily
temperature responses (22).
5. Identify responses to the full distribution of temperature and rainfall measures. Many studies
looked at single climatic events, or parts of the temperature or rainfall distribution (e.g., heatwaves
in (69)). As we are modeling annual impacts, we chose only those studies that included the full
distribution of realised climate outcomes, and ensured the validity of results by comparison to
numerous studies looking at single phenomena or sub-populations.
6. Account for seasonal patterns and trends in the outcomes. Cyclicity and seasonality of re-
sponses to climate forcings are sources of major concern, so we selected only those studies that
robustly accounted for seasonal patterns and time trends in their analysis.
7. Ecologically valid. We required studies to be valid for real-life circumstances and levels of ex-
posure, which led us to prefer studies that were quasi-experimental in design, using observational
data. For example, in the case of labor, numerous laboratory studies exist on the intensive mar-
gin effects of temperature upon productivity (e.g., (70)). As these raised a question of ecological
validity when applied to the labor sector, we chose to not include them.
Many of the impacts of climate change will unfold over years, but distinguishing between the role of
climate change and the role of social, technological, and economic evolution is very difficult over any
long time horizon. Our criteria for selecting studies requires that long-term trends are accounted for and
are not reflected in the measured impact response functions. As a result, the impacts that we measure
are from idiosyncratic distortions in the weather distribution that are orthogonal to long-term trends (13).
This approach has both strengths and weaknesses. Its key strength is that it clearly identifies the impacts
of weather as distinct from longer-term changes. Importantly, it only requires the weakest form of the
unit homogeneity assumption among all approaches used to measure climate impacts empirically (13).
However, it may miss many of the long-term impacts of climate change, such as impacts on groundwater
Numerous previous authors have incorrectly stated that this approach only identifies the effect of
weather and not the effect of climate. The assumptions necessary for these studies to be valid are derived
and analyzed in (13). Notably, the key assumption for these approaches to be valid is the marginal treat-
ment comparability assumption, which requires that “the effect of a marginal change in the distribution
of weather (relative to expectation) is the same as the effect of an analogous marginal change in the cli-
mate” (13). We refer readers interested in this method and discussions or tests of necessary assumptions
to (13).
We identify a number of studies using panel data to isolate the variation within the relevant spatial
unit, while controlling for unobservable difference between units. Estimates from each of the studies
were combined, as detailed in section C. We have been conservative in our choice of studies for the
current analysis, using only studies which we think most credibly identify the impact of climate upon
specific outcomes in each sector. However, our approach allows for future studies to be incorporated,
introducing new findings, and modifying the current results. The following is a complete list of empirical
response functions used in this study, with detailed discussion of each of the studies beneath:
Agriculture Maize yields vs. temperature (East)
Maize yields vs. temperature (West)
Maize yields vs. precipitation (East)
Maize yields vs. precipitation (West)
Wheat yield vs. temperature
Soybean yields vs. temperature (East)
Soybean yields vs. temperature (West)
Soybean yields vs. precipitation (East)
Soybean yields vs. precipitation (West)
Cotton yields vs. temperature
Cotton yields vs. precipitation
Maize yields vs. 100ppm CO2increase
Wheat yields vs. 100ppm CO2increase
Soybean yields vs. 100ppm CO2increase
Cotton yields vs. 100ppm CO2increase
Crime Violent crime vs. temperature
Violent crime vs. precipitation
Property crime vs. temperature
Property crime vs. precipitation
Health Mortality vs. temperature (all age)
Mortality vs. temperature (younger than 1 year)
Mortality vs. temperature (1 - 44 years)
Mortality vs. temperature (45 - 64 years)
Mortality vs. temperature (65 years and up)
Labor Hours worked in high-risk industries vs. tempera-
Hours worked in low-risk industries vs. temperature
B.1 Agriculture
Schlenker and Roberts (22)
Outcome data: Yields for maize, soybeans, and cotton from US Department of Agriculture Na-
tional Agricultural Statistical Service.
Climate data: PRISM temperature and rainfall, spatially and temporally interpolated from station
data to daily resolution in each county.
Sample period: 1950-2009
Sample unit: County-years, for counties with recorded yields of maize, soybeans, or cotton
Methodology: Piecewise linear response of log(yield) to cumulative temperature (degree days)
and polynomial response to precipitation (seasonal total), controlling for county
fixed effects and state-specific quadratic trends. Piecewise linear models are spe-
cific to each crop type, with thresholds that capture the beneficial effects of tem-
peratures below a certain point, and the deleterious effects above.
Result: Modified version of (22) (SI Appendix, p. 9, fig. A3; and p. 20, fig. 10).
Impact function: We contacted the authors of the study to select a preferred response function from
the multiple methods they had employed, selecting a piecewise-linear specification
using degree days for temperature and seasonal total precipitation. We obtained
impact functions for each of the three crops studied, for both temperature and pre-
cipitation. The authors note the distinct difference in response between counties
to the east and west of the 100th meridian for maize and soybeans, so we obtained
separate response functions in for these regions. On December 19th , 2013, we were
sent a complete list of response functions that were updated span the time period
up to and including 2011 (as presented in (71)).
Hsiang, Lobell, Roberts, and Schlenker (72)
Outcome data: USDA-NASS
Climate data: University of Delaware monthly temperature and precipitation
Sample period: 1950-2007
Sample unit: County-year
Methodology: Non-linear response of log(yield) to crop-specific seasonal average temperature
and precipitation, controlling for county and year fixed effects.
Result: (72) (p. 5).
Impact function: We use the response of wheat to seasonal average temperature presented in the
paper. Results were obtained from the authors. Calorie-weighted averages were
taken between maize and wheat in order to combine results, as detailed in section
McGrath and Lobell (23)
Outcome data: Yield from 1960-2004 from FAOStat.
Climate data: Keeling CO2concentrations and country average P/PET.
Methodology: Process model that develops the response of different crops to carbon dioxide con-
centrations and growing season P/PET from empirical studies. This is then used to
estimate the changes to historical yields under a 100ppm increase in CO2.
Result: (23) (p. 5, fig. 4, obtained US result from authors).
Impact function: We contacted the authors and received estimates of the CO2fertilization relation-
ship with yields of different crops on January 17th, 2014, specifically for the US.
Data were for 8 different crop types. We used an average of all types for cotton
1960 1970 1980 1990 2000 2010
predicted log(consumption)
Supplementary Figure S3: Predicted consumption of maize, modeled as a moving average of produc-
tion. Predicted values compare well to observed consumption, and allow us to project the smoothed
consumption values out to the end of the century.
B.1.1 Storage
In addition to the above impacts on yields, we observe that farmers store crops for sale in the future, and
so the overall impact of climate on supply of crops may appear smoother than if there were no storage.
For our projections, we also make use of Fisher et al. ( (73), Appendix p.xi, table A4) to estimate crop
consumption as a moving average process of crop production. We estimated the following equation for
crop c,
ln(consumption)c,t =
[c,l ln(production)c,tl]+ct+ct2+c,t
where tindexes years and L=2, except for soybeans where L=3, and we account for linear (c)
and quadratic (c) time-trends. Example results of this model are shown in Figure S3. We project the
smoothing of future crops with a time-series structure that incorporates these empirical results on storage.
Weights for each crop are constructed from the lagged coefficients, l, presented in Section D.1.
B.2 Crime
Jacob, Lefgren, and Moretti (26)
Outcome data: FBI National Incident Based Reporting System
Climate data: Weekly temperature and precipitation from the NCDC GHCN-Daily database.
Sample period: 1995-2001
Sample unit: Jurisdiction-weeks
Methodology: Linear response of log(crime rate) to average temperature and precipitation, con-
trolling for jurisdiction-by-year and month fixed effects, as well as jurisdiction-
specific 4th order polynomials in day of year.
Result: Modified version of (26) (p. 508-509, table 2).
Impact function: We obtained data and replication files from the authors and generated coefficients
for a month-long exposure window, to account for displacement of crime, as noted
in the text. The climate variables are at weekly resolution, and in order to make
this comparable to (27) we reran the analysis using maximum temperatures and
then scaled the coefficients in (26). We did this by first dividing the coefficient for
the monthly exposure by 7, to get a daily response, and further by 4 to account
for the lagged climate variables. This resulted in the marginal effect on crime of a
1F increase in daily temperature. Taking a reference point of zero response at a
temperature of 65F (to coincide with the central point of the reference bin of (27))
we derived a linear response of violent crimes and property crimes to temperature
and precipitation.
Ranson (27)
Outcome data: FBI Universal Crime Reporting Data.
Climate data: Daily temperature and precipitation from the NCDC GHCN-Daily database.
Sample period: 1960-2009
Sample unit: County-months
Methodology: Non-linear response of log(crime rate) to maximum temperature and precipitation,
controlling for county-by-year and state-by-month fixed effects. Temperature is
transformed into number of days within 10F bins, with the 60-69F bin as a refer-
ence point.
Result: (27) (p. 9, fig. 4).
Impact function: We contacted the author and received updated estimates of the percentage change
for each of 8 different classes of crimes on March 12th, 2014. To derive response
functions, we grouped these into violent crimes (murder, rape, aggravated assault,
and simple assault) and property crimes (robbery, burglary, larceny, and vehicle
theft), and combined results within each class of crimes.
B.3 Health
Deschenes and Greenstone (24)
Outcome data: National Center for Health Statistics Compressed Mortality Files.
Climate data: Daily temperature and precipitation from NCDC
Sample period: 1968-2002
Sample unit: County-years
Methodology: Non-linear response of mortality to temperature, controlling for county-by-age-
group and state-by-year-by-age-group fixed effects. Temperature is transformed
into number of days in an year-long window within 10F bins, with the 50-59F
bin as a reference point.
Result: Modifed version of (24) (p. 9, fig. 2).
Impact function: We contacted the authors and received estimates on November 5th, 2013. To make
the study comparable to Barreca et al. (25), the main analysis was rerun with
log(mortality) as an outcome.
Barreca, Clay, Deschenes, Greenstone, and Shapiro (25)
Outcome data: Mortality from the Mortality Statistics of the US (pre-1959) and the Multiple Cause
of Death files (post-1959).
Climate data: Daily temperature and precipitation from the NCDC GHCN-Daily database.
Sample period: 1929-2004
Sample unit: State-months
Methodology: Non-linear response of log(mortality) to temperature, controlling for state-by-
month and year-month fixed effects, and state-by-month-specific quadratic time
trends. Temperature is transformed into number of days in a two-month window
within 10F bins, with the 60-69F bin as a reference point.
Result: Modified version of (25) (p. 37, table 3, panel B).
Impact function: We contacted the authors and received estimates on 5th November, 2013. The pre-
ferred specification, to account for forward displacement, was to use monthly mor-
tality with a 2-month exposure window to temperature. We used the estimated
response from 1960-2004. To make this response comparable to the response of
Deschenes and Greenstone (24), the analysis was rerun with the reference point
changed to the 50-59F bin. To scale the coefficients, we divided each coefficient
value by a factor of six. We also obtained age-specific response functions for ages
0-1, 1-44, 45-64, and 65+.
B.4 Labor
Graff Zivin and Neidell (28)
Outcome data: Hours worked from the American Time Use Survey.
Climate data: Daily temperature, precipitation, and humidity from NCDC.
Sample period: 2003-2006
Sample unit: Person-days
Methodology: Seemingly-unrelated regression allowing for correlated errors between time spent
working, or indoor and outdoor leisure. Non-linear response to maximum temper-
atures controlling for county, year-by-month, and day of week fixed effects, as well
as individual level controls. Temperature is transformed into number of days within
5F bins, with the 76-80F bin as a reference point. High-risk sectors of the econ-
omy are defined as Agriculture, Forestry, Fishing and Hunting; Mining, Quarrying,
and Oil and Gas Extraction; Utilities; Construction; and Manufacturing.
Result: High-risk: (28) (p. 15, fig. 3); Low-risk: (28) (p. 16, fig. 4)
Impact function: We contacted the authors prior to publication and received full estimates for high-
risk and low-risk labor responses to temperature on December 18th, 2013.
C Meta-analysis approach
The dose-response functions are treated as probability distributions conditioned on weather variables,
such as temperature and precipitation. In the generic case, denoting weather variables as Hand the
impact on an outcome of interest I, then the dose response function is
where it is understood that (.)is only known with uncertainty. This representation allows us to account
for the range of uncertainty in previously published empirical estimates and motivates meta-analysis to
synthesize previous studies that are uncertain and may not agree perfectly with one another. In this
analysis, we note that some dose-response functions are based on a single study; others combine results
from more than one study.
The impact estimates that combine results from multiple studies apply a Bayesian hierarchical model
structure (61). This approach simultaneously estimates a distribution of possible underlying effect sizes,
as well as a degree of partial pooling. To the extent that the individual study estimates are consistent
with a single underlying effect, their estimates are pooled to accurately estimate the effect. However, to
the extent that the study estimates are inconsistent with each other, the hierarchical model determines a
study-specific idiosyncratic effect. The interpretation of this model averaging procedure is discussed in
detail in the context of climate impact estimation in (30).
Consider a collection of impact functions, zi(i|H), with Hrepresenting weather variables and
i2{1,...,N}indexing independently published results. The variable iis an estimate of a true (un-
observed) parameter ithat characterizes the response for study i. The true parameter combines both
a common effect, reflected by the hyperparameter µ, and a study-specific effect iµ. We wish to
combine the estimates iinto a single generalizable conditional distribution that only captures the effect
that is common across studies, (µ|H). We treat each value of Hindependently, so we will write these
functions as zi(i)and (µ).
The conditional parameter distributions are assumed Gaussian
i|µ, N(µ, 2)
Accordingly, i|µ, N(µ, 2+2
i). We are interested in estimating the underlying hyperparameter µ
and the between-study variance 2, which involves assessing their joint posterior probability distribution
p(µ, |,)=p(µ, )
p(i|µ, ,i)
We apply non-informative uniform priors µUnif (1,1)and Unif(0,1). The values of i
and 2
iare provided by the published studies, and the rest of the parameters are simultaneously estimated.
An analytic solution exists for how to generate draws from the posterior distribution of this hier-
archical model, and is described in chapter 5 of Gelman et al. (61). We approximate the posterior by
producing draws and constructing a histogram for each conditional distribution, as follows. First, we
compute q(|,)/p(|,)on a 100-point grid between 0 and twice the greatest standard error, using
i+2)1/2exp (iˆµ)2
where ˆµ=
i=1 1
i=1 1
and V1
i+2. We then construct the empirical CDF of |,from
these samples, and use the inverse CDF method to create draws from this distribution. For each draw of
, we compute the draws from the conditional posterior distributions µ|,,Nµ, Vµ).
All empirically derived dose-response functions after meta-analysis (where multiple studies were
available) are shown in Figure S4.
0 10 20 30 40
0 0.5 1 1.5
Precipitation (m)
0 10 20 30 40
0 0.5 1 1.5
Precipitation (m)
0 0.5 1 1.5
Precipitation (m)
0 10 20 30 40
0 0.5 1 1.5
Precipitation (m)
0 10 20 30 40
0 0.5 1 1.5
Precipitation (m)
0 10 20 30 40
2 0 2 4 6 8 10
Yield (% change)
6 8 10 12 14 16
Yield (% change)
6 8 10 12 14 16 18
Yield (% change)
6 8 10 12 14 16 18
Yield (% change)
10 0 10 20 30 40
Crime rate (% change)
0 5 10 15 20 25 30
Precipitation (mm)
Crime rate (% change)
10 0 10 20 30 40
Crime rate (% change)
0 5 10 15 20 25 30
Precipitation (mm)
Crime rate (% change)
0 10 20 30
0 10 20 30
10 0 10 20 30
Mortality rate (% change)
10 0 10 20 30
Mortality rate (% change)
10 0 10 20 30
Temperature (oC)
Mortality rate (% change)
10 0 10 20 30
Mortality rate (% change)
10 0 10 20 30
x10 4
Mortality rate (% change)
0 10 20 30 40
Maize vs. TDD (East) Maize vs. P (East) Maize vs. TDD (West) Maize vs. P (West)
Soy vs. P (East) Soy vs. TDD (West) Soy vs. P (West)
Cotton vs. TDD Cotton vs. P Wheat vs. TAVG
Maize vs. 100ppm CO2Soy vs. 100ppm CO2Cotton vs. 100ppm CO2Wheat vs. 100ppm CO2
Property Crime vs. TMAX Property Crime vs. P Violent Crime vs. TMAX Violent Crime vs. P
Highrisk Labor vs. TMAX
Lowrisk Labor vs. TMAX
Mortality vs. TAVG
Mortality (01) vs. TAVG Mortality (144) vs. TAVG
Mortality (4564) vs. TAVG Mortality (65+) vs. TAVG
Soy vs. TDD (East)
x10 3
x10 4
x10 4
x10 3
Temperature (oC)
Temperature (oC)
Temperature (oC)
Temperature (oC) Temperature (oC)
Temperature (oC)
Temperature (oC) Temperature (oC)
Temperature (oC) Temperature (oC)
Temperature (oC)
Temperature (oC)
Temperature (oC) Temperature (oC)
Supplementary Figure S4: All 26 dose-response functions used in our analysis, following Baysian
model averaging in cases where multiple findings are reported. Solid lines are medians of the condi-
tional posterior, 95% credible intervals are shaded.
D Applying climate projections to econometric dose-response func-
For each county and each year, we apply the full range of climate realizations and weather projections
for each RCP scenario to the 26 composite (posterior) dose-response functions for each sector (shown in
Figure S4) for each day of each projection, accounting for the statistical uncertainty in the dose-response
functions. For a given outcome, the impact Ifor county jin year tdepends on
the RCP scenario r
the climate realization m
the daily projection w, and
the empirical quantile of the dose-response function k.
Weather realizations are resolved for each day d, where d2tdenotes days that occur in year t. We apply
the weather variables Hrmw
j,d2tto each composite dose-response function (.)to recover annual impacts for
a given county:
jt =µk|Hrmw
where the superscripts denote the state of the world (RCP scenario-by-climate realization-by-weather
projection-by-quantile) in a specific projection and subscripts denote the time (year) and place (county)
for which the outcome is recorded.
In total, we build projections for three RCP scenarios (2.6, 4.5 and 8.5) which each have a large num-
ber of climate realizations that are the climate models and climate model surrogates used to reconstruct
the distribution of GMST change (29 climate realizations for RCP 2.6, 43 for RCP 4.5 and 44 for RCP
8.5) for a total of 116 climate realizations. The differing number of climate realizations reflects the dif-
ferent numbers of modeling teams that generated climate forecasts for the CMIP5 scenarios. Note that
within each RCP, each climate realization is assigned a weight rm so that the full weighted distribution
of realizations mirrors the distribution of climate sensitivities (19, 41) (recall Figure 1A). Each climate
realization is utilized to construct ten daily projections by resampling daily weather residuals (relative to
monthly climatologies) from the historical record in yearly blocks (to ensure autocorrelation structures
are preserved). We then implement Monte Carlo resampling (described further below) of the empirical
response functions to construct twenty five versions of each of the 26 dose-response functions, indexed
by k, for each daily projection. Thus, we calculate 116 10 25 = 29,000 possible values for each of
the 15 impacts in each of the 3,143 counties in each year (2013-2099). These possible future impacts for
each county-year represent a range of outcomes for each location and each moment in time, which we
use to construct conditional probability distributions for outcomes at those locations and times (described
in Section E).
Monte Carlo Our Monte Carlo approach captures the full range of uncertainty in dose-response func-
tion estimates, under the assumption that each function is independent (in the sense of its statistical
uncertainty). We randomly select quantiles, indexed by k, for each of the 26 empirical distributions
shown in Figure S4. (When specified, such as when we analyze uncertainty, only the median quantile is
used for all or some of these dose response functions.) The ordinality of the quantiles is chosen so that
these describe, in essence, low, median, and high impact scenarios. High quantiles correspond to greater
losses in yield and labor productivity, and greater increases in crime and mortality, within the range of
statistical uncertainty. The same quantile is used across the entire range of the conditioning variable. By
evaluating each impact function at a quantile, we generate a single-dimensional, deterministic function
which is used in the evaluation of the impact for each Monte Carlo run.
Below, we explain how Iis computed for each impact, drawing on the structure of results recov-
ered from the literature (Section B) and our meta-analysis (Section C). We use the notation TAV G for
mean daily temperature; TMIN and TMAX for minimum and maximum daily temperature, respectively;
and Pfor for precipitation. f(.)and g(.)are generic notations for functions that are described in each
Note that the impact results for crime, labor productivity, and mortality are all estimated by binning
weather values into discreet bins (13), since this is the model utilized in the previous analyses that we
draw on. In these cases, we construct a continuous impact curve by linearly interpolating between the
midpoints of these bins.
Throughout, impacts are ultimately reported relative to 2012, the baseline year. The definitions of
each impact below do not reflect this.
D.1 Agricultural Yields and Production
Percent changes in agriculture production, relative to 2012, were generated using fixed, county-specific
growing seasons. The growing season, denoted S(j)for county j, is determined using the centroid of
the county applied to the planting and harvesting dates in (74). Denote S(j)\tas the set of days in
year tthat are in the growing season. For maize and wheat, for which (74) provides two calendars (two
croppings for maize, and summer and winter wheat), the calendar that represented the greatest portion of
land area in each county was used.
Relative changes in yield are calculated based on seasonal temperatures and precipitation as follows:
Wheat Wheat uses a seasonal average temperature response function:
Yjt =f0
N(S(j)) X
TAV G,d1
where f(·)is calculated by (72), as a function of average mean daily temperature over the growing
season, and N(S(j)) is the number of days in the growing season for county j. This functional
form was only used for wheat, since a degree-day representation was unavailable.
Cotton Cotton uses a single degree-day function:
Yjt =ef(0.01 Pd2S(j)\tDDlow(TMAX,d,TMIN,d),0.01 Pd2S(j)\tDDhigh(TMAX,d,TMIN,d))+g(1103Pd2S(j)\tPd)
where DDlow and DDhigh are growing degree days below and above the crop-specific breakpoint
specified in (22), and calculated as specified there using the minimum and maximum daily temper-
atures. The functions f(·)and g(·)translate degree days and precipitation, respectively, into yield
Maize and Soybeans Maize and soybeans have two degree-day responses:
Yjt =8
efeast(0.01 Pd2S(j)\tDDlow (TMAX,d,TMIN,d),0.01 Pd2S(j)\tDDhigh(TMAX,d,TMIN,d))+geast(1 103Pd2S(j)\tPd)
efwest(0.01 Pd2S(j)\tDDlow (TMAX,d,TMIN,d),0.01 Pd2S(j)\tDDhigh(TMAX,d,TMIN,d))+gwest(1 103Pd2S(j)\tPd)
Here, feast(·)and geast(·)are used to the east of the 100th meridian, excluding Florida. In this
areas, irrigation is less common and the response to increased temperatures is more extreme.
CO2fertilization is modeled as a multiplicative factor applied to yields, and estimated as a linear
increase for each additional 100 ppm of CO2:
jt =Yjt 1+[CO2]t[CO2]2012
where [CO2]tis the CO2concentration in year tunder a given RCP, and is the estimated CO2fertiliza-
tion effect, which varies from 3% to 12% depending on the crop, from (23). (23) does not provide a value
for cotton, so the Bayesian combination of all provided crop effects is used for it.
As explained in Section B.1.1, economic output from the agricultural sector is not synonymous with
yield due to storage. For each crop, we model output as a distributed lag function of yields
Ijt =
where the coefficients Lare estimated from USDA data following (73) and described in Section B.1.1.
This leads to output that is less variable than yields (recall Figure S3).
D.2 Crime
Both violent and property crime are calculated as,
Ijt = 1+0.01 1
12 X
f(TMAX,d)! 1+0.01 1
12 X
where d2tis the set of days in year t,f(·)is a function of daily maximum temperature, and g(·)is a
function of daily precipitation. Both f(·)and g(·)are calculated as a Bayesian combination of the effect
for each sub-category of crime estimated by (27) and the average effect for violent or property crime
from (26).
D.3 Mortality
Both average and age-specific mortalities are calculated as,
Ijt =X
f(TAV G,d)
The parameters of f(·)are calculated as a Bayesian combination of the results from (24) and a corrected
form of (25). Age-specific mortalities, for newborns, ages 1-44, ages 45-64, and ages 65 and up, are
provided by (25).
Mortality is reported both as percentage changes, and as differences in the mortality rate. In either
case, the pooled and age-specific mortality rates per county are from (75).
D.4 Labor Productivity
High-risk sectors of the economy are defined as Agriculture, Forestry, Fishing and Hunting; Mining,
Quarrying, and Oil and Gas Extraction; Utilities; Construction; and Manufacturing. All others are con-
sidered low-risk. The structure of the labor productivity calculation is identical for high-risk and low-risk
Ijt =H+1
60 Pd2tf(TMAX,d)
where his the average number of hours worked per year in the baseline. For high-risk labor, h=
7.67 365, and for low-risk labor, h=6.92 365. The parameters of f(·)are provided by (28).
Supplementary Figure S5: Results were aggregated from county level to the modified NCA region level
(one color per region) for passing to the CGE model (Alaska and Hawaii were not included in the CGE
model results or national estimates, though impact results were calculated for them). Counties where
coastal damages from storm surge and sea level rise are calculated are darkened.
E Probabilistic and aggregated econometrically-derived impacts
Within each RCP, climate realizations are weighted to capture the distribution of GMST changes, as
described in (19). This allows the weighted distribution of projected outcomes to be interpreted as a
probability distribution. This adjustment is important because climate model ensemble members are
each individually “best guesses” and cannot be interpreted as unconditional independent draws from a
true underlying probability distribution.
The probability distribution of impact Ifor a county jin year tfor RCP scenario ris constructed by
computing an empirical CDF for all the possible future realizations. When rm is the weight assigned
climate realization min RCP rby (19) (constraining Pmrm =1) then the CDF is
it I]
where ¯m, the maximum index for m, is 29 for RCP 2.5, 43 for RCP 4.5, and 44 for RCP 8.5. Here,
1[.]is the indicator function that is equal to one if the statement inside the brackets is true and zero
otherwise. We are thus able to compute a full probability distribution of impacts for each county in
each year, conditional on the emissions scenario. An identical calculation can be implemented for larger
spatial units after aggregation, the only alteration to the calculation is that the index jis replaced by an
index for the more aggregated spatial unit (e.g., state).
Probability distributions for nationally aggregated impacts are reported in Table S1.
For many calculations, including the construction of national damage functions, impacts must be
aggregated to a larger administrative unit than the county level. In the main text, results at the national
level are used for Figures 5A-B, results at county-level are used for Figure 5C, and results at modified
National Climate Assessment (NCA) region are used to calibrate damages in the CGE model used for
Figure 5D. NCA region definitions used for the CGE model are shown in Figure S5 (note that due to
the implementation of separate coastal damages in the CGE model, coastal NCA regions are split into a
coastal portion and an inland portion).
To aggregate county-level impacts for impact Iin state of the world {rmwk}where Jis the set of
counties in the larger administrative units (Jis the set of all counties in the national aggregate case), then
the aggregated impact for year tis the weighted sum
Jt =Pj2J!jIrmwk
where the weights must be chosen so that Irmwk
Jt is a nationally meaningful number. Below we describe
how the weights !jare selected for each sector.
E.1 Crop impacts aggregation
Following (76), grains yields (maize and wheat) are combined within the same county and aggregated to
higher scales based on calorie totals. Within each county, the average impact is,
jt =Iwheat
jt Awheat
jCwheat +Imaize
jt Amaize
jCwheat +Amaize
where Awheat
jis the average acres of wheat planted between 2000 - 2005, and Amaize
jis the average
acres for maize. Cwheat and Cmaize, the calorie density of wheat and maize, are 1690 calories/kg and
1615 calories/kg, respectively. The weighting of each county result for aggregation to larger administra-
tive units is
jCwheat +Amaize
For cotton and soybean results, weights are simply the total area planted, as averaged over 2000 -
Because the impacts Iin agriculture are yield changes, this approach recovers national average yields
(calorie yields in the case of grains). To see this, denote yields yand note that national average yields in
the baseline are
national yieldspre =PjAjyj
since total national production is PjAjyj. After a change due to climate, national yields will be
national yieldspost =PjAj(yj+yj)
=national yieldspre +PjAjyj
Thus, since Ij=yj, then setting !j=Ajrecovers the change in national yields.
E.2 Crime impacts aggregation
Percentage changes in crime are aggregated by setting !jto the number of reported property and violent
crimes from the Uniform Crime Statistics, averaged over 2000 - 2005, and provided for reproduction
of (27). Counties that are not explicitly identified at the county level (of which there are 172) are assigned
the national average rates of property and violent crime.
E.3 Labor impacts aggregation
Labor supply impacts are aggregated by setting !jto the labor employment in each county averaged over
2000 - 2005, as reported by the Bureau of Labor Statistics (77). Following (28), this is done separately
for high-risk industries, consisting of agriculture, forestry, fishing and hunting; mining, quarrying, and
oil and gas extraction; utilities; construction; manufacturing; and transportation and warehousing. All
other industries are considered low-risk. The BLS statistics exclude the counties represented by FIPS
codes 02105, 02195, 02198, 02230, and 02275, since these were created after 2005.
E.4 Mortality impacts aggregation
Mortalities impacts are aggregated by setting !jto the 2010 census populations. All estimates (except for
the NCA region estimates used to drive the CGE model) use total populations and the pooled mortality
dose-response function.
For the aggregation from sub-NCA regions (in Figure S5) to NCA regions used in the analysis, the
census totals for each age are summed into impact cohorts and used for weighting. This procedure is
combined with using the age-specific dose-response functions. Tracking age is important in the CGE
model because the number of years of future foregone earnings are used to value the cost of labor lost to
Supplementary Table S1: Weighted impact result percentiles
RCP 8.5 RCP 4.5 RCP 2.6
Percentiles 5 17 50 83 95 5 17 50 83 95 5 17 50 83 95
Agricultural Yields (%)
2080-2099 -55.6 -41.7 -15.3 11.9 18.8 -43.1 -24.5 -3.4 6.1 10.4 -16.6 -11.5 -1.2 3.5 5.0
2040-2059 -19.7 -14.3 -3.3 7.4 11.8 -18.9 -12.7 -0.9 5.5 8.5 -13.1 -8.5 -1.8 3.2 5.3
2020-2039 -9.2 -6.5 -1.8 7.1 11.0 -11.3 -8.4 -0.6 6.2 9.2 -12.8 -6.9 -2.0 1.1 3.2
Agricultural Yields (%)
(w/o CO2fertilization)
2080-2099 -69.1 -59.2 -40.0 -19.5 -15.5 -49.8 -33.3 -14.4 -6.0 -2.0 -19.1 -14.2 -4.3 0.4 1.7
2040-2059 -28.8 -24.0 -14.3 -4.8 -0.9 -25.1 -19.4 -8.4 -2.5 0.3 -16.8 -12.5 -6.0 -1.2 0.7
2020-2039 -13.3 -10.7 -6.3 2.3 6.0 -14.3 -11.5 -4.1 2.5 5.4 -15.5 -9.8 -5.0 -1.9 0.1
High Risk Labor (%)
2080-2099 -3.2 -2.4 -1.4 -0.8 -0.6 -1.6 -1.1 -0.6 -0.2 -0.1 -0.6 -0.4 -0.3 -0.1 0.1
2040-2059 -1.1 -0.9 -0.5 -0.2 -0.1 -0.9 -0.7 -0.4 -0.1 0.0 -0.5 -0.4 -0.3 -0.1 0.1
2020-2039 -0.5 -0.4 -0.1 0.0 0.1 -0.5 -0.4 -0.2 0.0 0.2 -0.4 -0.3 -0.2 -0.1 0.1
Low Risk Labor (%)
2080-2099 -0.8 -0.5 -0.2 -0.1 0.0 -0.3 -0.2 -0.1 0.0 0.0 -0.1 -0.1 0.0 0.0 0.1
2040-2059 -0.2 -0.2 -0.1 0.0 0.0 -0.2 -0.1 -0.1 0.0 0.0 -0.1 -0.1 0.0 0.0 0.0
2020-2039 -0.1 -0.1 0.0 0.0 0.0 -0.1 -0.1 0.0 0.0 0.1 -0.1 -0.1 0.0 0.0 0.1
Mortality (per 100,000 yr1)
2080-2099 0.6 3.7 9.5 20.8 35.6 -4.5 -2.5 1.0 5.9 11.9 -3.9 -2.3 0.8 3.2 5.0
2040-2059 -2.8 -0.5 2.9 6.6 10.1 -5.0 -3.2 -0.1 3.9 7.4 -3.3 -1.8 0.9 3.4 5.5
2020-2039 -3.4 -1.7 1.5 4.2 6.1 -5.1 -3.3 -0.6 2.3 5.5 -3.2 -1.8 1.2 3.0 5.7
Property Crime (%)
2080-2099 0.3 0.4 0.7 1.0 1.1 0.0 0.1 0.5 0.9 1.0 -0.2 -0.1 0.2 0.5 0.7
2040-2059 -0.1 0.1 0.3 0.6 0.8 -0.1 0.0 0.4 0.7 0.8 -0.1 -0.1 0.2 0.5 0.6
2020-2039 -0.3 -0.1 0.0 0.4 0.5 -0.2 -0.1 0.2 0.5 0.6 -0.2 -0.1 0.1 0.3 0.4
Violent Crime (%)
2080-2099 1.7 1.9 3.0 4.5 5.4 0.2 0.6 1.5 2.5 3.2 -0.2 -0.1 0.6 1.3 1.5
2040-2059 0.3 0.6 1.2 2.1 2.5 0.0 0.2 1.1 1.8 2.0 -0.2 0.2 0.7 1.1 1.5
2020-2039 -0.5 0.0 0.4 1.1 1.4 -0.4 0.0 0.6 1.1 1.3 -0.2 0.0 0.4 0.8 1.0
climate weather dose-response interaction
0 200 400 600 800 1000
Variance (% baseline)
0 1 2 3 4 5
Variance (% baseline)
all age
age >64
age 45-64
age 1-44
age <1
0 .5 1 1.5
Variance (% baseline)
0 .2 .4 .6 .8
Variance (% baseline)
low risk
high risk
with CO2
no CO2
Supplementary Figure S6: Decomposing sources of uncertainty for direct impacts. Variance in 2080–
2099 avg. direct impacts attributable to different sources of uncertainty under RCP8.5, identified by
sampling single inputs one at a time while holding other inputs at median values. Units are in percent
change over baseline in 2011 squared, since variances have squared units. “Climate” uncertainty comes
from uncertainty in GMST and in the expected spatiotemporal distribution of weather conditional upon
GMST, across climate realizations. “Weather” uncertainty comes from random within-month variations
in weather that differ across daily projections within a climate realization. “Dose-response” uncertainty
comes from statistical uncertainty in econometric estimates of dose-response functions. “Interaction”
uncertainty is the residual variance (may be negative) relative to the variance when all factors are sampled
simultaneously, which may be nonzero when nonlinear response functions interact with variance in model
projections. Uncertainty in (A) agricultural impacts, with and without CO2fertilization, (B) heat-related
mortality by age, (C) property and violent crime, (D) labor supply in high-risk and low-risk occupations.
F Decomposition of uncertainty for econometrically-derived impacts
Following the general framework laid out by ref. (43), we evaluate which sources of uncertainty con-
tribute to the overall uncertainty of our projections for econometrically derived impacts in Figure S6.We
focus our attention on understanding the variance
V ar(Ir=RC P 8.5,mwk
where the impacts are aggregated to the national level (J) for the period 2080-2099, as described in
Section E. We restrict our attention to scenario (r) RCP 8.5.
2030 2040 2050 2060 2070 2080 2090
Attributed Variance
Grains (by calorie)
2030 2040 2050 2060 2070 2080 2090
Grains (by calorie), without CO2
2030 2040 2050 2060 2070 2080 2090
Attributed Variance
Mortality, all ages
2030 2040 2050 2060 2070 2080 2090
Soybean yields
2030 2040 2050 2060 2070 2080 2090
Attributed Variance
Source of Variance:
total variance
plus interaction
Soybean yields, without CO2
2030 2040 2050 2060 2070 2080
Cotton yields
2030 2040 2050 2060 2070 2080
Cotton yields, without CO2
2030 2040 2050 2060 2070 2080
Mortality, ages <1
2030 2040 2050 2060 2070 2080 2090
Mortality, ages 144
2030 2040 2050 2060 2070 2080 2090
Mortality, ages 4564
2030 2040 2050 2060 2070 2080 2090
Attributed Variance
Mortality, ages >64
2030 2040 2050 2060 2070 2080 2090
Lowrisk labor productivity
2030 2040 2050 2060 2070 2080 2090
Property crime
2030 2040 2050 2060 2070 2080 2090
Highrisk labor productivity
2030 2040 2050 2060 2070 2080 2090
Violent crime
Supplementary Figure S7: Decomposing sources of uncertainty for damages over time. Same as
Figure S6 but for multiple time periods and normalizing variances to by the sum of variances from climate
models, weather, and econometric uncertainty. Approach is same as ref. (43). Green line indicates the
total variance once the “interaction” component is accounted for. can be read as the difference
between 1 and the green line at each moment, it is possible for <0.
We decompose the variance of impacts for the uncertain state of the world {mwk}into contributions
from the climate realization r, the daily projection w(largely due to within-month weather), and quantile
kin the econometric model. To look at each of these contributions separately, we hold two of these
sources of uncertainty fixed while allowing the third to vary. We do this procedure for each of three
factors, and then compare the sum of these three marginal variances to the total variance. Any difference
between the total variance and the sum of these three variances is attributed to interactions between
sources of uncertainty, which may occur in cases where response functions are nonlinear (derived below).
For the remainder of this section, we omit r,jand tsuper/subscripts for clarity, since they are held fixed
throughout this portion of the analysis.
We are thus interested in decomposing the variance
V ar(Imwk )=V ar(Imwk |m, w)+V ar(Imwk|m, k)+V ar(Imwk|w, k)+
where is the term that emerges from the interaction of different sources of uncertainty. Specifically, we
compute weighted empirical distributions over impacts for each of the following:
Climate uncertainty, V ar(Imwk|w=w0,k =50), from results for each climate realization m,
of which there are 44 under RCP 8.5. We hold the within-month realization of weather used to
construct each daily projection fixed at w0. We hold the empirical quantile kfixed at the median
Within-month weather uncertainty, V ar(Imwk|m=m0,k =50), from 10 realizations of within-
month weather w. We set the fixed climate realization m0to the HadGEM-AO GCM model,
as it recovers scenario that is “near median” by many measures (discussed below). We hold the
empirical quantile kfixed at the median value.
Econometric uncertainty, V ar(Imwk |m=m0,w =w0), from 25 draws of econometric uncertainty
by varying ksystematically. We set the fixed climate realization m0to the HadGEM-AO GCM
model and the weather used to construct each daily projection fixed at w0.
Total uncertainty, V ar(Imwk ), from 11000 impact estimates where we resample from all GCMs,
within-month weather realizations, and draws from the distribution of econometric results.
The interaction term is computed as a residual. These values are computed for each sector and many
subsectors, displayed in Figure S6 for end of century uncertainty, as a fraction of baseline damages. The
evolution of the fractions of total variance driven by climate, weather, econometric uncertainty, and in
projections over the century is shown in Figure S7, following the same approach as in ref. (43).
Below we derive the form of and also check that it correctly relates to values recovered in each
sector in Section F.2. We also explore how these results change if we select a different climate realization
as the benchmark m0.
F.1 Analytical derivation of
To see why has the magnitudes and signs we display in Figure S6, we consider a simplified model where
an outcome Yis a function of mean temperature T. A single parameter Acharacterizes the structure of
the econometrically derived dose-response function. Aand Tare independent random variables. We
compute Y=f(A, T ), and wish to understand V ar(Y)as a function of the distribution of the random
variables Aand T. To do so, we derive the relationships between the following quantities
V ar(Y|A=A0), the climate-driven uncertainty
V ar(Y|T=T0), the econometric-driven uncertainty
V ar(Y), the total uncertainty
where the interaction term is defined as
=V ar(Y)V ar(Y|A=A0)V ar(Y|T=T0).
F.1.1 The linear case
Let Y=+A+T. Then
V ar(Y)=2V ar(A)+2V ar(T)
V ar(Y|A=A0)=2V ar(T)
V ar(Y|T=T0)=2V ar(A)
For this linear case, this result is invariant to the choice of T0and A0. This would imply that in this case
of our actual calculations, the variances will not depend on the choice of GCP used as m0.
F.1.2 The multiplicative case
Let Y=AT , as would be the case for a regressed linear relationship between temperature and an
outcome, with an estimated coefficient A. In this multiplicative case, interacting uncertainty causes the
total variance to differ from the sum of individual uncertainties, and the variance attributable to individual
uncertainties differs depending on the A0and T0.
V ar(Y)=E(A)2V ar(T)+E(T)2V ar(A)+V ar(A)V ar(T)
V ar(Y|A=A0)=A2
0V ar(T)
V ar(Y|T=T0)=T2
0V ar(A)
So the interaction term is
=E(A)2V ar(T)+E(T)2V ar(A)+V ar(A)V ar(T)A2
0V ar(T)T2
0V ar(A)
=V ar(A)V ar(T)+E(A)2A2
0V ar(T)+E(T)2T2
0V ar(A)
If A0=E(A)and T0=E(T), then
=V ar(A)V ar(T)
which is always positive. Note that this interaction term is distinct from the covariance of Aand T, which
is assumed 0.
F.1.3 Nonlinear functions of climate variables
Let Y=Af(T). We derive a general approximation to the variance under any function, show that the
sign of the interaction is negative for sufficiently concave functions, and quantify this relationship in the
special case where f(T)=T.
First, we apply a transformation of variables, under a Taylor approximation,
E(f(T)) f(E(T)) + f00 (E(T))
2V ar(T)
V ar(f(T)) f0(E(T))2V ar(T)
We can then substitute these expressions into the variance of terms for the multiplicative case above
V ar(Y)E(A)2f0(E(T))2V ar(T)+
f(E(T)) + f00 (E(T