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This is a pre-print version of a paper published in Nature Climate Change titled
“Anthropogenic Climate Change Has Slowed Global Agricultural Productivity
Growth”
URL:
https://doi.org/10.1038/s41558-021-01000-1
Note: This is a pre-submission version that does not incorporate revisions in response
to the peer-review process in that journal.
The Historical Impact of Anthropogenic Climate Change on Global Agricultural
Productivity
Ariel Ortiz-Bobea
1
*, Toby R. Ault
2
, Carlos M. Carrillo
2
, Robert G. Chambers
3
, David B.
Lobell
4
.
Affiliations:
1
Charles H. Dyson School of Applied Economics and Management, Cornell University, Ithaca,
NY, USA.
2
Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, USA.
3
Department of Agricultural and Resource Economics, University of Maryland – College Park,
College Park, MD, USA.
4
Department of Earth System Science, Stanford University, Stanford, CA, USA.
*Correspondence to:
ao332@cornell.edu
.
Abstract:
Agricultural research has fostered productivity growth, but the historical influence of
anthropogenic climate change on that growth has not been quantified. We develop a robust
econometric model of weather effects on global agricultural total factor productivity (TFP) and
combine this model with counterfactual climate scenarios to evaluate impacts of past climate
trends on TFP. Our baseline model indicates that anthropogenic climate change has reduced
global agricultural TFP by about 21% since 1961, a slowdown that is equivalent to losing the last
9 years of productivity growth. The effect is substantially more severe (a reduction of ~30-33%)
in warmer regions such as Africa and Latin America and the Caribbean. We also find that global
agriculture has grown more vulnerable to ongoing climate change.
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Main text
Enhancing agricultural productivity is vital to lifting global living standards and advancing
sustainable food production in the face of escalating challenges to agriculture and the
environment (1-7). Investments in agricultural research have boosted agricultural productivity,
but this growth in productivity has been distributed unequally across the world (8-10), and there
are signs that it is slowing down (11-14). At the same time, human activities during the last
century and a half caused global temperatures to rise by more than 1°C above their pre-industrial
values (15). This increase affects the global weather patterns that are essential to agriculture (16-
17). However, the impacts of this anthropogenic climate change (ACC) on the agricultural sector
has not yet been quantified, as most research has focused on future impacts (18-19).
Research to date on the historical impact of ACC focuses overwhelmingly on yields of
major cereal crops (20-21) or on total Gross Domestic Product (GDP) (22). However, recent
studies in this area are of limited value for assessing overall agricultural productivity for the
following reasons: (i) cereal crops represent only about 20% of agriculture’s global net
production value (Fig. S1), (ii) variations in measures such as yield, could deviate from changes
in overall productivity if farmers also adjust inputs in response to weather (23-25), and (iii)
growth and levels of total and agricultural GDP diverge considerably in most countries (26-28),
and thus climate change impacts on total GDP could deviate considerably from agricultural
impacts (29-30). There is much needed research on agricultural climate impacts beyond the
effects on yields of the major staple crops (31).
We quantify the impact of ACC on global agricultural productivity since 1961. Instead of
focusing on crop yield or agricultural output, we rely on a measure of agricultural Total Factor
Productivity (TFP). TFP measures aggregate output per unit of
measured
aggregate input (32-
35). TFP thus captures interactions between output and input adjustments that eluded earlier
research. Here we rely on official TFP statistics for which agricultural output includes crops and
livestock, while inputs encompass labor, land, physical capital and materials (12). However,
these TFP statistics do not incorporate the effect of weather, as is generally the case.
Consider the production function
𝑌
𝑖𝑡
= 𝑒
𝑓(𝑍
𝑖𝑡
)
𝐴
𝑖𝑡
𝑋
𝑖𝑡
𝑈
𝑖𝑡
, where
𝑌
𝑖𝑡
is aggregate
agricultural output,
𝑒
𝑓(𝑍
𝑖𝑡
)
is the effect of weather
𝑍
𝑖𝑡
,
𝐴
𝑖𝑡
measures technological knowledge
and
𝑋
𝑖𝑡
and
𝑈
𝑖𝑡
are the observed and unobserved aggregate inputs, respectively. The subscripts
refer to individual countries (
𝑖
) and year (
𝑡
). The percentage change in TFP is approximated as
Δ ln 𝑇𝐹𝑃
𝑖𝑡
≡ Δln( 𝑌
𝑖𝑡
) − Δ ln(𝑋
𝑖𝑡
) = Δ ln 𝐴
𝑖𝑡
+ Δ𝑓(𝑍
𝑖𝑡
) + Δ ln 𝑈
𝑖𝑡
where
Δ
denotes change. TFP growth reflects technological improvements embodied in
Δ ln 𝐴
𝑖𝑡
,
but also the unmeasured effects of random year-to-year weather changes
Δ𝑓(𝑍
𝑖𝑡
)
and
unobserved input adjustments
Δ ln 𝑈
𝑖𝑡
. While this aggregate representation may conceal fine-
scale production processes that are important to practitioners in the field, it helps provide a much
needed macro-economic picture about the global agricultural economy.
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We ground this conceptual framework empirically by estimating an econometric model
linking country-level TFP growth with weather change. Our model characterizes
𝑓
as a quadratic
function of average temperature (T) and total precipitation (P) over the 5-month period centered
around the greenest month of the year of each country or “green season” (See Methods):
Δ ln 𝑇𝐹𝑃
𝑖𝑡
= 𝛼
𝑖
+ 𝜃
t
+ 𝛽
1
Δ𝑇
𝑖𝑡
+ 𝛽
2
Δ𝑇
𝑖𝑡
2
+ 𝛽
3
Δ𝑃
𝑖𝑡
+ 𝛽
4
Δ𝑃
𝑖𝑡
2
+ 𝜖
𝑖𝑡
Country-fixed effect
𝛼
𝑖
controls for average country TFP growth rates, and year-fixed effect
𝜃
𝑡
for global shocks common to all nations. Conceptually, these parameters seek to control for
technological change embodied in
Δ ln 𝐴
𝑖𝑡
. Thus the
𝛽
coefficients are estimated via the within-
country and within-year variation of TFP growth and year-to-year weather changes. The
inclusion of squared terms
Δ𝑇
𝑖𝑡
2
and
Δ𝑃
𝑖𝑡
2
allows the effect of changes in weather to vary with
baseline levels of
𝑇
or
𝑃
. Unobserved changes in inputs that are not absorbed by
𝛼
𝑖
or
𝜃
𝑡
and
measurement errors in the TFP data are captured in the error term
𝜖
𝑖𝑡
. Note that measurement
error in the TFP data (see Methods) that remain uncorrelated with year-to-year changes in
weather do not introduce bias. We account for the uncertainty in the estimated parameters with a
block bootstrap where we sample observations with replacement 500 times by year and region.
We later consider more than 200 systematic variations of this model. For instance, we explore
whether estimating separate response functions for various sub-regions of the world affects our
results.
We summarize the key source data in Figure 1. The first panel, Fig. 1A, shows that
average agricultural TFP has more than doubled since 1961 but that there is wide cross-country
variation. Fig. 1B shows that there is a substantial range of variation in
Δ ln 𝑇𝐹𝑃
𝑖𝑡
across
countries for any given year. We also observe that TFP has grown much more slowly in certain
countries, particularly in Sub-Saharan Africa (Fig. 1C). In Fig. 1D we show how observed
annual country-level average temperature (in circles) fall closer within the range of
counterfactual weather trajectories with ACC (gold band) than without ACC (grey band). Fig. 1E
shows analogous information for precipitation without any discernible pattern.
We find a robust relationship between agricultural TFP growth and weather changes (Fig.
2, Tab. S1). The temperature response function is roughly linear and downward sloping (Fig 2A)
indicating that warmer temperatures over the green season are detrimental to TFP growth. We
conduct two placebo checks that suggest this relationship is unlikely to arise by chance. These
checks are based on the idea that incorrectly matching TFP growth and weather changes, and re-
estimating, should yield results suggesting no or insignificant effects of weather on TFP. We first
estimate models based on 10,000 “reshuffled” datasets that mismatch the
year
variable of the
TFP growth and weather change data. The sample estimate (in Fig. 2A) falls outside the resulting
distribution of spurious “reshuffled estimates” (Fig. 2B). In a second check we mismatch the
country
variable of the TFP growth and weather change data with similar results (Fig. 2C). The
precipitation response function is non-linear and peaks at around 500 mm over the green season
(Fig 2d). We demonstrate that this relationship is not likely spurious with the same placebo
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checks shown in Figs. 2E,F. We also find that the shape of the response functions is not driven
by either hot or cold countries (Figs. S2, S3).
A critical question for climate change adaptation is whether agriculture is becoming more
or less sensitive to climatic extremes. This would be reflected empirically as changes over time
in the response functions shown in Fig. 2. We estimate a model based on the first (1962-1988)
and second (1989-2015) halves of the sample and find that the temperature response function is
noticeably steeper for the latter half (Figs. S4, S5). This indicates that higher temperatures have
become more damaging. We formally confirm this by testing whether the temperature coefficient
has changed between these two periods in a model with a linear specification for temperature (
P
= 0.035). We also find that the change in the temperature response function over time is not
driven by isolated changes in outlying countries in the temperature distribution (Figs. S6-S9).
This mirrors recent findings in US agriculture (36, 37).
We find no evidence that weather has a persistent effect on TFP growth. Our baseline
specification only considers contemporaneous weather effects. But a weather shock could
conceivably affect TFP growth in future years, for example if growth is faster following a year
with bad weather. This would result in cumulative weather events affecting TFP growth. By
introducing lags for weather in prior years, we cannot reject the hypothesis that the cumulative
effect of changes in weather conditions up to 10 years in the past have no effect on TFP growth
(Tab. S2). But rejecting this hypothesis may be challenging with aggregate data.
We subsequently link our econometric estimates with counterfactual weather trajectories
from climate experiments with and without ACC to derive the cumulative impact of ACC for
each country since 1961. We obtain the counterfactual weather trajectories from the Coupled
Model Intercomparison Project Phase 6 (CMIP6). This approach combines both the statistical
uncertainty from the econometric model regarding the climate-agriculture relationship and the
climate uncertainty from the CMIP6 ensemble regarding the effect of human emissions on the
climate system (see Methods).
The cumulative impact of ACC on global agricultural TFP growth over the 1961-2020
period is about
−20.8%
with a 90 percent confidence interval between
−36.2
and
−11.0%
(Fig.
3A). In Fig. 3B, we represent this finding in levels by combining the counterfactual cumulative
impacts of ACC on global TFP growth with the observed (1961-2015) and projected (2016-
2020) global TFP level trajectory. This illustrates how much higher global TFP would have been
without ACC. Specifically, we find that the global TFP level projected to be reached in 2020 in
our world with ACC, would have been reached in 2011 in a world without ACC, with a 90
percent confidence interval between 2007 and 2015. That is, the impact of ACC represents a loss
of the past 9 years of productivity growth.
This global result conceals sizeable regional and cross-country disparities. Figure 4
shows that the cumulative impact of ACC since 1961 is greater for warm regions like Africa
(−32.9%
) and Latin American and the Caribbean (
−30.0%
) than for cooler regions like North
America (
−18.6%
) and Europe and Central Asia (
−16.0%
) (see Tab. S3). The large negative
impacts for Africa seem particularly worrisome given the large portion of the population
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employed in agriculture. Overall, these findings are consistent with documented slowdowns in
agricultural productivity (11-14), particularly in Sub-Saharan Africa (38,39) but also with studies
analyzing economy-wide ACC impacts that exacerbate inequality between poor and rich
countries (22, 40).
Our baseline global finding of the impact of ACC on global agricultural productivity is
robust to 200 variations of the econometric model. Fig. 5 summarizes global estimates for the
baseline and alternative models. The baseline model is shown in blue and corresponds to the
estimate shown in Fig. 3A. Notice that using minimum (Tmin) and maximum (Tmax)
temperature as alternative temperature variables or excluding precipitation does not substantially
change our baseline estimate. In addition, using a cubic functional form to relax the symmetry of
our baseline quadratic specification does not alter our baseline result. We also consider
regressions with observations weighted by revenue and find those results to be systematically
more pessimistic than our baseline model using equal weights. But aggregating weather data to
the country level based on areas covered only by cropland or both cropland and pasture has little
effect on our findings. We also consider models with weather variables aggregated over the
entire calendar year. We find that those models fit less well and point to noticeably smaller
damages. Finally, our baseline model imposes a single response function for the whole world.
But allowing separate response functions for three equally-sized latitudinal groups of countries
does not alter our findings. Overall, the 192 models that do not exclude observations point to an
average mean impact of
−17.6%
with a standard deviation of
5.3%
(indicated with a horizontal
red line and band in Fig. 5).
The exclusion of certain countries does not substantially affect our baseline estimate, but
restricting the analysis to certain temporal subsamples does. A potential concern is that certain
countries may overinfluence our estimates and thus drive our findings. But excluding certain
large countries like China, the United States, India or Brazil, or the 10 percent coldest or hottest
countries does not substantially alter our baseline finding (Fig. 5). However, basing our analysis
on the latter part of the sample (1989-2015) points to even larger damages than our baseline
estimate, on the order of
−30%
(Fig. 5). This reflects our finding that the response function is
changing over time and suggests that global agriculture is growing increasingly sensitive to
ongoing climate change.
Finally, we find that ignoring input responses by analyzing output rather than TFP,
overstates the impact of ACC. The temperature response function is steeper for output than for
TFP (Fig. S10), suggesting that farmers reduce aggregate input quantity in response to
detrimental weather conditions. Ignoring confounding input adjustments, Fig. S11 indicates that
ACC would have reduced output by about
32.3%
with a 90 percent confidence interval between
−61.3
and
−16.8%
. This is noticeably higher than the
20.8%
reduction based on TFP.
Our estimates should not be interpreted as the effect of a world without fossil fuels on
global agricultural production. Agriculture has benefitted tremendously from agricultural
research and carbon-intensive inputs that would not have been as available without fossil fuels.
The counterfactual in our study only removes
the effect
that fossil fuels and other anthropogenic
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influences have on the climate system. For instance, our estimates do not remove the direct effect
that rising CO
2
concentrations has on agricultural production or the presence of agricultural
research or carbon-intensive inputs. In addition, the reader may be rightfully concerned about
measurement error of our TFP metric. TFP estimates are notoriously difficult to construct, and
require considerable background work sometimes using imperfect data sources. However, as
long as the measurement error remains uncorrelated with year-to-year changes in TFP growth,
which seems plausible, such errors do not bias our econometric estimates but simply render them
more imprecise. Moreover, the TFP metric we rely upon likely mismeasures certain inputs, such
as irrigation water use. Our own analysis shows that ignoring all measured inputs overstates
ACC impacts, so the present analysis is a first step while more detailed international TFP
statistics are produced. In conclusion, our study suggests that ACC is increasingly reducing
agricultural output as we drift away from a climate system without human influences, cumulating
into a detectable and sizeable impact as of 2020. Given recent productivity slowdowns (11-14),
the long lags in agricultural research, and the rapid pace of ACC, our findings raise the question
whether current levels of investments in agricultural research are sufficient to sustain 20
th
century rates of productivity growth in the 21
st
century.
Methods
Data sources and data processing
We obtain agricultural data from USDA ERS International Agricultural Total Factor
Productivity (TFP) dataset (41). This dataset provides the most comprehensive set of
international TFP estimates for the agricultural sector. The dataset provides country-level TFP
indices (in levels) for 172 countries over the 1961-2015 period. The regression dataset has 9,255
observations with 172 countries and 54 years (1962-2015; note that one year is lost because of
first differencing to compute growth rates). The dataset is balanced but for one nation, Palestine,
for which we only have complete data from 1995. Note that some recent smaller nations were
aggregated to their former larger countries to extend the time span of the dataset (e.g.
Czechoslovakia, Yugoslavia, Ethiopia, Sudan, etc.).
TFP levels, annual growth rates and average growth rates are shown in Fig. 1A-C. The TFP
growth rate for country
𝒊
and year
𝒕
is constructed by USDA as:
Δ ln 𝑇𝐹𝑃
𝑖𝑡
= ∑ 𝑅
𝑖𝑡𝑗
ln Δ𝑌
𝑖𝑡𝑗
− ∑ 𝑆
𝑖𝑡𝑘
ln Δ𝑋
𝑖𝑡𝑘
𝑘
𝑗
where
𝑅
𝑖𝑡𝑗
is the revenue share of the
𝑗
th output
𝑌
𝑖𝑡𝑗
and
𝑆
𝑖𝑡𝑘
is the cost share of the
𝑘
th input
𝑋
𝑖𝑡𝑘
. As indicated by USDA, TFP growth is the value-share-weighted difference between total
output growth and total input growth. To avoid index number bias, the USDA adjusts weights
𝑅
𝑖𝑡𝑗
and
𝑆
𝑖𝑡𝑘
every decade. Outputs include crop and livestock commodities aggregated based on
a common set of international prices derived by the Food and Agriculture Organization (FAO).
Inputs include farm labor, agricultural land (quality adjusted), capital inputs (including farm
machinery and livestock) and intermediate inputs (inorganic fertilizer and animal feed) which are
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mostly obtained from FAO. Thus changes in inventory in livestock herd size are taken into
account. See ref (42) for more details. Note that although the data is constructed in terms of TFP
growth rates, the data is transformed and reported in levels in the USDA website. Geographical
delimitations in this study follow as close as possible FAO region definitions (Fig. S12). Note
that
the TFP metric we rely upon likely mismeasures certain inputs, such as irrigation water use.
As discussed in ref (42), irrigation is accounted for in the land input through a quality adjustment
of land equipped for irrigation. Thus changes in irrigation intensity remain unaccounted for.
However, estimates of weather driven variability in global irrigation withdrawals remain modest
at a global scale (~10%) (43).
We obtain the historical weather data from the Global Meteorological Forcing Dataset
(GMFD) for land surface modeling developed by the Terrestrial Hydrology Research Group at
Princeton University (44). The GMFD provides data on daily minimum and maximum
temperature and total precipitation over 1948-2016 with a 0.25° spatial resolution (~28 km at the
equator). Following standard practice in the literature, we aggregate these variables to the
monthly level and then spatially aggregate the grids to the country level based on either cropland
or cropland and pasture weights. We obtain these weights by resampling the 10km gridded land
cover data in ref. 45 to the GMFD grid using a bilinear interpolation (Fig. S13). Although
weighting weather data by production value may seem desirable, we find that 1- adopting
alternative weighting schemes makes little practice difference, and 2- constructing a globally
consistent set of grid-level production value weights would be prohibitive. We show the annual
evolution of the country-level average temperature and percentage change in total precipitation
for the 1961-2015 period in Fig. 1D,E.
We obtain the counterfactual monthly weather trajectories for average temperature and
total precipitation for 1961-2020 from three sets of simulations in CMIP6. The “hist-nat”
experiment (1961-2020) simulates the influence of natural forcing alone on the climate system.
The “historical” experiment (1961-2014) simulates the influence of both human and natural
forcings on the climate system. As stipulated by CMIP6, we complement this experiment with
data for 2015-2020 from the SSP2-4.5 experiment. We rely (so far) on 7 GCMs (see Tab. S4).
To aggregate these modelled weather trajectories to the country-level using the same
approach as above, we first downscale these data from their native GCM grid to the GMFD grid
using
the bias-corrected spatial disaggregation (BCSD) approach (46). BCSD corrects the bias of
the modelled climate data and increases the spatial resolution with the ultimate goal of having a
product of higher resolution that conserves the statistics of the global climate scenarios. The
BCSD approach is performed in two steps. In the first step, we create a bias-corrected (BC)
dataset by performing a quantile mapping to correct the bias (47, 48), which ref. 48 calls a
“transformation”. In the quantile mapping, we transform the GCM time series field to match the
quantile distribution of the observed GMFD weather dataset, Q
GCM
→ Q
OBS
, using a common
period for the transformation function (1961-2014). Because the transformation is done at every
grid cell of the GCM, the observed GMFD dataset was aggregated to match the coarser GCM
resolution. The approach was applied to both temperature and precipitation. In the second step,
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we increased the spatial resolution of the BC data by applying the spatial disaggregation (SD)
approach. In the SD approach, we first removed the monthly observed climatology from the
coarse resolution BC data,
∆𝐹 = 𝐹 − 𝐶𝐿𝐼𝑀
𝐶𝑂𝐴𝑅𝑆𝐸
. We then convert the anomaly to a high
resolution by linear interpolation,
∆𝐹 → ∆𝐹
𝐻𝐼𝐺𝐻
. Finally, we added the climatology with high
resolution,
𝐹
𝐻𝐼𝐺𝐻
= Δ𝐹
𝐻𝐼𝐺𝐻
+ 𝐶𝐿𝐼𝑀
𝐻𝐼𝐺𝐻
. Here, the anomaly calculation (
∆𝐹
) is only valid for
temperature. For precipitation the anomaly is computed using a ratio,
∆𝐹 = 𝐹/𝐶𝐿𝐼𝑀
𝐶𝑂𝐴𝑅𝑆𝐸
with
𝐹
𝐻𝐼𝐺𝐻
= ∆𝐹
𝐻𝐼𝐺𝐻
× 𝐶𝐿𝐼𝑀
𝐻𝐼𝐺𝐻
.
The baseline econometric model relies on weather variables aggregated over a 5-month
period centered around the greenest month of year of each country based on Normalized
Difference Vegetation Index (NDVI) climatology data (50). The NDVI data is the 3
rd
generation
of NASA/GFSC GIMMS’s NDVI dataset for 1981-2015.We first temporally aggregate the data
to bi-weekly climatologies. We then smooth the climatology series within the year based on a
14-week moving window. We then identify the “greenest” month based on the month that
includes the highest NDVI level of the year for each grid cell. The spatial distribution of the
“greenest” month for each grid cell is shown in Fig. S14A. To obtain a country-level value, we
first resample land cover weights to match that of the NDVI data. We then compute for each
country the most frequent “greenest” month based on either cropland or cropland and pasture
frequency weights. These country-level aggregations are shown in Fig. S14 B and C. For two
small island nations (Fiji and Polynesia) there is no NDVI data. We therefore assign the greenest
month to match that of the neighboring island nation of Vanuatu.
Deriving the response function
In order to help map our conceptual framework to the USDA TFP estimates, we consider the
following relationship between aggregate output, aggregate input, weather, and technological
knowledge
𝑌
𝑖𝑡
= 𝑒
𝑓(𝑍
𝑖𝑡
)
𝐴
𝑖𝑡
𝑋
𝑖𝑡
𝑈
𝑖𝑡
, where
𝑌
𝑖𝑡
is aggregate agricultural output in country
𝑖
and year
𝑡
,
𝑒
𝑓(𝑍
𝑖𝑡
)
is the effect of weather
𝑍
𝑖𝑡
,
𝐴
𝑖𝑡
measures current technological knowledge, and
𝑋
𝑖𝑡
and
𝑈
𝑖𝑡
are observed and unobserved aggregate inputs, respectively. By definition, TFP for country
𝑖
at time
𝑡
is
𝑌
𝑖𝑡
/𝑋
𝑖𝑡
so that the percentage change in TFP for country
𝑖
at time
𝑡
is approximated
as
Δ ln 𝑇𝐹𝑃
𝑖𝑡
≡ Δln( 𝑌
𝑖𝑡
) − Δ ln(𝑋
𝑖𝑡
) = Δ ln 𝐴
𝑖𝑡
+ Δ𝑓(𝑍
𝑖𝑡
) + Δ ln 𝑈
𝑖𝑡
Empirically, our econometric models seek to control for
Δ ln 𝐴
𝑖𝑡
through country and
year fixed effects (
𝛼
𝑖
and
𝜃
t
respectively) and model
Δ𝑓(𝑍
𝑖𝑡
)
in various ways. Because the
model is specified in growth terms, the inclusion of a country-specific dummy variable
𝛼
𝑖
is
analogous to controlling for a linear country-specific time trend in
ln 𝑇𝐹𝑃
. Unobserved inputs
that are not absorbed by the fixed effects are captured in the error term
𝜖
𝑖𝑡
. This error term also
captures measurement errors in the TFP metric, which includes changes in irrigation water use
not fully captured by changes in irrigated area. Perhaps with the exception of water withdrawals,
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measurement errors in the TFP data are unlikely to be correlated with year-to-year weather
changes, which does not bias our results.
Our baseline model regresses
Δ ln 𝑇𝐹𝑃
𝑖𝑡
on first
differences of green-season average temperature and precipitation:
Δ ln 𝑇𝐹𝑃
𝑖𝑡
= 𝛽
1
Δ𝑇
𝑖𝑡
+ 𝛽
2
Δ𝑇
𝑖𝑡
2
+ 𝛽
3
Δ𝑃
𝑖𝑡
+ 𝛽
4
Δ𝑃
𝑖𝑡
2
+ 𝛼
𝑖
+ 𝜃
t
+ 𝜖
𝑖𝑡
To
capture the statistical uncertainty of the regression model we conduct a block
bootstrap estimation where we sample observations by year-region with replacement. While
there is serial dependence in TFP levels, previous work has shown there is no serial dependence
in growth
Δ ln 𝑇𝐹𝑃
𝑖𝑡
(e.g. 14, 36). We thus focused on accounting for contemporaneous regional
dependence. Regions correspond to the seven FAO regions shown in Fig. S12. We show the
response function with a 90% bootstrapped confidence band for temperature and precipitation in
Figs. 2A, D. We show regression coefficients for the baseline model in Tab. S1. Weather
parameters
𝛽
are subsequently used in a simulation to derive the effect of ACC on global
agricultural TFP. Importantly, note that measurement error in
Δ ln 𝑇𝐹𝑃
𝑖𝑡
would need to be
correlated with
Δ𝑇
𝑖𝑡
and/or
Δ𝑃
𝑖𝑡
to induce any form of bias in the estimation of
𝛽̂
. In addition,
classical measurement error in
Δ𝑇
𝑖𝑡
and/or
Δ𝑃
𝑖𝑡
would induce attenuation bias, reducing the
magnitude of our findings.
The placebo checks shown in Figs. 2B, C, E, F evaluate whether the estimated
relationship is spurious. The idea is to evaluate the chances that the result is spurious by
contrasting the estimated coefficients in our sample with a distribution of coefficients from
“reshuffled” datasets where we should, on average, expect no effect of weather. We perform
10,000 regressions based on datasets that are mismatched by year and by country. In all cases the
estimated coefficients fall clearly outside the distribution of “reshuffled” estimates, in support of
our baseline model.
Robustness checks
A crucial concern in applied econometric analysis is that baseline models proposed by
researchers may not be robust to even small variations in model specification or the underlying
data. We conduct a systematic exploration spanning 200 variations of the econometric model to
assess the robustness of our baseline finding (Fig. 5).
We consider all possible combinations of models along the following dimensions: 1-
relies on either Tmax, Tmin or Tmean, 2- includes or excludes precipitation, 3- adopts a
quadratic or cubic functional form for all weather variables, 4- relies on equal or revenue
regression weights, 5- relies on weather data aggregated over cropland or cropland and pasture,
6- relies on a the calendar year or the “green season” (5 months centered around the greenest
month) for aggregating weather conditions, and 7- relies on a single global response function or
on separate response functions for 3 equally-sized latitudinal regions. This corresponds to 192
variations of the model.
Page 10
10
We find most these variations have relatively little bearing on the baseline result
presented in the paper in Fig. 3. The adoption of revenue regression weights and a “green
season” for weather aggregation represent the two most consequential modeling choices,
pointing to larger damages.
We also consider 8 data restrictions including country exclusions (China, USA, India,
Brazil, coldest 10%, hottest 10%) and temporal subsets (1962-1988 and 1989-2015) which are
discussed in the main paper.
Measurement error
Measurement error affects all econometric analyses and its consequences are well understood
(51). Here we characterize how it might affect our study. As stated earlier, our dependent
variable
Δ ln 𝑇𝐹𝑃
𝑖𝑡
is possibly mismeasured. Measurement error in
Δ ln 𝑇𝐹𝑃
𝑖𝑡
that is
uncorrelated with weather (classical measurement error) does not introduce bias in the estimation
but renders our less precise. Only measurement error in
Δ ln 𝑇𝐹𝑃
𝑖𝑡
that is correlated with weather
fluctuations (non-classical measurement error) introduces bias. It seems unlikely that weather
may affect the collection and reporting of output and input quantities. Thus systematic
differences across country in data reporting would not introduce bias.
However, omitted or mismeasured variable input adjustments in response to weather
fluctuations could be problematic. The USDA ERS International Agricultural Total Factor
Productivity dataset (39) we rely upon accounts for irrigation via the amount of land equipped
for irrigation (40), not through water withdrawals directly. If farmers increase groundwater
irrigation intensity in response to unfavorable conditions, but such short term increases in
irrigation are overlooked, then unfavorable weather conditions would appear less damaging.
Note that surface irrigation (e.g. flood irrigation) may be procyclical with precipitation, so the
overall relationship between irrigation intensity and weather fluctuations seems indeterminate.
Our analysis focusing on output (rather than TFP) suggests that
ignoring input responses affects
the estimation of the sensitivity to weather conditions (Fig. S10). But the overall role of
irrigation may be limited because weather-driven variability in global irrigation withdrawals
remains modest at a global scale (~10%) (43). Moreover, our main global finding remains stable
when we estimated the response function separately for various regions of the world (Fig. 5).
Another potential concern is measurement error in our independent weather variables.
Classical measurement error in independent variables, here
Δ 𝑇
𝑖𝑡
and
Δ 𝑃
𝑖𝑡
, cause attenuation bias
(bias toward zero). This means that such errors would tend to “dilute” our findings toward no
results. On the other hand, measurement error that is correlated with weather fluctuations could
bias our findings in either direction. However, comparisons of regression results across
alternative datasets in other studies generally show minimal discrepancies.
Impact of anthropogenic climate change
Page 11
11
We compute the impact of anthropogenic climate change on each country’s agricultural TFP
growth by subtracting the cumulative impact of a weather trajectory with ACC for a given GCM
from the cumulative impact of a weather trajectory without ACC for the same GCM. For a
country
𝑖
, the cumulative impact from 1962 to year
𝑡
0
for a weather trajectory (with or without
ACC) is computed as:
𝐼
𝑖𝑡
0
= ∑
Δ ln 𝑇𝐹𝑃
𝑖𝑡
̂
𝑡
0
𝑡=1962
= 𝛽
1
̂ ∑ Δ𝑇
𝑖𝑡
𝑡
+ 𝛽
2
̂ ∑ Δ𝑇
𝑖𝑡
2
𝑡
+ 𝛽
3
̂ ∑ Δ𝑃
𝑖𝑡
𝑡
+ 𝛽
4
̂ ∑ Δ𝑃
𝑖𝑡
2
𝑡
where the changes in weather variables (e.g.
Δ𝑇
𝑖𝑡
) are the differences between the sequence of
seasonal weather conditions relative to the 23-year climatology centered around 1961 (1950-
1972) for the scenario without ACC for that particular GCM. Thus, the cumulative impact of
ACC is
𝐼
𝑖𝑡
0
with ACC
− 𝐼
𝑖𝑡
0
without ACC
in year
𝑡
0
. We can compute this cumulative impact for all years
between 1962 and 2020 for a particular set of values of the
𝛽̂
coefficients and a GCM.
To reflect the joint statistical uncertainty from the econometric model and climate
uncertainty arising from various GCMs in CMIP6, we compute cumulative impacts of ACC for
2,000 random pairs of bootstrapped coefficients
𝛽̂
and GCMs. Figure 3A shows the 2,000
trajectories of the cumulative impact of ACC for all years in 1962-2020, as well as the
distribution of those impacts on 2020, on the right.
In Fig. 3B we illustrate the impact of ACC by contrasting counterfactual TFP level
trajectories with the observed TFP level trajectory. Specifically, we obtain a counterfactual TFP
level trajectory
𝐿
𝑖𝑡
0
for country
𝑖
at year
𝑡
0
by taking the exponential of the observed TFP level
trajectory (mostly
> 0
) minus each one of the 2,000 counterfactual cumulative impacts of ACC
(mostly
< 0
):
𝐿
𝑖𝑡
0
= exp
(
∑
Δln𝑇𝐹𝑃
𝑖𝑡
observed
𝑡
0
𝑡=1962
⏟
Observed TFP level trajectory
− (𝐼
𝑖𝑡
0
with ACC
− 𝐼
𝑖𝑡
0
without ACC
)
⏟
Counterfactual cumulative
impact of ACC
)
These counterfactual TFP level trajectories are shown in grey with a blue line and band showing
their mean and 90% confidence intervals, respectively. The red solid line shows the observed
TFP level trajectory,
exp(
∑
Δln𝑇𝐹𝑃
𝑖𝑡
observed
𝑡
0
𝑡=1962
)
, for the 1962-2015 period. Because the TFP
dataset extends only to 2015, we project the TFP trajectory for 2016-2020 (shown in a dashed
red line) based on the average growth rate over the previous 10 years (2006-2015) for each
country.
Regional and global cumulative impacts of ACC are obtained by aggregating country-
level cumulative impacts based on the fixed revenue weights for each country, and then
converting these to levels after regional aggregation. TFP level trajectories are normalized to 100
in 1962.
Page 12
12
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Acknowledgments:
We thank Chris B. Barrett and participants at the AERE and EAAE summer
meetings, Giannini Foundation’s Big Ag Data Conference, and at seminars at Cornell University,
Arizona State University, University of Arizona, North Carolina State University and Duke
University for useful comments
.
Funding:
AOB was partially supported by the USDA National
Institute of Food and Agriculture, Hatch/Multi State project 1011555.
TRA and CMC were
partially supported by NSF grants 1602564 and 1751535, as well as the Atkinson Center for a
Sustainable Future, the Cornell Initiative for Digital Agriculture, and the Braudy Foundation.
Author contributions:
AOB conceived the study, conducted and led research and the writing of
the manuscript. CMC obtained and downscaled modelled climate data. TRA, RGC, DBL
provided detailed guidance and advice throughout the project. All authors contributed to writing
the manuscript
.
Competing interests:
Authors declare no competing interests.
Data and
materials availability:
All data and code
necessary to fully reproduce results in this study are
deposited in a permanent online repository at the Cornell Institute for Social and Economic
Research (CISER):
https://doi.org/10.6077/pfsd-0v93
.
Page 16
16
Supplementary Information:
Figures S1-S14
Tables S1-S4
Page 17
17
Fig. 1: Recent trends in agricultural productivity and climate.
(
A
) Country-level growth in
agricultural Total Factor Productivity (TFP) over 1961-2015. Grey lines indicate observed TFP
level trajectories for all countries in the sample. Colored lines correspond to the average TFP
level trajectories for countries with varying average TFP growth rates. (
B
) Distribution of first
differences in the log of country-level TFP. The boxes represent the first 3 quartiles (Q1, Q2,
Q3). Whiskers extend to 1.5 times the interquartile range (IQR=Q3-Q1). Observations falling
beyond 1.5 IQR are represented with small circles. (
C
) Map representing the annual average
growth rate in agricultural TFP over 1961-2015. (
D
and
E
) Evolution of global average annual
temperature and annual precipitation of the
Global Meteorological Forcing Dataset
(GMFD)
observations (circles). The golden band extends to the range of modelled variables from CMIP6
(7 GCMs). Simple averages of country-level variables are shown, thus small countries are over-
represented.
Page 18
18
Fig. 2: The response of agricultural productivity to weather.
(
A
) Response function of TFP
growth to changes in green-season average T. Response functions are centered vertically so that
the exposure-weighted marginal effect is zero. The colored bands represent 90 and 95%
confidence bands based on 500 year-by-region block bootstraps. The blue bars represent the
country-level distribution of green-season average T over the sample period 1962-2015. The
average green-season T is indicated for a select number of large countries. (
B
) Panel shows the
result of a placebo check whereby TFP and weather data are randomly mismatched or reshuffled
by years. The distribution represents the linear and quadratic T coefficients based on 10,000
reshuffled datasets. (
C
) Same as previous panel but based on datasets reshuffled by country. (
D
)
Response function of changes in country-level TFP to changes in green-season total P. (
E
) Same
as panel
B
but for P coefficients. (
F
) Same as panel
C
but for P coefficients.
Page 19
19
Fig. 3: Global impact of anthropogenic climate change on productivity.
(
A
) 2,000
counterfactual paths ways combining statistical uncertainty and climate uncertainty. Blue line
shows ensemble mean and the blue cone represents a 90 percent confidence band. The error bars
on the right indicate 90 and 95% confidence intervals for the impact on 2020. (
B
) Same results
presented in levels relative to the observed (1962-2015) and projected (2016-2020) level of TFP
(in red).
Page 20
20
Fig. 4: Regional and country-level impacts of anthropogenic climate change.
(
A
)
Impact estimates for the baseline mode for each
5
region. The white circles represent 2,000 estimates for each region. The blue bars represent 90 and 95% confidence bands and the
solid line indicates the ensemble mean. (
B
) The color corresponds to the ensemble mean impact for each country in the sample.
Page 21
21
Fig. 5: Global impact of anthropogenic climate change under multiple econometric models.
Vertical lines represent the 90 and
95% confidence intervals (in light and dark color, respectively) around the ensemble mean estimate for a particular model. ACC
impacts for the baseline model, also shown in Fig. 3A, is highlighted in blue whereas alternative models are shown in grey. The red
horizontal line and band represent the average mean impact of the 192 models out of the 200 that do not exclude observations, plus
5
and minus a standard deviation (
−17.6 ± 5.3%
). The vertical bars directly below the impact estimates represent the reduction in out-
of-sample MSE of a 10-fold cross-validation (whereby years of data are sampled together) relative to a model that excludes weather
variables. Thus, higher bars indicate better model fit. The dotted table below provides information about the characteristics of each
econometric model.
Document Outline