US major crops' uncertain climate change risks and greenhouse gas mitigation benefits

Following the recent climate-economics literature (Schlenker and Roberts 2006, 2009, Deschênes and Greenstone 2007, 2012, Lobell and Burke 2010, Ortiz-Bobea 2013, Burke and Emerick 2015) we quantify the potentially nonlinear influence of climate on yields using semi-parametric cross section-time series regressions. Previous studies exploit the historical co-variation between yields and weather shocks to infer the effects of future climate. Motivated by Burke and Emerick's (2015) finding that long-run adaptations are limited in their ability to alleviate the short-run impacts of extreme heat, we extend their approach using a dynamic modeling framework that statistically distinguishes between the effects of short-run (weather) and long-run (climate) shocks. Since farmers' planting, management and harvesting decisions are based on land quality and expectations of weather, yields and meteorological variables share a long-run equilibrium relationship. In any given year, weather shocks cause yields to diverge from their expected long-run values, prompting farmers to revise their long-run expectations, and make management decisions that can have persistent effects⁶ .

To statistically identify the former equilibrium and latter disequilibrium responses we employ an error-correction model (ECM)⁷ . Our data are an unbalanced panel of $c$ counties over $t$ years, recording yields, $Y$ (calculated as the ratio of production, $Q,$ to harvested area, $H),$ as well as three-hourly observations of growing season temperature, precipitation and soil moisture, indexed by $v=\{T,P,S\}$, respectively. Interannual variation in log annual yield ($y)$ is modeled as a function of a vector of county-specific effects ($\mu ,$ which capture the influence of unobserved time-invariant local characteristics such as topography and soils), a vector of climatic covariates $\left(\phantom{\rule[-0000]{0ex}{2.4ex}}\right.$within each annual growing season, the cumulative exposure over $g$ crop growth stages to $j$ temperature intervals, ${\xi }_{j,g}^{T},$ $k$ precipitation intervals, ${\xi }_{k,g}^{P},$ and $l$ soil moisture intervals, $\left.{\xi }_{l,g}^{S}\right),$ and a vector of time-varying county-level statistical controls $\left({\boldsymbol{X}}\right)$.

Our model, which is derived and explained in the supplementary information (SI), is written:

$$\begin{eqnarray}&&{\rm{\Delta }}{y}_{c,t}={y}_{c,t}-{y}_{c,t-1}\\ &&\quad =\;\mathrm{log}\left(\displaystyle \frac{{Q}_{c,t}}{{H}_{c,t}}\right)-\;\mathrm{log}\left(\displaystyle \frac{{Q}_{c,t-1}}{{H}_{c,t-1}}\right)\\ &&\quad ={\mu }_{c}+{{\rm{\Sigma }}}_{g}\left\{{{\rm{\Sigma }}}_{j}{\beta }_{j,g}^{T}{\rm{\Delta }}{\xi }_{j,g,c,t}^{T}+{{\rm{\Sigma }}}_{k}{\beta }_{k,g}^{P}{\rm{\Delta }}{\xi }_{k,g,c,t}^{P}\right.\\ &&\quad \quad \quad +\left.{{\rm{\Sigma }}}_{l}{\beta }_{l,g}^{S}{\rm{\Delta }}{\xi }_{l,g,c,t}^{S}\right\}+{\rm{\Delta }}{{\boldsymbol{X}}}_{c,t}{\boldsymbol{\gamma }}\;+\theta \left[{y}_{c,t-1}\right.\\ &&\quad \quad \quad -{{\rm{\Sigma }}}_{g}\left\{{{\rm{\Sigma }}}_{j}{\eta }_{j,g}^{T}{\xi }_{j,g,c,t-1}^{T}+{{\rm{\Sigma }}}_{k}{\eta }_{k,g}^{P}{\xi }_{k,g,c,t-1}^{P}\right.\\ &&\quad \quad \quad +\left.\left.{{\rm{\Sigma }}}_{l}{\eta }_{l,g}^{S}{\xi }_{l,g,c,t-1}^{S}\right\}-{{\boldsymbol{X}}}_{c,t-1}{\boldsymbol{\lambda }}\;\right]+{\varepsilon }_{c,t}\end{eqnarray} \tag{ 1 }$$

and is estimated via ordinary least squares for five crops (corn, soybeans, wheat, cotton, sorghum), indexed by $i.$ Interannual difference terms (prefixed by ${\rm{\Delta }})$ model the yield impacts of transitory disequilibrium shocks, the expression in square braces captures the long-run equilibrium relationship between yields and the covariates, and $\varepsilon$ is a random disturbance term. Parameters to be estimated are the disequilibrium (weather) impacts (β^v), equilibrium (climate) impacts (η^v), short- and long-run effects of non-climatic variables (γ and λ), and the error-correction parameter ($\theta )$ measuring producers' speed of adjustment to the long-run equilibrium. The parameters (η^v) are vectors of semi-elasticities indicating the percentage by which yields shift relative to their conditional mean levels in response to additional time spent in a given interval. The vectors' elements—the individual coefficient estimates—each capture the distinct marginal effect of exposure within the corresponding interval (e.g., the average impact of an additional hour to 70–80 °F versus 80–90 °F temperatures). Collectively, the elements of ${{\boldsymbol{\eta }}}^{v}$ flexibly capture $v's$ overall long-run effect as a piecewise linear spline. The shape of the resulting function is identified from the covariation between observed yields and meteorology within each interval, as well as the distribution of observations across intervals over the historical period of the sample. With regard to temperature, the advantage of this approach is that it more precisely resolves the yield impacts of extreme heat relative to the standard degree-day specification (see Schlenker and Roberts 2009). Our dataset is described in the SI.

Omitted from equation (1) is the CFE. Rising CO₂ concentrations are a time-varying shock that simultaneously affects yields in all counties. However, there is near-perfect collinearity between the CFE and long-run impacts of other strongly trending, spatially homogeneous, beneficial influences such as total factor productivity improvements or technological progress. Data constraints preclude quantification of the latter with accuracy sufficient to construct credible statistical controls⁸ . Given the potential for the long-run coefficient on CO₂ concentrations to erroneously capture these confounding secular effects, we eschew empirical estimation of the CFE and instead incorporate its effect on our yield projections using relationships based on the literature.

Climate change impacts are quantified by combining the fitted values of the equilibrium meteorological parameters (${\hat{{\boldsymbol{\eta }}}}^{v})$ with meteorological exposures derived from ESM simulations of different warming scenarios. We spatially aggregate simulated 3-hourly fields of temperature, precipitation and soil moisture to the county level (${\tilde{{\boldsymbol{T}}}}_{c},$ ${\tilde{{\boldsymbol{P}}}}_{c}$ and ${\tilde{{\boldsymbol{S}}}}_{c})$ and bin the results into the $j,$ $k$ and $l$ intervals (respectively) over crop growth stages in current and future growing seasons to generate exact analogs of the regression covariates, ${\tilde{\xi }}^{v}$ ⁹ . Yields under irrigated and rainfed management regimes (indexed by $m=\{I,R\})$ exhibit different responses to precipitation and moisture as well as elevated CO₂. Accordingly, we model them separately (see SI), specifying rainfed impacts as a function of temperature, precipitation, soil moisture and ambient CO₂ concentrations $\left(\tilde{{\mathcal{C}}}\right),$ and irrigated impacts as a functions of temperature and CO₂:

$$\begin{eqnarray}&&{\psi }_{i}^{R}\left({\tilde{{\boldsymbol{T}}}}_{c},{\tilde{{\boldsymbol{P}}}}_{c},{\tilde{{\boldsymbol{S}}}}_{c},\tilde{{\mathcal{C}}}\right)\\ &&\quad ={{\rm{\Sigma }}}_{g}\left\{\displaystyle \sum _{j}{\hat{\eta }}_{i,j,g}^{T}{\tilde{\xi }}_{j,g,c}^{T}\right.+\displaystyle \sum _{k}{\hat{\eta }}_{i,k,g}^{P}{\tilde{\xi }}_{k,g,c}^{P}\\ &&\quad \quad \left.+\displaystyle \sum _{l}{\hat{\eta }}_{i,l,g}^{S}{\tilde{\xi }}_{l,g,c}^{S}\right\}+\;\mathrm{log}\;{\mathcal{F}}_{i}^{R}(\tilde{{\mathcal{C}}}),\end{eqnarray} \tag{ 2a }$$

$$\begin{eqnarray}&&{\psi }_{i}^{I}\left({\tilde{{\boldsymbol{T}}}}_{c},\tilde{{\mathcal{C}}}\right)={{\rm{\Sigma }}}_{g}\left\{\displaystyle \sum _{j}{\hat{\eta }}_{i,j,g}^{T}{\tilde{\xi }}_{j,g,c}^{T}\right\}+\;\mathrm{log}\;{\mathcal{F}}_{i}^{I}(\tilde{{\mathcal{C}}}).\end{eqnarray} \tag{ 2b }$$

Here, ${\mathcal{F}}_{i}^{m}$ is a concave function that captures the differential benefits of CO₂ fertilization under different moisture stress conditions, based on Hatfield et al (2011) and McGrath and Lobell (2013). Our calibration of the CFE index is documented in the SI.

The terms ${\psi }_{i,c}^{m}$ indicate the partial effects of climate on the logarithm of irrigated and rainfed yields. Our normalized decadal index of climate impact is the yield ratio:

$$\begin{eqnarray}&&{{\rm{\Psi }}}_{i,c}={\mathbb{E}}\left[{\bar{\phi }}_{c}^{R}\mathrm{exp}\left\{{\psi }_{i}^{R}\left({\tilde{{\boldsymbol{T}}}}_{c}^{\begin{array}{c}{\rm{Future}}\\ {\rm{Climate}}\end{array}},{\tilde{{\boldsymbol{P}}}}_{c}^{\begin{array}{c}{\rm{Future}}\\ {\rm{Climate}}\end{array}},{\tilde{{\boldsymbol{S}}}}_{c}^{\begin{array}{c}{\rm{Future}}\\ {\rm{Climate}}\end{array}},\right.\right.\right.\\ &&\quad \quad \quad \left.{\tilde{{\mathcal{C}}}}^{\begin{array}{c}{\rm{Future}}\\ {\rm{Climate}}\end{array}}\right)-{\psi }_{i}^{R}\left({\tilde{{\boldsymbol{T}}}}_{c}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}},{\tilde{{\boldsymbol{P}}}}_{c}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}},\right.\\ &&\;\quad \quad \quad \left.\left.{\tilde{{\boldsymbol{S}}}}_{c}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}},{\tilde{{\mathcal{C}}}}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}}\right)\right\}\\ &&\quad \quad \quad +{\bar{\phi }}_{c}^{I}\mathrm{exp}\left\{{\psi }_{i}^{I}\right.\left({\tilde{{\boldsymbol{T}}}}_{c}^{\begin{array}{c}{\rm{Future}}\\ {\rm{Climate}}\end{array}},{\tilde{{\mathcal{C}}}}^{\begin{array}{c}{\rm{Future}}\\ {\rm{Climate}}\end{array}}\right)\\ &&\quad \quad \quad -\left.\left.{\psi }_{i}^{I}\left({\tilde{{\boldsymbol{T}}}}_{c}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}},{\tilde{{\mathcal{C}}}}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}}\right)\right\}\right]\end{eqnarray} \tag{ 3 }$$

in which ${\mathbb{E}}$ is the expectation operator and ${\bar{\phi }}_{c}^{v}$ denotes the average shares of irrigated and rainfed cultivation from the MIRCA dataset (Portmann et al 2010), which we treat as remaining fixed into the future. (This assumption is discussed in § 3.2.) ${{\rm{\Psi }}}_{i,c}$ is interpretable as the climatically-attributable fractional change in a county's average yield relative to its own conditional mean¹⁰ . Accordingly, holding the current geographic distribution of harvested area constant as well, the change in production of each crop is simply the quantity ${{\rm{\Psi }}}_{i,c}\times {\bar{Y}}_{i,c}^{\begin{array}{c}{\rm{Current}}\\ {\rm{Climate}}\end{array}}$.

Our simulated meteorological fields and ambient CO₂ concentrations are taken from the CIRA project (Waldhoff et al 2014), a 15-member ensemble of simulations using the MIT Integrated Global System Model-Community Atmosphere Model (IGSM-CAM) modeling framework (Monier et al 2013)¹¹ . CIRA is underlain by three consistent socioeconomic and emissions scenarios: a reference scenario with unconstrained emissions and two climate stabilization scenarios that impose uniform global taxes on GHGs to limit total radiative forcing to 4.5 W m⁻² and 3.7 W m⁻² by century's end. Reductions in climate damages to agriculture in moving from the reference to the policy scenarios are interpretable as the benefits of GHG mitigation, and the associated differences in US agriculture sector output and relative prices are crucial to our cost estimates (Paltsev et al 2013). For each emission scenario, IGSM-CAM was run with different values of climate sensitivity and aerosol forcing, and different representations of natural variability, resulting in a 60-member ensemble (Monier et al 2015). We focus on simulations with a climate sensitivity of 3 °C, with each scenario run as a 5-member initial condition ensemble in an attempt to span the potential range of natural variability. Spatially disaggregating these projections to the county scale and using equations (2) and (3) enables us to calculate yield impacts at the middle and the end of the century (2036–2065 and 2086–2115) for each combination of scenario and ensemble member. We analyze 30-year time periods over 5 ensemble members with different representations of natural variability, resulting in a total of 150 years defining changes from the present day to the middle and end of the century, in order to obtain robust estimates of climate impacts on yield where the anthropogenic signal is extracted from the noise associated with natural variability.

Our long-run estimates are for the most part broadly consistent with current agronomic understanding of weather effects on field crop yields. Space constraints preclude detailed description of these results for all five crops. We highlight our findings for corn and consign the remaining results to the SI. Figure 1 shows corn's meteorological yield response functions (panel A) and the changes in exposure to weather conditions experienced by an average county in our three scenarios circa 2050 and 2100 (panels B and C). Yields decline precipitously with extreme temperature (Schlenker and Roberts 2009, Burke and Emerick 2015), but stratification of our responses by growth phase highlights the large impact in the first half of the growing season (Ortiz-Bobea 2013)—each additional 3 h period below 15 °C increases yields by as much as 0.005% relative to their conditional mean, but similar exposure above 40 °C triggers a reduction of more than 0.01%. Over the second half of the growing season, temperatures cause slight yield declines below the latter threshold but a marked increase above (as much as 0.01% per 3 h)¹² . A key point of divergence with prior results is our finding that yields increase strongly and approximately linearly with precipitation, with trace amounts associated with slight declines but 3 h extreme exposures (>15 mm) increasing yields by up to 0.01% (0.015%) in the early (late) sub-periods. The instantaneous soil moisture response exhibits a generalized inverse U shape with an apex at the conditional mean exposure, a very slight negative influence over most of its range and sharply negative impact at the upper extreme (>35 kg m⁻²), with reduction of up to 0.004% (0.008%) in the early (late) sub-periods. Other crops' responses share many of these characteristics (figures S3–S6)¹³ .

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In panels B and C, movements in the average distribution of exposure due to unmitigated climate change shifts the relative weights on different spline segments. The larger the increases in exposure within intervals associated with negative semi-elasticities (the pink bars), the greater the downward pressure on yield. Throughout the growing season temperature increases shift exposure out of low-temperature intervals into high-temperature intervals, negatively affecting yields, particularly in early stages of crop growth. Climate change is also associated with increases in both rainfall and soil moisture that shift exposure from low to high ranges of these variables, which is generally beneficial. But where the latter intervals are associated with negative marginal effects, the sign of the yield impacts is negative as well.

GHG mitigation's broad influence is to partially reverse these shifts in probability mass (the green and blue bars). Across meteorological variables, the most common pattern is for the bars indicating the policy scenarios to be of smaller magnitude but mostly opposite sign to those corresponding to the reference case. Crucially, such reversals are not always beneficial. In the reference scenario, exposure to low precipitation declines in both halves of the growing season circa 2100, and, relative to this outcome, GHG emission mitigation increases the average frequency of such dry episodes, with adverse late-season yield impacts. Similarly, increases in large precipitation events under the reference scenario improve yields, but mitigation reduces these increases, curtailing this particular benefit from unmitigated climate change. Finally, as indicated in the SI (figure S2), a pervasive consequence of mitigation is the reduction in the CFE and its attendant yield benefits.

Conditions within individual counties can diverge markedly from the aforementioned average changes in exposure. Maps of projected yield changes in figure 2 indicate the spatial patterns of the threat to the five major crops posed by unmitigated climate change, as well as the substantial threat reduction due to moderate mitigation. Panel A shows the counties where crop production is concentrated, while panels B and C illustrate the percentage changes in yields calculated using equation (3). All crops experience both beneficial and adverse effects, depending on the region. In the reference scenario, wheat yields increase in the northwest and decline in the south central and southwest regions circa 2050, a pattern that intensifies markedly toward century's end. For the remaining crops, the patterns of impact tend to follow the north-south temperature gradient. Soybean and corn yields suffer pronounced negative impacts in the South and the Mississippi River valley that first lessen before turning positive with proximity to Canada. For cotton, the largest adverse effects are dispersed across the crescent of southernmost counties, while for sorghum negative impacts are concentrated in the southwest. The reductions in changes in climatic variables as a consequence of mitigation policies attenuate the amplitude of beneficial as well as adverse yield shocks. Even a 4.5 W m⁻² GHG stabilization policy limits impacts to ±10% from baseline levels in the majority of cultivated counties. Results for the stringent 3.7 W m⁻² scenario (not shown) are similar but further accentuated.

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However, the risk to agricultural supply arises out of the spatial intersection of yield shocks and patterns of crop production in future decades when climatic changes occur. Although the latter will likely differ from today, given the challenges that attend prediction of agriculture's future geographic distribution (see, e.g., Ortiz-Bobea and Just 2012, Iizumi and Ramankutty 2015), we follow the empirical literature in assuming that irrigated and rainfed crop cultivation will continue to follow the current geographic pattern in panel A. We quantify the implications at the scale of US climate regions in table 1.

Table 1.  Changes in crop production (%) relative to current climate in the no-policy reference and GHG mitigation scenarios, circa years 2050 and 2100: by US climate regions.

Note: Square braces: changes in output from the reference scenario; shaded cells: losses relative to the current period (in cells with square braces, relative to reference scenario); bold: major producing regions.

Under reference warming, circa 2050, there are increases in yields of corn and sorghum, declines in wheat and soybeans, and mixed impacts on cotton in the regions where production of these crops is concentrated. Climate impacts that manifest in one or two regions at mid-century often spread geographically by 2100, with production in regions that suffer early adverse impacts (e.g., the southeast, and, to a lesser extent, south central regions) often experiencing further declines. Mitigation often only softens the blow in regions with the largest percentage losses, and, paradoxically, changes in weather patterns associated with stringent emission reductions may have smaller ameliorative impacts (see south, southeast and central sorghum and corn), likely due to the interplay between the impact of changes in meteorological variables and the CFE. Conversely, climate change improves yields in the cooler northeast, northwest, and, less reliably, north central areas around mid-century, with declines in the pool of regions experiencing beneficial weather as warming proceeds. Mitigation offsets output declines from regions experiencing losses at the cost of curtailing gains to those benefiting from climate change. However, rarely does mitigation transform gains under the reference into outright losses: more commonly regions that gain experience smaller benefits.

Our projected percentage changes in aggregate yield understate those of prior studies, although a clean comparison is elusive because of differences in the scenarios of future warming and their meteorological consequences as elaborated by ESMs (see table S3). Our inclusion of the CFE accounts for some of this divergence. Re-running our projections without the CFE¹⁴ results in yield losses that are 20% larger for wheat and between 2 and 4 times as large for soybeans and cotton, and yield gains for corn and sorghum that are 10%–15% smaller (table S2). More consequential are our findings of countervailing effects of extreme heat on corn yields (adverse early, beneficial late), and the importance of precipitation generally. The latter is particularly important given that our estimates assume no water stress, and therefore no impact of projected changes in precipitation or soil moisture, on the irrigated fraction of the crop in each county. Relative to the customary method of applying a single fitted yield response function everywhere, our approach reduces yield losses (gains) in regions experiencing precipitation and soil moisture declines (increases).

The implications for aggregate climate damage costs and GHG mitigation benefits are summarized in table 2. Costs (negative entries)and benefits (positive entries) are assessed by establishing two baselines from which to compute the absolute changes in output that correspond to US-wide percentage changes. Panel A, which collapses table 1, demonstrates that, under reference warming, adverse national average yield impacts are dominated by wheat, soybeans and, toward century's end, cotton. Conversely, corn and sorghum experience large increases in national average yield. Panel B shows the result of a comparative static calculation of the associated costs and benefits of climate change if crop production and prices remain at today's levels. Output losses (i) follow the reference pattern in Panel A, but negative impacts on wheat are lessened and on soybeans are reversed by mitigation's reduction of warming to beneficial levels. The corresponding economic impacts (ii) are expressed as changes in revenue, calculated by multiplying the quantity shocks by each crop's 1981–2010 average real farmgate price. Broadly echoing Deschênes and Greenstone's (2007) findings, climate change has a net beneficial impact which is modest at mid-century ($1 B) but becomes negligibly small by 2100. Relative to the reference, moderate mitigation generates additional annual benefits of $1 B ($2 B) circa 2050 (2100), while stringent mitigation's benefits are smaller: $0.6 B ($0.8 B) per year by 2050 (2100). Panel B's estimates incorporate future increases in production, and associated price changes, as simulated by MIT-EPPA's CIRA runs. Impacts are identical in sign, but expansions in crop output and revenue increase the magnitude of costs and benefits¹⁵ . Net annual benefits under reference warming are still small ($3 B circa 2050, $1B by 2100), while moderate (stringent) mitigation gives rise to modest additional annual benefits of $3 B ($1 B) by 2050 and $17 B ($7 B) by 2100.