Global agricultural responses to interannual climate and biophysical variability

GCAM is a dynamic recursive model that represents the linkages between the energy system, water, agriculture and land use, the economy, and the climate. The model has been involved in the AgMIP (Nelson et al 2014, von Lampe et al 2014) and widely used for studying climate impacts on agriculture and land use (Thomson et al 2011, Kyle et al 2014). GCAM with the incorporation of regional agricultural markets is employed in this study. There are 14 crops in GCAM, including 12 food or fiber crops aggregated from FAO crops (see the mapping in table S1) and two dedicated biomass energy crops. The model is global in scope and aggregates the world into 31 regions. The base calibration year is 2010. That is, the model and its database represent the technology, factor productivity, socioeconomic conditions, and market equilibrium in 2010. The GCAM reference scenario uses population and GDP projected in the SSP2, 'Middle-of-the-Road', scenario (O'Neill et al 2014, Samir and Lutz 2017). For biophysical yield growth in the GCAM reference scenario, we use a linear interpolation based on the Food and Agriculture Organization (FAO) of yield projections in 2030 and 2050 (Alexandratos et al 2006, Bruinsma 2009), which represent a trend of total factor productivity (TFP) improvement. The GCAM data system is written in an open-source R package (Bond-Lamberty et al 2019). Both the GCAM model and the data system are publicly available. GCAM, by default, runs to 2100 with 5 year steps. For this study, the model is modified to run in annual time steps to 2050 using external drivers in the reference scenario. A more detailed description of GCAM is provided in SI section S1.2.

For this study, we make modifications in the nested logit land allocation framework in GCAM to incorporate adaptive expectations of prices and yield into the model. It is assumed that a representative profit-maximizing agricultural producer of output $k$ makes production and management decisions by determining the uses of land, water, fertilizer, and other inputs, given a vector of input and output prices and a technology that is constant return to scale. Instead of perfectly predicting prices and yield, agricultural producers form the expectations of the output price (${p^{\,E}}$) and yield (${g^{\,E}}$) based on existing information. Denote $w$, $f$, and $l$, as the price for water, fertilizer, and other inputs, respectively and ${\text{ }}{y^w}$, ${y^f}$, and ${\text{ }}{y^l}$ as the output yield regarding water, fertilizer, and other inputs, respectively. The expected rental profit, ${r^{\,E}}$, earned from land use $k$ using irrigation option $i$ (irrigation or rainfed) and fertilizer technology $m$ (high or low fertilizer) for producers in water basin $b$, region $j$, and period $t$ can be derived from the zero pure profit condition, as shown in equation (1).

$$\begin{align}r_{k,i,m,b,j,t}^{\,E} & = \left( {p_{k,j,t}^{\,E} - \frac{{{w_{k,b,j,t}}}}{{y_{k,i,b,j,t}^w}} - \frac{{{f_{k,b,j,t}}}}{{y_{k,m,b,j,t}^{\,f}}} - \frac{{{l_{k,b,j,t}}}}{{y_{k,b,j,t}^l}}} \right) \nonumber\\ & \quad \cdot g_{k,i,m,b,j,t}^{\,E}.\end{align} \tag{ 1 }$$

Note that $\frac{w}{{{y^w}}}$, $\frac{f}{{{y^f}}}$, and ${\text{ }}\frac{l}{{{y^l}}}$ are input cost per unit output of $k$ for water, fertilizer, and other inputs, respectively. If farmers have perfect foresight on market prices and yield, i.e. ${p^{\,E}} = p$ and ${g^{\,E}} = g$, equation (1) becomes the rental profit used in the original GCAM. Note that incorporating yield expectations ($g_{k,i,m,b,j,t}^{\,E}$) at the technology level allows further reflecting suboptimal management decisions so that endogenous yield responses, modeled as technology transitions through land use change, could be imperfect. We employ the Nerlove adaptive expectation (equation (2)), which has been extensively studied in the literature (Pashigian 1970, Hommes 1992, 1994) and also explored in recent studies (Féménia and Gohin 2011, Mitra and Boussard 2012, Chaudhry and Miranda 2018). It depicts that the expectation of a variable ($x_t^{\,E}$) is adaptively revised in proportion to the difference between the previous observation (${x_{t - 1}}$) and the previous expectation ($x_{t - 1}^{\,E}$) with a constant coefficient of expectations ($\alpha$), and $\alpha \in \left( {0,{\text{ }}1} \right]$.

$$\begin{align}x_t^{\,E} - x_{t - 1}^{\,E} = \alpha \left( {{x_{t - 1}} - x_{t - 1}^{\,E}} \right).\end{align} \tag{ 2 }$$

Equation (2) can be rearranged to $x_t^{\,E} = \alpha \cdot {x_{t - 1}} + \left( {1 - \alpha } \right) \cdot x_{t - 1}^{\,E}$, which implies that the current expectation is a weighted average of the lagged observation and the lagged expectation. It collapsed into a naïve expectation when $\alpha$ equals one. In line with previous studies (Boussard et al 2006, Féménia and Gohin 2011), we use a relatively small coefficient of expectation, i.e. $\alpha = 0.1$, to avoid unrealistic bifurcation or chaotic oscillations (Gouel 2012), and a uniform value is used for all regions and crops. We also test the sensitivity of the IAV of climate impacts on agriculture to $\alpha$ with a range of [0.05, 0.2]. Further details of expectation schemes and discussions of parameters are provided in SI section S2.

In this study, we rely on future climate scenarios of biophysical yields estimated in the context of the inter-sectoral impact model intercomparison project (ISIMIP) (Warszawski et al 2014) and the AgMIP. We employ the results from the combinations of two global gridded crop models (GGCMs), EPIC (Kiniry et al 1995, Izaurralde et al 2006) and LPJ-GUESS (Smith et al 2014) and two general circulation models (GCMs), HadGEM2-ES and GFDL-ESM2M. We focus on RCP 8.5 (540 ppm CO₂ concentration in 2050) and allow carbon fertilization. The climate and agronomic scenarios have been widely used in previous studies (Nelson et al 2014, Springmann et al 2016), and they are at the extremes (high and low ends at the global aggregated estimates) in their respective model intercomparisons (Rosenzweig et al 2014, Warszawski et al 2014). Thus, there are four climate scenarios evaluated in our study: HadGEM2-ES and EPIC (HE), GFDL-ESM2M and EPIC (GE), HadGEM2-ES and LPJ-GUESS (HL), and GFDL-ESM2M ES and LPJ-GUESS (GL). Future biophysical crop yield shocks reported by crop models are mapped and aggregated to GCAM crops (table S2) following methods developed in Snyder et al (2020) and Müller and Robertson (2014).

The GCAM reference scenario, i.e. no climate impacts but with imperfect foresight, is used as the baseline in this study. Note that the only difference between climate scenarios and the baseline scenario is the external driver of biophysical yield. The biophysical yield by 2050 in the reference and climate scenarios are compared in SI figures S1 and S2. The reference scenario uses a linear interpolation of the FAO projections of crop yield in 2030 and 2050, which implies a trend of TFP growth and does not account for climate variations. The world average biophysical yield in the climate scenarios is projected to be about 5% (GL) to 24% (HE) lower than reference by 2050 relative to 2010 ³ . It is important to note that projections in climate scenarios are constructed by applying biophysical yield shocks to the reference GCAM projections following the AgMIP convention (Müller and Robertson 2014, Nelson et al 2014). In other words, the biophysical yield projections in climate scenarios provide an agronomic representation of climate variables on top of a linear trend of TFP growth. Note that the variability in biophysical yield in climate scenarios, when detrended by the TFP trend in baseline, mirrors only the natural climate variability implied by variables in climate models, e.g. temperature, precipitation, surface radiation, wind speed, air pressure, humidity (see discussions in SI section S1.3).

We estimate climate impacts on agricultural economic variables in a future year as the relative ratio between a climate scenario and the baseline scenario (no climate impacts), i.e. ${S_t} = X_t^{{\text{climate}}}/X_t^{{\text{baseline}}}$. The ratio is compared to one (i.e. ${S_{t = 0}} = 1$), implying a temporally cumulative measure of impacts, and climate impacts on a variable in year, $t$, relative to a base year can be calculated as $\left( {{S_t} - 1} \right)100\%$ (Nelson et al 2014). Note that the corresponding interannual climate impacts can be calculated as $\left( {{S_t} - {S_{t - 1}}} \right)100\%$. However, in this study, we employ the logarithmic changes of cumulative impacts, $\log \left( {{S_t}} \right) - \log \left( {{S_{t - 1}}} \right)$, to measure interannual climate impacts. Using logarithmic changes, implying continuously compounded growth rates, permits a consistent measure of the IAV of climate impacts as the standard deviation of the interannual climate impacts, i.e. ${\text{IAV}} = {\text{SD}}\left[ {\log \left( {{S_t}} \right) - \log \left( {{S_{t - 1}}} \right)} \right]$, which has been widely used for measuring market variability (Gilbert and Morgan 2010, Haile et al 2015). It also allows a consistent comparison across climate scenarios for interannual climate impacts when the same baseline scenario is used, i.e. $\log \left( {{S_t}} \right) - \log \left( {{S_{t - 1}}} \right) = \log \left( {X_t^{{\text{climate}}}/X_{t - 1}^{{\text{climate}}}} \right) - \log \left( {X_t^{{\text{baseline}}}/X_{t - 1}^{{\text{baseline}}}} \right)$, and for IAV when the baseline variability is small (e.g. linear TFP growth in GCAM baseline).

Furthermore, we define relative interannual variability (RIV), as the ratio of the IAV of economic responses ($a$) to the IAV of biophysical yield shocks ($b$), i.e. ${\text{RI}}{{\text{V}}_{a,{\text{ }}b}} = \frac{{{\text{IA}}{{\text{V}}_a}}}{{{\text{IA}}{{\text{V}}_b}}}$. RIV normalizes IAV by biophysical yield so that it can be compared across scenarios, regions, or crops. More importantly, RIV enhances the explanation of the results since it can be decomposed as the ratio of beta coefficient to the correlation coefficient, both between economic responses and biophysical yield shocks, i.e. ${\textrm{RI}}{{\textrm{V}}_{a,{\textrm{ }}b}} = \frac{{{\textrm{co}}{{\textrm{v}}_{a,{\textrm{ }}b}}/{\textrm{IAV}}_b^2}}{{{\textrm{co}}{{\textrm{v}}_{a,{\textrm{ }}b}}/\left( {{\textrm{IA}}{{\textrm{V}}_a} \cdot {\textrm{IA}}{{\textrm{V}}_b}} \right)}} = \frac{{{\textrm{Bet}}{{\textrm{a}}_{a,b}}}}{{{\textrm{Correlatio}}{{\textrm{n}}_{a,b}}}}$. Beta coefficient implies the magnitude of the interannual economics responses against climate impacts on biophysical yield, and correlation coefficient indicates the extent to which IAV in economic responses is explained by biophysical variability.

Figure 2 presents a time-series (annual) evaluation of agricultural economic responses to climate-induced biophysical shocks by mid-century, under the assumption of adaptive expectations. Note that point estimating of the climate impacts by the year 2050 will also indicate the interannual mean impacts over the study period (see density bars in figure 2 top panels). On average across climate scenarios, regions, and crops, by 2050, biophysical yield is estimated to decrease by 11.2%. It results in higher agricultural area expansion (+7.8%) and yield intensification (+0.5%), which alleviate some of the effects of climate impacts on production. Specifically, production only declines by 4.3% despite the higher decline in yield. The negative impact on crop supply leads to significantly higher crop prices (+36%) and lower consumption (−6%). The average impact on consumption tends to be higher than production due to the higher average impact on export (+24%) relative to import (+13%). The strong regional heterogeneity in biophysical yield shocks alters comparative advantage across the regions. As a result, trade patterns change, with small exporters being more responsive. In addition, scenarios with relatively stronger impacts on biophysical yield (i.e. HadGEM2-ES and EPIC scenarios) show more severe climate impacts on the agricultural market by mid-century. These mean climate impact results are generally consistent with previous studies (Nelson et al 2014), as the expectation scheme has a fairly small influence on the mean impacts (SI section S3.1).

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We use the standard deviation of logarithmic interannual changes to measure the IAV of climate impacts (boxplot in figure 2 bottom panels; see SI table S3 for summary statics and SI figure S7 for the sensitivity of IAV to the coefficient of expectation). On average, across climate scenarios, regions, and crops, the IAV of biophysical yield shocks is about 3.05%, which is largely mirrored in the production responses (3.08%). The average IAV of harvested area responses (0.55%) is fairly small as acreage responses are relatively rigid, especially with planting and harvesting decisions separated. The average IAV of crop consumption (2.10%), as mediated by trade and crop substitutions, is considerably smaller than production. Price volatility has been an important characteristic in the agricultural crop market. The average IAV of price responses is 6.33%, which is more than double the average IAV of biophysical yield shocks. Similar to the mean impact, scenarios with higher IAV in biophysical yield shocks also show higher IAV in the economic responses. However, the mean and IAV of climate impacts are separate measurements, which is important when comparing scenarios. For example, EPIC scenarios have higher impacts in both mean and IAV compared with LPJ-GUESS scenarios, while GFDL scenarios show lower mean impacts but significantly higher IAV compared with HadGEM2-ES scenarios.

Our results demonstrate that climate variables are the major sources of variability across time, while agronomic and economic responses contribute relatively more to variability across regions and crops. This is supported by the analysis of variance (ANOVA) conducted for comparing the relative contribution of variation to climate impacts across five factors, i.e. climate model, crop model, region, year, and crop, and their interactions (table 1). For the variability of climate impacts on biophysical yield and economic variables within climate and crop scenarios, year is a significantly more important contributor compared with region and crop, implying relatively higher overall variations across time. When comparing across scenarios, GGCM appears to contribute more to the overall variation. However, when it comes to IAV, the GCM plays a more important role, as implied by the higher interaction with year compared with crop model in the ANOVA (i.e. GCM:year vs GGCM:year).

How farmers form expectations of market and weather conditions plays a key role in making decisions and adapting to a changing climate. We investigate the role of expectation schemes in modeling climate impacts on agricultural markets by comparing the adaptive expectation with the perfect foresight (see figure 3 for results from the GE scenario). This comparison indicates the degree to which previous studies using perfect foresight have underestimated the economic responses to climate variability since adaptive expectations is a relatively more realistic representation of farmer behavior. Conversely, such comparisons also provide insights on to what extent climate impacts can be alleviated by improving farmers' predictions of prices and yield. The expectation scheme has a relatively small influence on assessing the mean climate impacts, while its influence on the IAV of economic responses is considerable. With perfect foresight, the average IAV (across climate scenarios, regions, and crops) of harvested area increased by a factor of 2.3 compared with adaptive expectation as adaptations through land use change become more responsive to climate variability with perfect expectations. However, the average IAV of price decreases by 55% with perfect foresight, which reflects the magnitude of endogenous market fluctuations generated under adaptive expectation. In other words, the variation in real shocks of biophysical yield, when transferring to market prices, was magnified (by an average factor of 2.2) due to endogenous market fluctuations. With no endogenous market fluctuations, the average IAV of production (−5%), consumption (−41%), and trade (−25% for export and −29% for import) would also decrease compared with adaptive expectation. Consumption is more sensitive to the expectation scheme than production since consumption is more responsive to prices while production is more responsive to biophysical yield shocks. Furthermore, trade responses become relatively less pronounced under perfect foresight as adaptations through land use change, and intensification are more accessible compared with adaptive expectations. These results are consistent across scenarios (see SI figures S3–S5 and table S5) that assuming perfect foresight would underestimate market volatility. They also imply that the volatility of prices and consumption induced by climate impacts can be reduced if farmers can improve their expectations.

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To illustrate how IAV is transferred from biophysical shocks to economic variables, we calculate RIV between economic responses and biophysical yield shocks, which measures the magnitude of the variance transmission. As described in section 2.3, RIV can be decomposed into a ratio between (a) the magnitude of the interannual economic responses against biophysical yield shocks (measured by the beta coefficient, see y-axis in figure 4)) and (b) the correlation coefficient between economic responses and biophysical yield shocks (x-axis in figure 4). That is, the slope of the lines presented in figure 4 represents the average RIV across crop-regions and scenarios, respectively for adaptive expectation (figure 4(a)) and perfect foresight (figure 4(b)). With adaptive expectations, the results show harvested area and consumption are less responsive to interannual biophysical shocks (i.e. absolute beta coefficient smaller than one) in most crop-regions, compared with production, price, or trade. The magnitude of the economic responses is different across economic variables since the climate and biophysical shocks were transferred to economic variables through different market-mediated responses, e.g. land reallocation, yield intensification, trade responses, and substitutions in consumption in the economic system. The correlation analysis indicates that, under adaptive expectation, biophysical yield shocks explain more IAV in crop supply responses (i.e. an R-squared of, on average, 92% for production and 67% for export) but less in price and demand responses (i.e. an R-squared of, on average, 36%, 33%, and 31% for price, import, and consumption, respectively). That is, the correlation between biophysical yield shocks and the economic responses is weaker when the climate variability is transferred from supply to demand variables. Thus, the relatively stronger interannual responses to biophysical shocks along with relatively larger shares of unexplained variations by biophysical shocks determined the more pronounced variance transmission from climate and biophysical variables to prices (with an average RIV of 2.8), under adaptive expectation, compared with other variables.

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Area responses, however, only obtained about a quarter of variations in biophysical shocks (RIV is 0.25 on average) under adaptive expectations. Due to the lag between planting and harvesting under adaptive expectations, farmers cannot immediately respond to changes in biophysical shocks by reallocating land, dampening both area responses and its correlation with biophysical shocks. When farmers can adapt immediately (or make better predictions) with perfect foresight (figure 4(b)), increases in the magnitude of area responses are larger than the correlation increases so that higher variations in biophysical shocks are transferred to area responses (RIV increases to 0.54 on average). Also, the stronger land reallocation and intensification responses under perfect foresight reduce both production responses and its correlation with biophysical shocks at a similar magnitude, which explains the insignificant changes in RIV for production. For prices, consumption, and trade, perfect foresight encourages lower variance transmissions compared with adaptive expectation (i.e. the average RIV decreased from 2.8 to 1.1 for prices and decreased from 0.85 to 0.49 for consumption). The reduction in RIV is driven by a combination of reductions in responsiveness to biophysical shocks and increases in the share of explained variations. Note that despite the considerable heterogeneity across regions and crops, the RIV and decomposition are generally consistent across climate scenarios (SI figures S9 and S10).

The economic responses to biophysical variability, though generally consistent across climate scenarios at the global scale, were considerably heterogeneous across regions and crops within a scenario. Crop-regions with higher IAV of biophysical yield shocks tended to have a higher IAV in economic responses while the relationship was substantially nonlinear, particularly for consumption and prices (figure 5 and SI figures S11–S13), as also indicated by the high heterogeneity in RIV (figure 4). It was mainly because the IAV of consumption and prices was mediated across crops and regions through crop substitutions and international trade. That is, crop-regions with higher (lower) IAV of biophysical yield shocks tend to have a smaller (larger) magnitude of variance transmission to consumption and price responses, i.e. smaller (larger) RIV. Note that if the magnitude of IAV transmissions from biophysical yield shocks to market responses is the same across crop-regions (e.g. perfect foresight with no trade or other crop-region specific market-mediated responses), RIV should be the same across crop-region. Thus, a negative relationship between RIV and IAV of biophysical yield suggests a mediation effect across crop-regions (SI figure S14). Also, the mediation effects are important regardless of the expectation schemes, while the effects were stronger under adaptive expectation, as implied by the steep slopes compared with perfect foresight. Despite being subject to barriers and costs, trade plays a unique role in reducing agricultural market variability from climate impacts, particularly when consumption is sourced from regions with negatively correlated biophysical yield shocks or crop supply responses. Thus, the IAV distributions of consumption across regions mostly ⁴ have a smaller dispersion due to the mediation effect, but also shifted to the left, implying a reduction effect (i.e. RIV < 1 for consumption), compared with the IAV distributions of biophysical yield shocks (SI figure S15). However, the reduction effect was not seen for price distributions mainly because of the endogenous market fluctuations (see SI section S3.2 for additional discussions on regional results). This could also be true at the sub-regional level, given the high spatial heterogeneity of climate impacts on crop productivity, that intraregional trade could help reduce and mediate market variability due to climate impacts.

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