Impacts of interannual climate and biophysical variability on global agriculture markets

Most studies assessing climate impacts on agriculture have focused on average changes in market-mediated responses (e.g., changes in land use, production, and consumption). However, the response of global agricultural markets to interannual variability in climate and biophysical shocks is poorly understood and not well represented in global economic models. Here we show a strong transmission of interannual variations in climate-induced biophysical yield shocks to agriculture markets, which is further magnified by endogenous market fluctuations generated due to producers’ imperfect expectations of market and weather conditions. We demonstrate that the volatility of crop prices and consumption could be significantly underestimated (i.e., on average by 55% and 41%, respectively) by assuming perfect foresight, a standard assumption in the economic equilibrium modeling, compared with the relatively more realistic adaptive expectations. We also find heterogeneity in interannual variability across crops and regions, which is considerably mediated by international trade. 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 interannual variation in crop supply responses (i.e., an R-squared


Introduction
Climate is essentially an indirect input to agricultural production, and its economic impacts on agriculture have been extensively assessed in the past three decades [1][2][3] . The assessment requires a combined use of climate, crop, and economic models to translate climate and biophysical shocks to changes in economic variables such as agricultural production, price, and land use 3,4 . With the advances in the understanding of the biophysical consequences of changes in temperature, precipitation, and other climate variables on agriculture 3,5,6 , studies are shifting focus from mean to the variability of future climate and biophysical shocks [7][8][9][10] . Interannual variability (IAV), in particular, is an important characteristic of climate and biophysical shocks.
However, how interannual variations in climate and biophysical shocks are transformed and transferred to global agricultural markets has been overlooked 11 . Previous studies focused on assessing economic consequences of climate impacts in a future period (e.g., 2050) as most economic models were designed for mid-or long-term projections. More importantly, perfect foresight has been a standard assumption used in economic modeling even though its lack of realism has been criticized 12,13 . With perfect foresight, agricultural producers can perfectly predict future climate and market information and make adaptations accordingly and immediately (e.g., adjusting land use and management practices to compensate for changes in productivity).
Nevertheless, for understanding dynamics in the agricultural market, it is undisputed that farmers make suboptimal decisions due to the time lag between planting and harvesting. In reality, farmers make production, land allocation, and management decisions based on their expectations of future yield and prices. As a result, erroneous expectations of prices and yield due to imperfect foresight could undermine the market equilibrium and, thus, generate "endogenous" market fluctuations 14 in addition to the variation stemmed from exogenous climate and biophysical shocks. The assumption of perfect foresight, ignoring the endogenous market fluctuations, may lead to misleading assessments of the IAV of agricultural economic responses 14,15 .
Understanding the IAV of the climate impacts on agricultural economics is crucial to formulating agricultural policies that facilitate agricultural adaptation and maintain food security since changes in the variability of climate and weather patterns will have considerable consequences on agricultural production and market fluctuation 7 . In this work, we quantify the IAV of climate impacts on agriculture by incorporating adaptive expectations 16 of annual prices and yield into a well-established global economic model, the Global Change Analysis Model (GCAM). That is, agricultural producers make production and land allocation decisions at planting time based on their expectations of prices and yield at harvesting time and adaptively adjust their future expectations with new information. In contrast to perfect foresight, adaptive expectation offers an intuitive and effective approach to characterize the "endogenous" market fluctuations in agricultural market equilibrium modeling 12 . Furthermore, we rely on biophysical yield projections estimated from combinations of two climate models, HadGEM2-ES and GFDL-ESM2M and two crop models, EPIC and LPJ-GUESS under representative concentration pathway (RCP) 8.5. The modeling chain is shown in Fig. 1. The climate and agronomic scenarios have been widely used in previous studies 3,17 , and they are at the extremes in their respective model intercomparisons 5,18 (see Methods for a more detailed description of GCAM and the coupled scenarios). We study the impacts of natural climate-induced biophysical yield shocks on agricultural economics to midcentury and assess both mean and IAV of the climate impacts. Our results demonstrate that studying IAV provides fundamentally new insights on measuring and understanding climate impacts on global agriculture.

Results
We provide a time-series (annual) evaluation of agricultural economic responses to climate-induced biophysical shocks by mid-century, under the assumption of adaptative expectations (Fig. 2). 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 Fig. 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 3 , as the expectation scheme has a fairly small influence on the mean impacts (SI Section 2.1).
Throughout this study, we use the standard deviation of logarithmic interannual changes to measure the IAV of climate impacts (boxplot in Fig. 2 bottom panels). 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) 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 scheme in modeling climate impacts on agricultural markets by comparing the adaptive expectation with the perfect foresight (see Fig. 3 for results from the GFDL-ESM2M& EPIC scenario). This comparison indicates that 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 (SI Section 2.1), 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 adaptative 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 (SI Fig. S1-S3), 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.
To illustrate how interannual variation is transferred from biophysical shocks to economic variables, we calculate relative interannual variability (RIV) between economic responses and biophysical yield shocks, which measures the magnitude of the variance transmission (Methods).
RIV can be decomposed into a ratio between (1) the magnitude of the interannual economic responses against biophysical yield shocks (measured by the beta coefficient, see y-axis in Fig.   4)) and (2) the correlation coefficient between economic responses and biophysical yield shocks (x-axis in Fig. 4). That is, the slope of the lines presented in Fig. 4 represents the average RIV across crop-regions and scenarios, respectively for adaptative expectation (Fig. 4a) and perfect foresight (Fig. 4b). 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 interannual variation 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  (Fig. 4b), the magnitude of area responses grows faster than the correlation 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 higher variance transmission compared with adaptative 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 Fig. S5-S6).
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 (Fig. 5 & SI Fig. S7-S9), as also indicated by the high heterogeneity in RIV (Fig. 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 IAV of biophysical yield shocks tend to have a smaller magnitude of variance transmission (smaller RIV) to consumption and price responses. Also, the mediating 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 (Fig. S10). 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 have a smaller dispersion due to the mediation effect, but also shifted to the left due to the reduction effect, compared with the IAV distributions of biophysical yield shocks (see SI Fig. S11). However, the reduction effect was not obvious for price distributions because of the endogenous market fluctuations (see SI Section 2.3 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.

Discussion
To our knowledge, this is the first study to systematically examine how global agriculture responds to climate and biophysical variability. However, there are some limitations to our analysis. Although we focused on assessing climate impacts from the natural climate-induced biophysical shocks, other external shocks such as extreme weather events and government policies may further buffer or exacerbate the economic responses, depending on the magnitude of the variation and the extent to which agricultural producers predict these shocks. Also, there could be great uncertainties around endogenous market fluctuations regarding the magnitude of the responses, the heterogeneity of the responses across regions, and crops, and the rationality and heterogeneity of the expectation schemes. Our sensitivity tests indicate that with faster adjustment in expectation implied by the higher coefficient of expectation, biophysical shock triggered endogenous market fluctuations would become stronger so that the IAV increases for all economic variables, with relatively higher sensitivity for price and harvested area (see supplementary discussions in SI Section 2.2). Empirical studies demonstrated incorporating expected prices and yield provided better identifications in evaluating agricultural supply responses 13,19,20 , and it is certain that with no endogenous market fluctuations, results from perfect foresight would exaggerate adaptation responses and underestimate market variations.
Furthermore, it has been challenging to include stockholding in global economic models 11,21 , which would likely have a moderating impact on market volatility 22,23 . A realistic modeling of storage would also require information on storage cost, government interventions, and stochastic exogenous shocks, which are usually not available at the global scale 22,24 . As with many studies, we abstract from including a speculative interannual stockholder 11,21 . Nevertheless, the main impacts from including storage implied by a stochastic competitive storage model 15,25 , e.g., positively skewed and shifted price distribution, could be mostly reflected in a deterministic adaptative expectation model by adjusting production cost and coefficient of expectation. Thus, we do not investigate the interplay between storage modeling and climate impacts in this paper.
Future studies are needed to refine data and parameters to study storage impacts under a changing climate. This paper focused on four widely used climate scenarios of future biophysical yield shocks and showed relatively consistent economic responses to biophysical interannual variations (i.e., RIV) at the global scale while highlighting the important role of trade in explaining regional heterogeneity in the responses. It is also important to note that the high uncertainty in biophysical yield projections, particularly at the regional scale, would be mirrored in the IAV of their economic responses (See the discussion of regional decompositions in SI Section 2.3).
More scenarios could be explored in the context of model intercomparison tasks using the framework showcased in this paper. These caveats notwithstanding, our study provides fundamental new insights on climate impacts on agricultural market variability and lays the foundation for further investigating the full range of climate impacts on biophysical and human systems.

Global Change Analysis Model (GCAM). 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 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 model is modified to run in annual time steps to 2050 using external drivers of population, GDP, agricultural productivity, and technological progress. The GCAM data system is written in an open-source R package 26 to clean and process source data and parameters into the format required in the model while maintaining transparency and traceability. GCAM was involved in the AgMIP 3,27 and widely used for studying climate impacts on agriculture and land use 28,29 . Note that GCAM version 5.1 with the incorporation of regional agricultural markets is employed in this study. Both the GCAM model and the data system are publicly available. A more detailed description of GCAM is provided in SI Section 1.2.
Climate and baseline scenarios. 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) 18  Adaptive expectation in GCAM. We made 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 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 (CRTS). Instead of perfectly predicting prices and yield, agricultural producers form the expectations of the output price ( ) and yield ( ) based on existing information. Denote , , , as the price for water, fertilizer, and other inputs, respectively and * , + , and , as the output yield regarding water, fertilizer, and other inputs, respectively. The expected rental profit, , earned from land use using irrigation option (irrigation or rainfed) and fertilizer technology (high or low fertilizer) for producers in water basin , region , and period can be derived from the zero pure profit condition, as shown in Equation (1).
Note that We employ the Nerlove Adaptive expectation (Equation 2), which has been extensively studied in the literature [33][34][35] and also explored in recent studies 12,14,36 . It depicts that the expectation of a variable ( 9 )

Data availability
The GCAM data system is publicly available 26 . The biophysical yield data projected from climate and crop models are publicly available at https://esg.pik-potsdam.de/search/isimip-ft/.

Code availability
The GCAM model is publicly available 37 . The modified version of GCAM created for this study is available upon request. A repository including the data and R code for generating main figures will be made available when published.