Climate change poses a significant threat to agricultural productivity, with projected extreme temperatures reducing average yields for major US crops. However, impacts vary spatially, with some areas potentially benefiting from warmer temperatures and increased irrigation. Farmers are expected to respond by shifting crops and relocating production. This study aims to quantify the potential economic benefits of crop reallocation as a climate adaptation strategy for six major crops in the US: barley, corn, cotton, soybeans, rice, and wheat. Understanding the spatial distribution of climate impacts, the availability of productive land, and the costs of crop switching is crucial for assessing the effectiveness of this adaptation strategy. The research employs a spatial optimization approach to maximize profits by reallocating crops, using a novel Bayesian hierarchical model to estimate yield potential under changing climatic conditions. This approach addresses limitations of traditional empirical models that struggle to predict yields in new locations and face a resolution-variance trade-off when incorporating region-specific effects.

Existing literature highlights the negative impacts of climate change on crop yields globally (Lobell & Gourdji, 2012; Hsiang et al., 2013; Challinor et al., 2014; Moore et al., 2017). Studies have also shown regional variations in climate impacts, with some areas experiencing benefits (Schlenker & Roberts, 2009; Hsiang et al., 2017). The potential for adaptation through crop shifting and relocation has been recognized (Mendelsohn et al., 1994; Beddow & Pardey, 2015; Costinot et al., 2016), but the extent of these benefits remains uncertain. Empirical agricultural models often use weather data to explain yield variation, but these models struggle to extrapolate to new locations or fully capture complex regional variations. Econometric techniques, while accounting for unobserved regional differences, can only model yield changes and not absolute levels, hindering their ability to assess the potential for crop shifting.

The study develops a Bayesian hierarchical model to predict crop yields under changing climatic conditions. This model addresses the limitations of traditional empirical models by allowing for regional variation in yield responses to weather while simultaneously predicting yields in new locations. The model includes terms for the non-linear effects of temperature, crop water deficits, and a linear technology trend. County-level data from 1949 to 2009 for six crops (barley, corn, cotton, soybeans, rice, and wheat) were used to estimate the model parameters. The parameters are allowed to vary for each US county, but regional variations are constrained using spatial covariates (annual mean temperature, isothermality, temperature seasonality, annual precipitation, precipitation seasonality, and irrigation fraction). The Bayesian approach allows for 'partial pooling,' where the degree of pooling between regions is determined by the data, allowing for more accurate estimation of regional differences in temperature sensitivity. The model's predictive power was validated using cross-validation, comparing its performance to several ordinary least-squares (OLS) regression models. The best-performing Bayesian model, which used county-specific intercepts and a uniform error variance, was then used to project yields under future climate scenarios. A linear programming model was employed to determine the profit-maximizing allocation of crops across counties for the current and future climate conditions, considering crop prices and cultivation costs from the USDA Economic Research Service. Future climate projections were based on downscaled and bias-corrected CMIP5 data from 17 GCMs. The optimization procedure was constrained to maintain current national-level land allocation for each crop, preventing unrealistic price changes due to major shifts in production.

The Bayesian yield model revealed considerable spatial variation in climate sensitivity across crops and counties. Corn and cotton exhibited lower sensitivity to extreme temperatures in the southern US, likely due to adaptation in farming practices and seed varieties. For wheat and barley, sensitivity was strongly linked to water availability. The model showed substantial regional variation in the yield response to extreme temperatures, and a significant portion of this variation was explained by county mean temperature, highlighting existing adaptation to higher temperatures. Cross-validation demonstrated that the Bayesian model outperformed OLS models in predicting future yields, highlighting the improved accuracy of the Bayesian approach in capturing county-level variations and extrapolating yields to new locations. Under current climate conditions, the optimal crop allocation resulted in a 13% increase in total profits compared to observed patterns. This optimization primarily involved shifts between soybean and corn production, reflecting common crop rotation practices. Under RCP 8.5, projections for 2050 and 2070 showed that without crop reallocation, total profits would decrease by 31%. However, by optimizing crop allocation, this loss is reduced by half, to 16%. The optimal reallocation patterns involved significant changes in crop distribution. By 2070, 53% of counties experienced crop switching (36% excluding corn-soybean swaps), including notable shifts in corn production, soybeans moving northward, and cotton expansion to higher latitudes. However, a significant portion of land in the southern US (5%) becomes unsuitable for any of the six crops studied by 2070. Although the optimization model aims to maximize profits, this analysis does not account for potential societal costs and impacts from crop switching, such as disruptions to farmers, food supplies, and environmental habitats.

The findings demonstrate the potential of crop switching as a climate change adaptation strategy in US agriculture. The substantial reduction in projected profit losses due to crop reallocation highlights the importance of considering spatial adaptation strategies. The spatial variations in climate sensitivity across crops and regions underscore the need for location-specific adaptation measures. However, the model’s limitations emphasize that crop switching is not a complete solution to climate change impacts. The persistent losses even with optimal reallocation suggest a need for additional adaptation strategies, including development of climate-resilient crop varieties and improvements in agricultural management practices. The study's focus on economic impacts does not fully capture broader societal and environmental consequences of large-scale crop shifts.

This study provides strong evidence of the substantial economic benefits of crop switching as a climate adaptation strategy for US agriculture. The developed Bayesian hierarchical model effectively captures regional variations and predicts yield changes under climate change. While crop relocation can significantly mitigate losses, it cannot fully eliminate them, highlighting the necessity of complementary adaptation strategies like developing climate-resilient crop varieties. Future research should focus on incorporating additional factors such as irrigation expansion, risk aversion, and the integration of non-economic impacts into the optimization framework. A deeper investigation into the socio-economic impacts of significant crop shifts, and the ability of farming communities to adapt to these changes, is also warranted.

The study's optimization model assumes perfect knowledge of future crop responses to climate and neglects factors like farmer mobility, risk aversion, and unexpected weather events. The model also does not account for the full range of potential adaptation measures, such as irrigation expansion or changes in agricultural management practices. The results should be interpreted as an upper bound on the potential benefits of crop switching, and actual realized outcomes may be different. Finally, while the model considers multiple sources of uncertainty, it does not explicitly address potential general equilibrium effects on crop prices.