Nonlinear temperature effects indicate severe damages to U.S. crop yields under climate change

Abstract

The United States produces 41% of the world's corn and 38% of the world's soybeans. These crops comprise two of the four largest sources of caloric energy produced and are thus critical for world food supply. We pair a panel of county-level yields for these two crops, plus cotton (a warmer-weather crop), with a new fine-scale weather dataset that incorporates the whole distribution of temperatures within each day and across all days in the growing season. We find that yields increase with temperature up to 29 degrees C for corn, 30 degrees C for soybeans, and 32 degrees C for cotton but that temperatures above these thresholds are very harmful. The slope of the decline above the optimum is significantly steeper than the incline below it. The same nonlinear and asymmetric relationship is found when we isolate either time-series or cross-sectional variations in temperatures and yields. This suggests limited historical adaptation of seed varieties or management practices to warmer temperatures because the cross-section includes farmers' adaptations to warmer climates and the time-series does not. Holding current growing regions fixed, area-weighted average yields are predicted to decrease by 30-46% before the end of the century under the slowest (B1) warming scenario and decrease by 63-82% under the most rapid warming scenario (A1FI) under the Hadley III model.

Fig. 1.

Nonlinear relation between temperature and yields. Graphs at the top of each frame display changes in log yield if the crop is exposed for one day to a particular 1° C temperature interval where we sum the fraction of a day during which temperatures fall within each interval. The 95% confidence band, after adjusting for spatial correlation, is added as gray area for the polynomial regression. Curves are centered so that the exposure-weighted impact is zero. Histograms at the bottom of each frame display the average temperature exposure among all counties in the data.

Fig. 2.

Predicted climate-change impacts on crop yields under the Hadley III climate model. Graphs display predicted percentage changes in crop yields under four emissions scenarios. Frame A displays predicted impacts in the medium term (2020–2049) and frame B shows the long term (2070–2099). A star indicates the point estimates, and whiskers show the 95% confidence interval after adjusting for spatial correlation. The color corresponds to the regression models in Fig. 1.

Fig. 3.

Out-of-sample prediction comparison for various model specifications. Bar charts display the percent reduction in the root-mean-squared prediction error (RMS) for each model in comparison with a baseline model with no weather variable. Each model is estimated 1,000 times, where each replication randomly selects 48 of the 56 years in our full sample. Relative performance is measured according to the accuracy of each model's prediction for the omitted eight years of the sample (≈14%). We sample years instead of observations because year-to-year weather fluctuations are random, but there is considerable spatial correlation across counties within each year. Step function, polynomial (eighth order), and piecewise linear are the models developed in this paper; the other models are from the existing literature.