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With climate change threatening agricultural productivity and global food demand increasing, it is important to better understand which farm management practices will maximize crop yields in various climatic conditions. To assess the effectiveness of agricultural practices, researchers often turn to randomized field experiments, which are reliable for identifying causal effects but are often limited in scope and therefore lack external validity. Recently, researchers have also leveraged large observational datasets from satellites and other sources, which can lead to conclusions biased by confounding variables or systematic measurement errors. Because experimental and observational datasets have complementary strengths, in this paper we propose a method that uses a combination of experimental and observational data in the same analysis. As a case study, we focus on the causal effect of crop rotation on corn (maize) and soybean yields in the Midwestern United States. We find that, in terms of root mean squared error, our hybrid method performs 13% better than using experimental data alone and 26% better than using the observational data alone in the task of predicting the effect of rotation on corn yield at held-out experimental sites. Further, the causal estimates based on our method suggest that benefits of crop rotations on corn yield are lower in years and locations with high temperatures whereas the benefits of crop rotations on soybean yield are higher in years and locations with high temperatures. In particular, we estimated that the benefit of rotation on corn yields (and soybean yields) was 0.85 t ha⁻¹(0.24 t ha⁻¹) on average for the top quintile of temperatures, 1.03 t ha⁻¹(0.21 t ha⁻¹) on average for the whole dataset, and 1.19 t ha⁻¹(0.16 t ha⁻¹) on average for the bottom quintile of temperatures. This association between temperatures and rotation benefits is consistent with the hypothesis that the benefit of the corn-soybean rotation on soybean yield is largely driven by pest pressure reductions while the benefit of the corn-soybean rotation on corn yields is largely driven by nitrogen availability.