Seasonal and Spatial Heterogeneity in Climate–Input Interac-tions on Cereal Crop Yields: Evidence from 30 Indian States (1997–2020)

Abstract

Climate variability remains a major challenge to agricultural productivity in India, yet the effects of rainfall may differ across cropping seasons and exhibit nonlinear patterns. This study examines the relationship between annual rainfall and cereal crop yields using a panel dataset of 3,754 observations covering 30 Indian states, five major cereal crops (rice, wheat, maize, jowar, and bajra), and the period 1997–2020. Fixed-effects panel models were employed to account for un-observed heterogeneity across states, crops, and years, while Random Forest and Extreme Gradient Boosting (XGBoost) models were used to complement the econometric analysis by capturing complex nonlinear relationships. The linear fixed-effects model indicates a positive but modest association between annual rainfall and crop yield (β = 0.11), although the magnitude of the relationship varies across cropping seasons. The interaction analysis suggests that the association is weaker during the Rabi season (β = −0.21, p < 0.10) than in other cropping systems. The nonlinear specification further reveals significant threshold effects for Whole Year and Winter cropping systems, indicating that rainfall–yield relationships are not adequately represented by a simple linear function. Machine learning models achieved an out-of-sample R² of 0.79, with rainfall and seasonal indicators accounting for more than 60% of the overall variable importance, and the partial dependence analysis demonstrated clear nonlinear response patterns. Overall, the findings suggest that the relationship between annual rainfall and cereal production in India is heterogeneous across cropping seasons and exhibits important nonlinear characteristics. By integrating panel econometric techniques with machine learning methods, this study provides complementary evidence on climate–yield relationships and highlights the importance of season-specific adaptation strategies for enhancing agricultural resilience under changing climatic conditions.