Detecting cumulative effects of inputs within the flexible production function framework through LASSO shrinkage estimation: Implications for potassium fertilizer use in India

Despite recognition of the potentially significant cumulative effects of input use on annual crop output—such as the effect of applying inorganic fertilizer in one year on crop output in the subsequent year—real-world evidence from smallholder farmers’ fields in lower-income countries remains scarce. We narrow this knowledge gap using unique district-level and farm-household-level annual panel datasets in India. We start with flexible translog production functions, which are well-suited for identifying cumulative effects in farmers’ actual production environments. We then apply shrinkage methods (LASSO and GMM-LASSO) to approximate the production function with reduced parameter dimensions, addressing various challenges such as multicollinearity among multiple inputs, including the same inputs from the current and previous years, and potential endogeneity in inputs. Our results indicate that, throughout the shrinkage process, potassium remains a key predictor of outputs, while other inputs (land, labor, capital, irrigation, and other fertilizer nutrients) drop out. More important, the cumulative quantity of potassium from both the previous and current years is a consistently more critical determinant of production than the quantity of potassium from the current year alone, demonstrating the potassium’s significant cumulative effects. These patterns hold at both the district and farm levels across diverse agroecologies and cropping systems. Furthermore, the dynamic panel data analyses suggest that farmers’ use of potassium in the current year is significantly negatively affected by its use in the previous year, potentially stabilizing outputs across years. Our results support earlier agronomic findings suggesting that the cumulative effects of potassium may be relevant across wider geographic regions than previously thought.