Are Shocks to the Grazing Land Footprint Permanent or Transitory? Evidence from a Machine Learning-Based Unit Root Test

Understanding the dynamic behavior of the grazing land footprint (GLF) is critical for sustainable land management. This study examines the GLF in 92 countries to determine if the series is stationary, a statistical property indicating that shocks have transitory effects, or non-stationary, which implies that shocks have permanent, cumulative impacts (a phenomenon known as persistence). We employ a novel machine learning framework that uses an XGBoost algorithm to synthesize information from multiple conventional tests and time-series characteristics, enhancing analytical robustness. The results reveal significant cross-country heterogeneity. The GLF exhibits stationary behavior in a subset of nations, including China, India, and Norway, suggesting that their ecosystems can absorb shocks. However, for most countries, the GLF is non-stationary, indicating that ecological disruptions have lasting and cumulative impacts. These findings underscore that a one-size-fits-all policy approach is inadequate. Nations with a stationary GLF may find short-term interventions effective, whereas those with non-stationary series require profound structural reforms to mitigate long-term degradation. This highlights the critical role of advanced methodologies in shaping evidence-based environmental policy.