A Sustainability Index for Agrarian Expansion: A Case Study in Mato Grosso (Brazil)

Since the early 2000s, sustainable development in agriculture has attracted substantial political attention, institutional support, and financial commitment, raising expectations for tangible outcomes. Yet, measurable progress remains uneven. As a leading food exporter, Brazil, in particular, has come under global scrutiny for practices deemed unsustainable—such as deforestation, excessive use of agrochemicals, and socio-environmental conflicts—despite its agricultural sector being a vital contributor to global food security. To provide policymakers with a robust monitoring tool, this study develops a nonlinear regression model that quantifies rural sustainability across economic, social, and environmental dimensions. We selected seven indicators—gross value added, average rural income, life expectancy, schooling years, preservation-area deficit, legal-reserve deficit, and water-scarcity deficit—to compute individual sub-indexes. These are combined into a composite rural sustainability index and applied to data from 141 municipalities in Mato Grosso. The results demonstrate that only municipalities achieving high and balanced scores in all three pillars can be deemed sustainable. Our framework contributes to the growing body of triple-index methodologies by offering a replicable, statistically robust tool tailored to agrarian contexts. It provides actionable insights for regional decision-makers aiming to balance productivity, environmental preservation, and social well-being in agricultural frontier regions.