MODELING OF THE E-COMPONENT INTEGRAL INDEX BASED ON A MULTILEVEL SYSTEM OF INDICATORS

Abstract

The article develops a scientifically grounded methodology for modeling an integral index of environmental efficiency (E-component of the ESG system) for small and medium-sized agricultural enterprises in Ukraine. Key methodological problems in constructing integral indices related to the subjectivity of expert assessment, heterogeneity of indicators, and complexity of their aggregation into a single comprehensive indicator are analyzed. Based on information theory and the Shannon entropy method, an objective approach to determining weight coefficients is proposed, which relies exclusively on data structure without involving expert judgments. A system of environmental efficiency indicators has been developed, where each indicator is classified by impact type and linked to corresponding UN Sustainable Development Goals. Particular attention is paid to the mathematical apparatus of the methodology: normalization of heterogeneous indicators, calculation of entropy weight coefficients, and aggregation using the weighted linear sum method.

The mathematical apparatus of the methodology encompasses three sequential stages. The first stage involves normalization of indicators using the min-max method to transform heterogeneous data into a dimensionless form within the range from zero to one, with direct normalization applied to stimulator indicators and inverse normalization to destimulator indicators, ensuring that higher normalized values always correspond to better environmental efficiency regardless of the original indicator type. The second stage determines entropy weight coefficients through a four-step algorithm based on the Shannon entropy method: calculating enterprise shares for each indicator, computing information entropy that measures the uniformity of value distribution, determining the degree of diversification as a complement of entropy to unity, and calculating normalized weights where indicators with higher variation receive greater weights due to their higher information value for differentiating enterprises. The third stage aggregates normalized indicators with entropy weights into an integral index using the weighted linear sum method, where the resulting index possesses properties of boundedness within the zero to one interval, monotonicity with respect to each indicator, compensatory nature allowing trade-offs between indicators, and additivity enabling decomposition into individual indicator contributions for identifying improvement reserves. The methodology was tested on a sample of four real agricultural enterprises and one hypothetical benchmark enterprise, which demonstrated the high discriminant ability of the model. A five-level classification scale for interpreting integral index values is proposed: critical, low, medium, high, and leading levels of environmental efficiency. The research results can be used in formulating ESG strategies for agricultural enterprises, justifying investments in environmental modernization, benchmarking, and monitoring progress toward achieving the Sustainable Development Goals.