Dynamic Equilibrium of Sustainable Ecosystem Variables: An Experiment

Developing indicators to monitor the dynamic equilibrium of sustainable ecosystem variables has been challenging for policymakers, companies, and researchers. The new method matrix decomposition analysis (MDA) is an adaptation of the Leontief input-output equations for the disaggregated structural decomposition of key performance indicators (KPI). The main problem that this work addresses is related to the behavior of MDA when compared to traditional methodologies such as data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Can MDA be considered robust enough for wide applicability? To compare the models, we developed a methodology called marginal exponentiation experiments. This approach is a type of simulation that raises the inputs and outputs of an entity to a marginal power, thus making it possible to compare a large number of models with the same data. RMarkdown was used for methodological operationalization, wherein data science steps are coded in specific chunks, applying a layered process with modeling. The comparison between the models is operationalized in layers using techniques such as descriptive statistics, correlation, cluster, and linear discriminant analysis (LDA). Given the results, we argue that MDA is a Leontief partial equilibrium model that produces indicators with dual interpretation, enabling the measurement of the dynamic equilibrium of sustainable ecosystem variables. Furthermore, the method offers a new ranking system that detects relative changes in the use of resources correlated with efficiency analysis. The practical value for decision-makers relates to the fact that we found evidence that MDA can be considered robust enough to identify whether a given ecosystem is in equilibrium and that the excessive use of resources or abnormal productivity can cause instability.