Dynamic Benefit of the Doubt Decomposition for Panel Data: Evidence from Sustainable Energy in the EU

In sustainability and environmental performance assessment, as in many other multidimensional policy contexts, Benefit of the Doubt (BoD) composite indicators are widely used to compare units across multiple dimensions. However, their interpretation remains limited when panel data are available. In these settings, observed changes over time may reflect two distinct sources: a unit may move closer to cumulative best practices, thereby generating a catch-up effect, or the best-practice frontier itself may evolve, generating a benchmark shift effect. The present paper proposes a dynamic decomposition framework that separates these two components. Building on the reference technology approach pioneered by Tulkens and Vanden Eeckaut, the BoD setting is adapted to include contemporaneous, sequential, and intertemporal frontiers. This yields three indices that satisfy an exact multiplicative decomposition at the unit level. The framework is fully non-parametric, producing unit-specific measures of catch-up alongside a cross-sectional summary measure of benchmark shift. The results of simulation experiments conducted under pure benchmark shift, pure catch-up, and mixed dynamics demonstrate the efficacy of the method in accurately recovering the underlying data-generating processes. As an empirical illustration, the framework is applied to renewable energy performance across European Union countries over the period 2015–2024, using Eurostat SHARES (Short assessment of renewable energy sources) data. The empirical results indicate an average annual benchmark expansion of approximately 3.3%, together with heterogeneous catch-up dynamics across country groups.