Participation Membrane Hardness in Poland (2015–2024): Aggregate Identification Bounds Without Microdata

This paper demonstrates that publicly available aggregates (AROP and persistent at-risk-of-poverty rates) are sufficient to partially identify the one-step transition geometry of the participation membrane in Poland over 2015–2024. Without accessing EU-SILC microdata, we derive algebraic bounds on lock-in (p_EE), reintegration (p_EA), and inflow (p_AE). These bounds define a non-trivial admissible region for any microdata-consistent transition matrix. The results show a persistent lower bound of approximately 0.45–0.51 on exclusion retention, indicating structural membrane hardness independent of full transition estimation. The study establishes a replicable aggregate-based identification framework compatible with official GUS and Eurostat data. Keywords: poverty dynamics, EU-SILC, persistent poverty, identification region, transition bounds, Poland, aggregate inference