🤖 AI Summary
This study addresses the identification of deterministic monotone conditional mappings governed by refreshment samples in panel data subject to unrestricted attrition. By leveraging set dominance theory to characterize consistent mappings, and integrating density ratio control, explicit rationalization of the attrition process, and rank condition analysis, it derives identified sets and trimmed bounds for mean effects both with and without attrition. The work reveals a novel property that tail behavior does not determine the identified set, quantifies biases across various matching strategies, and demonstrates that refreshment designs can identify path curvature. Empirically validated using Japanese panel data, this research provides a robust identification framework for handling complex panel attrition.
📝 Abstract
Refreshment samples are the standard remedy for panel attrition, and the identification results behind them maintain that participation does not change measurement. We characterize what a refreshment sample identifies about panel conditioning, modelled as a deterministic monotone map at reinterview, when attrition is unrestricted. A candidate map is consistent with the data if and only if the retention-scaled distribution of the stayers' implied latent outcomes is setwise dominated by the refreshment distribution; every such map is rationalized by an explicit attrition process. Without attrition the map is identified on the latent-outcome support; with attrition, a density-ratio condition governs the identified set, and tail behaviour alone does not determine it. For an unrestricted map the survivors' mean effect has the familiar trimming bounds; for an item with all categories reported, the model reduces to a test of no conditioning. Within a cohort, other waves, dropout patterns and entry-wave items leave the set unchanged unless restrictions link selection across waves. Under explicit selection restrictions, survival matching, symmetric matching and entry-wave correction identify survivor effects. We derive their biases and give rank conditions under which refreshment schedules identify curvature in the conditioning path. A Japanese panel illustrates the results.