National versus domain: Coverage properties of hierarchical Bayes credible intervals under survey redesign

A companion paper to Tam (2026a) reports an extended Monte Carlo (MC) study examining the frequentist coverage of 95% hierarchical Bayes (HB) credible intervals at the national and domain levels under four stress-test scenarios. The extended study covers 140 strata and 13 estimation domains separately, adds a classical direct-estimator benchmark, and tests two strategies for restoring domain coverage: prior sensitivity and Prasad–Rao (PR) MSE correction. At the national level, HB credible intervals achieve near-nominal coverage across all four scenarios and all three labour-force variables (Employment 93–96%, Unemployment 87–97%, Hours Worked 99.5–100%). At the domain level, Hours Worked coverage is near-nominal (94–98%) in all scenarios; Employment and Unemployment coverage is below nominal for scenarios with low between-domain heterogeneity, a direct consequence of HB shrinkage toward the national mean. A key operational finding emerges from the Rare Event scenario (D): the classical direct estimator collapses to 0% national coverage for Employment and Hours Worked because five unsampled strata introduce a systematic bias; the HB estimator achieves 96–100% national coverage at roughly 15% of the classical sample cost. Neither a weaker prior nor PR MSE correction reliably restores domain coverage, confirming that the failure is bias-driven and cannot be remedied by variance inflation alone.