Underrated Bootstrap Correction for Linkage-Induced Estimation Biasntitled Item

This paper studies estimation bias arising from imperfect record linkage and proposes an iterated bootstrap correction that accounts for the feedback between linkage error and parameter estimation. The method repeatedly re-estimates the bias using bootstrap samples that preserve the estimated linkage structure, yielding higher-order bias reduction relative to conventional bootstrap corrections. We establish consistency and higher-order bias reduction under general regularity conditions and show that the procedure delivers asymptotically valid inference even when linkage probabilities are unknown and estimated from the data. Monte Carlo experiments demonstrate substantial finite-sample improvements in bias, root mean squared error, and coverage accuracy across linear and nonlinear models. The results provide a practical and general approach to bias correction for econometric analysis using imperfectly linked data.
We also introduce a statistical test to determine when additional iterations yield negligible bias reduction relative to increased variance. Simulations using hormone data and a real-world application linking Australian Bureau of Statistics labour mobility surveys demonstrate substantial bias reduction and enhanced estimation accuracy.
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