Small area estimation with covariates perturbed for disclosure limitation

We exploit the connections between measurement error and data perturbation for disclosure limitation in the context of small area estimation. Our starting point is the model in Ybarra and Lohr (2008), where some of the covariates (all continuous) are measured with error. Using a fully Bayesian approach, we extend the aforementioned model including continuous and categorical auxiliary variables, both possibily perturbed by disclosure limitation methods, with masking distributions fixed according to the assumed protection mechanism. In order to investigate the feasibility of the proposed method, we conduct a simulation study exploring the effect of different post-randomization scenarios on the small area model.