Sample Attrition in the Presence of Population Attrition

This paper develops a method that accounts for non-ignorable sample attrition in the presence of population attrition for use with a non-representative panel sample. The method is applied to obtain attrition-correcting weights for the native and immigrant samples in the matched Current Population Survey (CPS). Of the two samples, the immigrant sample suffers from sample attrition due to changes in residence as well as population attrition caused by selective return migration. When there is population attrition, the second period cross-section is not representative of the first period population. Therefore, the existing sample attrition-correcting method developed by Hirano, Imbens, Ridder, and Rubin (2001) and Bhattacharya (2008) cannot be applied. We resolve this problem by generating a counterfactual, but representative cross-section prior to applying their method. The counterfactual sample can be obtained by weighting the second period cross-section by one minus the probability of population attrition. We show that the sample attrition and the population attrition processes are separately identified. This is useful because samples usually do not indicate which missing observations are due to sample attrition and which are due to population attrition. The attrition-correcting weights, once obtained, can be used in various studies of immigration using the CPS.