We are grateful to all those who submitted comments on the paper. Their comments give us an opportunity to revisit some of the key points in our paper, as well as to elaborate on some important issues which we could not cover in sufficient detail in the paper.
Specific assumptions and general applicabilityThe three assumptions related to the potential DSE bias are concerned with linkage errors, erroneous records, and heterogeneous list capture probabilities, as commented by Baffour, Chai, Eleanor, Shlomo and Smith. While the first two types of error seem to have their own distinct causes, heterogeneous capture probabilities may be confounded with list dependence. Nevertheless, since the consequence of any list dependence is just heterogeneous capture probabilities, one only needs to focus on whether the capture probability of at least one list is sufficiently constant given the relevant covariates, such as by post-stratification, rather than deliberating whether independence can or cannot be assumed for different register sources. Diagnostics and tests for homogeneous B-list capture probability are useful tools in practice.In reality, where question marks cannot be entirely eradicated for any of the error sources, there are only two logical steps one can take.The first step is to define a strategy, by which some types of error can be reduced to a negligible extent compared to the remaining ones. In the PECADO system, decisions are made to make A-list undercounting the predominant problem that remains, which can be solved by the traditional wisdom of DSE implementation. Whereas the system described by Bernardi et al. sets up EPR overcounting as the main issue to be solved. This shows how different practical approaches are possible following the same strategy of 'reduce-and-conquer', given the data situations in different countries.The second step is to develop adequate methods to support the chosen strategy. For instance, trimming source-registers instead of individual records is found to be useful for the PECADO system. But it may not be feasible if the statistical agency has only limited access to various signs-of-life data sources. Chipperfield et al. ( 2023) investigate capture-recapture estimation given both non-negligible linkage errors and erroneous records. In particular, a record-level score for trimming can be modelled on linking census and administrative spine, such that the trimmed spine containing negligible erroneous records can be used as a list for capture-recapture estimation.
Methodological extensionsSeveral needs and possibilities for methodological extensions are mentioned by Abbott, Allin, Eleanor, Henry and O'Farrell, Pfeffermann and Shlomo, which pertain to potential uses of more sophisticated models, disaggregating statistics to more detailed levels including special subpopulations, and producing attribute statistics by similar methods.