Estimation of the net error rate of population size in China’s household registration

A combined three-source estimator is used to estimate the net error rate of population size in household registration. It avoids the bias in the two-source estimator due to the fact that the registration of an individual on one list affects his or her registration on another list. It makes better use of frequencies than the ordinary three-source estimator. It yields an estimated net error rate that is closest to 1% of error. The combined three-source estimator combines missing-cell estimators of ordinary three-source estimators working on the contingency table of presence or absence in the census population list, the post-enumeration survey population list, and the household population list. Matching of these three registration lists is filled into the seven non-missing cells of the contingency table. The missing-cell estimator involved in the combined three-source estimator is based on the missing-cell estimators of the ordinary three-source estimators. It requires that the three population lists fully register the post-strata population. In the case of sample registration, it is based on the sampling weights and population sizes of the sampled small census areas. It provides a lower mean square error than the ordinary three-source estimator, which itself provides a lower mean square error than the two-source estimator. The estimated 0.96% net under-registration rate of population size for the country as a whole in household registration is close to the 1.00% rate found in the rectification of household registration carried out by China’s Ministry of Public Security between May 15, 2010, and September 30, 2010. Despite the bias coming from the residual heterogeneity of individuals in each post-stratum, as the sample can only accommodate a limited total number of post-strata, the combined three-source estimator should yield a smaller mean square error than the ordinary three-source estimator of the net error rate of population size in household registration.