Multiplicity Sampling of Migrant Stock

Multiplicity sampling, introduced by Monroe Sirken in 1970, is a survey design for counting rare and hard-to-reach populations by letting respondents report not only about themselves but about eligible relatives living elsewhere. For migration research the appeal is direct: emigrants and dispersed migrants are, by definition, absent from the sampling frame of the place that wants to count them, so an ordinary household survey misses them. Under multiplicity sampling a sampled household reports its migrant relatives — say, children or siblings who have moved abroad — according to an explicit counting rule, which dramatically raises the effective coverage of the rare group because many households can each contribute reports. The price of this expanded reach is that the same migrant may be reportable by several households, so each reported migrant must be weighted by the inverse of the number of households eligible to report them, the migrant's 'multiplicity.' Sirken showed that this multiplicity-weighted estimator is unbiased and that, by enlarging the set of reporters, it can sharply reduce the sampling variance for rare populations compared with conventional surveys.