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The problem of estimating the size of a population based on a subset ofindividuals observed across multiple data sources is often referred to ascapture-recapture or multiple-systems estimation. This is fundamentally amissing data problem, where the number of unobserved individuals represents themissing data. As with any missing data problem, multiple-systems estimationrequires users to make an untestable identifying assumption in order toestimate the population size from the observed data. If an appropriateidentifying assumption cannot be found for a data set, no estimate of thepopulation size should be produced based on that data set, as models withdifferent identifying assumptions can produce arbitrarily different populationsize estimates -- even with identical observed data fits. Approaches tomultiple-systems estimation often do not explicitly specify identifyingassumptions. This makes it difficult to decouple the specification of the modelfor the observed data from the identifying assumption and to providejustification for the identifying assumption. We present a re-framing of themultiple-systems estimation problem that leads to an approach which decouplesthe specification of the observed-data model from the identifying assumption,and discuss how common models fit into this framing. This approach takesadvantage of existing software and facilitates various sensitivity analyses. Wedemonstrate our approach in a case study estimating the number of civiliancasualties in the Kosovo war. Code used to produce this manuscript is availableat https://github.com/aleshing/central-role-of-identifying-assumptions.

The Central Role of the Identifying Assumption in Population Size Estimation