  The problem of estimating the size of a population based on a subset of
individuals observed across multiple data sources is often referred to as
capture-recapture or multiple-systems estimation. This is fundamentally a
missing data problem, where the number of unobserved individuals represents the
missing data. As with any missing data problem, multiple-systems estimation
requires users to make an untestable identifying assumption in order to
estimate the population size from the observed data. If an appropriate
identifying assumption cannot be found for a data set, no estimate of the
population size should be produced based on that data set, as models with
different identifying assumptions can produce arbitrarily different population
size estimates -- even with identical observed data fits. Approaches to
multiple-systems estimation often do not explicitly specify identifying
assumptions. This makes it difficult to decouple the specification of the model
for the observed data from the identifying assumption and to provide
justification for the identifying assumption. We present a re-framing of the
multiple-systems estimation problem that leads to an approach which decouples
the specification of the observed-data model from the identifying assumption,
and discuss how common models fit into this framing. This approach takes
advantage of existing software and facilitates various sensitivity analyses. We
demonstrate our approach in a case study estimating the number of civilian
casualties in the Kosovo war. Code used to produce this manuscript is available
at https://github.com/aleshing/central-role-of-identifying-assumptions.
