  Data on historical populations often extends no further than numbers of
people by broad age-sex group, with nothing on numbers of births or deaths.
Demographers studying these populations have experimented with methods that use
the data on numbers of people to infer birth and death rates. These methods
have, however, received little attention since they were first developed in the
1960s. We revisit the problem of inferring demographic rates from population
structure, spelling out the assumptions needed, and specialising the methods to
the case where only child-woman ratios are available. We apply the methods to
the case of Maori populations in nineteenth-century Aotearoa New Zealand. We
find that, in this particular case, the methods reveal as much about the nature
of the data as they do about historical demographic conditions.
