Indirect methods of mortality and fertility estimation: new techniques for new realities

The work of demographers in developing countries is limited by the fact that demographic data are either nonexistent or of too bad quality to be usable. Therefore, indirect estimation techniques based on survey data are used to estimate levels and trends of mortality and life expectancy. But also mortality researchers in developed countries are often faced with the problem of nonexistent data when they are interested in specific phenomena of mortality differentials. In order to improve the availability of information on specific mortality differentials in cases where no official data are available, Luy (2009, 2012) suggested a modified version of the orphanhood method (MOM) for indirect estimation of adult mortality from survey information on maternal and paternal survival to permit its application to populations of developed countries. The aim of this paper is to demonstrate the formal demographic relationships behind the MOM and to illustrate the method’s potentials and limitations by summarizing the findings of different empirical applications. The latter will provide additional insights not only for the general usefulness of indirect estimation techniques in developed countries but also for the application of the traditional variants of the orphanhood method in developing countries.

This study presents two approaches of constructing adult mortality table or life table from an appropriate set of survival probability (p-values) from a given set of 5-year cumulative life table survival ratios (in short, 5-cum-LSRs), defined by the ratios T(x+5)/T(x), beyond age 5. The set of survival probability (p-values) over ages, so obtained, is not only consistent with the given set of 5-cum-LSRs but also satisfy the usual properties and depicts the true trends of life table p-values over ages. The two approaches for estimating survival probabilities at various quinquennial ages are as follows -- one makes use of algebraic chain relationships between two survival probabilities in the adjacent 5-year age-intervals for a given set of 5-cum-LSRs, and the other one is based on an iterative procedure under conventional and Greville’s approximations for estimating L(x, x+5) from l(x). The empirical investigations of the two approaches based on model life tables show that the estimated p-values and hence the mortality table so obtained beyond age 5 are almost identical to the true one under certain condition. The empirical and analytical investigations show that non-conventional method (that of Greville's) converges much faster than the conventional method of life table construction. Convergence can be proved mathematically .

Census survival ratios (CSRs) are the oldest and most widely applicable methods of estimating adult mortality. For populations with negligible migration they can provide excellent results of both mortality and expectation of life. Swanson and Tedrow developed a new approach for using CSRs that is less involved than the existing approach. Tests on available data indicate that the alternative approach works reasonably well. In this paper we extend the use of their approach to a population defined by ethnicity, Native Hawaiians. We use the early 20th century as the period for this examination, which is a time when this population was subject to negligible migration. The development of life tables for this population allows us to compare our life expectancy estimates to those derived from the “gold standard” of life expectancy. Our examination suggests that the alternative CSR method works well in estimating life expectancy for Native Hawaiians, which suggests that it can be used elsewhere. Our study also has revealed some cautionary notes about the effect of migration, net census undercount error, and changing conceptions of ethnic identity.