Advances in life table analysis

A classic problem in life table construction is the calculation of the probability of death in an age interval (x,x+n) from the observed age-specific death rate _n M_x. For period life tables one typically makes the assumption that _n M_x= _n m_x and proceeds to apply conversion formula _n q_x=(n* _n m_x)/(1+n*(1- _n a_x )* _n m_x ). However, the application of this formula derived from a cohort perspective to estimation for life tables calculated from period data can be problematic. Cohort measure are different from their period counterparts in that cohort measures are concerned with all events that occurred to the cohort members while period measures are only concerned with the events that occurred to individuals within a given period and age interval. Three issues might preclude the direct application of the formula above to period life table construction: the ambiguity in the definition of _n a_x; the definition of _n M_x; the conversion formula between _n m_x and _n q_x. In this paper, we give clear definition for _n a_x and _n M_x from period perspectives, and derive the conversion formula between _n m_x and _n q_x for the construction of period life tables. We use simulated data to illustrate the problems with traditional indicators and asses the performance of our revised definitions.

Numerous studies show that high life expectancy is closely related to low life disparity. Unlike life expectancy, which can be increased by mortality decline at any age, averting deaths may either reduce or increase life disparity. Disparity can thus be decomposed into two opposite components, called compression and expansion, according to the effect of mortality decline on the age distribution of mortality. Conventional measures of disparity do not distinguish between the two components and inevitably provide misleading information on the equalization of life chances in a population. Based on the relevant properties of the change in disparity, we develop a new measure of disparity, the ratio of expansion to compression (REC), which can account for the relative importance of the two components. With this simple measure, we can obtain not only a clearer vision of the evolution of disparity, but also a consistent interpretation of the change in disparity related to mortality decline, just as we do with life expectancy. Empirical analysis shows the advantages of the new measure over conventional measures of disparity.

Intercensal methods have been broadly used to estimate mortality in developed and less developed countries with deficient or incomplete data. These methods have several advantages over indirect methods because they do not require the use of model life tables and provide sufficiently accurate results even in the presence of age distortions and death under-registration. The drawback of these methods, however, is that generated life tables do not provide ex post projections of the baseline population that are consistent with the subsequent enumeration, even after adjusting for migration and age misreporting. This article demonstrates these inconsistencies by reviewing and comparing the results of three well established methods. We introduce a simple procedure to solve this inconsistency by providing life tables that are accurate and which generate identical projected and input populations. The empirical illustration demonstrating its efficacy draws on data from Vietnam, but the method can be extended to any context and time period.

Rectangularization - the development of an increasingly rectangular
shape of the survival curve - has been theoretically predicted and
empirically noted among humans in nearly all low mortality countries in
the last decade. Explanations that account for rectangularization and
test their applicability to empirical data, however, remain limited. We
propose a new approach that distinguishes between two different kinds of
rectangularization, inner and outer rectangularization. Inner
rectangularization refers to the rectangular shape produced by the
mortality schedule, whereas outer refers to the used maximum living
potential determined by the highest attained age. This allows us to
implement the Maximized Inner Rectangle Approach (MIRA), which
determines the biggest rectangle under the survival curve, thereby
enabling a decomposition of the area below and above the survival curve.
The empirical application of our models reveals that rectangular
movement is not a new development, and has been a visible feature of the
survival curve since the earliest survival data we have access to.
Furthermore, our approach provides empirical evidence against
compression as a mechanism underlying rectangularization, and supports
the explanation that rectangularization is the result of a premature
mortality decline.

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.