Formal demography, innovative methodologies, and their applications

We present a methodology based on Cubic Splines to fit the general mortality curve in Mexico by sex at all ages for the years of 2000, 2005 and 2010. This method consists in fitting a polynomial of degree three in the first four ages (fitting them perfectly); between ages 4 and 80 we fit a cubic spline using five nodes; we fit another third-degree polynomial beginning at age 80. We employ 24 parameters to estimate the mortality curve in the full age range. This model presents an excellent goodness of fit in men, which increases over the years; for women, the goodness of fit is, in general, better than men’s. This methodology is considered to be a relatively parsimonious estimation of mortality; it maintains the mortality curve’s changes in concavity; and it allows the realization of mortality projections in different contexts and causes of death.

Old-age mortality accounts for large fractions of death. Yet for many developing countries, old-age mortality are often only referred by model life tables using mortality data at young ages, or sometimes at young and adult ages; and reliable estimates of old-age mortality using data collected from old-age population can hardly be found. Based on the fact that migration is rare and death risk is high at old ages, this paper proposed a method, namely the Census method, to estimate old-age mortality, using census data on old-age population. The Census method aims to eliminate the effects of age-reporting errors, and is composed of three models. The first model is the variable-r method that converts the census populations into the person-years of the underlying stationary population. The second is an adjustment model, which uses a common relationship between the survival ratios that is found in model life tables to eliminate the effects of age-reporting errors in censuses. And the third is the extended Gompertz model, which estimates the number of survivors at exact ages of the underlying stationary population based on the commonly observed mortality pattern. Examples are provided using census data from developing countries in Africa and Asia.

The aim of this paper is to develop a new theory to project the life expectancy at birth, called the Auto Regressive Functional Bounded, which is a result of the union of two theories, the Multiple Auto Regressive, that allows you to estimate the value of stability in the future and the Generatrix of Bounded Functions which constructs an increasing function that is bounded by the estimated value of stability.

The Multiple Auto Regressive is a model based on three fundamental assumptions. If these assumptions are true can be proved the life expectancy at birth ( ) when time tends to infinity converges to specific value, so, under these assumptions that specific value is an estimation of the value of the stability. In Norway, Netherlands, New Zealand, Australia and Iceland there are periods of stability in their historical series, by what the model was applied by estimating the values of stability and were compared with the observed values. The predictions and observations are almost equal.


Finally, in Japan, Switzerland and Italy both theories were applied, estimating the values of stability and constructing an increasing function that is bounded for each of these countries. With the functions was projected life expectancy at birth in these countries until the year 2050.

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.

In classical population projection it is inherently assumed equality between census survival ratios and the corresponding life table survival ratios, which hold true only when the population under study is stationary or stable. The proposed technique makes use of ten-year cumulative census survival ratios which run more smoothly than the conventional census survival ratios (as shown by Coale and Demeney, 1967). These ten-year cumulative census survival ratios have been estimated from the corresponding ten-year cumulative life table survival ratios (defined by the ratio Tx+10/Tx in life table terminology) through a formula developed by Lahiri (2003) under generalized population model assuming that the age-specific growth curve follows a second-degree polynomial. The technique proposed here has been applied to project the Indian populations in 2001 and 2011 taking 1991 and 2001 census age-returns as bases respectively. The projected age-sex populations in 2001 and 2011 are sufficiently close to those of the 2001 enumerated population and 2011 expected population respectively. The technique can also be extended for long-term adult population projection by estimating the prospective growth rates over time.

In 2012, the French National Institute of Statistics (INSEE) and the French National Institute of Demography (INED) conducted a national survey on homeless people. The previous one was carried out in 2001: it was the first national homelessness survey in Europe.
The 2012 survey shows some differences compared to the 2001 survey which the presentation will comment on. Indeed, we wanted to approach a larger number of unsheltered homeless. A survey conducted in 2009 in the town of Toulouse showed that other services could be included in the scope of the survey. In addition, we have oversampled services which offered meals. Moreover, we wished to have some information about non French speaking people. Then, we have created a self-administered questionnaire : it existed in 15 languages including French.
The survey sampling is an example of time-location sampling. The survey was carried out with an indirect sampling method: the three degrees of the sampling method, the protocol used to conduct this survey, the weighing method, and their limits will be given.
The first results will be published in France, on March 2013, so the presentation will also describe these results.

Cohort Change Ratios (CCRs) have a long history of use in demography, but they appear, however, to have been overlooked in regard to stable population theory. In this paper, we explore the use of CCRs as a tool for examining the idea of a stable population. Our exploration utilizes four case studies that represent current populations that have very difference dynamics. In comparing the approach using CCRs to the traditional approach, we note benefits and drawbacks. Benefits of the CCR approach include the ability to easily deal with both sexes, all of the components of change, including migration, and, importantly, an indication of how much time would be needed under a constant set of CCRs for a given population to become stable. To this end, we have developed an Index of Stability and demonstrate its use in the context of regression modeling.