Page 48 - IJPS-2-1

Life expectancy at birth and life disparity: an assessment of sex differentials in mortality in India

where
l x = Number of survivors at age x
d y = Expected number of deaths in age interval [y,y+1)
T x = Total number of person-years lived above age x
e y+1 = Life expectancy at age y+1
a y = Average number of years lived in age interval [y,y+1)
ω = 100+
2.4 Decomposition of Sex Differences in Life Expectancy and Life Disparity

The purpose of the decomposition is to estimate the contribution at each level of the underlying fac-
tor which can be added to the overall difference between values of the aggregated measure. A step-
wise algorithm was developed for decomposing differences between aggregated demographic meas-
ures and applied it to analyzing the change in life expectancies, healthy life expectancies, pari-
ty-progression ratios, and total fertility rates (Andreev, Shkolnikov, and Begun, 2002). Using a step-
wise algorithm programmed with VBA/Excel, Shkolnikov and Andreev (2010) generated a spread-
sheet to decompose the age-specific difference in any life table indicator between two populations.
With the help of a general stepwise replacement algorithm, age decompositions for different types of
life-table based quantities can be executed. This Excel spreadsheet was used in this study to decom-
pose the sex difference in life expectancy at birth or life disparity, that is, the difference between
male and female life expectancy at birth or the life disparity. Decomposition was performed for all
periods, yet we only presented the results for two periods (1970–1975 and 2006–2010) to show the
transition in age-specific contributions of sex difference in both periods. Because the life tables for
Bihar and West Bengal were available only from 1981–1985 onward, the figures for these two states
are for the time period of 1981–1985, not 1970–1975.

3. Results

3.1 Male-female Differences in Life Expectancy and Life Disparity
Figure 1 shows that there was not much difference between the observed and fitted values of ab-
ridged ln( nq x) for males and females in both periods. The ln( nq x) values from the Heligman-Pollard
model are also compared with the ln( nq x) values of United Nations life tables and shown in Appendix
1. It is evident from the figures that there are no major differences in the values from the two sources
in both periods, except some differences in the adult age group during 1970–1975. These compari-
sons indicate that the complete life table estimates based on the fitted nq x values are good enough
to be used for further comparison and decomposition analyses.
Figure 2 shows that over time, larger numbers of survivors (the l x column of the complete life
tables) had reached the older ages. Deaths are shifting to the older age, which leads to a compression
of deaths. The difference in male and female survivors is evident in both 1970–1975 and 2006–2010
periods. In 1970–1975, as compared to that of females, a higher proportion of male survivors
reached at age 50 from age 5. No significant sex difference was found in the older ages. In
2006–2010, the number of survivors in the initial ages was almost the same between males and fe-
males, but the gap became noticeable after age 40. The curves for males and females did not con-
verge at any point after this age. The graph clearly shows a major transition in mortality in India:
females, who were lagging behind males in the earlier decades, have outpaced males in survival in
the recent years.
Figure 3A clearly shows that the sex difference in life expectancy at birth increased over the pe-
riod. The male advantage in life expectancy at birth was mainly observed until 1981–1985. There is
an apparent increasing trend in sex difference in life expectancy at birth in India, with females at the
higher end. The female life expectancy at birth was 3.0 years higher than the male life expectancy

42 International Journal of Population Studies | 2016, Volume 2, Issue 1