Human Well Being: A Decile Group Analysis on Indian Household Data

Abstract

This is an attempt to measure human well being across different sections of the society in India over time where sections have been made in terms of ten decile groups of income. In this context, the extent to which rural sector is lagging behind the urban sector is another dimension of the study. The study uses grouped household data, collected and made available by National Sample Survey Organisation between 1987–1988 and 1999–2000. The inter decile group analysis does not show parity in the attainment levels of the individual indicators of human well being, although an overall systematic inter temporal betterment for each decile group is very clear. Rural–urban gaps in terms of attainment of these indicators is also not so small.

Appendices

Appendix I

Suppose that the chance of living to age x is l(x), and l(x) is a function of age but not of time. A population whose births number B, uniformly spread through each year, where B does not change, and which is closed to migration will contain just Bl(x)dx individuals between ages x and x + dx at any given time. It will contain B₅Lx = B∫ ⁵₀ l(x + t)dt individuals between exact ages x and x + 5.

As NSSO provides estimated number of migrants by last residence, we can subtract from total population figure the number of migrants from other countries obtaining the closed population for the country as a whole. Then the above said concept can be applied to estimate the ELB for one sex at a time using separate survivorship function l(x) for each sex (Keyfitz 1985).

The stationary population produced by this assumption of fixed annual births and a fixed life table for each sex is generalized by supposing births to follow the exponential Be^rt. Now consider the female (or male) part of a large population closed to migration and subject to a fixed life table, with births increasing exponentially. These conditions are sufficient to produce a stable age distribution, in which the number of persons living in each age group, as well as the deaths in each age group and the total population, are all increasing exponentially in the same ratio.

If the probability of living to age x is l(x), and the births at time t are B₀e^rt, then, to find out the expected number of individuals between age x and x + dx we have to go back in time x to x + dx years, when the number of births was B₀e^r(t−x)dx. The fraction of these births that survive to time t must be l(x); therefore the absolute number of persons aged x to x + dx at time t is

$$ \hbox{B}_{0}\hbox{e}^{\rm r(t-x)}\hbox{l}(\hbox{x})\hbox{dx}. $$

The integral of this quantity is the total population at time t, and dividing by this total gives the fraction of the population aged x to x + dx at time t, say, c(x)dx:

$$ \hbox{c}(\hbox{x})\hbox{dx}=\frac{e^{-rx}l(x)dx}{\int_0^w {e^{-rx}l(x)dx} } $$

(1)

where B₀e^rt has been canceled out from numerator and denominator.

From Eq. 1 it follows that the average age in the stable population is

$$ \bar{{x}}=\int_0^w {xc(x)dx} =\frac{\int_0^w {xe^{-rx}l(x)dx} }{\int_0^w {e^{-rx}l(x)dx} } $$

So level of mortality, l(x), rate of growth of population all are considered in calculation of average age of any population which indicates that it may be considered as an good indicator level of that population.

The NSSO (NSSO 1990, 1997, 2001b) gives us the age distribution of population by sex and by MPCE classes for rural and urban sectors separately. Once the age data by MPCE classes are available, we can use these to estimate the average age of each MPCE class by sex and by region. Then the tables of stable populations and model life tables presented by Coal and Demeney (1983) can be used to estimate ELB, of the people belonging to different age groups.

The four families of stable populations prepared by Coal and Demeney (1983) were namely, North, South, West and East. As was suggested by them that "West" family should be utilized in the usual circumstances of underdeveloped countries where there was no reliable guide to the age pattern of mortality. So, the "west" table have been used for the present purposes.

Appendix II

Table A2.1 Percentages of ADLI, SCHAT, and EDU by decile groups, all India

Table A2.2 ELB by decile groups, all India

Table A2.3 MPCE by decile groups, all India