Measurement of Population
Growth. . Having
obtained the measures of mortality and fertility, our next objective is to find
out if the given population has a tendency to increase, decrease or remain
stable, Fertility rates are inadequate to give us any idea about the rate of
population growth since they ignore the sex of the newly born children and
their mortality. Obviously the populatlon Increases through female births Thus
if a majority of 'births are those of girls, the population is bound to
increase while it will have a downward trend if the majority of births are
boys. Similarly we ignore the mortality
of the newly born children we can not form a correct idea of the rate of growth
of the population, since it is possible that a number of female' children may
die before reaching the reproductive age. In the following sections we shall
study some measures of the growth of population .
Gross
Reproduction Rate (G.R.R.). In order to have a better idea about the rate of
population growth, in addition to the age and sex composition of the population
we must take into account the sex of the new born children since it is
ultimately the female births who are the potential future mothers and result in
an Increaee in the population, The gross reproduction rate (G.R.R.) is a step
In this direction and is defined as 'the sum of age-specific fertility rates
calculated from female births for each
year of reproductive period. Symbohcally, if is
the number of female births to the women of age x during the given period in
the given region, then in the usual notations, we have
$$\boldsymbol{G} . \boldsymbol{R} . \boldsymbol{R}=\sum_{\lambda_{1}}^{\lambda_{2}} \frac{\boldsymbol{f}_{B_{x}}}{\boldsymbol{f}_{\boldsymbol{p}_{x}}} \times \boldsymbol{K}=\sum_{\lambda_{1}}^{\lambda_{2}} \boldsymbol{f}_{i_{x}}$$
$$
where K=1000, \lambda_{1}=15, \lambda_{2}=49$$
Gross reproduction rate is thus
a modified form of total fertility rate and gives the number of females
expected to be born to k newly born daughters.
As a measure
of fertility G.R.R is quite useful for
comparing the fertility in different regions or in the same region at different
periods of time.
If G.R.R is less than unity (1) the
population would decline no matter how low the death rate may be and if G.R.R
is greater than unity then the population would increase no matter how high the
death rate may be.And if G.R.R is equal to 1 then female sex in this case is
replacing itself, it is the criteria for exact replacement.
The accuracy of the G.R.R depends
upon the accuracy of the age specific
fertility rate.Also the main limitation of
G.R.R is it ignores the current mortality.
Net Reproduction Rate. (N.R.R.). As
already pointed out the principal limitation of G.R.R. is that it completely
ignores the current mortality and takes into account only the current
fertility. Net Reproduction Rate (N.R.R.) is nothing but gross reproduction
rate adjusted for the effects of
mortality. According to Benjamin, “N.R.R. measures the extent to which mothers
produce female infants who survive to replace them. It measures the extent to
which a generation of girl babies survive to reproduce themselves as they pass
through the child-bearing age group.”
$$
\boldsymbol{N}\cdot \boldsymbol{R}\cdot \boldsymbol{R}=K \sum_{x} \boldsymbol{n}\left[\frac{\boldsymbol{n}^{f} \boldsymbol{B}_{x}}{\boldsymbol{n}^{f} \boldsymbol{P}_{x}} \times \boldsymbol{n}^{f} \pi_{x}\right]
$$
$$\ n^{f} B_{x}$$ = Number of female births to
the women in the age group {x} to {x+n}
$$n ^{f} P_{x}$$ = Female population in the age group x to x+n.
$$n^{f} \pi_{x}$$= Survival factor.
=1 - Mortality ráte perwomen
$${\boldsymbol{N} \cdot \boldsymbol{R} . \boldsymbol{R}=\boldsymbol{K} \sum_{x}[\boldsymbol{n} \times female age S.F.R \times Survival factor ]}$$
Remarks;
1. $$N \cdot R \cdot R \leq G \cdot R \cdot R$$
the sign of equality holding if and only if all the new born girls survive at least till the end of the reproductive period. Thus G.R.R. provides an upper limit to N.R.R. and hence, in theory, N.R.R. also ranges from 0 to 5 per annum.
2. It may be pointed out that out of a number of girls born to women, some die in infancy and some do not marry at all. Of the married women some become widows and it is only the balance who pass through the fertility period and thus add to the population growth. thus N.R.R. may be interpreted as the rate of replenishment of that population.
3. If N.R.R.=1, we may conclude that "if the current fertility and female mortality rates prevail in future, then a group of new born girls will exactly replace itself in the next generation, i.e., the present female generation will exactly maintain itself. Thus in this case the population has a tendency to remain more or less constant. On the other hand if N.R R. is greater than unity then the population has a tendency to increase while N.R.R. less than unity indicates a declining population.
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