Abstract
This paper investigates the effect of mortality and fertility on the net reproduction rate (NRR) from a dynamic perspective and the impacts they have on India’s demographic characteristics. As a dynamic extension of the net reproduction rate considers both mortality and fertility changes, it has the potential to provide a more realistic and accurate picture of India’s fertility regimes. The estimated values of our “dynamic” NRR are found to be less than the conventional NRR for India as well as for all the states we examined. The results indicate that this difference is mostly driven by changes in fertility. In addition to using several classic demographic measures under both conventional and dynamic approach to study the implications of the NRR on the demographic aspects of the population, we also provide estimates of the minimum time required for attaining stationarity for India and some of its selected major states under the hypothetical condition of imposition of the replacement-level fertility based on both the conventional and dynamic scenario. This comparison reveals that in cases where (1) the difference between conventional and dynamic NRR is small, the projected year of attaining stationarity under the hypothetical situation of imposing the replacement-level fertility does not differ significantly, and (2) there is a striking difference between the conventional and dynamic NRR, the projected year of attaining stationarity differs significantly.
Résumé
Dans cet article, nous étudions les effets de la mortalité et de la fécondité en Inde sur le taux net de reproduction (TNR) d’un point de vue dynamique, ainsi que leur incidence sur les autres caractéristiques démographiques du pays. En tenant compte des évolutions de la mortalité et de la fécondité, l’extension dynamique du TNR permet de présenter une image plus fidèle et réaliste des régimes de fécondité du pays. Pour l’Inde, les valeurs estimatives de notre taux net de reproduction “dynamique” sont inférieures à celles du taux conventionnel, ce qui est également le cas pour tous les états indiens que nous avons étudiés. Les résultats montrent que ces différences sont principalement dues aux évolutions de la fécondité. Pour évaluer les répercussions du TNR sur les aspects démographiques de la population, nous utilisons plusieurs mesures démographiques traditionnelles dans le cadre d’approches à la fois conventionnelles et dynamiques, et nous proposons également une estimation du délai minimum qu’il faudra à l’Inde et à certains de ses principaux états pour atteindre la stationnarité démographique. À cette fin, nous appliquons les seuils de remplacement des générations théoriques fondés sur les scénarios conventionnels et dynamiques. Grâce à cette comparaison, il ressort que dans les cas où: 1) la différence entre les TNR conventionnels et dynamiques est faible, l’année de stationnarité démographique prévue ne diffère pas de façon significative dans les deux cas; et 2) lorsqu’il y a une grande différence entre les TNR conventionnels et dynamiques, l’année de stationnarité démographique prévue varie fortement dans les deux cas.
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Data Availability
All data used in this study are secondary and taken from well-known published sources.
Notes
The annual rate of change of probabilities of death for any age group x to x + n is given by
\({{}_nr}_x=\left(\frac{_nq_x}{_n{\overline q}_x}\right)^\frac1t-1,\); Denton and Spencer (2011) where nqx is the probability of death for the age group x to x + n in the reference period life table and \({}_{{}_{n}{}{\overline{q} }_{x}}{}\) is the corresponding probability in the earlier period table.
Using this rate of change of probabilities of death, the probability that a member of the cohort (defined as lxx, which we may term as the dynamic cohort), who has survived up to the exact age y, will die in the interval y to y + n (where y ≥ x) is obtained by
$${}_{n}{}{q}_{xy}={}_{n}{}{q}_{y}{\left(1+{}_{n}{}{r}_{y}\right)}^{y-x}$$where \({}_{n}{}{q}_{y}\) is the probability of death in the age group y to y + n in the reference period, \({}_{n}{}{r}_{y}\) is the annual rate of change of that probability and (y − x) is the number of years between the subsequent age and initial age; hence, the number of years over which the age probability has changed.
The number of person-years lived by survivors of the lxx cohort in the interval y to (y + 1) is obtained by
$${L}_{xy}=\left({l}_{xy}+{l}_{x,y+1}\right)/2$$where \({l}_{xy}\) denotes the population of initial age x that survives to age y. (For more details, please see Appendix 1).
\(TF{R}^{D}=5\times \left(\sum {}_{n}{}{f}_{xy}\right)/1000\) where \({f}_{xy}\) denotes the dynamic age-specific fertility rate of women in the age group [x, y].
BIMARU is an acronym formed from the first letters of Bihar (BI), Madhya Pradesh (MA), Rajasthan (R), and Uttar Pradesh (U). The acronym BIMARU has a resemblance to the Hindi word “Bimar” meaning sick. In the book, Headcount: Memoirs of a Demographer, Ashish Bose (2010) calls these states BIMARU in the eastern dialect of Uttar Pradesh referring to depressing demographic indicators, viz., poor average age at marriage, number of children per woman, family planning practices, maternal and infant mortality rates, and life expectancy at birth
In populations with low levels of mortality, a TFR of 2.1 corresponds approximately to an NRR of 1.0 (Preston et al., 2001).
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Appendices
Appendix 1
1.1 Estimation of NRR for India Under Dynamic Consideration Over the Previous 40-year Interval
For the calculation of dynamic NRR, we first need to calculate the dynamic age-specific maternity rates.
Table 7
Next, we need to calculate \({L}_{xy}\) (the dynamic analogue of \({L}_{x}\) column of a period life table) which represents the number of person-years lived by survivors of the \({l}_{xx}\) cohort in the interval y to y + 1.
Table 8
Lastly, we calculate the dynamic NRR for India as follows
Table 9
Appendix 2
2.1 Method to Find the Projected Year of Attaining Stationarity Under the Hypothetical Situation of Imposition of the Replacement-level Fertility
The observed population growth rate at time t, \(r\left(t\right)\) can be divided into two parts as
where r is the intrinsic growth rate which reflects the contribution of fertility and mortality to \(r\left(t\right)\) and \(\rho (t)\) is the residual which measures the contribution of the age distribution at time t (Espenshade, 1975). \(\rho (t)\) → 0 as the observed population converges to a stable population.
Without going into too much of the details of non-stable and stable momentum, we devise a simple method of estimating the minimum time for an observed population to become a stationary population once the replacement-level fertility is imposed on it and maintained thereafter.
Suppose the size of the observed population at time 0 is P and the total population momentum of this population is M. The size of the ultimate stationary population will be S = P × M. We have the observed growth rate of initial population, \(r\left(0\right)\); the intrinsic growth rate, r, can be estimated, and the contribution due to age distribution of this initial population can be obtained from
Once the replacement-level fertility is imposed on this initial population, then the growth rate will only be due to age distribution as r becomes zero, i.e., \(r\left(0\right) = \rho (0)\). Assuming \(\rho = \rho (0)\) to be constant, i.e., independent of time (t), we can project the size of the observed initial population on the time axis until it reaches the size of the stationary population S:
Thus, t is the time taken for the observed initial population to reach stationarity.
Now,\(\frac{S}{P} = M = {e}^{\rho t}\)
i.e., \(t = \frac{1}{\rho }\mathrm{ln}\left(M\right)\).
However, in reality, \(\rho (t)\) decreases with time, and hence, the time to reach stationarity will be more than the one obtained by assuming \(\rho (t)\) to be constant, Thus, the time we have estimated by assuming \(\rho (t)\) to be constant can be thought of as the lower bound of the time interval by which the observed initial population becomes stationary when the replacement-level fertility is imposed on it and maintained thereafter. The closer the observed population to its stable equivalent population, the more accurate this estimated time of reaching stationary population.
Taking the initial year as 2016, we shall impose the replacement-level fertility in 2016. Equating the population size obtained after imposing the replacement-level fertility in 2016 and continuing at a constant growth rate, which is due to age composition, with that of the size of the stationary population already obtained, we can thus obtain the lower bound of the time interval by which the observed population reaches the stationary population.
2.2 Projected Year of Obtaining Stationary Population Under Both Conventional and Dynamic Consideration, India
Actual growth rate, \(\begin{array}{c}r\left(2016\right)=\frac1{10}\ln\left(\frac{\mathrm{Total}\;\mathrm{female}\;\mathrm{projected}\;\mathrm{population}\;\mathrm{in}\;2021}{\mathrm{Total}\;\mathrm{female}\;\mathrm{population}\;\mathrm{in}\;2011}\right)\\=\frac1{10}\ln\;\left(\frac{662383}{587585}\right)=0.0119823\end{array}\)
\({r}_{1}\)= intrinsic growth rate (Conventional) = − 0.00003
\({r}_{2}\)= intrinsic growth rate (Dynamic) = − 0.00578
\({\rho }_{1}(2016) =\)Growth rate due to age composition (Conventional) = \(r(2016)\)–\({r}_{1}\) = 0.0120123
\({\rho }_{2}(2016) =\)Growth rate due to age composition (Dynamic) = \(r(2016)\)– \({r}_{2}\) = 0.0177623
\({M}_{1} =\) Population Momentum (Conventional) = 1.379
\({M}_{2 } =\)Population Momentum (Dynamic) = 1.532
P = Actual Projected Female Population in 2016 = 626890 (‘000)
\({S}_{1} =\)Stationary Population Size (Conventional) = P\(\times {M}_{1} =\)864481 (‘000)
\({S}_{2} =\)Stationary Population Size (Dynamic) = P \(\times {M}_{2} =\) 960395 (‘000)
\({t}_{1}=\) Lower bound of the time interval by which P reaches \({S}_{1}= \frac{1}{{\rho }_{1}}\mathrm{ln}\left({M}_{1}\right)\) = 27
\({t}_{2}=\)Lower bound of the time interval by which P reaches \({S}_{2 }= \frac{1}{{\rho }_{2}}\mathrm{ln}\left({M}_{2}\right)\) = 25
Thus, India’s population becomes stationary under the hypothetical condition of imposing the replacement-level fertility in 2016 and maintained thereafter at least in the year \(2016+{t}_{1}= 2016+ 27= 2043\) under usual consideration and in the year \(2016+{t}_{2}= 2016+ 25= 2041\) under dynamic consideration.
Table 10
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Sarma, R., Hussain, N. & Choudhury, L. India’s Demographic Aspects from the Perspective of Dynamic Net Reproduction Rate. Can. Stud. Popul. 50, 6 (2023). https://doi.org/10.1007/s42650-023-00077-7
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DOI: https://doi.org/10.1007/s42650-023-00077-7