COMMENTS ON THE CLOSE SIMILARITY BETWEEN INDIAN
POPULATION PROJECTIONS FROM THE
CONSTRAINED COALITION AND LOGISTIC MODEL AND THE CENSUS,
GOVERNMENT OF INDIA AND UN ESTIMATES
V.K.C. Sanghi
National Institute of Science, Technology
and Development Studies
New Delhi - 110 012, India.
-
Abstract
The close similarity between the Indian census, Government
of India and UN population estimates and those from the
Constrained Coalition and Logistic Model (CCLM) has been
demonstrated which enhances the usage of differential equation
modelling for studies on population growth processes. The CCLM
incorporates the legitimate requirement of an upper bound for the
aggregate population thereby implying the rate of natural
increase to reach the zero level, The numerical value assumed
for the upper bound is based on food supply - arable land
availability, and accounts for advances in apriculture
productivity. However, other factors such as quality of life,
environmental degradation, per capita income, etc. can also be
used to arrive at an upper bound. The model holds good promise
for usage for other developing countries.
Key words: Differential Equation Models, Logistic, Indian
Population Dynamics,Less Developed Regions, UN
Estimates, Validation.
983
System Dynamics ‘90
COMMENTS ON THE CLOSE SIMILARITY BETWEEN INDIAN
POPULATION PROJECTIONS FROM THE
CONSTRAINED COALITION AND LOGISTIC MODEL AND THE CENSUS,
GOVERNMENT OF INDIA AND UN ESTIMATES
V.K.C. Sanghi
National Institute of Science, Technology
and Development Studies
New Delhi - 110 012, India.
In a paper{1] different types of differential equation
models have been examined to represent the dynamics of population
growth in India. The solutions of these models have been
obtained using analytical and grapho-analytical techniques. The
comparative analysis of the projections from the different models
points to a particular model designated as the Coustrained
Coalition and Logistic Model (CCLM) as the best and this is given
by
s 1
: a ko:
-( = ON
aN s A N
wn = rN 2A l-e : (i--) N
dt : : M
_ _ (1)
where N = aggregate population, r = rate of natural increase,
i.e. the difference of birth and death rates, A = saturation
value for the rate of natural increase, i.e. 2.88 percent per
annum, M = saturation value for the aggregate population, i.e.
System Dynamics '90 985
2200 million, a and k are parameters, values for which are fixed
with reference to the best-fit using census statitics and found
to be
~38
a = .1145197*10 and k = ,3.
At the outset, it is interesting to bring out that there has
been a direct coincidence between the 1981 Indian census figure
for the aggregate population, i.e. 685.2 million [2] wnicn really
tends to the 700 million mark duly taking into account an under
count of 1.7 per cent which is normal for such a huge operation
{3] and the projection from the CCLM for the year 1981, which
also placed the country's population at 700 million. The 1991
projection of 850 million from the CCLM is also expected to be
within close proximity to reality, while the backward projections
i.e. those for the period 1921-71 also compare remarl.ably very
well with census data(Table 1).
The model becomes further interesting when the lLong-tera
projections obtained from it lead to certain inferences: that are
very closely similar to the United Nations estimates (4-9) as
brought out herebelow:
a. The population yrowth curve represented by the CCLM has
been derived by following the trend curve for the rate
° of natural increase(r) which is thus depicted to
stabilize at 2.88% per annum and by fixing an upper
bound for the Indian population at 2200 million, argued
from food supply~arable land considerations including
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advances in agricultural productivity. How2ver, the
model structure is such that the rate of natural
increase can never attain stabilization because of the
constraint offered by the bounded population, whereby it
progresses to a peak value of 2.184 per annum only
(Fig.1)- With this. model mechanism and using the
graphical method of isoclines, the N-N trajectory is
obtained (Fig. 2), the inverse of which (Fig. 3) yives
the growth projections for the population (Table 1) by
measurement of time in Fig. 3. The projection for the
year 2101 works out to 2099 million and for the year
2111 as 2128 million, the growth getting slower for the
period ahead. Due to the asymptotic nature of the
growth trajectory, the mathematical limit of 2200
million can be realized only at infinite time, and
therefore, some period +, say, 2-3 decades - ahead of
2101 can thus be seen to be the stabilization period for
the Indian population, which is in perfect unison with
the stabilization period 2110-2130 identified by the
United Nations for the world population which really
implies the less developed regions depending cn whether
fertility decline is modest or moderate [4,6,7,9].
With the Indian population stabilizing at 2200 million
during the period 2101-2131 against the 1981 population
of 700 million as projected by the CCLM, therety meaning
a 3-fold increase and more, an analogy can be drawn with
System Dynamics '90 987
the United Nations assessment for the less developed
regions, wherein a stable population exceeding 9 billion
has been estimated during the stabilization pertod
2110-2130 [4,6,7,9] against the 1980 population of 3313
million [38], which also represents an increase
approaching 3-fold. The saturation value of 2200
million as taken for India, as such corresponds to the
overall dynanism of the less developed regions system
with regard to growth of population.
Further, the average annual yrowth rate for the decade
1971-81 obtained from the projections given by the CCLY
is found to be 2.10% per annum which is synchronous with
the UN estimate for the period 1975-30 for the less
developed regions [5,6,8]. Interestingly, the parallel
tonotonic declination th the growth rate as projectec
for all times henceforth in both the cases as well as
the UN estimate for India, medium variant [8], as showr
in Table 2, further confirms the probably irreversible
downward trend in global population growth and the
anticipated acceleration of this trend.
The annual increments in the aggregate population as
obtained from the CCLM continue to rise uptill the
decade 2001 - 2011 inspite of the fact that the average
annual growth rate as projected by the CCLM is already
declining since 1971-81 - which is followed by continual.
System Dynamics 'SO
declination as anticipated almost alike the situation
for the less developed regions as assessed by the United
Nations [8], wherein the annual increments reath a peak
during 1995-2000 and start monotonically declining
thereafter (Table 3). The UN medium variant estimate
for India also follows a similar tendency [8], excepting
for a slight undulation during 2015-202u, which appears
to be inconsistent, however, the UN estimates a somewhat
steeper decline in comparison to the CCLM. Due to the
higher peak value of these annual increments ‘or India,
the UN estimates for the aggregate population for India
medium variant (8] as shown in Table 1, project: a faster
growth for the period 1990-2010 and appear to be
coinciding with the CCLM projections by the period
2021-2031.
The current Government of India estimates for population by
the turn of the century (year 2U01) are high 1021.9, medium 986.1
and low 966.6 million [2]. On comparing these estimates with the
projection of 1012 million for the year 2001 from the CCLM, it is
seen that this figure falls in between the medium and high values
and as such thus reinforces the high possibility of crossing the
one billion mark in the first census count of the next century.
Of course, with speedier and more extensive direct and indirect
efforts over fertility control - possibly, signifying the ‘low
variant' as envisaged in the UN estimates [4,6] - it could be
oO
System Dynamics ‘90 989
possible to restrain the population at the low projection level
of 966.6 million and thus bring about stabilization by the year
2070 or so. Of course, the accelerating pattern of decline in
fertility as observed for the tnadustrialized regions of the
globe, does convey a certain degree of optimism about the same,
in the light of a gradual furtherance of urbanization and
industrialization all over the country, although other relevant
areas such as assured maternal and child health care,
supplementary nutritional programmes, extensive medical care
facilities and the like have certainly a long way to go.
The keen comparability and accuracy of projections from the
CCLM as brought out herein, promote a high degree of validity to
the dynamic model which could thus describe the population growth
phenomenon in other developing countries as well, besides
bringing oul the powerful tuel contatned fa methemat teat
modelling for studies on population growth processes.
References,
1. K.K. Murthy and V.K.C. Sanghi, Predictive Model Studies
for Indian Population Growth and Energy Demand, in
J.M.L. Janssen, L.F. Pau and A. Straszak (editors),
Models and Decision-Making in National Economies,
North Holland, 241-288 (1979). Proceeding, of the
Second International Conference _on Dynamic Modelling and
System Dynamics ’90
Control of National Economies, V
nna(Austria),
ary
1977.
Government of India, Office of the Registrar-General,
Demography Division, Report of the Expert Committee on
Population Projections, Census of India 1981,
Occasional Papers No. 4 of 1988, New Delni, (1988).
United Nations Fund for Population Activities (UNFPA),
The Subcontinent Takes Stock, Population, UNFPA
Newsletter, Vol. 7, No.5, 2-3, New York (May 1981).
United Nations, Department of International Economic and
Social Affairs (DIESA), Long-range Global Population
Projections, Population Division Working Paper,
ESA/P/WP. 75, New York (August 1981).
United Nations, DIESA, World Population Prospects As
Rafael M. Salas, State of World Population 19%1:Beyond
2000, Populi, UNFPA Journal, Vol.3, No.2, 3-11, New
York (1981).
Nafis Sadik, Safeguarding the Future, Populi, Vol.15,
No.2, 4-37, New York (1988), also in UNFPA Annual Report
1987, 7-44, United Nations Population Fund, New York,
System Dynamics '90
(1988).
United Nations, DIESA, World Population Prospects
1988, Population Studies No. 106, Population Division,
New York (1989).
United Nations Population Fund, State of World
Population 1989, UNFPA, New York (1989).
(percent/year)
RATE OF NATURAL INCREASE r
AGGREGATE POPULATION SATURATION
AT 2200 MILLION
400 600 800 1000 1200 1400 1600 1800 2000 2200
POPULATION N (millions)
Fig.l PIECEWISE-LINEARIZATION OF r & N
06, SoTurentg wrezskg
X 10 (millions/year)
500 a
re) vt T/
nu Oo fe) Q!
400 fe) % = —
. ' J‘ '
iy “ a u
ane < « «~ «<
200 + [ T
100 4
+
te)
200 400 600 800 1000 1200 1400 1600 1800 2000 2200
POPULATION N (millions)
Fig.2 RESPONSE TRAJECTORY FROM
ISOCLINES IN THE PHASE PLANE
06, Soyureudq ure}shS
666
(yeara/i lion)
at
mM
ol
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2.52 sqecmom 1 decade
Ro
400 ol) BOR" 100d 1200 PENT) ToT ISCO
POPULATION n (millions)
Pig.3} POPULATION PROJECTION BY WEASUREMENT OF TIME
Table 1 : Comparison of Population Projections for India from the Constrained
*. Coalition and Logistic Model (CCIM) with Census Population, Govt.
of India Projections & UN Estimates for India . millions
LLG RT NG NE NEE LTE ERE EET LN TF ON RS OE NLR ENR EE TEEN RTE EE NE EN TE IG
Census / Census CCLM Projections Govt. of India UN Estimates for Dece-
Decennial Population Projections India nnial
Year High Med Low High Med Low Year
mute ne sn anesen sr saateanasentee ne nannsecenenanan are tr ere ert erro
BACKWARD PROJEC IONS .
1921 251.3 251.3
1931 279.0 278.0
1941 318.7 314.0
1951 - 361.1 370.0
1961 439.2 456.0 .
1971 547.9 563.5 . \
FORWARD PROJECTIONS
1981 685.2 700.0
1990 865.2 853.3 847.9 1990
1991 850.0 841.7 837.2 834.8 871.5
2000 1080.2 1042.5 1010.9 2000
2001 1012.0 1021.9 987.1 966.6
2010 : 1299.3 1225.3 1159.6 2010
2011 1180.0
2020 E 1513.4 1374.4 1257.8 2020
2021 1340.0
2031 1490.0
2041 1627.0
2051 1767.0
z2u61 1864.0
2071 1944.0
2081 2010.0
2091 2061.0
2101 2099.0
2111 2128.0
2121 Approaching
2131 stabilization at
2200.0
06. soyurentg w193s4S
S66
go
996 System Dynamics ‘90
Table 2 : Comparison of average annual population growth rate
for India from the CCLM with UN Estimates, medium
variant, 1971-2031
coat wee eennn-
Quinquennial/ UN
Decennial Period Estimates for India Projec-
for Less Develo- tions
ped Regions
lead baled tale tadeialeteieteteeiaiateteteiets eed ater rere eee nee
1975-1980 2.10 2.08
1971-1981 2.10
1980-1985 2.10 2.21
1985-1990 2.10 2.08
1981-1991 1.96
1990-1995 2.06 2.09
1995-2000 1.92 1.92
1991-2001 1.76
2000-2005 1.74 1.72
2005-2010 1.56 1.51
2001-2011 1.55
2010-2015 1.41 1.28
2015-2020 1.25 1.02
2011-2021 1,28
2020-2025 1.13 1.01
2021-2031 : 1.07
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Table 3: Comparison of annual population increments for India
from the CCLM with UN Estimates, medium variant,
1971-2031.
million
oe ee te en re ee ee eee eee:
Quinquennial/
Decennial
Period
UN increments
for Less Devel~ for India
oped Regions
UN increments
CCLM
incres
ments
1971-1981
1980-1985 73.3 16.1
1985-1990 81.4 16.8
1981-1991
1990-1995 88.9 18.8
1995-2000 91.5 19.0
1991-2001
2000-2005 90.7 18.7
2005-2010 88.3 17.8
2001-2011
2010-2015 86.2 1o.2
2015-2020 81.6 13.6
2011-2021
2020-2025 78.4 14.2
2021-2031
Ce telltale bela otters Slate tale Caleta ated Salle Soll eletatata alata tatatatad =
15.0
16.2
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