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8/3/2019 Population and Health- Session 10- Population Projection
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POPULATION AND HEALTH :
TECHNIQUES OF A NALYSIS AND POLICY
PERSPECTIVE
POPULATION PROJECTIONMA (SDP), 2nd Semester, 20121
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PROJECTION
A projection may be defined as the numerical outcome of a particular set of assumptions regarding the future
population
Estimates or forecasts are made, in absence of census orrelated data
Some methods projects for total population
Other for sub-groups i.e., age, sex, race, other
demographic and socio-economic characteristics
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POPULATION PROJECTION: FUTURE
ESTIMATES
Raise our understanding of the determinants of populationchange
y What impact would a 20% decline in birthrates have on a country·s population size and age structure in 50 years?
y How many people would move into a local area if a new f actory employing 1000 people were opened?
Projections often serve as a basis for producing other
projections (e.g., households, f amilies, school enrollment,income, and labor force)
Provides scopes for informed decision making for policy makers
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A SSUMPTIONS IN PROJECTION
Every projections/estimates/forecasts are made oncertain assumption
It does not attempt to predict whether those
assumptions actually will hold true
Range of scenarios and made alternative assumption
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SOME APPLICATIONS:
National population projections- Future Social Security andMedicare obligations
State projections- determine future water demands, welf are
expenditures
Local projections- new public schools, sites for fire stations,
Business enterprises- to predict demands for their products,
demand for housing
The assumptions are made based on past-trends of population
change, since ¶future is intimately tied to the past·.
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POPULATION PROJECTION METHODS
Subjective methods: data, techniques, and assumptions are not clearly identified; difficult for replication
Objective methods: data, techniques, and assumptions
are clearly identified, can be replicated exactly
Smith et al. (2001) classified objective methods under-
(1) Trend extrapolation,
(2) Cohort-component methods, and
(3) Structural models
(4) Other socio-economic projections
However, these are often not ¶mutually-exclusive·
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INPUT DATA -SOURCE FOR PROJECTION
Census
Population Registers
Vital Registers
Other records
Surveillance statistics
Etc.
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USEFUL TERMS:
Base year: year of the earliest data used
Launch year: year of the most recent data used to make a projection
T arget year: year for which the population is projected
Base period: the number of years between the base year andlaunch year
P rojection horizon: number of years between the launchyear and target year
P rojection interval: the time increment for which projections are made (e.g., annually or every 5 years)
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TREND EXTRAPOLATION
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TREND EXTRAPOLATION
Involves fitting mathematical models to historical data andusing these models to project population values-
S imple extrapolation methods: requires data for only two
dates linear change, geometric change, and exponential
change;
C omplex extrapolation methods: requires data for a number
of dates to calculate, linear trend, polynomial curve, logistic
curve, and ARIMA time series
Ratio extrapolation methods: population of a smaller area is
expressed as a proportion of the population of its larger, i.e.,
constant share, shift share, and share of growth
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SIMPLE EXTRAPOLATION
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LINEAR PROJECTION
A ssumption: population will change by the samenumerical amount over a given period, as has registered in the past
Linear change: Pt=Po (1+r*t)
= (Pt- Po)/t, where,
y Pt=Launch year
y Po= Base year
y
t= Base period
Target year (Y)= Pt+(t* ), where t= projectionhorizon
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LINEAR PROJECTION, EXAMPLE
Brazil
1960 = 70,119,071, 2000= 169,544,443
Project population for year 2010
2010 - 190,755,799 (Official statistics, Govt. of
Brazil)
r= 0.033719
2010 194,400,786
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GEOMETRIC PROJECTION
A ssumption: population will change by the samepercentage rate over a given increment of time in the
future as during the base period
Geometric change: Pt=Po (1+r)t
r= (Pt/Po)1/t -1
where,
y r= annual rate of change
y
Pt=Launch yeary Po= Base year
y t= Base period
Target year (Y)= Po(1+r)t where t= projection horizon
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GEOMETRIC PROJECTION, EXAMPLE
Brazil
1960 = 70,119,071, 2000= 169,544,443
Project population for year 2010
r 0.022318418
2010 211,419,680
2010 - 190,755,799 (Official statistics, Govt. of Brazil)
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EXPONENTIAL GROWTH
A ssumption: closely related to the geometric one,but it views change as occurring continuously
rather than at discrete Intervals
Exponential change Pt= Po* ert
r= {ln(Pt/Po)}/t
Where,
y r= annual rate of change
y Pt=Launch year
y Po= Base year
y t= Base period
Target year (Y)= Po*ert where t= projection
horizon
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EXPONENTIAL PROJECTION, EXAMPLE
Brazil
1960 = 70,119,071, 2000= 169,544,443
Project population for year 2010
r 0.022073007
2010 211,419,680
2010 - 190,755,799 (Official statistics, Govt. of Brazil)
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COMPLEX EXTRAPOLATION METHOD
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COMPLEX EXTRAPOLATION METHOD
Uses base-period data for more than two dates.Better deals with nonlinear population change
Three basic steps:
To assemble historical population data for differentdates during the base period
To estimate the parameters of the model selected togenerate the projection. Fit of a particular model
should be understood by studying base yearparameter data
To generate projections using the model(s) selected
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EXTRAPOLATION METHOD
Linear Models: Y i = a + b( Xi ),
Where,
Y i is a set of i observations of values of a ´dependent variable,
Xi is a set of i observations of an ´independent variable,µ
a= is the constant term
b= is the slope of the line describing the ́ best fitting linearµ
relationship between X and Y
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LINEAR EXTRAPOLATION
P i = a + b(T i )
Where,
P i = is the population for a set of time points (e.g., years) over theperiod i
i= b to l (b = base year and l = launch year)
a and b are the estimated intercept and slope, respectivelyT i= is time over the period i = b to l
Regression Equation(y) = a + bx
P i = a + b(T i )
Slope(b)= (N Ti*Pi- (Ti)(Pi) / (NTi2 - (Ti)2)
Intercept (a)= (Pi - b(Ti)) / N
N= number of values/ elements
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TO CALCULATE
Time period
(Ti)
Population
(Pi)
Ti*Pi Ti*Ti b a
1990 Y1
1995 Y2
2000 Y3
2005 Y4
(N Ti*Pi- (Ti)(Pi)
/ (NTi2 - (Ti)2)
(Pi -
b(Ti)) / N
N=5, and once all the values are known, projection can be done for
Year 2010
P i = a + b(T i )
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POLYNOMIAL MODELS
Polynomial models is used for projections in which change
is not constrained to be linear
Where,
Y i = is a set of i observations of values of a dependent variable
Xi= is a set of i observations of an independent variable
a = represents the constant term
bj = the slope of the line describing the ´best-fittingµ
relationship between X ji and Y
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LOGISTIC MODELS
Logistic approach explicitly allows one to place an upper
limit on the ultimate size of the population for a given area
The logistic model is consistent with Malthusian and other
theories of constrained population growth
Where,
Y is the population X is the time period
a ref lects the upper asymptote
b and c are parameters that define the shape of the curve
e is the base of the natural logarithm
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ARIMA (´A UTOREGRESSI VE INTEGRATED
MO VING A VERAGEµ)
ARIMA models have occasionally been used in the
analysis and projection of populations as a whole and
of their demographic attributes.
It deals with time-series data
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R ATIO EXTRAPOLATION METHOD
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Ratio extrapolation methods may be used where an
area containing the population to be projected is partof a larger (´parentµ) area for which projections are
available
The ma jor types include,
(1) the constant-share,
(2) the shift-share, and
(3) the share-of growth approaches.
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THE CONSTANT SHARE
Where,
P it= is the population projection for smaller area (i) in the target
year
P il= is the population of the smaller area in the launch year
P jl= is the population of the parent area ( j) in the launch year
P jt is the projection of the parent area in the target year
The constant-share method requires historical data for only
one date
Ma jor drawback- assumes all small areas will grow at same
pace
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SHIFT-SHARE METHOD
Where,
The smaller area is denoted by i, the parent area by j,
z is the number of years in the projection horizon,
y is the number of years in the base period, and
b, l, and t refer to the base, launch, and target years, respectively
It can lead to substantial population losses in areas that
grew very slowly (or declined) during the base period
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SHARE-OF-GROWTH METHOD
Deals with shares of population change rather than
population size
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LIMITATION OF EXTRAPOLATION METHOD
Do not account for differences in demographic
composition or for differences in the components of
growth
Provide little or no information on the projected
demographic characteristics of the population
Limited usefulness for analyzing the determinants of population growth or for simulating the effects of
changes in particular variables or assumptions
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COHORT COMPONENT
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COHORT COMPONENT
Most widely used method for producing national-level states/provinces, and sub-county area population projections
Introduced by Cannan (1895), subsequently used by Bowley(1924), and later rediscovered independently by Whelpton(1928)
Cohort-component method divides the launch-year populationinto age-sex groups (i.e., birth cohorts) and accounts separately for the fertility, mortality, and migration that the cohort goes through in projection horizon
Provide in-depth knowledge on population dynamics
Cohort-component models typically use either single years or5-year groups- important methodological advancement
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STEPS IN COHORT COMPONENT METHOD
Step 1: Mortality Step 2: Migration (Out or net)
Step 3: Fertility
Step 4: Population (M/F)
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PROJECTING MORTALITY
Age-specific mortality will remain constant (short-
horizon)- Simple A ssumption
Long-horizon needs adjustment for changing rates
with changing socio-economic scenario
Various extrapolation techniques are used, based on
assumption on various socio-economic determinants
shaping mortality trends
A ssumption- future will mirror the past in important
ways
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CONTINUED«
Number of techniques ties mortality rate in one population to
those in another
¶Targeting approach·- is based on assumption realistic forpopulation to be projected
Choice is based on similarities in SE, cultural, behavioral characteristics, medical technology and primary causes of death
Targeting approach- ¶cause-delay·, considering younger cohort inthe same population, instead of same cohort in anotherpopulation
Mortality probability gets reduced due to advancement in medical technology
Mortality probability can also be taken from life-tables
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PROJECTING FERTILITY
Cohort perspective
Period perspective (more commonly used)
y Current A SFRs- assumed will remain constant through
projection horizon. Data based on recent year data or
average data for several years
y Non-linear models used for projecting A SFRs for a wider
horizon, and also for countries that completed demographic
transition
¶Targeting approach·- checking for realistic assumption
for convergence
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PROJECTING MIGRATION
Importance in population growth at national and sub-national level
Gross & Net migration approaches- both used widely
Gross migration approach-
y Out-migration rate:
y Applying out-migration rate to the launch year of population to
provide a projection of the total ¶pool· of inter-state out-migrants forall states.
y This ¶pool· is then allocated to each state based on proportion of in-migrant population received in the base period
Age-sex data (5year before the census)
Age-sex data for decennial census
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CONTINUED«.
Net Migration Approach:
y Top down: 1) Projection on net-migration
2) Projection on age-sex specific migration
y Bottom-up: 1) Separate age-sex group projection
2) Projection of net-migration based on age-sexratio
Projecting migration need careful considerations, based
on contemporary and historical trends
Local and national level projections needs separate focus
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STRUCTURAL MODELS FOR PROJECTION
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STRUCTURAL MODELS FOR PROJECTION
Adjusting for f actors beyond demography.
Economic-demographic models: projection of
population for larger geographic region andeconomic activity; i.e., labour-market, states,
nations
Urban-Systems model: small geographic areas forland-use, transportation pattern etc.
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OTHER SOCIO-ECONOMIC PROJECTION
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OTHER SOCIO-ECONOMIC PROJECTION
Most useful for feeding policy-requirement anddirectly affected by policy decision
Two ma jor approaches:
´Participation ratio methodµ (also known as the´participation rate methodµ, ´prevalence ratio
method,µ and ´incidence rate methodµ)
Cohort progression method
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P ARTICIPATION RATIO METHOD
Current and historical data are used to construct
participation ratios
These ratios are projected into the future
Projected ratios are then applied to population
projections (stratified by age, sex, and other
characteristics) for the geographic area(s) underconsideration to obtain a set of socioeconomic projections
Must have sufficient demographic detail
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COHORT PROGRESSION R ATIO
Numbers with the socioeconomic characteristic or
the corresponding participation ratios are
projected on a cohort basis
Using information on changes in the numbers or
participation ratios between two previous dates.
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REFERENCE
Methods and Materials of Demography, Chapter
21