multiregional and bi-regional population projection methods: a brief overview prepared for: summer...
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Multiregional and bi-regional population projection methods: a brief overview
Prepared for:Summer School on Projection Methods for Ethnicity and
Immigration Status
Leeds University, July 2009
Tom Wilson
Multiregional and Bi-regional Population Projection Methods
What is a multiregional model?
“Formal multiregional demography ... is concerned with the mathematical description of the evolution of human populations over time and space” Rogers, 1995 p 1
A multiregional model is one which explicitly includes migration between regions
Multiregional and Bi-regional Population Projection Methods
Why use a multiregional model ?(rather than a simple net migration / net migration rate model)
Conceptual reasons* No such thing as a net migrant, just people moving from one place to another* Net migration rates do not relate to a correct PAR * Origin-destination migration rates model migration as a function of origin population size
Practical reasons* Net migration models can give negative populations* They can result in “rogue cohorts” & thus implausible age profiles* If you are dealing with many regions it is difficult to ensure that migration within the system sums to zero.* Difficult to smooth net migration rate profiles because they are highly variable in shape & there are no models/theory to draw upon (much easier to do this for directional migration age profiles)
Multiregional and Bi-regional Population Projection Methods
Birth of multiregional demography in a nutshell
Began in 1960s with work of Andrei Rogers
He was interested in generalising the uniregional Leslie matrix and the uniregional life table to the multiregional case
Many other researchers contributed to this emerging stream of demographic work in the 1960s & 1970s
Phil Rees and Alan Wilson approached multiregional demography from a population accounting perspective
Much theoretical development and empirical work done at IIASA in 1970s and 80s
Multiregional and Bi-regional Population Projection Methods
Population accounts (movement perspective)
K = Population M = internal migration E = emigrationI = immigration D = deathsØ = ignored R = accounting residual
Multiregional and Bi-regional Population Projection Methods
Notation
“a a+1” subscript denotes the period-cohort aged a at time t and aged a+1 at time t+1
Multiregional and Bi-regional Population Projection Methods
Movement accounts multiregional model
Accounting equation
Projection equation
Either solve this iteratively, or . . .
Multiregional and Bi-regional Population Projection Methods
Movement accounts multiregional model
Matrix M
Matrix projection equation
See Rogers (1995) “Multiregional Demography”
Multiregional and Bi-regional Population Projection Methods
Population accounts (transition perspective)
Keisj = Pop existing in i at time t and surviving in j at time t+1
Multiregional and Bi-regional Population Projection Methods
Transition accounts multiregional model
Accounting equation
Projection equations (term by term)
etc.
See Rees & Wilson (1977) “Spatial Population Analysis”
Multiregional and Bi-regional Population Projection Methods
Practical challenges with the implementation of multiregional models
Models can contain a large number of elementsNo. of migr. rates:
no. of regions x no. of regions -1 x no. of sexes x no. of age groups x no. of time periods
Requires large data to be purchasedSuppression of small values in cellsLots of random noise in dataDifficult to smooth age profiles with vast amounts of noiseComputing difficultiesIssue of setting assumptions
Multiregional and Bi-regional Population Projection Methods
What can be done?
Aggregationof age groups, spatial units, time periods etc.e.g. switch from single year age groups to 5 year age groups
DecompositionBreak up multiregional systems into a no. of relatively independent systemse.g. model O-D flows between areas within a region/state and a simple distribution for other migrations
ParameterisationReplace age profiles with a mathematical model described by a small no. of parameters
Migration pool modelsOut-migration from each region goes into a pool; it is then distributed back to regions using shares of the pool
Multiregional and Bi-regional Population Projection Methods
What can be done? (2)
Bi-regional models (a form of spatial aggregation)Model migration between a region and the rest of the system
Use uniregional net migration models? NO!
Multiregional and Bi-regional Population Projection Methods
Decomposition
Fully multiregional model used for flows within a broad region or state
Pool model used for flows to distant areas:Out-migr to distant areas = out-migr rate x PAR Migration to area j = out-migr to distant areas x share going to j
e.g. migration between regions within Australian states modelled using a fully multiregional model; migration between regions in different states modelled using shares of total out-migration
Multiregional and Bi-regional Population Projection Methods
Migration pool model
Step 1Out-migr from each regions is product of out-migration rate and population at risk
Step 2All out-migration placed in a common 'pool'
Step 3Pool of migrants distributed to regions on basis of shares
Multiregional and Bi-regional Population Projection Methods
Parameterised model migration schedules
Developed by Rogers, Castro & colleagues
Migration intensity =childhood component+ labour force component+ retirement component+ constant component
Multiregional and Bi-regional Population Projection Methods
Bi-regional models
Internal system (excl. rest of the world) is divided into just two regions. Actually series of bi-regional models knitted together.
Migration between each region & rest of systemmodelled in turn
etc.
Minor adjustment required to ensure that projected internal out-migration and in-migration to/from all regions is the same.
Multiregional and Bi-regional Population Projection Methods
Do bi-regional models give similar results to a fully multiregional model?
Series of empirical tests with fully multiregional model & several other models, including the bi-regional (BR) model
Multiregional and Bi-regional Population Projection Methods
Do bi-regional models give similar results to a fully multiregional model? (2)
Similarity of projected age profiles:
Multiregional and Bi-regional Population Projection Methods
Strengths of the bi-regional model
Maintains the important conceptual strength of the fully multiregional model of handling place to place migration flows (rather than net migration)
Considerably reduced data requirements (and $$$)
Less randomness in age profiles & less adjustment/smoothing needed (and less staff time)
Considerably reduced no. of assumptions that need to be made► important in persuading govt (& others) to use such methods
Empirical results not far off those produced by the fully multiregional model
Less projections data to check
Population projections for NSW
Model: New South Wales Demographic Simulation System (NEWDSS)
Projections calculated at 3 levels:
(1) NSW as a whole
& Rest of Aus
(2) Regions of NSW
(3) Statistical Local Areas (SLAs)
Local Government Areas (LGAs)
Strategy regions / subregions
Multiregional and Bi-regional Population Projection Methods
Multiregional and Bi-regional Population Projection Methods
Regional geography
Multiregional and Bi-regional Population Projection Methods
NEWDSS
State & Rest of Australia levelmovement accounts-based bi-regional modelsingle years of age 0-120
Regional levelmovement accounts-based tri-regional model(i) region; (ii) rest of NSW; (iii) rest of Australiasingle years of age 0-120Constrained to State level
Statistical Local Area leveltransition accounts-based bi-regional model(i) Statistical Local Area; (ii) rest of Australia5 year age groups to 85+Constrained to regional level
NEWDSS input and output
Data assembled, checked & adjusted in Excel workbook
Input files prepared as csv files
Projection program(fortran 95)
Output csv files
Excel workbook used to visualise outputs
Multiregional and Bi-regional Population Projection Methods
Age patterns of interstate migration
Bi-regional model reduces no. of age profiles required: just in- and out-migration profiles needed (not whole set of O-D profiles)
Much easier to smooth as graphs demonstrate
NSW male out-migration NSW male in-migration
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0 20 40 60 80age
mig
ratio
n ra
te
raw datafitted curve
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0 20 40 60 80age
mig
ratio
n ra
te
raw datafitted curve
Multiregional and Bi-regional Population Projection Methods
The changing age profile of Sydney
Bulge in age groups in20s & 30s due to migration- bulk of net migration gainsconcentrated at these ages
50,000 25,000 0 25,000 50,000
0
10
20
30
40
50
60
70
80
90
100
110
age
males females
2036
2006
Multiregional and Bi-regional Population Projection Methods
Projected population of the Mid-North Coast
2006: 297,000 2036: 387,000
4,000 2,000 0 2,000 4,000
0
10
20
30
40
50
60
70
80
90
100
110
age
males females
2036
2006
0
50
100
150
200
250
300
350
400
450
2006
2011
2016
2021
2026
2031
2036
Year
Pop
ulat
ion
(tho
usan
ds).
Multiregional and Bi-regional Population Projection Methods
Projected population of the Central West
2006: 179,000 2036: 183,000
2,000 1,000 0 1,000 2,000
0
10
20
30
40
50
60
70
80
90
100
110
age
males females
2036
2006
0
50
100
150
200
250
300
2006
2011
2016
2021
2026
2031
2036
Year
Pop
ulat
ion
(tho
usan
ds).
Multiregional and Bi-regional Population Projection Methods
Multiregional and Bi-regional Population Projection Methods
Bi-regional Statistical Local Area model gives plausible age profiles
Leichhardt council Hunter's Hill
The previous net migration rate model produced several 'rogue' cohorts
M a le s F e ma le s
4,000 3,000 2,000 1,000 0 1,000 2,000 3,000 4,000 5,000
0–45–9
10–1415–1920–2425–2930–3435–3940–4445–4950–5455–5960–6465–6970–7475–7980–84
85+
Age
gro
up
2 0 0 6
2 0 3 6
M a le s F e ma le s
1,500 1,000 500 0 500 1,000 1,500
0–45–9
10–1415–1920–2425–2930–3435–3940–4445–4950–5455–5960–6465–6970–7475–7980–84
85+
Age
gro
up
2 0 0 6
2 0 3 6
Multiregional and Bi-regional Population Projection Methods
Projected pop'n change 2006-21, NSW Statistical Local Areas
text
Multiregional and Bi-regional Population Projection Methods
Concluding remarks
Multiregional & bi-regional models are conceptually much better than net migration models because they incorporate place to place migration flows
The bi-regional model is a reduced form of the fully multiregional model which retains directional migration whilst reducing data requirements and input assumptions
Much work remains to be done on assumption-setting, esp. in having regionally consistent assumptions
The end
Any questions?
Multiregional and Bi-regional Population Projection Methods