Multiregional and bi-regional population projection methods: a brief overview Prepared for:

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


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)


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


Population accounts (movement perspective)

K = Population M = internal migration E = emigrationI = immigration D = deathsØ = ignored R = accounting residual


Notation

“a a+1” subscript denotes the period-cohort aged a at time t and aged a+1 at time t+1


Movement accounts multiregional model

Accounting equation

Projection equation

Either solve this iteratively, or . . .


Movement accounts multiregional model

Matrix M

Matrix projection equation

See Rogers (1995) “Multiregional Demography”


Population accounts (transition perspective)

Keisj = Pop existing in i at time t and surviving in j at time t+1


Transition accounts multiregional model

Accounting equation

Projection equations (term by term)

etc.

See Rees & Wilson (1977) “Spatial Population Analysis”


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


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


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!


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


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


Parameterised model migration schedules

Developed by Rogers, Castro & colleagues

Migration intensity =childhood component+ labour force component+ retirement component+ constant component


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.


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


Do bi-regional models give similar results to a fully multiregional model? (2)

Similarity of projected age profiles:


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



Regional geography


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


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


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 50,0000

10

20

30

40

50

60

70

80

90

100

110

age

males females

20362006


Projected population of the Mid-North Coast

2006: 297,000 2036: 387,000

4,000 2,000 0 2,000 4,0000

10

20

30

40

50

60

70

80

90

100

110

age

males females

20362006

050

100150200250300350400450

2006

2011

2016

2021

2026

2031

2036

Year

Pop

ulat

ion

(tho

usan

ds).


Projected population of the Central West

2006: 179,000 2036: 183,000

2,000 1,000 0 1,000 2,0000

10

20

30

40

50

60

70

80

90

100

110

age

males females

20362006

0

50

100

150

200

250

300

2006

2011

2016

2021

2026

2031

2036

Year

Pop

ulat

ion

(tho

usan

ds).



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 0 062 0 36

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 62 0 3 6


Projected pop'n change 2006-21, NSW Statistical Local Areas

text


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: a brief overview Prepared for:

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