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

1. 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

2. 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

3. 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

4. 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

5. Population accounts (movement perspective) K = Population M = internal migration E = emigration I = immigration D = deaths Ø = ignored R = accounting residual Multiregional and Bi-regional Population Projection Methods

6. 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

7. Movement accounts multiregional model Accounting equation Projection equation Either solve this iteratively, or . . . Multiregional and Bi-regional Population Projection Methods

8. Movement accounts multiregional model Matrix M Matrix projection equation See Rogers (1995) “Multiregional Demography” Multiregional and Bi-regional Population Projection Methods

9. 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

10. 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

11. Practical challenges with the implementation of multiregional models Models can contain a large number of elements No. 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 purchased Suppression of small values in cells Lots of random noise in data Difficult to smooth age profiles with vast amounts of noise Computing difficulties Issue of setting assumptions Multiregional and Bi-regional Population Projection Methods

12. What can be done? Aggregation of age groups, spatial units, time periods etc. e.g. switch from single year age groups to 5 year age groups Decomposition Break up multiregional systems into a no. of relatively independent systems e.g. model O-D flows between areas within a region/state and a simple distribution for other migrations Parameterisation Replace age profiles with a mathematical model described by a small no. of parameters Migration pool models Out-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

13. 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

14. 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

15. Migration pool model Step 1 Out-migr from each regions is product of out-migration rate and population at risk Step 2 All out-migration placed in a common 'pool' Step 3 Pool of migrants distributed to regions on basis of shares Multiregional and Bi-regional Population Projection Methods

16. 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

17. 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 system modelled 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

18. 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

19. 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

20. 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 Multiregional and Bi-regional Population Projection Methods

21. Multiregional and Bi-regional Population Projection Methods 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

22. Regional geography Multiregional and Bi-regional Population Projection Methods

23. NEWDSS State & Rest of Australia level movement accounts-based bi-regional model single years of age 0-120 Regional level movement accounts-based tri-regional model (i) region; (ii) rest of NSW; (iii) rest of Australia single years of age 0-120 Constrained to State level Statistical Local Area level transition accounts-based bi-regional model (i) Statistical Local Area; (ii) rest of Australia 5 year age groups to 85+ Constrained to regional level Multiregional and Bi-regional Population Projection Methods

24. Multiregional and Bi-regional Population Projection Methods 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

25. 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

26. Multiregional and Bi-regional Population Projection Methods The changing age profile of Sydney Bulge in age groups in 20s & 30s due to migration • bulk of net migration gains concentrated at these ages

27. Multiregional and Bi-regional Population Projection Methods Projected population of the Mid-North Coast 2006: 297,000 2036: 387,000

28. Multiregional and Bi-regional Population Projection Methods Projected population of the Central West 2006: 179,000 2036: 183,000

29. 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 Multiregional and Bi-regional Population Projection Methods

30. Projected pop'n change 2006-21, NSW Statistical Local Areas text Multiregional and Bi-regional Population Projection Methods

31. 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 Multiregional and Bi-regional Population Projection Methods

32. Multiregional and Bi-regional Population Projection Methods The end Any questions?