Adjusting General Growth Balance Method for Migration

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Adjusting General Growth Balance Method for
Migration

• Kenneth Hill
• Bernardo Queiroz
• Marconi Conference Center, 8-11 July, 2004

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Introduction

• GGB and SEG assess completeness of death by
  comparison with the recorded age distribution
  through age specific growth rates
• models assume closed population, but literature
  notes that it is straightforward to adapt these
  methods for the effects of migration if magnitude
  and age distribution are know
• objective of the paper is to explore the
  possibility of using prior information about the
  age pattern of migration to adjust the GGB for
  use in population with substantial net migration.

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GGB and Migration (1)

• In closed populations, entries to the population
  age a and over occur as result of members of the
  population having birthdays at age a, and exits
  consist only of deaths of members of the
  population at ages a and over.
• Thus,
• r(a) b(a) - d(a) (1)
• Following Hill (1987),
• b(a) ro(a) (1/t) ln(k) qddo(a) (2)
• where b(a) and do(a) are the rate of entry and
  exit in the population, ro(a) is the observed
  growth rate, t is the intercensal interval, k is
  the completeness of the first census relative to
  the second and qd is the completeness of
  reporting deaths relative to the average
  population coverage.

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Fig.1 - Original GGBMexico
Puerto Rico
k1/k2 0.981 Slope 0.899
k1/k2 1.018 Slope 0.913
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GGB and Migration (2)

• Bhat (2002) generalizes the method for
  populations affected by migration
• r(a) b(a) - d(a) nm(a) (3)
• where nm(a) is the net migration rate for the
  population age a and over
• however, to apply equation (3) data on
  intercensal migration are necessary. Since this
  information is not always available the author
  suggests the use of a standard pattern.

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GGB and Migration (3)

• We present a similar method, introducing a
  two-step iterative approach that first estimates
  net migration rates and then adjusts GGB for
  migration.
• From Equation (3)
• r(a) d(a) - b(a) nm(a) (4)
• Assuming that net migration rates have a typical
  age pattern we can rewrite (4) as
• ro(a) do(a) - b(a) knm qnm nms(a) (5)
• where knm is a constant, and qnm relates the
  quantum of migration in the standard rate set to
  the migration in the actual population.

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GGB and Migration (4)

• And
• nms(a) ? 5nmsx 5PYLx / ? 5PYLx (6)
• where 5PYLx is the average annual person-years
  lived by the population aged x to x 5
• The adjusted values of knm qnm nms(a) can now
  be substituted in equation (3)
• b(a) ro(a) (knm qnmnms(a))
  (1/t)ln(k) qddo(a) (7)

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Migration Pattern

• To obtain a set of net migration rates, we use
  Rogers and Castro (1981) basic migration standard
  intended to represent a gross migration flow
  generated by labor force mobility
• The original model combines an exponentially
  decaying with age incidence of child migration
  with a double exponential to represent the rapid
  increase and more gradual decline with age
• We also added an additional double exponential
  term to provide for return migration peaking at
  age 55.

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Fig.2- Migration Model Age Patterns
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GGB and Migration

• ro(a) do(a) - b(a) knm qnm nms(a) (5)
• nms(a) ? 5nmsx 5PYLx / ? 5PYLx (6)
• where 5PYLx is the average annual person-years
  lived by the population aged x to x 5
• The adjusted values of knm qnm nms(a) can now
  be substituted in equation (3)
• b(a) ro(a) (knm qnmnms(a))
  (1/t)ln(k) qddo(a) (7)

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Fig.3a - Mexico - Intensity of Migration
Slope -0.526 Intercept 0.0033
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Fig.3b - Puerto Rico - Intensity of Migration
Slope -0.804 Intercept 0.0087
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Fig.4a Mexico GGB with Migration
k1/k2 1.001 Slope 0.998
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Fig.4b Puerto Rico - GGB with Migration
k1/k2 1.000 Slope 1.000
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GGB and Migration

• ro(a) do(a) - b(a) knm qnm nms(a) (5)
• nms(a) ? 5nmsx 5PYLx / ? 5PYLx (6)
• where 5PYLx is the average annual person-years
  lived by the population aged x to x 5
• The adjusted values of knm qnm nms(a) can now
  be substituted in equation (3)
• b(a) ro(a) (knm qnmnms(a))
  (1/t)ln(k) qddo(a) (7)

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Fig.5a - Mexico - Intensity of Migration
Slope -0.516 Intercept 0.0028
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Fig.5b - Puerto Rico - Intensity of Migration
Slope -0.800 Intercept 0.0057
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Fig. 6a - Mexico GGB with Migration
k1/k2 1.021 Slope 0.977
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Fig. 6b - Puerto Rico - GGB with Migration
k1/k2 1.011 Slope 0.968
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Conclusions

• Death distribution methods assume no net
  migration, problematic to apply to sub-national
  populations and national populations affect by
  migration
• it appears that the procedure proposed here work
  reasonably well in populations that have
  generally good data and high net migration rates
• no reason to prefer the use of the revised
  migration model to the original Rogers-Castro
  formulation
• more applications are needed to test the
  procedure in conditions in which data are less
  good (e.g. regional mortality in Brazil).