NEA Demographic and Household Model 2006 Technical Updates

1
NEA Demographic and Household Model2006
Technical Updates
RSS Technical Group Meeting 9 January 2007 Stella
House, Newcastle-upon -Tyne

• David Mell
• Knowledge Manager
• North East Regional Information Partnership

2
NEA Demographic and Household Model

• Overview of the model
• Technical update details
• Current status

3
The population model is a hybrid of one-year and
five-year age bands and projections
Generally age bands have a 5 year span
0 yrs and 1-4 yrs bands are exceptions
The population is modelled at 5 year intervals
Except 0 yrs band modelled annually
After accounting for deaths and effects of
migration 5-9 yrs band in 2005 becomes 10-14 yrs
band in 2010
Similarly for other 5 year bands
Less Deaths plus Net Migration
0 yrs and 1-4 yrs combine to give the 5-9 years
band
0 yrs band from 4 successive years provides the
1-4 yrs band
0 yrs band is product of female population and
fertility rate
Intermediate years calculated either directly
(1-4 yrs band) or by interpolation (other bands)
Intermediate years (female) population allows
calculation of intermediate years births
Future population Current population Births
Deaths Migration
4
The population model is a set of mechanistic
calculations

• Pop(Band1,Year5) Pop(Band,Year)
  Surv(Band,Year)?(Band1,Year5)
  Migr(Band1,Y5)
• where Pop(Band,Year) mid-year population in
  age band Surv 5-year survival rate Migr
  Cumulative effect of migration into age band
  over 5 year period (defined by period end)
• Births(Year) SPop(Band,Year) Fert(Band,Year)
• where Pop is female population Summation is
  over age bands of child-bearing age Fert is
  fertility rate

Key values are Survival Rates, Fertility Rates
and Migration
5
Population Projections are converted to
Projections of Households and Dwellings Required
Population Projection byLocal Authority
Population living in Households
Occupied Households
6
Migration is dealt with through a scenario
representing policy assumptions
Migration into 30-34 Age Band over 5 years ending
mid-2015
7
Five year survival calculation is based on annual
mortality rates
Know mb,y - Mortality rate by band and year
Surviving populationy1 Popb,y (1-mb,y)
Surviving populationy5 Popb.y (1-my)
(1-my1) (1-my2) (1-my3) (1-my4)
Popb,y (1-mAve)5
8
Mortality rates are projected on basis of
national rate changes
mb,y1 mb,y (nb,y1/nb,y) where m local
authority mortality rate n national mortality
rate

• National rates are projected by Government
  Actuarys Department (GAD)
• All future rates for a local authority can be
  projected from a starting (base year) rate (LA
  specific)
• Relationship implies mb,y Constantb nb,y
  (for all y)
• Relationship has been tested
• Fertility rates projected in exactly same way
• Again, local/national rate assumption tested

9
Establishing the base rates for projection has
been a complex process
Spreadsheet model Base Year 2003
There has to be a better way!
10
Mortality Rates in Practice 1

• Any process for projecting rates will contain
  statistical error
• The calibration factors represent these errors
• Statistical errors random, systematic (bias)
• Time effects confirmed by ANOVA and ANCOVA models

11
Mortality Rates in Practice - 2

• Mortality is a convex function of age
• Consequently, experienced average rate is less
  than arithmetic average of two age bands

12
Mortality Rates Problem and Solution

• Use 2001-2005 actual data
• No projection of mortality rates
• Apply averaging process to estimate deaths in
  period
• Compare with actuals
• Persistent bias 3-3.5 at regional level based on
  calculations performed at local authority level
• 1995-2000 similar
• This is what calibration factors attempting to
  correct
• Underlying problem is the 5050 weighting of
  successive age bands
• Convexity means 5050 overestimates mortality
  rates and hence deaths
• 6040 eliminates bias
• Pragmatic finding
• Theoretical approaches which model mortality
  rates using an exponential function suggest
  similar weighting with little age variation
• No need for calibration factors (calibrating in
  random error!)

Outcome use 6040 weightings in 5 year rate
calculations
13
Estimating Base Year Mortality Rates(Base Year
2005)

• Fit linear regression model to 2001-2005 data
  using OLS
• Base year value fitted value for 2005
• Regression is trend-based average
• If fitted value is negative use simple average
  instead
• In practice only ages from around 55 upwards
  matter
• Same approach for fertility less critical for
  housing!!

14
Summary of Technical Updates 2006

• Simplification of calculation of base year
  mortality and fertility rates
• Complex process replaced by simple linear
  regression
• Calculation of 5-year survival rates adjusted
• 5050 weighting of successive bands replaced by
  6040
• Correction of errors in migration accumulation
  calculation (migration roll-up)
• Some incorrect co-efficients detected in
  spreadsheet
• Re-implementation of model in MS Access
• Makes re-basing a 3 minute job instead of 3
  months
• Data and calculations one and once only more
  maintainable
• Separates calculations from presentation
• Validation of population calculations via
  spreadsheet
• Right tool for the job
• Stepping stone to a 1-year model

Otherwise, unchanged !!
15
NEA Demographic and Household Model

• Overview of the model
• Technical update details
• Current status