Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Experimental Stochastic Population
Projections for New Zealand:
2009(base)–2111
Statistics New Zealand Working Paper No 11–01
Kim Dunstan
1
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
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Citation
Dunstan K (2011). Experimental Stochastic Population Projections for New Zealand: 2009(base)–
2111 (Statistics New Zealand Working Paper No 11–01). Wellington: Statistics New Zealand
Published in April 2011 by
Statistics New Zealand
Tatauranga Aotearoa P O Box 2922
Wellington, New Zealand
[email protected]
[email protected]
www.stats.govt.nz
ISSN 1179-934X
ISBN 978-0-478-35397-6 (online)
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Contents
List of figures .................................................................................................................................... iv
Abstract .............................................................................................................................................. vi
1
Introduction............................................................................................................................. 1
Conventional population projections .................................................................................................. 1
Stochastic population projections ........................................................................................................ 1
Feedback sought ......................................................................................................................................... 2
Method ..................................................................................................................................... 3
2
General model applied............................................................................................................................. 3
Simulations .............................................................................................................................................. 4
Base population .......................................................................................................................................... 6
Modelling uncertainty in base population ................................................................................... 7
Births ............................................................................................................................................................. 10
Modelling uncertainty in fertility ................................................................................................... 10
Modelling uncertainty in sex ratio at birth ................................................................................ 13
Deaths .......................................................................................................................................................... 13
Modelling uncertainty in mortality ............................................................................................... 14
Migration...................................................................................................................................................... 19
Modelling uncertainty in net migration ...................................................................................... 20
3
Results..................................................................................................................................... 23
Population size and growth ................................................................................................................. 23
Births and deaths ..................................................................................................................................... 25
Population age structure ....................................................................................................................... 27
Dependency ratios .................................................................................................................................. 31
Discussion .............................................................................................................................. 34
4
Summary of method .............................................................................................................................. 34
Nature of projections .............................................................................................................................. 34
Summary of results ................................................................................................................................. 35
Implications for national population projections ......................................................................... 36
Practical issues..................................................................................................................................... 37
Implications for other projections ...................................................................................................... 39
National labour force projections ................................................................................................. 39
National ethnic population projections...................................................................................... 40
National family and household projections ............................................................................. 40
Subnational demographic projections ....................................................................................... 41
Conclusion .................................................................................................................................................. 43
References ...................................................................................................................................... 44
Appendix 1: List of abbreviations ............................................................................................ 48
Appendix 2: Examples of simulations .................................................................................... 49
Appendix 3: Additional projection results ............................................................................ 51
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
List of figures
1 Assumed standard error in base population, by single year of age and sex, at
30 June 2009 ............................................................................................................................................ 8
2 Assumed relative standard error in base population, by single year of age and
sex, at 30 June 2009 .............................................................................................................................. 8
3 Base population probability distribution, by single year of age, at 30 June
2009 ............................................................................................................................................................ 9
4 Period total fertility rate, 1962–2009 ............................................................................................ 11
5 Assumed total fertility rate probability distribution, 2010–2111 ........................................ 12
6 Assumed age-specific fertility rate probability distribution, 2061 ....................................... 12
7 Estimated sex ratio at birth, 1900–2008 ..................................................................................... 13
8 Cohort life expectancy at birth, by sex, 1876–1934 ............................................................... 15
9 Assumed male life expectancy at birth probability distribution, 2010–2111 ............... 16
10 Assumed female–male difference in life expectancy at birth probability
distribution, 2010–2111 .................................................................................................................... 17
11 Assumed female life expectancy at birth probability distribution, 2010–2111 ........... 18
12 Assumed male age-specific survival rate probability distribution, 2061 .......................... 19
13 Net migration by class, 1900–2009 .............................................................................................. 20
14 Assumed net migration probability distribution, 2010–2111 ............................................. 21
15 Assumed net migration by age probability distribution, from 2013.................................. 22
16 Projected population probability distribution, 2009–2111 .................................................. 24
17 Projected annual growth rate probability distribution, 2010–2111 .................................. 24
18 Projected births probability distribution, 2010–2111 ............................................................. 25
19 Projected deaths probability distribution, 2010–2111........................................................... 26
20 Projected natural increase probability distribution, 2010–2111 ........................................ 27
21 Projected single-year of age probability distribution, 2031 ................................................... 27
22 Projected single-year of age probability distribution, 2061 ................................................... 28
23 Projected age-sex pyramid probability distribution, 2061 ..................................................... 29
24 Projected baby boomer population (born 1946–65) probability distribution,
2009–61 ................................................................................................................................................... 29
25 Projected population aged 65+ probability distribution, 2009–2111 ............................. 30
iv
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
26 Projected percentage of population aged 65+ probability distribution, 2009–
2111 ......................................................................................................................................................... 30
27 Projected 0–14 dependency ratio probability distribution, 2009–2111 ........................ 32
28 Projected 65+ dependency ratio probability distribution, 2009–2111 .......................... 33
29 Projected total dependency ratio probability distribution, 2009–2111........................... 33
30 Example #1 of simulated total fertility rate, male and female life expectancy at
birth, net migration, total population, births and deaths, and 65+ population,
2010–2111 ............................................................................................................................................. 49
31 Example #2 of simulated total fertility rate, male and female life expectancy at
birth, net migration, total population, births and deaths, and 65+ population,
2010–2111 ............................................................................................................................................. 50
32 Projected population aged 0–14 probability distribution, 2009–2111 .......................... 51
33 Projected percentage of population aged 0–14 probability distribution, 2009–
2111 ......................................................................................................................................................... 51
34 Projected population aged 15–39 probability distribution, 2009–2111 ....................... 52
35 Projected percentage of population aged 15–39 probability distribution,
2009–2111 ............................................................................................................................................. 52
36 Projected population aged 40–64 probability distribution, 2009–2111 ....................... 53
37 Projected percentage of population aged 40–64 probability distribution,
2009–2111 ............................................................................................................................................. 53
38 Projected population aged 85+ probability distribution, 2009–2111 ............................. 54
39 Projected percentage of population aged 85+ probability distribution, 2009–
2111 ......................................................................................................................................................... 54
40 Projected median age probability distribution, 2009–2111 ................................................ 55
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Abstract
The demographic future is uncertain. Conventionally, this uncertainty is conveyed by
different scenarios with specific, stated assumptions about the components of
population change (fertility, mortality, and migration). Alternative projection scenarios
give an indication of possible uncertainty, although the uncertainty is not quantified. A
stochastic or probabilistic approach to projections can potentially help their interpretation
by quantifying the inherent uncertainty.
This paper outlines a stochastic method and summarises the results for projections of
the New Zealand population from a 2009 base. Uncertainty is modelled from historical
data for fertility (total fertility rate), mortality (life expectancy at birth), and net migration,
as well as for the sex ratio at birth. Uncertainty in the base population is modelled using
expert judgement. Simulations of these parameters give probability distributions around
Statistics New Zealand’s deterministic mid-range projection.
The results illustrate that the deterministic scenarios give a poor indication of uncertainty
for some key demographic characteristics. Even for other characteristics, the uncertainty
indicated by the scenarios is neither consistent across the projection period, nor
consistent between characteristics. This largely reflects that the low and high
deterministic assumptions are not equivalent to a given probability interval that is
consistent among the fertility, mortality, and migration components. Moreover, the
uncertainty is rarely symmetrical.
There are few practical obstacles to producing stochastic population projections, other
than the additional resource required to formulate measures of uncertainty and produce
multiple simulations. A stochastic approach could also be applied to other demographic
projections produced by Statistics NZ, aiding their interpretation where uncertainty is
even greater (eg ethnic population and subnational projections). However, the method
outlined in this paper can be applied to the New Zealand population projections without
compromising the current methods or results of those other demographic projections.
Key words
Stochastic, probabilistic, projection, population, uncertainty.
Acknowledgements
The author thanks John Bryant who assisted with data visualisation, Richard Speirs and
the New Zealand Treasury who assisted with a 2004-base prototype, and anonymous
reviewers for their helpful comments.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
1 Introduction
The demographic future is uncertain. Conventionally, this uncertainty is conveyed by
different scenarios with specific, stated assumptions about the components of
population change (fertility, mortality, and migration). Alternative projection scenarios
give an indication of possible uncertainty, although the uncertainty is not quantified.
A stochastic or probabilistic approach to projections can potentially help their
interpretation by quantifying the inherent uncertainty. However, it is important to note
that the measures of uncertainty are themselves uncertain because of subjective
decisions that inevitably have to be made about how to estimate such uncertainty.
Conventional population projections
Statistics New Zealand has traditionally published a set of New Zealand or national
population projections every two to three years. The latest national population
projections are a 2009-base set released in October 2009. These have a projection
horizon of 2061, although projections to 2111 have also been derived and are
available.
All these projections were derived 'deterministically'. That is, they are scenario-based
projections produced using specific assumptions. These assumptions are not just an
extrapolation of historical trends, but are formulated after analysis of short-term and
long-term demographic trends, patterns and trends observed in other countries,
government policy, and other relevant information. Different combinations of these
assumptions result in different projection scenarios (or series), although the likelihood of
each scenario (or the range covered by the different scenarios) is never quantified.
Stochastic population projections
The main advantage of stochastic population projections is that they provide a means of
quantifying the demographic uncertainty, although it is important to note that the
estimates of uncertainty will themselves be uncertain. While it is possible to estimate
uncertainty based on the historical variability of the demographic parameters, it is more
difficult to estimate the uncertainty that arises from the choice of models, or from the
choice of time period(s) that affect the model parameters.
Dowd et al (2010) refer to these three different types of uncertainty as:
1.
model uncertainty (eg we do not know the true fertility model)
2.
parameter uncertainty (eg whatever mortality model we use, we do not know the
true values of its parameters)
3.
forecast uncertainty (eg the uncertainty of future migration rates given any particular
model and its calibration).
Stochastic methods also produce projection trajectories that are more realistic, in that
they are more variable than a deterministic projection. In fact, deterministic projections
are really indicating average trajectories given long-run assumptions. Bryant (2003,
2005) and Booth (2006) give good summaries of the advantages of a stochastic
approach.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Stochastic population projections have not hitherto been widely adopted by national
statistical offices. Examples exist for Denmark, Sweden, the Netherlands, and China (eg
Qiang Li et al, 2009). These have generally been produced by academic researchers or
research institutes rather than national statistical offices. However, several countries have
been exploring stochastic methods (eg US Census Bureau: see Long and Hollmann,
2004; Statistics Sweden: see Hartmann and Strandell, 2006; UK Office of National
Statistics: see Rowan and Wright, 2010).
Statistics NZ produces a range of different demographic projections, but this paper
presents an experimental set of stochastic projections for the total New Zealand
population only. The focus of the paper is to describe a method to quantify the
uncertainty inherent in projections of New Zealand’s future population (section 2:
Method) and to summarise the stochastic projection results (section 3: Results). A
summary of the key points, practical considerations, and implications for other
demographic projections produced by Statistics NZ are discussed (section 4:
Discussion). The paper is therefore of interest to both producers and users of
projections.
The stochastic population projections presented in this paper are tagged ‘experimental’
to differentiate them from any official projections produced by Statistics NZ. The
methodology and associated uncertainty parameters are similarly experimental. They are
subject to revision if and when a stochastic approach becomes integrated within
Statistics NZ’s projection methodology.
Feedback sought
The aim of this paper is twofold. First, it documents Statistics NZ's recent work in the
area of stochastic (or probabilistic) population projections. Second, it provides a basis for
users of projections to comment on the stochastic approach. Statistics NZ welcomes
comments on the specific stochastic methodology outlined in this paper, but is also
interested in hearing the views of users around broader questions such as:
·
Is there demand for a different projection methodology?
·
What is the value/advantage to users of stochastic population projections?
·
Do the benefits to users outweigh the added complexity and production costs?
·
What are the implications for the suite of demographic projections produced by
Statistics NZ – should a stochastic approach be applied to all national and
subnational projections?
·
What do users want from the projections?
·
Are these needs currently being met?
·
Do users of projections want a prediction of the future population, or is it sufficient
to have an indication based on simplified but sensible assumptions?
Feedback can be provided to the author (email [email protected], phone 03
964 8330) or Statistics NZ's Population Statistics Unit (email
[email protected]).
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
2 Method
This section describes the modelling approach used to derive stochastic population
projections of the New Zealand population from 2009 (base) to 2111.
General model applied
The approach adopted here is to apply a stochastic framework to the mid-range
deterministic projection series produced by Statistics NZ, which combines the medium
fertility, medium mortality, and medium migration assumptions (ie series 5 of the 2009base national population projections released in October 2009). This is similar to the
approach adopted by Wilson (2004, 2005), and is preferable to stochastically deriving a
median trajectory.
There are several advantages of this approach. First, it allows the incorporation of
assumptions that have been deterministically formulated from assessing a wide range of
information. This includes the latest New Zealand demographic trends, cohort fertility
rates, immigration policy, immigration applications and approvals, and international
trends in fertility and mortality. Assumptions about demographic trends, especially in the
short term (ie in the initial years of the projection period), are perhaps best formulated
deterministically rather than stochastically. For example, expert judgement can be
applied to interpreting available information such as immigration applications and
approvals as a precursor to actual migration trends. In contrast, a pure stochastic
approach is driven by historical data and does not incorporate knowledge about real
world events.
Second, this approach maintains compatibility with other demographic projections
produced by Statistics NZ. Projections of ethnic populations, labour force, and families
and households, at both national and subnational levels, are designed to be consistent
with national population projections (specifically the mid-range series). This reflects the
top-down approach adopted by Statistics NZ and the importance of additivity, which is
valued by users of the projections.
Third, this approach allows direct comparison of the stochastic population projections
with the official national population projections released in October 2009. For example,
the lowest and highest growth scenarios (series 1 and 9 respectively) can be compared
with the range of stochastic projection outcomes.
Fourth, this approach can utilise the work that already exists in a New Zealand context.
Tom Wilson, while at the Queensland Centre for Population Research, applied a
stochastic framework to Statistics NZ’s 2004-base national population projections
(Wilson, 2005). Statistics NZ itself developed an experimental set of 2004-base
stochastic population projections, including SAS programs to produce these, in
collaboration with the New Zealand Treasury in 2005. This working paper builds on both
of these previous developments.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The alternative is to stochastically derive all assumptions, including the median trajectory,
by time series modelling. Such an approach does require subjective selection of
historical data or time series models. For example, time series modelling of fertility
conducted within Statistics NZ concluded that the forecasts were sensitive to the length
of the historical data and the specific model chosen, and often produced implausible
fertility results. Nevertheless, time series models have been successfully applied in other
cases, notably for mortality (eg Lee & Carter, 1992; Lee & Miller, 2001). For a fuller
discussion, see Hyndman and Booth (2006).
The approach taken here is to develop probability distributions for the three
components of population change – fertility, mortality, and migration – and overlay
these on the medium fertility, mortality, and migration assumptions of the 2009-base
national population projections (Statistics New Zealand, 2009a). Fixed age profiles are
effectively used for all assumptions, although these are scaled according to the
simulated parameters. In comparison with Wilson's work, two additional components are
modelled with probability distributions:
1.
uncertainty in the base population
2.
uncertainty in the sex ratio at birth.
This approach assumes that all the parameters of uncertainty can be estimated with
certainty and remain constant over the projection period. The parameters may of course
be overestimated or underestimated, but they also ignore the uncertainty that can arise
from model or parameter uncertainty (Dowd et al, 2010). This underscores the
importance of acknowledging that any estimates of uncertainty are themselves
uncertain.
In terms of modelling, autoregressive integrated moving average (ARIMA) models
provide satisfactory approximations of the fertility, mortality, and migration time series.
Other types of models were not explored but ARIMA models have also been used in
other stochastic projections (eg Wilson, 2004, 2005; Keilman, 2005; Lee & Tuljapurkar,
1994). Different ARIMA models were assessed for each time series, using the BoxJenkins approach, with diagnostics such as autocorrelation plots and checks supporting
the specific models selected in this paper. For further background and discussion of
ARIMA models, see for example Chatfield (2009).
Simulations
Simulations (or iterations or sample paths) are created for the base population, births,
deaths, and net migration, and combined as per the fundamental population equation:
P(T) = P(T–1) + Births – Deaths + Arrivals – Departures
where P(T) is the population at the end of the time period, P(T–1) is the population at
the beginning of the time period (base population), and Births – Deaths (natural
increase) and Arrivals – Departures (net migration) relate to events occurring during the
time period.
No simulation is more likely, or more unlikely, than any other. However, if a random
variable is measured many times, a distribution of the values it can take can be
constructed. Collectively, therefore, the simulations provide a probability distribution
which can be summarised via percentiles. Two examples of simulated assumptions and
projection results are given in appendix 2.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Calculating the simulations involves several assumptions (de Beer, 2000):
1.
Type of probability distribution. For calculating the simulations, a complete
probability distribution needs to be specified for each component for each
projection year. If a normal distribution is assumed, only two parameters have to be
specified: the mean (corresponding with the medium variant) and the variance. If a
uniform distribution is assumed, the minimum and maximum values need to be
specified. If an asymmetrical distribution is assumed, at least one additional
parameter indicating the skewness has to be specified. One disadvantage of an
asymmetrical distribution is that the mean of the distribution does not correspond
with the most probable value. This may be confusing for the users of the forecast.
2.
Correlation between age-specific rates. The age-specific fertility and mortality rates in
a given forecast year can be expected to be positively correlated. If the economic
and social situation is favourable for having children, it can be expected that all agespecific fertility rates will be relatively high. However, for cohort data, a negative
correlation may be plausible. If the economic situation drives people to postpone
having children, age-specific fertility rates at young and old ages may be negatively
correlated. Similarly, a selection mechanism may cause a negative relationship
between mortality rates at young and old ages for the same cohort.
3.
Serial correlation. The probability distributions of fertility, mortality, and migration in
successive forecast years are correlated. If fertility is very high in one forecast year, it
is not very probable that fertility will be very low in the next year. Thus if a high
value of fertility is drawn in one forecast year, the probability of drawing a high value
in the next year should be higher than that of drawing a low value. In the short run
a negative correlation may also be possible. For example, if the number of deaths is
relatively high in one year due to a severe winter, the number of deaths may be
relatively low in the next year, due to a selection mechanism, as many frail people
died in the previous year.
4.
Correlation between components. The values of fertility, mortality, and migration can
be correlated. For example, if immigrants have more children than the native
population, an increase in the number of young immigrants may lead to an increase
in the fertility rates in later years. Note that even if independence between fertility
and mortality rates and migration numbers is assumed, there is no independence of
numbers of births and deaths, and numbers of migrants. For example, if
immigration is high in a certain year, this will result in larger numbers of births and
deaths in later years for given values of fertility and mortality rates.
In the case of the stochastic projections derived here:
1.
Normal probability distributions are assumed for all parameters, although the base
population has different variances above and below the median.
2.
Age-specific fertility rates, survival rates, and base populations are assumed to be
perfectly correlated across age.
3.
The probability distributions of fertility, mortality, and migration in successive
projection years are assumed to be serially correlated, as evident from the fitted
models.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
4.
All components of the population equation are assumed to be independent. For
developed countries, there is no reason for, or evidence of, correlation between
these components (Lee & Tuljapurkar,1994; Keilman, 1997), at least not at a
national level.
An alternative to the simulation approach is to analytically derive the projections.
However, applying a stochastic cohort-component model is described as “very
complicated” and requires a large number of simplifying assumptions (de Beer, 2000)
or approximations (Keilman, 2005).
Base population
The projections have as a base, or starting point, an estimate of the population that
usually lives in New Zealand: the estimated resident population (ERP). The ERP is largely
derived from the latest census count, but includes allowances for people not included in
the census. This includes people who were temporarily overseas at the time of the
census (residents temporarily overseas), as well as people missed by the census (net
census undercount). The ERP also includes allowances for changes in the population
since the census due to births, deaths, and migration.
The base for the 2009-base national population projections was the ERP (provisional)
of New Zealand at 30 June 2009, 4.316 million people. The same base was used for
all projection series. This provisional estimate was subsequently ‘finalised’ in November
2009, after the projections were released in October 2009, following further birth and
death registrations (which permitted a more refined estimate of the number of births
and deaths occurring up to 30 June 2009). The differences between the final and
provisional estimate were negligible, although this ‘final’ ERP will be further revised
following results from the 2011 Census of Population and Dwellings (as will all postJune 2006 population estimates).
In recognition that the base ERP inevitably has some uncertainty, a probabilistic
distribution was applied to the base ERP (by age and sex). Although the ERP is a
historical dataset and largely derived from census counts, uncertainty in the ERP can
arise from two broad sources:
1.
Census enumeration and processing. Coverage errors may arise from nonenumeration and mis-enumeration (eg residents counted as visitors from overseas,
and vice versa), either because of deliberate or inadvertent respondent or collector
error. Errors may also arise during census processing (eg scanning, numeric and
character recognition, imputation, coding, editing).
2.
Adjustments in deriving population estimates. This includes the adjustments applied
in deriving the ERP at 30 June of the census year: net census undercount (NCU),
residents temporarily overseas (RTO), and demographic reconciliation (Statistics
New Zealand, 2010a). It also includes uncertainty associated with the post-censal
components of population change (eg estimates of births occurring in each time
period based on birth registrations; changes in classification of external migrants
between ‘permanent and long-term’ and 'short-term').
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The ERP is largely based on census enumeration and recorded events (births, deaths,
arrivals, departures). There is potential for both undercount and overcount of people in
the respective data collections. There are many reasons for people being missed or
double-counted, including deliberate avoidance, people shifting residence around the
time of data collection, and people with multiple residences including students at tertiary
institutions and children in shared custody (Statistics New Zealand, 2007a).
Modelling uncertainty in base population
Population estimates already make an allowance for coverage errors based on the
census post-enumeration survey (PES). Although the PES provides one measure of
uncertainty, namely estimates of sampling error associated with the estimates of NCU,
the overall probability distribution associated with the base ERP was subjectively derived,
based on the author’s knowledge of the strengths and weaknesses of the different data
sources. A subjective approach is necessary because it is very difficult to quantify all nonsampling errors in census enumeration and the various adjustments applied in deriving
population estimates.
The uncertainty in the base ERP is assumed to have equal probability that the
population is lower or higher than the official ERP. Significantly, however, it is also
assumed that for most ages any underestimate is likely to be larger than any
overestimate. This reflects the nature of the ERP and how it is derived. First, the
adjustments for NCU, RTOs, and unregistered births are based on empirical evidence
but tend to be conservative to avoid over-adjusting.
Second, external migration trends between 2006 and 2009 suggest permanent and
long-term migration data are probably an underestimate of the contribution of migration
to New Zealand’s population change over that period. Similarly, between 30 June 2001
and 30 June 2006, New Zealand recorded net permanent and long-term migration of
116,600, compared with an estimated net migration of 160,800 (Statistics New
Zealand, 2008, p13 and 28).
Consequently, if the ERP is still an underestimate after the collective adjustments and
updating for post-censal births, deaths, and migration, then this is potentially larger than
any overestimate.
Owing to the nature of the uncertainties, the estimated uncertainty in the population
estimates is designed to indicate broad approximate potential error. In absolute terms
(figure 1), uncertainty is assumed to be highest among young adult ages (16–45
years). The adjustments for NCU and RTO are also highest at these ages. In relative
terms (figure 2), uncertainty is assumed to be highest at the oldest ages (90+ years)
where the small populations are sensitive to census miscount. At the oldest ages there
is more potential for an overestimate, based on demographic analysis conducted within
Statistics NZ involving retrospective comparisons between death registrations and census
counts.
The uncertainty in the base population is referred to in terms of ‘standard errors’ (SE) to
reflect that it is based on an assumed underlying distribution. In contrast, the
uncertainties in the other parameters (ie fertility, mortality, and migration) are referred to
in terms of ‘standard deviations’ to reflect that they are estimated from observed
historical data.
7
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 1
Assumed standard error in base population
By single year of age and sex
At 30 June 2009
Population
800
700
Male +1 SE
600
Female +1 SE
500
Male -1 SE
400
Female -1 SE
300
200
100
0
-100
-200
0
10
20
30
40
50
Age (years)
60
70
80
90
100+
90
100+
Figure 2
Assumed relative standard error in base population
By single year of age and sex
At 30 June 2009
5
Percent
0
-5
-10
Male +1 SE
Female +1 SE
-15
Male -1 SE
Female -1 SE
-20
-25
0
10
20
30
40
50
Age (years)
8
60
70
80
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Given the asymmetrical pattern of uncertainty assumed around the base ERP, the
approach adopted here is to assume perfect correlation across age-sex. That is, for any
given simulation, all ages for males and females are above or below the official ERP.
This asymmetrical approach results in the median of the probability distribution equating
to the base ERP, but the mean of the probability distribution does not. An alternative
approach of assuming adjacent ages are imperfectly correlated would be appropriate if
the uncertainty was assumed to be symmetrical around the base ERP.
For each simulation, the magnitude of the difference from the base ERP was
determined by drawing a random number from a normal distribution with a mean of
zero. The absolute value of this random number was multiplied by the assumed
standard error for each age-sex to give the difference between the base ERP and the
alternative base population. A set of 1,000 alternative populations were derived by
adding the differences to the base ERP (by age and sex) at 30 June 2009 (figure 3).
The percentiles are impossible to distinguish in figure 3 which underscores that there is
relatively little uncertainty in the base population in absolute terms. The total ERP has a
90 percent probability interval of 4.28–4.43 million, compared with the official ERP of
4.32 million.
Figure 3
Base population probability distribution
By single year of age
At 30 June 2009
Note: Percentiles shown are 5, 25, 50, 75, and 95. Age 100 is 100 years and over.
9
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The probability distributions and intervals illustrated in this section are based on
theoretical modelled results, not simulated results. The 50th percentile (50% line)
should be interpreted as signifying that there is a 50 percent chance that the given
parameter for a given year will be below this line, and a 50 percent chance that the
given parameter for a given year will be above this line. Similarly, the 75th percentile
(75% line) signifies that there is a 75 percent chance that the given parameter for a
given year will be below this line, and a 25 percent chance that the given parameter for
a given year will be above this line. It follows that there is a 50 percent chance that the
given parameter for a given year will be between the 25% line and the 75% line (the
interquartile range), and a 90 percent chance that the given parameter for a given year
will be between the 5% line and the 95% line.
Births
Projected (live) births are derived by applying age-specific fertility rates (ASFRs) to the
mean female population at ages 12 to 49 years. The ASFRs for each year represent the
average number of births to females of each age in that year. The set of ASFRs for each
year is summarised by the total fertility rate (TFR). The mean female population for each
age is derived by averaging the population at the beginning and end of each year. The
sum of the number of births derived for each age of mother gives the projected number
of births for each year. The relative number of male births and female births is derived
by the sex ratio at birth.
The medium fertility variant of the 2009-base national population projections assumes
that the TFR drops gradually from 2.14 births per woman in the year ended June 2009
to 1.90 in 2026, and then remains constant. This assumption was based on an analysis
of New Zealand period and cohort fertility rates, rates of childlessness, and ethnic fertility
patterns, as well as international comparisons. These factors suggest a general decline in
overall New Zealand fertility rates from current levels is most likely (for further discussion
see Statistics New Zealand, 2009b). The medium fertility variant also assumed ASFRs of
women aged under 32 years will decline between 2009 and 2026, with ASFRs
increasing for women aged 32 years and over.
Modelling uncertainty in fertility
Initial investigations centred on modelling uncertainty in disaggregated (age-specific)
fertility rates. ASFRs for the total New Zealand population are available from 1962
(Statistics New Zealand, 2010b). However, uncertainty modelled on the ASFRs gave an
implausibly wide range of future fertility in the short-term and long-term, albeit treating
each age independently. The range was only partly improved by limiting the historical
time series to more recent data. Future work could include modelling ASFRs to account
for correlation across age.
Nevertheless, the TFR is a useful summary measure of the ASFRs prevailing in a given
year, even though its cross-sectional nature can conceal important patterns occurring
across ages and/or birth cohorts. Over the 47-year period, 1962–2009, New Zealand’s
TFR varied between 1.9 and 4.2 births per woman (figure 4). However, the range has
been much narrower since 1977 (1.9–2.2).
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 4
4.5
Period total fertility rate
1962–2009
Births per woman
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1962
1967
1972
1977
1982
1987
1992
December year
1997
2002
2007
Standard deviations were calculated for the entire 1962–2009 TFR time series.
However, this implied an overly wide probability distribution for the TFR (eg 90 percent
probability distribution of 1.1–2.7 births per woman in 2021, 0.5–3.6 in 2061, and
0.2–4.2 in 2111).
In the final model, standard deviations were calculated for 1977–2009 (December
years). Fertility patterns over this period, following the post-war baby boom, could be
considered a better basis for formulating a probability distribution for future fertility. By
comparison, Wilson (2005) modelled the uncertainty of future fertility on the TFR for
the 30-year period 1975–2004.
After considering different data periods, a simple random walk with drift model was
deemed appropriate for producing future fertility simulations, as with Wilson. As far as
the historical data was concerned, this is the equivalent of fitting an ARIMA(0,1,0) model
to annual TFR. The mathematical formula for deriving future TFRs was:
TFR(T) = TFR(T–1) + e{TFR}(T) + drift{TFR}(T)
where TFR(T) > 0, T denotes a one year interval, e{TFR} are random errors sampled
from a normal distribution with the calculated standard deviation (0.06229) and a
mean of zero, and drift{TFR} shifts the median of the future simulations of TFRs to
follow the medium fertility variant of the 2009-base national population projections.
ASFRs were subsequently derived by scaling the ASFRs from the medium fertility variant
of the 2009-base national population projections, to match each TFR simulation for
each projection year. The final distributions for TFR (by year) and ASFRs (in 2061) are
illustrated in figure 5 and figure 6. These figures also illustrate the low and high fertility
variants from the 2009-base national population projections. These variants encompass
the interquartile range in the short term, but beyond 2031 they encompass an
increasingly smaller probability interval.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 5
Assumed total fertility rate probability distribution
2010–2111
Figure 6
Assumed age-specific fertility rate probability distribution
2061
Note: Percentiles shown are 5, 25, 50, 75, and 95.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Modelling uncertainty in sex ratio at birth
The sex ratio at birth has only a small impact on the projected population, but it is an
uncertain component that affects future birth numbers and uncertainty because of its
impact on the female population. Based on estimated births by date of occurrence
(Statistics New Zealand, 2009c), the mean sex ratio at birth for births occurring in the
109-year period 1900–2008 (December years) was 1.055 males per female, with a
standard deviation of 0.010 (figure 7). For each simulation and for each year of the
projection period, the assumed sex ratio at birth was determined by drawing a random
number sampled from a normal distribution with the calculated standard deviation
(0.010) and a mean of 1.055 (the constant assumption adopted in the 2009-base
national population projections).
Figure 7
Estimated sex ratio at birth
1900–2008
1.08
Males per female
1.07
1.06
1.05
1.04
1.03
1.02
1900
1910
1920
1930
1940
1950
1960
Year of birth
1970
1980
1990
2000
2010
Source: From cohort mortality data updated in September 2009, which includes births registered
to June 2009.
Deaths
The projected number of deaths is calculated indirectly. The detailed mortality
assumptions are formulated in terms of age-specific survival rates (ASSRs) for males and
females separately. This is because in the projection model the base population is
survived forward each year. The male and female ASSRs for each year represent the
proportion of people at each age-sex who will survive for another year. In general,
survival rates are highest at ages 5–11 years and then decrease with increasing age. The
set of ASSRs for each year is summarised by male and female life expectancy at birth.
Annual survival rates are applied separately to births, migrants, and the population at the
beginning of each year. For further explanation, refer to Statistics New Zealand (2010c).
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The medium mortality variant of the 2009-base national population projections
assumes that ASSRs will increase at different rates at different ages. The period life
expectancy at birth (e 0 ) for males increases from 78.0 years in 2005–07 to 85.6 years
in 2061. The corresponding e 0 increase for females is from 82.2 years in 2005–07 to
88.7 years in 2061.
These assumptions were driven by the observed age-specific death rates from complete
cohort life tables for the 1876–2007 birth cohorts. Exponential curves were fitted to
historical cohort mortality data for each age-sex. Complete cohort life tables were
derived for selected birth cohorts (eg 1956, 2006, 2061) and intermediate cohorts
were interpolated. Cohort ASSRs were then transformed to period ASSRs, with some
adjustment to give plausible death numbers by age-sex in the initial years of the
projection period. International comparisons of mortality and longevity served as a useful
check on plausibility. Despite differences in methods, the New Zealand life expectancy
assumptions are broadly consistent with the latest available projection assumptions from
national statistical agencies in Australia, Canada, Japan, United Kingdom, and the United
States.
Modelling uncertainty in mortality
As with fertility, initial investigations centred on modelling uncertainty in disaggregated
(age-specific) death or survival rates. ASSRs for the total New Zealand population are
available from the complete period life tables that Statistics NZ derives every five years
(Statistics New Zealand, 2009d). The complete cohort life tables, updated and extended
annually, provide an even more comprehensive mortality time series from 1876
(Statistics New Zealand, 2009c). This same cohort mortality data was used to formulate
the mortality assumptions of the 2009-base national population projections (Statistics
New Zealand, 2009a). A third potential data source is the Human Mortality Database
(HMD), which in early 2010 contained annual life table data for New Zealand for the
period 1948–2003 and birth cohorts 1867–1973.
Uncertainty modelled on the cohort age-specific death/survival rates gave an implausibly
wide range of mortality/survival results in both the short term and long term. The range
was only partly improved by limiting the historical time series to more recent data.
However, ages were treated independently, and future work could include modelling
with different levels of correlation across age.
Uncertainty was eventually modelled on e 0 , specifically cohort e 0 for 1876–1917
(December years of birth) (figure 8). The usefulness of e 0 is partly as a summary
measure of the ASSRs prevailing in a given year. A limitation of e 0 is its cross-sectional
nature, which can conceal important patterns occurring across ages and/or birth cohorts.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 8
Cohort life expectancy at birth
By sex
1876–1934
80
Years of life
75
70
Female
65
60
Male (excluding war deaths)
55
Male (including war deaths)
50
1875
1880
1885
1890
1895
1900 1905 1910
Year of birth
1915
1920
1925
1930
1935
Note: Dashed lines indicate that life expectancy is partly based on projected mortality experiences
at ages above 74 years.
Source: Based on cohort life tables derived in September 2009, which include deaths registered
to June 2009.
To model variation in e 0 , it is preferable that annual e 0 data are available on a consistent
basis. Such data are available from cohort life tables but not from period life tables.
Definitive period e 0 measures are only available every five years, and interpolation of
annual period e 0 from five-yearly e 0 would not give a robust measure of annual
uncertainty. The alternative HMD source is neither up-to-date nor entirely reliable for
New Zealand data. The appropriateness of modelling uncertainty in future period e 0
using past uncertainty in cohort e 0, is based on two premises. First, that uncertainty in
cohort e 0 reflects annual variations in people’s actual life expectancy at birth that results
from changes in age-specific death rates. Second, that cohort and period e 0 will
experience similar, if not identical, trends – given that both are a function of the same
underlying age-specific death rates.
However, two refinements were applied. First, birth cohorts after 1917 were excluded
where remaining mortality experience needed to be projected at ages above 90 years.
As more mortality experience is projected, the derived e 0 is liable to become
increasingly smooth from cohort to cohort. Second, war deaths were excluded as this
adds to the year-to-year uncertainty in male e 0 . The projections are not designed to
account for extreme events such as major wars (see ‘Nature of projections’ in section 4:
Discussion).
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The refined cohort time series may still overestimate uncertainty, because of the
inclusion of birth cohorts with relatively high infant and child mortality due to infectious
epidemics. Such epidemics were a feature of mortality in New Zealand before World
War II (Dunstan et al, 2006). Although it could be argued that increasing globalisation
and ease of international travel are resuming the risk of infectious epidemics.
After considering different data periods, the experience with the fertility models, and
Wilson's work with New Zealand population projections, it was decided that a simple
random walk with drift process would be used to model male e 0 . As far as the historical
data was concerned, this is the equivalent of fitting an ARIMA(0,1,0) model to annual
male e 0 . The mathematical formula for deriving future male e 0 was:
e 0 (males, T) = e 0 (males, T–1) + e{e 0 }(males, T) + drift{e 0 }(males, T)
where T denotes a one year interval, e{e 0 } are random errors sampled from a normal
distribution with the calculated standard deviation (0.57459) and a mean of zero, and
drift{e 0 } shifts the median of the future simulations of male e 0 to follow the medium
mortality variant of the 2009-base national population projections (figure 8). Also
illustrated in that figure are the low and high mortality variants from the 2009-base
national population projections. These variants approximate the interquartile range over
the projection period.
Figure 9
Assumed male life expectancy at birth probability distribution
2010–2111
Given the strong correlation between male and female e 0 , future female e 0 was derived
by adding together the simulations of male e 0 and female–male differences in e 0 (de 0 ).
Again, a simple random walk with drift process was used to model female–male
differences in e 0 . And again as far as the historical data was concerned, this is the
equivalent of fitting an ARIMA(0,1,0) model to annual e 0 differences:
de 0 (T) = de 0 (T–1) + e{de 0 }(T) + drift{de 0 }(T)
16
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
where T denotes a one-year interval, e{de 0 } are random errors sampled from a normal
distribution with the calculated standard deviation (0.37400) and a mean of zero, and
drift{de 0 } shifts the median of the future simulations of female–male differences in e 0
to follow the medium mortality variant of the 2009-base national population projections
(figure 10 and figure 11).
Figure 10
Assumed female–male difference in life expectancy at birth probability distribution
2010–2111
Also illustrated in figure 11 are the low and high mortality variants from the 2009-base
national population projections. These variants give a slightly narrower range than the
interquartile range over the projection period. The contrast with males (figure 9) is
interesting and reflects:
·
In the deterministic projections, the difference between the low and high variants is
higher for males than females (eg 6 years compared with 5 years in 2061, and 10
years compared with 8 years in 2111).
·
In the stochastic projections, the uncertainty is effectively higher for females than
males (eg 90 percent probability interval of 16 years compared with 14 years in
2061, and 23 years compared with 19 years in 2111). This is the result of adding
the female–male difference in e 0 variable to the male e 0 variable. However,
explicitly modelling female e 0 from the same historical data used to model male e 0
gives a similar result of higher female uncertainty in e 0 . This supports deriving
female e 0 from male e 0 (by adding female–male difference in e 0 ) rather than
deriving male e 0 from female e 0 (by subtracting female–male difference in e 0 ).
In terms of female–male differences in life expectancy at birth (figure 10), there are no
explicit low or medium variants in the 2009-base national population projections.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 11
Assumed female life expectancy at birth probability distribution
2010–2111
ASSRs were subsequently derived by scaling the ASSRs from the medium mortality
variant of the 2009-base national population projections to match each e 0 simulation
for each projection year. The probability distribution for male ASSRs in 2061 is illustrated
in figure 11.
A feature of the ASSR distribution is the very high rates and narrow probability interval
under 60 years of age, where there is currently less than 1 death per 100 people
(Statistics New Zealand, 2009d). In contrast, there is significant uncertainty for ASSRs
above 80 years of age, indicating that projections of the population at the oldest ages
are sensitive to mortality assumptions.
Also illustrated in figure 12 are the low and high mortality variants from the 2009-base
national population projections. These variants approximate the interquartile range in
2061.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 12
Assumed male age-specific survival rate probability distribution
2061
Note: Age 100 is 100 years and over.
Migration
Projected net migration is calculated directly in terms of a specific age-sex distribution for
each specific net migration level.
New Zealand has a rich source of external migration data in the passenger cards
completed by people travelling into and out of the country. In 2009, there were 4.5
million arrivals and 4.5 million departures. However, only a small proportion of these
movements translate to changes in the resident population of New Zealand. For
population estimates purposes, net migration is based on the ‘permanent and longterm’ classing of passengers, mainly on the basis of self-reported travel intentions.
Therefore, for projections of the resident population, there is the issue as to whether
‘permanent and long-term’ or ‘all movements’ data should inform measures of
uncertainty in future migration (figure 13). For further description of this issue and data
availability, see Dunstan et al (2006, pp5, 25–29) and Statistics New Zealand (2008,
p28).
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 13
80
Net migration by class
1900–2009
Thousand
All movements
60
40
20
0
-20
-40
Permanent and long-term
-60
1920
1930
1940
1950
1960
1970
June year
1980
1990
2000
2010
Note: ‘All movements’ includes permanent and long-term as well as short-term (less than 12
months) movements.
Despite the long historical time series, there is also the issue of what period should be
used to model migration uncertainty. New Zealand’s migration flows continue to evolve
in response to changes in immigration policy (both in New Zealand and abroad), the
advent of relatively cheap air travel, and the increasing globalisation of education and
labour markets.
The 2009-base national population projections medium migration variant assumed a
long-run annual net migration gain of 10,000, with higher net gains in the short run
(2010–12). This assumption was based on an analysis of immigration permits,
residence applications and approvals, overseas student numbers, and arrivals and
departures analysed by characteristics such as citizenship, country of last/next
permanent residence, and age.
The medium migration variant also assumed the main net outflow at ages 22–25 years,
mainly due to young New Zealanders embarking on overseas travel and the departure
of students from overseas after studying in New Zealand. Net inflows were assumed for
most other ages, with the highest net inflows at 15–20 and 27–37 years. The age-sex
distribution of net migration remains constant in the long term.
Modelling uncertainty in net migration
Standard deviations were calculated using permanent and long-term data for 1980–
2009 (June years). Migration patterns over this period, which included significant
changes in immigration policy (notably in 1987), were considered to be a better basis
for formulating a probability distribution for future migration than a longer historical time
series, or a time series using all passenger movements. An ARIMA(1,0,1) model was
fitted to this data, which was also the type of ARIMA model that Wilson (2005) used.
The mathematical formula for deriving the future net migration levels was:
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
N(T) = F{N}N(T–1) + Q{N}e{N}(T-1) + e{N}( T) + drift{N}(T)
where T denotes a one-year interval, F{N} is an autoregressive parameter (0.49112),
Q{N} is a moving average parameter (-0.61052), e{N} are random errors sampled from
a normal distribution with the calculated standard deviation (12,204) and a mean of
zero, and drift{N} shifts the median of the future simulations of net migration levels to
follow the medium migration variant of the 2009-base national population projections
(figure 14). The probability distribution is much wider than the alternative 5,000 (low)
and 15,000 (high) long-run net migration levels used in the 2009-base national
population projections.
Figure 14
Assumed net migration probability distribution
2010–2111
The associated age-sex net migration distributions were derived by using the patterns
adopted with the 2009-base national population projections. These patterns are
constant over the projection period. The projected net migration distribution by age-sex
was derived by interpolating or extrapolating between the low and high net migration
patterns for any given net migration level (figure 15). As with the net migration levels,
the probability distribution is much wider than the alternative 5,000 (low) and 15,000
(high) long-run net migration levels used in the 2009-base national population
projections.
21
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 15
Assumed net migration by age probability distribution
From 2013
Note: Percentiles shown are 5, 25, 50, 75, and 95. Age 100 is 100 years and over.
The described approach to migration differs from Wilson, who modelled immigration
and emigration (as immigration minus net migration) separately. While it is intuitively
appealing to model arrivals and departures separately, Wilson did have to reject some
implausible simulations and apply floor/ceiling limits. Earlier work within Statistics NZ
found no suitable ARIMA models for historical arrivals data that could produce
satisfactory future simulations. Moreover, the disaggregation of net migration into arrivals
and departures is beyond the current scope of Statistics NZ’s national population
projections.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
3 Results
This section summarises the results of the stochastic population projections of the New
Zealand population from 2009 (base) to 2111.
The results presented here are not exhaustive, but illustrate the probability distributions
relating to different characteristics of the population, and how these compare with the
published deterministic scenarios (eg low growth series 1 and high growth series 9 of
the 2009-base national population projections). The stochastic results presented in this
section are representative of the projection results that would be available to users, if
and when stochastic projections were produced. Additional projection results are
illustrated in appendix 3.
The projection results are based on running 1,000 simulations of the assumptions
described and discussed in section 2. All simulations produced plausible results (eg
there were no negative populations). Note that the median (the 50th percentile as
indicated by the 50% label in each figure) is taken directly from the 2009-base national
population projections, while all projection results relate to June years.
The probability distributions and intervals illustrated in this section are based on the
specified assumptions, with associated probability distributions and intervals from the
simulated results. The 50th percentile (50% line) should be interpreted as signifying
that there is a 50 percent chance that the given result for a given year will be below this
line, and a 50 percent chance that the given result for a given year will be above this
line. Similarly, the 75th percentile (75% line) signifies that there is a 75 percent chance
that the given result for a given year will be below this line, and a 25 percent chance
that the given result for a given year will be above this line.
Population size and growth
These experimental stochastic population projections indicate considerable uncertainty
in the future total population of New Zealand (figure 16, overleaf). The 90 percent
probability interval for New Zealand’s population is 4.89–5.41 million in 2031, 4.82–
6.69 million in 2061, and 3.58–10.35 million in 2111. Interestingly, the low growth
series 1 and high growth series 9 of the 2009-base national population projections
equate roughly to the 5 percent and 95 percent probability distributions until the 2060s,
but a narrower range thereafter.
Stochastic projections can also enhance the information not otherwise available from
deterministic projections. For example, the stochastic projections indicate a 50 percent
probability that the New Zealand population will reach 5 million during 2024–29; an 80
percent probability that the population will reach 5 million before 2030; and a 1 in 3
probability that the population will reach 6 million before 2060.
23
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 16
Projected population probability distribution
2009–2111
In terms of growth rates, the projections indicate a general decline until the 2050s
(figure 17), which is driven by the trends in births, deaths, and natural increase (figure
18–figure 20). The low growth series 1 and high growth series 9 approximate the
interquartile range over the projection period.
Figure 17
Projected annual growth rate probability distribution
2010–2111
24
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Births and deaths
These experimental stochastic population projections indicate considerable uncertainty
in the annual number of (live) births (figure 18). Even in the first year of the projection
period, 2010, there is a 50 percent probability that births will be outside the range
61.6–64.2 thousand. The interquartile range expands to 55–67 thousand by 2031, to
49–79 thousand by 2061, and to 39–105 thousand by 2111. The divergence of
uncertainty from the late 2030s reflects that the uncertainty in future fertility rates is
compounded by the uncertainty in the future number of women of childbearing age. By
comparison, the low growth series 1 and high growth series 9 encompass the
interquartile range for most of the projection period.
Figure 18
Projected births probability distribution
2010–2111
In comparison with births, the future number of deaths is more certain, especially before
2030 (figure 19, overleaf). In the first year of the projection period, 2010, there is a 50
percent probability that deaths will be outside the range 28.4–31.0 thousand. The
interquartile range expands to 37–46 thousand by 2031, to 52–64 thousand by 2061,
and to 58–73 thousand by 2111. There is a strong indication of increased deaths until
the 2050s, despite the continued increases in life expectancy assumed at all ages. This
is due to more people reaching the older ages.
25
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Of the nine official series published in the 2009-base national population projections,
series 3 and 7 give the highest and lowest number of deaths, respectively, for most of
the projection period. Compared with the stochastic projections, the range given by
these series is very narrow. The alternative series “allow users to assess the impact on
population size and structure resulting from changes in the assumptions for each of the
components of population change” (Statistics New Zealand, 2009a, emphasis added).
However, this nuance may not be fully understood by users of the projections, who
might expect the range of deterministic scenarios to give a good indication of uncertainty
in all characteristics of the projected population, including deaths. Furthermore, users
might expect the lowest growth and highest growth series (series 1 and 9) to give the
widest indication of uncertainty, but this is not true for all population characteristics.
Figure 19
Projected deaths probability distribution
2010–2111
The uncertainty in natural increase is a function of the uncertainty in both births and
deaths (figure 20). The general trend is for shrinking natural increase until the 2050s,
driven by more deaths. The projections indicate a 2 in 5 probability of natural decrease
from 2060. Again, the low growth series 1 and high growth series 9 encompass the
interquartile range for most of the projection period.
26
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 20
Projected natural increase probability distribution
2010–2111
Population age structure
Population projections are particularly important for indicating changes in the age
distribution of the population. In 2031, 22 years after the base year, demographic
uncertainty varies significantly by age (figure 21). Ages under 20 years have relatively
large uncertainty bounds, mainly reflecting the uncertainty of future fertility rates. Above
age 80, the uncertainty of future mortality/survival rates causes uncertainty in
proportional terms, but the uncertainty is small in absolute numbers.
Figure 21
Projected single-year of age probability distribution
2031
Note: Percentiles shown are 5, 25, 50, 75, and 95. Age 100 is 100 years and over.
27
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
By 2061, 52 years after the base year, demographic uncertainty is relatively large for
ages under 50 years, reflecting the uncertainty of future fertility rates, and to a lesser
extent the uncertainty of future migration (figure 22).
The impact of fertility on uncertainty is cumulative in that the number of births in 2061
is affected by the uncertain number of women of childbearing age alive in 2061, which
in turn is driven by uncertain births (and fertility patterns) before 2050.
Those aged 52 years and over in 2061 are already alive in the base year, so only deaths
and migration can alter their numbers. The uncertainty at these ages is largely driven by
the uncertainty of future mortality/survival rates.
Figure 22
Projected single-year of age probability distribution
2061
Note: Age 100 is 100 years and over.
Other measures can also be used to indicate changes in the age distribution of the
population. For example, the median age indicates the age at which half the population
is younger, and half is older. From a median age of 36.5 years in 2009, the stochastic
projections indicate that the interquartile probability interval is 39.4–40.9 years in 2031,
40.8–46.1 years in 2061, and 40.6–51.6 years in 2111 (figure 40, appendix 3). The
largest increases in the median age are therefore likely to occur between 2021 and
2041.
Population age pyramids are commonly used to illustrate changes in the age distribution
of the population, and can also be used with stochastic projections.
Figure 23 reiterates the results of the previous two figures, namely the relatively large
uncertainty at the youngest ages (driven by uncertainty in future fertility rates). To a
lesser extent, there is also relatively high uncertainty at the oldest ages (driven by
uncertainty in future mortality/survival rates).
28
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 23
100+
Projected age-sex pyramid probability distribution
2061
Age (years)
90
Males
Females
80
70
60
50
40
30
20
10
95%
0
60
75% 50% 25%
40
5%
20
5%
0
Thousand
20
25% 50% 75%
95%
40
60
Ages can also be transformed into birth cohorts (people with a common year of birth)
and stochastic projections used to convey uncertainty in cohort populations (Figure 24).
Figure 24
Projected baby boomer population (born 1946–65) probability distribution
2009–61
Note: Percentiles shown are 5, 25, 50, 75, and 95.
29
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 25
Projected population aged 65+ probability distribution
2009–2111
Figure 26
Projected percentage of population aged 65+ probability distribution
2009–2111
30
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The stochastic projections indicate a significant increase in the population aged 65+
years (figure 25). From 0.55 million in 2009, the 90 percent probability interval
indicates a population of 0.95–1.18 million in 2031, 1.10–1.75 million in 2061, and
1.23–2.56 million in 2111. The uncertainty is driven by mortality/survival rates, as
future fertility rates do not impact on the projected numbers aged 65+ until the 2070s.
The low growth series 1 and high growth series 9 encompass the interquartile range
throughout the projection period, but by 2111 these series actually equate closer to the
90 percent probability interval.
The stochastic projections do help negate the myth that the increase in the 65+
population is a temporary phenomenon driven by the ageing of the large birth cohorts
of the 1950s and 1960s (the ‘baby boomers’). Instead, the projections indicate a
sustained structural shift in both the number and proportion of the population aged 65+
years (figure 26). This shift is far from being some artefact of the projection
assumptions. From 13 percent in 2009, the 90 percent probability interval indicates a
proportion of 19–23 percent in 2031, 19–31 percent in 2061, and 18–44 percent in
2111. However, it is noteworthy that the alternative low growth series 1 and high
growth series 9 give no indication of demographic uncertainty for the proportion aged
65+ years.
The above results are underscored by results for other age groups (appendix 3).
Uncertainty is greatest for the youngest age groups because of the uncertainty in births
(fertility rates), and the oldest age groups which are most sensitive to mortality
assumptions. Deterministic projections, such as the low growth series 1 and high growth
series 9, are poor at indicating the uncertainty in population proportions.
Dependency ratios
Dependency ratios are simple measures that relate the number of people in broad
‘dependent’ age groups (such as 0–14 and 65+ years) to the broad ‘working-age’
population (such as 15–64 years). ‘Dependency’ has a variety of connotations and
need not imply financial or economic dependency. Furthermore, the dependency status
of the older age group could be expected to change over time, reflecting changes in life
expectancy, physical and mental well-being, and labour force status. Nevertheless,
dependency ratios illustrate the changing age structure by simply relating the numbers
of people in the youngest and oldest age groups to the numbers in the middle age
groups (most of whom are in the workforce).
The trend in the 0–14 (or ‘youth’) dependency ratio largely reflects the trend in birth
numbers. The interquartile range of 29.4–31.6 in 2021 is relatively narrow, but
uncertainty increases quickly (figure 27, overleaf). The interquartile range expands to
27.3–31.5 in 2031, to 24.4–32.4 in 2061, and further to 22.2–34.2 in 2111. Of the
alternative deterministic series, series 2 and 8 (which use alternative fertility
assumptions) give the widest range in the long-term 0–14 dependency ratio. These
series encompass the interquartile range in the short term, but are well within this range
in the long term.
31
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 27
Projected 0–14 dependency ratio probability distribution
2009–2111
Compared with the 0–14 dependency ratio, the probability interval of the 65+ (or
‘elderly’) dependency ratio is narrower in the short term, but wider in the long term. The
interquartile range of 32.5–35.2 in 2031 increases to 37.6–47.2 in 2061, and further
to 41.7–64.5 in 2111 (figure 28). However, the projections suggest an increase in the
65+ dependency ratio, from about 19 in 2009 to over 30 beyond 2030, is almost
inevitable. Of the alternative deterministic series, series 3 and 7 (which use alternative
mortality assumptions) give the widest range in the long-term 65+ dependency ratio.
These series reflect the interquartile range in the short term, but are also well within this
range in the long term.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 28
Projected 65+ dependency ratio probability distribution
2009–2111
The probability interval of the total dependency ratio expands from an interquartile range
of 61.0–65.6 in 2031, to 66.9–75.4 in 2061, and further to 74.0–90.0 in 2111 (figure
29). An increase in this ratio from its 2009 level of 50 therefore seems inevitable. Series
3 and series 7 reflect the interquartile range over the entire projection period.
Figure 29
Projected total dependency ratio probability distribution
2009–2111
33
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
4 Discussion
This section discusses the issues, both conceptual and practical, of incorporating a
stochastic approach to future demographic projections produced by Statistics NZ.
Summary of method
The previous sections describe a method of quantifying the uncertainty for projections of
the New Zealand population. Probability distributions around a deterministic mid-range
projection are produced by combining simulations of the base population, births (via
fertility rates), deaths (via survival rates), and net migration. All simulations of all
components were retained, with none discarded because of outright implausibility.
Simulations of population projections are produced by combining the simulated
components. All simulated projections were also retained.
The results are plausible, but the estimates of uncertainty are uncertain for several
reasons. First, where historical data are used to drive the estimates of uncertainty,
choices must be made as to which data series are used (eg period or cohort data,
aggregated or age-specific data). Second, choices must be made as to what time
periods are used. Third, there is a choice of models to apply to time series to estimate
parameters such as standard errors. Fourth, any historical data series will have issues of
coverage and accuracy relating to its collection and coding, which will affect the
estimation of parameters.
Inevitably, the process of formulating measures of uncertainty for stochastic projections
is similar to that of formulating assumptions for deterministic projections. They both
require a balance of empirical data analysis and judgement.
Nature of projections
A stochastic projection extrapolates observed variability in demographic data to the
future (Keilman, 2005). For a proper assessment of the variability, Keilman suggests that
one needs long series with annual data of good quality; the minimum is about 50 years,
but a longer series is preferable. New Zealand’s demographic time series are high quality
but imperfect. Keilman notes that when time series analysis cannot be used to compute
predictive distributions, one has to rely strongly on expert opinion. This expert opinion
can be drawn from a mix of experts within an organisation and/or external to an
organisation such as Statistics NZ. The challenge of eliciting experts’ opinions, particularly
in avoiding too narrow prediction intervals, is discussed in Lutz et al (1996, 2001),
O’Hagan (2005), Kynn (2008), and Lutz (2009).
Regardless of how projection assumptions are formulated and demographic projections
derived, they are neither predictions nor forecasts. They represent the statistical
outcomes of various combinations of selected assumptions about future changes in the
dynamics of population change (eg future fertility, mortality, and migration patterns).
These assumptions are formed from the latest demographic trends and patterns, as well
as international experiences, to represent some possible scenarios. Each projection
scenario gives a picture of the changing population, but is not designed to be an exact
forecast or to project specific annual variations.
34
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The difference between projections and predictions is provided in an analogy made by
the Australian Productivity Commission (2005). They give the example of someone
seeing a large boulder on a train track. The projection is that there will be a rail disaster
and many deaths if the boulder is not moved or the train is not stopped. The prediction
is that someone will move the boulder, averting the accident. It is likely that the
projection is much more useful for policy formulation and planning.
This analogy is relevant to demographic projections. A number of organisations,
including central and local governments, may initiate strategies to avert the population
trends implied by the projections. Examples include changes to immigration policy and
local economic development strategies (eg to retain residents or attract new residents).
One of the roles of projections is to enable future demographic changes to be
understood and managed, if not averted. In such instances, it is illogical to criticise the
projections if they do not match actuality, especially when projections have been used
to inform those strategies.
These nuances are important to understanding both conventional deterministic
projections and stochastic projections. Any projections and associated measures of
uncertainty are inherently uncertain and subject to update. Indeed, they should be
regularly updated to maintain their relevance.
In interpreting the measures of uncertainty, it is also important to note that extreme
events such as major wars, catastrophes, and pandemics, as well as major government
and business decisions, are not realistically accounted for in either deterministic
scenarios or stochastic projections. That is, the measures of uncertainty do not
encompass all possibilities.
Summary of results
Demographic uncertainty is generally much greater than can be discerned from an
analysis of a limited range of deterministic scenarios. This is not necessarily because the
alternative scenarios have assumptions that are too narrow, but simply that there is no
quantification of likelihood attached to the alternative scenarios. Moreover, a limited
number of scenarios cannot convey how the different assumptions interact and fluctuate
over time.
The deterministic projections, including alternative low growth and high growth
scenarios, do illustrate plausible projection outcomes. However, they only partly convey
an indication of uncertainty.
The stochastic projections derived here are based on a multitude of simulations. Each of
these simulations is plausible – some more so than others – but collectively they give
an indication of demographic uncertainty in both the short term and long term. Results
from 1,000 simulations are surprisingly stable for most distributions, although more
simulations may be needed if stochastic projections were to be implemented officially.
35
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
The results in this section, although not exhaustive, illustrate that the deterministic
scenarios give a poor indication of uncertainty for some key demographic characteristics.
Even for other characteristics, the uncertainty indicated by the scenarios is neither
consistent across the projection period, nor consistent between characteristics. For
example, at times the alternative scenarios are analogous to a 50 percent probability
interval, while at other times they are equivalent to a 90 percent (or higher) probability
interval. This largely reflects that the low and high deterministic assumptions are not
equivalent to a given probability interval that is consistent among the fertility, mortality,
and migration components.
Moreover, the uncertainty is rarely symmetrical, unlike that typically conveyed by
deterministic projections. Although the probability of outcomes below and above the
median may be equal, the uncertainty is usually skewed. For population growth
outcomes, for example, there is a greater range of outcomes above the median than
below.
Stochastic projections are much better at conveying the uncertainty in some
characteristics of the population, such as deaths, percentage age distribution, and
dependency ratios. They also seem much better at conveying the large uncertainty that
exists in long-range projections beyond 50 years, and the extent to which this
uncertainty expands over time.
Given the widening probability distribution, the stochastic projections can indicate how
far into the future the projections are useful. However, ‘usefulness’ will vary from user to
user depending on which type of demographic projection is being used (eg national
population, subnational ethnic population), which demographic characteristics are being
used (eg total population, 65+ population, births), and how the projection is being used
(eg the specific application and the respective risks of an over-projection or underprojection).
Implications for national population projections
This paper describes a method for producing plausible stochastic population projections
for New Zealand. The question remains as to whether such an approach should be
embedded within the official demographic projections regularly produced by Statistics
NZ.
Methodological enhancements and developments continue to shape the statistical
environment. However, it is impractical for any producer of statistics to adopt every
enhancement as it unfolds. As Lutz et al (1998) discuss, "the change of a longestablished tradition" generally requires the following:
1.
The new practice must have clear advantages when compared with the current one.
2.
It should be consistent with other work done by the producing institution, and
present an evolution along established lines rather than a discontinuity.
3.
The proposed approach should be internally consistent and based on accepted
scientific work.
4.
It should be practical for both the users and producers, and not cost too much.
36
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
These points deserve some elaboration. In the context of the independence and
integrity of Statistics NZ as a producer of (population) statistics, a high priority is put on
the statistical rigour of data, concepts, and methods, including incorporating international
standard practices. However, there is also an onus on Statistics NZ to provide statistical
leadership (eg in statistical methodologies), which can run counter to more conservative
statistical practices. Furthermore, the usefulness of any alternative or new method needs
to be evaluated against the costs, complexity, and transparency for users and producers.
Even if stochastic projections become a formal aspect of Statistics NZ’s demographic
projections, deterministic scenarios will continue to remain useful. ‘What if?’ scenarios
have been published in recent releases (eg Statistics New Zealand, 2009a). They
illustrate specific fertility, mortality, and migration scenarios relative to the mid-range
scenario, such as:
·
a very high fertility scenario (long-run total fertility rate of 2.5)
·
a very low mortality scenario (continued fast increases in life expectancy at birth, to
reach 95 years of life for males and females in 2061)
·
no migration scenario (a ‘closed’ population)
·
very high migration scenario (25,000 annual net migration).
The ‘What if?’ scenarios have received positive feedback. Stochastic and deterministic
approaches could therefore be seen as complementary.
Practical issues
Practical issues affecting implementation include:
1.
Impact on quality. Most national statistical organisations provide guidelines and
discussion of the dimensions of quality as they relate to statistics (eg Statistics New
Zealand, 2007b; Australian Bureau of Statistics, 2009; Office of National Statistics,
2004; Statistics Canada, 2002). Such quality dimensions provide a framework for
evaluating the usefulness of a methodological change such as a stochastic approach
to population projections. For projections, the quality dimensions can be described
as follows:
a.
Relevance. Do the projections cover the necessary geographic areas,
demographic characteristics (eg age, sex, ethnicity), and future time periods as
required by different users? Are the projections produced to satisfy the
expectations and aspirations of individuals or groups, or are they based on an
objective assessment of demographic trends?
b.
Timeliness. Are the projections updated and available when they are needed?
c.
Coherence. Is the choice of methods, data, and assumptions consistent with
accepted practices and do they account for the relevant factors? Are the
projection results plausible given known constraints and limitations?
d.
Accessibility. Is the information readily available to everyone? Are there costs to
access?
e.
Interpretability. Is the information about the projections (eg methods,
assumptions, results) available, understandable, and even replicable? Do the
projections provide measures of uncertainty?
37
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
f.
Accuracy. How do the projected trends compare with actuality? Do the
projections adequately illustrate changing demographic patterns?
A stochastic approach would enhance the interpretability of projections, while the
only quality dimension that could be compromised is that of timeliness. Inevitably,
producing stochastic projections would require more person-hours, as the additional
parameters of uncertainty would need to be calculated and reassessed in future
projections. Running multiple simulations and subsequent summarising and
dissemination could be expected to add work time to the production cycle.
2.
Computing capacity. A stochastic approach using multiple simulations involves more
time and larger datasets than the conventional deterministic approach, although this
is becoming less of an issue with rapidly progressing technology (eg virtual
memory). This paper illustrates how as few as 1,000 simulations can enhance the
projections with robust measures of uncertainty. A larger number of simulations
would increase the smoothness of the probability distributions (eg for growth rates
and natural increase).
3.
Managing user expectations. A stochastic approach does not necessarily mean that
projections are more 'accurate'. The advantages of a stochastic approach are in
quantifying uncertainty and in more realistic, variable projection trajectories. But the
estimates of uncertainty are themselves uncertain.
4.
Applying stochastic methods to subgroup populations. Most users of Statistics NZ
demographic projections want additivity or internal consistency. For example, that
subnational projections sum consistently to national projections. Or, that ethnic
population projections are consistent with those of the total population. There may
be expectations that a stochastic approach could be readily applied to national
projections of labour force, families and households, and ethnic populations.
Because there are more parameters to model, these would be more difficult than
the application to national population projections. Similarly, stochastic projections for
subnational areas need to deal with multiple geographic areas with small
populations. The implications for other projections are discussed in the following
section.
5.
Effective dissemination of methods and results. Any projection methodology and
underlying assumptions need to be transparent to users. Stochastic methods are,
arguably, more difficult to explain concisely, especially in a non-technical way. If and
when stochastic projections are produced, their use and understanding would be
helped by appropriate explanatory notes and metadata that typically accompany any
Statistics NZ release.
There are additional issues in summarising and presenting the results of thousands
of projection trajectories or simulations (eg graphical representation of uncertainty
bands). In addition, many projection results (eg percentage age distributions) would
need to be explicitly provided for users, as they cannot be accurately derived from
conventional results (eg population by age). However, this paper illustrates how
stochastic assumptions and projections can be presented using fan charts,
developed using R and Excel statistical software, although it is difficult to display
multiple variables (eg births and deaths) in one chart.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Furthermore, all the stochastic results presented in this paper (section 3) can be
disseminated through existing tools, such as Statistics NZ’s Table Builder (Statistics
New Zealand, 2010e). Alternative percentiles that summarise the probability
distributions could be published in preference to the current practice of publishing
selected deterministic series.
Implications for other projections
Statistics NZ produces an integrated and comprehensive suite of demographic
projections for national and subnational areas. Advocates of stochastic projections rarely
comment on the implications and methodology for the full range of projections typically
produced by national statistical organisations, tending to focus on one dimension (eg
national population projections or subnational population projections). And yet, this
consistency of assumptions and projections across the suite of demographic projections
is critical for data users, who expect additivity and plausibility at all levels.
In principle, a similar stochastic approach as that applied to the national population
projections, could be applied to the other demographic projections produced by
Statistics NZ. Some practical aspects are discussed here.
National labour force projections
Projections of the labour force are derived by applying labour force participation rates
(LFPRs) to population projections, by age-sex. The most recent national labour force
projections assumed LFPRs remain constant at most ages beyond 2021 (Statistics New
Zealand, 2010d). The major exception to this was at ages above 55 years, where
current trends and international comparisons suggest continued increases in LFPRs are
likely. This reflects increasing flexibility in the retirement age (with no compulsory
retirement age), and increasing life expectancy and well-being at the older ages.
However, as with all projection assumptions, any constancy does not signify an
expectation of actual stability, but is merely a simplification of a complex reality. The
constancy also reflects that the level and trend of LFPRs is uncertain in the long term. A
stochastic approach to labour force projections would therefore seem to enhance their
interpretation.
Historical LFPR time series are available from two sources, although with some
definitional differences and changes over time:
1.
the five-yearly Census of Population and Dwellings, which provides single-year of
age detail
2.
the quarterly Household Labour Force Survey, which provides official measures of
the labour force, but with sampling error even for grouped ages.
Estimates of LFPR uncertainty would therefore need to draw on both data sources,
perhaps with expert judgement being applied.
39
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
National ethnic population projections
These projections include two additional parameters, namely paternity rates by age of
father (to allow for births where the mother is not of the specified ethnic group, but the
father is) and inter-ethnic mobility rates by age-sex (to allow for people changing their
ethnic identification over time). One issue with all ethnic parameters, including those
related to the conventional fertility, mortality, and migration assumptions, is the much
shorter time series of historical data compared with that of the total New Zealand
population. Moreover, the measurement of ethnicity has changed over time in many
collections, while it is not captured at all in some collections (eg external migration data).
Fertility rates for the broad Pacific and Asian populations are only available for 1996,
2001, and 2006. This partly reflects the limited availability of population estimates and
the introduction of new birth (and death) registration forms in 1995. Official life tables
do not exist for either population, reflecting their relatively small populations and few
deaths. The limited ethnic time series may therefore require a more subjective approach
to estimating parameter uncertainty.
Nevertheless, ethnic population projections are a good example of where some
quantification of uncertainty, even though uncertain, would assist interpretation of the
projection results. Ethnic population projections are more uncertain than projections of
the total population. But how much more uncertain? And ethnic population projections
are produced with a shorter projection period – providing measures of uncertainty could
help justify why the projection period is shorter. An example of stochastic methods
applied to ethnic group projections is given for the United Kingdom population in
Coleman and Scherbov (2005).
One of the key issues relating to ethnic populations is their overlap, reflecting that
people can and do identify with multiple ethnicities. Stochastic projections of individual
ethnic groups could be produced independently. However, they could not be
meaningfully combined or contrasted with stochastic projections of the total New
Zealand population (eg to calculate ethnic shares), other than using the median
projection which is deterministically derived.
National family and household projections
Statistics NZ currently projects families and households using a propensity method. In
this method, living arrangement type rates (LATRs) by age-sex are applied to population
projections to give projections of the population in 11 different living arrangement types.
These projections are subsequently aggregated to give projections of families (by broad
family type) and households (by broad household type).
Uncertainty in the family and household projections can arise from the underlying
population projections, the LATRs, and four additional univariate parameters:
1.
average number of families per family household
2.
average number of people per other multiperson household
3.
proportion of two-parent families with dependent children
4.
proportion of one-parent families with dependent children.
40
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Variances for all of these parameters could be modelled from historical census data.
However, the data are essentially limited to a maximum of six censuses (1981 to 2006
at five-year intervals), where the requisite data are available electronically. Furthermore,
changes to census collection and processing procedures from census to census mean
that the census parameters are not necessarily consistent over time. This may lead to an
overestimate of the respective variances.
Alho and Keilman (2010) have developed a method that involves a random breakdown
of the population according to household position (eg single, cohabiting, living with a
spouse, living alone). These positions are analogous to LATRs, so the random share
method could be incorporated into the propensity method to provide some
quantification of uncertainty in LATRs in addition to the uncertainty in the underlying
population projections.
One aspect that could be problematic in stochastic family and household projections is
the significantly different numbers of male and female partners (in ‘couple without
children’ and/or ‘two-parent families’). The deterministic mid-range series is carefully
formulated to project similar numbers of male and female partners, bearing in mind the
numbers need not be identical because of same-sex partnerships and differences in
self-identification (eg differences between partners as to whether they are usually
partnered or even as to whether they usually live in New Zealand or at the same
address). Without a reconciliation, the stochastic projections could be demographically
implausible.
Subnational demographic projections
Statistics NZ produces various demographic projections for three key geographic units:
1.
regional council areas (regions). Based on boundaries and estimated resident
populations at 30 June 2010, there were 16 regions – ranging in size from
Auckland (1.46 million people) down to West Coast (33,000)(Statistics New
Zealand, 2010f).
2.
territorial authority areas (TAs). The new Auckland Council area (effective 1
November 2010) reduces the number of TAs to 67, with a median size of 30,000
people. Three-quarters of TAs have a population between 7,000 and 60,000.
3.
area units (AUs). In 2010, there were almost 2,000 AUs (equivalent to ‘suburbs’ in
major urban areas), with a median size of 2,000 people. Three-quarters of AUs had
a population between 100 and 4,000. AUs also form the building blocks for
deriving projections for other geographic areas, such as wards and urban/rural areas.
Projection accuracy is generally proportional to the population size of geographic areas
(Keilman, 2005; Statistics New Zealand, 2008). That is, demographic uncertainty
generally increases as the size of the geographic area decreases. Conveying this
uncertainty to users of subnational population projections would seem to be prudent.
41
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
However, in practice, any estimates of uncertainty are likely to be much more uncertain
than those at the national level. This is largely because of the much shorter historical
time series available for subnational fertility, mortality, and migration measures. In turn,
this partly reflects the major geographic boundary changes that have occurred. For
example, the local government reorganisation that took effect on 1 November 1989
caused significant boundary changes when establishing regional council and TA areas.
Historical time series for AUs are complicated by their ongoing proliferation, which saw
the number of AUs increase from 1,775 in 1996 to 2,013 in 2011.
Although fertility, mortality, and migration can be assumed to be largely independent at
the national level, at the subnational level this is less true. For example, the migration of
people in the prime reproductive ages, 20–44 years, is often associated with the
loss/gain of reproductive potential – their offspring. Or, ‘greenfield’ developments that
attract younger adult migrants can result in significant changes in local fertility patterns as
family formation occurs. There are also some significant, although often complex,
migrations of older people related to changes in their well-being and independence,
which result in correlations between migration and mortality.
A further limitation of stochastic subnational population projections is apparent for areas
subject to high growth trajectories, either in the past or the future. For areas that have
reached capacity or have very limited scope for further residential development, past
demographic patterns may be a poor basis for formulating projection assumptions, let
alone demographic uncertainty. Similarly, for areas of future high growth (eg greenfield
developments), past demographic patterns are unlikely to indicate the uncertainty
around the pace and timing of future population growth. Extrapolative techniques are
likely to be unsuitable in such circumstances.
Cameron and Poot (2010) outline a method for producing stochastic population
projections for subnational areas. While this work seems promising, their projections are
only for selected geographic areas and are unconstrained to higher-level geographies
(eg national population projections). The uncertainty parameters are based on national
data and are assumed to be the same for all ages, both sexes, and all geographic areas.
Cameron and Poot suggest a stochastic approach can mitigate the inherent
conservatism of projections, where the fastest growing areas tend to be under-projected
and the slowest growing (or declining) areas tend to be over-projected. This appears to
be achieved by using migration rates, rather than migration levels. The use of age-andsex-specific migration rates is already an implicit part of Statistics NZ's method, as
evidenced by changing migration levels (although limited) over the projection period.
Yet the use of explicit migration rates intuitively appeals. However, all the stochastic
projections presented by Cameron and Poot are higher than the mid-range Statistics NZ
deterministic projections, which suggests that slow growing (or declining) areas will be
further over-projected and underscores the importance of constraining to plausible
higher-level projections. If explicit migration rates were used, constraining to higher-level
projections would not be as straightforward.
42
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Cameron and Poot also do not examine if and how a stochastic method is transferable
to the AU geography, which remains a critical part of Statistics NZ's subnational
population projections. One option, not discussed in their paper, is whether different
methods are preferable for different geographies. For example, is a stochastic approach
suitable for TAs, but unsuitable for AUs? An important consideration in this context may
be the added time and cost of a more complex method, when producers of population
projections are under pressure to reduce the time and costs of production.
Conclusion
Both deterministic and stochastic projections are a simplification or model of complex
and variable phenomena, with projection assumptions designed to convey future
average long-run patterns. However, deterministic scenarios give a poor indication of
uncertainty for some key demographic characteristics. Stochastic projections offer the
clear advantage of giving estimates of uncertainty. They therefore give users of
projections a better indication of uncertainty and the associated probability intervals.
Moreover, given the nature of projections, a stochastic approach is consistent with how
statistical agencies would like projections to be conveyed and interpreted.
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
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Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Appendix 1: List of abbreviations
ARIMA autoregressive integrated moving average
ASFR
age-specific fertility rate
ASSR
age-specific survival rate
AU
area unit
de 0
female–male difference in life expectancy at birth
e0
life expectancy at birth
ERP
estimated resident population
HMD
Human Mortality Database
LATR
living arrangement type rate
LFPR
labour force participation rate
NCU
net census undercount
PES
post-enumeration survey
RTO
resident temporarily overseas
SE
standard error
TA
territorial authority
TFR
total fertility rate
48
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Appendix 2: Examples of simulations
Illustrations of simulation #1 (figure 30) and simulation #2 (figure 31) of 1,000
simulations, for selected assumptions and projection results.
Figure 30
Example #1 of simulated total fertility rate, male and female life expectancy at birth, net
migration, total population, births and deaths, and 65+ population
2010–2111
Male and female life expectancy at birth
Total fertility rate
Births per woman
3.0
Years of life
105
2.5
100
2.0
95
1.5
90
1.0
85
0.5
80
Female
Male
0.0
75
2006
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2106
2006
Net migration
2026
2036
2046
2056
2066
June year
2076
2086
2096
2106
2086
2096
2106
2086
2096
2106
Total population
Thousand
50
2016
Million
8
40
7
30
6
20
5
10
4
0
3
-10
2
-20
1
-30
-40
0
2006
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2106
2006
Births and deaths
120
2016
2026
2036
2046
2056
2066
June year
2076
65+ population
Thousand
2.5
100
Million
2.0
80
1.5
Births
60
1.0
40
20
0.5
Deaths
0
2006
0.0
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2006
2106
49
2016
2026
2036
2046
2056
2066
June year
2076
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 31
Example #2 of simulated total fertility rate, male and female life expectancy at birth, net
migration, total population, births and deaths, and 65+ population
2010–2111
Male and female life expectancy at birth
Total fertility rate
Births per woman
3.0
2.5
100
2.0
95
1.5
90
1.0
85
0.5
80
0.0
75
2006
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2106
Female
Male
2006
Net migration
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2106
2086
2096
2106
2086
2096
2106
Total population
Thousand
50
Years of life
105
Million
8
40
7
30
6
20
5
10
4
0
3
-10
2
-20
1
-30
-40
0
2006
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2106
2006
Births and deaths
120
2016
2026
2036
2046
2056
2066
June year
2076
65+ population
Thousand
2.5
100
Million
2.0
80
1.5
Births
60
1.0
40
20
Deaths
0.5
0
2006
0.0
2016
2026
2036
2046
2056
2066
June year
2076
2086
2096
2006
2106
50
2016
2026
2036
2046
2056
2066
June year
2076
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Appendix 3: Additional projection results
Figure 32
Projected population aged 0–14 probability distribution
2009–2111
Figure 33
Projected percentage of population aged 0–14 probability distribution
2009–2111
51
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 34
Projected population aged 15–39 probability distribution
2009–2111
Figure 35
Projected percentage of population aged 15–39 probability distribution
2009–2111
52
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 36
Projected population aged 40–64 probability distribution
2009–2111
Figure 37
Projected percentage of population aged 40–64 probability distribution
2009–2111
53
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 38
Projected population aged 85+ probability distribution
2009–2111
Figure 39
Projected percentage of population aged 85+ probability distribution
2009–2111
54
Experimental Stochastic Population Projections for New Zealand by Kim Dunstan
Figure 40
Projected median age probability distribution
2009–2111
55