The impact of population dynamics and foreign labour policy on dependency: the case of Singapore

Abstract

Understanding population dynamics is crucial to understanding current and future health care needs and designing systems to meet those needs. In this paper, we provide a methodological approach to investigate population dynamics in a system dynamics model configurable to initialise in dynamic equilibrium or disequilibrium. We then use the model to investigate how the current measured population compares to a population of the same size in equilibrium, and how a dependency ratio will change over time under different scenarios. We apply our approach to Singapore, which, like many other countries, has a rapidly increasing proportion of elderly in the population.

Full text

The impact of population dynamics and foreign labour
policy on dependency: the case of Singapore
John Pastor Ansah
1
•Crystal M. Riley
2
•
James P. Thompson
1
•David Bruce Matchar
1
Published online: 5 June 2015
Springer Science+Business Media Dordrecht 2015
Abstract Understanding population dynamics is crucial to understanding current
and future health care needs and designing systems to meet those needs. In this
paper, we provide a methodological approach to investigate population dynamics in
a system dynamics model configurable to initialise in dynamic equilibrium or
disequilibrium. We then use the model to investigate how the current measured
population compares to a population of the same size in equilibrium, and how a
dependency ratio will change over time under different scenarios. We apply our
approach to Singapore, which, like many other countries, has a rapidly increasing
proportion of elderly in the population.
Keywords Population Ageing Dependency ratio System dynamics Fertility
rate Mortality rate Foreign labour Immigration Simulation Dynamic
equilibrium
Introduction
Singapore is a city-state in Southeast Asia with a population of 5.4 million
(Singapore Department of Statistics 2014). Over the past several decades,
Singapore’s population demographics have been shifting as birth and mortality
rates have declined, leading to an increasing average age of the population. Since
the 1970s, the birth rate has been below a replacement rate of roughly two children
per woman over her childbearing years (Asher and Nandy 2008). Pro-family
&John Pastor Ansah
john.ansah@duke-nus.edu.sg
1
Duke-NUS Graduate Medical School, Singapore, Singapore
2
Washington University, St. Louis, MO, USA
123
J Pop Research (2015) 32:115–138
DOI 10.1007/s12546-015-9145-9

policies were introduced in the 1980s in an attempt to raise the birth rate, but
Singapore remains in the ‘ultra-low’ fertility range (Straughan et al. 2009).
As fertility rates were decreasing, mortality rates in all age cohorts also decreased
(World Bank 2011). These lower mortality rates reflect improved public health
measures and medical technology. Mortality rates have decreased to the point that
Singapore currently has among the highest life expectancies at birth in the world, at
84.6 years for females and 80.2 years for males as of 2013 (Singapore Department
of Statistics 2014). This combination of low birth rates and high life expectancies
has made Singapore one of the most rapidly ageing nations.
The ageing of Singapore’s resident population has resulted in a proportionately
smaller class of working-age citizens. In his 2010 National Day address, Prime
Minister Lee Hsien Loong said, ‘‘We also need to reinforce the Singapore team with
talent and numbers from abroad…. We must make up for the shortage of
Singaporean workers in our economy and the shortfall of babies in our population,’’
(Prime Minister’s Office Singapore 2010). As of June 2014, there are 1.1 million
foreign workers in Singapore (Ministry of Manpower 2014). The majority of
foreigners are men who are issued work permits to work in the construction,
maritime, and manufacturing sectors. A special work permit is issued to foreign
women working as domestic workers, who live with families and tend to household
duties such as cooking, cleaning, and child care. Work permits, whether for a
construction worker or a domestic worker, are issued for a limited period of about
2 years. Workers on these short-term passes are counted in the total Singapore
population, but are not eligible to immigrate or become permanent residents, and are
not able to bring family members or children into Singapore to live with them
(Ministry of Manpower 2014).
A separate class of foreign workers generally work in professional or executive
positions, and hold Employment Passes that allow them to apply for Dependent’s
Passes for their spouses and/or children to live here with them (Ministry of
Manpower 2014). Employment Pass holders and their dependents are able to apply
to become permanent residents, which in turn makes them eligible to apply for
Singaporean citizenship (Immigration and Checkpoints Authority 2011).
The final class of workers are called S-Pass holders. S-Pass holders are mid-level
skilled workers such as technicians, who may only apply for Dependent’s Passes for
spouses and children if they meet minimum monthly salary requirements (Ministry
of Manpower 2014).
The definition of ‘total population’ includes Singaporeans by birth, naturalisation
or permanent residency plus foreign labour (see Bloom and Williamson 1998 for
detailed explanation). The definition of ‘resident population’ includes only
Singaporeans by birth (including those born to naturalised citizens or permanent
residents), naturalisation or permanent residency, not temporary foreign labour.
As we note further on, the dynamics between foreign labour and the resident
population indicate long-term population disequilibrium and an effort to balance
economic goals with social policies that are becoming increasingly dependent on
foreign labour. With foreign labour comprising over 20 % of the population, the
reliance on foreign labour is significant and it is arguable that the observed
Singapore—characterised by economic prosperity and rich cultural diversity—
116 J. P. Ansah et al.
123

would not be possible without it. In other words, Singapore depends on foreign
labour, and immigration policy operates to maintain socioeconomic balance.
Declining birth rates, increasing life expectancies, and higher numbers of foreign
labourers all affect the dependency ratio. The notion of dependency ratio varies by
field of interest—economics, sociology, or geography (see, for example Leff 1969).
The term expresses how one group of people rely on another group of people for
social support. The dynamics of dependency are complex. A change in birth rate (a
flow) affects population (a system state) for decades into the future. A change in
mortality rates amongst older population cohorts can arise from emergent dynamics
such as changing public health initiatives. Foreign labour policies, unlike birth and
mortality rates, can be fine-tuned to meet the needs of the total population. The
complicated dynamics of birth and mortality, dependency ratio, and foreign labour
are explored in further detail with the use of a System Dynamics model.
System Dynamics is a methodology that explicates observed behaviours of
complex systems with explicit representations of feedback and time delays
(Forrester 1961). As Forrester notes, the behaviour of complex systems frequently
defies one’s intuition and calls for the use of simulation models to improve
understanding and inform policy decisions. A priori the dynamic tendencies of any
complex system arise from its internal causal structure and the notion of two-way
causation or feedback (Meadows and Robinson 1985). In the current research, we
utilised this methodology in an effort to answer the following questions: (1) Given a
current resident population of approximately 3.8 million (Singapore Department of
Statistics 2014) and stable average mortality rates, how does the current population
compare to a steady-state distribution of population and an equilibrium birth rate?;
and (2) Given a current foreign labour population of about one million persons who
contribute to the economy, what is the dependency ratio now and in the future,
under four different scenarios? These scenarios are: business-as-usual; no immi-
gration; baby boom; and ageing in place. Business-as-usual scenario assumes status
quo conditions where current policies remain unchanged over the simulation time.
No immigration scenario assumes a situation where immigration is zero, i.e.
stopping the transition from foreign labourer to permanent resident. Baby boom
scenario assumes a cessation of the transition from foreign labourer to permanent
resident, coupled with increased fertility. Lastly, ageing in place scenario assumes
increased attractiveness of Singapore to the elderly to stop emigration. It is worth
noting that this research does not explore ways to realise these end states described
above.
Methods
A System Dynamics model was built, following the process described by Randers
(1980), to understand demographic dynamics in Singapore. The concept of a
shortage of native Singaporeans (as suggested by statements such as Prime Minister
Lee’s) suggests a policy feedback loop (Richardson and Pugh 1981) in which the
desired population and the Singaporean population are not in equilibrium, and the
action taken to achieve the goal is attraction and retention of foreign labour.
The impact of population dynamics and foreign labour…117
123

Figure 1illustrates an endogenous foreign labour policy system in which there are
six balancing and one reinforcing feedback loops with subtle feedbacks.
Figure 2illustrates an ageing chain of the Singaporean population. The
population is categorised into four cohorts (juvenile =0–14 years, fe-
cund =15–44 years, mature =45–64 years, and elderly =65 years and up). The
population ageing chain shows births, deaths, immigration and emigration as the
four determinants of population change over time. Births are a function of the
current birth rate and fecund population, while deaths are a function of cohort
population and a constant death rate. The ageing process is conceptually
straightforward: births flow into the juvenile cohort, the surviving population in
each age cohort continuously flows into the subsequent cohort with the exception of
Singaporean
Fecund
Singaporean
Mature
Singaporean
Juvenile
Singaporean
Elderly
births
birth rate
deaths
-
-
-
-
Resident
Population target population
(population planning value)
population gap
-
desired foreign
labour
change in foreign
labour
Foreign
Labour -
immigration
R1 B3
B4 B5
B6
B1
B2
fecund
immigrantion
rate
mature
immigrantion
rate
immigration
rate
foreign labour
adjustment time
Fig. 1 Balanced foreign labour policy loops (polarity assumed positive unless noted). Balancing loops
are marked B1–B6; reinforcing loop is R1
Juvenile
becoming 15
birth
TIME
JUVENILE
BIRTH RATE
Fecund
becoming 45
fecund dying
MORT RATE FECUND
juvenile dying
MORT RATE JUVENILE
Mature
becoming 65
TIME MATURE
Elderly
elderly dying
MORT RATE ELDERLY
mature dying
MORT RATE MATURE
measured birth rate
SWITCH TO
MEASURED DATA
BIRTH RATE F
immigrating
FRACT FECUND
IMMIGRATING
emigration
NM RETIREMENT
AGE EMIGRATION
RATE
YEAR OF RETIREMENT
AGE EMIGRATION RATE
CHANGE
TIME OVER WHICH TO
AVERAGE EMIGRATION
RATE CHANGE
CHANGE IN
RETIREMENT
EMIGRATION RATE
retirement age
emigration rate
<immigration of
ep to pr>
<immigration of
sp to pr>
mature
immigrating
fecund
immigrating
<time fecund>
Fig. 2 Ageing-chain of the Singaporean population
118 J. P. Ansah et al.
123

the final elderly group. The non-surviving contingent in each age cohort is removed
via an outflow that reflects fixed average mortality rates for that age cohort.
The following equations summarise the evolution of the age structure as shown in
Fig. 2.
In the model, Juvenile population increases by birth, and decreases by Juvenile
death (jdying) and maturation from the Juvenile to the Fecund cohort (becom15).
JuvenileT¼JuvenileT0þZ
T
T0
ðbirthtjdyingtbecom15tÞdt ð1Þ
whereas:
BirthT¼BirthRatetFecundT
Becom15T¼JuvelineT=TimeJuvelinet
jdyingT¼JuvelineTMortJuvenilet
where BirthRate is the current birth rate, TimeJuvenile is the time spent in the
Juvenile cohort and MortJuvenile is the fixed 10 years’ average Juvenile mortality
rate.
The Fecund population increases by Fecund immigration (immigF) and
maturation from the Juvenile to Fecund cohort (becom15). The Fecund population
decreases by Fecund dying (fdying) and maturation from the Fecund to Mature
cohort (becom45).
FecundT¼FecundT0þZ
T
T0
becom15tþimmigFtfdyingtbecom45t
ðÞdt ð2Þ
whereas:
immigFT¼immigTFractionFecund Immigratingt
fdyingT¼FecundTMortFecundt
Becom45T¼FecundT=TimeFecundt
where Immig is the total foreign labour immigration to permanent resident,
FractFecundImmigrating is the fraction of the immigrants within the Fecund age
cohort, MortFecund is the Fecund mortality rate, and TimeFecund is the time spent
in the Fecund cohort.
The Mature population is the integration of transition from the Fecund to Mature
cohort (becom45), Mature immigration (immigM),Mature dying (mdying) and
transition from the Mature cohort to the Elderly cohort (becom65).
The impact of population dynamics and foreign labour…119
123

MatureT¼MatureT0þZ
T
T0
becom45tþimmigMtmdyingtbecom65t
ðÞdt ð3Þ
Whereas:
immigMT¼immigTð1FractFecund ImmigratingtÞ
mdyingT¼MatureTMortMaturet
becom65T¼MatureT=TimeMaturet
where MortMature is the Mature mortality rate and TimeMature is the average
amount of time spent in the Mature cohort.
Elderly population is defined as the integration of transition from the Mature to
Elderly cohort (becom65), emigration (emig) and elderly dying (eddying).
ElderlyT¼ElderlyT0þZ
T
T0
becom65temigtedyingt
ðÞdt ð4Þ
<resident
population>
target population (population
planning value)
S Pass
chg s pass
s pass leaving
Work Permit
chg work permit
work permit
leaving
Foreign Domestic
Worker Work Permit chg domestic
worker
domestic worker
leaving
Employment and
Dependent Pass
chg employment and
dependent pass
employment and
dependent pass
leaving
immigration of
E&D-Pass to PR
immigration of
S-Pass to PR
AVERAGE STAY
FRACTION
emplyment/dependent
pass
FRACTION
domestic worker
FRACTION
Work permit
FRACTION S-pass
desired foreign
labour
foreign labour
adjustment time
desired s- pass
RECRUITMENT
TIME
desired work
permit
desired domestic
worker
desired employment
and dependent pass
FRACTION
MIGRATING EP
FRACTION
MIGRATION SP
population gap
<RECRUITMENT
TIME>
<RECRUITMENT
TIME>
<RECRUITMENT
TIME>
change in target
population
year of targe
t
change
time to archieve
target
initial target
p
o
p
ulation
initial desired
foreign labour
Fig. 3 System to endogenously simulate foreign labour policy
120 J. P. Ansah et al.
123

whereas:
EmigT¼ElderlyTRetirementAgeEmigrationRatet
EdyingT¼ElderlyTMortElderlyt
where RetirementAgeEmigrationRate is the elderly emigration rate and MortElderly
is the Elderly mortality rate.
Immigration is the transition from foreign labour to permanent resident status,
and is determined by a constant fraction of eligible foreigners immigrating. Due to
age limits for work permits (Ministry of Manpower 2014), we assume that the
foreign labour population sector in Singapore is in the Fecund (age 15–44 years) or
Mature (age 45–64 years) age cohorts. Emigration is the estimated resident
population migrating from Singapore; the causes of emigration are outside the scope
of this research. The emigration rate is determined through calibration, by aligning
simulated data with measured data of the elderly population. The population model
accounts only for emigration among the elderly population.
Figure 3illustrates the foreign labour sector, which comprises the four categories
of foreign labour described in the introduction: S-pass; employment/dependent pass;
work permit; and foreign domestic worker work permit holders. The sector also
illustrates the decision to supplement the resident population with foreign labour,
and the number of foreign labourers immigrating. According to Singaporean
immigration law, only S-pass and employment/dependent pass holders are eligible
for immigration (Ministry of Manpower 2014). In the foreign labour model, this is
represented as a constant fraction (obtained by optimisation) of S-pass and
employment/dependent pass holders that immigrate to permanent resident status
yearly.
Based on observation, we assume that, on average, it takes a year to recruit
foreign labourers, who then work in Singapore for 2 years (unless they immigrate
before then). Desired foreign labour is represented in the model as the difference
between the target population (the population planning value of 6.5 million
mentioned by Mah 2007) and the resident population adjusted over a 19-year
period. The distribution of foreign labour into the four categories mentioned above
is determined by applying the actual distribution from the year 2009 over the length
of the simulation (2009 was the only year in which this data was made available, so
we used the 2009 breakdown of foreign labour, held constant over the simulation
time). Appendix 1shows a list of parameters used for the foreign labour model.
This model form allows initial values to be determined analytically and with
measured data. Accordingly, initial values can be switched from analytical
equilibrium to measured data.
1
Population and age distribution are essential to understanding the dependency
ratio. A four-level model provides sufficient demographic dynamics without
detailed complexity, e.g. gender and employment rates. While these and other
demographic distinctions are desirable for prediction, the purpose of this research is
to explicate policy.
1
All model equations available from the authors on request.
The impact of population dynamics and foreign labour…121
123

A four-category foreign labour population provides sufficient detail to understand
the dynamics of foreign labour, such as labourers that are added to the population
but not permitted to become permanent residents or naturalised citizens. The notions
of a shortfall in Singaporean workers (i.e. working-age citizens and permanent
residents of Singapore) and a shortage of babies (i.e. low birth rate) imply
disequilibrium.
With a 2010 measured population of about 5 million (3.771 million residents and
1.305 million foreign workers) (Singapore Department of Statistics 2010), our
understanding of foreign labour policy begins with dynamic equilibrium. This
assumes aggregate average mortality rates and total population are exogenous
constants so the initial equilibrium of the age cohorts, the birth rate, and the desired
dependency ratio can be determined in a steady state, viz. that initial inflows equal
outflows, and thus system states are steady and stable until perturbed, as described
in Industrial Dynamics (Forrester 1961).
Steady-state population
To derive a hypothetical total population of Singapore in a steady-state, the initial
levels can be derived from mortality rates and the time of progression (maturation)
from one system-state to the next: Juvenile,Fecund,Mature, and Elderly. The
distinctions between age levels are somewhat arbitrary but can be changed simply
by changing parameter values for mortality and maturation rates. The important
distinction is between child-bearing years (Fecund), working ages (Fecund and
Mature), and dependent ages (Juvenile and Elderly).
At steady-state, the inflow to the Juvenile cohort equals the outflow from that
cohort, i.e. birth =jdying ?becom15. Therefore, the equation representing the
initial Juvenile population at a steady state is:
Juvenile ¼BirthRate Fecund TimeJuvenile
ðMortJuvenile TimeJuvenile þ1Þð5Þ
where BirthRate and Fecund are determined analytically from Eqs. (6) and (10)
respectively; TimeJuvenile is 15 years; and MortJuvenile is 0.00023.
A steady-state birth rate replenishes the levels of Juvenile and Fecund for deaths
and those maturing. The equation representing the steady-state Birth Rate is defined
as:
BirthRate ¼ðMortFecund TimeFecund þ1ÞðMortJuvenile TimeJuvenile þ1Þ
TimeFecund
ð6Þ
where MortFecund is 0.00056;TimeFecund is 30 years; MortJuvenile is 0.00023;
and TimeJuvenile is 15 years.
At steady-state, the inflow to the Mature cohort equals the outflow, i.e.
becom45 =mdying ?becom65. We assume that at steady-state, immigration is
zero, because immigration is used to supplement the population when the birth rate
is below replacement level. For a population in dynamic equilibrium, the birth rate
122 J. P. Ansah et al.
123

always equals replacement level; therefore, immigration is expected to be zero. This
is why immigration is not included in the steady-state formulation. Hence, the
equation representing the initial Mature population at steady state is:
Mature ¼Fecund TimeMature
TimeFecund ðMortMature TimeMature þ1Þð7Þ
where Fecund is determined analytically from Eq. (10), TimeMature is 20 years;
TimeFecund is 30 years; MortMature is 0.0041.
At steady-state, the inflow to the Elderly cohort equals the outflow, i.e.
becom65 =edying. We assume that at steady-state, emigration is zero, because
ceteris paribus, the only outflow from the Elderly cohort is death. In a population in
dynamic equilibrium, maturation to Elderly always equals Elderly death; therefore,
emigration is expected to be zero at equilibrium. That is why emigration is not
considered in the steady-state formulation. Therefore, the equation representing the
initial Elderly population at steady state is:
Elderly ¼Mature
TimeMature MortElderly ð8Þ
where Mature is determined analytically from Eq. (7), TimeMature is 20 years; and
MortElderly is 0.0679738.
Further, it is logical to assume that the resident population (measured population)
is the sum of the age cohorts and is equal to measured population as of 2010.
2
To
derive the initial Fecund population equation at steady-state, we assume that
MeasuredPopulation ¼Juvenile þFecund þMature þElderly ð9Þ
From Eq. (9) above, by substituting Juvenile with Eq. (5), Mature with Eq. (7),
and Elderly with Eq. (8), the initial Fecund population is:
Fecund ¼ðMeasuredPopulation TimeFecund
(MortMature TimeMature þ1Þ
ðMortJuvenile TimeJuvenile þ1Þ
MortElderly / BirthRate TimeJuvenile
MortElderly TimeFecund
MortMature TimeMature þBirthRate
TimeJuvenile MortElderly
TimeFecund þMortElderly
MortJuvenile TimeJuvenile TimeFecund
MortMature TimeMature þMortElderly
2
Measured population data are published by Singapore Department of Statistics and include estimates
made by that department. The mortality rate parameter values are drawn from data published by the same
department and adjusted for simulation as discussed in Chapter 2 of Meadows et al. (1974).
The impact of population dynamics and foreign labour…123
123

MortJuvenile TimeJuvenile TimeFecund
þMortElderly TimeFecund MortMature
TimeMature þMortElderly TimeFecund
þTimeMature MortElderly
MortJuvenile TimeJuvenile þTimeMature
MortElderly þMortJuvenile TimeJuvenile þ1Þð10Þ
where BirthRate is analytically determined; MeasuredPopulation at 2010 is
3771,721 persons, TimeFecund is 30 years; MortMature is 0.0041; TimeMature is
20 years; TimeJuvenile is 15 years; and MortJuvenile is 0.00023; MortElderly is
0.0679738.
Dependency ratio
Our model determines the overall Dependency Ratio with resident population and
foreign labour:
DependencyRatio ¼DependentPopulation
WorkingAgePopulation
¼Juvenile þElderly
ForeignLabour þFecund þMature ð11Þ
The model was set to run simulations for the years 2000–2100. A test simulation
(or base disequilibrium run) was conducted, and simulated output from 2000 to
2010 was compared to measured data to determine whether the model was properly
calibrated. Then the model was set to steady state, which is a hypothetical system
condition that simulates the population in dynamic equilibrium. The model
estimates that about 12.5 percent of S-Pass and 17.5 percent of employment and
dependent pass holders immigrate annually. These estimates were obtained through
calibration (i.e. comparing measured and simulated Fecund and Mature
populations).
Results
Base run
A base disequilibrium run of the model was done to compare simulated data with
measured data. Figure 4shows a comparison of simulation with measured data and
the equilibrium run with year 2010 population. The results show that the model is
able to replicate measured data with reasonable accuracy.
Table 1, however, shows the analytical results of comparing 11 years’
(2000–2010) time series measured data with the results of the base disequilibrium
run. Summary statistics of historical fit are a standard test for System Dynamics
models (Theil 1966; Sterman 1984; Oliva 1998). The analysis in Table 1indicates
124 J. P. Ansah et al.
123

that the model reproduced major variables ranging from R
2
of 0.969–0.997,
indicating a strong correlation between the simulation and measured data.
Table 1shows total error decomposed from mean-square-error into bias (U
M
),
unequal variance (U
S
) and unequal covariance (U
C
). In summary, when compared
with measured data, simulated variables had root mean-square-errors (RMSE)
below three percent. For all population cohorts, error was limited to covariation, and
the error was unsystematic, i.e. simulated variables tracked the underlying trend
well, but diverged point by point.
Equilibrium scenario
Question 1: Given a current resident population of approximately 3.8 million
(Singapore Department of Statistics 2010) and stable average mortality rates, how
does the current population compare to a steady-state distribution of population and
an equilibrium birth rate?
Fig. 4 Comparison of simulated, measured and equilibrium (2010) population cohorts
Table 1 Error decomposition
and R-square Variable RMSE Inequality statistics R
2
U
M
U
S
U
C
Juvenile 0.008 0.071 0.008 0.928 0.995
Fecund 0.012 0.377 0.002 0.659 0.991
Mature 0.010 0.122 0.097 0.793 0.997
Elderly 0.020 0.349 0.006 0.680 0.992
Total population 0.018 0.357 0.043 0.600 0.969
Resident population 0.011 0.291 0.008 0.730 0.994
The impact of population dynamics and foreign labour…125
123

After the base disequilibrium run, the model was set to an initial steady state, i.e.
dynamic equilibrium. Comparing the steady-state and measured values indicated
that the current population is spread far from equilibrium. Figure 5shows the
steady-state population distribution for the year 2010 juxtaposed with the measured
population distribution, and Fig. 6shows the steady-state birth rate compared with
the measured birth rate for the year 2010.
As shown in Fig. 5, the steady-state Juvenile and Elderly cohorts were larger than
the measured Juvenile and Elderly cohorts, while the steady-state Fecund and
Mature cohorts were smaller than the measured Fecund and Mature cohorts.
Figure 6shows that the steady-state and measured birth rates reflect that the
measured rates are below the replacement rate and the expected total fertility rate is
inadequate to sustain the current resident population.
Disequilibrium scenarios
Question 2: Given a current foreign labour population of about one million persons
who contribute to the economy, what is the dependency ratio now and in the future,
under the following scenarios?
Fig. 5 Steady-state and
measured population, 2010
Fig. 6 Steady-state and
measured birth rate, 2010
126 J. P. Ansah et al.
123

1. Business-as-Usual: Current birth, immigration, and emigration rates.
2. No Immigration: Current birth and emigration rates but with the immigration
rate set constant at zero.
3. Baby Boom: Equilibrium birth rate, immigration rate set constant at zero, and
current emigration rate.
4. Ageing in Place: Current birth and immigration rates, emigration rate set
constant at zero (Fig. 7).
Business-as-usual scenario (BAU)
The business-as-usual scenario is simulated using birth rate data from 2000 to 2010,
assuming the 2010 birth rate remains constant over time, and constant immigration
and emigration rates. The dependency ratio is projected to decrease from year 2000
to 2020, and then increase gradually thereafter. The dependent population, however,
is projected to remain somewhat constant from 2000 to 2018, and then increase
gradually. The working-age population is projected to increase in the first 20 years
then stabilise subsequently. Lastly, foreign labourers are projected to increase and
peak at year 2020 and afterwards decrease gradually.
No-immigration scenario (IMMG)
The no-immigration scenario is simulated using birth rate data from 2000 to 2010,
assuming the 2010 birth rate remains constant over time. The current emigration
Fig. 7 Simulation results of the scenario definition with key indicators
The impact of population dynamics and foreign labour…127
123

rate is held constant, but the immigration rate is held at zero over the simulation
time. The dependency ratio is projected to decrease throughout the simulation. Also,
the dependent population is projected to decrease gradually over the simulation
period. Nevertheless, the working-age population and the population of foreign
labourers are projected to increase significantly over time. (Note that immigration
does not include the hiring of new foreign labourers, but only includes the transition
of foreign workers to permanent resident or citizen status.)
Baby boom scenario (BB)
The baby boom scenario is simulated using constant emigration rate, an equilibrium
birth rate, and an immigration rate set to zero over the simulation time. The
dependency ratio is projected to decrease gradually from year 2000 to 2030, and
then remain nearly stable afterwards. The dependent population, on the other hand,
is projected to increase gradually over time. The working-age population and the
number of foreign labourers are projected to increase from year 2000 to 2030, and to
remain nearly stable after that.
Ageing-in-place scenario (AGIP)
The ageing-in-place scenario is simulated using birth rate data from 2000 to 2010,
assuming the 2010 birth rate remains constant over time, a constant immigration
rate, and an emigration rate set to zero over the simulation time. The dependency
ratio is projected to decrease from year 2000 to 2015, and then increase steadily
from 2015 to 2050. The dependent population, however, is projected to increase
significantly over the simulation time. Moreover, the working-age population is
projected to increase initially, stabilise somewhat briefly in the year 2025–2030, and
decrease gradually afterwards. Foreign labour is projected to increase initially and
peak at the year 2020, and then decrease gradually thereafter.
Summary and discussion
In the comparison of simulated data from the base run and measured data for the
years 2000–2010, the high R
2
values, low RMSE values, and unsystematic error
(see Table 1) indicate that the model closely simulates measured data for
11 years.
The question of how the current disequilibrium state of Singapore’s population
compares to a steady-state distribution of population cohorts with an equilibrium
birth rate (Question 1) was addressed by comparing the results of the model in
equilibrium with measured data. Results indicated that the steady-state Fecund and
Mature cohorts were smaller than the measured Fecund and Mature cohorts, while
the steady-state Juvenile cohort was larger than the measured Juvenile cohort. These
results suggest that (a) the actual birth rate was above the replacement birth rate
between 1965 and 1995, and has been below the replacement rate for 15 years or
(b) immigration occurred. We note Singapore’s total fertility rate was 2.1 in 1965
128 J. P. Ansah et al.
123

(45 years ago), representing replacement birth rate, but fell to 1.7 by 1995 (15 years
ago) (Jones et al. 2009). These observations suggest that a higher birth rate
combined with immigration accounts for the higher measured Fecund and Mature
cohorts compared to steady-state Fecund and Mature cohorts. The measured Elderly
cohort was less than half the steady-state Elderly cohort, suggesting (a) a relatively
small Elderly population years ago, or (b) a higher mortality rate in the past 65 years
that has been decreasing recently. As mentioned above, the life expectancy at birth
has been increasing, from 63.7 in 1960 to 80.7 in 2008 (World Bank Data Bank
2011), supporting the observation that mortality rates have been steadily decreasing
for the elderly in recent decades.
The question of what the dependency ratio is now and in the future, under the
business-as-usual, no-immigration, baby boom and ageing-in-place scenarios was
addressed by simulating each scenario to understand the likely future state of affairs.
The business-as-usual scenario showed a decrease in the dependency ratio for the
first 20 years and a gradual increase in the dependency ratio afterwards. However,
the dependency ratio at 2050 is lower than that of the year 2000, suggesting that
current policies, ceteris paribus, are likely to deliver an improved dependency ratio
in the future. This result highlights the importance of foreign labour, not only as a
source of workers to maintain economic success, but also as a supply of permanent
residents, and thereafter, Singaporean babies to augment the declining resident
population.
The no-immigration scenario showed that dependency ratio would decrease
significantly in the future. The no-immigration scenario produced the lowest
dependency ratio of all of the scenarios. However, the consequence is that foreign
labourers are projected to surpass the resident population in the near future,
suggesting a different Singapore than the one we see currently.
The baby boom scenario showed a decrease in the dependency ratio in the
future. However, foreign labourers are projected to increase more significantly in
the future than under the business-as-usual scenario. This suggests that if
Singapore were able to increase its birth rate (which is a stated goal of the
government), it would almost certainly rely on foreign labour for support in
caring for dependents.
The ageing-in-place scenario showed a higher dependency ratio in the future. The
result illustrates the transition from current dependency ratio to a higher dependency
ratio in the future. This suggests that, as Singapore becomes a more attractive place
for permanent residents to stay after retirement, the dependent population will
increase significantly. As a consequence, foreign labourers and the working-age
population are expected to decrease. This has economic and health consequence for
Singapore. For example, the demand for long term care would be expected to
increase significantly.
The model developed for this study provides insights into the complex reality
that exists with respect to policy choices and their impact on demographic dynamics
and foreign labour in Singapore. The value of this paper is not in laying out policy
recommendations but in disentangling the complex impact of population dynamics
and foreign labour policy on dependency in a low-fertility and rapidly ageing
population, and extracting from that complexity a set of issues that are recognizable
The impact of population dynamics and foreign labour…129
123

to policy-makers to support policy-making. Among the scenarios explored herein,
the no-immigration scenario appears to be the most desirable policy due to the
relatively low dependency ratio (0.11); however, the reliance of Singapore as a
nation on increasingly larger numbers of foreign labourers (60 % of the total
population under the no-immigration scenario is projected to be foreign labour) is
undesirable and not sustainable. Hence, the current policy (business-as-usual) of
carefully calibrating the number of immigrants per year to revitalize the resident
Singapore population is thought to be the ideal policy, even if it produces a high
dependency ratio (0.25) relative to the no-immigration scenario (0.11). The
calibration of the number of foreigners becoming permanent residents and citizens
should account for changes in fertility and the desired increase in the resident
population.
Limitations
The model herein can only ever be a simplified representation, and is constrained
by the availability of data for some required input parameters. For instance, the
model does not take into account the effect of the performance of the local and
regional economy and its impact on Singapore’s ability to attract foreign labour
from other countries. Also, the model assumes that children born during the
course of the simulation make fertility decisions similar to the current generation
irrespective of the prevailing conditions. In addition, there are some differences
in fertility rates among Singapore’s three main ethnic groups, but these
differences and their potential effects on the overall population were not
accounted for in the model. Finally, emigration was only included as a factor for
the Elderly cohort due to lack of available information on emigration rates in
other cohorts.
Conclusion
Our work in health systems design is centred on the changing needs of the
population; accordingly, we created a population simulation model that is
configured for a resident population with foreign labour, and policies for
immigration and emigration. The model may be initialised in analytical equilibrium
or disequilibrium. In this paper we provide the results of several scenarios and their
impact on the dependency ratio. The results highlight the importance of considering
current and future population dynamics in making policy decisions.
Conflict of interest The authors declare that they have no conflict of interest
130 J. P. Ansah et al.
123

Appendix 1: Key model parameters
Parameters Values Sources
Population model
Mortality rate juvenile 0.0008 Estimated from Singapore Department of Statistics
(2010)
Mortality rate fecund 0.0007 Estimated from Singapore Department of Statistics
(2010)
Mortality rate mature 0.0057 Estimated from Singapore Department of Statistics
(2010)
Mortality rate elderly 0.0195 Estimated from Singapore Department of Statistics
(2010)
NM retirement age emigration rate 0.0500 Optimization
Fraction fecund immigrating 0.0900 Optimization
Foreign labour model
Fraction S-PASS 0.085 Ministry of Manpower (2014)
Fraction work permit 0.200 Ministry of Manpower (2014)
Fraction employment/dependent pass 0.260 Ministry of Manpower (2014)
Fraction foreign domestic workers
pass
0.155 Ministry of Manpower (2014)
Fraction immigration S-PASS 0.125 Optimization
Fraction immigration employment
pass
0.175 Optimization
NM retirement age emigration rate 0.050 Optimization
Appendix 2: Steady-state equations
To simulate a hypothetical total population of Singapore in a steady-state, four-level
model of the kind discussed in Chapter 2 of Meadows et al. (1974) the initial levels
can be derived from constant mortality rates and the time of progression
(maturation) from one system state to the next: Juvenile (age 00–age 14), Fecund
(age 15–44), Mature (age 45–64), and Elderly (age 65?). The distinctions between
age levels are somewhat arbitrary but can be changed by changing parameter values
for mortality and maturation rates. The important distinction is roughly between
child-bearing years, working ages, and dependent ages.
The stock of Juveniles is determined by the inflow of births and the outflows to
dying and maturing:
The impact of population dynamics and foreign labour…131
123

Birth Rate * Fecund =
Juvenile
* mort rate Juvenile
+ Juvenile
/ Time Juvenile
Juvenile =
Birth Rate
* Fecund
* Time Juvenile
/ ( mort rate Juvenile
* Time Juvenile
+ 1) [1]
The steady state birth rate replenishes the levels of juvenile and fecund for deaths and those maturing:
Maturing To 15 =
Fecund Dying
+ Maturing To 45
Juvenile / Time Juvenile =
Fecund
* mort rate Fecund
+ Fecund
/ Time Fecund
Substituting for Juvenile using equation (1)
Birth Rate * Fecund / ( mort rate Juvenile * Time Juvenile + 1) =
Fecund
* mort rate Fecund
+ Fecund
/ Time Fecund
Birth Rate =
( mort rate Fecund
* Time Fecund + 1)
* ( mort rate Juvenile
* Time Juvenile + 1)
/ Time Fecund [2]
The initial steady state of Mature may be written
Maturing To 45 = Mature Dying + Maturing To 65
Fecund / Time Fecund =
Mature
* mort rate Mature
+ Mature
/ Time Mature
Fecund / Time Fecund =
Mature
* ( mort rate Mature
* Time Mature
+ 1)
/ Time Mature
Mature =
Fecund
* Time Mature
/ (Time Fecund
* ( mort rate Mature
* Time Mature
+ 1)) [3]
132 J. P. Ansah et al.
123

The initial steady state of Elderly is more simply:
Maturing To 65 =
Elderly Dying
Mature / Time Mature =
Elderly
* mort rate Elderly
Elderly =
Mature
/ (Time Mature
* mort rate Elderly) [4]
We assume resident population = measured population and resident population is the sum of the age
cohorts:
resident population =
Juvenile
+ Fecund
+ Mature
+ Elderly
Substituting using (1) and (4):
Resident Population =
birth rate
* Fecund
* time Juvenile
/ ( mort rate Juvenile
* time Juvenile
+ 1)
+ Fecund
+ Mature
+ Mature
/ ( time Mature
* mort rate Elderly)
Resident Population =
( birth rate
* Fecund
* time Juvenile
* time Mature
* mort rate Elderly
+ Fecund
* time Mature
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
+ Fecund
* time Mature
* mort rate Elderly
+ Mature
* time Mature
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
+ Mature
* time Mature
* mort rate Elderly
+ Mature
* mort rate Juvenile
* time Juvenile
+ Mature )
/ ( ( mort rate Juvenile
* time Juvenile
+ 1)
* time Mature
* mort rate Elderly)
The impact of population dynamics and foreign labour…133
123

Substituting using (3)
Resident Population =
( birth rate
* Fecund
* time Juvenile
* time Mature
* mort rate Elderly
+ Fecund
* time Mature
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
+ Fecund
* time Mature
* mort rate Elderly
+ Fecund
* time Mature
^ 2
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
/ ( time Fecund
* ( mort rate Mature
* time Mature
+ 1) )
+ Fecund
* time Mature
^ 2
* mort rate Elderly
/ ( time Fecund
* ( mort rate Mature
* time Mature
+ 1) )
+ Fecund
* time Mature
* mort rate Juvenile
* time Juvenile
/ ( time Fecund
* ( mort rate Mature
* time Mature
+ 1) )
+ Fecund
* time Mature
/ ( time Fecund
* ( mort rate Mature
* time Mature
+ 1) ) )
/ ( ( mort rate Juvenile
* time Juvenile
+ 1)
* time Mature
* mort rate Elderly)
Resident Population =
Fecund
* ( birth rate
* time Juvenile
* mort rate Elderly
* time Fecund
* mort rate Mature
* time Mature
+ birth rate
134 J. P. Ansah et al.
123

* time Juvenile
* mort rate Elderly
* time Fec und
+ mort rate Elderly
* mort rate Juvenile
* time Juvenile
* time Fec und
* mort rate Mature
* time Mat ure
+ mort rate Elderly
* mort rate Juvenile
* time Juvenile
* time Fec und
+ mort rate Elderly
* time Fec und
* mort rate Mature
* time Mat ure
+ mort rate Elderly
* time Fec und
+ time Mature
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
+ time Mature
* mort rate Elderly
+ mort rate Juvenile
* time Juvenile
+ 1)
/ ( time Fecund
* ( mort rate Mature
* time Mat ure
+ 1)
* ( mort rate Juvenile
* time Juvenile
+ 1)
* mort rate Elderly)
Initial Fecund =
measured population
* time Fecund
* ( mort rate Mature
* time Mature
+ 1)
* ( mort rate Juvenile
* time Juvenile
+ 1)
* mort rate Elderly
/ ( birth rate
* time Juvenile
* mort rate Elderly
* time Fecund
* mort rate Mature
* time Mature
+ birth rate
* time Juvenile
* mort rate Elderly
* time Fecund
+ mort rate Elderly
* mort rate Juvenile
* time Juvenile
* time Fecund
* mort rate Mature
* time Mature
+ mort rate Elderly
* mort rate Juvenile
* time Juvenile
* time Fecund
The impact of population dynamics and foreign labour…135
123

+ mort rate Elderly
* time Fecund
* mort rate Mature
* time Mature
+ mort rate Elderly
* time Fecund
+ time Mature
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
+ time Mature
* mort rate Elderly
+ mort rate Juvenile
* time Juvenile
+ 1)
and substituting for resident population, we find the initial steady state for Fecun
d
INITIAL FECUND =
measured population
* time Fecund
* ( mort rate Mature
* time Mature
+ 1)
* ( mort rate Juvenile
* time Juvenile
+ 1)
* mort rate Elderly
/ ( birth rate
* time Juvenile
* mort rate Elderly
* time Fecund
* mort rate Mature
* time Mature
+ birth rate
* time Juvenile
* mort rate Elderly
* time Fecund
+ mort rate Elderly
* mort rate Juvenile
* time Juvenile
* time Fec und
* mort rate Mature
* time Mature
+ mort rate Elderly
* mort rate Juvenile
* time Juvenile
* time Fec und
+ mort rate Elderly
* time Fec und
* mort rate Mature
* time Mature
+ mort rate Elderly
* time Fec und
+ time Mature
* mort rate Elderly
* mort rate Juvenile
* time Juvenile
+ time Mature
* mort rate Elderly
+ mort rate Juvenile
* time Juvenile
+ 1)
136 J. P. Ansah et al.
123

Measured population data are published by Singapore Department of Statistics
and include estimates made by that department. The mortality rate parameter values
are drawn from data published by the same department and adjusted for simulation
as discussed in Chapter 2 of Meadows et al. (1974).
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