Dynamic Aging Population in Germany: A case
study about demographic change
by
Aziiz Sutrisno and Oliver Handel
Submitted in Partial Fulfillment of the Requirement of GEO SD304
System Dynamics Modeling Process
University of Bergen
November 2011
Dynamic Aging Population in Germany:
A case study about demographic change
Aziiz Sutrisno and Oliver Handel
Recent trends in demographic changes in Germany mainly because of rapid population ageing
represented as increasing ratio of older population over total population, have become a major problem
for the German government. They are worry if recent trends continues it would cause massive
disturbance in Germany socio-economic system, starting from vast amount of pension fund government
have to pay to immerse fall of countries GDP. Therefore, by using System Dynamics approach this paper
offers systemic point of view on how population structure changed in Germany; it explain why fertility
rate in Germany stays low and how economic indicators would trigger changes in population structure.
Moreover, it also illustrates feedback effect from population age structure to economic indicators. The
result shows that current trends will continue and will not dampen if there is no adequate policy
intervention from government. Hence, this paper offers set of policy measures to stabilize increasing ratio
of older population. By opening more immigration opportunity for productive age workers, increasing
child incentives, increasing pension age, and promoting gender equality as a set of policy measures might
exhibit a better result to stabilize the population age structure. This policy measures effect shows
desirable result toward expected behavior. As the population structure responds by increasing fertility
rate, increasing workers age population and lowering older age population rate thus made population
age structure more stable.
Keywords: Population Ageing, System Dynamics, Fertility Rate, Germany
Preface
A high collaboration of both authors makes it difficult to allocate the corresponding
work share among the writing team. The following can only give an approximate clue.
Aziiz Sutrisno is responsible for modeling the fertility sector and writing the following
chapters: Introduction, Dynamic Problem, Policy Design and Implementation, Conclusion,
Appendix A and C (and Excel Dashboard). Oliver Handel is accountable for modeling the
population, migration and mortality sector plus writing the following parts: Hypothesis for
the Dynamic Problem, Model Analysis, A ppendix B (and data research).
Introduction
After a dramatic increase of birth rate in 1960’s that produced the “baby boomer”
generation, Germany now faces a difficult problem on its aging population. This baby
boomers’ generation form a demographic transition starting to happen in Germany on
1990’s that raises big concem for the government. The ratio of young people support the
elderly is low and continues over time. This demographic transition can create a massive
problem for future generations. Because, if the older population dominate other age group,
Germany tax income, public saving and goverment investment will be decreasing.
(Borsch-Supan and Chiappori 1991; Kim and Lee 2008; Van Dalen, Henkens et al. 2010).
Production sector also becomes major interest at this point. Germany needs more workers
than predicted to support its gigantic production capacity in order to maintain its position as
one of the European Union workhorses.
This demographic transition partly happens because of almost constant low birth
rate and increasing life expectancy in Germany ((Borsch-Supan and Chiappori 1991; Lee
and Mason 2010). Low birth rate in Germany has been continuing from approximately 1975
to now, this has become an unfavorable situation for Germany’s government. The
government worries over long-term effect of this situation it can drag down government tax
income since number of people working is decreasing. Moreover, lower number of people
working in the country will also lead to decreasing consumption in the country. While
consumption decreases the whole economic activity in Germany, it will trigger another
major domino effect as the snowball continues to grow.
On the other hand high retirement rate that occur nowadays because of baby boomer
generation maturation enforce Germany to pay high amount of pension program. Y et, high
retirement rate would not be a big trouble if Germany has enough young population to
support and replace it. Unfortunately, their replacement rate now is lagging behind goal
value. It means the elder people will dominate the country and there will be not enough
young people to support it as the population pyramid shifting over the years (Statistisches
Bundesamt 2011). The reason why such condition happens still be an unsettled discussion
in Germany.
However, increasing Germany urbanization rate toward major region has also
considered as one big reason why the number of births in Germany is declining. This
urbanization means that more and more people in Germany live in big cities. While,
housing policy in major big city cannot cope with this increasing rate of urbanization, that
fact triggers rise of house prices and a reduction of overall house area. Additionally, this
might explain why couples are reluctant to have children. Beside housing policy,
economists and demographers for the most part agree that improved living standards, which
occur in Germany leading in turn to lower fertility. In addition, the reasons behind German
increasing living standards mostly are industrialization, increasing opportunities for non-
agrarian employment. Furthermore, one leading factor that might explain German low
fertility rate is improvement educational level that changed parental perceptions of the cost
and benefits of children(Sinding 2009)
The second main reason of population aging in Germany is its increasing natural
life expectancy. Besides the fact of higher living condition, peacetime and better nutritional
situation. Germans also gain benefit from their government policy of social health
insurance. In 2006 more than 70 million out of 82 million Germans are covered by the
social health insurance system (Ulla Schmidt 2006). Therefore, the Germans have more
access to better health facility. These facts lead to healthier Germans that live longer and
slowing mortality rate which cause increasing number of old population.
Germany government raised pension age from 65 age to 67 in 2007 as a
policy measure to counter increasing pensioner population growth. So far, the counter
policy measures tend to reduce government spending on pension payment and increase
country overall productivity. In the meantime, Germany government also has been working
on fertility issue by introducing family policy. Nonetheless, this policy measure does not
produce desirable results for German government. Germany birth rate slightly increase
in 2007 but then the number plunge again in the following year as the policy resistance
behavior shows. Government fears that if this trend continues Germany population will
decrease from 82 million people in 2010 to 74 million people in 2050 while it has
decreasing already from 2004(David Gordon Smith 2008).
Previous research conducted in Germany and several countries shows that
demographic change caused by low birth rate and rapid increasing of retirement rate in the
workforce will harm region’s economic outlook(Christoph Hendrik Borgmann 2005). In
addition, how German goverment manage to increase fertility rate in order to make the
fertility and mortality flows balance enough to support Germany sustainable economic and
demographic grow are main issues on EU socio-demographic research. Recent studies in
Sweden carried by Granados and Ionides(Tapia Granados and Ionides 2008) and Bengtsson,
T. and K. Scott(Bengtsson and Scott 2011) using econometrics shows this issue has become
a tricky issue to handle as both papers come out with two different ideas. Moreover,
findings from Borsch-Supan and Chiappori explain how the population age structure change
using descriptive statistical analysis and An and Jeon that investigates how demographical
change can produce different outcome in economic indicators using econometrics provide
basic understanding on how the system works.
Dynamic Problem
Decreasing birth rate and aging population over time in Germany could lead to
unfavorable conditions. The age structure at working age will shift in favor of older people.
At present, the medium age group of the 30 to 49-year-olds accounts for 50% of working-
age people, the older age group of 50 to 64 years for 30% and the younger age group of 20
to 29 years for nearly 20% of people at working age. By 2020, the older age group, then
accounting for about 40% of working-age people, will be almost as much as the medium
age group, which will still grows for a mere 42%. By 2050, the situation will have changed
just slightly toward the medium age group(Matthias Eisenmenger, Olga Potzsch et al.
2006). The consequences of such condition is Germany labor market will need to rely on
older people as much as it relies on people at medium age to support current production
rate.
Germany government has tried to implement a counter measure policy to tackle
birth rate issue. However, the birth rate keeps on a constant low level and the policy
measure desirable result has not shown yet. Because of low birth rate and growing
maturation rate of big portion of the population, Germany elder age ratio over total
population continue to grow. Figure 1 shows the reference mode and behavior over time of
the system that indicates increasing elder population ratio in Germany. It shows that
Germany elder population ratio keep on increasing from 2000’s and the trend continues to
2010. The blue line indicates the business as usual scenario with implementation of family
policy in 2007. Government hopes that the policy would be able to increase births rate and
make the flow balance (orange dotted line) and stabilize Germany population in 2040
(Matthias Eisenmenger, Olga Potzsch et al. 2006; Statistisches Bundesamt 2011).
Moreover, prediction from German statistical office shows that with this current
trend the increasing rate of older population could become faster. As, they suggest that
German total fertility rate is more likely to go down(Matthias Eisenmenger, Olga Potzsch et
al. 2006). Therefore, mean age of German population is increasing even more than linear
extrapolation because growing imbalances between young and retired population.
(index Point)
Ratio of Ekler Population /Total Popubation
{ Business As Usual => «Government Desirec Policy Resut |
Figure 1 Reference Mode of Population aging of Germany
A growing elder rate ratio over total population would cause a disastrous condition
toward all sectors in Germany. Lack of workforce and high dependency ratio cause by the
imbalance between birth rate and retirement rate will trigger series of fatal disasters such as
increasing pension and health care fund. Such an effect will pull out government resources,
decreasing productivity, which in the long term would harm Germany’s financial stature.
Moreover, as one big workhorse of European Union especially Eurozone, Germany
condition would also determine regional development and geopolitical condition (Coleman
and Rowthorn 2011). Therefore, a smart strike to knock the root cause of this problem will
be critical decision. Thus, the government will gain benefit of long-term investment not
only by avoiding such adversity but also achieve long-term benefit from a balance
population.
Dynamic Hypothesis
The problematic demographic changes in Germany are caused by the interplay of
four different demographic determinates(W eber 2010):
Fertility (average number of births per woman in life)
Life expectancy (average lifespan from birth to death)
Migration (immigration and emigration together)
Structure of the population (age distribution)
PwoNr
The first three variables are predominantly mutual independent from each other.
The last determinant is influenced by all and describes the distribution of the population in
various age categories. Hence, interaction of fertility, life expectancy and migration changes
the population structure over time. For this interdependency a model is conceived which
generates historical and hypothetical scenarios of the changing population structure since
Germany’s reunion in the year 1990. The whole model is divided into submodels according
to the described determinants. Consequently, four interacting subsystems are arranged as
figure 2 shows.
/ Migration
\ subsystem
ectancy
subsystem
Figure 2. Overlapping subsystems (Source: own figure)
In the following, an overview of the main population subsystem is given first.
Afterwards the big picture of the interaction in the whole model is provided. Finally the
three peripheral subsystems are discussed sequentially (the SFDs for them are in Appendix
A).
The population subsystem
The causal loop diagram (Lecture 4, p. 24ff) in figure 2 shows the basic
interdependency of the demographic determinants in the population sector. The population
variable is located in the center with three influencing factors around. High fertility
increases the number of births. A high number of births lead to a high population and a high
population comes to many births. This relationship is a reinforcing one (Lecture 3, p. 25).
High life expectancy decreases the amount of deaths. The connection between deaths and
the population is the opposite than the other loop, an implicit goal seeking
relationship(Sterman 2000). A high population leads to more deaths, more deaths reduces
the population. And third, immigration increases, emigration decreases population.
Immigration
+
+ @
Population
®) Co}
2 Births Deaths
+ + -
Fertility Rate Life expactancy
Figure 3. CLD of population structure without different cohorts
The main task of investigation is to focus on the elder population. To do this, the population
is split up into four age group specific population stocks. Four stock population models are
good manageable and provide accurate results(Bossel 2007). This resulting aging chain is
shown in the stock and flow diagram (Lecture 3, p. 18) of figure 4.
Population dynamics
Migration 1546 44 Migfation 45 tg 64 Migkation 65 Plus
Migration 0 to 14
B i y Matufation Matutation Déefaths
ad 44 tb 45 64 tb 65 69 Plus
Total fertility 4+ Fa , ;
Mortali rorta Wortality
Oto 14 Db
key world3 Lkeyte key world3 key world3
Life expectancy Deaths
Mortality
65 Plus
Figur 4. SFD of the population structure with different cohorts
The population is divided into four different cohorts: prereproductive cohort (0 to
14 years), reproductive cohort (15 to 44 years), not-reproductive cohort (45 to 64 years) and
pensioner cohort (65 years and older). Every cohort stock has one inflow (births or
maturation), two outflows (maturation or deaths) and one biflow (immigration), except the
pensioner cohort with only one outflow (deaths) and one biflow (immigration). The main
inflow births of the first stock is calculated with the total fertility rate, the reproductive
cohort stock and the average reproductive lifetime. The inflows of the last three cohort
stocks are the respective core outflows of the first three cohort stocks. The transition from
cohort to cohort is computed with the average dwell time (=adjustment time) of the
particular stock. The population is divided through the associated adjustment time - the
interval of the cohort stock. For example population 15 to 44 > adjustment time = 30 years
(this interval represents also the mentioned reproductive lifetime). Furthermore all cohort
stocks have the outflow deaths. Cohort specific death rates are calculated by two variables:
First by the appropriate stock size and second by the cohort specific mortality for the first
three population stocks and alternatively by the cohort specific life expectancy for the
population stock 65 plus. The second variable is in both cases at the mercy of the actual life
expectancy through an empiric relationship. The amounts of all deaths are summarized into
the variable deaths. Moreover, cohort specific immigration biflows are depending from the
total net immigration and cohort specific distribution fractions of the various immigration
flows. Immigration flows can change the population size in both directions, but migration
can also lead to redistribution between population stocks when the fractions have different
polarities. All population stocks are aggregated in the variable population.
The big picture
Figure 5. Interdependency between the subsystems
Figure 5 illustrates the big picture of the developed model with associations
between important variables. The major feedback loops are visible and minor ones are
faded out. Furthermore extemal variables and parameters are also shielded; only the two
important ones GDP and world are mapped. The four words in bold are the gists of the
different subsystems, which are color-coded. The left of the map show the fertility sector.
On the one hand is the sexually productive period an important factor, on the other hand the
desired children of a family is also important for the fertility average in the population. Both
factors have a link to the population structure. On the lower right side, the life expectancy
sector is located. In terms of population structure, the amount of monetary measured health
service and the amount of pension payments differ. Prosperity is as a function of both latter
mentioned variables. Life expectancy is substantial governed by health service and
pensions. In the top of the map the importance of the migration aspect is emphasized.
The fertility subsystem
The fertility sector explains two major theories(W eber 2010):
1. Family formation theory, which resembles from Easterlin’s hypothesis
2. Postponement effect on women giving first birth is resembled from Gary Becker’s
hypothesis
The family formation theory might explain on how much children a family eager to have
based on their real income compared to their expected cost of carrying babies. This family
formation theory follows the Easterlin hypothesis. Increasing income in family is a result of
growing economy and this would increase family eagerness on having babies. On the other
hand, if economic growth is faster than family income growth then it will decrease
eagerness of having babies. The model structure exhibits an increasing economic growth
and family income in almost same pace. In addition, the model shows a desired result
consistent with the theory. Moreover, the submodel also tries to take postponement effects
on women giving first in consideration. If income increases the mean age of women giving
first birth also increases. This increase means age will reduce fertility in total. Furthermore,
if we combine these two factors, it will produce anticipated behavior similar with historical
data.
The life expectancy subsystem
In consideration of discussing the life expectancy subsystem, it is the primary
interest to find macro-level trends for the dynamics of life expectancy. Data research shows
a remarkable causality between life expectancy and monetary macro-developments,
especially health care, prosperity and thus GDP. Many other candidates that can be listed as
reasons for the life expectancy increase can be aggregated to those monetary factors: public
health, medical care, personal income and poverty but also education and vaccination.
Individual decisions that affect life expectancy (e.g. smoking) should not be focused.
Moreover the study started from the assumption that a maximum value for life expectancy
cannot be stated in general(Oeppen and V aupel 2002).
Life expectancy is changed by two equivalently basic factors: health and prosperity.
The driving forces for those two multipliers are characteristics of the population structure
and the real GDP. Real GDP is an exogenous factor based on historical data and the
resulting trend equation. Both multipliers rise when the appropriate proportion per capita
increases in comparison to the initial 1990-value (normalized change). Furthermore, two
adjustment values for the lifetime multipliers are used to make both factors equipollent.
Health service capital accumulates investments and decline through depreciation. The stock
is initialized with the real GDP adjusted value from Germany’s statistical federal agency.
The depreciation flow is determined by the average life of health service capital. Health
service investment is a fraction of the real GDP. This fraction is depending from the actual
and the desired health services capital amount. The desired amount is influenced by an
effect of the population structure. The effect variable is normalized with the initial value of
the simulation (1990-value). Health care for elder people is much more expensive than for
younger people. The indicator population structure summarizes the multiplication of the
population cohorts with their age group specific average cost of illness. Data from year
2002 to 2008 is used as average cohort specific costs of illness. To calculate the average
cost of illness of the population cohort 65 plus the average age of this stock is used because
costs are increasing strongly when average age increases in this stock. The average ages of
the other stocks are roughly constant and are lying in the middle of the corresponding
interval. Joining the population structure closes the big health care feedback loop. Next, the
prosperity part is described in detail. Prosperity capital is the real GDP minus health service
capital and pension payments capital. The pension calculation loop is structural similar to
the health service loop. Investments increase and depreciation decrease pension payment
capital. Pension payments capital is also initialized with the real GDP adjusted 1990-value.
As the prosperity capital, the investment of health services is also computed by a fraction
from the GDP. Investments rise on a percentage basis as much as the desired pension
payments increase. Latter mentioned variable is depending from a normalized effect of the
population structure. The decisive influencing factor is the change of the ratio between the
65 plus population and the employed people. The sum of the two middle population stocks
determines the potential of employed workers (working age population). From this potential
works only a fraction employed. The fork of this partial feedback loop is closed with the
connection to the population structure.
The migration subsystem
Migration is a global phenomenon. Reasons for migration are eclectic and
complex(Erik Pruyt, Thomas Logtens et al. 2011). In general they can be divided into push
and pull factors. Push factors are lying outside the boundary of the national model. Pull
factors are significantly influenced by national political decisions. In the past Germany was
once already confronted with a big wave of intentional immigrates in the 1960" and 70". A
high need for employers was the reason for this political decision. The structural change in
Germany can lead to a situation where new employees are needed again. In consideration of
this trend a tiny immigration subsystem is build.
The migration subsystem works with historical data as far as possible. Up to the
year 2010, the immigration flow weakens strongly in Germany, so that the flow is set to
zero. What the subsystem does is to calculate the need for migration. Need for migration is
depending from two factors, first, by a double weighted need for labor multiplier and
second, by a need for population decline compensator. The former compares the
unemployed and the employed people and the latter compares births and deaths. The last
comparison generates the socket for immigration need. Everything else to this subsystem
can be found in the policy part.
Model Analysis
For validation, a rigorous series of tests was made in the modeling process
repeatedly. These tests are examined for de-bugging, stress-testing and diagnosing the
dynamics of the model (Guidelines for a modeling report, p. 5f). In this chapter, we present
a series of tests on the final version of the model.
Unit consistency test
Units are important to validate associations between different variables. Units check if
equations are coherent. For all parameters and variables in the model are units defined. Unit
consistency (Lecture 5, p. 12) can be tested with the special Check Units algorithm in
iThink. No inconsistencies can be found for the final model. Mistakes happen often in flow
variables, so that we present all flow equations and their units in the population sector here.
The full list of equations can be found in appendix A.
1. births = total fertility * population * fraction women / reproductive lifetime
persons / year = unitless * persons * unitless / year
persons/ year = persons / year
2. deaths = population / mortality
persons / year = persons * (1 / year)
persons / year = persons / year
3. maturation = population / interval
persons / year = persons / year
Extreme condition test
Extreme condition tests (Lecture 5, p. 16) have two major reasons: On the one hand
the procedure proofs if an equation makes sense even if the inputs take on extreme values.
On the other hand, the test investigates how the system reacts when extreme policies or real
world conditions are used. Two different scenarios are imagined next.
1. Limits of the system structure are demonstrated by the first test. We make the
assumption to set births to zero from the beginning. Factored out is also migration. The
expectation is that the population stocks will successively get empty. After 15 years the
first stock should be depleted, after 45 years the second one and so on. Through the fact
that maturation is calculated with an adjustment time the behavior different as figure 6
shows.
10
?
Figure 6. Extreme scenario 1: Births and migration set to zero from simulation start. In the
diagram is the behavior for 100 simulated years of different population cohorts represented.
Notwithstanding, four stock aging chains have proved their worth for demographic
questions. In many demographic system dynamics models four stock aging chains are
used successful to describe realistic population dynamics.
. Life expectancy is increased by a factor of 1.5 in year 2000. The expectancy is that the
amount of deaths decrease dramatically and the population explodes after the change. In
figure 7 is the expected behavior produced.
a
?
Figure 7. Extreme scenario 2: Increase of life expectancy by 50% in year 2010. The diagram
shows the population (blue line; 1) and the amout of deaths (red line; 2) for the simulation
interval 1990 to 2010.
Deaths decrease immediately after the increased life expectancy value. That means the
outflows of the population stocks drop sharply while the inflows deliver (almost) the
same amount. The consequence is the plotted accumulation process of the population
variable.
It appears useful to clarify that not every absurd entry produces plausible output. Errors can
occur when equations try to divide through zero or table functions are running out of range.
But the testing under extreme value conditions helped to optimize the model.
Reference mode comparison test
Introductorily the reference mode was visualized. The reference mode compares elder
people with the whole population. Now we want to compare the reference mode with the
default behavior of our simulation (Lecture 5, p. 18). To do so the original data was inserted
in iThink. Figure 8 shows the result.
11
Figur 8. Comparision between the reference mode and the appropriate simulation. The diagram
shows the elder population ratio for 50 simulated years. The blue line (1) is data of the reference
mode, the red line (2) is the simulated behavior of the developed model.
The starting values of both graphs are to the fourth decimal point identical. From the
displayed perspective both graphs look very similar. The simulated curve is smoother than
the histrorical data. A small gap in the middle can be seen as disfigurement. A more precise
answer of sameness gives a statistical comparative meassurement. For this comparrison the
coefficient of determination R? and the pearson correlation coefficent p is used. The
statistical coefficients confirm the high sameness of both graphs. The elder population is
computed well (R? = 0.957, p =0.978)
Structure-behavior tests
In the hypothesis part the major feedback loops were shown in the big picture. Now
we want to analyze how strong different loops act. To do so we compare the different loops
when they have and when they have not impact. The structure-behavior test results (Lecture
5, p. 19ff) are presented in Appendix B.
Parameter sensitivity tests
GDP is an important factor in our model. The further development is hardly predictable.
The default mode of the model is formed by a linear trend function. The parameter
sensitivity analysis (Lecture 5, p. 26ff) investigates how the population development
changes with different GDP growth fractions under the ceteris paribus assumption. For this
GDP is modified by an increase and decrease of 10 % in the future years. The behavior of
the aggregated population is shown in figure 9.
Py Las
Figur 9. Sensitivity analysis: M odification of the GDP future developement. The blue line (1) shows
the population behavior of an 10% decreased GDP development after the year 2010, the red line
(2) shows the default mode and the pink line (3) shows the development if the GDP development is
10% higher then intended.
12
As the diagram exhibits changes in the GDP development do not lead to fundamentally
different behavior of the aggregated population. The results are only numerically
different in the order of 1%.
Policy Design and Implementation
Increasing elder population ratio in Germany has been one major issue for the
govemment. They aware of the long-term consequences they face over this demographic
shifting condition. In order to tackle this issue, Germany government introduces several
policy measures to reduce increasing rate of elder population ratio. For example, in 2001
government passed series of reformation on pension age pass and child incentives in order
to balance increasing elder population with the newly born.
Current condition of Germany demographic outlook shows that policy measures
implemented by seem to have good impacts on increasing population fertility rate.
However, these impact considered only as a short term impacts(Thyrian, Fendrich et al.
2010) rather than long term impacts. The government seems not to deal with real problems
of low fertility rate in Germany as the fertility rate of Germany back to stabilize at small
number, which is lower than replacement rate.
One of new government measures on increasing child incentives is a classic
goverment approach on increasing fertility rate. While, previous Germany government has
also introduced almost the same policy package in 1976 (in Germany Democratic Republic
(GDR)). At that time, this pronatalist policy-package intention was raising family income
thus encouraging families to have more children. In addition, several authors report that this
family package incentive make immediate boost on fertility rate(Buttner and Lutz 1990).
Moreover, Legge and Alford paper suggest that this policy measures taken by GDR
govemment work most sustainably in comparison with other pronatalist measures in
Eastem European (measures example: restriction to abortion) (Legge and Alford 1986).
However, government cannot carry out this measure by increasing incentives all
year. Not only it is economically un-feasible but also it is impossible to do as budgeting
political decision maker in Germany to pass one legislation, could take more than one year.
Furthermore, this measure in 1976 was limited in time for two reasons:
e Such measures do accelerate family formation, but they do not have an
appreciable effect on completed fertility
e Certain measures in the 1976 package cancelled out the effect of other
measures.(Jonathan Grant , Stijn Hoorens et al. 2004)
Instant impact from these policy measures proved that the system would react on
such policy package. Therefore, in order to develop more policy that is robust package to
tackle on the root cause problem, these policy measures is a good starting point. Set of
policy based on family incentives package is aiming on increasing family salary so family
income is adequate to support more kids. Two other policies measures that could be
incorporated into this policy package is increasing pension age in a short time to lengthen
productive period and increasing women participation might increase family income in
general. Those policy measures is visualize in system diagram in figure 10.
13
ye Pancion Age I WonenPartcistion
a a
Health per ‘00 s
Service population)
em]
=
es ecg
Demand bd
Population . 7
Ageing index) stakeholders
Working System citizen, EU, NGO, UN
Figure 10 Germany Demography system diagram
Therefore, based on empirical theory and Figure system diagram, we suggest implementing
set of policy that consists of:
e increasing child incentives
Increasing pension age in short term
Promoting women participation in workforce
Opening more immigration channel for productive age family
The policy measures in improving child incentives started by developing a wishful
thinking link to perceived cost of carrying baby and developing a variable that will decrease
that cost. Assumed for every single baby bom in Germany, government will provide
incentives as much as 10-30% of baby cost by providing direct incentives or prolong
matemity leaves with payment. That amount of money will decrease family pressure on
having baby. The amount of money then will be adjusted every two years following report
on Cost of Living allowance to match growing price of living standard. This policy was
extension of previous policy measures of German government, the previous policy itself has
stand unchanged since first 1994 and just recently improved in 2007. Our idea is giving
more adjusting capabilities for child incentives so the impact is not only for a short period
but also in longer period(Thyrian, Fendrich et al. 2010).
Our second policy measures is trying to hold in a short period increasing rate of
older population or receiving pension population by increasing pension age. Recently
German government implemented this policy measure, by increasing normal pension age
from 65 to 67 gradually starting from 2012 to 2023. However, this policy measures is
considered as one unpopular policy in the society. Nevertheless, we still think that the entire
population system will gain benefit if this policy is implemented. We start building this
policy measures by gradually increasing pension age from 65 to 67 in a faster pace. So,
instead of having 67 age at 2023 we push program implementation to 2018, making a5 year
differences on higher pension age. This faster changing prolongs breathing space for
German govemment on paying pension bill. As government can use benefit from such
policy to fund child incentives for new family.
Our third policy measures focus on increasing women participation in workforce
employment. By doing so, average family income will increase and increasing family
opportunity of having more kids. Nevertheless, this policy also debatable, many
14
demographers believe women involvement in workforce will also reduce fertility rate, as
women tend to focus on their career rather than raising children.
Our fourth policy measure is to open more immigration flow especially for young
age family. By introducing desired value of immigration that count gap between working
age population and desired ratio of older population over working population In reality the
system can described as easiness of issuing immigration certificate and promotion of
migrating to Germany. However, this policy also raises long debate. Hence, the
effectiveness of migration as a strategy towards preventing population ageing and a
decreasing the size of the population depends on the ability of national governments to
implement suitable migration policies(Espenshade and Minarik 1987; Coleman 2008). The
extent to which immigrants are ready and able to integrate into the receiving population
appears to be a crucial factor for the success of immigration strategies(Jonathan Grant ,
Stijn Hoorens et al. 2004).
On the other hand, in Figure we can see that this particular problem is not only
interesting for German govemment. Broader audiences also interested in this issue,
European Union (EU) put big attention on how German government will overcome this
problem. Moreover, German govemment itself consists on different agencies, departments
and political parties that have probabilities on having different interest creating a big
potential implementation problem for setting the policy.
Respectfully, Table 1 shows six major German political parties multi actor perspectives
point of view and how might they react over these set of policies. It might be important
realizing that it will become major issue to pass the legislation process.
Table 1 Political
Current Parlimentary
Interest ible Standing
Posi
Child Incentives : Supporting
CHRISTIAN Christian Democracy and | «sone puting party) Pension Age : Indifferent
DEMOCRATIC UNION | Liberal Conservatism Women Participation : Supporting
Immigration Channel: Indifferent
(Child Incentives : Supporting
CHRISTIAN SOCIAL | Christian Democracy and | Weak (Government _[Pension Age : Indifferent
UNION Social Conservatism Coalition party) Women Participation : Supporting
Immigration Channel: Indifferent
Child Incentives : Supporting
SOCIAL DEMOCRATIC Social Democracy Strong (Opposition party) (Pension Age : Oppossing =
PARTY Women Participation : Supporting
Immigration Channel: Slight Oppose
Child Incentives : Supporting
Moderate (Opposition [Pension Age : Slight Opposs
‘THE GREENS Green Politics ——e 7
party) ‘Women Participation : Supporting
immigration Channel: Indifferent
Child Incentives : Supporting
FREE DEMOCRATIC ee Moderate (Government [Pension Age : Indifferent
Classical Liberalism i oT 7
PARTY Coalition party) iWomen Participation : Supporting
immigration Channel: Supporting
Child Incentives : Supporting
Moderate (Oppositi Pi Age : 01 i
‘THE LEFT PARTY Democratic Socialism CAREAELODpOSHON | Eonalen Aes Usneae
party) Women Participation : Indifferent
immigration Channel: Oppossing
Policymaking and analysis especially long-term domain like demographic change always
raise a never-ending debate on optimum policy measures and its implementation. However,
set of policies that we offer supported by strong ground based theory and proven result in
15
other countries, although there are no single silver bullet to tackle similar problems in
different countries but behavior analysis shows that the system reacting toward desired
behavior after implementation of these policies. Still, implementation problems in these
policies could stop the effect even before it was totally running.
Conclusion
Growing number of elder population in Germany heavily affects country economic
performance. This problem emerges into a bigger concem as it will also create social
imbalances inside society as the effect of slowing economic performance. This paper
investigates how ageing in Germany occur and suggest several policy measures that might
useful to reduce the effect of current issue and try to push the system into desired condition.
Major reasons behind growing ratio number of elder population in Germany are low
fertility rate and increasing life expectancy. Despite of high complexity between fertility
rate, population and life expectancy; this paper result indicates how fertility rate is changing
because of economic activities in the society. As family formation theory determines how
big fertility rate in the society is. We formularized family formation based on Easterlin
hypothesis and Gary Becker’s argument that incorporate income as driving factor of having
child. The result of the fertility sector model is coherent with both underlying theory. When
income is increasing too fast, women tend to postpone their willingness of having babies.
Moreover, if country’s living standard grow too fast the cost of having babies will also go
high and many people will reluctant to have babies. Therefore, one policy that we suggest is
giving more child incentives and increasing gender equality. So, family income will
increase and creates more economic opportunities for family on having more children.
Moreover, this paper has well explained connection between economic activities and
demographical change. It shows consistencies as two economist papers that previously
suggested economic-population structure correlation. On the other hand, the usage of
System Dynamics in this paper provides better explanation on feedback effects occur in the
real system. Moreover, it also provides policy maker more options on policy testing and
analysis rather than parameter changing in the model.
However, this paper is only a starting phase to explain demographical change
phenomena in Germany. A deeper data gathering should be conducted to have detailed
result on the structure and effect of the issue. For example, one major obstacle is getting
enough past data for making arrayed population structure. In addition, future research
should also consider feedback effect from increasing women participation rate in workforce
because; there are discussions whether increasing women participation will also lower
desire on having children.
16
Appendix A: List of Equations and Documentation
We divide appendix in sectors:
Figure: SFD of the population model subdivided into four age groups
Population Sector
oo Population Sear
Reproductive Fraction
migration
Matufation
14 fo 15.
Intervall 0 to 14
Mortality 0 to 14
1990 to 2010
data tabl
Mortality 45 to 64
Fraction
migration
65 plus
Further
1990 to 2010 __ Life expectancy
Mortality Conversion a a feexpectancy Deaths aia 65 plus data
Figure 4 Population sector
oo Fertility Rate Sector ral
Total fer
iy Total Fertility
Data 1990-2020 for fertity & biths
historical data Historical Data
Births
Gary Beckers Argument
Postponment Loop
Ifereasing Worlen ihfowement
Initial mean age
gf women giving
Maximum
Productive
8
fi Petiod
Policy
Suk pokey Perceived
Cost Pressure a
Adjusiment Time J ealGop Effect Coefficient of
i cain ti EarlyM Employed people onralized Mean Age mean age effect
increasing Child Incentives arly Measures _
Germany Govemment growth Gonastta.
Figure 5 Fertility Sector
17
Mortality and Life Expectancy Sector ry
Actual Actual
life expectancy life expectactancy
ae he ce data data 1990
health services
Gal GDP
mil
equation
multiplier
adjustment value
Prosperity
GDP Constanta
multiplier
adjustment value health se
health services normalized
Real GDP a GDP
normalized per capita
wth A
pita gro) cf mil
Population
Average\life Avergge life
hestthzeNiee Health Pension payments
pensiod payments
Real GDP
mil
capital
capital
Galth service
in pret of GDP
health in prctof GDP in pret ofneed :
Gap fraction Pension payments Gap fraction
desired and actual in pret of GOP desired and actual
health service 1990 pension payments
Normalized effect Population —Populatiin 65 plus Normalized effect
population structure per efrployed population structure
on health care need ‘on pension need
Population nomenyzed
Oto 14 Empoyed people Employment
ulation Population nagon cers
to 64
65 Pus
>
Average cost of illness ferage age Further
Under 15 65 Plus _ life expectancy
65 plus
‘Average cost ofiliness Average cost of illness Average cost of illness
15 to 45 45 to 65 Over 65
Figure 6 Life Expectancy and Mortality
Immigration Sector 8 |
ro
Spulation
ma
net imi “
Total os, {>
immigration bcs =
data Immigration Policy Immigration Pol
policy start length »pulation decline
ay
OQ aay aa orvenston pens
Figure 7 Immigration Sector
18
List of Equations:
Health_service_capital(t) = Health_service_capital(t - dt) + (Health_service_investment -
Health_service_depreciation) * dt
INIT Health _service_capital = 219208
{Euros}
UNITS: Euros (EUR)
INFLOWS:
Health_service_investment =
Real_GDP_mil*Health service investment_need_in_prct_of_GDP
{Eur/Y ears}
UNITS: EUR/Y R (EUR/yr)
OUTFLOWS:
Health_service_depreciation = Health_service_capital/Average_life health_service_capital
{Eur/years}
UNITS: EUR/Y R (EUR/yr)
Pension_payments_capital(t) = Pension_payments_capital(t - dt) +
(pension_payments investment - Pension depreciation) * dt
INIT Pension_payments_capital = 265473
{Euros}
UNITS: Euros (EUR)
INFLOWS:
pension_payments_ investment =
Pension_payments investment_need_in_prct_ofneed*Real_GDP_mil
{EUR/Y ears}
UNITS: EUR/Y R (EUR/yr)
OUTFLOWS:
Pension_depreciation = Pension_payments_capital/Average_life pension_payments capital
{Eur/Y ears}
UNITS: EUR/Y R (EUR/yr)
Population_0_to_14(t) = Population 0_to_14(t- dt) +(Births + Net_immigration_0_to_14-
Maturation 14 to 15- Deaths 0 to 14) * dt
INIT Population_0_to_14 =12937503*(1-
Equilibrium_ Multiplier) +14430472.986*Equilibrium_Multiplier
{people}
UNITS: people (person)
DOCUMENT: Germanys population: 0-14 years old
INFLOWS:
Births = (Total_fertility * Population 15 to _44*
Fraction. Women_15_to_44)/Reproductive_lifetime*Birth_Equalizer+
Births Historical_Data*0
+
((34643682+10000000*T otal_fertility* Births Shock* Fraction Women_15_to_44)/Reproductiv
e lifetime)*Equilibrium_Multiplier
19
{people/years}
UNITS: person/yr
DOCUMENT: Total number of births in Germany.
(Multiplication with 0.5 --> Only women reproduce)
Net_immigration_0_to_14=Total_net_immigration*Fraction_migration_0_ to 14
{people/years}
UNITS: person/yr
OUTFLOWS:
Maturation__14 to 15 =Population_0 to_14/ Intervall_0 to 14*1
{people/years}
UNITS: person/yr
DOCUMENT: The fractional rate at which people aged 0-14 mature into the next age cohort
(15-44),
Deaths _0 to 14 =Population_0 to_14* Mortality 0 to 14
{people/years}
UNITS: person/yr
DOCUMENT: The number of deaths per year among people 0 to 14 years of age.
Population_15 to_44(t) =Population_15 to 44(t- dt) +(Maturation 14 to 15+
Net_ _immigration_ 15 _to_44- Maturation 44 to_45 - Deaths _15_to 44) * dt
INIT "Population 15 to 44 =34643682*(1-
Equilibrium_Multiplier)+33362872.342*Equilibrium Multiplier
UNITS: people (person)
DOCUMENT: Germanys population:15-44 years old
INFLOWS:
Maturation__14 to_15 =Population_0 to_14/ Intervall_0 to 14*1
{people/years}
UNITS: person/yr
DOCUMENT: The fractional rate at which people aged 0-14 mature into the next age cohort
(15-44).
Net__immigration_15 to 44 =Total_net_immigration*Fraction_migration_15_ to 44
{people/years}
UNITS: person/yr
OUTFLOWS:
Maturation_44 to_45 =Population_15 to_44/ Intervall_15 to 44*1
{people/years}
UNITS: person/yr
DOCUMENT: The fractional rate at which people aged 15-44 mature into the next age cohort
(45-64).
Deaths _15 to 44 =Population_15 to_44* Mortality_15 to 44
{people/years}
UNITS: person/yr
DOCUMENT: The number of deaths per year among people 15 to 44 years of age.
Population_45 to_64(t) =Population 45 to_64(t- dt) + (Maturation 44 to 45+
Net ; immigration. 45 to_64 - Maturation_ 64, to_65 - Deaths 45 to 64) * dt
20
INIT Population 45 to_64 =20259902*(1-
Equilibrium_Multiplier) +24545074.133*Equilibrium_Multiplier
UNITS: people (person)
DOCUMENT: Germanys population: 45-64 years old
INFLOWS:
Maturation_44 to_45 =Population_15 to_44/ Intervall_15 to 44*1
{people/years}
UNITS: person/yr
DOCUMENT: The fractional rate at which people aged 15-44 mature into the next age cohort
(45-64).
Net_immigration_45 to_64 =Total_net_immigration*Fraction_migration_45 to_64
{people/years}
UNITS: person/yr
OUTFLOWS:
Maturation__64 to 65 =Population_ 45 to 64/ Intervall_45 to _64*1
{people/years}
UNITS: person/yr
DOCUMENT: The fractional rate at which people aged 45-64 mature into the next age cohort
(65 Plus).
Deaths 45 to _64=Population_45 to_64* Mortality _45 to_64
{people/years}
UNITS: person/yr
DOCUMENT: The number of deaths per year among people 45 to 64 years of age.
Population_65_Plus(t) = Population _65_Plus(t- dt) +(Maturation 64 _to_65 +
Net_immigration_65_plus - Deaths 65 plus) * dt
INIT Population_65_Plus = 11912140*(1-
Equilibrium_Multiplier)+64831831.257*Equilibrium_Multiplier
UNITS: people (person)
DOCUMENT: Germanys population: 65 years and older
INFLOWS:
Maturation__64_to_65 =Population_45 to_64/ Intervall_45 to 64*1
{people/years}
UNITS: person/yr
DOCUMENT: The fractional rate at which people aged 45-64 mature into the next age cohort
(65 Plus).
Net_immigration_65_plus =Total_net_immigration*Fraction_migration_65_plus
{people/years}
UNITS: person/yr
OUTFLOWS:
Deaths_65_plus = Population_65_Plus/Further_life expectancy__65_plus
{people/years}
UNITS: person/yr
DOCUMENT: The number of deaths per year among people 65 years and older.
Actual_life expectactancy_data_1990 = 75.2
{years}
UNITS: years (yr)
21
Actual_life expectancy_data = GRAPH(time
{years})
(1990, 75.2), (1991, 75.4), (1992, 75.9), (1993, 76.0), (1994, 76.3), (1995, 76.5), (1996, 76.8),
(1997, 77.2), (1998, 77.6), (1999, 77.8), (2000, 78.1), (2001, 78.4), (2002, 78.5), (2003, 78.6),
(2004, 79.2), (2005, 79.3), (2006, 79.7), (2007, 79.8), (2008, 79.9), (2009, 80.0), (2010, 80.2)
UNITS: years (yr)
DOCUMENT: Source: http://www.lebenserwartung.info/index-Dateien/ledeu.htm
Actual_life expectancy__65_plus_ data =GRAPH(TIME)
(1990, 16.1), (1991, 16.2), (1992, 16.3), (1993, 16.2), (1994, 16.5), (1995, 16.5), (1996, 16.6),
(1997, 16.8), (1998, 17.0), (1999, 17.2), (2000, 17.4), (2001, 17.6), (2002, 17.7), (2003, 17.8),
(2004, 18.0), (2005, 18.2), (2006, 18.5), (2007, 18.6), (2008, 18.8), (2009, 18.9), (2010, 18.9)
UNITS: Unitless
Actual__Life expectancy =Actual_life expectancy_data*0
+
(Actual_life expectactancy_data_1990*lifetime multiplier from_health_services)*0
+
(Actual_life expectactancy_data_1990*lifetime multiplier from_prosperity)*0
+
(Actual_life expectactancy_data_1990*(lifetime multiplier from_health services+lifetime_mu
Itiplier_from_prosperity)*0.5)*1
{years}
UNITS: years (yr)
Average Employment_per Family =1+step(Test_Policy_Empl,2015)
{people}
UNITS: people (person)
DOCUMENT: STATISTISCHES JAHRBUCH 2011
Statistisches Bundesamt (Federal Statistical Office), Wiesbaden
2011
Average_age__65_Plus =65+(Further life expectancy__65_plus)
{years}
UNITS: years (yr)
Average_cost_of illness 15 to 45 =1.198
{unitless}
UNITS: Unitless
Average_cost_of illness 45 to_65 =2.431
{unitless}
UNITS: Unitless
Average_cost_of illness Over_65 =GRAPH(Average_age__65 Plus
{unitless})
(75.0, 4.97), (90.0, 11.8)
UNITS: Unitless
DOCUMENT: Anpassen fYr eine Sterbetagel mit entsprechenden Daten (2002 - 2008)
Average_cost_of illness Under 15 =1
{unitless}
22
UNITS: Unitless
Average_life health service_capital =1
{years}
UNITS: years (yr)
Average _life pension payments capital =1
{years}
UNITS: years (yr)
Births_Historical_ Data =GRAPH(TIME
{person/years})
(1990, 905675), (1991, 830019), (1992, 809114), (1993, 798447), (1994, 769603), (1995,
765221), (1996, 796013), (1997, 812173), (1998, 785034), (1999, 770744), (2000, 766999),
(2001, 734475), (2002, 719250), (2003, 706721), (2004, 705622), (2005, 685795), (2006,
672724), (2007, 684862), (2008, 682514), (2009, 665126), (2010, 677947)
UNITS: person/yr
Births Shock =if Shock Switch and Equilibrium_Switch =1 then pulse(1.05,5,1) else 0
{unitless}
UNITS: Unitless
Birth_Equalizer = If Equilibrium_Multiplier=1 then 0 else 1
{unitless}
UNITS: Unitless
Change_prosperity_normalized =
(Prosperity_capital_per_capita/Init(Prosperity_capital_per_capita))
{unitless}
UNITS: Unitless
Change__health_services_ normalized =
Health_service_per_capita/Init(Health_service_per_capita)
{unitless}
UNITS: Unitless
Coefficient_of_mean_age_effect = 0.4328
{unitless}
UNITS: Unitless
Data = If Time >2010 then TFR_2050 else Total_Fertility_historical_data
UNITS: baby (baby)
Deaths = Deaths 0 to 14+Deaths 15 to 44+Deaths 45 to_64+Deaths 65 plus
{people/years}
UNITS: person/yr
DOCUMENT: Total number of deaths in Germany.
Desired_health_service =
Health_service_capital*Normalized_effect_population_structure_on_health_care_need
{Euros}
UNITS: Euros (EUR)
Desired_Immigration = IF(Immigration_policy=1 AND Time>=Policy_start AND
Time<=(Policy_start+Immigration_Policy_length) )
23
THEN Need _for_ Immigration
ELSE 0
{person/years}
UNITS: person/yr
Desired_pensions =
Pension_payments_capital*Normalized_effect_population_structure_on_pension_need_normali
zed
{Euros}
UNITS: Euros (EUR)
Desired_Children_in_ Familly =
(Average Employment per Family*GDP__ Per Employed Person*Income_Percentage_on_rai
sing children/Perceived_Cost_Pressure_on_Having Babies)
{baby}
UNITS: baby (baby)
Early_Measures_Germany_Government = 0+step(500,2007)
(Bomb, McCormick et al.)
UNITS: Eur/baby (EUR/baby)
Effect_Mean_Age_Contanta = 0.5671
{unitless}
UNITS: Unitless
Effect_income_on_mean_age_of women_having first_birth =
(Coefficient_of_mean_age_effect*Real_GDP_normalized_growth+Effect_Mean_Age_Contant
a)*Perception_on_future_growth
{unitless}
UNITS: Unitless
DOCUMENT: Equation derived from a simple linear regression taken from 1985-2006 time
series data
all data has been normalized and treated as normal distribution data
GDP Data: Wordl Bank WDI Data
Age on forst child data: UNECE Statistical Division Database, compiled from national and
international (Eurostat and UNICEF TransMONEE) official sources.
Effect_on_mean_age_giving_birth_over fertility_rate =
Init(Sexually_Productive_Period)/Sexually_ Productive Period
UNITS: Unitless
Elder_population_per_employed = Population_65 Plus/Employed_people
UNITS: Unitless
Employed_people = Working_age_population*Employment_fraction_average
{people}
UNITS: people (person)
Employment _fraction_average = 0.718
{unitless}
UNITS: Unitless
EQ =If Equilibrium_Switch = 1 then 0 else 1
UNITS: Unitless
24
Equilibrium_Switch =IF Equilibrium Multiplier = 1 then 1 else 0
{unitless}
UNITS: Unitless
Equilibrium_Multiplier = 0
UNITS: people (person)
Fraction_migration 0 to_14=GRAPH(TIME
{unitless})
(1990, 0.22), (1995, 0.26), (2000, 0.16), (2005, 0.13), (2010, -1.02), (2015, -1.02)
UNITS: Unitless
Fraction_migration_15_to_ 44 =GRAPH(TIME
{unitless})
(1990, 0.62), (1995, 0.6), (2000, 0.77), (2005, 0.99), (2010, -1.83), (2015, -1.83)
UNITS: Unitless
Fraction_migration 45 to_64=GRAPH(TIME
{unitless})
(1990, 0.12), (1995, 0.1), (2000, 0.05), (2005, -0.06), (2010, 2.23), (2015, 2.23)
UNITS: Unitless
Fraction_migration_65_plus =GRAPH(TIME
{unitless})
(1990, 0.04), (1995, 0.03), (2000, 0.02), (2005, -0.06), (2010, 1.63), (2015, 0.02)
UNITS: Unitless
Fraction Women_15_to_44 =0,487662
{1/baby}
UNITS: 1/baby (1/baby)
DOCUMENT: Units: Women/Baby
Further _life expectancy_65_plus_equation =((-0.0037*Actual__Life expectancy + 0.3375)*0
+
(0.5984*A ctual__Life_ expectancy - 29.218)*0
+
1.538376*A ctual__Life expectancy - 99.321028)
{years}
UNITS: years (yr)
DOCUMENT: The fractional mortality rate for people aged 65 and older.
Another smoothing equation
(0.063081*A ctual__Life expectancy “2 - 9.216724*Actual__Life expectancy + 352.419689)*0
Further life expectancy__65_plus =IF(TIME> 1010) THEN
Further _life expectancy_65 plus equation ELSE Further Life expectancy__65_plus data
{years}
UNITS: years (yr)
Further Life expectancy__65_plus_data =GRAPH(TIME)
(1990, 16.6), (1991, 17.0), (1992, 17.8), (1993, 17.7), (1994, 18.2), (1995, 18.4), (1996, 18.5),
(1997, 19.1), (1998, 19.4), (1999, 19.9), (2000, 20.5), (2001, 21.2), (2002, 21.3), (2003, 21.4),
(2004, 23.1), (2005, 23.3), (2006, 24.0), (2007, 24.0), (2008, 23.7), (2009, 23.6), (2010, 23.4)
UNITS: years (yr)
25
Gap_fraction_desired_and_actual_health service =
Desired_health_service/Health_service_capital
{unitless}
UNITS: Unitless
Gap_fraction_desired_and_actual__pension_payments =
Desired_pensions/Pension_payments_capital
{unitless}
UNITS: Unitless
GDP_per capita mil =Real_GDP_mil/Population
{EUR/People}
UNITS: EUR/Person (EUR/person)
GDP__Per Employed _Person = Real_GDP_mil*1000000/Employed_people
{EUR/people}
UNITS: EUR/Person (EUR/person)
DOCUMENT: Based on http://www.indexmundi.com/facts/germany/gdp-per-person-employed
on 1990 USD value based
GDP Deflator 1990 based on World Bank WDI 2011 publication is 84.55728
Initial value: 34,481 USD
GDP_Constanta = 1
{Eur/Y ears}
UNITS: EUR/Y R (EUR/yn)
Health_service_investment_need_in_prct_of GDP =
Health_service_in_prct_of_ GDP_1990*Gap_fraction_desired_and_actual_health_service
{Euros}
UNITS: 1/year (1/yr)
Health_service_in_prct_of_GDP_1990 =0.096605
{unitless}
UNITS: 1/year (1/yr)
Health_service_per_capita = Health_service_capital*1000000/Population
{Euros/people}
UNITS: EUR/Person (EUR/person)
Immigration_policy =0
UNITS: Unitless
Immigration__through_policy =
SMTH3(Desired_Immigration, MAX (5,Immigration_Policy_length/2))
{person/years}
UNITS: person/yr
Immigration_Policy_length =7.5
UNITS: years (yr)
Income_Percentage_on_raising_children = 0.315
{unitless}
UNITS: Unitless
26
DOCUMENT: Assumption made: Author
Based on Businessweek article
http://www. businessweek.com/investor/content/nov2007/pi2007119_694057.htm
Increasing Child_Incentives = 1000
UNITS: Eur/baby (EUR/baby)
Increasing Women_Involvement = 0.02
UNITS: people (person)
Initial_baby_costs = 12500
(Bomb, McCormick et al.)
UNITS: Eur/baby (EUR/baby)
Initial_mean_age_of_women_giving first_birth = 26.28
{years}
UNITS: years (yr)
Intervall_0_to_14=15
{years}
UNITS: years (yr)
Intervall_15_to_44 =30
{years}
UNITS: years (yr)
Intervall_45_to_64 =Pension_Age-(45)
{years}
UNITS: years (yr)
lifetime multiplier from_health_services =
(Change__health services normalized“Mmultiplier__adjustment_value_health_services)*1
{unitless}
UNITS: Unitless
lifetime_multiplier_from_prosperity =
Change_prosperity_normalized“Mmultiplier_adjustment_value_prosperity
{unitless}
UNITS: Unitless
Maximum_Productive Period = 40
{years}
UNITS: years (yr)
Mean_Age_of Women_Having Child =
Min(Effect_income_on_mean_age_of_women_having_first_birth*Initial Mean Age of Wom
en_Giving_First_Birth,Maximum_Productive_ Period)
{years}
UNITS: years (yr)
Mortality_0_to_14 =IF(TIME>1010) THEN Mortality_0_to_14 equation ELSE
Mortality_0 to 14 1990 to 2010 data table/1000000
{1/years}
UNITS: 1/year (1/yr)
27
Mortality_0_to_14 1990 to 2010 data table =GRAPH(TIME
{1/years})
(1990, 737), (1991, 669), (1992, 586), (1993, 555), (1994, 519), (1995, 490), (1996, 464),
(1997, 463), (1998, 438), (1999, 428), (2000, 408), (2001, 401), (2002, 382), (2003, 388),
(2004, 366), (2005, 363), (2006, 340), (2007, 350), (2008, 331), (2009, 325), (2010, 319)
UNITS: 1/year (1/yr)
Mortality_0_to_14 equation =(-0.00005930*Actual__Life expectancy +
0.00505824)/Mortality_Conversion_Constanta
{1/years}
UNITS: 1/year (1/yr)
DOCUMENT: The fractional mortality rate for people aged 0-14.
Formula:
1. Average of year interval aggregated motriliy rates
2. Average of age group interval aggregated mortility rates
3, 2011-11-22 Average cohort mortality distribution function
Mortality 15 to 44 =IF(TIME>1010) THEN Mortality 15 to 44 equation ELSE
Mortality 15 to 44 1990 to 2010 data table/1000000
{1/years}
UNITS: 1/year (1/yr)
Mortality 15 to 44 1990 to 2010 data table =GRAPH(TIME
{1/years})
(1990, 1078), (1991, 1168), (1992, 1143), (1993, 1126), (1994, 1119), (1995, 1101), (1996,
1066), (1997, 1020), (1998, 962), (1999, 954), (2000, 938), (2001, 889), (2002, 970), (2003,
953), (2004, 804), (2005, 768), (2006, 737), (2007, 711), (2008, 694), (2009, 682), (2010, 668)
UNITS: 1/year (1/yr)
Mortality_15 to_44 equation =(-0.00011023*Actual__Life expectancy +
0.00951890)/Mortality_Conversion_Constanta
{l/years}
UNITS: 1/year (1/yr)
DOCUMENT: The fractional mortality rate for people aged 15-44.
Mortality 45 to 64 =IF(TIME>1010) THEN Mortality 45 to 64 equation ELSE
Mortality 45 to 64 1990 to 2010 data table/1000000
{1/years}
UNITS: 1/year (1/yr)
Mortality 45 to 64 1990 to 2010 data table =GRAPH(TIME
{I/years})
(1990, 7518), (1991, 7686), (1992, 7505), (1993, 7478), (1994, 7275), (1995, 7111), (1996,
6970), (1997, 6726), (1998, 6533), (1999, 6402), (2000, 6301), (2001, 6126), (2002, 6033),
(2003, 5910), (2004, 5627), (2005, 5485), (2006, 5236), (2007, 5079), (2008, 5018), (2009,
4923), (2010, 4843)
UNITS: 1/year (1/yr)
Mortality 45 to_64 equation =(-0.00060437*Actual__Life expectancy +
0.05339422)/Mortality_Conversion_Constanta
{1/years}
28
UNITS: 1/year (1/yr)
DOCUMENT: The fractional mortality rate for people aged 45-64.
Mortality_Conversion_Constanta = 1
{years“2}
UNITS: yr72 (yr-yr)
multiplier_adjustment_value_prosperity = 0.5
{unitless}
UNITS: Unitless
multiplier__adjustment_value_health services = 0.13
{unitless}
UNITS: Unitless
Need_for Immigration =
Need_for Labor multiplier*Need_for population _decline_compensation
{person/years}
UNITS: person/yr
Need_for Labor multiplier = (Population/Employed_people)
{unitless}
UNITS: Unitless
Need_for population_decline_compensation = Births-Deaths
{person/years}
UNITS: person/yr
Normal_productive_period = 35
{years}
UNITS: years (yr)
Normalized_effect_population_structure_on_health_care_need =
Population_structure_cost_of_illness_indicator/Init(Population_structure_cost_of_illness_indic
ator)
{unitless}
UNITS: Unitless
Normalized_effect_population_structure_on_pension_need_normalized =
Population_65_plus per employed/Init(Population_65_plus_per_employed)
{unitless}
UNITS: Unitless
Normalized_effect_population_structure_on_pension_need_normalized_2 =
Population_65 plus per employed/Init(Population_65_plus_per_employed)
UNITS: Unitless
Normalized_effect_population_structure_on_pension_need_normalized_3 =
Population_65_plus_ per employed/Init(Population_65_plus_per_employed)
UNITS: Unitless
Pension Age = 65
UNITS: years (yr)
Pension_payments investment_need_in_prct_ofneed =
Gap_fraction_desired_and_actual__pension_payments*Pension_payments in prct_of GDP_19
90
29
{Euros}
UNITS: 1/year (1/yr)
Pension_payments in prct_of_ GDP_1990 =0.117
{unitless}
UNITS: 1/year (1/yr)
Perceived_Cost_Pressure_Adjustment_Time =2
{years}
UNITS: years (yr)
Perceived_Cost_Pressure_on_ Having Babies =
SMTH3(Initial_baby_costs*GDP_per capita _mil/init(GDP_per_capita_mil),Perceived_Cost_Pr
essure_Adjustment_Time,Initial_baby_costs)-step(Test_Policy,2012)-
Early_Measures_Germany_Government
{EUR/Baby}
UNITS: Eur/baby (EUR/baby)
Perception_on_future_growth =GRAPH(Employed_people/Init(Employed_people)
{unitless})
(0.00, 1.00), (1.00, 1.00), (2.00, 1.05)
UNITS: Unitless
Policy_start = 2010
UNITS: years (yr)
Policy_Switch =0
{unitless}
UNITS: Unitless
Population = Population_0 to 14+ Population _15 to 44+ Population 45 to 64+
Population_65_Plus
{people}
UNITS: people (person)
DOCUMENT: Total population of Germany (all ages)
Population_65_plus_per employed =Population_65 Plus/Employed_people
{unitless}
UNITS: Unitless
Population_structure_cost_of_illness_indicator =
(Average_cost_of illness Under_15*Population_0_to_14+Average_cost_of illness 15 to_45*
Population 15 to 44+Average_cost_of illness 45 to_65*Population_45 to_64+Average_cost
_of illness Over 65*Population_65_Plus)/(Population)
{unitless}
UNITS: Unitless
Productive Age Start =15
{years}
UNITS: years (yr)
Prosperity_capital = Real_GDP_mil-Health_service_capital-Pension_payments capital
{Euros}
UNITS: Euros (EUR)
30
Prosperity_capital_per_capita = Prosperity_capital/Population
{Eur/People}
UNITS: EUR/Person (EUR/person)
Ratio_Population_65_Plus = Population_65_Plus/Population
{unitless}
UNITS: Unitless
Ratio_poulation 65 Plus data =GRAPH(time)
(1990, 0.149), (1991, 0.15), (1992, 0.15), (1993, 0.152), (1994, 0.154), (1995, 0.156), (1996,
0.157), (1997, 0.158), (1998, 0.159), (1999, 0.162), (2000, 0.166), (2001, 0.171), (2002, 0.175),
(2003, 0.18), (2004, 0.186), (2005, 0.193), (2006, 0.198), (2007, 0.201), (2008, 0.204), (2009,
0.207), (2010, 0.21)
Real_Fert_Rate =
(Desired_Children in Familly/Effect_on_mean_age_giving_birth_over_fertility_rate)*1
{baby}
UNITS: baby (baby)
Real_GDP_mil =(Real_GDP_mil data*0
fi
Real_GDP_mil_equation*0
+
(IF (time<=2010) THEN Real GDP _mil data ELSE Real GDP_mil equation)*1)
(Bomb, McCormick et al.)
UNITS: Euros (EUR)
Real GDP mil data =GRAPH(TIME
{Euros})
(1990, 2.3e+006), (1991, 2.3e+006), (1992, 2.4e+006), (1993, 2.3e+006), (1994, 2.4e+006),
(1995, 2.5e+006), (1996, 2.5e+006), (1997, 2.5e+006), (1998, 2.6e+006), (1999, 2.6e+006),
(2000, 2.7e+006), (2001, 2.8e+006), (2002, 2.8e+006), (2003, 2.7e+006), (2004, 2.8e+006),
(2005, 2.8e+006), (2006, 2.9e+006), (2007, 3e+006), (2008, 3e+006), (2009, 2.8e+006), (2010,
2.9e+006)
UNITS: Euros (EUR)
Real_GDP_mil_ equation = (((35.391*(time-1989) + 2255.3)*1000))*GDP_ Constanta
{Euros}
UNITS: Euros (EUR)
Real_GDP_normalized_growth = Real_GDP_mil/Init(Real_GDP_mil)
{unitless}
UNITS: Unitless
Reproductive_ lifetime = 30
{years}
UNITS: years (yr)
DOCUMENT: The time interval of the reproductive stock in this model: 15 to 44 years --> 30
years
31
(Number of years people can reproduce)
30 Y ears according to German statistical database definition
Unit should be year only
Sexually_productive_period = Productive Age__Start+Normal_productive_period-
Mean_Age_of_Women_Having Child
UNITS: years (yr)
Shock Switch =1
UNITS: Unitless
Test_Policy =If Policy Switch =1 then Increasing Child_Incentives else 0
{EUR/baby}
UNITS: Eur/baby (EUR/baby)
Test_Policy_Empl =If Policy_Switch =1 then Increasing Women_Involvement else 0
UNITS: people (person)
TFR_2050 = GRA PH(time)
(2010, 1.39), (2040, 1.20)
UNITS: baby (baby)
Total_immigration_data = GRA PH(time
{person/years})
(1990, 681872), (1991, 602523), (1992, 782071), (1993, 462096), (1994, 314998), (1995,
397935), (1996, 282197), (1997, 93664), (1998, 47098), (1999, 201975), (2000, 167120),
(2001, 272723), (2002, 219288), (2003, 142645), (2004, 82543), (2005, 78953), (2006, 22791),
(2007, 43284), (2008, -55743), (2009, -12782), (2010, 0.00)
UNITS: person/yr
Total_net_immigration =Immigration__through_policy*0
$
Total_immigration_data
{people/years}
UNITS: person/yr
Total_fertility = Total_Fertility_historical_data *0
+2.04 *0
+
Real_Fert_Rate*1
{baby}
UNITS: baby (baby)
Total_Fertility_historical_data = GRA PH(time
{baby})
(1990, 1.45), (1991, 1.33), (1992, 1.29), (1993, 1.28), (1994, 1.24), (1995, 1.25), (1996, 1.32),
(1997, 1.37), (1998, 1.36), (1999, 1.36), (2000, 1.38), (2001, 1.35), (2002, 1.34), (2003, 1.34),
(2004, 1.36), (2005, 1.34), (2006, 1.33), (2007, 1.37), (2008, 1.38), (2009, 1.36), (2010, 1.39)
UNITS: baby (baby)
DOCUMENT: Source: Statistisches Bundesamt
Working _age_population =(Population_15 to_44+Population 45 to_64)
UNITS: people (person)
32
Zuwachs 0 to_15 =- Deaths 0 to_14+Births +Net_immigration_0 to 14-+
Maturation__14 to 15
UNITS: person/yr
Appendix B
The approach of structure-behavior tests is to cut all loops except one and too examine
the remaining behavior of the unseparated loop. Two tests are made for the major
feedback loops in the life expectancy subsystem. To extinguish influences of the
fertility subsystem the fertility is set to its reproduction level (approximately 2.14) and
migration is cut off. The two tests examine how the population behaves if the GDP is
on the one hand constant and on the other hand growing.
Test 1: Impact of health service
Figur 11. For the analysis of the health service loop are all other loops cut
In the first test all loops are cut except the health service loop (figure 11). The effects
from the health service variable on prosperity remains also ineffective. In figure 12 the
behavior of the population is plotted for dynamic and constant GDP.
Population: 1-2
i rson0000-+
1600.00 2005 00 2020.00 2035.00 72080,00
Pages Years
Figur 12. Impact of health service: Blue line (1) GDP is growing, red line (2) GDP is constant.
Simulation period = 50 years
Both curves are as expected. If the GDP is constant, the population amount becomes
constant after the asymetric distribution in the population stock has overcome. There is
no force which leads to a growth in life expectancy. If the GDP is growing, the
33
population is growing because life expectancy increases as a reason of an improving
health care.
Test 2: Impact of prosperity
Figur 13. Proof of the prosperity variable, health service influences prosperity but this variable is
not effecting as a multiplier anymore.
Now the effect of the prosperity variable is investigated. The effect from the health
service variable on the prosperity is still active. In figure 14 the simulation results are
shown.
1800.00 2015.00 2040.00 2085 00 2090,00
Pages Years
Figur 14. Impact of prosperity: Blue line (1) GDP is growing, red line (2) GDP is constant.
Simulation period = 100 years
The simulated behavior looks similar as the one in figure 12. The explanation is almost
the same. The only tiny difference is that the curve with constant GDP shows a small
overshoot.
34
Appendix C: Alternative Methodology Approach
Increasing ratio of elder population over total population especially over
working age population attracts many researchers on looking what are its main root
cause problems and its consequences. In general, unbalance population age structure
because increasing inflow of older population with decreasing inflow of young
population over time have bad effects on Germany’s economy. Economist and
demographers believe that there will be a massive baby boomers retirement in the
upcoming year in Germany. Meanwhile, the problem appears when the number of
working age population supporting retiree is decreasing. In other words, the Old
dependency ratio of Germany is rising, and will continue rising over the year as more
and more baby boomers generation reach their pension age. Economist and
Demographers call this phenomenon as population ageing reflecting on the condition
that average age of Germany population is now increasing because of growing ratio of
more older people than young population.
Now this demographic issue becomes more serious when economist and
demographers saw potential disastrous effect on economic and social system of
Germany. First hit of this demographic structure changing is the pension system, less
and less working age population support pension payment for retiree(Coleman and
Rowthor 2011). Economist also believes if the current trend continues they will face
even bigger problems like massive reducing of tax income, saving rate, investment
rate(Kim and Lee 2008) and causing changing customer behavior.
Two economic papers address similar problem using econometrics, one paper
specifically giving detailed descriptive condition on West Germany and United States
population ageing(Borsch-Supan and Chiappori 1991). In addition, the second paper
gives empirical explanation on how demographic change can cause inverted U-shape
growth in economy(An and Jeon 2006).
Borsch-Supan and Chiappori papers explain how the demographical change in
Germany and United states occur. This paper investigates Germany and United States
system mechanism in labor, financial and housing markets, providing in
comparisons between German and US institutions to determine the role of taxes,
subsidies and regulations. The results demonstrates that economic policies have
powerful effects; some of them are also interact with existing market imperfections,
so that a serious consideration of policy options which may moderate the
implications of population aging is called for. Author provide statistical table
supporting his argument on how important the issue, he also put regression equation in
the paper to prove that the correlation between economical and demographical
indicators exist. Furthermore, authors engaged discussion in the paper by proposing
several policy measures option. He summarized several arguments on the effect of
demographical change on economic indicators. The authors put on statistical and
mathematical verification on his regression equation. He verified his model by
comparing to the historical values and statistical goodness of fit test.
35
Second Paper delivered by An and Jeon investigates how demographical change
can produce different outcome in economic indicators. Authors suggest that economic
growth follows Kuznet’s hypothesis of age-income profile. They use simple cross-
country regression on 25 countries over the period 1960-2000 data.
PGDPGR = C +«, LPGDPINI +«, INVR +3 OPEN +, EDU +X, AGESTR
where the dependent variable of PGDPGR is log GDP per capita growth rate and
the explanatory variables LPGDPINI, INVR, OPEN, EDU, and AGESTR indicate the
logarithm of initial GDP per capita, the total investment per GDP, import and export per
GDP, average schooling years of the population aged 15 and over, and the variables
representing the age structure respectively. Here, LPGDPINI captures conditional
convergence and INVR is a measure of physical capital accumulation. Other control
variables are meant to detect cross-country differences in the level and rate of growth of
technology. In our formulation, we explore the shape of the relationship between
demographic change and economic growth in three different functional forms: linear,
quadratic and cubic. In addition, authors used statistical goodness of fit test to validate
their empirical equation findings.
The empirical findings attempted in this paper show that demographic changes
appear to first increase and then decrease economic growth. This can be named as the
Demographic U Hypothesis (Curve) — an inverted U-shape relationship between
demographic change and economic growth. The economic growth increasing when
mean age in population also increasing, but then it start to slow down after certain age
and begin to decrease after reaching its peak point. This paper mention Japan as one
example how population ageing can harm economic development.
From those two papers mentioned above, we can see how economist and
demographers proved there is strong correlation between demographic change and
economic development. However, both papers only show one-way relation. In reality,
the system works in dynamic feedback mechanism. Therefore, System Dynamics
approach would add better understanding on explaining system behavior. Nevertheless,
both papers would be a good starting point to develop dynamic hypothesis and
providing basis theoretical explanation. Feedback mechanism allows expansion of
theoretical explanation from demographic change to economic development to
demographic change — economic development — demographic change.
In terms of policy planning, System Dynamics provides broader option rather
than parameter changing and sensitivity analysis. Both econometric papers provide
policy maker chances on designing policy by changing parameter in the equation. On
the other hand, System dynamics approach enhances this parameters changing policy
analysis by adding structural new policy structure. This approach provides System
Dynamics edge on bringing wishful thinking policy to implementation policy structure.
Moreover, white box method that System Dynamics use would present better
understanding for actors involved in the decision maker or other interested parties.
Therefore, System Dynamics provide better policy analysis instrument to develop
robust policy design.
36
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39
