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An economic analysis of the PAYG retirement system
and the expected consequences from a transition to an
FF scheme.
L.V. Petrides* and B.C. Dangerfield®
Centre for O.R. and Applied Statistics
University of Salford
Salford MS 4WT
UK
Abstract: Jn this paper an attempt is made to illuminate the basic
problems that are associated with financing retirement. The currently
prevailing, in most developed countries, Pay-As-You-Go (PAYG) system
and its deficiencies are analysed initially from a traditional economic
perspective and the expected consequences from a transition to a Fully-
Funded (FF) scheme are also presented. A System Dynamics model is
subsequently described which enables the employment of considerably
more realistic assumptions than are commonly employed in economic
models, and its results prove to challenge mainstream economic findings.
In addition many novel features of PAYG schemes are uncovered.
Keywords: social security; pay-as-you-go; economics; system dynamics; simulation
1, INTRODUCTION
One of the most pressing economic challenges that the overwhelming
majority of developed countries have to face is to do with the expected (in
some countries) or the already existing (in many others) tremendous gaps
between the outlays and inflows of their social security (SS) systems. SS
payments encompass all benefits intended to supplement individual or
family income, including the provision of funds when sources of income
are disrupted (or terminated) or when exceptionally heavy expenditures
have to be incurred. Thus, payments for, say, unemployment, sickness,
“E-mail address: L.V.petrides@nepheli.gr
® E-mail address: B.C.Dangerfield@salford.ac.uk
disability, crop failures, maternity, loss of marital partner, retirement etc.
all constitute different examples of SS outlays. The revenues of these
systems on the other hand emerge out of taxation. Today’s worldwide SS
crisis naturally has as much to do with the unrestrainable, as they have
developed, outlays of SS systems, as with the inability to keep increasing
the already high taxation levels to boost revenue further. At the same time
that ageing populations promise ever greater SS outlays for the
foreseeable future therefore, the upper tax limits seem to have been
reached setting the very viability of SS systems around the world in
jeopardy.
Despite the fact that in the pages that follow we focus upon only one
particular area of SS systems, namely that of pension schemes, the
importance of this issue alone cannot be overstated. The magnitude of the
pension scheme problem is in fact so great that the majority of
economists simply refer to it as the SS problem (see for example
Brauninger 1996, Mankiw 1998, Galasso and Profeta 2002). The reason
for the intended confusion of the two terms of course is not hard to
comprehend. The amounts of money that are involved for pension
schemes alone are tremendous. To give an idea it should be noted that:
e To prevent the bankruptcy of their pension schemes, payroll taxes
in many countries (for pensions alone) already exceed 25% of
wages. (Shipman (2003, p.2))
e Italy’s public retirement system already consumes 15% of its gross
domestic product and accounts for at least 34% of government
expenditures (Eurostat; Boldrin et al (1999 p.293))
e Unless changes are made to Germany’s pension system the
government will be forced to increase its spending by 9.7% of GDP
within the next 30 years (Disney (2000 p.4); OECD (1996) Table
5.3) while by the year 2030 it is estimated that 16.5% of
Germany’s GDP will be spent on pensions (Disney (ibid); OECD
(1998) Table 2.3)
e In most EU countries the implicit debt of unfunded pension
programs is two or three times greater than the explicit national
debt (OECD 1998 p. 22);
Such is the magnitude of the problem associated with pension schemes
therefore that its characterisation as ‘the SS problem’ does not seem
unreasonable. In addition, the two diametrically opposed ways of tackling
this problem which will be subsequently explored, have also had their
share to play’.
1.1 The root of the problem
There should be little doubt that the emergence of this problem has
occurred for a number of reasons. The most obvious one perhaps is that
after the conclusion of the Second World War, SS outlays started to
increase at a tremendous pace. The extension of coverage, the widening
of the risks covered, and the greater generosity of benefits which at times
even exceeded the full replacement of normal earnings (see for example
Provopoulos (1987 p.186) as regards the Greek system) describe some of
the reasons for this increase. The results of such policies were not
surprising. As written in Encyclopaedia Britannica (1994-8) ‘While social
security spending amounted to less than 10 percent of the gross national
product in nearly all countries in 1950, it had risen to 20 to 30 percent or
more in many European countries by 1980.’
Another source of even greater concern though did not have as much to
do with the outlays of these systems per se, as with the way a great
proportion of these outlays were financed. The way pension schemes
were funded in particular was very similar, if not identical, to the way
(the illegal) pyramid schemes are financed (see for example Mankiw
1998, Borden 1995). Let us now explore the characteristics of today’s
national pension schemes in greater detail.
1.2 The five defining characteristics of pension schemes
Provopoulos (ibid p.8) identifies five key issues as regards the principles
of organization and operation of pension schemes.
e The schemes can be either mandatory or discretionary
e The institutions that enable the functioning of these schemes can be
either public or private
' Health care spending should also occupy a prime position in the discussion of SS yet the lack of a
clear financing alternative, equivalent to the one that exists when it comes to pension reform, has
apparently contributed to its relative marginalization. Different views as to the handling of health care
do of course exist (see for example Iriart, Merhy, and Waitzkin 2001) while the magnitudes involved
therein also cannot easily be ignored. The President’s Council of Economic Advisors (1997) in the US
for instance projects that Medicare and Medicaid spending will increase from 2.7% and 1.2% of GDP
in 1996 to 8.1% and 4.9% of GDP in 2050 respectively. Bohn (1999) in fact notes that the U.S. SS
system is ‘almost certainly viable economically as well as politically’ if only Medicare expenditure is
to be contained.
e The schemes can be either PAYG or FF ones
e The benefits paid out can be calculated either on a Defined-Benefit
(DB) or a Defined-Contribution (DC) basis
e The inflows to those systems can result from either (general or
special) taxation or from special contributions
Apart from the first of these issues which has long been settled in favour
of the mandatory approach, the remaining four are so tightly intertwined
that they are commonly distinguished under two headings: the prevailing
PAYG system on the one hand, and the FF one on the other.
1.2.1 The prevailing PAYG system
PAYG pension systems have prevailed in the overwhelming majority of
all developed countries. The essence of these schemes can be summarized
as follows: the funds for the pensions that are paid out to today’s
pensioners are all coming out of taxing today’s working population. If
employment suddenly reduced to zero therefore, there would simply be
no one to provide for pensions. This scheme is consequently also
commonly known as the ‘unfunded scheme’, since the amount of money
that is raised through taxation instead of going into some sort of
investment fund, goes for the immediate imbursement of pensioners.
PAYG systems are usually” connected with the Defined-Benefit approach
for estimating the amounts of money that will be paid to pensioners.
According to this method this amount will be determined from a formula
(different for every country) that takes into account: a) the length of time
one has stayed in employment, and b) the wages s/he have been paid
during the last few years of their working lives®. Since the benefits paid
out do not correspond to the contributions made by individuals, the
inflows to PAYG systems necessarily emerge out of taxation. Not
surprisingly therefore it has been customary for the public sector to
provide these services.
1.2.2 FF systems
FF schemes on the other hand are usually” characterized by the Defined-
Contribution approach for estimating the pensions that are to be paid out
* It is possible for PAYG schemes to feature defined contributions and for FF schemes to feature
defined benefits, albeit the latter ones in that case could not be considered pure FF systems. See
Espinosa-Vega and Russell (1999 p.4* )
* These naturally represent the highest wages they have been receiving in their working lives.
to pensioners. The essence of the DC FF scheme is again simple:
Pensions are paid out according to the contributions individuals have
been making during their working lives. Throughout employment in other
words, a certain proportion of an employee’s (or employer’s) monthly
income is withheld and directed as a contribution into his/her individual
account which has been set up by special investment funds. These funds,
which can be managed by private companies, are subsequently allowed to
invest into bonds, stocks or any other forms of investment that is seen fit
by law. At the (happy) time of retirement therefore, any particular
individual is entitled to the full amount of money that has been
accumulating into their personal accounts plus the net accumulated
investment gains, minus expenditure. The insured may subsequently
decide to make scheduled withdrawals out of his/her account, purchase an
annuity, or opt out for a combination of the two.
1.3 The reasons for the prevalence of the PAYG system
The conditions that prevailed from the end of the Second World War up
until the first oil crisis in 1973 clearly favoured the establishment of
PAYG rather than FF schemes for a number of reasons: PAYG schemes
for a start have an immediate impact on senior citizens’ finances. At such
great times of full employment and high growth rates, it only felt right for
Governments to try to improve the financial position of those who could
not enjoy a share of the riches. Besides, the hardships those generations
went through when younger could not be easily forgotten.
Another major reason for the predominance of PAYG schemes is that
with the then prevailing and forecasted economic growth rates, the
benefits that the then current workers would enjoy when eventually
reaching retirement would exceed by far their own past contributions to
the system. It should be easy to see then, that PAYG systems offered at
the time an unbeatable formula for winning elections. Both senior citizens
and the working age population, viz. the whole electorate body, would
benefit from the scheme. Additional reasons for this pervasiveness also
exist, but they are of relatively minor importance. Obvious examples
would include the intragenerational redistribution of income that takes
place which benefits the relatively less well-off, the prevalence of the
scheme in most other countries etc.
The major disadvantages of PAYG schemes however also came to the
forefront soon after the first oil crisis. The marked reduction in
employment and growth rates reduced SS revenue at the same time that
major demands were made on the system. From the late 1970s onwards
there was consequently talk of a crisis in SS financing.
2. A BASIC ANALYSIS OF THE PAYG SCHEME AND THE
NATURE OF THE PENSION CRISIS
2.1 The basic economic principles of PAYG systems
In this section we will attempt to explore the economics of PAYG
systems from a somewhat more formal economic approach to
demonstrate its properties. The analysis at this point is equivalent as in
Disney (2000 p.f14), Gramlich (1999 p. 490-1), and Sebald (2002 p.5-7).
A PAYG pension scheme is in equilibrium when:
cwL=pB (1)
Where: c: contribution rate (1)
w: average wage (£/(persons*time))
L: number of workers —_ (persons)
p: average pension (£/(persons*time))
B: number of pensioners (persons)
In plain English, a PAYG system is in equilibrium when the inflows to
the system, viz. the contribution rate (c) times the average wages per
worker (w) times the number of workers (L), equal the outflows, viz. the
average pension per pensioner (p) times the total number of pensioners
(B).
Equation (1) can be transformed into:
c=(B/L)*(p/w) (2)
which shows that for equilibrium to prevail, the contribution rate (c) must
be equal to the so-called (old age) dependency ratio, viz. the division of
the total number of pensioners (B) by the total number of workers (L),
times the replacement rate, defined as the division of pensions (p) by
average wages (w). Assuming that governments are not willing to alter
either the contribution rates (c) of the working population, or the pensions
(p) that are to be paid out, the demographic and macroeconomic shocks
that can knock the system out of equilibrium become evident. All
demographic alterations that can cause the dependency ratio to increase
(decrease) are clearly detrimental (beneficial) for a PAYG system, while
positive (negative) growth rates, which are normally associated with
higher (lower) wages and increased (decreased) labour force levels, are
beneficial (detrimental). It naturally follows that PAYG schemes can be
sustainable even if adverse, say, demographic circumstances prevail, as
long as these are counterweighted by improving macroeconomic
conditions (or vice-versa). In the face of today’s demographic crisis (see
section 2.2), hopes for the sustainability of PAYG schemes rest solely on
the improvement of growth rates. Sadly however, the macroeconomic
outlook does not allow much room for optimism either (section 2.3).
2.2. Demographics
Let us now focus our attention on some real life statistics to illuminate the
magnitude of the prevailing problem as that manifests itself through
demographics only. As shown in equation (2), this analysis will revolve
around the dependency ratio, viz. around the actual numbers of senior
citizens* (B) as they stand in relation to the numbers of the working age
population? (L).
Figure 1 shows the dependency ratios in Germany, France, the US, and
Japan as they are predicted to evolve until the year 2050.
07
a 06
4 05
GERMAN
04 Y
H 03 ——FRANCE
0.2 —uwS
i 01
1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050
Years
Figure 1 Dependency ratios (Source: US Census Bureau)
All sampled countries as can be seen above (Figure 1) are expected to
experience a marked increase in their dependency ratios in the following
50 years or so. Even in the US, the country that is expected to be
influenced the least, the dependency ratio will go from a low of
approximately 19% which holds today, to over 34% by the end of 2050.
At the other extreme of course, we can see Japan whose dependency ratio
is expected to reach the 64% levels from the currently prevailing 21%.
* Senior citizens are taken to be all citizens that are 65 years old and over.
5 The working age population includes all persons between 15 and 64 years of age.
The corresponding ratios for most remaining developed countries
including France and Germany lay somewhere in between the two
extremes.
Let us now try to perceive more clearly what those numbers actually
mean as regards the viability of PAYG pension schemes. To do so we
will first consider the inverse of the dependency ratio, the support ratio,
which simply shows the number of workers that are required to sustain
one pensioner (Figure 2)
——GERMAN
wor
Y
——— FRANCE
N
Support ratio (1)
—as
0
1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050
Years
Figure 2 Support ratio (Source: US Census Bureau)
Figure 2 shows that from the approximate 5 workers to 1 pensioner ratio
in the sampled countries, we go down to 2.5 to 1 or so, with Japan
approaching the 1.5 to 1 ratio. Let us consider the implications of such a
change.
Equation (1) is here reproduced for convenience:
cwL=pB (1)
Where: c: contribution rate (1)
w: average wage (£/(persons*time))
L: number of workers —_ (persons)
p: average pension (£/(persons*time))
B: number of pensioners (persons)
Portraying average pensions (p) as a percentage replacement rate of
wages, we have:
p=rw @)
Where: p: average pension (£/(persons*time))
r: replacement rate (1)
w: average wage (£/(persons*time))
Substituting (3) in (1) and after an algebraic manipulation we get:
(cwL)/(twB)=1 (4)
But (L/B) represents the support ratio which we shall call (s). Thus with:
s=L/B (5)
and substituting (5) in (4) and then simplifying we get:
(c/r)*s=1 (6)
which of course equals
c=t/s (7)
Equation (7) shows that for a PAYG system to remain in equilibrium the
contribution rate (c) must equal the division of the replacement rate (r) by
the support ratio (s). Let us consequently put some numbers in equation
(7) to see how the observed reduction of the support ratio in Figure 2
influences an economy. Table 1 shows the required contribution (tax)
rates as a percentage of wages that would keep a PAYG system in
equilibrium based on a combination of different replacement rates and
support ratios.
Table 1 Contribution rates
i Contribution
Rate
Table 1° shows that the reduction in the support ratio in the case of Japan,
where public pension benefits replace about 60% of after tax annual
earnings (Horioka 1999 p.295), would require taxes (contribution rates)
to be raised to the approximate 40% level of wages just to keep the
finances of the pension system unaltered. The US on the other hand, with
a replacement rate of about 53% (Bérsch-Supan 2000 p.29) is much
better off. The expected reduction in the support ratio there can be met by
increasing taxes up to the approximate 17% levels according to Table 1. It
should be noted however that such an increase represents a rise in taxes of
approximately 80%. Politically such changes are very hard to handle.
Trying to locate the reasons for these adverse demographic pressures, we
can identify two prime causes (see accordingly for example Cremer and
Pestieau (2000 p.977), Bohn (1999 p.9), Joines DH (1999 p.55))
a) low fertility rates
b) increasing life expectancies
Table 2 shows how the fertility rates have developed through the years
for the four sampled countries, and how they are expected to grow in the
future.
° The figures in Table | are only indicative of the magnitude of the problem different countries will be
facing since they are based only on demographics. The actual numbers differ from those in Table 1 due
to a number of important macroeconomic variables which have been assumed away. Some of these
variables would include the extent of tax evasion, varying productivity and/or retirement age, a possible
tripartite funding of pension schemes, previous mismanagement of PAYG funds etc.
Table 2 Fertility rates
2.36 2.01 1.44 1.56
(1989)
2.92 2.73 2.48 1.95 1.78 1.78 1.70
3.02 3.64 2.48 1.84 2.08 2.18 2.19
3.64 2.00 2.13 1.75 1.52 1.53 1.70
(Source: US Census Bureau)
The persistent downward trend in fertility rates can be easily ascertained.
After the boost in the number of birth rates that followed the aftermath of
the Second World War, and which persisted until the late 60s, a
sustaining decline in fertility rates followed. But such a decline puts a
considerable strain on PAYG pension schemes. As the sizeable
generations of the 50s and 60s are approaching retirement, the upcoming
generations that are required to provide for their pensions are
considerably smaller. Hence of course the one of the two reasons for the
estimated reduction in the dependency and the support ratios we
examined earlier.
The examination of life expectancies in the sampled countries only makes
matters worse (Figure 3).
86
rel
84
~ 82 ——Germany
j —France
2 80 —uwS
=o —) apan
: 78
76
s 14
OD oh od Gh © AO nh Ad nt nO AD oh 1d VW ©
Po OP? Gh GF gh oh of aR
PPPS SP QP PF Po
Years
Figure 3 Life expectancy at the age of birth (Source: US Census Bureau)
Figure 3 shows that life expectancies in all sampled countries are
expected to continue their considerable rising trend. The consequences of
this are simple to understand. Through a prolongation of average life
spans, the numbers of senior citizens will inevitably rise and so will the
required expenditures of PAYG schemes.
As a result of these two underlying causes, the expected age structures of
the selected countries’ population for the year 2050 as compared to the
ones prevailing today should not seem bewildering (Figure 4).
Age structure of Gem an population for Age structure of French population for
‘the years 2000 and 2050 in percentage the years 2000 and 2050 in percentage
tems tems
014 12
12
tno me Ot
EF I F Joss
008 eos J
Ta fox 4 In
a 004 . 004
*FL: * Fhe
ic} Cc}
ee » Oa op » > ¢ am & ge ~ ~ cca cu ca & ah &
SPH GY SH Sp Ye YS
TVEearZ000] Age TaYear2000 Age
mYear2050| myYear2050
Age structure of US population for the Age structure of Japanese population
years 2000 and 2050 in percentage tem s forthe years 2000 and 2050 in
percentage tems
I 61
'
r 008
I 006
k 004
I 02
1
. C}
'
wD Pm mh Ph Gah gk
Bb Ab Ak eg mK %
» ea om oh Gt at g
Sg ew Se
wee we ew
pvear2000 Age avear2000 Age
Year2050 wYear2050
g
Figure 4 Age structure of the four sampled countries (Source: US Census Bureau)
The peaks that appear in Figure 4 for the cohorts between the ages 40 and
55 for the year 2000 (blue bars) in all sampled countries result from the
increased fertility rates that were prevalent during the 50s and 60s. The
fall in birth-rates thereafter leads to the observed decline in the size of the
younger cohorts. The number of senior citizens on the other hand for the
year 2000 is not that great, corresponding to only about 4% of the total
population in the sampled countries. This state of affairs of course is quite
beneficial for the baby-boom generation (the generation born at the 50s
and 60s) since their increased size allows for smaller per capita pension
contributions. Besides, the number of people they have to sustain is quite
small when compared to the size of their own generation.
The emergent pension problem however is also in sight from the data of
the year 2000. These large cohorts that are now still in their 40s and 50s
are about to retire during the next 20 years or so. How easy will it be for
younger generations to finance the baby boomers’ retirement given their
(the younger generations’) considerable reduction in size?
By the year 2050 the dire consequences of the previously persistent lower
fertility rates and the rise in average life spans are clearly shown. All
cohorts between the ages of | to about 55 can be seen to be much smaller
when compared to their year 2000 equivalents, while the number of
senior citizens is set to increase markedly. The size of the over 80s cohort
alone is expected to compare and some times even exceed the cumulative
size of all persons above 65 for the year 2000. As shown in Figure 4, the
over 80s cohort by itself is set to represent 13% of the total population in
some cases (see Germany and Japan within the sampled countries). Under
such circumstances the deficiencies of the PAYG scheme become clear.
A much-reduced labour force will be called upon to sustain a much-
increased number of pensioners.
2.3 Macroeconomic factors
2.3.1 Factors affecting the size of the labour force and the number of
pensioners.
Apart from the (adverse) demographic pressures that have been seen to
influence the finances of PAYG schemes, there also exist a number of
non-demographic factors that exert an important sway. Unemployment
provides an obvious case in point.
The dependency and support ratios as examined in the previous section,
implicitly assumed that all people between the ages of 15 and 64 were
employed and contributing towards the sustainment of pensioners. We
know for a fact however that this is not the case if only because of
unemployment. Unemployment naturally restricts (L), the actual size of
the contributing labour force. The significant slow down in most
countries’ economies that was experienced from the first oil shock in
1973 onwards naturally caused a considerable rise in unemployment rates
as Table 3 reveals.
Table 3 Unemployment rates
2 05 2.8 5 8.1
16 25 65 91 94
55 49 7.1 5.6 4
2.3 1,2 2 2.1 48
(Source: US Census Bureau)
The upward trend for all sampled countries but the US is hard to miss
(Table 3). And the future is not expected to be markedly different than it
is today.
Another factor that influences PAYG funding schemes adversely can be
identified in a relatively long standing tradition that has been fostered by
many governments across the world: early retirement. ‘...[S]ocial
security regulations across the world have encouraged early retirement,
thus aggravating the imbalance between the number of workers and
pensioners in times of population ageing’ writes Bérsch-Supan (2000
p.45) concluding his paper (see similarly Gruber and Wise (1999),
Bléndal and Scarpetta (1998))). One of the major reasons for these
provisions of course was the containment of unemployment in
‘acceptable’ or, in any case, in the lowest possible levels (B6rsch-Supan
ibid, von Restorff 2000 p.24).
The results of such incentives can be seen quite clearly in Figure 5.
1.
08
07
06 101960s
05 12000
04
03
02
01
0
Germany France us Japan
Figure 5 Labour force participation rates of the 55-64 age cohort in 1960 and 2000 (Source: OECD,
Labour market statistics; Conde-Ruiz and Galasso 2003)
With the exception of Japan, the tendency to retire early from the labour
force has resulted in a marked decrease in the labour force participation
rates of the 55-64 years old. Such a decision of course not only
contributes to a decrease in the size of the labour force (L), but it also
increases the numbers of pensioners (B).
2.3.2 Wages
Let us now examine in greater detail how wages can affect the finances of
PAYG schemes. As we have argued earlier on, increased wages can take
some of the strain off the shoulders of PAYG schemes. This can be
shown mathematically quite easily if we assume a standard two-period
overlapping generations (OG) model.
OG models are general equilibrium models and they came to the forefront
of economic analysis after Samuelson’s (1958) work’. They now
constitute, as Minford (1998 p.13) explains, ‘the way economists model
the interaction of private behaviour and government pension policy’.
Their defining characteristic is that people are assumed to be born only
once a generation. Not surprisingly, the two-period OG model that we
will use in this case makes the assumption that only two generations are
alive at any one time t’, a young one that contributes to the system, and an
old one that receives pensions. At time t+l, the previously young
generation obviously becomes the old generation, the previously old
generation is assumed to have died, and a new young generation has
emerged. Under such a scheme, equation (1) must be transformed into:
cw.L=pB (8)
Where: c: contribution rate (1)
W;! average wage at time t (£/(persons*time))
L: number of workers (persons)
Pr! average pension at timet —(£/(persons*time))
B: number of pensioners (persons)
while equation (3) must change into
’ The first overlapping models can be found in the appendix of Allais' (1947) book of as Malinvaud
(1987) has stressed.
* To make some sort of sense, the duration of t must be in the range of 35 years or so.
Pr = TW (9)
Where:
Pr average pension at time t (£/(persons*time))
r: replacement rate (1)
W,.1: average wage at time t-1 (£/(persons*time))
Workers in other words are being taxed out of the wages they currently
earn (at time t), while pensioners receive a percentage replacement of the
income they used to earn when working, viz. of the wages they earned in
the previous time period (t-1).
Assuming that wage rates grow at a rate of (n), we have
w;, = (1+n) wis (10)
Where:
w;! average wage at time ¢ (£/(persons*time))
n: growth rate in wage rates (1)
W,.1: average wage at time ¢-/ (£/(persons*time))
But from (5), (8), (9) and (10), we ultimately get
c=1/(s(I+n)) (11)
which shows that an x% increase in wage rates reduces the required
contributions (c) by x% as well. Rising wages can consequently have a
very beneficial effect on the finances of PAYG schemes.
Let us now explore some data to see whether any potential increases in
wages can mitigate the adverse demographic effects previously
established. Figure 6 shows how wage rates” in all sampled countries
have developed through the years, taking as a base (=100) the year 1992.
° These figures apply for the manufacturing sector of the selected countries’ economies
eg
= i 80 — Germany
—France
60 —uvs
Hl
40 — apan
2
1955 1965 1975, 1985 1995 2005
Years
Figure 6 Real wage rates (Source: US Census Bureau)
A significant upward trend in real wages is evident in all countries
(Figure 6). Given the very tight association between productivity and
wage rates, the significant upward trend found in wages should also be
expected to be visible when plotting productivity figures. Indeed, Figure
7 verifies this hypothesis.
i 160
§ 120
fz —Germany
§ 80 —France
§ j —us
—) apan
BEE 40 ep
i,
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Years
Figure 7 Productivity (Source: US Census Bureau)
Even though these increases seem quite beneficial for PAYG pension
schemes, on a closer examination important deficiencies can be
uncovered. Figure 8 depicts the ratio of the increase in real wages against
productivity gains.
' The figures for the US are available only from 1977 onwards.
&
iw
N
1992)
—Germany
—France
—uwsS
—J apan
(Average real wages)/(averag:
productivity) in manufacturing
(Index 100:
0.5
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Years
Figure 8 Wages/Productivity (Source: US Census Bureau)
Figure 8 shows that, with the exception of Germany, real wages have not
managed to keep pace with the realized productivity gains. In fact a
distinct declining trend can be seen to characterize the relationship
between the two variables. Given that productivity determines wage rates
and not the other way around, it is easy to deduce that even if
productivity gains continued strongly into the future, wage rates would be
expected to rise on a less than 1 to 1 ratio, unless of course this downward
trend changes. For the time being however there does not exist much
evidence for such alterations.
Let us now examine how the rates of growth of productivity have
developed year on year through the years (Figure 9).
0.14
§ D012
2 Poa — Germany
ad
@ 0.08 —France
3 : 0.06 —Us*
3 0.04 Japan
g : 0.02
on 1970 1980 1990 2000
Years
Figure 9 Productivity growth (Source: US Census Bureau)
* US figures represent output per hour in the whole of the business sector
Figure 9 shows that productivity growth has dropped markedly when
compared to its past values. This slow down can also be evidenced
through the reduction in the growth rates of the sampled countries’ GDP
(Figure 10).
0.14
i po. |
Hl & Obey — Germany
; Po.08 —France
H B 8 0.06 | —uSs
q £0.04 4 Japan
a
a 4
rc) wen?
0
1950 1960 1970 1980 1990 2000 2010
Years
Figure 10 Annual percentage of GDP growth —5 year moving average (Source: US Census Bureau)
It is quite clear from Figure 9 and Figure 10 that after the first oil shock in
the 70s Western economies never quite managed to regain their
momentum. It should be also easy to realize however that if the
downward trends captured in Figure 8-Figure 10 continue, and there is no
reason to assume that they won’t, then wages cannot be expected to even
approach the required levels needed to counter the adverse demographic
pressures examined in section 2.2.
2.4 The macroeconomic effects of pension schemes according to
contemporary economic thought.
PAYG schemes, as Espinosa-Vega and Russell (1999 p.1*) explain,
‘have important effects on macroeconomic variables such as national
savings, interest rates, investment and growth.’ Indeed, the principal
reason for the distinction between PAYG and FF schemes is that these
two different systems have markedly different macroeconomic effects
(ibid p.7*)''. In this section of our analysis then, we will deal with the
way these schemes are considered to influence the macroeconomy. The
analysis that follows draws on Espinosa-Vega and Russell (ibid).
The easiest way to shed light into the macroeconomic consequences of
the two different pension schemes is to conduct a ‘thought experiment’.
Consider an economy which has no pension scheme in place but which is
about to introduce one. Before the introduction of the scheme, the citizens
"' Here should be added that the greater the bequests from one generation to another are, the more the
macroeconomic results of PAYG schemes will approach those of FF schemes. See for example Barro
(1974)
20
of this economy had to finance their own retirement through private
savings. Throughout employment in other words they had to put aside
some of their annual income for their old age. After the introduction of a
pension scheme (of whichever type) though, active workers will have to
start paying taxes (or contributions) in order to receive pensions after they
retire. As a result, workers are expected to cut back on their saving rates
not only because the government will now provide for them in their old
age, but also because they will want to restore consumption in its pre-tax
levels (see also Brauninger (1996 p.227)).
Now, the net effect on total savings in such an economy will differ
according to the type of pension scheme that will be chosen. If a PAYG
scheme is preferred, total savings in the economy are expected to fall.
The reasoning is straightforward. The government, after the imposition of
taxation on workers, will receive revenue which will be immediately
distributed to pensioners’. Pensioners on the other hand will naturally
spend these monies, thereby increasing consumption. Given that workers
will be cutting back on their saving rates after the system is in place, total
savings inevitably reduce (see also Provopoulos ibid p.141-2).
With a reduction in savings and an increase in consumption, economic
theory predicts that growth will be hampered”’. Following the analysis in
Provopoulos (ibid p.165-6)'*, consider the Production Possibility
Frontier'® (PPF) of that hypothetical economy in Figure 11.
" The first generation of senior citizens obviously gets a free gift.
'° These are naturally the results that are found by the majority of OG models as well. See for example
Auerbach and Kotlikoff (1987), Saint-Paul (1992), Wiedmer (1996), Storesletten , Telmer, and Yaron
(1999) etc. According to different assumptions however, the results can vary. This can be seen clearly
in Kemnitz and Wigger (2000) for example, where the engine of growth of their OG model is taken to
be hu capital.
'’ See similar analysis in Samuelson and Nordhaus (2001 p.12-13)
'S The PPF, or else the transformation curve, is according to the Penguin dictionary of economics
(1992) ‘a graphical representation of the maximum amount of one good or service that an economy
can produce (say consumption goods in our case) by reducing production of a second good or service
(capital goods) and transferring the resources saved to the production of the first good.’
21
Consumption
goods
Oo KK R R R Capital goods
Figure 11 Production Possibility Frontier
Assuming that the x-axis represents the production of capital goods and
the y-axis the production of consumption goods, a chosen combination
(along the PPF) that favours the greater production of capital goods will
enable a greater expansion of the PPF in the future. If we decide to
produce OK capital goods and OC consumption goods in other words
(point E), the PPF in the future can be assumed to move outwards from
RR to R2Ro. If on the other hand we choose to produce more
consumption goods selecting the combination E’, the PPF in the next
period will only move from RR to R\R;. The choice on which
combination of Consumption-Capital goods to produce will naturally
depend on the consumption habits of the economy’s citizens. Only by
sacrificing consumption will it be made possible to fund the production of
capital goods. It follows, that an increase in consumption will reduce the
production of capital goods. Samuelson and Nordhaus (2001 p.34)
summarize this point ‘If people are willing to save — to abstain from
present consumption and wait for future consumption — society can
devote resources to new capital goods. A larger stock of capital helps the
economy grow faster by pushing out the PPF.’
An increase in the production of capital goods of course does not benefit
an economy at all times. The beneficial effects occur only if the economy
is dynamically efficient, viz. only if the rate of return on marginal capital
is relatively high. Since most developed economies are considered to be
22
dynamically efficient (Abel et al 1989) PAYG schemes are generally
considered to restrict growth'® (see also footnote 18).
A reduction in savings also has an adverse effect on interest rates
provided that the economy is not completely open'’, Assuming an
investment setting and a closed economy, Figure 12 shows how interest
rates equalize the demand for investment funds with the availability of
credit — represented by savings.
Interest
fate Savings ,
Savings ,
/
NN Demand for investment
> funds
I, I, Investment spending
Figure 12 Interest rates as determined from the demand for investment funds and savings
The reduction in savings naturally causes an upward (leftward) shift of
the savings curve (from savings; to savings>), and interest rates adjust
'© Samuelson (1958) and Aaron (1966) have shown that PAYG schemes can increase welfare when the
rate of growth of the population (which implicitly equals the growth rate of the people employed) and
the growth rate of real wages ( viz. real per capita income) exceed the growth in interest rates. That is
the reason why PAYG systems are likened to Ponzi schemes. They bear the same characteristics as the
schemes of Charles Ponzi, the originator of chain letters to raise money (see Blanchard and Fisher
(1989 p.84)).
"7 When considering a fully open economy, interest rates are assumed to be set exogenously and
therefore independently of the domestic demand for investment funds or the domestic savings levels.
There exist two main reasons however for assuming an endogenously determined rate of interest (Miles
1999 p. 12). Firstly there exists plenty of evidence that domestic investment is financed by domestic
savings (Feldstein and Horioka 1980, Obstfeld 1995). And secondly, even if interest rates were
dependent upon global savings and investment funds demand, the nature of the SS crisis is such that it
affects almost all developed countries and it would consequently affect the relevant global magnitudes
anyway.
23
upwards (from r; to r2) to ensure equality between investment funds and
savings °.
Vega and Russell (ibid p8*) consequently conclude: ‘a basic prediction
of social security theory is that establishing a pay-as-you-go system
should cause the amount of saving in an economy to fall and the interest
rate in the economy to rise’.
Now, if the hypothetical economy in question decides to adopt a FF
scheme instead, the level of savings, and consequently the level of the
interest rates in the economy should remain unchanged. This can be
easily deduced. The amount of money that the government would receive
from the workers’ contributions instead of being distributed to
pensioners, they are directed into investment funds. The reduction in
private savings that would result from the imposition of the contribution
rates on workers would be consequently exactly counterbalanced by the
direct increase in investment funds. The supply schedule in Figure 11
therefore would remain unchanged, and so would the interest rate levels.
Consequently Vega and Russell (ibid) write: ‘a second basic prediction of
social security theory is that establishing a fully funded social security
system should have little or no effect on the economy. Stated differently,
an economy with a fully funded social security system is not much
different [in macroeconomic terms] from an economy with no social
security system.’ They subsequently reason (ibid) ‘/t follows that
switching from a pay-as-you-go system to a fully funded system should
cause the total amount of savings to rise, producing a decline in the
interest rate.’ On the same line of reasoning explicated above, they add
that such a switch would eventually boost investment and consequently
growth (ibid p.9*; see similarly James (1998), Orszag and Stiglitz (1999))
The transition from PAYG to FF systems however cannot be achieved
painlessly. With a sudden adoption of a FF system, the problem of how to
finance the benefits of existing and near-future beneficiaries who have
been making contributions to the PAYG system for years emerges. To
force existing workers to provide both for their own future retirement as
well as for the sustenance of those beneficiaries would simply put too
much strain on them. Such measures would consequently seem unfeasible
from either a political or from an economic point of view. As a result
'S As shown in Figure 12 increased interest rates are also considered to hamper investment and
consequently growth since they increase the cost of capital -see for example Niggle (2000 p.7*,9*) who
also presents the counterarguments to this hypothesis (ibid p.9-11*), Bohn (1997)
24
Espinosa-Vega and Russell (ibid p.10) note ‘[‘]he transition strategies
that seem most likely to be politically feasible would involve spreading
the burden of financing the social security benefits due ...across a
number of future generations of workers.’ And the obvious strategy to
accomplish this task would involve the issuing of long-term debt", as for
example was the case in Chile which was the first country that handled
the transition (Williamson (2001), Pifiera (1999)). Given mainly the
difficulties associated with this transition along with some additional
issues some of which will be subsequently touched upon, a heated debate
takes place over the potential improvement or deterioration in welfare in
the case of replacement of PAYG systems by FF ones. (See indicatively
the World Bank (1994), Feldstein (1995), Shipman (1998), and Kotlikoff
(1992) who argue in favour of the transition, and Ball (1997), Boldrin et
al (1999), Mueler (1998), and Niggle (2000) who argue against.) It must
be added though that in favour of the transition have been set many
international financial institutions including the World Bank as we have
seen, the IMF, and the Inter-America Development Bank (Williamson
2001 p.296)
3A SYSTEM DYNAMICS MODEL
It was previously maintained that OG models set the standard in
economics when analysing pension policy. OG models however by
adhering to the neoclassical tradition of economic analysis include many
assumptions which are made solely for mathematical convenience rather
than realism. The two standard assumptions found in almost all OG
models include an optimising behaviour by all parties involved in the
model, and an equilibrium concept that reconciles people’s decisions with
their fellow beings, government policy, and technology (De Nardi et al
(2001)). Both of these assumptions however seem quite odd within the
context of real economies since the real world is generally fraught with
disequilibrium dynamics and genuine uncertainty (in Knight’s sense). In
fact the invocation of rationalisation within the context of pension
economics is twice as striking given the main reason for the obligatory
nature of pension schemes around the world. Diamond (1993 p.143)
explains ‘[A]nalysts of social insurance generally recognize that a
critical part of the case for having social insurance is the failure of
individuals to adequately look ahead and provide for their own
' The mere issuance of long-term bonds in itself does not imply that a country is moving away from a
PAYG scheme to a FF one. Of vital importance is for that country’s government to gradually retire
those bonds instead of keeping rolling them over indefinitely (Espinosa- Vega and Russell (ibid)).
25
retirements.[see similarly De Nardi et al (ibid p.21)] Thus social
insurance analysis is one place where the rationality assumptions of
economists are not given a full rein as in most other areas of economic
analysis’
These two assumptions, as far away from reality as they are, are not the
only ones that produce discrepancies between real economies and OG
modelling. Additional simplifications that can be generally found in many
(but not necessarily all) such models include: time being measured in
units of generation (Samuelson (1958), Diamond (1965)); zero risk
(Pemberton 1999); infinitely-lived people (Weil 1987); constant
probability of death in all periods (Blanchard (1985)); unchanging
marginal propensities to consume for all generations (Blanchard (ibid),
Weil (ibid)); perfect annuities markets viz. elimination of uncertainty
about the time of death (Gertler (1999)) etc. The emergent results of OG
models therefore can be potentially misleading. A different modelling
methodology is consequently adopted herein, which allows for a
considerably more realistic approach to modelling and understanding
pension economics. The previously described thought experiment is here
simulated via an aggregate SD model which enables nevertheless the
examination of the basic macroeconomic issues associated with pension
economics. The model’s results will be shown at times to be quite
counter-intuitive.
3.1 Demographics
Figure 13 depicts the spinal flow of the population sector of this model.
Youth death Adults death
rate rate
Youth Adults Seniors
——<— | ee a od
(0-17) | youth (18-64) | naar (64) | schiors
maturity rate maturity rate death rate
Birth rate
Figure 13 Population sector
As can be seen, total population is separated into three categories
according to age: the youth, the adults, and the senior citizens. From the
time people are born until their 18" birthday they are considered to be
youths subsequently entering adulthood where they remain until they are
26
65. From 65 onwards they are transferred into the senior citizens category
where they stay until they die. Figure 13 also makes clear that people die
not only after they reach seniority, but throughout their lives. Different
death probabilities of course are associated with the three identified
categories. The youth death fraction in particular equals 0.0025, the
equivalent for the adults is 0.0075, and for seniors 0.067 approximately.
As one might imagine, different numbers may be tested. Regarding death
rates they are evenly spread out throughout the lives of individuals while
in the youth and adult categories, whereas when reaching seniority a first
order death rate delay applies signifying that the majority of senior
citizen's deaths occur before reaching 80. The birth rate on the other hand
is set exogenously. As is often the case in SD, the initial values of the
three levels along with the birth and death rates have been chosen to
allow for an initial equilibrium. In that way the exploration of different
dynamic hypotheses can be carried out more clearly avoiding possible
mistakes.
Let us now perform a few tests to see how well this model handles
demographics. Figure 14 shows the dynamic behaviour of the three
identified levels when the birth rate doubles for only one instance in year
20 through a pulse function.
=; 1,000,000
> 8,550,000
-3- 20,400,000 f]
-4- 5,250,000
] 2 —-Birth_rate
-1- 700,000
—5—Youth
8,400,000 | 2
-3- 19,560,000 4 —3—Adults
“a 18,100,000 —4— Seniors
500,000) | 4 Ba Be 4 @ 4 4
¢,300,000 ° 2 2 222? 23 23 2
—y- 8,300,
-3- 19,000,000 ttt +——t—-1—+ 1
-4- 5,000,000
Figure 14 Doubling the birth rate for only one instance through a PULSE function: Plot of birth
rate, youth, adults, and senior citizens
27
Figure 14 above shows that indeed before the doubling of the birth rate in
year 20 no dynamics occur since the model is set in equilibrium. After
year 20 however youths increase in numbers. A slight uniform reduction
in the number of youths as time progresses can be observed which of
course signifies the deaths of the youth. After 17 years, viz. at year 37
approximately, a sudden reduction in the youth numbers is observed with
an equivalent increase in the number of the adults. As previously, the
number of the adults decreases uniformly thereafter until the surviving
adults reach seniority (year 84 app.). At that point, again, the number of
the adults drops instantaneously and that of the senior citizens increases.
The first order delay in the death rates of senior citizens thereafter
concentrates the majority of deaths within the first 15 years of their life
(years 84-100 app.), while by the year 130 almost all the dynamics
produced due to the increase in birth rates 110 years ago, die off.
Let us now explore the consequences of a doubling in the birth rates for a
period of 25 years which corresponds approximately to one generation.
This augmented generation will be referred to as generation Z for
convenience. Two step functions are used in this case with the birth rate
doubling at year 20, staying at those increased levels for 25 years, and
finally returning back to its original levels by year 45. Figure 15 depicts
the output.
=1- 1,000,000
2h 35,000,000 b om
eae
<4 10,000,000
4 _,—Birth_rate
-- 700,000 : 1
Youth
2 3 3 a Se
17,000,000 }+
=i
Be —3— Adults
-4- 7,000,000 2 4 _4— Seniors
2
\ 4
-1- 500,000
2 2 2 2 2
eae =4 al ——S
-3-p 5,000,000 J a * . ° * a *
=
0 25 50 75 100 «125 150175200
Time
Figure 15 Doubling the birth rate for 25 years: Plot of birth rate, youth, adults and senior citizens
28
The dynamics in Figure 15 are somewhat more complicated than before.
Without going into the details of the stocks and flows” relationship we
can note that after the step increase in the birth rate, the number of youths
increases uniformly as expected”!. Between years 37 and 45 the number
of youths remains unchanged which should be again expected given the
equilibrating inflows and outflows of the youth stock. Thereafter the
number of youths declines towards its initial value which it eventually
reaches by year 62. Evidently, this number emerges from the time the
birth rate is re-established back to its original levels (year 45), plus the
number of years youths have to wait until they reach maturity (17 years).
The number of the adults on the other hand increases uniformly from year
37 app. (derived from the time the birth rate first doubled (yr 20) plus the
number of years it takes for youths to mature (17 years)) until year 62
where the previously increased birth rates cease to exert an influence. The
subsequent uniform decrease until year 84 app. takes place due to the
increased death rates of generation Z which cannot be compensated by
the now reduced youth maturity rates. Once year 84 is reached the
reduction in the number of the adults gets more aggravated since
generation Z is gradually entering seniority. The senior citizens stock
therefore starts to increase until it also falls back into its initial levels after
year 155 approximately.
The complexity of the output in Figure 15 probably justifies the
presentation of all relevant rates of the population sector which are
provided below (Figure 16).
*°See Sterman (2000 Ch.6-7), Goodman (1980 Ch.2, Ex.2) for greater details.
*! Here should be reminded that death rates for youths and adults are assumed to take place uniformly
throughout their youth and adulthood -see Figure 16.
29
ae
_ 1e6
nie
=g- 45,000 ot
-5- 220,000 | |
6 1e6 _,—Birth_rate
4 4 —>~Youth_maturity_rate
5 mal — 3 Adult_maturity_rate
] Ca —q—Youth_death_rate
== 1 1 1 1
if —5—Adult _death_rate
=7~$ 300,000
_,Seniors_death_rate
“Fy 36 4 gra 6: 6
-4- 20,000 + : y :
-5- 140,000
~g- 300,000
Figure 16 Doubling the birth rate for 25 years: All relevant rates required to explicate the dynamics
of Figure 15
The next test that is performed deals with the dynamic effects that would
emerge solely from an increase in the average life span of senior citizens.
An assumption is made therefore that at year 20 of the simulation a 60-
year process is initiated that will ultimately increase the average
remaining life of senior citizens from 15 to 20 years. This process is
evidently gradual and the increase in the average remaining life of senior
citizens takes place uniformly throughout the 60 years. Figure 17 shows
the results of such an increase.
= 8,440,000
=z 20,200,000
3 345,000 [ttt
nin 20 4 ———
-s- 7,000,000) + geet 3 :
\ ~ ao —y-Youth
7 a _ Adults
A 3 ae
| —3--Seniors_death_rate
5 ig Remaining_lfe_span
1 8,300,000) | :
19,000,000 uf X42 tof 1a 2g 121g 1g Seniors
As —
3 310,000
wie 45
-5- 5,000,000
0 2 50 75 100 125 150 175 200
Figure 17 Increasing average lifespan of senior citizens by 5 years: Plot of youth, adults, seniors,
seniors’ death rate, and the average remaining life span
30
As expected, both the youth and the adults stocks remain unaltered, while
the stock of senior citizens increases. The reason for this increase of
course is the reduction in seniors’ death rate that can be seen in Figure 17,
which of course emerges from the increase in the average remaining life
of senior citizens.
Finally, an extreme test is performed with the birth rate reducing to zero
at year 20. The output is presented below (Figure 18)
Ts
—Birth_rate
-1- 200,000 = ts
_5-Yout
iki Lie 4 4 ‘
-3-} 5,000,000 ‘ : go hts
\ — —g— Seniors
2 23234 — 23:4 — 23:42
-- 500,000
3
= 20,000,000 fF:
24
o
a
-4-
2
a. 0
me
+} -5,000,000 f t - t x t # t a
Mae:
0 25 50 75 100 125 150 175 200
Figure 18 Extreme test with birth rates reducing to zero: Plot of birth rates, youth, adults, and
senior citizens
Indeed, all three stocks in the model reach zero at the expected times.
3.2 The economy
Let us now explore the structure of the economy in an aggregated form.
The influence diagram in Figure 19 shows some of the main postulated
interrelationships in such a model.
31
Average selling
7 price
Quantities supplied
Gipiateaiiicent ~~ OS
Qualitative
ss attractiveness of
domestic goods
a
Labour
availability
nar
cm
Investment
"
Propensity to
import
Firms' money
balances
Desired
employment
+
+
Fes quantities
supplied
Domestic demand
Figure 19 High-level influence diagram of the model
As shown above, employment varies according to its desired levels which
depends in turn on the desired quantities of goods and services that the
domestic economy would like to supply. Evidently, an increase in the
desired quantities supplied of domestic products will result in a wave of
new recruits in an attempt to boost employment and consequently supply.
Employment however cannot increase unrestrainedly. The less the
number of the unemployed within the economy the more difficult it will
be to hire new personnel. Such pressures would consequently lead to a
rise in wages (Figure 20) since the only way to increase personnel in an
economy where almost everybody has a job is simply to hire people who
are already working in other firms; but to attract such people more
lucrative wages must be offered.
Returning to the analysis in Figure 19, the greater the quantities supplied
are, the less the average selling prices will be all other things equal.
Lower prices will naturally affect profits and consequently firms’ money
balances adversely, yet they will also boost domestic demand not only
through an income but also through a substitution effect since domestic
products will become more competitive internationally. Lower average
selling prices thus are assumed to reduce the propensity to import and
domestic demand rises even more. Not surprisingly, such rises boost
32
firms’ money balances and they also increase the desired quantities
supplied closing a positive feedback loop.
Investment next is considered to depend upon firms’ money balances.
Naturally, the greater the firms’ funds, the greater investment will be.
Investment-related expenditure of course, like all expenditure, reduces
these funds, yet they ultimately allow for a growing base of capital
equipment. In this model, such an increase is associated with a betterment
of the products’ quality and therefore with a greater attractiveness of
domestic products both at home and in the international markets. The
propensity to import therefore reduces further, exports increase (not
shown), and another positive feedback loop is closed.
Figure 20 below shows an aggregate picture of the consumption-related
variables included in the model.
Unemployment
benefit
a
Unemployed’ st
consumption
Employees’ =
i spending TA unemployed's Unemployment
ip ads | consumption
Consumption HDIOV ERS: 3
income
+R Kt
Imports +
+ re
i Tight unemployment
Domestic <3 ! pressures.
consumption Investments Dividends
4 +
i =
Profits
Wage rates
Figure 20 Influence diagram concentrating on consumption-related variables
Tracing the wider arrows in the diagram above two important feedback
loops can be distinguished: the positive employees’ consumption loop,
and the balancing consumption from the unemployed loop. The former of
33
the two loops shows that the greater employment is, the greater the
employees’ income will be and consumption subsequently raises leading
to even greater employment levels and so on. There exist however two
opposing forces that restrain this growth. Firstly it is the gain of the loop
which lies well below one, and secondly the consumption from the
unemployed loop which acts as an automatic stabilizer. In particular, the
less the number of the unemployed in the economy, the fewer
unemployment benefits will be paid out by the government, the more the
consumption from the unemployed will reduce and total consumption
will naturally fall at lower levels than would have otherwise been the
case.
Figure 20 finally also depicts the adverse effects that an increase in wage
rates can have on profits providing a third reason for the containment of
the positive employees’ consumption loop. Although increased wages
add to employees’ income they also reduce profits which lead, in turn, to
reduced dividend payments and thus lower consumption and demand.
3.2.1 Pensioners and the workforce
In most of the runs examined in this paper the workforce and the number
of pensioners correspond exactly to the adults and senior citizens levels
accordingly. Alternative runs where the retirement age rises, thereby
expanding the workforce, have however also been included (section
3.3.1c). The stock-flow diagram for modelling this expansion is shown
below (Figure 21).
Seniors
Adult maturi (64) Seniors
nie death rate
Senior
workforce Senior workforce
death rate
Retirement rate
Pensioners
Pensioners death
rate
Figure 21 Stock-flow diagram of Expanded Workforce
34
As can be seen in this case also most of the dynamics are driven from the
population sector (section 3.1). Instead of retiring when reaching
seniority, senior citizens join the so-called senior workforce where they
remain for a specified length of time before they join the pensioners level.
From the analysis in this section it becomes clear that the number of
pensioners itself, whether in the expanded or the constant version of the
time required for retirement, is independent of employment. This
deficiency is countered however by the inclusion of the employment rate
multiplier which determines the levels of average pensions that are to be
paid out according to the average duration people spend in employment
(see section 3.2.3)
3.2.2 The flow of money
Depicted in the figure below (Figure 22) is the flow of money of the
model.
Tega Interest paid on Interest paid
evestineat employees money apes
Interest paid on
firms' money Wages Vv
=P rims money Employees money Savings for
balances balances eae retirement
Income Dividends rate’
Employees!
TN sot Withdrawal rate
Income taxes Interest
paid on _,
Imports PAYG taxes pasones
Exports
(Government mone! ar
E | Pensioners' money
balances due to -—SZ pe
Interest paid on 3 .
Governments» L_PAYG scheme _] Pension
funds oe payments
Pensioners’
consumption
Consumption from
the unemployed
Figure 22 The flow of money
Starting from firms’ money balances, we can see that they increase due to
four different incoming rates, the consumption from the employed, the
unemployed, the pensioners, and from exports. Assuming positive
35
interest rates, firms’ money balances, just like all other stocks shown
above, also increase when they exceed zero. Firms’ outlays on the other
hand are constituted by investment expenditure, the wages they have to
pay out, and dividend payments. The two latter outflows constitute the
incoming flows of employees’ money balances. The assumption made
here therefore is that dividends get paid only to the employed although
we could have just as easily assumed that they get equally distributed to
all parties including the unemployed and pensioners. Employees
subsequently save some of this money for retirement and they consume
the rest according to a first order exponential delay. Employees’
consumption is directed to both imported and domestically produced
products according to the propensity to import as shown earlier on
(section 3.2).
Savings for retirement accumulate throughout the working life of
individuals and they are cumulatively withdrawn upon retirement. The
withdrawal rate subsequently accumulates in pensioners’ money balances
which are eventually depleted by pensioners’ consumption. As
previously, consumption is again directed to both imported and
domestically produced products according to the propensity to import.
At some chosen time of the simulation (see section 3.3), a PAYG scheme
is introduced with the Government starting to collect taxes from the
employees and subsequently paying them out to pensioners according to
the desired wages' replacement rate. Evidently, pension payments also
accumulate in pensioners’ money balances before they are spent. If
government money balances are at some point less than what is required
for paying out the pensions (additional) income taxes are instantaneously
levied on employees’ funds to cover the difference. The instantaneous
nature of income taxes although highly unrealistic saves the modeller
from augmenting the model unnecessarily.
In the alternative scenario where the PAYG scheme is replaced by a FF
one, some adjustments need be made in the flow of money as highlighted
in Figure 23.
36
Interest charged on
government debt
Government debt -——== =>
Debt repayment
—2 — >|
Government
borrowing rate
Government money|
due to the transition} $2 yp = Pensioners
money balances
Government money
balances due to PAYG = =
scheme: Transferred funds Transitory pension
payments
‘Taxes to fund debt
Employees money
balances:
Figure 23 Required adjustments for modelling the transition from a PAYG to a FF scheme
Firstly, as depicted in Figure 23, an additional stock, government debt, is
introduced. As was the actual case with all countries that attempted the
transition, the government in this model is assumed to take up debt in
order to finance the required expenditure for the transition. As the model
currently stands, this is assumed to be foreign debt in its entirety. Debt
naturally increases by government borrowing and the interest surcharges
on that money, while debt repayment depletes it. For simplicity, the
government is again assumed to borrow money according to the
instantaneous needs it has for paying out the transitory pensions. These
comprise of the pensions that must be paid to both current and future
pensioners who have already been making contributions to the SS system
under the old (the PAYG) regime which is now dismantled. Debt
repayment on the other hand ensures that the borrowed funds along with
interest surcharges are returned in equal instalments within the next 100
years from the debt's inception.
Another stock that can be usefully introduced in the analysis is the one
identified above as government money due to the transition. This stock
handles explicitly all the inflows and outflows that are necessary for the
transition. As shown above (Figure 23), this level increases by any
surplus funds that might have accumulated in the government’s coffers as
a result of the previously established PAYG scheme as well as by
government borrowing and taxation. This latter variable of course
signifies the taxes that must be raised domestically to repay for the
borrowed funds, and they are all assumed to come out of employees’
37
funds” as can be seen. Transitory pension payments and debt repayment
on the other hand deplete the stock as expected. Here it should be added
that the government is firstly assumed to spend all transferred funds for
paying out the transitory pensions before resorting to borrowing.
Additional stocks for modelling the accumulation of funds under the new
FF system were not considered necessary for the purposes of the model as
it currently stands. These funds simply accumulate undifferentiated in the
savings for retirement stock shown in Figure 22.
3.2.3 Further assumptions: initial conditions, constants, table functions,
and the capital equipment sector.
In this simulated economy, total population stands at approximately 32
million people with approximately 8 million youths, 19 million adults,
and 5 million senior citizens. The annual birth and death rates, which as
will be remembered stand in initial equilibrium, equal 500K people.
Employment initially stands at 90% the workforce levels and it is set to
adjust to its desired levels with a mean time of three years. The precise
relationship that holds between increasing employment and the eventual
pressures that arise due to the diminution of unemployment is presented
below (Figure 24).
Labour availability
0.9 0.92 0.94 0.96 0.98 1
Employment rate (1)
Figure 24 Effect of labour availability
It can be seen from Figure 24 above that at a 90% employment rate no
pressures are set in place constraining employment. As the employment
rate slowly exceeds the initial 90% levels though, labour availability
reduces, initially only in those limited areas of the economy where
» Evidently, the outflow rate ‘PAYG taxes’ Figure 22 ceases to deplete employees’ money balances
once the PAYG scheme is eliminated.
38
unemployment is already below the average. Employment pressures are
consequently pretty much contained and average hiring rates reduce by
only little. If average employment continues to climb however, these
pressures become much more widely felt and the restraining pressures on
hiring become considerable as shown by the steep fall of the table
function shown above (Figure 24). Should the employment rate approach
the 96-97% levels the pressures become so great that further increases in
employment make only relatively little additional difference given the
already very high restraints in hiring. Naturally, in the extreme case
where the employment rate reaches 100%, hiring falls to zero.
The average quantities supplied and demanded upon which employment
and pricing decisions are made as already seen, are averaged over a mean
period of three years, while any discrepancies in the order backlogs are to
be desirably eliminated also in three years (mean) time.
Moving on to the money flows, the (net of interest) firms’ money
balances initially stand at 100 billion money units, which for simplicity
we shall call pounds (£), and they naturally determine the level of
dividend payments that are to be paid out. In particular, dividends deplete
firms’ money balances through a first order material delay with a mean
delay time of 5 years.
As regards the annual (average) wage rates, they stand initially at £17000
but they vary according to the levels of the existing workforce and
desired employment. If wage rates are set to increase, the increase is
assumed to take place relatively quickly, viz. with an average delay time
of 2 years; if they are to reduce though a much greater average delay time
is involved which is set at 16 years. This signifies the great difficulties
that employers have to face when cutting back on wages. The annual
unemployment benefit rate on the other hand remains constant throughout
the simulation at £6300.
Spending delays for the consumption of the yearly income of the
workforce is at an average of 3 years, while pensioners and the
unemployed are assumed to spend within only a one year mean delay
time. The cumulative withdrawals that pensioners take out of the savings
they had been accumulating while working on the other hand are spent
with a first order delay and a mean time that matches their life
expectancy. The propensity to save for retirement equals 0.2 of wage
income although it will vary with different runs.
39
The propensity to import on the other hand equals 0.3 initially, yet it
varies with the domestic average price levels and the attractiveness
multiplier® according to the figure below (Figure 25)
Propensity to import (1)
0 0,5 1 1,5 2 2,5 3
(Average/Referenced price levels)/Attractiveness multiplier (1)
Figure 25 Propensity to import
We can see that even if domestic products were given away for free, there
is still assumed to be some small demand for imported products. With
average selling prices equal to their referenced, viz. their initial —for
simplicity- price levels, and with the attractiveness multiplier, equal to
one, the propensity to import goes up to 0.3. Domestic price increases or
declining qualitative product attractiveness increase the propensity to
import up to the point where domestic prices triple in respect to their
referenced values. At that extreme point all domestic demand is assumed
to be diverted away into imported products.
Regarding pension payments, it is assumed that they are provided at
approximately 73% replacement rate of an employee’s average wage rate,
which is in turn calculated simply as a first order information delay with
an average delay time of 15 years. In that way the fact that pension
payments are influenced the most from the wages one earns during the
last years of his/her employed life (viz. before retirement) is captured in
the model. With varying employment levels however the full replacement
rate is not necessarily paid out to every pensioner at all times. The
employment rate multiplier -depicted in Figure 26- captures the
relationship between average employment and the proportion of the full
pensions that are to be paid out for all possible employment rate values.
°3 The attractiveness multiplier will be remembered signifies the products’ quality and consequently the
degree to which domestic products are attractive both in the domestic as well as in the international
markets. See Figure 28 for its depiction.
40
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Average employment rate (1)
Employment rate multiplier |
Figure 26 Employment rate multiplier
It is illustrated above (Figure 26) that with average employment standing
at 90% the workforce levels, average pension payments reach 94% of
their full levels while for full pensions to be paid out the average
employment rate need not actually reach unity. This happens due to the
fact that in almost all countries full pensions are paid after a particular
minimum number of years (normally around 30-35) are spent in
employment. Even with some unemployment prevailing therefore (3%
app.) most people in this model are assumed to manage to complete this
period in employment given the substantially greater length of time they
belong to the workforce. Following this same reasoning, while average
employment stays at relatively high levels, the employment rate
multiplier also stays quite high. If there is a reduction below the 90%
levels though, the average pensions that will be paid out reduce quite
drastically. The reason for this reduction is explicated as follows: Low
levels of employment usually correspond with low demand and low
profitability. Firms at such difficult times usually try to trim down their
costs and one of the measures they assume is to fire employees before
they are made eligible for the wage increases which are associated with
the number of years one stays employed. As a result labour turnover
increases. The people who have been recently dismissed however find it
harder to get another job because they would cost more to their new
employer. It can be understood then that their chances of staying
employed for long periods of time diminishes more than proportionately
with the increase in unemployment. In any case though different shapes
for the employment rate multiplier can be easily tested. The main
41
alternative that is used in this paper simply assumes a 45° straight-line
relationship between the multiplier and the employment rate.
As regards capital equipment, they are represented by a stock which
increases through the delivery rate of new equipment and depletes
through depreciation as shown below (Figure 27).
x S Capital equipment ————— >
Delivery rate Depreciation
——_
Investment rate Non negative Desired capital
discrepancy equipment
> tl
Figure 27 Stock-flow structure of capital equipment
The delivery rate is a first order delay of the investment rate with an
average delay time of 3 years, while the investment rate itself depends
upon the non-negative discrepancy of the desired minus the actual capital
equipment. This discrepancy is to be eliminated in an average time of 4
years. If actual capital equipment exceeds its desired levels on the other
hand, the investment rate simply reduces to zero and the stock eventually
reduces due to depreciation. The average life of capital equipment equals
15 years and their average unit price equivalent comes up to £5,000.
As previously noted, the attractiveness multiplier™ of domestic products
depends on the levels of capital equipment that exist within the economy.
The precise relationship for the base-case scenario is depicted below.
Bg 15
=
3 13
Sal
ao
at
5 09
Z
Z 0.7
<= 05+
0 02 04 06 08 1 12 14 16 18 2
Actual/referenced capital equipment (1)
Figure 28 Attractiveness multiplier
42
With a 20% addition to capital stock thus, the attractiveness multiplier
rises by 13% to 1.13, while a 20% reduction leads to a 15% reduction in
the attractiveness multiplier. It is also assumed however that these rates of
increase and decrease respectively cannot continue ad_ infinitum.
Specifically it is hypothesised that once the level of the actual stock
exceeds the initial (referenced) levels by 40%, product quality rises to
such levels that its further improvement becomes much more difficult to
attain. Increasingly more capital is needed therefore to achieve only
modest quality increases and that is captured by the eventual levelling off
of the table function in Figure 28. Similarly, a continuous reduction in
capital stock would reduce the quality of domestic products but only up to
a point. Even if the capital base reduced to zero therefore, product quality
would fall to only half its initial values.
The remaining numerical assumptions in the model include:
e The level of average domestic selling prices is equal to £10 per unit
and the average delay time required to adjust them to their desired
levels comes up to 3 years
e Zero interest rates to be paid according to the accumulated money
balances of all identified groups for most runs.
e A 2% surcharge rate per year to be paid back on government debt due
to the transition.
e The initial support ratio comes to 3.8 approximately
3.3 Model output and analysis
Multiple scenarios will be tested in this section in order to enhance our
understanding of pension economics. Extending the practice that was
initially conveyed when exploring the population dynamics of this model,
in all scenarios that follow no dynamics develop before some arbitrary
year during which time some sort of shock is imposed. In all cases the
nature of these shocks and the exact time that they take place will be
clearly highlighted. All subsequent dynamics will be occurring
endogenously.
3.3.1 Testing the effects of demographic alterations when a PAYG scheme
is already in place
In section 2.2 of this paper it was maintained that the currently prevailing
demographic pressures have had an important role to play in the
43
worsening state of PAYG pension finances. In this section of the paper
we test our model to see whether our previous analysis corresponds with
the model’s output. The basic assumptions involved for the runs in this
section is that a PAYG scheme is already imposed in the economy and
that employees do not find it necessary to save any of their wages for
their eventual retirement. In terms of Figure 22, the savings for retirement
level disappears along with all its inflow and outflow rates. The initial
government money balances due to the PAYG scheme (PAYG funds) are
arbitrarily set at 10 million pounds. The choice for an initially positive
instead of a nil balance is made to enable an easier identification of a
possible reduction in its level. In addition we also assume that the
attractiveness multiplier stays constant at one throughout these tests and
that the employment rate multiplier (Figure 26) becomes a straight line
with a slope of 1. These two assumptions are made in an attempt to
minimise any unwanted interference which would force us to divert
attention from our intended goal. Both will be relaxed later on.
3.3.1a Testing a 20% step decrease in birth rates
Figure 29 shows how PAYG balances develop after the birth rate
suddenly reduces by 20% at the 20" year of the simulation. This
reduction is modelled by a step function.
=1- 20,000,000
=} 6.5e10
+
\
~4- 520,000 (J6—6
12510 i PAYG_fund
° “ane | | 1 ees
6 20,000,000) | J J) aYG wes
3
as =z PAYG_pensions
te 0 5 —q— Birth_rate
4 4 4 4—$4 zt 4 4
2h 45e10 | | ce —5~Additional_income_tax
58 : 5
3 — Pg I35 «| __, Workforce
-4- 360,000f"> ° T Tt T Tt posta 6
Figure 29 Testing a 20% step decrease in birth rates: Plot of PAYG funds, PAYG taxes, PAYG
pensions, birth rates, additional income taxes required, and workforce levels.
As expected, a reduction in birth rates leads to a considerably worsening
situation for PAYG finances. Eighteen years after the reduction in birth
44
rates, workforce levels begin to reduce since the younger cohorts that
have now grown and start joining the workforce are smaller in size than
the cohorts that preceded them. Employment (portrayed in Figure 30)
naturally also declines and incoming (PAYG) taxes drop since there is a
reduction in the number of contributors. This reduction alone along with
the unchanging (at the time) number of pensioners (Figure 30) would be
quite adequate to explain the fall in PAYG balances. Both Figure 29 and
Figure 30 show however that pensions, instead of staying at their initial
levels, follow an upward trend that is initiated at the same time that the
reduction in PAYG taxes materialises. This may seem initially quite
baffling. Why would a reduction in birth rates cause an increase in
pension payments 18 years down the line? The answer becomes clear
once we consider the behaviour of employment rate. As shown below
(Figure 30), the employment rate increases at the same time that the
reduction in the number of the employed takes place.
= 1.00
-2- 17,300,000
-3- 5,100,000 by
‘ 3 34
asp 5.7e10 eae
os 100 (4 t —<—-—
1 oe ee) —1—Employment_rate
5
| 4, _5— Employment
Le 2— Employ!
4 \ 3 —3— Pensioners
a 9-4-7,
DN 442 payG_pensions
ie 0.65) | 3K 4 -
> 13,000,000 3 ~—3_3__,__Employment_rate_muttiplier
-3- 3,800,000 ' ' ' ' ' ' ' 1
ge 4e10
-5- 0.80
0 2 50 75 100 125 150 175 200
Time
Figure 30 Testing a 20% step decrease in birth rates. C onsidering the reasons for the short-term
increase in pension payments after birth rates reduce: Plot of employment rate, employment,
pensioners, PAYG pensions, and employment rate multiplier
The increase in employment rate occurs exactly because of the reduction
in the workforce levels on the one hand and the less than proportionately
affected total domestic demand on the other. Total domestic demand,
should be remembered, is comprised of the demand from the employed,
the unemployed, the pensioners, and from exports. The initial decline of
the workforce undoubtedly reduces total consumption from the employed
and the unemployed since there has been a reduction in their numbers.
45
Pensioners’ consumption however has no apparent reason to drop and so
is the case with exports too’. With total domestic consumption falling at
a lesser pace than the reduction in the workforce levels, the employment
rate, viz. the ratio of the employed to the total workforce, rises. But with a
greater employment ratio the employment rate multiplier, which as will
be remembered determines the levels of average pensions to be paid, rises
(Figure 30) hence the increase in pension payments.
After the 100" year of the simulation approximately, the behaviour of all
variables does not offer any further surprises. Pensioners’ numbers begin
to decline and by the 150" year approximately all dynamics die off. The
consequences for PAYG at the end of the simulation prove to be, as
previously noted and according to expectations, disastrous. The transient
effects from the permanent reduction in birth rates effectively call for an
increase in PAYG taxes until the system returns to its new equilibrium
position. Indeed, Figure 29 (see variable additional income tax) shows
that an increase in taxation does take place in order to keep the PAYG
scheme alive.
3.3.1b Increasing pensioners’ life spans
In this run we test the model’s results for an increase in pensioners’ life
spans. Three years will be gradually added to the average remaining life
of pensioners and, as previously, the process will be gradual. It will
initiate at the 20" year of the simulation and it will be completed within
20 years. Figure 31 demonstrates how this alteration affects pensioners’
numbers and consequently the support ratio while Figure 32 shows that
the results as regards PAYG finances meet our expectations.
oe Actually if exports are plotted they are seen to eventually drop. Their reduction however is attributed
to the increase in domestic prices which emerge as a result of the restriction in the supply of domestic
products due to the reduction in employment
46
ps 18.0
-y- 6,100,000
ane 38
] 3 Remaining_life_span_of_seniors
~ 156 j — 9_life_span_of_
-y- 5,320,000 _7- Pensioners
_ i
“ 34 3 Support ratio
te A
as ml Sg
-y- 4,800,000
_— aa
Figure 31 Increasing pensioners’ average life spans by 3 years: Plot of average life span of senior
citizens, pensioners, and of the support ratio
5.38e10
=1- 15,000,000
= 5.5e10
_ 7.4210 (] ae ee
=i 11e10 Oo
J 3-33 _,_PAYG_funds
6,000,000 2 2 _ 2 2 2
YY _PAYG_taxes
—3—PAYG_pensions
5.96e10 [| 4
4.4e9 _,—Additional_income_tax
07] 3 4 7 -
5.3e10 4
selofit + t t t t t t 1
Figure 32 Increasing pensioners’ average life spans by 3 years: Plot of PAYG funds, PAYG taxes,
PAYG pensions and additional income tax required to sustain the PAYG scheme
With a permanent worsening in the support ratio, it is clearly indicated in
Figure 32 that there is little choice but to increase PAYG taxes to keep
the scheme afloat. As was the case in the previous section that is indeed
in effect what does take place above since we can see that income taxes
are permanently imposed to meet the difference.
47
3.3.1¢ Prolonging the duration of employment
In this section we test the implications of extending the number of years
people must spend in the workforce before retiring. At the 20" year of the
simulation therefore the time required to be spent in employment rises by
3 years taking total working time up to 50 years. (The stock-flow
structure for this expansion was presented in Figure 21). Figure 33 shows
the relevant dynamics.
-_ 56.0
-z- 21,000,000
-3 1,000,000 4
-4- 5,100,000 3 33
-- 55
5555-5 _,_Average_remaining_life_of_senior citizens
-2- Workforce
—3~ Senior_workforce
Pensioners
«ae
_ Support_ratio
a)
Ais 44.0
~z- 19,000,000
ae 0.0
-4- 3,800,000
_ 3.5
Figure 33 Expanding the duration of employment by 3 years: Plot of time required to stay in the
workforce before retiring, workforce, senior workforce, pensioners, support ratio
Figure 33 shows that at the 20" year of the simulation the senior
workforce levels pick up increasing total workforce numbers while the
number of pensioners reduces. Naturally, the potential support ratio
increases quite markedly. As a result, the dynamics of PAYG finances
shown next should not seem bewildering.
48
N
5 + a ft
“a
7 PAYG_fund:
ae Bell =, PAYG_funds
ae t _,- PAYG_taxes
z : 2 -
ere = PAYG_pensions
ici 0 1 3
1 ee
gsi 3
= reo ' ' '
a
0 50 100 150
Time
Figure 34 Expanding the duration of employment by 3 years: Plot of PAYG funds, PAYG taxes,
and PAYG pensions
With a permanent increase in the support ratio PAYG taxes settle at
higher levels than PAYG pensions and PAYG funds increase linearly ad
infinitum given the unchanging contributions and pension pay out rates.
The effects of this policy thus can be seen to work in the opposite
direction from those established in the previous section.
The one point that emerges from this run, which need not be necessarily
evident when referring to an expansion of the duration of employment
though, is to do with unemployment. Figure 35 quite eminently depicts
that unemployment increases quite markedly as a result of this expansion.
This rise however need not be always associated with bad news for the
economy if only for two reasons: firstly, because in this case more
unemployment is not necessarily associated with less employment. The
increase in unemployment in other words takes place not because of slack
capacity or dim forecasted demand, but because there is an increase in the
numbers of the workforce. Evidently, even if employment increased
(within certain limits) unemployment should still be expected to rise. And
secondly because, as Figure 35 shows, greater unemployment levels
could reduce wage rates enabling firms to increase their profits and
consequently their investments.
49
1 4,000,000
- —-17,500
3 shell
J ee
1 fo
| —,— Unemployment
2,500,000 3 1
_ 16,300 2 —>-Wage_rates
3-0 LMell —3—Fims_money_balances
secs |
1 ——— 2
-1- 1,500,000
- 15,500 ‘ ‘ ' ‘ ‘
37 se10)
0 50 100 150 200 250
Figure 35 Expanding the duration of employment by 3 years: Plot of unemployment, wage rates,
and firms’ money balances
Such increases could in turn improve the attractiveness of domestic
products and consequently lead to greater growth.
3.3.1d Increasing pensioners’ life spans as well as prolonging the duration
of employment
Before moving on to simulations with markedly different sets of
assumptions we test the implications of jointly increasing pensioners’ life
spans as well as prolonging the duration of employment in our economy.
To enable a finer analysis we assume that both processes are initiated at
year 20 and that they are both completed within 3 years. Senior citizens
again prolong their average lifetimes by three years viz. they gain one
extra year of life for every year that goes by after the 20" year of the
simulation until year 23 is reached. The ultimate results as regards PAYG
funds may seem quite odd at a first glance since they are seen to increase
linearly (Figure 36). But no other result should be expected under the
circumstances tested in this run.
50
-- 18.0
-y- 21,000,000
-3- 5,200,000
sigs 5.0
“57 Tell
xe —, Average_remaining_lfe_of_senior_citizens
2Y¥—-2— 275 2— 2 -,-Workforce
5 —3—Pensioners
<4 —4—Support_ratio
as 20 4—4 4
Py _.PAYG_funds
-2- 19,000,000 5 -
-3- 4,000,000 $4 —_L
=a 35
— 0.0
Figure 36 Increasing pensioners’ life spans as well as prolonging the duration of employment:
Plot of average remaining life span of senior citizens, workforce, pensioners, support ratio, and PAYG
funds
An increase in the number of years one must stay in employment that
matches the increase in the average lifetime of senior citizens will always
result in a permanent increase of the support ratio since the extra years
that are gained are ultimately spent completely in extending the years one
stays in employment. Hence of course the permanent increase in the
workforce levels and the relatively unchanged number of pensioners in
Figure 36.
3.3.2 Introducing a PAYG scheme
Let us now proceed to perform the experiment previously discussed
whereby a PAYG system is introduced in an economy with no previously
established pension scheme in place. With the introduction of the PAYG
scheme at the 10" year of the simulation a 20% tax on annual wages is
imposed to pay for pensions. Employees on the other hand are assumed to
stop saving for retirement completely thereby maintaining their
consumption expenditure unchanged (since they voluntarily saved 20% of
their wages before the PAYG scheme.) Finally, the employment rate
multiplier returns to its original shape (Figure 26).
3.3.2a Constant attractiveness multiplier
For additional simplicity throughout this run we will assume that the
attractiveness multiplier stays constant at one. Capital equipment levels in
other words are assumed to rise or fall without affecting the quality of
51
domestic products. Figure 37 shows the results for total domestic
spending, total savings, and the government’s money balances due to the
PAYG scheme.
_,—PAYG_ introduction
Se (Ow rt
== BOLT _ 7 Total_domestic_consumption
3,
2, =, Total_savings
Figure 37 Introducing a PAYG scheme with a constant attractiveness multiplier: Plot of total
domestic consumption and total savings
As expected from the conventional macroeconomic analysis (section 2.4),
after the introduction of the scheme at year 10, total domestic
consumption initially increases while total savings reduce. The reason for
the short term increase in consumption of course is attributed to the ‘free
gift’ that pensioners receive by the working generations which enables
them to increase their spending. The eventual return of total spending to
its original levels is again easily explicated given the one-off nature of the
free gift. Once the ‘free gift’ is spent the economy moves back to where it
started. A complete explanation for the permanent reduction in savings
however is somewhat trickier to provide, for the answer entails a solution
to the paradoxical result that is shown in Figure 38.
52
—1—Pensioners_domestic_consumption
~~ Pensioners_money_balances
noe
Figure 38 Introducing a PAYG scheme with a constant attractiveness multiplier: Plot of
pensioners’ domestic consumption and of pensioners’ money balances
How can, as clearly shown in Figure 38, pensioners’ consumption
ultimately return to its initial levels at the same time that their money
balances fall from approximately £900 billion down to approximately
£100 billion? The answer of course is ultimately pretty simple. Initially it
will be remembered pensioners funded their consumption through the
accumulation of funds which they subsequently spent with a delay that
matched their average lifetime expectancies (viz. 15 years). After the
PAYG introduction, however, they receive a yearly income that gets
spent with only a one-year average delay. Smaller time delays reduce the
contents of stocks by increasing outflows, hence the explanation for the
dynamics both in Figure 37 and Figure 38.
Let us now explore whether any funds accumulate in government’s
coffers as a result of the PAYG scheme (Figure 39)
53
=a 7el0
oo 1e9
1
= aa
-2- 800,000,000
= ceil
-2- 600,000,000
-a- 2.8e10 —— PAYG_funds
=" eae ~7~Additional_income_taxes
oe 1.4e10 \
-2- 200,000,000 1
50 100 150 200 250
Time
Figure 39 Introducing a PAYG scheme with a constant attractiveness multiplier: Plot of PAYG
funds and of the additional income taxes required to keep the scheme in operation
The dynamics that occur in governments’ funds due to the PAYG scheme
may seem quite odd initially. Not only do they increase almost
immediately after the imposition of the PAYG scheme reaching a
maximum at year 60, but also after year 115 app. the government is
forced to levy extra income taxes on employees to keep the scheme alive.
It should be here reminded that this behaviour emerges despite the
unchanging population composition and the unchanging per person
PAYG taxes (contributions) that have to be paid in. The system in other
words moves from affluence to bankruptcy within a hundred years
without any policy or any other exogenous alterations. Its design from the
very beginning seems to be flawed.
The more obvious reasons for this kind of behaviour are depicted below
(Figure 40°) (see also section 3.3.2b)
*> Plotting in Figure 40 starts from time 10 and not form 0 to enable for a finer view of the
discrepancies between PAYG taxes and PAYG funds. So is the case also in Figure 44 and Figure 45.
54
-- 19,000,000
a 6.9210
37 6.3e10 2
al 880,000,000
ES 6.3e10 x o ig
itis
=1— Employment
f
—7- PAYG. funds
—y-PAYG_taxes
ee | ~y-Additional_income_taxes
se Hro00 008 a __—PAYG_pensions
SNTSRLSS™]'SS413'591 SF ~
“4
tt
— 0 +
> 5.ge10 {id , _, _, _,“i
= 0
— 5.8e10
0 25 50 75 100 125 150 175 200 225 250
Time
Figure 40 Introducing a PAYG scheme with a constant attractiveness multiplier. Partially
explaining the behaviour depicted in Figure 39. Plot of employment PAYG funds, PAYG taxes,
additional income taxes, and PAYG pensions
With the initial boost in total domestic consumption (Figure 37)
employment increases to meet demand. The increase in employment
however brings into the PAYG system more revenue given the
unchanging PAYG tax rate since more people are employed and more
people are taxed. The pensions that have to be paid to existing pensioners
on the other hand remain obviously unchanged. With a greater incoming
rate than before and a relatively constant outgoing rate, funds accumulate
in governments’ coffers. As time progresses and total consumption begins
to fall however, so does employment. Yet the previously increased
employment levels have in the meantime created a higher burden of
future liabilities to the system. At the time when increased pensions must
be paid out, employment is falling and the outflow naturally begins to
exceed the inflows to the PAYG scheme subsequently bankrupting the
system.
Before moving on to the next section it should be added that the long
period that it takes for the system to move from affluence to bankruptcy
can create the false impression that the initially accumulated funds
constitute permanent net gains from the transition. The temptation to
spend this ‘extra’ money carelessly can prove too great to resist especially
given the 4 or 5 five years that any one government spends in power
before the next election.
55
3.3.2b Variable attractiveness multiplier
In this run the feedback loop that was previously cut off due to the
constancy of the attractiveness multiplier is here reactivated according to
the table function presented in Figure 28. The PAYG system is again
introduced at the 10" year of the simulation. Figure 41 illustrates the
dynamic behaviour of total domestic consumption and total savings.
== 10
mye fell 1 1 1 a 1 1
-3- 4e12
.. —,—PAYG_imposition
-- «(04 3 2 1 _impositi
-2- 4e11 & —z~ Total_domestic_consumption
-3- 2e12
3 —,— Total_savings
3 lL
id oo) -—
—- 3ell
— re12 |
0
Figure 41 Introducing a PAYG scheme with a variable attractiveness multiplier. Plot of total
domestic consumption and savings
Whereas Figure 41 depicts yet again a reduction in total savings,
consumption is clearly seen to stabilise at higher levels than before.
Figure 42 demonstrates how this outcome comes about.
4 4.4e11
me L7el1
2a 4.3e10
L
=4- 86,000,000 6 4
-5- 1.24 | 4 2 —1~ Total_domestic_consumption
-e 033) | of —7~Firms_money_balances
66 3:
ee — 3 Investment_rate
= 3.2e11) | wai ae —4-—Capital_equip ment
jell |5 pp "Ss —5—Altractiveness_multiplier
fy
—_ 1
3 2e10 | | a , § —g—Propensity_to_import
-4- 60,000,000 eee
aa 1.00
gs 0.26
Figure 42 Introducing a PAYG scheme with a variable attractiveness multiplier. Explaining the
dynamics depicted in Figure 41. Plot of total domestic consumption, firms’ money balances, the
investment rate, capital equipment, the attractiveness multiplier and the propensity to import
56
The initial increase in total domestic consumption naturally boosts firms’
money balances and consequently firms increase their investments.
Higher investment rates eventually lead to an increase in capital stock
levels which enable a betterment of the domestic products’ quality which,
in turn, makes them more attractive. The greater the attractiveness of
domestic products the more the demand (captured by the reduction of the
propensity to import”’) and, in turn, the greater the firms’ money balances
closing a positive feedback loop which leads the whole economy in the
path of growth (see also Figure 19). Indeed, the positive feedback loop
effects that drive the simulation early on become clearly evident when
extending the length of the simulation for the previously graphed
variables (Figure 43).
4 Sell
a
35 5e10
-4- 140,000,000
os aad _,—Total_domestic_consumption
mez 0.34 1
_7-Firms_money_balances
=3—Investment_rate
~g-Capital_equipment
be 0.00
ae _5-Attractiveness_multiplier
3- 2e10 —g~Propensity_to_import
=- 60,000,000
ad 1.00
Hes 0.22
Figure 43 Introducing a PAYG scheme with a variable attractiveness multiplier. Extending the
plots of the variables presented in Figure 42. Plot of total domestic consumption, firms’ money
balances, the investment rate, capital equipment, the attractiveness multiplier and the propensity to
import.
Let us now explore the dynamics of the PAYG scheme funds. Figure 44
depicts the results.
°° The initial upward movement in the propensity to import takes place because of the increase in prices
(not shown) that results from the sudden increase in demand. The slight oscillations that can be seen in
the domestic consumption plots in many of the previous figures are again caused by these price
increases.
ST
=1- 19,000,000
= 13ell
=
6.5e10 2
=} "i
] a ee
f 3 33
i 3 1 1 1 1
4 _1— Employment
-1- 17,800,000
_ PAYG_funds
oii 5.2e10 = a
ae —3PAYG_taxes
6.11e10
a | —4—PAYG_pensions
-1- 17,000,000
a 0
=} 5. aseio|
nan
0 50 100 150 200 250 300
Figure 44 Introducing a PAYG scheme with a variable attractiveness multiplier. Plot of
employment, PAYG funds, PAYG taxes, and PAYG pensions
Their behaviour again seems somewhat counterintuitive. Even though
PAYG balances initially increase — as expected — from the boost in
employment, they subsequently show a definite downward trend despite
the settling of employment at permanently higher levels. Indeed incoming
(PAYG) taxes remain at permanently lower levels than pension payments
and should the simulation be extended, PAYG balances would eventually
fall to zero while extra taxation would be required thereafter to keep the
scheme alive. The employment rate multiplier in Figure 26 of course is
responsible for these results. As explained at that part of the thesis and as
Figure 26 clearly indicates, for full pensions to be paid out the average
employment rate need not equal one. This policy however can cause
outflows to exceed inflows when employment settles at permanently
higher levels than initially. This is because the initial PAYG tax rate is
calculated upon the desired replacement wage rate and the ratio of
pensioners to employees. Sticking to the initial values chosen for the
model, let us say that employment stands at 90% of the workforce levels.
Pensioners on the other hand are represented by all senior citizens. In
addition we know that if employment increases to 94%, full pensions are
to be paid out (Figure 26). Let us assume for simplicity that employment
eventually settles at those levels. Every person who subsequently retires
gets paid the full replacement rate. Since employment lies below 100% of
the workforce, the ratio of PAYG taxes to pension payments reduces
permanently. Thus the discrepancy previously observed (Figure 44).
58
Through a slight alteration in the employment rate multiplier which is
now assumed to have a slope of one for the interval of 0.9 to 1 of the
employment ratio, the different PAYG balances along with its inflow and
outflow rates are plotted below (Figure 45)
= lel
Se
=} Te10 F FPS rcs es F
2
23
\ oo ——— 23 2
; PAYG_funds
-1- 5e10 —1— PAYG
os _5~PAYG_taxes
2 pou 2 eae
ie —3—PAYG_pensions
Figure 45 Introducing a PAYG scheme, variable attractiveness multiplier but also assuming a
slightly altered employment rate multiplier. Demonstrating a deficiency of PAYG schemes. Plot
of PAYG funds, PAYG taxes, and PAYG pensions.
The results confirm our analysis. Despite the boom that was initiated in
this run because of the introduction of PAYG, the inherent deficiency of
the PAYG system that is associated with permanently higher employment
levels is clearly revealed. Of course it could always be persuasively
argued that a somewhat flawed pension system which enables permanent
growth would always be welcome especially if its flaws are very unlikely
to be revealed in anything other than simulations.
3.3.2c Positive interest rates, constant attractiveness multiplier
In this section we assume that positive interest rates are paid in according
to the accumulated cash balances thereby contributing to the consumption
of consumers by boosting their income (see Figure 22). They are set at
2% per year right from the start. In addition, the employment rate
multiplier goes back to being a 45° straight line. All remaining
assumptions are the same as with the run explored in section 3.3.2a. Let
us explore the consequences of a PAYG scheme introduction in the
simulated economy.
59
= 1.0
= 3.8e11
3° 5.3e12 Y T 1 1
~4- 19,000,000
24
—,—PAYG_ introduction
= 0.4 1
<p 2.96011 7 Total_domestic_consumption
-3 2.72812 3 Total_savings
va 15,400,000 ~g— Employment
= 0.0
- 24el1
ae 1el2
-4- 13,000,000
Figure 46 Introducing a PAYG scheme, positive interest rates, and constant attractiveness
multiplier. Plot of total domestic consumption, total savings, and employment
Here it can be seen that not only do total savings end up at much reduced
levels than initially, but so do both total domestic consumption and
employment soon after the introduction of the scheme. The initial adverse
effects that the introduction of a PAYG scheme has on savings, in
combination with the positive feedback loop that is created between
interest rates and total savings, drives the whole system into decline.
Lower savings in particular reduce the total interest paid into the accounts
of consumers and consumption reduces. Firms detecting a fall in demand
lay off personnel and employees’ money balances reduce even more. The
income subsequently received from interest rates falls further and so it
continues until eventually two negative feedback loops come into play:
the consumption from the unemployed which acts as an automatic
stabiliser, and the lower investment expenditure which has no impact on
the attractiveness of domestic firms’ products in this run.
As regards PAYG finances, they evolve in exactly the same way as in
section 3.3.2a (Figure 40) and they do so for the same reasons that were
described in that section. Further commentary is consequently omitted.
Before leaving this section it should be perhaps stressed that in traditional
economic literature the role of interest rates is not frequently associated
with the effects they may have on consumption. From the simulation runs
in this section however it is seen that such an omission can be crucial.
60
3.3.3 Transition from a PAYG to a FF system
In the last few runs presented, we consider the dynamics that emerge
through the transition from a PAYG to a FF scheme. A PAYG scheme is
assumed in operation from the very beginning of the simulation and the
transition takes place at year 10. There are assumed to be zero
accumulated funds in the government’s treasury as a result of the PAYG
scheme although any other (non-negative) number can be chosen instead.
The employed are once again considered not to save any of their funds for
retirement before the transition takes place while after the transition they
are forced to save 20% of their annual wages.
The different treatment of pension payments that is hypothesised in this
model once the transition occurs calls for a separate identification of two
distinct pensioner groups. Those who have already retired and are still
alive at the time of the transition, viz. the ‘old pensioners’, and the ‘new
pensioners’ group which comprises the workforce at the time of the
transition who will be retiring in the near future’’. After the transition,
‘old pensioners’ are assumed to continue receiving their yearly pension
payments as normal (but by the government instead of the workforce).
“New pensioners’ on the other hand receive all they are due from the
contributions they had been making under the old PAYG scheme at the
time of retirement. Different assumptions of course can be tested, yet the
ones included in this model are largely based on the actual transition
procedures as they took place in Chile (Kritzer 1996 p.47). For
determining how much money must be paid to new pensioners upon
retirement an inverse countdown is initiated from the time that the
transition takes place. The ‘new pensioners’ who will retire immediately
after the transition for example will be receiving full money”*. The ones
who will retire having spent only half of their working lives under the old
scheme will get paid half of what the aforementioned group received and
so on.
Figure 47 shows the three main magnitudes that characterise the
simulated economy assuming a constant attractiveness multiplier.
°7 A third group also arises yet it need not be treated in any special way. This final group comprises of
all those people who have not made any contributions to the old PAYG scheme either because they
were too young to work, or because they weren’t born at the time.
*8 Full money should not be confused with full replacement rates. The proportion of the replacement
rates that is to be paid, as previously noted, depends upon the average employment rate.
61
eS 3.3e12
= 3.4e11 '
i———
=3- 18,000,000 15 =
2
_,—Total_savings
- 1.62e12 1 saving
ne 2.92e11 7 Total_domestic_consumption
=3- 10,200,000 _4 Employment
it al
= 2.6e11 Kh 2 ;
Le 5,000,000 |
0 50 100 150 200 250 300
Figure 47 Transition from a PAYG to a FF scheme assuming a constant attractiveness multiplier.
Plot of total savings, total domestic consumption, and employment
Not contradicting our previous economic analysis we can see that after
the transition a strong increase in savings” is initiated while total
domestic consumption and employment initially drop. The hardships
associated with the transition thus are clearly visible. As the simulation
proceeds both employment and domestic consumption return back to
their initial levels while savings reach considerably higher levels. Despite
the broader agreement of the model’s results with traditional economic
findings, two noteworthy results emerge from Figure 47. Firstly, we can
see that savings increase in two distinct steps the first one occurring right
after the transition while the second one is initiated at approximately the
110" year of the simulation. With the benefit of hindsight it is quite easy
to explain this behaviour.
* Tn the calculation of savings government debt has not been included. Should we consider it as
negative savings then total savings initially fall.
62
Si wt *
3e124
MN a
1
2e12+4
~~ Total_savings
ee —7—Pensioners_money_balances
1e124 3,3 —3— Workforce_savings_for_retirement
a
i a ad 2
3
0. Hl +t +t +t +t +t 1
0 50 100 150 200 250 300
Time
Figure 48 Transition from a PAY G toa FF scheme assuming a constant attractiveness multiplier.
Explaining the rise in total savings. Plot of total savings, pensioners’ money balances, and
workforce’s savings for retirement
Figure 48 above shows that immediately after the transition pensioners’
money balances, along with the money balances intended to fund future
retirement, rise quite rapidly as expected. Evidently, it is the ascent of
both of these variables that is responsible for the initial boost in savings
(just like their descent was responsible for the fall in total savings in
sections 3.3.2a and 3.3.2b). For the second round of increases however, it
is employees’ money balances (Figure 49) that lead the way. As will be
remembered the assumption that has been made earlier on is that debt is
to be repaid within 100 years from its inception and that it is to be repaid
by taxes levied on employees’ income. Figure 49 shows that the need for
borrowed funds to manage the transition is greatest immediately after its
imposition both because the number of ‘old pensioners’ is greatest at that
time, and because the ‘new pensioners’ who have just retired get paid full
money.
63
3 4e12 f] 422
<g- Bell 4 a
3
% f ~~ Government_borrowing_rate
4 —7— Government_debt_repayment
_Government_debt
-3- 212 [] yf -3
-g- Sell a —4—Employees_money_balances
oy
3
Figure 49 Transition from a PAYG toa FF scheme assuming a constant attractiveness multiplier.
Explaining the two-step increase in savings. Plot of Government borrowing rate, government debt
repayment, government debt, and employees’ money balances
As borrowing starts and debt accumulates the government imposes
income taxes to start paying off the debt. It is clearly seen however that
100 years after the transition date the initially borrowed funds along with
interest surcharges are paid back in full with debt repayment starting to
drop thereafter. But a fall in debt repayment also implies a cut back on
employees’ income taxes and hence an increase in their money balances
hence of course the second rise in savings (Figure 48).
The second point that emerges from Figure 47 is that the usually
identified ‘short-term’ transition difficulties can last for a pretty long
‘short-term’ duration. In fact the implication is that the transition
difficulties should be expected to match the time it takes the government
to repay the debt it has taken to finance the transition, and that would
only enable the initiation of the recovery process. More time would be
required thereafter to match the pre-transitory employment and
consumption levels. This is not an unavoidable result however. Assuming
a variable attractiveness multiplier as we do in Figure 50 enables a much
faster recovery with both employment and total domestic consumption
levels exceeding their original levels quite quickly and quite distinctly.
64
ah 19,000,000
3
} 4ell paar
=
a ae
Employment_Constant_att
[Lye sap meumenk
_>—Employment_Variable_att
24 2 Be .
/ —3— Total_domestic_consumption_Constant_att
Neer
E } 15,400,000
=} 3.0de11 f
li 4
af 3
} 13,000,000 HH 1
=, V
ie: ~—+— 1
3 } 2 seni}
0
50 100 150 200 250 300 350 400
—4—Total_domestic_consumption_Variable_att
Time
Figure 50 Transition from a PAYG to a FF scheme. Comparison plot demonstrating a quicker
recovery process. Plot of employment and total domestic consumption levels under a constant and a
variable attractiveness multiplier
This happens of course at the expense of a greater short-term shock to the
economy as again clearly illustrated above. The reason for this kind of
behaviour can be established by examining firms’ cash balances as they
develop through time. Figure 51 shows that firms’ money balances
irrespectively of the shape of the attractiveness multiplier pick up quite
quickly after their initial fall and they soon exceed their original levels.
This happens because, as shown in Figure 51, a lessening in wage rates
occurs due to increased unemployment levels, which is not reflected back
fully through a consumption reduction for two reasons: firstly because
30% of employees’ consumption is directed to imports and secondly
because consumption from the unemployed rises when more people
become unemployed, and given a reduced cost structure more profits can
be realised.
65
a
a
, am
j By —1—Firms_money_balances_Variable_att
2
Ng ~~ Firms_money_balances_Constant_att
4 41 ;
3 1-3 Wage_rates_Variable_att
\ —4—Wages_rates_Constant_att
3
3.
100 150 200 250 300 350 400
Time
Figure 51 Transition from a PAYG to a FF scheme. Comparison plot demonstrating the different
effects that prevail under a constant and a variable attractiveness multiplier scenario. Plot of
firms’ money balances and wage rates.
We can see therefore that accepting a cut in wage rates can in principle
allow for a faster and stronger recovery later on in the simulation. Indeed,
the output depicted in Figure 52 verifies our assertion. Assuming constant
wage rates, both for the case when the attractiveness multiplier is a
straight line and when it is made a variable, we can see that the adverse
effects in our chosen variable (employment) are much more severely felt.
20,000,000
ag 34-34 3
p12
4
zi ~~ Employment_Constant_att_Variable_wage_rates
aS et
a — 2 Employment_Constant_att_Constant_wage_rates
2°) 11,600,000
eee 3 Employment Variable_att_Constant_wage_rates
= —g— Employment Variable_attVariable_wage_rates
ae
- 3
2 6,000,000 4
ces
iia
0 100 200 300 400
Time
Figure 52 Transition from a PAYG to a FF scheme. Comparison plot demonstrating the
importance of wage rates with regard to employment. Plot of employment levels under constant and
variable attractiveness multiplier scenarios, and under constant or variable wage rates.
66
But this may be questioned. Figure 52 makes clear that the previous
assertion holds only if the extra funds that firms will be making by
reducing employees’ wages are spent on profitable investments which
will enable future growth. If that money is misused instead, both the
recovery takes longer to materialise and the transition shock is greater.
With regard to the initial steeper fall of employment and consumption
when the attractiveness multiplier is made variable, it should be expected
to materialise given the initial lessening of firms’ money balances. Such a
drop leads unsurprisingly to an early reduction in investment which
causes in turn a fall in capital equipment and therefore in the
attractiveness of domestic goods as Figure 53 shows, further exacerbating
the fall in domestic consumption.
+ 1.05el
= 3e10
=3- 65,000,000 (]
— 1.05
-———
4 a. —1—Firms_money_balances
aS aes Investment_rate
a 1.8e10 = =
-3- 53,000,000 (| =3— Capital_equipment
47 0.90 Nee —4Altractiveness_multiplier
a= 7.5e10
ae 1e10
-3- 45,000,000
ge 0.80
Figure 53 Transition from a PAYG to a FF scheme. Explaining the initial steeper fall of
employment and consumption when the attractiveness multiplier varies. Plot of firms’ money
balances, the investment rate, capital equipment, and of the attractiveness multiplier
Finally, it should be noted that despite the similarities of this model’s
output with the expectations that emerge from a traditional economic
analysis as regards some of the ultimate transition effects, the reasons that
explain those results are quite distinct. Growth in neoclassical models is
attributed to the accumulation of savings whereas growth in this model
ultimately rests upon firms’ profits and consumption.
67
4 CONCLUDING REMARKS
In this chapter we have attempted to verify the importance of pension
economics, to highlight some of its main problems and to widen our
understanding of the issues involved. A system dynamics model has been
formulated to allow for a systemic analysis of this issue under realistic
assumptions and to enable the exploration of multiple scenarios along
with the identification of the main transitory dynamics that would result
from different policies. A number of novel findings have been presented
and explicated by the model, including for example how funds may
accumulate or disperse in PAYG schemes despite unchanging policies,
and how permanent economic growth can emerge as a result of a PAYG
scheme introduction. The importance of three parameters, namely that of
the employment rate multiplier, the attractiveness multiplier and the
interest rates has also been clearly highlighted. Interest rates in particular
have come to the forefront of the analysis not in their usual investment-
defining role but rather as consumption determinants demonstrating quite
clearly the pitfalls involved if they are not explicitly so considered.
Finally the transition from a PAYG to a FF scheme has also been
modelled and despite ultimately producing the same effects as those
predicted by standard economic theory, different reasons are identified as
responsible for bringing them about.
It is important to stress finally that despite the many scenarios that have
been tested in this paper the model allows for still more simulation
experiments to be made. Productivity increases for example have not
been considered at all despite the simplicity with which they could have
been introduced in the analysis, especially if we assumed them to be
exogenous. Interest rates have been assumed not to exert any influence on
the decisions of firms to invest whereas we could have easily include
them in and so on. Accordingly, many different possible combinations
can be made of assumptions that have been considered in this paper but
have not been put together. For example the model easily allows for
modelling a situation of rising birth rates occurring at the same time that
life spans prolong in an economy whose consumption is strongly
dependent upon the interest rates they earn on the savings they have and
so on. Our initial goal of building a flexible model that can handle all
these tests thus appears to have been broadly met.
On a final note it should be reminded that this model simply enables a
greater understanding of the effects different pension policies may have
68
upon an economy. The model’s highly aggregated structure along with
the vast complexity of the real economic system and the inherent
unpredictability of people’s behaviour cannot allow for any sort of
forecasts to be made especially given the time duration involved with
pension related manners. The usual practice of many economists to make
grossly unrealistic simplifying assumptions in their models’ structures
and to subsequently attempt to calibrate them as accurately as possible, as
though it was numerical accuracy that prevented them from achieving
perfect forecasts remains a mystery to this author. Table 4 summarizes
the main findings from this model-based analysis.
Table 4 Summary of the main findings
Section Main hypotheses Main results
PAYG in place from very
beginning; attractiveness
331 multiplier constant at 4“ nla
employment rate multiplier
straight line with a unitary
slope
e Worsening PAYG
20% step decrease in birth finances
3.3.1a ,
rates e Short term increase of
pension payments
33.1b Increasing pensioners' life |e Worsening PAYG
~ spans finances
e Never-ending
Prolonging the duration of improvement of PAYG
333.1¢ finances
employment :
e Increase in
unemployment
Prolonging pensioners' life
spans as well as the |e Never-ending
3.3.1d duration of employment] improvement of PAYG
for three years in both] finances
cases.
Introducing a PAYG
332 scheme; __ restoring ; the nla
employment rate multiplier
to its original shape
69
Constant attractiveness
e Reduction in savings
e Transitory increase in
spending and
3.3.2a wae employment
multiplier
e PAYG system moves
from affluence to
bankruptcy
e Reduction in savings
e Permanently higher
consumption levels
33.2b Variable attractiveness e Beneficial effects for the
multiplier economy
¢ Deficiency associated
with the employment
rate multiplier
Positive interest rates;
constant attractiveness | | Adverse effects for the
3.3.2 multiplier; employment
rate multiplier straight line economy
with a unitary slope
e Consumption and
employment levels
reduce after the
Transition from a PAYG to | transition yet ultimately
3.3.3 a FF system; constant; they reach their initial
attractiveness multiplier
levels
e Savings increase and the
process takes place in
two distinct steps
Variable
multiplier
attractiveness
e Quicker recovery if
firms' funds are invested
properly.
e Steeper initial reduction
in employment and
consumption
70
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