E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9
86

Submitted  
04/2015

Accepted for  
publication 
07/2015

European Integration Studies
No. 9 / 2015
pp. 86-99
DOI 10.5755/j01.eis.0.9.12798 
© Kaunas University of Technology

Criteria for 
Sustainability of Old-
Age Pension System 
Based on the NDC 
Principles

EIS 9/2015

Abstract

Criteria for Sustainability of 
Old-Age Pension System 
Based on the NDC Principles

http://dx.doi.org/10.5755/j01.eis.0.9.12798

Inara Dundure, Maris Pukis
University of Latvia. Aspazijas blvd.5, LV -1050, Riga, Latvia

The topicality of the research subject. The foundations of the old-age pension scheme based on notional 
accounts, also referred to as the “notional defined contribution” or “non-financial defined contribution” 
(NDC) old-age pension scheme, were laid in Sweden in 1994, when the prevailing view was that a sus-
tainable defined-contribution PAYG old-age pension scheme is impossible.
Since then, the NDC system modifications have been implemented in several countries; since 2000, this 
scheme is also part of the Latvian pension system and works significantly better than the other part of 
the pension system - the funded pension scheme. However, the sustainability of NDC scheme is still 
being questioned.
To prevent the NDC pension system sustainability problems, the authors (Pukis, M., & Dundure, I., 2012) 
in their publication “The Sustainability of the Pension System in Latvia” and (Dundure, I., 2015), the article 
“Sustainable Old-age Pension System by Developing Notional Defined Contribution Pension Scheme” 
have proposed a modified NDC model that provides sustainability of the pension system considering the 
known risks inherent in the pension system.
The aim of the paper is to research and analyse the conditions for building a sustainable pension system 
by developing a Notional Defined Contribution pension scheme and working out an adjusted (modified) 
old-age pension calculation formula.
In order to achieve the above mentioned aim, the authors set the following tasks:

 _ Define the old-age pension system based on NDC principles;

 _ Define the primary objectives of pension systems and perform analysis of pension adequacy;

 _ Define the conditions for achieving a sustainable old-age pension system based on NDC principles;

 _ Develop an adjusted (modified) old-age pension calculation formula based on NDC principles.
In order to achieve the established aim and tasks, the following scientific research methods have been used in 
the work: analytical method, comparative method, logically and abstractedly constructive method.
The analytical method and the comparative method are employed for conducting pension adequacy 
analysis and examination of pension capital indexation and indexation of pensions after retirement, as 
well as for the purpose of studying the Notional Defined Contribution pension system. The logically and 
abstractedly constructive method is employed for making forecasts and defining the main research 
results – the conditions for ensuring pension system sustainability that have been determined by the 
authors in the course of the research.
The authors proved that by basing on the principle of generation solidarity and equity and through 
improvement of NDC pension calculation formula, it is possible to create the old-age pension system, 
which would be capable of excluding the old-age pension instability causes.

KEYWORDS: Sustainability of pension system, NDC, pension model. 
JEL code: H55



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The old-age pension system should be financially stable (robust) in the changing demographic 
and economic environment and at the same time display cross-generational equity (fairness) 
and equity among various income groups by diversifying economic and demographic risks. 
Scholars researching the pension sphere consider that the “Non-financial defined contribution” 
(NDC) scheme has a number of advantages over PAYGO systems, one of these being stable. 
Pension scheme of the NDC type ensures known level of fiscal stability because the promised 
profitability reflects the PAYGO characteristics, which form the basis of the programme rather 
than are based on the rate of return from investment operations on the market.

The authors of the paper analyse the principles of operation of the NDC-based pension system. The 
paper highlights the primary goals of pension systems, the adequacy or sufficiency of the pension 
income and the provisions for ensuring sustainability of the pension system based on NDC principles. 

Basing on the NDC structure, the principles of solidarity, equity and voluntariness as well as the 
defined provisions, the authors of the paper propose to introduce changes in the pension calculation 
method to ensure financial, political and social sustainability of the NDC old-age pension system.

According to the proposed model, the virtual retirement system is used for calculation of the 
pension capital, where in the annual indexing not only the amount of tax that is assigned for 
old-age pensions is taken into account, but also the demographic changes (the changes in the 
number of the deceased and the new pensioners).

The paper shows that it is possible to achieve political stability if the two conditions are met. First, in 
the same way as in another physical or notional models of the funded pension systems, the system 
needs to be supplemented with a minimum guaranteed pension for those individuals, who have not 
been able or have not been willing to accumulate pension capital. Secondly, it is deemed necessary to 
keep explaining the motives for accumulation during the entire working life of a contributor.

The paper demonstrates stability of the model in respect of the key known risks immanent to 
pension systems: 

Introduction

1 the scheme is stable against the risk of 
aging population, because it provides a 
reasonable level of income regardless of 
demographic changes;

2 the scheme is stable against the economic 
crisis, because the proposed universal in-
dexing allows to ensure  improvement for 
all participants in equal measure; 

3 the scheme is stable against the risk of de-
fault, because it stimulates each scheme 

participant to make the maximum contri-
bution every year;

4 the system is stable against the insuffi-
ciency of the pension during the time after 
retirement, because the universal indexing 
procedure is equally applied to both the pe-
riod of accumulation and the payout period;

5 the scheme stimulates an earlier start of 
the work life and later retirement, thus 
minimizing the amount of funding required 
to ensure sustainability of the system.

The authors proved that by basing on the principle of generation solidarity and equity and through 
improvement of NDC pension calculation formula, it is possible to create the old-age pension 
system, which would be capable of excluding the old-age pension instability causes.

The “Notional accounts” old-age pension schemes - the so-called “Notional contribution” or 
„Nonfinancial defined contribution” (NDC) old-age pension schemes were first introduced in 
Sweden in 1994, at the time when it was predominantly considered that a sustainable defined 
contribution PAYG old-age pension scheme is hardly ever possible to achieve. The new Notional 
accounts old-age pension scheme proved that it is still possible to build a sustainable old-age 
pension system that would be based on PAYG principle.

Ten years later, being encouraged by Sweden’s example many other countries introduced a new 
NDC model. In Latvia, the NDC reform was formulated and provided a legal basis on the 1st of 

Description of 
the Notional 
defined 
contribution 
(NDC) old-age 
pension scheme



E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9
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January, 1996; in Italy the NDC scheme was introduced in 1995; Poland also started its NDC 
reform in 1999. NDC can be also found in the reformed pension systems of other countries, for 
example, in 2002 the NDC pension scheme was introduced in Russian Federation, Norway and 
Kyrgyzstan (Holzmann, R., & Palmer, E., 2003).

Similar to any old-age pension system, upon joining the NDC old-age pension scheme, a par-
ticipant goes through the two phases, which approximately correspond to the periods of work 
and retirement. During the period of work an individual’s payroll tax is transferred to the virtual 
account. Similar to an individual account within the framework of the actual DC scheme, a certain 
value is set to a virtual account within the NDC scheme, which increases every year thanks to 
the made contributions and the interest yield, accrued on the account balance. Unlike the balance 
of funds on an individual account under the DC plan, the NDC individual accounts are notional 
because the financial information on the accruals is virtual and the rate of return is based on 
the internal growth rate of the system. When a person retires, he/she receives a pension benefit 
(annuity), which is based on the notional accrued pension amount at the time of retirement (Au-
erbach, A.J. & Lee, R., 2006).

Social insurance contributions made by the employed in a certain year are used to pay out old-
age pensions to existing retirees. The government defines the contribution rate applicable to the 
employment and self-employment earnings by observing the following principle: the contribu-
tion rate for all generations is the same and the contributions are made either by individuals or 
by the employers in the name of such individuals. 

The age, at which individuals become entitled to use the accumulated notional capital upon re-
tirement, i.e., to receive fixed pension payments (annuities) from the pension plan, differs in dif-
ferent countries. The rules for paying out annuities are dependent on the mortality rate at the 
time when a certain generation  reaches the age of retirement stipulated by legislation (for exam-
ple, 65 years), and on the interest yield earned by a particular pension plan, which may be accrued 
at the same rate that was used during the pre-retirement accumulation phase.

Researchers, Holzmann, R., Palmer, E. & Robalino, D., et.al., (2012), who study pension sphere, 
consider that the NDC scheme possesses a number of potential advantages over PAYGO sys-
tems, and one of these is stability. A pension scheme of a NDC type ensures a fair level of finan-
cial stability because the promised yield reflects the PAYGO characteristics, which form the pro-
gramme basis, rather than is based on the rates of return obtained from investment operations 
on the market. The aim of the NDC system is to imitate a funded DC system structure, and, at the 
same time, to ensure financial stability by using a relevant internal rate of return (keeping in mind 
also the context of a fragile situation), rather than the market rate of return.

In order to ensure political sustainability of the pension system – adherence to the principals of 
pension adequacy and equity towards members of the community - international organisations 
and national lawmakers advocate the policy shift away from the PAYG system towards the pri-
vate, primarily pre-paid pensions. That is mainly supported by economic considerations about 
the fiscal austerity of financial sustainability of the ageing community and promotion of the de-
velopment of financial and capital markets in order to facilitate economic growth.

As a result of pension reform, over the recent decades the size of the state pension has decreased, 
the pension qualification age has been raised and privately funded pensions became more widely pro-
moted. However, Schludi, M., (2005) being affected by the economic and financial crisis, the majority 
of the EU member states experienced an economic downslide or economic recession followed by an 
increase in social expenditure. The state budget deficit (and debts) only further increased the pressure 
on pension schemes, because these had to be at least partially financed from the state budget. 

Primary 
objectives 
of pension 

systems 
and the 

essence and 
objectives 
of pension 
adequacy



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Natali, D., (2010) writings about pension policies demonstrate agreement of the opinion on the 
fact that pension programmes (both in the state and private sector) are not protected from the 
aftermath of economic downslide and financial crisis. 

When analysing the implemented pension reforms, the authors of the article came to the conclu-
sion that, although the reforms sought to promote sustainability, the adequacy of the retirement 
income or pension sufficiency is pretty often being neglected and does not become the subject 
of public debate, mainly for the reason that poverty in the old age no longer seems a pressing 
issue in the European countries with advanced welfare systems. Although the level of poverty 
and the inequality of incomes differ in various European countries, at large, they demonstrate 
a tendency to grow - in many places the state pensions continue to decrease in size, whereas 
reliance on voluntary contributions in private pension funds is increasing. Financial crisis of 2000 
and the financial tumbledown of 2008-2009 brought to the surface the problems related to fund-
ed pensions – their inability to provide the expected yield. These changes brought out the key 
points concerning the growing role of private pensions: whether retreat from the public (state) 
responsibility leads to a higher private initiative, which is supposed to fill in the future old-age 
income gaps? To what extent the risk of ensuring the retirement income is transferred upon an 
individual, and whether the inequality of incomes will continue to grow?

If we look back at the primary goals of the pension system, then, according to Holzman, R., Hinz, 
R.P., & Dorfman, M., (2008)  the primary goals of any pension system should be to provide ade-
quate, affordable, sustainable, fair and predictable old-age pension, while seeking for the possibil-
ities to maximise the overall community welfare in a manner appropriate to the individual country. 
An adequate system is one which provides benefits to the full breadth of the population that are 
sufficient to prevent old age poverty on a country specific absolute level in addition to providing a 
reliable means to smooth lifetime consumption for the vast majority of the population. 

The essence of pension adequacy in the EU pension policy documents is determined in the fol-
lowing way: 

Securely financed adequate income that does not destabilise public finances or impose excessive 
burden upon future generations, while maintaining fairness and solidarity and responding to the 
changing needs of individuals and society (Social Protection Committee, 2000). 

EU member states have undertaken to ensure adequate and sustainable pensions guaranteeing 
appropriate pension arrangements for all individuals and the opportunity to receive the pension 
that would allow them to maintain the reasonable living standards after retirement in accordance 
with the principles of intergenerational solidarity and fairness.

The European Commission (2001) defines the following pension adequacy objectives:

The pension system should ensure that all older people enjoy a decent living standard, share in 
the economic well-being of their country and participate actively in public, social and cultural life.

After retirement due to old age or invalidity or in case of a breadwinner loss, maintain the living stan-
dard of an individual’s choice, by providing to all individuals access to proper pension arrangements.

These objectives European Commission (2003) were further specified as:

 _ preventing social exclusion;

 _ enabling people to maintain the accus-
tomed living standards, and

 _ promoting solidarity between generations. 

The Council of the European Union (2001) singles out the three basic principles for ensuring 
the long-term sustainability of pension system, which are adequacy, financial sustainability and 
adaptability to change. 



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90

Borella, M., & Fornero, E., (2009) suggested that it is important to build a proper and fair relation 
between contributions and benefits since the sufficiency of income is the key objective of pension 
system. Whereas, the UK pension institute researchers Redwood, D., Carrera, L., Armstrong, J., 
& Pennanen, T. (2013) with reference to retirement income express an opinion that there are two 
major definitions of adequacy: first, to what extent does the pension income enable individuals 
to meet their basic needs at retirement, and, second, to what extent the pension income is able 
to ensure the living standard compared to the income received during the working life. While the 
first definition is given in order to apply the minimum guaranteed income standards and prevent 
the risks of poverty in the old age, the second definition is designed to evaluate the adequacy by 
analysing the replacement rate. For evaluation of the pension income adequacy the authors use 
one of the dimensions – the wage replacement rate. There is one matter, which does not cause 
any controversy of opinion - the pension system should be build in a way to protect individuals 
from poverty, as well as to enable them to maintain their former living standards. 

Based on the conducted analysis and performed computations, the authors concluded that the 
replacement rate (%) in Latvia for the newly awarded pensions in relation to the average insur-
ance contribution wages was 38% in 2007, 44% - in 2008, 60% in 2009, 64% - in 2010, 58% - in 
2011, 52% - in 2012 and 38% - in 2013. 

Studies of the replacement rate in Latvia in the context of the influence of all the three levels lead 
the authors -Pukis, M. & Dundure, I. (2012) - to the conclusion that given the existing pension 
system in Latvia  the theoretical replacement rate of 70% for the old-age pensions in Latvia in re-
ality is an unattainable objective. For a sustainable pension system it is necessary to ensure that 
senior citizens would not be affected by the poverty risk and could enjoy a decent living standard. 

An old-age pension system must be financially stable in a changing demographic and economic 
climate, and at the same time it should create fairness among generations and income groups 
by diversifying the economic, financial and demographic risks.

The basic building block of political sustainability of the pension system is adherence to the prin-
ciple of fairness (equity) towards community members. In theory, a fair pension system is the 
one, which ensures redistribution of income from the financially robust in favour of the poor in 
accordance with the society priorities, furthermore, does that in such a way so that no burden is 
laid upon the rest of the community members, who do not participate in the system. The princi-
ple of fairness (equity) is also ensured by a direct link between the contributions and the pension 
level within the context of NDC, since individuals are rewarded with a higher pension for every 
additional contributed monetary unit. Contribution of each insubstantial unit creates equal pen-
sion rights. This principle that ensures horizontal equality is at the root of NDC representation, 
which implies that it is based on the principle of fairness (equity). 

On the macroeconomic level, fairness with respect to future generations and long-term financial 
stability are dependent on the real-life system build-up (structure) and the system’s susceptibility 
to demographic and economic changes. 

A well-functioning institutional system is also fundamental for a stable pension system, i.e., the 
government plays a significant role in any pension system. All pension systems to a large extent 
depend on the technical capacity of the public sector. As for the NDC pension system Holzmann, 
R. & Palmer, E. (2003) argue that it includes the ability to collect taxes and contributions, the 
ability to track the mobility of employees and, what is most important, the ability to monitor the 
contributions over a long time period and to forecast the volume of further contributions and 
benefits with a sufficient accuracy. 

Conditions 
for achieving 
sustainability 

of the old-
age pension 

system 
based 

on NDC 
principles



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NDC pension schemes may achieve the desired results only on the provision that the system is 
well developed and implemented in the right manner, by providing: 

 _ economic stimuli to individuals to stay on 
the labour market;

 _ flexibility in making retirement decisions;
 _ visibility (predictability) of distribution;
 _ motivation to pay taxes;
 _ mechanisms, which ensure financial equi-
librium;

 _ stability amid the economic crisis; 

 _ ability to withstand the impact of demo-
graphic changes;

 _ observation of the principle of fairness  
(equity) and solidarity.

Proceeding from the NDC structure, the principles of solidarity, fairness and voluntariness and 
the above mentioned provisions, the authors of the article propose to introduce changes in the 
method of calculating pensions to ensure long-term financial, political and social sustainability 
of the NDC old-age pension system.

In development of the new formula for calculating the old-age retirement benefits the authors 
proceed from the NDC pension system operation principles. Specifically, for each contributor 
- payer of social insurance - an individual account is established, which registers information 
on paid contributions. Interest income is accrued on the account balances, and a pension plan 
announces the amount of interest yield on an annual basis. Notional contributions are paid into 
the mentioned accounts throughout the lifetime, thus reflecting the actual taxes and payments. 
Together with the announced yield the notional contributions make up the value of such account 
at any given point of time. This information enables to perform calculation of the appropriate size 
of an individual’s pension benefit at the time of retirement.

The basic elements of the proposed model are similar to that of Swedish and Latvian NDC model, 
however a range of peculiarities of the suggested solution allows to prevent all currently known 
instabilities against internal or external factors. Describing the proposed model with the help of 
the formulas, the authors chose a number of description principles: 

Modified 
(adjusted) 
old-age 
pension 
calculation 
formula 
based 
on NDC 
principles

1 small letters define an individual pension-er or an individual contributor;
2 capital letters define the figure country wise;

3 small indexes define the year or the ordi-nal number;
4 superscripted indexes are not meant for summing up or multiplying, these are 
applied for characterisation purpose only.

Further description refers solely to the old-age pension accrued within the NDC system. Sources 
of the social (minimum) pension benefit, which should be provided in any case, are not reviewed, 
because there always be found certain individuals, who failed to accrue virtual pension.

In the consecutive year marked with the index k, a payer of social tax (payroll tax) pays a certain 
amount deductible from his tax, which is directed to old-age pension:

Where the notations used are:

s
ik
 – i-th payer’s contribution in the k-th year;

w
ik
 – i-th payer’s taxable income (wage) in the 

k-th year;

(1)

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

(all formulas, except the fourth, created by authors Dun-
dure, I.,& Pukis, M., (2015))

L – the contribution rate applied to taxable income directed to old-age pension (in Latvia’s case - 
the rate L=20% is applied to those, who do not participate in the creation of the funded pension). 



E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9
92

The total contribution during a year is the sum of all payments performed by the payers in that 
year - S

k. 
This amount in the consecutive year can be forecasted with a pretty high level of accu-

racy. In contrast to other NDC models, here we introduced the equilibrium (balance) of contribu-
tions and payoffs.  

Whereas P
k
 is the amount of pension in the k-th  

year, which consists of individual pensioners’ old-age  
pensions. 

Where the notations used are:
k

i,k+1 
  – the ith pensioner’s pension capital in the fore-

casted year; 

(Formula (4) in accordance with Article 12 of the Law 
“On State Pensions“, Latvia.) 

(2)

(3)

(4)
5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

Formula (2), unlike the generally accepted payment procedure, shows the volatile nature of the 
amount of pensions in payment: depending on the aggregate contributions and the change in the 
number of pensioners, the size of the pension calculated for each consecutive year’s changes. If 
the volume of contributions by working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed amount, the size of the pension 
would also decrease. Until now, the traditional view was that an individual has “earned” a partic-
ular pension amount. In such a case the pension changes alongside with the changing amount 
earned by the respective generation of wage earners.

In the proposed model, similar to other NDC models, every i-th payer of social tax accumulates 
the pension capital from year to year, increasing it by means of his contributions s

ik, 
however, the 

earlier contributed sum is indexed. The novelty is the introduction of a general-purpose index I
k
, 

which can be equally applied to pension capital accumulation and for indexing earlier awarded 
old-age pensions.

Pension capital of an i-th taxpayer is accumulated every year by the following formula

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

Pension in the year of retirement D is calculated by the formula 

I
k+1 

 – the general-purpose (universal) index forecasted for the kth year; 

k
ik  

–
 
the ith pensioner’s pension capital in the kth year; 

s
ik  

 – the ith contributor’s payment in the kth year. 

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

From now forth the pension is indexed by the formula: 

Where the notations used are:

p
iD 

–
 
 ith pensioner’s pension in the year of retirement; 

k
i
 – ith pensioner’s accrued pension capital in the year of retirement; 

G
i 
– ith pensioner’s forecasted average life expectancy in the year of retirement is a function of age 

and statistical data for a particular year. 

Where the notations used are:
p

i,k+1
  – the ith pensioner’s pension in the k+1th year 

(forecast); 
(5)

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

I
k+1    

– a general-purpose (universal) index in the k+1th year; 

p
i,k  

 – the ith pensioner’s pension in the kth year.



93
E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9

Annually indexed pension in the n-th year after retirement 

Where the notations used are:
p

i,D+n  
-the  i- pensioner’s pension in the year n-th year 

after retirement;
(6)

The annual general-purpose (universal) index is calculated by the formula:

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

p
iD  

– ith pensioner’s pension in the year of retirement; 

I
m  

 – the universal index.

The value α
k
 is determined by taking into account the solidarity provision (2) and the changes in 

the number of pensioners in the kth year, i.e., the pension benefits unpaid to deceased pensioners 
in a certain year and pensions in payment to new pensioners in the same year are taken into 
consideration. Although the value of α

k 
is small, still, it does reflect demographic changes.

The α
k
 value is calculated in the following way:

Where the notations used are:
S

k   
– the sum of social insurance contributions in the 

kth year; 
(7)

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  

S
k-1 

– the sum of social insurance contributions in the preceding year. 

Where the particular expenditure items are forecasted 
every year:

M
kP∆   – pensions unpaid to deceased pensioners in the 

kth year; 
J

kP∆   – pensions in payment to the new pensioners in 
the kth year; 

(8)

In this article sustainability is illustrated as stability against the major known risks, which may 
cause insolvency or dissatisfaction of recipients of the old-age pensions. 

Political stability

The major risk associated with the proposed model lies in the political stability. While the impact 
of the political factors can be set off through optimisation of the sources of pension resources 
and improved distribution, political stability strongly depends on the perception of justice present 
in the community, which may be both subjective and shifty.

The proposed model provides that every old-age pensioner receives the pension, which source 
is the generation solidarity. There are no major problems associated with this aspect, since in 
many developed countries for almost a hundred years this has been a time tested and well prov-
en principle of funding, therefore it should not cause any notably negative public attitudes.

At the same time, the pension size is proportional to the life-long contribution. Crucial signif-
icance is attributed to the amount that has been contributed over the working life rather than 
to time in employment or other factors. The wage amount at any given point of time is not 
that important (for example, at the time of retirement or at any time shortly before retirement). 
Those, who have been paying a lot for several years and those, who have been contributing small 
amounts for many years will receive pensions equal in size.

5 

In the consecutive year marked with the index k, a payer of 
social tax (payroll tax) pays a certain amount deductible from his 
tax, which is directed to old-age pension: 

ikik Lws =                 (1) 
 (all formulas, except the fourth, created by authors Dundure, I.,& 
Pukis, M., (2015))  
Where the notations used are: 
 sik – i-th payer's contribution in the k-th year; 
 wik – i-th payer's taxable income (wage) in the k-th year; 
 L – the contribution rate applied to taxable income directed to 
old-age pension (in Latvia's case - the rate L=20% is applied to 
those, who do not participate in the creation of the funded 
pension).  

The total contribution during a year is the sum of all payments 
performed by the payers in that year - Sk. This amount in the 
consecutive year can be forecasted with a pretty high level of 
accuracy. In contrast to other NDC models, here we introduced 
the equilibrium (balance) of contributions and payoffs.   

kk SP =                  (2) 
Whereas Pk is the amount of pension in the k-th year, which 

consists of individual pensioners' old-age pensions. Formula (2), 
unlike the generally accepted payment procedure, shows the 
volatile nature of the amount of pensions in payment: depending 
on the aggregate contributions and the change in the number of 
pensioners, the size of the pension calculated for each 
consecutive year’s changes. If the volume of contributions by 
working individuals grows, the earlier calculated pension may go 
up as well, and vice versa. With the decrease of the contributed 
amount, the size of the pension would also decrease. Until now, 
the traditional view was that an individual has "earned" a 
particular pension amount. In such a case the pension changes 
alongside with the changing amount earned by the respective 
generation of wage earners. 

In the proposed model, similar to other NDC models, every i-
th payer of social tax accumulates the pension capital from year 
to year, increasing it by means of his contributions sik, however, 
the earlier contributed sum is indexed. The novelty is the 
introduction of a general-purpose index Ik, which can be equally 
applied to pension capital accumulation and for indexing earlier 
awarded old-age pensions. 

Pension capital of an i-th taxpayer is accumulated every year 
by the following formula 

ikikkki skIk += ++ 11,               (3) 
Where the notations used are: 
ki,k+1   - the ith pensioner's pension capital in the forecasted year;  
Ik+1  - the general-purpose (universal) index forecasted for the kth 
year;  
kik  - the ith pensioner's pension capital in the kth year;  
sik   - the ith contributor's payment in the kth year.  

Pension in the year of retirement D is calculated by the 
formula  

i

i
iD G

k
p =                (4) 

 (Formula (4) in accordance with Article 12 of the Law "On 
State Pensions“, Latvia.)  
Where the notations used are: 
piD -  ith   pensioner's pension in the year of retirement;  
ki – ith   pensioner's accrued pension capital in the year of 
retirement;  
Gi – ith   pensioner's forecasted average life expectancy in the year 
of retirement is a function of age and statistical data for a 
particular year.  

From now forth the pension is indexed by the formula:  

kikki pIp ,11, ++ =                 (5) 
Where the notations used are: 
pi,k+1  - the ith pensioner's pension in the k+1th year (forecast);  
Ik+1    - a general-purpose (universal) index in the k+1th year;  
pi,k   - the ith pensioner's pension in the kth year. 

Annually indexed pension in the n-th year after retirement  

              (6) 
Where the notations used are: 
pi,D+n  -the  i- pensioner's pension in the year n-th year after 
retirement; 
piD  - ith   pensioner's pension in the year of retirement;  
Im   - the universal index.  

 The annual general-purpose (universal) index is calculated 
by the formula: 

)k
k

k
k S

S
I α−=

−

1(
1

              (7) 

Where the notations used are: 
Sk   - the sum of social insurance contributions in the kth year;  
Sk-1 – the sum of social insurance contributions in the preceding 
year;  

 The value αk is determined by taking into account the 
solidarity provision (2) and the changes in the number of 
pensioners in the kth year, i.e., the pension benefits unpaid to 
deceased pensioners in a certain year and pensions in payment 
to new pensioners in the same year are taken into consideration. 
Although the value of αk is small, still, it does reflect 
demographic changes. 

The αk value is calculated in the following way: 








 Δ
−








 Δ
−

−=

−1

1

1
1

k

J
k

k

M
k

k

P
P
P
P

α             (8) 

Where the particular expenditure items are forecasted every 
year: 

M
kPΔ     - pensions unpaid to deceased pensioners in the kth year;  Pk  – pension amount in the k

th year; 

P
k-1 

–
 
 pension amount in the preceding year. 

Stability 
(robustness) 
of the 
proposed 
NDC model



E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9
94

It follows from the above formulated model that contribution in the pension capital made every 
year of the working life is proportional to relative wage (taxable income) of the i-th contributor 
(payer) in the k-th year:

Where the notations used are:
w

ik
 – taxable income (wage) of a certain i taxpayer 

in a certain k year;

Where the notations used are:
L – social security rate on taxable income directed 
to old-age pensions;

(9)

(10)

Wage replacement rate for a certain pensioner i in the year of retirement is calculated by the 
following formula created by the author.

6 

J
kPΔ    - pensions in payment to the new pensioners in the kth 

year;  
Pk  - pension amount in the kth year;  
Pk-1 –  pension amount in the preceding year.  

 
5. Stability (robustness) of the proposed NDC model 
 In this article sustainability is illustrated as stability against 

the major known risks, which may cause insolvency or 
dissatisfaction of recipients of the old-age pensions.  

 
5.1.  Political stability 
The major risk associated with the proposed model lies in the 

political stability. While the impact of the political factors can be 
set off through optimisation of the sources of pension resources 
and improved distribution, political stability strongly depends on 
the perception of justice present in the community, which may be 
both subjective and shifty. 

The proposed model provides that every old-age pensioner 
receives the pension, which source is the generation solidarity. 
There are no major problems associated with this aspect, since in 
many developed countries for almost a hundred years this has 
been a time tested and well proven principle of funding, therefore 
it should not cause any notably negative public attitudes. 

At the same time, the pension size is proportional to the life-
long contribution. Crucial significance is attributed to the amount 
that has been contributed over the working life rather than to time 
in employment or other factors. The wage amount at any given 
point of time is not that important (for example, at the time of 
retirement or at any time shortly before retirement). Those, who 
have been paying a lot for several years and those, who have been 
contributing small amounts for many years will receive pensions 
equal in size. 

It follows from the above formulated model that contribution 
in the pension capital made every year of the working life is 
proportional to relative wage (taxable income) of the i-th 
contributor (payer) in the k-th year: 

              (9) 
Where the notations used are: 
wik  – taxable income (wage) of a certain i taxpayer in a certain 

k year; 
- the average taxable income (salary) k-th year of payers.

 Pursuant to the adopted pension capital indexing system, the 
pension capital accumulated till the year of retirement is 
presented as follows: 

         (10) 
Where the notations used are: 

L – social security rate on taxable income directed to old-age 
pensions; 

   –  the average wage in retirement year; 
MD  – number of payers of social tax; 
   – the value that characterises the change in the 

number of pensioners; 
Mj  – number of payers of social tax;  
riD  – relative accumulated contribution by a certain payer i in 

the year of retirement; 
rij  – relative amount of accumulated contributions by a 

certain payer i till the year of retirement. 
Wage replacement rate for a certain pensioner i in the year of 

retirement is calculated by the following formula created by the 
author. 
     

i

i
iD G

LDr
R =              (11) 

Where the notations used are: 
L – social security rate on taxable income directed to old-age 
pensions; 
D – length of service (working career) (number of social tax 
payment years); 
Gi  – average life expectancy of a certain pensioner i in the year 
of retirement; 
ri   – relative payer's contribution accumulated till the moment 
of retirement. 

The formula for calculation of the wage replacement rate for 
a certain i pensioner in the year of retirement (12) shows the 
commitment of an individual contributor to assume responsibility 
for his or her old days.  

Pension in the n-th year after retirement by applying the 
universal pension adjustment index is calculated by Formula 7.    

              (12)  
Where the notations used are: 
 pi,D+n  – a certain i pensioner's pension in a certain year after 
retirement; 
piD  – a certain i pensioner's pension in the year of retirement; 
Im  – forecasted index. 

What is important is that after many years - also in the year of 
death - the pension would not get devalued, as it happens now. 
Many years on we continue to compare pension with the average 
wage in that year. If the multiplication of indexes would be close 
to 1, in that case a pensioner's relative income would be preserved 
as long as the absolute income during the period of retirement 
keeps pace with the solidarity wage growth. 

The liberal approach, which is based on responsibility of each 
particular individual for his/her own welfare, does not happen to 
be highly valued in the modern world. Nevertheless, the hope for 
the system stability is supported by the fact that since the 

- the average taxable income (salary) k-th year of payers. Pursuant to the adopted pension 
capital indexing system, the pension capital accumulated till the year of retirement is presented 
as follows:

6 

J
kPΔ    - pensions in payment to the new pensioners in the kth 

year;  
Pk  - pension amount in the kth year;  
Pk-1 –  pension amount in the preceding year.  

 
5. Stability (robustness) of the proposed NDC model 
 In this article sustainability is illustrated as stability against 

the major known risks, which may cause insolvency or 
dissatisfaction of recipients of the old-age pensions.  

 
5.1.  Political stability 
The major risk associated with the proposed model lies in the 

political stability. While the impact of the political factors can be 
set off through optimisation of the sources of pension resources 
and improved distribution, political stability strongly depends on 
the perception of justice present in the community, which may be 
both subjective and shifty. 

The proposed model provides that every old-age pensioner 
receives the pension, which source is the generation solidarity. 
There are no major problems associated with this aspect, since in 
many developed countries for almost a hundred years this has 
been a time tested and well proven principle of funding, therefore 
it should not cause any notably negative public attitudes. 

At the same time, the pension size is proportional to the life-
long contribution. Crucial significance is attributed to the amount 
that has been contributed over the working life rather than to time 
in employment or other factors. The wage amount at any given 
point of time is not that important (for example, at the time of 
retirement or at any time shortly before retirement). Those, who 
have been paying a lot for several years and those, who have been 
contributing small amounts for many years will receive pensions 
equal in size. 

It follows from the above formulated model that contribution 
in the pension capital made every year of the working life is 
proportional to relative wage (taxable income) of the i-th 
contributor (payer) in the k-th year: 

              (9) 
Where the notations used are: 
wik  – taxable income (wage) of a certain i taxpayer in a certain 

k year; 
- the average taxable income (salary) k-th year of payers.

 Pursuant to the adopted pension capital indexing system, the 
pension capital accumulated till the year of retirement is 
presented as follows: 

         (10) 
Where the notations used are: 

L – social security rate on taxable income directed to old-age 
pensions; 

   –  the average wage in retirement year; 
MD  – number of payers of social tax; 
   – the value that characterises the change in the 

number of pensioners; 
Mj  – number of payers of social tax;  
riD  – relative accumulated contribution by a certain payer i in 

the year of retirement; 
rij  – relative amount of accumulated contributions by a 

certain payer i till the year of retirement. 
Wage replacement rate for a certain pensioner i in the year of 

retirement is calculated by the following formula created by the 
author. 
     

i

i
iD G

LDr
R =              (11) 

Where the notations used are: 
L – social security rate on taxable income directed to old-age 
pensions; 
D – length of service (working career) (number of social tax 
payment years); 
Gi  – average life expectancy of a certain pensioner i in the year 
of retirement; 
ri   – relative payer's contribution accumulated till the moment 
of retirement. 

The formula for calculation of the wage replacement rate for 
a certain i pensioner in the year of retirement (12) shows the 
commitment of an individual contributor to assume responsibility 
for his or her old days.  

Pension in the n-th year after retirement by applying the 
universal pension adjustment index is calculated by Formula 7.    

              (12)  
Where the notations used are: 
 pi,D+n  – a certain i pensioner's pension in a certain year after 
retirement; 
piD  – a certain i pensioner's pension in the year of retirement; 
Im  – forecasted index. 

What is important is that after many years - also in the year of 
death - the pension would not get devalued, as it happens now. 
Many years on we continue to compare pension with the average 
wage in that year. If the multiplication of indexes would be close 
to 1, in that case a pensioner's relative income would be preserved 
as long as the absolute income during the period of retirement 
keeps pace with the solidarity wage growth. 

The liberal approach, which is based on responsibility of each 
particular individual for his/her own welfare, does not happen to 
be highly valued in the modern world. Nevertheless, the hope for 
the system stability is supported by the fact that since the 

   –  the average wage in retirement 
year;

M
D
  – number of payers of social tax;

(1–α
m

) – the value that characterises the 
change in the number of pensioners;

M
j
  – number of payers of social tax; 

r
iD

  – relative accumulated contribution by a certain 
payer i in the year of retirement;

r
ij
  – relative amount of accumulated contributions 

by a certain payer i till the year of retirement.

The formula for c alculation of the wage replacement rate for a certain i pensioner in the year of 
retirement (12) shows the commitment of an individual contributor to assume responsibility for 
his or her old days. 

Pension in the n-th year aft er retirement by applying the universal pension adjustment index is 
calculated by Formula 7.   

Where the notations used are:
L – social security rate on taxable income directed 
to old-age pensions;

(11)

6 

J
kPΔ    - pensions in payment to the new pensioners in the kth 

year;  
Pk  - pension amount in the kth year;  
Pk-1 –  pension amount in the preceding year.  

 
5. Stability (robustness) of the proposed NDC model 
 In this article sustainability is illustrated as stability against 

the major known risks, which may cause insolvency or 
dissatisfaction of recipients of the old-age pensions.  

 
5.1.  Political stability 
The major risk associated with the proposed model lies in the 

political stability. While the impact of the political factors can be 
set off through optimisation of the sources of pension resources 
and improved distribution, political stability strongly depends on 
the perception of justice present in the community, which may be 
both subjective and shifty. 

The proposed model provides that every old-age pensioner 
receives the pension, which source is the generation solidarity. 
There are no major problems associated with this aspect, since in 
many developed countries for almost a hundred years this has 
been a time tested and well proven principle of funding, therefore 
it should not cause any notably negative public attitudes. 

At the same time, the pension size is proportional to the life-
long contribution. Crucial significance is attributed to the amount 
that has been contributed over the working life rather than to time 
in employment or other factors. The wage amount at any given 
point of time is not that important (for example, at the time of 
retirement or at any time shortly before retirement). Those, who 
have been paying a lot for several years and those, who have been 
contributing small amounts for many years will receive pensions 
equal in size. 

It follows from the above formulated model that contribution 
in the pension capital made every year of the working life is 
proportional to relative wage (taxable income) of the i-th 
contributor (payer) in the k-th year: 

              (9) 
Where the notations used are: 
wik  – taxable income (wage) of a certain i taxpayer in a certain 

k year; 
- the average taxable income (salary) k-th year of payers.

 Pursuant to the adopted pension capital indexing system, the 
pension capital accumulated till the year of retirement is 
presented as follows: 

         (10) 
Where the notations used are: 

L – social security rate on taxable income directed to old-age 
pensions; 

   –  the average wage in retirement year; 
MD  – number of payers of social tax; 
   – the value that characterises the change in the 

number of pensioners; 
Mj  – number of payers of social tax;  
riD  – relative accumulated contribution by a certain payer i in 

the year of retirement; 
rij  – relative amount of accumulated contributions by a 

certain payer i till the year of retirement. 
Wage replacement rate for a certain pensioner i in the year of 

retirement is calculated by the following formula created by the 
author. 
     

i

i
iD G

LDr
R =              (11) 

Where the notations used are: 
L – social security rate on taxable income directed to old-age 
pensions; 
D – length of service (working career) (number of social tax 
payment years); 
Gi  – average life expectancy of a certain pensioner i in the year 
of retirement; 
ri   – relative payer's contribution accumulated till the moment 
of retirement. 

The formula for calculation of the wage replacement rate for 
a certain i pensioner in the year of retirement (12) shows the 
commitment of an individual contributor to assume responsibility 
for his or her old days.  

Pension in the n-th year after retirement by applying the 
universal pension adjustment index is calculated by Formula 7.    

              (12)  
Where the notations used are: 
 pi,D+n  – a certain i pensioner's pension in a certain year after 
retirement; 
piD  – a certain i pensioner's pension in the year of retirement; 
Im  – forecasted index. 

What is important is that after many years - also in the year of 
death - the pension would not get devalued, as it happens now. 
Many years on we continue to compare pension with the average 
wage in that year. If the multiplication of indexes would be close 
to 1, in that case a pensioner's relative income would be preserved 
as long as the absolute income during the period of retirement 
keeps pace with the solidarity wage growth. 

The liberal approach, which is based on responsibility of each 
particular individual for his/her own welfare, does not happen to 
be highly valued in the modern world. Nevertheless, the hope for 
the system stability is supported by the fact that since the 

D – length of service (working career) (number of social tax payment years);

G
i
  – average life expectancy of a certain pensioner i in the year of retirement;

r
i
   – relative payer’s contribution accumulated till the moment of retirement.

What is important is that aft er many years - also in the year of death - the pension would not get 
devalued, as it happens now. Many years on we continue to compare pension with the average 
wage in that year. If the multiplication of indexes would be close to 1, in that case a pensioner’s 
relative income would be preserved as long as the absolute income during the period of retire-
ment keeps pace with the solidarity wage growth.

The liberal approach, which is based on responsibility of each particular individual for his/her 

Where the notations used are:

p
i,D+n 

 – a certain i pensioner’s pension in a certain 
year aft er retirement;

(12)

6 

J
kPΔ    - pensions in payment to the new pensioners in the kth 

year;  
Pk  - pension amount in the kth year;  
Pk-1 –  pension amount in the preceding year.  

 
5. Stability (robustness) of the proposed NDC model 
 In this article sustainability is illustrated as stability against 

the major known risks, which may cause insolvency or 
dissatisfaction of recipients of the old-age pensions.  

 
5.1.  Political stability 
The major risk associated with the proposed model lies in the 

political stability. While the impact of the political factors can be 
set off through optimisation of the sources of pension resources 
and improved distribution, political stability strongly depends on 
the perception of justice present in the community, which may be 
both subjective and shifty. 

The proposed model provides that every old-age pensioner 
receives the pension, which source is the generation solidarity. 
There are no major problems associated with this aspect, since in 
many developed countries for almost a hundred years this has 
been a time tested and well proven principle of funding, therefore 
it should not cause any notably negative public attitudes. 

At the same time, the pension size is proportional to the life-
long contribution. Crucial significance is attributed to the amount 
that has been contributed over the working life rather than to time 
in employment or other factors. The wage amount at any given 
point of time is not that important (for example, at the time of 
retirement or at any time shortly before retirement). Those, who 
have been paying a lot for several years and those, who have been 
contributing small amounts for many years will receive pensions 
equal in size. 

It follows from the above formulated model that contribution 
in the pension capital made every year of the working life is 
proportional to relative wage (taxable income) of the i-th 
contributor (payer) in the k-th year: 

              (9) 
Where the notations used are: 
wik  – taxable income (wage) of a certain i taxpayer in a certain 

k year; 
- the average taxable income (salary) k-th year of payers.

 Pursuant to the adopted pension capital indexing system, the 
pension capital accumulated till the year of retirement is 
presented as follows: 

         (10) 
Where the notations used are: 

L – social security rate on taxable income directed to old-age 
pensions; 

   –  the average wage in retirement year; 
MD  – number of payers of social tax; 
   – the value that characterises the change in the 

number of pensioners; 
Mj  – number of payers of social tax;  
riD  – relative accumulated contribution by a certain payer i in 

the year of retirement; 
rij  – relative amount of accumulated contributions by a 

certain payer i till the year of retirement. 
Wage replacement rate for a certain pensioner i in the year of 

retirement is calculated by the following formula created by the 
author. 
     

i

i
iD G

LDr
R =              (11) 

Where the notations used are: 
L – social security rate on taxable income directed to old-age 
pensions; 
D – length of service (working career) (number of social tax 
payment years); 
Gi  – average life expectancy of a certain pensioner i in the year 
of retirement; 
ri   – relative payer's contribution accumulated till the moment 
of retirement. 

The formula for calculation of the wage replacement rate for 
a certain i pensioner in the year of retirement (12) shows the 
commitment of an individual contributor to assume responsibility 
for his or her old days.  

Pension in the n-th year after retirement by applying the 
universal pension adjustment index is calculated by Formula 7.    

              (12)  
Where the notations used are: 
 pi,D+n  – a certain i pensioner's pension in a certain year after 
retirement; 
piD  – a certain i pensioner's pension in the year of retirement; 
Im  – forecasted index. 

What is important is that after many years - also in the year of 
death - the pension would not get devalued, as it happens now. 
Many years on we continue to compare pension with the average 
wage in that year. If the multiplication of indexes would be close 
to 1, in that case a pensioner's relative income would be preserved 
as long as the absolute income during the period of retirement 
keeps pace with the solidarity wage growth. 

The liberal approach, which is based on responsibility of each 
particular individual for his/her own welfare, does not happen to 
be highly valued in the modern world. Nevertheless, the hope for 
the system stability is supported by the fact that since the 

p
iD

  – a certain i pensioner’s pension in the year of retirement;

I
m

  – forecasted index.



95
E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9

own welfare, does not happen to be highly valued in the modern world. Nevertheless, the hope 
for the system stability is supported by the fact that since the implementation of such pension 
model in a typical welfare country like Sweden (where the majority of population upholds the val-
ues of social democracy) no public concerns were raised for more than 20 years. This indicates 
that in case of a welfare state oriented community a certain part of the social insurance benefits 
may be based on social responsibility.

The next element of fairness, which may have a significant effect on public perception, is appli-
cation of the equal life expectancy standard both for men and women.  Women on average live 
longer. Which means that women in retirement are going to receive part of the redistributed 
men’s virtual accumulated pension. Such situation is characteristic to all NDC schemes. It is par-
tially justified by the fact that women contribute less toward their retirement due to the period of 
childbirth and childcare. That also happens in cases when the retirement age for women is set to 
a lower level. At the same time women “are responsible” for existence of the new generation of 
pension providers. Previous experience is not indicative of any conflict of opinions with respect to 
such approach to the redistribution of accumulated pension. 

One of the drawbacks in other NDC models is devaluation of pension over time after retirement. 
In this model the devaluation rate is minimal or even does not exist at all. This is an additional 
argument in favour of strengthening the sense of justice and fairness.

In any case, political stability may evaporate as a result of the government ineffectual commu-
nication policy. The fundamental issue is - which way to choose: either inform the community 
about the essence of the implemented pension system and operation of corresponding mecha-
nisms or hold back these details from the public. 

If political stability is needed as a sustainable process, then it would be better in every respect to 
inform the community and start explaining how one can earn larger pension already by doing it 
already in the secondary school.

The proposed old-age pension in principle cannot be sustainable unless a minimum pension is 
introduced and appropriately increased in proportion to the welfare level achieved by the society. 
At the same time, the more stimulating is the process of shaping the basis for such pension 
while augmenting the welfare of the society, the relatively less additional resources will be re-
quired to fund the minimum pensions. Therefore, it is possible to separate these pension types 
and review them on an individual basis.

Stability against the changes in age structure 

This, in particular, is a great concern for the majority of the world pension schemes. Pretty much 
none of the most successful world economies can expect any positive change in this area - the 
share of pensioners keeps increasing while the share of contributors is decreasing.

In order to prevent these concerns, it is necessary to change the goods and services production 
structure by bringing the impact of technological progress into balance. Which means the relation 
between the producers and controllers should be slightly increased. Technological development 
leads to increased life expectancy. At the same time the number of employees in manufacturing 
and agricultural sectors decreases, with an excessive growth of the service industry and inflated 
bureaucracy. Sooner or later life will make adjustments to these proportions ensuring adequate 
living standards to the pensioners.

However, change of the employment structure is not the subject matter of this article. Let us 
consider pension adequacy in connection with the current tendency - ageing of population.

Formula (11) demonstrates a number of simple coherences: replaceability is directly proportion-



E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9
96

al to the deduction rate applied to earnings and the duration of the working life and is inversely 
proportional to the part of life spent in retirement.

If the relative investment r
i 
is equalled to one, then the replaceability will be calculated for a pen-

sioner of the formerly “moderate means”, who have been earning a countrywise average income 
throughout his life. Let us consider two cases:

1 the average earner started to work at the age of 16 and retired at the age of 65, his D=50. If the 
average life expectancy is 25 years and keeping L=0,2, we obtain R

iD
 = 0,4.

2 the average earner started to work at the age of 26 and retired at the same age of 65. Then 
D=40 and, ceteris paribus, the replaceability rate decreases R

iD
 = 0,32.

It should be remembered that an individual, who starts his career at such a young age will not 
be able to dedicate much time to his education, while an individual, who dedicated much time 
to studies, on the contrary, may potentially earn more if during his studies he acquires the skills 
that are highly assessed by the employer. Therefore, the prospects to obtain r

i > 
1 and compensate 

for the missing years in employment are higher.

In every respect it is important that in each subsequent year the pension is indexed in accordance 
with general-purpose (universal) index. Experience of dozens of years proved that wages use 
to increase in the long run. Therefore, except for the years of crisis - which is a special case, a 
pensioner is convinced that his pension does not decrease in value.

In general, the system resembles a social family model. The more the employable earn, the better is 
the life of the old people. The more children are born, the more comfortable is the life of the seniors 
in the society in general. However, there are no steep declines in the system, and in accordance with 
the formula (12), a pensioner maintains his earned “virtual” level till the very end of his life.

Stability against economic crises

If the pension amount is fixed at retirement, then the welfare of a pensioner becomes dependant 
on the economic cycle. At times when the number of employees drops, it seems unfair to cut the 
fixed “earned pension”. That creates the need to borrow, which would be covered at the expense 
of future expenditures (normally - future pensions). 

Under traditional NDC systems some years are favourable and some are unfavourable for re-
tirement.

If indexing is linked to economic success of the society in general, then the system becomes 
stable. This is secured by the general-purpose (universal) index. From year to year the workers’ 
virtual pension capital and pensioners’ pension benefits are equally indexed according to the 
formula (3) and (4).

There is no reason both for the pensioners and the workers to be afraid of the short-term de-
crease of earnings or capital, because there is an assurance that things will improve over the 
next phase of the economic cycle.

Stability against early retirement tendency

If formulas (11) and (12) would be taught at school, each worker would easily evaluate his/her 
expected pension amount and act accordingly. In the systems, which lack firm assurance that 
longer working life would also ensure higher pensions, large part of the society endeavours to 
make their working life shorter. If the community become fully aware of the direct proportion 
of the length of the working life, the number of those who start their working career early and 
retire later would grow. Staying in the labour market also after the age of retirement will make 
payment of pensions easier to those who do not work.



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E u r o p e a n  I n t e g r a t i o n  S t u d i e s 2 0 1 5 / 9

Stability against tax evasion

In the proposed model the pension capital is calculated on the basis of actual contribution. If an 
employer reports smaller wages and pays less tax, the worker’s pension is decreased. If the 
employer has social tax debts to the state, the pension decreases again. Under such system it 
becomes disadvantageous to work in a company to which tax privileges apply. An employee 
becomes embroiled in conflict with a dishonest employer.

Stability against decrease of value of the earned pension

The currently applied NDC schemes do not use equal indexing before and after retirement. This 
problem is going to become more aggravated with the growing average life expectancy. The 
high initial replacement rate is insufficient. Introduction of the general-purpose (universal) index 
solves this problem. 

If after retirement the proportion of workers continues to decrease, the pension will grow propor-
tionally with the increase of the aggregate wages and will decrease proportionally with the ratio 
between the pensioners and workers. This is evidenced by the formula (12). Previous practice 
shows that productivity caused by technological progress grows at a higher rate compared to 
increase of life expectancy. That is why the system remains stable against pension devaluation 
for many decades after retirement.

The paper shows that political stability is possible under the two conditions:

First, like in other physical or notional models of the funded pension systems, the system needs 
to be supplemented with a minimum guaranteed pension for those individuals, who have not 
been able or have not been willing to accumulate pension capital. Second, an active explanation 
of the accumulation motives is necessary during the entire working life of a contributor.

The paper demonstrates the stability of the model with respect to the main known risks of a 
pension system:

Conclusions

1 the scheme is stable against the risk of 
aging  population, because it provides a 
reasonable level of income regardless of 
demographic changes;

2 the scheme is stable against the economic 
crisis, because the proposed universal in-
dexing allows improvement for all partici-
pants in equal share; 

3 the scheme is stable against the risk of de-
fault, because it stimulates each scheme 

participant to make the maximum contri-
bution every year;

4 the system is stable against the insuffi-
ciency of pension during the time after re-
tirement, because the universal indexing 
procedure is equally applied both to the ac-
cumulation period and the payout period;

5 the scheme stimulates an earlier start of 
the work life and later retirement, thus 
minimizing the payments required to en-
sure sustainability of the system.

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INARA DUNDURE 

PhD student 

University of Latvia

Address
Aspazijas blvd.5, LV -1050, Riga, Latvia
Tel. +371 26486654
E-mail: inara.dundure@gmail.com 

MARIS PUKIS  

Dr. oec., Dr. phys., Associate Professor

University of Latvia

Address
Aspazijas blvd.5, LV -1050, Riga, Latvia
Tel. +371 29197602
E-mail:  maris@lps.lv 

About the 
authors