Pension Reform in an OLG Model with Multiple Social Security Systems
ABSTRACT One measure of the health of the Social Security system is the difference between the market value of the trust fund and the present value of benefits accrued to date. How should present values be computed for this calculation in light of future uncertainties? We think it is important to use market value. Since claims on accrued benefits are not currently traded in financial markets, we cannot directly observe a market value. In this paper, we use a model to estimate what the market price for these claims would be if they were traded. In valuing such claims, the key issue is properly adjusting for risk. The traditional actuarial approach â€“ the approach currently used by the Social Security Administration in generating its most widely cited numbers - ignores risk and instead simply discounts â€œexpectedâ€ future flows back to the present using a risk-free rate. If benefits are risky and this risk is priced by the market, then actuarial estimates will differ from market value. Effectively, market valuation uses a discount rate that incorporates a risk premium. Developing the proper adjustment for risk requires a careful examination of the stream of future benefits. The U.S. Social Security system is â€œwage-indexedâ€: future benefits depend directly on future realizations of the economy-wide average wage index. We assume that there is a positive long-run correlation between average labor earnings and the stock market. We then use derivative pricing methods standard in the finance literature to compute the market price of individual claims on future benefits, which depend on age and macro state variables. Finally, we aggregate the market value of benefits across all cohorts to arrive at an overall value of accrued benefits. We find that the difference between market valuation and â€œactuarialâ€ valuation is large, especially when valuing the benefits of younger cohorts. Overall, the market value of accrued benefits
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ABSTRACT: Population ageing and pension reform will have profound effects on international capital markets. In order to quantify these effects, we develop a computational general equilibrium model. We feed this multi-country overlapping-generations model with detailed long-term demographic projections for seven world regions. Our simulations indicate that capital flows from rapidly ageing regions to the rest of the world will initially be substantial, but that trends are reversed when households decumulate savings. We also conclude that closed-economy models of pension reform miss quantitatively important effects of international capital mobility. Copyright (c) The London School of Economics and Political Science 2006.Economica 01/2006; 73(292):625-658. · 1.15 Impact Factor
- Contributions to Political Economy 02/2007; 26(1).
Article: Dynamic fiscal policy /[Show abstract] [Hide abstract]
ABSTRACT: Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001.
Economic Research Center
Middle East Technical University
Ankara 06531 Turkey
ERC Working Papers in Economics 08/05
Pension Reform in an OLG Model
with Multiple Social Security Systems
Department of Economics
Middle East Technical University
Ankara 06531 Turkey
Pension Reform in an OLG model
with Multiple Social Security Systems
C ¸a˘ ga¸ can De˘ ger∗
Primarily due to financial sustainability problems, social security re-
forms have been on the policy agenda of both developed and developing
countries for the last decade.Research literature on the subject tends
to use overlapping generations (OLG) models with single representative
household and presents reforms as shock to the constructed model. This
study presents an OLG model with three separate social security institu-
tions where the heterogeneity is through different benefit payments and
contribution rates. Convergence across various institutions is enabled by
a replacement ratio shock and model dynamics are discussed.
JEL Codes: C68, D91, I38
∗PhD Candidate, Department of Economics, Middle East Technical University.
Last decade has seen a considerable wave of social security system reforms in
both developed and developing countries. This wave has been triggered mainly
by the concerns on financial sustainability of social security systems in both
the short and the long run (Holzmann & Hinz, 2005, p. 23-34). The ques-
tion of whether proposed reforms would contribute to the solution of financial
sustainability problems and uncertainties regarding the effects of proposed and
performed reforms on macroeconomic dynamics of reforming countries have led
to a rich research literature.
In order to asses the impact of these reforms, economists take the path of
constructing general equilibrium models and introduce reforms as policy shocks
to the constructed models. Given the intergenerational transfer mechanism
created by social security systems, the models constructed for such analysis
need to take into account two major modeling concerns.
Firstly, since social security systems introduce an intergenerational transfer
system to the economy, constructed models have to include a time dimension;
that is, they need to be dynamic models. Such dynamism is introduced by focus-
ing on the intertemporal optimizing behavior of agents. Modeling intertemporal
behavior is possible through formulation of infinite lifetime agents, as in the case
of well-known Solow and Ramsey models, or through finite lifetime agents, as
in the case of overlapping generations (OLG) type models.
Second modeling concern is related to agent homogeneity. Analysis of social
security systems need to take into account the fact that at a given time there are
workers that provide financial resources for the system and retired people that
receive benefits from the system. This implies that a study of social security
system needs to take into account the fact that at any point in time there
exist various types of individuals; that is, agents are heterogeneous rather than
homogeneous. The minimum level of heterogeneity required by social security
system analysis is the differences in ages. The model must be able to generate
behavior of various age groups that coexist at any point in time. Such concerns
exclude Solow or Ramsey type models that assume infinite lifetime horizon
for homogenous agents and bring forward OLG type models as major tools of
A leading work on application of OLG models to fiscal policy problems is
Auerbach and Kotlikoff (1987). After presenting the basics of OLG models
through a simple example, Auerbach and Kotlikoff (1987) proceeds to set up
an OLG model that has 55 generations of consumers, single sector production
side, a government that uses taxes and debt to finance consumption and a
self-financing social security system. The consumers are assumed to come into
being at the age of 21 and die at the age of 75. Thus every time period in
the model corresponds to a year. The model takes labor supply endogenous
and retirement takes place when labor supply is chosen by the consumer to
be zero; i.e. retirement age is an endogenous variable. This model has been
used by Auerbach and Kotlikoff (1987) to analyze tax reforms, government con-
sumption shocks with different financing strategies, investment incentives and
social security systems. It has also formed the basis of a considerable litera-
ture on social security research and has been improved by inclusion of voting
over social security (Gonzales-Eiras & Niepelt, 2007), open economy dimension
(Borsch-Supan, Ludwig, & Winter, 2006), enterpreneur behavior (Eren, 2008)
and uncertainty regarding, among others, productivity (Greco, 2008) and life-
time (Huggett, 1996).
Models put forward by the existing literature generally include a single social
security system and thus a single pension scheme for all individuals. One such
model has been formulated by Heer and Maussner (2005). The model includes 6
cohorts, endogenous labor supply, single sector production and a pay-as-you-go
(PAYG) social security system that pays benefits when a consumer becomes
of age 5. Following Heer and Maussner (2005), this study aims to develop an
OLG model that includes 6 cohorts and analyzes effects of replacement ratio
shocks. Taking the labor supply exogenous, the model to be presented below
contributes by introducing 3 different social security systems and thus enhancing
agent heterogeneity. With the stated aim in mind, the next section proceeds
to explain the formulated OLG model. Section 3 details steady state results
and responses to replacement ratio shocks in the model. Last section presents
The foundation of OLG models goes back to Samuelson (1958) and Diamond
(1965). Aimed to explore the role of money in financial markets and effects of
national debt, these models included two generations alive at any given time rep-
resented by one working and one retired individual.Even though they carry the
same rationales, modern versions, including the ones cited in the introduction,
are by far more complicated.
The model presented in this study is a relatively simple version designed
to study the existence of multiple social security systems. It includes a single
production sector and a slightly more detailed household behavior represented
through 6 cohorts. Along with the production and household sectors, a simple
public sector with three social security systems is also depicted in the model.
Lack of a medium of exchange implies that all variables in the model are real.
The model is built around a single good that can be used for consumption or
production. Therefore any saving done is actually a contribution to the capital
stock and has a rate of return equal to the return on capital.
Households are assumed to live for 6 periods. Out of these 6 periods, 4 are
assumed to represent working periods in exchange for wage and 2 are spent in
retirement, during which social security benefits are received. Thus a member of
the new born generation can be assumed to enter the economy at age 21, retire at
age 61 and die at age 80. Since there are three different social security systems,
at any given time, the model includes 18 representative households belonging
to either one of these three systems. Every year, a generation of equal measure
to be included in each of these social security systems is born. There is no
uncertainty regarding life length and all demographic dynamics are excluded.
All households are modeled without children or a detailed family structure.
The heterogeneity across households is introduced through differences in ages
and membership in different social security systems. Since households will have
different saving levels at different stages of their lives, members of the same
social security systems differ due to available material resources. The existence
of a multiple social security system contributes to heterogeneity of households
through differences in tax payments and benefit receipts.
The representative household of any social security system s is assumed to
have the instantaneous preferences represented by the following version of the
constant relative risk aversion (CRRA) utility function:
1 − ηs
The index t stands for time periods, a = 1, ..., 6 stands for the age of the
household and s=A, B, C stands for different social security systems.
parameter η of the function represents Arrow-Pratt measure of relative risk
aversion and would be interpreted as the inverse of intertemporal elasticity of
substitution for this specific case. Since η is regarded as a measure of curvature
of the utility function, a higher η implies a more curved function or a lower
intertemporal substitutability. Hence, higher risk aversion as represented by a
higher η would imply a smoother consumption through time.
In a lifetime of 6 periods, a representative household belonging to the social
security system s has the lifetime utility represented as:
1 − ηs
where β is the discount factor.t should be noted that there is no restriction on
the value of β other than that it be positive.
Households are assumed to receive no inheritance and leave no bequests.
While working, each household supplies a fixed amount of labor inelastically for
which she earns the market wage to finance current consumption, saving and
tax payments, implying the budget constraint to be:
s,t+1≤ (1 + rt)ka
s,t+ (1 − τs,t)wt
for a=1,...,4. In the equation above, ka
age a belonging to social security system s at the beginning of time t. Under
such specification, household savings become the basic tool for intertemporal
re-allocation of resources. Interest rate is denoted rt, wt is the market wage
rate and τs,tis the tax paid out of wage earnings by a household belonging to
social security system s. Note that the interest and wage rates are same for all
household types but tax rates differ according to membership in different social
s,trepresents saving of a household of