Generalised Social Security Finance in a Two‐Country World

AuthorMichael Bräuninger
Publication Date01 Aug 1999
Scottish Journal of Political Economy, Vol. 46, No. 3, August 1999
#Scottish Economic Society 1999. Published by BlackwellPubl ishersLtd, 108 Cowley Rd., Oxford OX4 1JF, UK and
350 Main St., Malden, MA 02148, USA
Michael Bra
This paper develops an overlapping generations model with generalised finance of
social security in a two-country world. Social security finance includes a pay-as-
you-go, a fully funded, and an optimal system as special cases. An increase in social
security funding of country 1 increases capital, income and consumption per head in
both countries. Also, it increases foreign assets in country 1 and foreign debt in
country 2. The optimal level of social security funding is below the golden rule level.
During adjustment an increase in funding has negative effects on country 1 and
positive effects on country 2.
In general the literature on social security finance considers either small open
economies or a closed economy. Initial contributions to the literature on small
open economies are Samuelson (1958) and Aaron (1966). In a small open
economy factor prices and therefore capital and income per head are given
exogenously. Savings affect the current account and foreign assets. By contrast
to this, in the closed economy private and public savings determine the capital
stock, and therefore factor prices and income (see Diamond, 1965; Feldstein,
1974; Samuelson, 1975; as leading references). In both kinds of models, steady
state welfare is improved by the introduction of an unfunded social security
system if the economy is dynamically inefficient, i.e. when the growth rate
exceeds the interest rate. On the other hand, if the economy is dynamically
efficient, an increased amount of social security funding is preferable in the long
run. Since this is the empirically relevant case, Feldstein (1995) states:
The inefficiency of the traditional unfunded social security program implies
that alternative methods of financing retirement consumption could achieve
the current degree of protection with far less deadweight loss.
As has been shown by Breyer and Wildasin (1993), results obtained for small
open and the closed economies are not valid for the intermediate case of a large
open economy: the expansion of unfunded social security can improve the
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welfare of the large open economy, even when the interest rate is above the
growth rate. Breyer and Wildasin assume that there is only one country in the
world large enough to have an effect on the world interest rate. All the other
countries take the interest rate as given. In contrast, this paper assumes a world
consisting of two countries, along the lines of Buiter (1981) and Persson (1985).
Different methods of social security finance are analysed within an overlapping
generations model. Social security finance is modelled in a general way; it
encompasses a pay-as-you-go, a fully funded, and an optimally financed social
security system. With an integrated international capital market, the method of
financeÐ a given level of social security benefitsÐ will affect income,
consumption and welfare in both countries. The model shows that a change
from an unfunded to a funded social security system in one country, such as
Great Britain, will increase the long run level of capital, income and
consumption in Great Britain. In addition, it will increase the long run level
of capital, income and consumption in those countries maintaining the unfunded
system, like France or Germany. However, if funding in one country leads to a
situation close to the golden rule, then this country can increase its own welfare
by reducing funding. This reduces welfare in the other countries. In addition to
the analysis of steady state levels, the path of adjustment induced by an increase
in funding is derived. It is shown that an increase in funding has negative short
run effects on the own country and positive effects on the other country.
Section II presents the model. Simplifications are made in order to
concentrate on the influence of social security. First, social security is the only
government activity. Second, countries are assumed to be identical except for
social security systems. This implies that they use equal technologies, are of
equal size, the labour force in both countries grows with the same rate, and
individuals have the same intertemporal preferences. Using these assumptions
the short-run and the long-run equilibria are derived. Section III analyses
stability. Section IV examines foreign assets in further detail. Section V
considers the optimal finance and Section VI derives the path of adjustment
when funding is increased. Section VII concludes the paper.
The world consists of two countries i1, 2. In both countries individuals live for
two periods, the working period and the retirement period. Both countries are of
same size and in each country there are Nyoung people who are working. Since
the working generation of the current period is the retired generation of the next
period, the number of the old is Nÿ1. The relation between the number of the
young and the old is therefore determined by the labour growth rate, nN=
Nÿ1ÿ1, which is assumed to be constant and identical in both countries.
The utility, ui, of a representative individual of either country depends on the
consumption while he is young, c1
i, and while he is old, c2
i. The preference
structure is described by a Cobb-Douglas-type utility function:
uilog c1
ilog c2
iwith 1 and ,>0. (1)
#Scottish Economic Society 1999

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