APPENDIX PAYG Algebra for Germany’s Public Pension System105
183. The basic budget constraint of a PAYG public pension system is given by:
where N* denotes the number of contributors, M* the number of pensioners, α the contribution rate, β the pension replacement rate, and W denotes average gross earnings. The ratio (M*/N*) is the system dependency ratio, i.e. the number of pensioners per contributor. To further approximate the institutional details of the main German pension fund—the wage and salary earners’ fund—two important characteristics need to be added:
Pensions are indexed to net wages. This can be modeled by replacing gross wage earnings (W) by net earnings ((l−α)W). This represents a rough approximation as in practice net wages are defined as gross wages minus employees’ social insurance contributions and minus wage income taxes.
And a (fixed portion) of pension spending τ is financed by budget transfers. Inserting these characteristics in (1) gives:
184. The link between public pension finances and population aging can be brought out by assuming that the number of pensioners is proportional to the number of persons aged 60-and-over: M* = δM, while the number of contributors is proportional to the number of persons at working age: N* = ηN. Thus, (M/N) is the elderly dependency ratio, a variable that depends only on demographic developments. Moreover, if the symbol Ψ is used to stand in for the ratio (δ/η), termed the pension system’s “coverage ratio,” the equation describing the evolution of the PAYG system’s equilibrium pension contribution rate is:
which corresponds to equation (1) in the main text.
185. Equation (A.3) is mute on the issue of income taxes on pensions. This reflects an idiosyncrasy of Germany’s income tax system: the income tax code assumes that only about 25 percent of public pension benefits represent previously untaxed income, an assumption that amounts in practice to a full income tax exemption. This assumption is, however, difficult to rationalize. It is based on the presumptions that: (i) all pension contributions were subject to income tax (although only employees’ pension contributions are subject to tax) and that public pension benefits include a tax-free interest income component of about 25 percent.
Chand, Sheetal K., and Albert Jaeger, 1996, Aging Populations and Public Pension Schemes, IMF Occasional Paper No. 147 (Washington: International Monetary Fund).
Chand, Sheetal K., and Albert Jaeger, 2000, “Reform Options for Pay-As-You-Go Public Pension Systems,” World Bank Primer Paper, World Bank.
Deutsche Bank, 1996, From Pension Reserves to Pension Funds: An Opportunity for the German Financial Market, Deutsche Bank Research.
Fox, Louise, and Edward Palmer, 1999, “New Approaches to Multipillar Pension Systems: What in the World is Going On?,” mimeo., World Bank.
IMF Staff Country Report No. 97/101, 1997, “Alternative Approaches to Pension Security in an Aging Society,” in Germany—Selected Issues, International Monetary Fund.
Mackenzie, G. A., Philip Gerson, and Alfredo Cuevas, Pension Regimes and Saving, IMF Occasional Paper No. 153, International Monetary Fund.
Prognos (1998), Prognos-Gutachten 1998: Auswirkungen veränderter ökonomischer und rechtlicher Rahmenbedingungen aufdie gesetzliche Rentenversicherung in Deutschland, edited by: Verband Deutscher Rentenversicherungsträger, Frankfurt.
Prepared by Albert Jaeger.
The historical roots of Germany’s public pension system reach back to Bismarck’s invalidity and old-age insurance law of 1889, which set up the first modern public pension scheme.
A reduced pension contribution rate of 12 percent (compared to a statutory rate of 19.3 percent in 2000) applies to workers holding small-time jobs (less than 15 work hours per week) that earn less than DM 630 per month.
Pilot projects are under way in four regions of Germany to study the labor market effects of fiscal subsidies at the lower end of the labor market.
One possible rule of thumb for projecting the longer-term trends of pension finances—used for example by the Social Security and Medicare Boards of Trustees in the United States—is to base the projection horizon on average life expectancies (75 years in the case of the U.S.).
The derivation of equation (1) is described in the appendix. This PAYG equation is strict in the sense that it ignores that Germany’s main public pension fund—the wage and salary earners’ fund—is required by law to maintain a small fluctuation reserve (equivalent to at least one month of pension expenditure).
These calculations were based on available time series for contribution rate, budget transfer rate, standard pension replacement rate, and the elderly dependency ratio. The time series for the pension system coverage ratio was calculated using equation (1).
The reform proposal would, however, suspend CPI indexation in 2001 and redefine the net wage concept; see next section for details.
This baseline projection assumes that the demographic factor that would have reduced pensions in relation to increases in life expectancies—and which was suspended by the present government—will not be reinserted in the pension benefit formula beginning in 2002.