# «Rates of Return of the German Pay-As-You-Go Pension System Reinhold Schnabel Department of Economics, University of Mannheim Working Paper Abstract ...»

First draft 2 July 1997

Revised version 11 October 1998

Rates of Return of the German Pay-As-You-Go Pension

System

Reinhold Schnabel

Department of Economics, University of Mannheim

Working Paper

Abstract

Due to population aging, contribution rates of the mandatory German pay-as-you-go pension

system are expected to increase dramatically during the next decades. This paper estimates the

impact on the expected returns of contributions for different cohorts. I show that rates of

return for younger cohorts will be between zero and one percent, depending on the demographic and economic scenarios; for some demographic groups they become negative.

The implicit tax rates reach levels of up to 80 percent of contributions for the youngest cohorts. If decreasing returns reduce incentives for labor supply and system participation, the whole system may become unsustainable. Indeed, I find empirical evidence for a recent decline of voluntary contributions and for a substitution away from taxable employment.

**Address:**

Dr. Reinhold Schnabel Department of Economics University of Mannheim D-68131 Mannheim Phone: (+49)-621 - 292-3181 Fax: (+49)-621 - 292-5426 E-Mail: reinhold@econ.uni-mannheim.de The previous version of this paper was based on the 1992 legislation, while this version considers the recent changes including the 1999 pension reform. I wish to thank Axel Börsch-Supan, Hans Fehr, Isabel Gödde, Joachim Winter and seminar participants at the Universities of Mannheim and Frankfurt/Main for helpful comments on earlier versions of this paper. Research in this paper was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 504 at the University of Mannheim.

1 Introduction Compared to many other OECD countries, population aging is particularly dramatic in Germany. The fertility rates have dropped rapidly from 2.5 during the baby boom to about 1.3 thereafter. Additionally to the fertility crisis, life expectancy has increased at a rate of about

1.5 years per decade. With the decline in average retirement age to 60 years, the average duration of pensions has increased by sixty percent from 10 years in 1960 to 16 years in 1996.

Thus, aging already puts considerable pressure on the German pay-as-you-go (PAYG) pension system, long before the fertility crisis unfolds: in the year 1995 only 24.3 million WestGerman workers (including unemployed) contributed for the pensions of 11.5 million pensioners and over 4 million widows in the public pay-as-you-go pension system - an old-age dependency ratio of about 60 percent (VDR 1997). The old-age dependency ratio is expected to exceed 100 percent by the year 2040 when the baby-boom generations are retired.

The net replacement rate of old age pensions has increased from some 60 percent in the sixties to 72 percent by the end of the seventies and has stayed at this level since then. This is substantially higher than the corresponding U.S. net replacement rate of about 53 percent (Casmir 1989). As a consequence of program generosity and demographic shifts, public pensions in 1997 made up for more than 12 percent of GNP and contribution rates reached

20.3 percent of the wage bill in 1997. Since 1992, the pension levels have been adjusted annually, so as to keep the net replacement rate fixed1. This amounts to a net wage indexation of net pensions. Due to the net wage indexation, productivity gains do not slow down the rise in contribution rates. Holding the replacement rates constant, the most optimistic forecasts yield a contribution rate of 27 percent in the year 2040. Even with a reduction of the net replacement rate from 70 percent to 64 percent (as in the 1999 pension reform) the contribution rates will reach a level of 24 percent in the optimistic scenario, and about 32 percent in status quo projections.

Population aging will not only drive up contribution rates. It will also reduce the implicit rates of return of a pay-as-you-go pension system. A well-known theoretical result for a constant rate of population and productivity growth is that the rate of return of the pay-asyou-go system is the sum of both growth rates. A projected shrinking of the German population of 1 percent per year with a 1 percent per capita economic growth would thus result in a steady state return of zero. However, this result may not be very informative for several reasons. (1) The population is not shrinking at a constant rate; (2) improvements of life-expectancy may change the profitability of the system; (3) different cohorts are affected

** Before 1992 the indexation was to gross wages.**

quite differently by population aging and changes in legislation; and (4) due to individual heterogeneity the returns vary widely within cohorts.

Hence, the aim of this paper is to derive empirical estimates of the returns of the German public pension system for different birth cohorts and demographic groups. There is some recent literature on this topic. In two papers Eitenmüller (1996) and Hain, Eitenmüller and Barth (1997) compute nominal rates of return for several cohorts based on the 1992 legislation. The advisory board of the department of economic affairs (Wissenschaftlicher Beirat des BMWi 1998) and very recently Frerich (1998) have presented estimates of returns based on the 1999 reform. My paper extends the recent literature in several respects. The estimates of the returns of the German PAYG pension system are in real terms and are based on the current social security legislation (Rentenreformgesetz 1999). In order to assess the effects of the assumptions on the rates of return, I consider three different demographic and economic scenarios. Finally, I compute expected pension wealth as the expected present discounted value of lifetime contributions and benefits. The literature so far has simply calculated the value of pensions as a function of life expectancy of a representative agent. One can show, however, that this leads to an upward bias of the rates of return by 0.5 percentage points.2 My estimation of expected present discounted values and of rates of returns takes into account the risks of longevity, disability, and surviving spouses. The (real) expected values have several important interpretations. First, from the point of view of an optimizing individual, the expected values can be interpreted as the ex ante return on investment in an uncertain environment for an individual of a given type (e.g. male/female; married/single;

cohort). Second, from a macroeconomic perspective, the expected values are the correctly aggregated average values of all individuals of the same type. The aggregation over all groups within a given cohort using the population weights of the specific groups gives the average value of the pension system for a whole cohort. Third, the expected values are life-cycle values and thus, a measure of intergenerational redistribution within that branch of the fiscal system.

I show that the real rates of return are quickly deteriorating for younger cohorts in all scenarios. The average return for the cohort born in the year 1930 is estimated to be about 3 percent. The average rates of return for the cohort born in the year 1980 are projected to be between zero and one percent, depending on the demographic and economic projections. This intergenerational difference is mainly due to demographic changes and only to a lesser degree induced by the reform of 1992, which treats the older cohorts more favorably than the younger This reflects the well-known fact that a non-linear function of the expected value of a random variable does not equal the expected value of this function. This is also closely related to the aggregation problem.

ones. The rates of return differ widely across demographic groups: as a rule, females get a higher return than males due to a higher life expectancy, and married persons are better off than singles due to survivor benefits.3 As a consequence, the rates of return for single males in the youngest cohorts are clearly negative in all scenarios.

These findings raise the question of incentives for participation in the pension system and for labor supply, since contributions to the pension systems may be increasingly perceived as taxes. The implicit tax for the youngest cohorts will rise to two-thirds of the pension contributions, which translates into a tax rate of 18 percent of the gross wage bill ????. Tax

**evasion may eventually destroy the basis of the system. Indeed, this seems to happen already:**

persons who have discretion over their program participation have reduced their contributions.

I present strong evidence for a dramatic decline of voluntary contributions. Moreover there is mounting evidence for a recent substitution away from taxable employment towards other types of employment.

The paper is organized as follows: The next section describes the set-up for the estimation of expected presented discounted values of pensions. Section 3 presents the different scenarios together with the resulting dependency ratios and contribution rates.

Section 4 reports the results on pension wealth, rates of return and implicit tax rates. Section 4 provides empirical evidence on behavioral reactions and section 5 concludes.

The Expected Present Discounted Value Function The rates of return are estimated for cohorts born between 1930 and 1980. Within each cohort, I differentiate by gender, marital status, earnings, mortality risk, entry to and exit from the labor force. Each type of worker faces the uncertainty of the date of death (or the risk of longevity) and the risk of disability prior to. The expected present discounted value function

**of contributions and pension is in general:**

In a related paper Börsch-Supan and Schnabel (1997) consider the intra-generational effects of the public pension system, namely the incentives to retire early. In another paper (Schnabel 1997), I study the effects of a transition to a partially funded system, which amounts to switching to a policy that holds the contribution rate fixed as opposed to the 1992 legislation, which fixes the net contribution rate. The 1999 reform can be PDV expected present discounted value of pension wealth s planning age Es expectation formed at age s R retirement age YLABt labor income at age t YPENt pension benefits at age t for retirement age R ct contribution rate at age t (where age = year – cohort) aRt pension per average annual earning (Aktueller Rentenwert) δ discount factor = 1/(1+r), with r = real interest rate.

Setting this function equal to zero and solving for the interest rate yields the rate of return for a specific demographic group. The present discounted value depends on several macro and micro variables, which have to be determined over the whole life-cycle. The contributions depend on the (aggregate) contribution rate ct and on the (individual) earnings YLABt. The pension income YPENt depends on the individual life-time earnings, on the aggregate level of pensions (aktueller Rentenwert, aRt), and on other specific features of the pension system. The individual retirement age R is an important determinant of pension benefits and is made explicit in the above formula.

Due to survival and disability risks the contributions and pensions on the individual level are state contingent. That is, for each type of worker all state contingent time paths of contributions and pensions have to be computed over the whole life-cycle. Then, the expected values of contributions and benefits are calculated with respect to the random variables date of death and disability using the probabilities for survival, for joint survival and for disability.

The expectation is formed conditional on the agent’s planning age s, which is chosen to be the entry to the labor force. In general, the expectation depends on the cohort and gender specific survival probabilities and on the probabilities of disability. The discounted sum over these expected values is the present discounted value function. Finally, setting the present discounted value function to zero and solving for the interest rate yields the rate of return for a given demographic group.

Longevity, Disability and Survivor Benefits In order to illustrate the computation of rates of return, the following formula gives a simple, stripped down version of the present discounted value of the pension system for a single

**person, neglecting survivor benefits and disability benefits:**