# Pay as you go

The pay-as-you-go method is a method of financing social security , especially old-age provision , but also health insurance and unemployment insurance . The contributions paid are used directly to finance the beneficiaries, i.e. paid out to them again. A small amount of reserves can be set up by the social security agency (e.g. sustainability reserve of the statutory pension insurance). In return for his contribution, the contributor is entitled to benefits in cases of unemployment , reduced earning capacity , illness and, ultimately, old age .

In contrast to the pay-as are the funded system , the contributions saved up and bear interest or invested in other forms of investment to be paid when providing benefits, such cases are at retirement, in the event of illness or unemployment in the (private) unemployment insurance or payment protection insurance .

## Features of the pay-as-you-go system

Some basic properties of the pay-as-you-go system are outlined using the example of old-age insurance.

### Initial debt / inherent debt

In a pay-as-you-go system, the first generation of recipients (e.g. pensioners) receives benefits without having paid contributions (to any significant extent) (“introductory profit”). This gift, known in English as "windfall gains" or "unfunded liability", is an inherent (initial) debt for the following generations, which they pay with their contributions. To the extent that the pay-as-you-go system remains in force, they in turn receive claims against their successors. In parallel to reducing the initial debt, new, inherent liabilities are built up. This continues in the system, which therefore always has an "inherent guilt".

The level of inherent debt does not remain stable, but changes to the extent that a “return” is granted on the contribution payments. This is illustrated by a simple example: The first generation of retirees receive total transfers of 100 monetary units, which are financed by employees in the same period. These contributors expect in the following period, idealized 25 years later, adjusted for inflation, a transfer in the amount of z. B. 164 monetary units (corresponds to an annual pension increase of 2%). Mathematically, the inherent debt has grown by a factor of 1.64 ( with n + p = 0.64, see section "Yield"), which is then also financed by the employees, who then receive a transfer of 269 in period 3 Expect monetary units ( ). In general, the inherent debt will have reached a value of 100 after generations . Accordingly, a system change becomes more expensive the older the system becomes. ${\ displaystyle 100 * (1+ (n + p))}$${\ displaystyle 100 * (1+ (n + p)) ^ {2}}$${\ displaystyle x}$${\ displaystyle 100 * (1+ (n + p)) ^ {x-1}}$

Conversely, in the case of a negative return (adjusted for inflation), the inherent debt decreases. In the hypothetical case of a “last” generation that no longer has any children, this generation would have to finance the costs of its own retirement and that of the previous generation.

### Effects of population and income development

Another question is how does the inherent debt show up on the contributors? If their income grows synchronously with the return on the pay-as-you-go system and if their number remains roughly constant, the percentage of their income that they have to pay does not change regardless of the absolute amount of the inherent debt , even if the absolute amount increases steadily . Example: 300 employees (E1 = 300) who earn an average of 200 monetary units each (GE1 = 200) finance 100 pensioners (R1 = 100) with 100 monetary units (GR1 = 100). Every employed person then has a contribution rate of 16.6% ( ). In the next period, 300 employees (E2) have to finance 100 pensioners (R2), but for this - because of the above. Growth - now raise 164 monetary units (GR2 = 164). Your absolute payload has increased by 64%. If, however, you have also achieved an increase in income of 2% per year yourself, then your income has also increased to E2 = 328 monetary units. The contribution rate, i.e. the percentage of your income that you have to pay, therefore remains stable. ${\ displaystyle GR1 * R1 / (GE1 * E1)}$

If, on the other hand, the next generation of contributors is smaller than the first, for example because too few children are being born, more people are unemployed or unable to work, then the contribution rate rises - with E2 = 200 (i.e. decrease in the number of contributors by a third) in the example to 25% . The increase is even greater if average earnings grow more slowly than pensions, for example because the proportion of part-time workers or low-skilled people increases among the employed.

### Compensation from tax revenues

In reality, any deficits can be financed by subsidies from tax revenue . In Germany, the grants that partially offset non-insurance benefits are currently around € 80 billion. To the extent that these taxes come from the employed, their effective burden increases; to the extent that it is financed by public debt , another form of inherent debt arises.

### Justification of Inherent Guilt

Debt is usually justified by the fact that the debtor has received a service from the creditor, such as a loan or an item. In the case of the pay-as-you-go system, the consideration (of the debtor) can again be seen in the fact that, as the older generation, he had invested heavily in the next generation. Raising and training the younger generation is the work of the older generation, which cannot be thought away without the younger generation's income from being lost. This consideration leads to the fact that no generation has received a “gift”, rather the younger generation pays back what they previously received in the form of “gifts”.

Another question is how these burdens are distributed within the generations: for example, those who do not have to pay contributions do not participate in the payments for their own parents / grandparents (via tax transfers) in a completely different way. Those who have no children themselves have only made indirect contributions to the next generation (again through taxes) and to a lesser extent; How extensive, how valuable and how effective the individual's donations to their children are, is also not taken into account in today's pay-as-you-go systems. Sometimes an attempt is made to influence this burden distribution through special design, for example the recognition of years of upbringing as contribution periods.

Above all, such considerations spark the question of the fairness of a pay-as-you-go system and its concrete form.

### More precise representation

A mathematical representation of the essential parameters looks like this:

#### Basic formula

Assume that the contribution payments in each period are withheld as a fixed percentage of the wages of the persons employed during that period. These contributions are used to finance the pension benefits for those who have retired during this period. In a pure pay-as-you-go system, the total contribution income must match the total pension payments in each period:

Contribution payments in period = benefits in period . ${\ displaystyle t}$${\ displaystyle t}$

If one assumes that all contributors and all beneficiaries are identical, one obtains formally the following budget identity of an allocation procedure:

(1) ${\ displaystyle Z_ {t} w_ {t} \ tau = E_ {t} b_ {t}}$

whereby the following notation is agreed:

• ${\ displaystyle Z_ {t}}$ = Number of contributors in period t
• ${\ displaystyle E_ {t}}$ = Number of grantees in period t
• ${\ displaystyle w_ {t}}$ = Wage rate in period t
• ${\ displaystyle \ tau}$ = Contribution rate
• ${\ displaystyle b_ {t}}$ = Unit pension in period t

#### Return

The (average) return of a pay-as-you-go system for a participating individual is calculated from the ratio of the benefits received to the contributions paid, more sensibly adjusted for inflationary effects:

(2) .${\ displaystyle yield = {\ frac {cash value \ of \ services} {cash value \ of \ contributions}} - 1}$

Since the benefits correspond to the contributions of the following period via the budget identity of the pay-as-you-go system, the average return on the pay-as-you-go system corresponds to the growth rate of the contributions.

The average return on the payments into a pay-as-you-go system can also be calculated using equation (1) as an example. It is assumed that an individual pays contributions in a period t and in the following period t +1 beneficiary (generally speaking, the length of the working life corresponds to the length of the retirement period). An individual pays in the amount and receives a pension in the amount . The resulting return is: ${\ displaystyle w_ {t} \ tau}$${\ displaystyle b_ {t + 1}}$

(3) ${\ displaystyle {\ frac {b_ {t + 1} -w_ {t} \ tau} {w_ {t} \ tau}} = {\ frac {(Z_ {t + 1} w_ {t + 1} \ tau ) / E_ {t + 1}} {w_ {t} \ tau}} - 1 = (1 + n) (1 + p) -1 \ approx n + p}$

where the following notation is used:

• ${\ displaystyle n}$ = Population growth rate,
• ${\ displaystyle p}$ = Growth rate of the wage rate.

Where: , , and${\ displaystyle E_ {t + 1} = Z_ {t}}$${\ displaystyle w_ {t + 1} = w_ {t} (1 + p)}$${\ displaystyle E_ {t + 1} = E_ {t} (1-n)}$${\ displaystyle b_ {t + 1} = {\ frac {Z_ {t + 1} w_ {t + 1} \ tau} {E_ {t + 1}}}}$

Since the product can be neglected numerically, the return can be approximated by . In a “mature” pay-as-you-go system, the return on contributions is therefore equal to the sum of wage and population growth. This result was first shown by Aaron (1966). As a result, the return on pay-as-you-go systems falls if population growth falls or even becomes negative or if wage rate increases are low. ${\ displaystyle np}$${\ displaystyle n + p}$

#### Demographic changes

The effect of demographic changes on the pay-as-you-go system can be illustrated by changing equation (1):

(4) .${\ displaystyle \ tau = {\ frac {E_ {t}} {Z_ {t}}} {\ frac {b_ {t}} {w_ {t}}}}$

This formulation determines the budget-balancing contribution rate if a desired pension amount is specified. The expression

(5) ${\ displaystyle {\ frac {E_ {t}} {Z_ {t}}}}$

corresponds to the number of recipients per contributors (also dependency rate, dependency ratio or old age dependency ratio called), the expression

(6) ${\ displaystyle {\ frac {b_ {t}} {w_ {t}}}}$

the ratio of the (average) pension amount to the (average) wage rate (the wage replacement rate ).

If the system is now under financial pressure, the following options are basically available to restore the budget identity:

• Increase in the contribution rate ,${\ displaystyle \ tau}$
• Lowering the wage replacement rate (essentially only possible by lowering the average pension) and
• Reduction of the old-age burden quotient (essentially only possible by increasing the working life, i.e. later retirement).

## Pay as you go in practice

### Pay as you go in Germany

In Germany, the pay-as-you-go system is used for social insurance ( DRV pension , statutory health , unemployment and accident insurance as well as long-term care insurance ). The amount of the contributions is based globally on the cost of the services provided, although income-oriented assessment guidelines are intended to ensure that the individual contribution burden does not exceed a certain level. On the other hand, there are also minimum contributions (in 2005, for example, around EUR 260 per month as the minimum contribution for statutory health insurance).

In addition, the U1 levy is used to halve the employer's continued payment of wages in the event of illness, and the U2 levy is used to offset the financial burdens from maternity leave ; Finally, the U3 levy pays the insolvency money.

### Pension insurance through the generation contract

The original system of statutory pension insurance was based on the funded procedure , according to which the pension contributions were saved, which had to be paid equally by employers and employees on pension accounts. With the exception of short periods, however, there was never sufficient funding. In particular, inflation and the two world wars ruined the attempt. That is why the pension system was actually operated in a kind of pay-as-you-go system long before 1957.

The system of funded funding was converted into a pay-as-you-go system with a dynamic pension in the 1957 pension reform under Konrad Adenauer . The theoretical basis for the introduction of the pay-as-you-go system (§ 1383 RVO , today § 153 SGB ​​VI ) was provided by the economist and representative of Catholic social teaching Wilfrid Schreiber with his work "Existential Security in Industrial Society" , also known as the " Schreiber Plan ". Schreiber initially used the term “solidarity contract”. There he spoke of a “solidarity contract between two generations” . Unlike in the Schreiber Plan, the child pension and double contributions for childless (now also specifically referred to as the three-generation contract ) were not implemented. The broad financial basis planned by Schreiber through the involvement of freelancers and the self-employed was not implemented either. The equalization of family burdens was implemented outside the pension system, mainly through child benefit .

In Switzerland, the term was also introduced into the political discussion as part of the statutory introduction of old-age and survivors' insurance (AHV) in 1947. The AHV is also based on a pay-as-you-go system. With the introduction of further welfare state redistribution mechanisms - for example in the Health Insurance Act of 1996 - the use of the term also expanded to these areas and today stands for a widely accepted principle of the Swiss welfare state.

### Problems in the financing of the pay-as-you-go system

Due to rising costs in the health care system, increasing life expectancy and thus also growing care costs, demographic shifts (falling birth rate , aging society), falling wage quota , mass unemployment as well as withdrawals not related to insurance and economic crises in many industrialized nations, the question of the future sustainability of the pay-as-you-go system is often asked. The financing of the insurance in the pay-as-you-go system is based on the wage share derived from the national income . The national income of the Federal Republic of Germany doubled between 1970 and 2000. Assuming that national income will double again in the next thirty years, while the population will decrease by 20%, then the national income per capita will more than double. From a macroeconomic perspective, the pay-as-you-go system will also be possible in the future. In order to achieve this, however, in view of the current falling wage share, the labor factor should be appropriately involved in productivity growth.

In Germany, during the first legislative period of the Schröder government , the Riester pension was a funded second pillar of pension insurance.

A federal subsidy is paid out of tax revenue to compensate for non-insurance benefits .