An Unconditional Basic Pension within the German Statutory Pension Insurance

Transcription

1 An Unconditional Basic Pension within the German Statutory Pension Insurance Valentin Vogt Catholic University Eichstätt-Ingolstadt, Auf der Schanz 49, Ingolstadt, Germany, Abstract Due to pension reforms in the last decade, the problem of old-age poverty is back on the agenda of German social policy. In order to address this problem, additional tax-financed subsidies to stabilize both net replacement ratio and contribution rate in the statutory pension system are being proposed by the German government. Due to the equivalence principle in the German pension system, pensioners benefit from these subsidies according to their individual life-time contributions. This however raises the question whether the subsidies should not better be used to directly combat old-age poverty. In this paper, I propose an unconditional basic income for pensioners (UBP) additional to the contributions-based system which is fiscally equivalent to the government proposal. I simulate the current pension system and both reform proposals for Germany until the year The model consists of a long-term projection of the budgets of German Statutory Pension Insurance including a full population projection and a calculation of remuneration points based on employment biographies for several types of potentially vulnerable pensioners. The results show that an unconditional old-age basic income scheme significantly reduces oldage poverty, whereas the government proposal mitigates the burden of demographic change mainly for medium and upper pension incomes. As a positive side effect, the UBP increases the internal rate of return of the pension system for low-income earners. However, compared to the status quo, both proposals require substantial additional tax-based subsidies. JEL: H55, J10, J11 Keywords: Public Pension, Old Age Assistance, Demography 1

2 1. Introduction Historically, the aim of the German pension system was to ensure that everybody could maintain the same standard of living in retirement as during the working ages (Schreiber 2004). Through the principle of participatory equivalence, there has always been a direct link between life-time earnings and the pension claims of an individual (both in relative terms: the former relative to the average income of each year, and the latter relative to the total amount of pension payments of each year). This meant that also low-income earners who stayed above the existence minimum throughout most of their working years received a pension above the existence minimum. Due to the pension reforms of the last decades, this is changing. To slow down the expected growth of the contribution rate, a reduction of the replacement ratio relative to the ratio between pensioners and contribution payers and to the contribution rate growth has been legislated. This means that people with low life-time earnings now can slide below the poverty line after retirement. So, the legitimacy of the pension insurance is seriously questioned, as the main goal of ensuring everyone s standard of living in old age has been given up. Especially, it acerbates the problem of old-age poverty (in this paper defined as the need for basic social assistance in old-age), which is expected to rise anyway due to the trend towards more fragmented labour biographies, unemployment and the growing low-income sector. A proposal by the German Ministry of Labour and Social Affairs (BMAS 2016) now suggested introducing a so-called double stop line (DSL), an upper limit to the contribution rate and at the same time an acceptable lower limit to the replacement ratio. The missing amount of funding caused by the artificially low contribution rate and high replacement ratio would be replaced by an additional tax-financed federal subsidy. The first question this proposal raises is whether the additional tax funding will remain bearable for tax-payers not only within the next years, but also in the long run. Börsch-Supan/Rausch (2018) suggest that this might at least be in serious doubt. The other main, and maybe even more important, question is if the proposed double stop line is the most effective measure to address the pending problems. Due to the principle of participatory equivalence, the highest share of the additional subsidies will be distributed to higher and highest pension receivers, so if old-age poverty is seen as the most important problem, it seems clear that the DSL cannot be the most effective way. In this paper, I propose an unconditional basic pension (UBP) additional to the contributionsbased system, which is fiscally equivalent to the government proposal. It is based on a full 2

3 exclusion of all federal subsidies from the normal pension system, thus reducing its replacement ratio so far that the pension payments can be fully financed by the contributions received. The federal subsidies are then equally distributed to all old-age pensioners, which forms the UBP. To estimate their long-term effects both on the whole pension system and the individual, I simulate the current pension system and both reform proposals for Germany until the year For the macro-level, I use a detailed projection of the budget of the German statutory pension insurance based on a deterministic population projection via Leslie matrices, a deterministic labour market participation projection and a human capital augmented Solow- Swan growth model. With this macroeconomic model, the necessary additional tax subsidies can be calculated in the very long run and be compared to the growth of GDP as a measure of the expected growth of the federal government budget. The effects on the individual are calculated via stylised labour biography types which are designed to represent the most common types of vulnerable and non-vulnerable pensioners. Their pension claims are deducted from the macro-level results through their accumulation of life-time contributions, so it can be shown how much these types of pensioners benefit from both reform proposals compared to the status quo. A brief summary of the macro-level results is that both reform proposals require additional funds of up to 68 Bill. Euros per year (in 2060), but that the difference to the status quo remains relatively small until On the individual level, the main result is that the DSL proposal mainly benefits receivers of pensions above the average pension and has only a marginal effect on old-age poverty, while the UBP can have a huge effect on the removal of old-age poverty, with losses mainly at the receivers of very large pensions. In the next section, I will explain the current legislation regarding contribution rate, net replacement ratio and the existing federal subsidies to the statutory pension insurance. Then, I will briefly explain the macro-projection model and show its results for the status quo. After that, I will introduce the DSL proposal, the way it is incorporated in the model, and its macroprojection results. Then, the UBP is defined so that it matches the long-term projections of the DSL. In the following chapter, the biography types are introduced, and DSL and UBP are both compared to the status quo regarding their consequences on each biography type until Finally, the results are summed up in the conclusion. 3

4 2. Current Legislation The current legislation is mainly dominated by some important reforms conducted since the year With the original aim to distribute the burden of low birth rates and higher life expectancies fairly between contribution payers and pensioners, two factors have been introduced in the formula projecting the value of one remuneration point (the unit representing one year of earnings at the average income of the respective year in the collection of life-time earnings which reduce its growth (which was previously directly linked to wage growth), the so-called Riesterfaktor and the sustainability factor: CPV $ = CPV $&' GW $&' GW $&+ 100 RR $&' CR $&' 100 RR $&+ CR $&+ 1 PQ $&' PQ $& Hereby CPV denotes the current pension value (the Euro value of one remuneration point for a monthly pension), GW denotes the gross wage, RR the recommended contribution rate to the private, so-called Riester pension, CR the contribution rate of the statutory pension insurance, PQ the pensioner per contribution payer ratio, and t the respective year. The Riesterfaktor is the second factor in the formula, and the sustainability factor the third. Both factors lead to a reduction of the replacement ratio, while they slow down the expected growth of the contribution rate. With 62.4 Bill. Euros (in 2015), the federal subsidies are the second biggest source of funds for the German statutory pension insurance after the contributions. There are three different types of subsidies defined by German social law, each with a different original purpose, a different source of tax funding, and a different projection method: the general federal subsidy, the additional federal subsidy, and the second additional federal subsidy (Erhöhungsbetrag). The general federal subsidy was introduced as a tax-financed topping-up of the sum of contributions in order to lift up the replacement ratio (and it was supposed to compensate the pension insurance for some social benefits it distributes, but it has never been defined for which benefits exactly and up to which amount). It is financed through the VAT, and projected by the following formula: GFS $ = GFS $&' GW $&' GW $&+ CRF $ CRF $&' 4

5 Hereby GFS denotes the general federal subsidy, and CRF a fictive contribution rate that would be necessary to balance the budget if the two additional federal subsidies didn t exist (the other notation follows the one in the CPV formula). The additional federal subsidy was introduced as a tax-financing of social, non-insurancerelated benefits of the pension insurance. It is financed by the VAT, and projected through the following formula: AFS $ = AFS $&' VAT $ VAT $&' Hereby AFS denotes the additional federal subsidy, and VAT the total VAT revenues. The second additional federal subsidy, at last, has again been introduced as a tax-financed stabilisation of the replacement ratio, and is financed by the so-called Ökosteuer, a tax on energy consumption. It is projected by the following formula (SAFS denotes the second additional federal subsidy): SAFS $ = SAFS $&' GW $&' GW $&+ Even though the additional federal subsidy was aimed to finance the non-insurance-related benefits of the pension insurance, it is not linked with them in any way. It also flows into the total sum of funds for the pension payments, thus actually lifting the replacement ratio/decreasing the contribution rate like the other two federal subsidies. The current pension value together with each pensioner s individual sum of remuneration points, the total number of pensioners, the sum of income subject to contributions (and gross wages), and the sum of federal subsidies form the set of determinants for replacement ratio and contribution rate. Though they are thus clearly defined as a function of the demographic and economic determinants, legislation has set some additional targets for both. Until 2020, the contribution rate has an upper limit of 20 %, and 22 % until The replacement ratio has a lower cap of 46 % until 2020, and 43 % until It is generally assumed that these targets were set so that they can be reached anyway as the Riesterfaktor and the sustainability factor will balance both variables within these borders until For the time after 2030, no targets for both variables have been set by legislation yet, but projections such as Börsch- Supan/Rausch (2018) show that both will go beyond those borders shortly after that. 5

6 3. The macro-model and its status quo results The macro-model consists of a deterministic population projection, a deterministic labour market participation projection, a human capital-augmented Solow-Swan growth model and a detailed computation of the budgets of the German statutory pension insurance. It is the same model as in Vogt/Althammer (2016) and Vogt (2017), albeit with minimal modifications of the basic assumptions due to data that has become available very recently. It is currently designed to run from the base year 2010 to the year The population projection is based on the method of Leslie matrices (see Caswell 2001), and uses the method of Bomsdorf/Trimborn (1992) for the mortality forecast. The total fertility rate is set to 1.4, like in most population projections for Germany, such as Destatis (2015). Migration is modelled as in the baseline scenario of Vogt (2017). For the projection of labour market participation rates, I use the method of Burniaux et al. (2004), which applies entry and exit rates to/from the labour market to project participation rates of one year to the next. I use it in the same slightly modified version as used in Werding/Hofmann (2008), and with the same exogenously set unemployment rate as Werding (2016). The overall economy is represented by a human capital-augmented Solow-Swan growth model. It has a Cobb-Douglas production function with the inputs capital and human capital, and with constantly growing total factor productivity and a constantly growing human capital quality index. The savings rate and depreciation ratio are kept constant throughout the whole projection period. Wage growth is directly derived from labour productivity growth. The pension insurance is represented by a computation based on the earnings history of an average member of each cohort. So, for each cohort and year it is tracked how many of its members are employees, unemployed, self-employed etc., and, based on the age of the cohort s members in that year, which fraction of the average wage an average member has earned. Differences within each cohort regarding the actual retirement age, labour market entry or times of inactivity/unemployment/immigration are taken into account in the cohorts average sums of remuneration points and deduction factors. On the other hand, wage heterogeneities within each cohort have to be ignored in the macro-model. Income subject to contributions, federal subsidies and pension payments are calculated iteratively year by year according to German Social Code. At the end of each iteration step, 6

7 the contribution rate for the respective year is defined to balance the budget. The net replacement ratio is calculated like in Werding (2014). For this paper, the demographic assumptions are kept identical in all scenarios. The same holds for all calibration parameters of the macroeconomy. The difference between the scenarios is the calculation of replacement ratio and contribution rate. In the status quo scenario, both are calculated the way German Social Code defines it: the CPV and the federal subsidies are calculated via the formulas specified above. This automatically defines the replacement ratio, and the contribution rate is then set to close the budget. Contribution Rate (in %) Replacement Ratio (in %) Contribution Rate Replacement Ratio Fig. 1: Contribution Rate and Replacement Ratio in the Status Quo (Source: own calculations) Results depicted in Fig. 1 show that the targets defined by laws so far are mainly met. The contribution rate hits the target of 22 % in 2031, and the replacement ratio hits the target of 46 % in 2026 and of 43 % in On the other hand, the contribution rate still increases immensely, only with a short break between 2034 and 2040, and reaches 25 % after The replacement ratio decreases heavily, almost to 40 %, also with a short break between 2034 and After that break, both variables reach values which currently nobody considers bearable for contribution payers and the economy on one side, and a large share of the pensioners on the other side. Both clearly show the necessity of a different approach, be it additional tax funding, a different method of pension distribution, or other possible measures. 7

8 4. The Double Stop Line (DSL) proposal and its macro-level impacts The double stop line proposed in BMAS (2016) is embedded in a larger package of suggested measures, albeit most other ones are special solutions for small details, or larger details, such as the so-called solidarity pension. The latter is aimed to lift up pensions of people who have payed contributions for an exceptionally long period, but would end up with a low pension due to far-below-average earnings. It could be helpful for a few people at risk of becoming poor in retirement, but it is not directly aimed at old-age poverty, rather at the tier above the one at risk of poverty. Also, it is still quite unclear whether such a measure will be introduced, so I leave it out in this paper. The DSL approach itself mainly consists of setting an upper cap for the contribution rate at 25 % after 2030 (22 % before 2030 and 20 % before 2020), and a lower cap for the replacement ratio of 46 %. Unlike the previously legislated stop lines, it is very unlikely that these targets can be met without adjustments elsewhere. And unlike the previous legislation, a concept is included which measures should be taken when the targets are not met. In that case, an additional federal subsidy, called the demographic federal subsidy, has to be introduced, so that both variables can remain within the targets. The subsidy has to be defined such that the budget is still closed even with the too low contribution rate. In order to model the DSL approach within the macro-model, exactly the same steps have to be incorporated in the model that were described in the last paragraph: At first, the replacement ratio for each year of projection is set to the maximum of either the replacement ratio as in the status quo scenario or 46 %. Then, the whole pension insurance module of the model is run to iteratively determine the contribution rate needed to reach exactly this replacement ratio. And, also the general federal subsidy has to be calculated newly, as it depends on the contribution rate development, unlike the two additional federal subsidies, which remain unchanged as their projection formulas are not affected. After that, the upper cap for the contribution rate is applied, and it is computed how much out of the contribution payments is lost due to the lower contribution rate. This value is then set as the demographic federal subsidy of the respective year. The results of the double stop line approach are depicted in Fig. 2. It shows that the replacement ratio reaches its cap much earlier than the contribution rate, even though the contribution rate is lifted up quite a lot due to the higher replacement ratio already from 2025 on. During the period when the replacement ratio of the status quo scenario remains constant 8

9 between 2034 and 2040, the contribution rate develops parallelly to the one of the status quo scenario, albeit with a higher slope. After that period, its increase is again steeper than in the status quo scenario, until it reaches the upper cap of 25 % in After that, the demographic federal subsidy is needed. Contribution Rate (in %) Replacement Ratio (in %) CR (Status Quo) RR (Status Quo) CR (Double Stop Line) RR (Double Stop Line) Fig. 2: Contribution Rate and Replacement Ratio in the DSL and Status Quo Scenarios (Source: own calculations) 250 Federal Subsidies in Bill. Euro General FS (SQ) Total Sum of FS (SQ) General FS (DSL) Total Sum of FS (DSL) Demographic FS (DSL) Fig. 3: Federal Subsidies in the DSL and Status Quo Scenarios (Source: own calculations) 9

10 Fig. 3 depicts the evolution of all federal subsidies including the demographic subsidy in both scenarios. It again shows that the demographic subsidy is not needed until 2047 (except for a small bump in 2030 which is caused by a delayed reaction of the contribution rate calculation to the upper cap of the replacement ratio), but that the general federal subsidy increases sharper from 2025 on, when the replacement ratio reaches the lower cap, due to the sharper increase of the contribution rate. After 2047, the total sum of federal subsidies starts to increase dramatically due to the sharp increase of the demographic federal subsidy, and also the share of the demographic subsidy among the total sum of subsidies increases, until it reaches almost one third in If we assume that the total federal budget increases with the same growth rate as the gross domestic product (so with a much slower growth rate than the general federal subsidy), this clearly confirms the doubts about the sustainability of the DSL approach raised by Börsch-Supan/Rausch (2018). And it confirms how urgent the question is whether the DSL approach is at least an efficient measure against the pending problem of old-age poverty, when it is such an expensive proposal. In order to address this question, I define the UBP in the following section, and then use representative biography types to assess the consequences of both proposals on them regarding the amount of pensions they receive. 5. The Unconditional Basic Pension (UBP) approach The UBP I propose in this paper is, at first, designed to be fiscally equivalent to the DSL proposal. This means that it requires the same demographic federal subsidy, and also the same other federal subsidies, and the same contribution rate. The difference between the two approaches is the distribution of these funds. The main idea of the UBP is that all the federal subsidies are tax-financed and not contributions-based, so it is not at all justified to distribute them according to the same mechanism as the contributions-based funds of the pension system. The principle of participatory equivalence cannot be applied to them in the same way. Instead, I propose a per-capita distribution of the subsidies to each old-age or reduced earnings capacity pensioner. This means that the current pension value has to be decreased by the same ratio as the funds: contributions by total funds. The contributions-based old-age and reduced earnings capacity pensions remain, but at a much lower level than before. It is now put on top of an equal basic pension which is paid out to everybody who reaches enough years of contribution to receive an old-age pension or enough years of contribution plus all other prerequisites to receive a reduced earnings capacity pension at all. There is no transfer 10

11 withdrawal rate to this basic pension, as it is a part of the total old-age pension, and not a social transfer. Thus, all macro-projections are equal for the UBP and the DSL proposal in this model. It can be argued that labour supply (especially regarding individual retirement age) and savings behaviour reactions had to be taken into account within the projection model, but this has to be left out to other papers. Nonetheless, a huge difference can be found between both proposals, and between each proposal and the status quo on the individual level, which will be shown in the following chapter. 6. Representative biography types and their pension claims in DSL and UBP For the analysis on the individual level, the method of representative biography types is chosen. It can offer less insights than a full projection of the distribution of remuneration points at entry into retirement on the micro-level, but such a micro-projection/simulation would be hardly possible for such a long projection period with full macro-level consistency. The method of representative biography types thus cannot replace a full distributive analysis, but it is still able to give important insights into the consequences of the reform proposals on an individual level. The first biography type is the average person as can be found in the macro-model as the average cohort member. This person enters retirement with 35 remuneration points, which is the average sum of remuneration points for an old-age pensioner in the macro-model. As can be seen from this sum, the average person differs quite a lot from the standard pensioner (Eckrentner) used to calculate the replacement ratio according to the standard method used by the German government, especially due to shorter employment histories than the 45 years which are the assumption for the standard pensioner. The second biography type is called minimum wage worker. This type has had an aboveaverage long working life with 45 years of contribution, but always very close to the minimum wage (in a full-time job). I assume for this calculation that the minimum wage grows as fast as the average wage, an assumption that might even overestimate the pension claims of this type, as it is quite likely that the minimum wage could grow with a smaller growth rate. This biography type represents the people who always stay in the low-income sector. It can also represent people who spend a few years in jobs above the low-income sector, but also a few years in unemployment or marginal employment or have a later entry into the labour market so that the few years above the low-income sector are compensated. The minimum wage 11

12 worker enters retirement at 23 remuneration points, which is quite low compared to the average person and especially compared to the standard pensioner. The biography type mixed represents people with a somewhat worse career development, with also 45 years between labour market entry and retirement, but with 5 years of unemployment and 5 years of marginal employment in between, and the rest of the time also filled with an income exactly at the minimum wage (full-time). This type seems representative for a larger share of the population than the minimum wage worker, as it is more common nowadays, but the minimum wage worker is supposed to become more common in the future due to developments such as the digitalisation and a growing low-income sector. The type mixed reaches only 19 remuneration points at retirement, which makes it clear that this type is very prone to old-age poverty. The last biography type, the marginally self-employed represents an even more problematic career: a person who spends the first 25 years of their working life close to the minimum wage, and then starts a small self-employment with contributions to the pension insurance at the minimum for self-employed people for 20 years. This type is still not even close to a worstcase biography, but can be seen as kind of the worst case of a person who is still able to make a living without transfers during working life, and thus, under the old main goal of the pension insurance of insuring each person s standard of living, should be able to reach a pension above the basic social security level. This biography type enters retirement with only 15 remuneration points, which is less than half of the remuneration points of the average pensioner. With the current pension value for each year until 2060 computed in the macro-model for the status quo, the DSL approach, and the UBP, I now calculate the monthly pension each of the four biography types approximately receives in each year. Fig. 4 depicts the pensions in the status quo scenario and for the DSL approach. It is clearly shown that the DSL approach can lift the pension claims of all four types, albeit it lifts them proportionally to their size, so the highest pension, the one of the average pensioner, is lifted much more than the lower three. For the marginally self-employed, the DSL has hardly any impact, and also the mixed type does not get lifted above the at-risk-of-poverty line of a single household of today. What is not directly included in the diagram, but can be assumed from this numbers, is that the main benefit of the DSL goes to receivers of pensions far above average. So clearly the DSL is not an effective measure against old-age poverty. 12

13 1760 Monthly Pension (in Euro) Average Person (SQ) Minimum Wage (SQ) Mixed (SQ) Self-Employed (SQ) Average Person (DSL) Minimum Wage (DSL) Mixed (DSL) Self-Employed (DSL) Fig. 4: Monthly Pensions in the DSL Scenario compared to the Status Quo (Source: own calculations) 1760 Monthly Pension (in Euro) Average Person (SQ) Minimum Wage (SQ) Mixed (SQ) Self-Employed (SQ) Average Person (UBI) Minimum Wage (UBI) Mixed (UBI) Self-Employed (UBI) Fig. 5: Monthly Pensions in the UBP Scenario compared to the Status Quo (Source: own calculations) Fig. 5 shows the comparison between status quo and UBP scenario pensions and reveals a very different situation than in the DSL scenario. The average pension reaches almost exactly the same path as in the DSL approach, but the other three types are lifted up heavily, especially in the longer run, when the demographic federal subsidy boosts the funds available for the UBP. All three types are lifted much closer to the poverty line, and above the basic 13

14 social assistance level for a single household already in the short run. In the very long run, at least two of them can reach values above the at-risk-of-poverty line, and even the marginally self-employed type can get close to it. It can be summarised that the UBP has a large impact on the biography types who represent groups with a high risk of old-age poverty in the status quo. And it actually shows even more: The UBP could lift a remarkable number of pensioners out of the basic social assistance in old-age, thus saving on a significant amount of costs for this social transfer. Thus, it is actually not fiscally equivalent to the DSL approach, if other social transfers are taken into account, but a much cheaper measure. The flipside of these advantages is that pensions above and especially far above average would be significantly reduced. From the point of view of the principle of participatory equivalence, this is nonetheless justified, as the current distribution mechanism of the federal subsidies in fact violates this principle, and would violate it even more if the DSL proposal with its large demographic subsidy was legislated. 7. Conclusion In this paper, I have first shown in the status quo projections that reforms have to be considered regarding old-age poverty and the financing of the pension insurance. The DSL proposal of the German Ministry of Labour and Social Affairs nonetheless would be a very expensive measure, with at most approx. 68 Bill. Euros of additional federal subsidies, and with much higher contribution rates than under the status quo between 2026 and And, which is even more important, the DSL approach would not be an effective measure against old-age poverty, as it mainly benefits receivers of above-average old-age pensions, and hardly receivers of low pensions. This violates the principle of participatory equivalence even more than the status quo already does, as most of the additional funds in the DSL approach are taxfinanced and not part of the efforts of contribution payers. On the other hand, an unconditional basic pension (UBP) based on the withdrawal of all federal subsidies from the remuneration-points-based pension, and a per-capita monthly payment of these funds with no transfer withdrawal rate could play an immense role against old-age poverty. Albeit designed to be fiscally equivalent to the DSL approach both in federal subsidies and contributions, it would actually be a much cheaper measure, as it could lift a remarkable number of pensioners out of the basic social assistance in old-age, and save a lot of money on this transfer. From the point of view of the principle of participatory equivalence, 14

15 this approach seems much more reasonable, as tax-financed funds are distributed equally per capita instead of on the basis of the efforts of contribution payers. The main gap this paper cannot close is the need for a full distributive analysis, which would require a simulation of the distribution of remuneration points at retirement at the individual level. But it could show that the UBP is a much more considerable proposal than a DSL when avoiding old-age poverty is the main reform goal. References Bomsdorf, E. and Trimborn, M. (1992), Sterbetafel 2000: Modellrechnungen der Sterbetafel, Zeitschrift für die gesamte Versicherungswirtschaft 81-3, pp Börsch-Supan, A. and Rausch, J. (2018), Die Kosten der doppelten Haltelinie, MEA Discussion Paper , Munich. Bundesministerium für Arbeit und Soziales (BMAS) (2016), Das Gesamtkonzept zur Alterssicherung. Das Konzept im Detail, Berlin. Burniaux, J., Duval, R. and Jaumotte, F. (2004), Coping with Ageing: A Dynamic Approach to Quantify the Impact of Alternative Policy Options on Future Labour Supply in OECD Countries, OECD Economics Department Working Papers 371, pp Caswell, H. (2001), Matrix Population Models: Construction, Analysis and Interpretation, Sinauer Associates. Destatis (2015), Bevölkerung Deutschlands bis koordinierte Bevölkerunsgvorausberechnung, Wiesbaden. Schreiber, W. (2004), Existenzsicherheit in der industriellen Gesellschaft: unveränderter Nachdruck des Schreiber-Planes zur dynamischen Rente aus dem Jahr 1955, Diskussionsbeiträge Nr. 28, Bund Katholischer Unternehmer (BKU), Cologne. Vogt, V. (2017), Alternating Migration Flows and their Age-Structure Effects on the Long- Term Sustainability of the German Statutory Pension Insurance, EcoMod 2017 International Conference on Economic Modeling Conference Proceedings. 15

16 Vogt, V. and Althammer, J. (2016), Linking Retirement Age to Life Expectancy in a Bismarckian System The Case of Germany, National Institute Economic Review 237, pp. R22-R29. Werding, M. (2014), Demographischer Wandel und öffentliche Finanzen: Langfrist- Projektionen unter besonderer Berücksichtigung des Rentenpakets der Bundesregierung, Arbeitspapier 01/2014, German Council of Economic Experts. Werding, M. (2016), Rentenfinanzierung im demographischen Wandel: Tragfähigkeitsprobleme und Handlungsoptionen, Arbeitspapier 05/2016, German Council of Economic Experts. Werding, M. and Hofmann, H. (2008), Projektionen zur langfristigen Tragfähigkeit der öffentlichen Finanzen, ifo Beiträge zur Wirtschaftsforschung 30/