On a national retirement savings scheme with annuitisation and cross-subsidies: a two-tiered economic model

Transcription

1 On a national retirement savings scheme with annuitisation and cross-subsidies: a two-tiered economic model Benjamin Avanzi a,1,, T. Sachi Purcal a,2 a Actuarial Studies, Australian School of Business UNSW Sydney NSW 2052, Australia Abstract We adopt a two-tiered economic approach to examine a national retirement savings scheme involving annuitisation and cross-subsidies. The first tier of our model is controlled by government, which mandates contribution rates, interest rates, and conversion into benefits. In contrast, agents decide on the level of contributions in the second tier, which earns interest at the market rate, reduced by an element reflecting the gap between actuarial market values and regulated values. In our model, the level of non-mandatory savings (the second tier component) is a function of the variables controlled by the government. We analyse their effect on the level of non-mandatory savings and provide substantial insight on how the system functions. This two-tiered model is implemented in Switzerland. We conclude with a discussion of the Swiss and Australian systems of retirement savings as seen through the lens of our model. Key words: mandated retirement savings, annuitisation, pensions, regulation JEL codes: J26, H55, D91, E21 Corresponding author. Tel.: ; fax: addresses: b.avanzi@unsw.edu.au (Benjamin Avanzi), s.purcal@unsw.edu.au (T. Sachi Purcal). 1 Benjamin Avanzi, PhD, is a member of the Swiss Association of Actuaries and an affiliate member of the Institute of Actuaries of Australia. 2 Sachi Purcal, PhD, is an Associate of the Society of Actuaries. June 25, 2009

2 1 Introduction The "annuity puzzle" stems from the observation that there is surprisingly small demand for voluntary lifetime annuities throughout the world (Purcal and Piggott, 2008). While the U.K. is the world s largest market for immediate lifetime annuities (some GBP 12 billion of business was written in 2005), the principal driver for this market is the compulsory annuitisation at retirement of tax-efficient defined contribution personal pension plans. In contrast, in the U.S. there is no such compunction to annuitise. However, although vast sums flow into U.S. annuities markets (USD $301 billion in 2004), almost without exception these funds find their way into tax-sheltered deferred annuities, with scant amounts ever being actually annuitised an overwhelming proportion are withdrawn as lump sums. In stark contrast, the market for voluntary lifetime annuities in Australia in 2008 was only some AUD $11.9 million, involving a miniscule 61 contracts to generate a paltry AUD $ of income flow (Plan for Life Research, 2008). One remarkable exception to this widespread trend is the case of Switzerland. There almost two-thirds of retirees freely choose to convert their accumulated retirement savings including a substantial component of voluntary savings into a lifetime income stream; only a quarter (Bütler, 2003) selected to take a lump sum. Recent figures indicate 78% of the income of the aged stems from annuities (OFS, 2007), of which slightly less than half stems from second pillar savings. Avanzi (2009) describes the Swiss retirement system in detail, as well as exploring the reasons why the Swiss annuitise. In this paper, we model the second pillar of this surprising retirement system, a system that not only involves a high degree of annuitisation, but also achieves this entirely through private provision, with remarkable stability of annuity prices. How does the extraordinary Swiss system work? In the next section, we present its salient features. In Section 3 we discuss the key features responsible for its well-functioning behaviour. We conclude in Section 4 by describing the case of Switzerland, where the model has operated successfully since 1985, before considering the hypothethical case of model s introduction to Australia. 2 A two-tiered retirement savings model 2.1 Macroeconomic landscape Consider an economy where agents may save some of their income into an organised system of retirement savings during n years of their life. At the end of these n years, 2

3 everyone is supposed to retire, or at least leave the organised system. For instance, if agents can contribute from the age of 18 and the ordinary age for retirement is 65, then n is equal to 48. It is assumed that these agents have an average salary of amount w k in year k, 1 k n. The proportion of the active population in year k is denoted by α k with n k=1 α k = 1 (without loss of generality). This allows for any repartition of the working force between ages, but this repartition remains constant over time. Furthermore, we assume that the long term return on investments (market rate) is equal to r p.a. We model this variable as a constant. However, our aim is to model long term behaviour of agents, and it is reasonable to assume a stable (real) market return in the long term. Also, our model is at the level of an entire economy, which further decreases the variability of this figure. Finally, we will see later that this variable s main impact is in a difference with another rate, the latter being a decision variable that can be monitored each year. 2.2 Retirement savings We model the level of savings of agents at the macroeconomic level. The government creates an organised system of retirement savings with two components. The first component will be referred to as the "mandated component". Agents must contribute to their mandated component savings at a rate β k on their income w k, 1 k n. Mandated savings accumulated in this way earn an interest rate of r p.a. At retirement, the global amount of mandated savings is multiplied by a conversion rate ξ and decumulated through a life annuity equal to this product. The difference between ξ and the actuarially fair conversion rate is denoted by ; a positive or negative difference represents a lack or an excess of resources to fund the annuity, respectively. The accumulation and decumulation of this first component are entirely controlled by the government. The law defines β k and ξ (who are stable over time, but can be modified by a change of the law) and the government decides on r each year. The overall level of mandatory savings is then n k M = α k β l w l (1 + r) k l. (1) k=1 l=1 Note that we assume here that r has been constant for the past n years, even though the government can modify this figure every year. It is a weak and reasonable assumption, for the same reasons as the ones given for r, as long as our figures are expressed in real terms. Each year, a proportion α n of the active population retires. Their mandatory 3

4 savings n α n l=1 can be expressed as a (constant) fraction ρ = of the overall mandatory savings M. β l w l (1 + r) n l α nl=1 n β l w l (1 + r) n l nk=1 α kl=1 (2) k β l w l (1 + r) k l The second component is not mandatory. However, it is different from a standard savings account in several ways. Contributions are tax exempt, providing a powerful incentive to save for retirement using this vehicle. Non-mandatory savings are guaranteed and in principle blocked until retirement. Agents contribute to their non-mandatory component at a (constant) rate γ on w k, 1 k n. Non mandatory savings earn interest at a rate r p.a. It is reasonable to assume that r < r, (3) otherwise agents could save money in a tax free, guaranteed environment, and get a higher rate of return on investment than r. The level of non-mandatory savings is then n k NM = γw l (1 + r ) k l, (4) α k k=1 l=1 The variables γ and r are endogeneous. 2.3 The propensity to save for retirement Our main focus is on the impact of the government decision variables r (in the short term) as well as and β k (in the long term) on the level of non-mandatory retirement savings. Although it is not realistic to assume that agents will save at a constant rate γ in the non-mandated tier component over their whole active life, γ gives an excellent (unique) indicator of the long term propensity to save on the top of the mandatory component. We have a closed, autarkic system. In other words, the government does not subsidise or levy any tax from the system at any time. Hence r (M + NM) = rm + ρm + r NM, (5) because M and NM are both invested in order to yield the long term rate r. The interest earned on the retirement savings (M + NM) is used to remunerate M at 4

5 the rate r and compensate the cost of annuitisation ρm. What is left represents the interest on the non-mandated component. Reorganising (5) yields ( r = r 1 + M ) M (r + ρ ) NM NM = r + 1 γ (r r ρ ) f(r ), (6) where f(r ) = f(r ; r, n, α 1,..., α n, β 1,..., β n ) = γ M NM is a decreasing function of r that is independent on γ and for which d dr f(r ) = f(r ) 1 + r (7) holds. Equation (6) means that the net rate r is equal to the market rate r, corrected by a certain factor. We can further develop (6) into r = r + π γ f(r ) (8) = r + πm NM, (9) where π = r r ρ < 0, (10) whose sign follows from condition (3). The variable π is the cost (as a rate of M) of the figures mandated by the government r, and b k (hidden in ρ). The product πm in (8) can be interpreted as an annual participation premium that is apportioned evenly to the mass NM as a correction to the market rate r. The direct relation between γ and r is obvious in (8), from which we get γ = π f(r ) r r. (11) 2.4 Comparative statics In this section, we study the relation between the demand for non-mandated retirement savings encapsulated by γ, with the rate of interest r and the government decision variables π and β k. 5

6 It is known that dx y)/ y = g(x, dy g(x, y)/ x, (12) where g(x, y) = 0 must be a continuous, once differentiable function on the range of x and y. We will use (8) and define For convenience, we begin by determining g(π, r, γ) = r r π γ f(r ) = 0. (13) g π = ) f(r = r r, γ π (14) g r = 1 r r f(r ) f (r ) = 1 + r 1 + r, (15) g γ = π γ 2 f(r ) = (r r ) 2 πf(r ). (16) The effect of π on γ follows from the application of (12). We have dγ dπ = g/ π g/ γ = γ π = f(r ) r r, (17) which is positive as long as π is negative, that is, if condition (3) holds. This is not surprising. A decrease on the internal subsidy (a increase on π) will yield a better deal on non-mandatory savings, and thus an increase on its demand. In addition, (17) teaches us that this effect is inversely proportional to the current spread between r and r. It also depends on f(r ), a function that reflects the demographic and economic structure of the active population of agents, as well as the mandatory contribution rates β k which the government has the power to change. In a similar way, we have dγ dr = g/ r g/ γ = γ r r ( 1 + r ) 1 + r = π f(r ) (r r ) 2 ( 1 + r 1 + r ). (18) If π < 0, (18) and thus dr /dγ are positive, which means that agents with nonmandated savings will always have an incentive to save more in this instrument, as r increases along with γ. Finally, dr dπ = g/ π = r r ( ) 1 + r > 0, (19) g/ r π 1 + r 6

7 which makes sense and provides an additional check of the reasonableness of the model. 3 Discussion Although the retirement savings system described in the previous section can be run without the operational action nor the money of the government, it is strongly influenced by its decisions. For that matter, the level of π is crucial. This figure is entirely determined by the government, given the demographical and economical structure of the economy. It determines the propensity of contributing to the nonmandatory component. Moreover, its size and sign are crucial for the system to work. The system with a π that would be positive or null is not an option. If π was positive, agents would get a higher return on their non-mandatory savings than the market rate, together with enjoying tax rebates and a government guarantee. In itself, this should mean an infinite propensity to save in the non-mandatory component. Apart from being ethically contestable, this situation is not acceptable given how the system is designed. Assume that π is positive and that the system is at an equilibrium. An increase of π will at the same time lead to an increase of r through (19) and a decrease of γ through (17); the direct increase of r has to be compensated by a decrease of non-mandated savings NM in order to keep the system self contained according to (5). In addition to the fact that agents are mandated to contribute to an unfair retirement system (M) that pays in average less that its contributions (π > 0), this is to the profit to a number of agents that is smaller (γ ) and better off (r ) as the unfairness increases (π ). The case π = 0 does not make sense either, as the system would generate unnecessary distortions on the mandatory component without any benefit. In both cases (π 0), our analysis suggests that it would make more sense to run a system with a single component, leading to a loss of all the attractive features of the two-tiered model. Hence, the government can and even has to induce internal subsidies from NM to M by setting r and/or high enough (for a given level of β k ) such that π is negative. This will ensure the system to be healthy. The system can be finely monitored by the government with short term decisions r, whose level is decided annually by the government, as well as long term decisions and β k, whose levels are the result of a democratic process and defined in the law. Of course, as time goes by, changes of the demographic (mortality) and economic (interest rates) structure of the economy will lead to shifts in, which would need to be updated regularly. However, this figure can remain more or less stable for decades 7

8 and as its (arguably slow) shift can be taken into account when r is determined for many years before a change is required. In the short term, the government can set r in order to keep π constant or modify it. The government can choose whose benefits it wants to uplift by choosing the contribution rates β k (which determine who has privileged mandated savings). In addition, the β k have both an impact on ρ, a component of π, and on the effect modifications of π have on γ through the function f(r ) in (17). Of course, as (17) is positive, there is a trade-off between higher subsidies (lower π) and higher levels of non-mandatory savings (higher π). Depending on the way the β k are defined this may mean a political choice between subsidising retirement savings of lower income agents (who would thus have most of their savings in M) and encouraging a higher overall level of retirement savings. The fact that the system needs a substantial level of non-mandatory savings in order to work properly with a negative π seems paradoxal, and even dangerous, as non-mandatory savings are... not mandated! But the way the system is designed still leads to an adequate level of non-mandatory savings, which makes it a very clever answer to many problems discussed in the retirement annuities literature. This system provides a liquid market for life annuities by mandating annuitisation of the component M at retirement. These annuities are not provided by the government, and they are fully financed by the disguised subsidy from NM to M. The mere management of this whole mass of assets as well as the life annuities is likely to make it a business profitable enough to interest private insurers. Insurers can then also offer annuitisation of the non-mandatory component of the retirement savings at an actuarially fair rate of conversion, as the critical mass for a healthy portfolio of life annuities has been reached and as it will help further mitigate their risk through diversification and a higher level of annuities. Moreover, the system provides security and stability for the retirement income of active agents. The accumulation of M and its decumulation is largely predictable (even deterministic for given income, r and ξ). Hence, agents can plan on a secured retirement income as they approach retirement, and need not fear for substantial market alteration as the one that is observed in the current financial crisis. In a different mindset, our model provides an interesting approach for the introduction of a single component system. During the first years after the introduction of such a model, retiring agents have a very incomplete contribution period, which leads to low and unattractive benefits. Note that π = 0 with positive leads to a transfer from active agents (with non-mandated savings) to retiring agents who enjoy boosted annuities. The proposed solution would then to introduce first a two-tiered model with an initial (positive) difference between r and r that would be kept equal to ρ (in order to have π = 0). This difference would then be grad- 8

9 ually decreased until r = r and = 0, when both components could finally be merged to yield a single component system. Note, however, that empirical evidence suggests that this final model would probably see the extinction of the provision of annuities. 4 A tale of two cities 4.1 Bern Switzerland had already substantial savings when the country introduced in 1985 a system of retirement savings with two components similar to the one described in this paper (Hepp, 1998). Existing savings were assimilated to non-mandatory savings and constituted the necessary initial reservoir for the two-tiered model to be introduced. Contribution rates to the mandatory component have not been modified since then, with the exception of the postponement of the ordinary retirement age for women. Agents can contribute from the age of 18 to the age of 65 (64 for women). The contribution rates β k are positive from the age of 25 and increase until retirement. In addition, they focus on low to medium incomes, as higher tranches of income can only contribute to the non-mandatory component. Non-mandatory savings are substantial, and Switzerland is one of the few countries with an amount of savings exceeding the gross domestic product (Gerber and Weber, 2007). At retirement, annuitisation is the default choice (on both components). However, pension funds can offer the option to take the capital as a lump sum and the vast majority of them do. The conversion rate ξ is a package of a lifetime annuity, as well as future survivor annuities and immediate children annuities. These additions are mandatory. A positive makes it a rational choice to annuitise on M, especially for agents that are married and/or have children; see Bütler and Teppa (2007) for a money s worth analysis and empirical study of the decision of annuitisation in Switzerland, as well as Avanzi (2009). Even though the rate of conversion on NM was usually equivalent to ξ until the beginning of the 21st century, it is now expected to be actuarially correct (and thus lower than ξ) and is highly regulated. Private insurers have to submit their annuitisation rates for approval by the regulation authority every year. As explained above, most of the Swiss choose to annuitise. In 2003, newly retired households achieved a replacement rate of 61.2% (OFS, 2007). This last proportion (ceteris paribus) is expected to increase as the system needs another 15 years before agents retire with a complete contribution period. 9

10 This looks like a success story, but the Swiss system is currently facing some issues. Our paper calls for an active monitoring of the components of π, in particular r and. However, the government variables r and ξ have remained constant for almost 20 years. This led to a de facto increase of as mortality rates decreased. Moreover, the financial crisis of the beginning of the century led private insurers to ask for a decrease of the variable r. This prompted indignation from the insureds associations, as no insurer had asked for increases of r during the golden years.... Notwithstanding, the government decreased r and has changed it every year since then. Also, ξ has been reduced, although it is difficult to tell if the resulting (current) is lower or higher than in 1985; it would require careful study since relevant mortality and fair (technical) interest rates have decreased since then. The system is in a crisis, as the government does not know how to set r, which is thus more the result of a lobbied political process than a rational process, and as a further reduction of ξ (and thus of ) is extremely actively discussed in the political arena and will be decided in a referendum in 2009 or Overall, the state of the debate suggests a general misunderstanding of how the system is working. Our paper provides substantial insight. Firstly, the current system with a π that would be positive or null is not an option. In order for the system to work, π has to be negative and there is thus a need for to be positive (ξ to be higher than actuarially fair) and r to be high. Current arguments of the government are the converse. Secondly, needs to be high enough to make annuitisation of the mandatory component a rational choice for most of the agents, and thus for reaching a critical mass of life annuities portfolio in Switzerland. Unless, of course, Switzerland chooses to renounce annuitisation. Thirdly, r should not be based only on the economic performance of the previous or current years, but on a long term average market return, and, more importantly, on a systemic approach taking into account demographics and the current level of in other words, based on the target value of π. More generally, the political choice that is given to the population can (and should) be expressed more clearly as the one of better subsidised (without any implication on the government s budget) annuities for lower income agents versus higher encouragement to save on non-mandated annuities (arguably for higher income agents). 4.2 Canberra Both Switzerland and Australia have private mandatory second pillar retirement savings policies, with Australia introducing its Superannuation Guarantee in One of the aims of the introduction of the Superannuation Guarantee was expanded 3 For a description of the Australian retirement system, see Bateman et al. (2001). 10

11 private provision of retirement benefits. In this section we explore the possibility of Canberra drawing closer to Bern. The retirement systems described in sections 2 and 4.1 above involve a mandated second pillar with retirement income streams provided by private life annuity suppliers. This is attractive to Canberra as it is in harmony with its private provision goals, as well as offering an opportunity to introduce a system geared towards provision of retirement income streams, rather than the current typical practice of retirees taking lump sum benefits. Lump sum benefits provide no longevity insurance and permit retirees to manage their affairs in such a way as to maximise entitlement to Australia s first pillar (means-tested) age pension. An important consideration with respect to the retirement systems described in sections 2 and 4.1 above is that an adequate supply of non-mandatory saving exists in the second pillar. Could Canberra ensure this supply would exist following a change toward such retirement systems? On the positive side, we have noted in the previous section that Bern s introduction of its current retirement system involved taking already existing second pillar retirement savings to create the nonmandatory savings of the current two-tiered model. Canberra could take a leaf out of Bern s book and turn the pool of Superannuation Guarantee savings into the non-mandatory savings of the model outlined in this paper. Numerous concerns exist as to whether Canberra could continue to maintain an adequate supply of non-mandatory savings. Currently, the two primary vehicles for tax preferred saving in Australia are superannuation (retirement savings) and owner-occupied housing. The latter receives both favourable income tax treatment and is excluded from the first pillar age pension means test, making it in the absence of mandated retirement saving the probable destination of private savings. Clearly, willingness to participate in non-mandatory savings also depends on the first pillar of the retirement system and its integration with the second pillar. Australians have been accustomed to controlling their retirement savings, having the ability to choose how their superannuation funds are invested in the accumulation phase and, in the most common case where a lump sum retirement benefit is taken, choosing how retirement savings are spent. This may work against the need to accumulate a sufficient pool of non-mandatory second pillar savings, as the loss of control of investing in such a pool and its ultimate conversion into a life annuity may prove unpopular. One of the outcomes of the Swiss second pillar retirement system is a very large private annuities market. Private institutions hold reserves for these annuities that are roughly half Swiss GDP. If Canberra decides to move towards a retirement system with default annuity provision it needs to ensure annuity providers have access to the financial instruments they need to supply life annuities. However, 11

12 one thing annuity providers lack are good quality assets to match their annuity liabilities. In recent years the Australian government has been running budget surpluses, and as the government moves more and more into surplus it is generating less and less debt. The result is a lack of good quality long term debt to back annuities. The problem of a lack of good supporting assets is particularly evident in the supply of indexed debt. While many Australian annuity customers are interested in linking their lifetime annuity payments to CPI increases, indexed debt is hard to find particularly at longer terms. The government has issued ten year indexed bonds in the past, but seems little interested in continuing to issue indexed debt. Annuity providers must then assume that after 10 years they will earn very low returns on the assets backing lifetime annuities, which materially hurts the attractiveness of the product. Any move to increased annuitisation in Australia would have to address such limitations. References Avanzi, B., What is it that makes the Swiss annuitize? A description of the Swiss retirement system. UNSW Australian School of Business Research Papers 2009ACTL06. Bateman, H., Kingston, G., Piggott, J., Forced saving: mandating private retirement incomes. Cambridge University Press, Cambridge, U.K. Bütler, M., 17 March Mandated annuities in Switzerland. Tech. rep., DEEP Université de Lausanne & CEPR. Bütler, M., Teppa, F., The choice between an annuity and a lump sum: Results from Swiss pension funds. Journal of Public Economics 91 (10), Gerber, D. S., Weber, R., Demography and investment behavior of pension funds: Evidence for Switzerland. Journal of Pension Economics and Finance 6 (3), Hepp, S., Mandatory occupational pension schemes in switzerland: The first ten years. Annals of Public and Cooperative Economics 69 (4), OFS, Une nouvelle méthode pour l enquête sur les revenus et la consommation: Nouveau modèle de pondération, résultats et étude sur la prévoyance vieillesse. Plan for Life Research, December The immediate annuity product and rate report. Tech. rep., Plan for Life Pty Ltd. Purcal, S., Piggott, J., Explaining low annuity demand: An optimal portfolio application to Japan. Journal of Risk & Insurance 75 (2),