3.1 Countries surveyed and their funded pension schemes

Our study of product choice regulation in the payout phase of funded pensions draws on a survey of seven representative European countries: Austria, France, Germany, Italy, Sweden, Switzerland, and the UK. For comparison, we also look at the USA. In all surveyed countries, the vast majority of the population is covered by some form of statutory pensionFootnote ². In Austria, France, Germany, and Italy, statutory pension programmes still provide rather high replacements rates and represent the main source of retirement income. At the same time, participation in occupational or personal pension schemes is either voluntary or individuals have the possibility to opt out. Consequently, the amount of assets accumulated within funded pension schemes is still small compared to the countries’ GDP and gross debt.

By contrast, statutory pension systems in Switzerland, the UK, and the USA provide relatively low benefits, resulting in high individual responsibility for generating retirement income from other sourcesFootnote ³. Switzerland and Sweden mandate participation in employment-linked old-age programmes, either through legislation, in the case of Switzerland, or through collective agreements between trade unions and employers, in the case of Sweden. In both countries, employees do not have the chance to opt out of the system. Consequently, second pillar savings in these two countries are significant, and the resulting payouts are high enough to substantially contribute to financing the cost of living in retirement. On top of the second pillar, Sweden is the only country in which the statutory pensions system is partially funded (so-called premium pension scheme).

In the UK and the US, despite the lack of mandatory participation, funded pension schemes have also accumulated a substantial amount of assets.

For each country surveyed, Table 1 provides an overview of the funded pension programmes currently open to new members, including information on the amount of assets accumulated. To put these numbers into perspective, we also relate them to the country's GDP and general government gross debt.

Table 1. Overview of representative funded pensions programmes

Notes: Programmes open to new participants (excl. government employees). Programme size based on the latest information available (ranging from 2009 to 2013). For non-Euro countries: Exchange rates as published by the Financial Times on 18^th July 2013.

¹ Prämienbegünstigte Zukunftsvorsorge – Sponsored Retirement Provision.

² Mitarbeiter Vorsorgekassen – Employee Provision Funds.

³ PERP (Le Plan d’Épargne Retraite Populaire) – People's Retirement Savings Plan.

⁴ PERCO (Le Plan d’Épargne pour la Retraite Collectif) – Group savings plan for retirement.

⁵ PPM (Premiepensionsmyndigheten) – Premium Pension Agency.

⁶ IRA – Individual Retirement Account (ranging from 2009–2013). (see note above). Sources: OECD (2013) ; Austria: ÖNB (2013a), FMA (2012), ÖNB (2013b) ; France: FFSA (2011), AFG (2012) ; Germany: BaFin (2011), BaFin (2012), Schwind (Reference Schwind2013), GDV (2012) ; Italy: Covip (2012) ; Sweden: OECD (2012), SPA(2012), Statistics Sweden (2013) ; Switzerland: BFS (2011), SVV (2009), Schweizerische Nationalbank (2013) ; UK: ONS (2013) ; USA: DOL (2012), ICI (2013) .

3.2 Overview and classification of product choice restrictions

Having presented the alternative funded pension schemes in the previous section, we now turn to discussing the main features of the associated restrictions with respect to product choice in the payout phase. Table 2 summarises our findings.

Table 2. Funded pension programmes restricting payout product choice

Source: Austria: FP (2013), VVÖ (2013), BMSVG (2010), Uniqua (2013); France: CGI (2013), FFSA (2013); Germany: FRG (2013); Italy: Pensplan (2012); Sweden: SPA (2012); Switzerland: SE (2013); UK: TPR (2013), TPAS (2013), HMRC (2013).

In the European countries surveyed, funded pension programmes predominantly require at least some form of annuitisation. The bulk of existing funded programmes, in terms of accumulated assets, are of the defined benefit variety, which implies a pooled payout solution at retirement. At the same time, most European defined contribution programmes are still at the beginning of the saving phase, and they have not yet accumulated as much assets as the older defined benefit programmes. Moreover, some defined contribution programmes also require pooled payout solutions at retirement, such as PERP in France, Riester plans in Germany, or the Pensionskasse in Austria. Thus, traditional pooled products, particularly fixed nominal annuities, remain the predominant payout solution, depriving retirees of financial flexibility but giving them guaranteed lifelong retirement income. Among the few programmes that allow unrestricted use of alternative payout solutions are PERCO in France, individual pension accounts in Sweden, and pillar 3a restricted accounts in Switzerland, all of which are still relatively small.

We also find that regulation for old-age saving programmes in Europe is quite complex. Even within a single country, regulations regarding the use of accumulated assets in retirement typically vary between different schemes. The only exceptions are the UK and occupational schemes in Italy, where one set of regulations applies to all tax-supported funded pension payout schemes, independent of the origin of funds. In both countries, however, this simplified regulation only applies to new pension schemes. To date, the US is the only country among those surveyed that does not impose restrictions on the choice of payout instruments, leaving retirees with a lot of freedom and flexibility regarding the use retirement funds. Recently, however, a political debate emerged over mandating at least partial annuitisation, driven by the low voluntary annuity take-up.

Restrictions on the use of capital in retirement can be imposed in two ways. Either regulators rely on outright restrictions, directly prescribing the use of funds at retirement, or they employ implicit restrictions, e.g., tax penalties as well as legal or regulatory uncertainties, as a means to channel the demand for payout products into the desired direction. The majority of countries surveyed use outright restrictions, mostly mandating the purchase of traditional pooled products (annuitisation) in retirement. Restrictions employed in the surveyed countries can be classified as outlined in Figure 1Footnote ⁴.

Source: Authors’ compilation based on the sources referred to in Table 2.

Figure 1. Classification of payout product choice restrictions.

Several pension schemes mandate full annuitisation of accumulated funds directly at retirement (Box 1 in Row 1). Among those programmes are the Austrian Pensionskasse, several French programmes (Article 83, Article 39, Madelin-Law, and PERP), as well as German Rürup plans. Some countries impose less strict annuitisation requirements (Boxes 2 and 3 in Row 1): Immediate partial annuitisation is mandated in Swiss occupational saving plans as well as under the new regulations for funded pension programmes in Italy. Partial annuitisation of funds may not be required immediately, but may be tied to reaching a certain age, such as age 85 in case of the German Riester programme. Annuity-tied alternative payout solutions are available in Sweden for the funded part of the statutory pension system and in the UK for all tax-supported funded pension plans (Box 1 in Row 2). Here, the maximum periodic payout for a non-pooled solution is determined by the amount the retiree would have received, had he converted the savings into annuity.

An alternative approach to restricting payout product choice in retirement is to explicitly and deliberately discourage using non-pooled solutions through taxation (Box 2 in Row 2). The Austrian Prämienbegünstigte Zukunftsvorsorge and Mitarbeitervorsorgekasse are good examples for this approach. Alternative payout solutions, particularly lump sum payments, are not prohibited per se, but they are subject to taxation, while annuity payments are largely tax-free. Only very high annuity payments from the abovementioned programmes are subject to partial taxation. Additionally, when alternative payout solutions are chosen for Prämienbegünstigte Zukunftsvorsorge, 50% of direct state subsidies received during the saving phase must be returned to the state.

A final approach to restricting product choice is more subtle (Box 3 in Row 2). While not explicitly prohibiting non-pooled solutions, several countries do not explicitly allow them either. The lack of regulatory information on the status of non-pooled products prevents potential retirees from demanding them and, as a result, they are not offered. The German Pensionskasse is a good example. Current legislation does not require complete and outright annuitisation of funds saved within the Pensionskasse. Yet, almost all of the nearly 160 Pensionskassen require outright annuitisation, and only a small number allow partial lump sum payments at retirement. Only recently, some Pensionskassen have begun to offer Riester plans, which by law allow a one-time lump sum payment of up to 30% of accumulated funds. Similarly, there is no official definition of permissible withdrawal products in Austria and Switzerland. In the absence of explicit restrictions or permissions, traditional thinking seems to limit product choice at least in the saving phase. While savers are free to choose between insurance and bank products in the tax-supported third pillar of the Swiss old-age saving system (pillar 3a savings), insurance assets are four times larger than those in the non-pooled, restricted old-age accountsFootnote ⁵. The latter, however, do not offer standardised drawdown products and are mostly paid out as a lump sum.

4.1 Motivation and research design

Regulation of payout products has its merits, but it also comes at a price. Rules have to be defined, implemented, and supervised, resulting in additional fees and duties. While these costs are measurable, the bulk of regulation costs are not directly observable. This particularly includes the utility losses suffered by those prevented from purchasing the desired payout products and thereby from structuring retirement cash flows in accordance with their preferences. Hence, in order to balance advantages and costs of regulation, it is vital to develop a framework that helps quantifying the utility impacts of product choice restrictions.

To this end, we implement a dynamic portfolio choice model and derive optimal consumption and investment patterns for a risk-averse male retiree that faces uncertain lifetime and stochastic capital market returnsFootnote ⁶. The retiree is endowed with a certain level of savings, accumulated during the active working life (pre-existing wealth), and an exogenous pension income in form of life-long, inflation adjusted fixed annuity benefits. This pre-existing pension income may be drawn from the statutory pension system, other social security arrangements, or from occupational pension systems of the defined benefit variety. This income is assumed to be at least equal or above the subsistence level. At the beginning of every year, the retiree has to decide how much to consume and how to invest his liquid wealth into risky stocks, risk-free bonds, and new illiquid fixed-payout life annuities in order to maximise his (expected) utility.

We first derive optimal policies in an unrestricted world, in order to have a benchmark against which we can evaluate the utility implications of preventing the retiree from following the optimal strategy by mandating annuitisation. Then, we quantify the utility losses from restricting product choice in retirement by integrating the three stylised restrictions defined in the previous section, i.e., immediate full annuitisation at retirement, immediate partial annuitisation at retirement, and deferred annuitisation. Finally, we look at the impact of mandating annuitisation on individuals that, for behavioural reasons, exclude annuities from their investment menu.

4.2 The model

Following Horneff et al. (Reference Horneff, Maurer, Mitchell and Dus2008a), we assume that the retiree maximises expected utility drawn from consumption and bequest, based on a recursively defined, additively time-separable utility function of the constant relative risk aversion (CRRA) type:

(1)$$V_{t} \equals {{\lpar C_{t} \rpar ^{\setnum{1} \minus \rho } } \over {1 \minus \rho }} \plus \beta \cdot E_{t} \left[ {p_{t}^{s} \cdot V_{t \plus \setnum{1}} \plus \lpar 1 \minus p_{t}^{s} \rpar \cdot k \cdot {{\lpar B_{t \plus \setnum{1}} \rpar ^{\setnum{1} \minus \rho } } \over {1 \minus \rho }}} \right]\comma $$

with terminal utility

(2)$$V_{T} \equals {{\lpar C_{T} \rpar ^{\setnum{1} \minus \rho } } \over {1 \minus \rho }} \plus \beta \cdot E_{T} \left[ {k \cdot {{\lpar B_{T \plus \setnum{1}} \rpar ^{\setnum{1} \minus \rho } } \over {1 \minus \rho }}} \right].$$

Here, C_t denotes the consumption level at time t, subject to being alive at that point in time. B_t represents the remaining financial wealth to be bequeathed, in case the retiree dies at time t. The retiree's subjective probability of surviving from t to t+1 is represented by p_t^s and calibrated to the German population male mortality table (2004/2006). The curtailed lifetime T is set to age 100, i.e., p ₁₀₀^s=0;. The parameter ρ represents the coefficient of relative risk aversion that also reflects the retiree's willingness to engage in intertemporal substitution of consumption. We set ρ to 5, a standard value in the life-cycle literature representing a retiree with moderate risk aversion (see, for example, Horneff et al., Reference Horneff, Maurer, Mitchell and Dus2008a). The parameter β, which we set to 0.96, reflects the retiree's time preference and k the strength of his bequest motive. For k>0, the retiree has a bequest motive and will always keep some liquid wealth. For our analysis of investors with bequest motive, we set k to a moderate level of 2, which is comparable with calibrations in Cocco et al. (Reference Cocco, Gomes and Maenhout2005) .

Each year, the retiree has to decide how to distribute current cash on hand W_t to consumption C_t, financial wealth S_t, i.e., stock and bond investments, and the purchase of additional inflation-indexed life annuities A_t. Hence, the budget constraint at time t is given by:

(3)$$W_{t} \equals S_{t} \plus A_{t} \plus C_{t} \comma $$

resulting in next period's cash on hand of:

(4)$$W_{t \plus \setnum{1}} \equals S_{t} \cdot \lpar R_{f} \plus \pi _{t} \cdot \lpar R_{t \plus \setnum{1}} \minus R_{f} \rpar \rpar \plus L_{t \plus \setnum{1}} \plus Y\comma $$

where π_t denotes the fraction of financial wealth invested in risky stocks, R_f denotes the real bond growth rate, and R_{t +1} the risky stock return. The annual income from all previously purchased annuities is L_{t +1}, and Y_t=Y represents the constant real lifelong annual pension income. If the retiree perishes at t+1, pension and annuity payments cease, and the remaining estate is given by B_{t +1}=S_t·(R_f+π_t·(R_{t +1}−R_f)). Moreover, the retiree is prevented from borrowing against future pension income and annuity payouts, as well as from short-selling stocks, bonds, or annuities.

In our base case, we set the annual real return on the risk free asset to 2%. Furthermore, we assume that the annual real return on stocks is i.i.d. log-normally distributed with an expected return of 8% and a volatility of 25%. To study the sensitivity of our results with respect to the capital market calibration, we also use a more pessimistic parameterisation in line with Gomes et al. (Reference Gomes, Kotlikoff and Viciera2008) . Here, the real annual risk-free return is set to 1%, the expected real return on stocks is reduced to 5%, and the volatility of stock returns is set to 20.5%.

In addition to stocks and bonds, the retiree has access to real fixed payout life annuities. Based on the actuarial principle of equivalence, at age x, the price of a payout annuity with fixed lifelong payments of L_t=1 is given by:

(5)$$A_{t} \equals \mathop{\sum}\limits_{t \equals \setnum{1}}^{T} {{{_{t}\,p_{x}^{a} } \over {\lpar R_{f} \rpar ^{t} }}.} $$

Here, $_{t} p_{x}^{a} \equals \prod _{i \equals \setnum{0}}^{t \minus \setnum{1}} p_{x \plus i}^{a} $ is the cumulative conditional probability for an individual aged x to survive until age x+t, according to the mortality table used by the insurer to price the annuity. These annuitants’ survival rates may differ from the subjective survival probability p_t^s, reflecting adverse selection in the annuity markets (see Brugiavini, Reference Brugiavini1993). In our base case, we price annuities using survival probabilities from the German DAV 2004 R male annuitants’ mortality table with base year 2008. We incorporate the DAV's first-order mortality trend to account for future mortality improvements. Moreover, we do not curtail the lifetime to age 100 for pricing the annuity but calculate with a maximum age of 121, i.e., the final age in the DAV table. Consequently, annuity prices include substantial implied cost loadings; about 37% at age 65 when compared with prices calculated using the population table. To evaluate the impact of these loadings on our findings, we also conduct our analysis under the assumption that annuities are priced using the population mortality table.

To analyse the influence of the level of pre-existing pension income on the utility implications of product choice restrictions, we study three alternative levels of retirement wealth relative to the exogenous annual pension income. We set this financial wealth-to-pension income ratio (WPR) to 2, 5, and 10. Retirees with a WPR of 2 already have a high exposure to annuities compared with their other assets, for example due to a generous pre-existing pension, whereas those with a WPR of 10 only receive a comparably small pension income. For the 17 countries of the Euro area, Eurostat (2013) reports a median equivalised net income of € 15,758 for the population age 65 and older in 2011 (the last year available). Based on this pension income, our WPR calibrations lie within the range of the lower three quintiles of the total wealth distributions of retirement-aged European households (see Börsch-Supan et al., Reference Börsch-Supan, Brugiavini, Jürges, Mackenbach, Siegrist and Weber2005, Table 4A.5).

We solve the optimisation problem by backward induction through a three-dimensional state space {W, L, t}, as analytical solutions to this type of optimisation problem do not exist. Based on the optimal consumption and investment policies derived, we conduct an extensive Monte Carlo simulation of 10,000 independent life-cycles to evaluate how the retiree's consumption, investments in liquid assets, and annuity purchases are expected to evolve over time. For further details on the numerical solution technology, we refer the reader to Horneff et al. (Reference Horneff, Maurer, Mitchell and Stamos2010).

4.3 Optimal unrestricted investment and consumption strategies in retirement

We begin our quantitative evaluation of the utility implications of restricting product choice in retirement plans by analysing the optimal consumption and investment patterns for male investors that live in an unrestricted world. Figure 2 presents the expected evolution of key parameters as well as the expected asset allocation throughout the retirement phase for a retiree with a moderate wealth-to-pension ratio (WPR=5) and without bequest motives for our baseline calibration of capital market parameters. Panel A of Figure 2 illustrates expected consumption, pension and annuity income, annuity wealth, the amount of new annuity purchases, and liquid wealth in each year, starting at retirement age 65 and ending at age 100. All parameters are normalised by pre-existing annual pension income. Panel B of Figure 2 shows the corresponding expected allocation to stocks, bonds, and annuities over time, where the investment in annuities, i.e., the annuity wealth, is measured by the actuarial present value of previously purchased life annuity claims.

Source: Authors’ calculation.

Figure 2. Expected life-cycle profiles and asset allocation – no bequest motive. Notes: Male retiree age 65. Moderate wealth/pension ratio (WPR=5). No bequest motive (k=0). Expected stock (bond) returns: 8% (2%), return volatility stocks (bonds): 25% (0%). Mortality assumptions for annuity pricing: DAV 2004 R (year 2008) plus trend.

At retirement, the investor receives a pre-existing, external pension income of 1 and holds financial wealth of 5. At this point in time, he withdraws approximately 1.5 for consumption purposes, spending the entire income from pre-existing pensions as well as about 10% of financial wealth. The largest fraction of remaining wealth, approximately 4.25, or 92%, is invested in stocks. Bonds only account for about 8% of the retiree's wealth, while voluntary annuity purchases, and hence annuity wealth, are virtually zero. In subsequent periods, consumption, although slightly falling, remains well above periodic pension income, resulting in decreasing financial wealth. While the amount invested in risky stocks is slowly reduced, the retiree starts purchasing additional annuities from age 67 and continues to do so until the mid-80s. Consequently, the retiree's periodic income increases as does annuity wealth. By the mid-70s, annuities have completely crowded out the equally risk-less bonds due to the extra return generated through the mortality credit. At this point in time, the individual holds 84% of his total wealth in stocks and 16% in annuities. Annuity wealth reaches its maximum around age 80 and declines thereafter, as diminishing annuity purchases cannot overcompensate the reduction in present value, which is due to progressing payments and increasing mortality. With liquid financial wealth being exhausted by the mid-90s, the retiree is fully invested in annuities and can no longer afford consumption in excess of periodic income. Due to the purchase of additional annuities earlier in retirement, however, this periodic income, and therefore consumption, exceeds the initial pre-existing pension income for the rest of the retiree's lifetime.

This picture changes when the investor draws utility from leaving a bequest. Figure 3 again presents the expected evolution of key parameters as well as the expected asset allocation throughout the retirement phase for a retiree with a moderate wealth-to-pension ratio (WPR=5) and our baseline calibration of capital market parameters. This time, however, the retiree is assumed to have a moderate bequest motive of k=2.

Source: Authors’ calculation.

Figure 3. Expected life-cycle profile and asset allocation – moderate bequest motive. Notes: Male retiree aged 65. Moderate wealth/pension ratio (WPR=5). Moderate bequest motive (k=2). Expected stock (bond) returns: 8% (2%), return volatility stocks (bonds): 25% (0%). Mortality assumptions for annuity pricing: DAV 2004 R (year 2008) plus trend.

Early in retirement, pensioners with moderate bequest motives consume less and invest less in risky stocks than retirees that do not draw utility from leaving bequests. The initial asset allocation consists of 85% stocks and 15% bonds. Retirees with bequest motives are even more reluctant to voluntarily purchase additional annuities than their counterparts without any interest in bequests, as funds invested in annuities are irretrievably lost when the retiree dies. Annuity wealth only increases slowly and stagnates at about 10% of the retiree's remaining wealth from the mid-80s until age 100, despite the substantial mortality credits at later ages. As a result, periodic pension income only rises marginally, and the retiree primarily has to rely on bonds when investing risk-free. Even late in life, the retiree will hold a measurable fraction of his wealth in stocks. With annuities being undesirable due to a lack of bequest potential, only stocks will provide an expected return significantly above the risk-free bond return. Consequently, at age 100, the retiree will still hold 20% of wealth in stocks, 70% in bonds, and 10% in annuities.

Our results are structurally robust with respect to changes in mortality assumptions as well as transaction costs on annuities. Pricing annuities with population mortality tables, i.e., higher mortalities will result in slightly earlier and higher annuity purchases. Introducing a front-end expense load on annuities leads to slightly lower and later purchasesFootnote ⁷.

Summing up, we find that retirees with moderate WPRs postpone annuitisation and only gradually increase their annuity holdings. Even investors without a bequest motive will not be fully annuitised before the mid-90s. Instead, they use liquid wealth to finance both annuity purchases as well as consumption in excess of periodic income from pre-existing pensions and additionally purchased annuities.

4.4 Welfare implications of mandatory annuitisation

Using our analysis for retirees in an unrestricted world as a benchmark, we now study the utility impacts of mandating annuitisation. To this end, we evaluate three alternative regulatory frameworks that differ in the extent to which product choice in retirement is restricted. In Case A, we require the individual to fully annuitise available wealth at retirement age 65, which is in line with current regulations in, e.g., Austria, France, or Germany. For our less strict alternatives, we draw on simplified regulations from two other European countries. In Case B, we mandate immediate annuitisation of 50% of the initial wealth at age 65, imposing no further restrictions on the use of the remaining half of retirement funds. Hence, the retiree may subsequently withdraw funds for consumption purposes or for purchasing additional annuities at any time. Such a set-up is comparable with regulation in, e.g., Italy. In Case C, the retiree has to fully annuitise all remaining wealth at age 75. Prior to that, withdrawals are limited to the annual benefit of an immediate annuity purchased at the respective age. This is comparable with regulation in the UK prior to 2011 and in the spirit of German Riester programmes.

To evaluate the economic costs of these regimes, we conduct a welfare analysis similar to Mitchell et al. (Reference Mitchell, Poterba, Warshawsky and Brown1999) and Horneff et al. (Reference Horneff, Maurer, Mitchell and Stamos2009). For each of the three regulatory frameworks, we determine the expected utility for a given level of initial wealth. We then solve for the level of initial wealth in the unrestricted world that generates the same expected utility. This enables us to measure the utility loss in monetary units. Our findings are summarised in Table 3, which presents the utility impacts of alternative regulations as a percentage change in initial financial wealth relative to the unrestricted world for alternative bequest motive strengths, WPRs, and financial market parameterisations.

Table 3. Welfare implications of alternative product choice restrictions – Fully rational individual

Notes: Change in utility equivalent wealth due to product choice restrictions in per cent of the initial wealth. Case A: Full mandatory annuitisation at retirement. Case B: Mandatory annuitisation of 50% of wealth at retirement, no further restrictions of use of remaining 50%. Case C: Mandatory annuitisation of remaining retirement funds at age 75, prior to that, withdrawals limited to the annual benefit of immediate life annuity purchased at the respective age. Male retiree age 65. No bequest motive: k=0, moderate bequest motive: k=2. Base case capital market parameterisation: Expected stock (bond) return: 8% (2%), return volatility stocks (bonds): 25% (0%). Pessimistic capital market parameterisation: Expected stock (bond) return: 5% (1%), return volatility stocks (bonds): 20.5% (0%). Mortality assumptions for annuity pricing: Annuitant mortalities: DAV 2004 R (year 2008) plus trend. Population mortalities: Population mortality table for German males 2004/2006. Source: Authors’ calculation.

First, we turn our attention to Panel 1 of Table 3, which presents utility impacts of restricting product choice for our base case capital market calibration, when assuming that annuities are priced using annuitant mortality tables. Independent of the level of pre-existing pension income, all forms of mandated annuitisation result in substantial utility losses, especially for retirees with bequest motives. We find that these losses are particularly high for Case A, i.e., full immediate annuitisation. For example, a retiree with a moderate WPR of 5 and no bequest motive suffers a utility loss equivalent to 24.8% of initial wealth. Stated differently, an individual with an initial endowment of € 100,000 in the most restrictive world is equally well off as his identical twin brother in an unrestricted world who is only endowed with € 75,040 at retirement. For retirees with moderate bequest motives, this loss in wealth even increases to 54%. Retirees with lower WPR tend to suffer higher utility losses. These individuals already have a comparably high, inflexible, annuity-like pension income. Consequently, they appreciate the flexibility offered by liquid assets much more than the marginal increase in periodic pension income this small amount of liquid wealth is able to buy. Retirees with a high WPR, on the other hand, only have comparably little pre-existing pension income that can be measurably increased when the substantial endowment is used to purchase additional annuities. Hence, utility losses are slightly smaller than for those retirees with low WPR. Nonetheless, their reduction in utility equivalent wealth still amounts to almost 20% when they do not have a bequest motive and to more than 40% in case they are moderately inclined to leave a bequest.

Requiring individuals to only annuitise 50% of their wealth at retirement (Case B), considerably reduces utility losses across all WPR levels. For retirees without bequest motives, utility losses are cut by more than 60% for a WPR of 2 and by even more than 80% for a WPR of 10. In the presence of a moderate bequest motive and independent of the WPR, Case B results in the smallest utility reductions of all restricted cases, as the retiree at any point in time has the opportunity to retain some non-annuitised wealth for bequest purposes.

Now, we turn to our Case C, which mandates full annuitisation of remaining funds at age 75 and, prior to that, restricts the use of funds. While utility losses are generally lower than Case A, utility losses still exceed those of Case B, particularly for retirees with bequest motives. This comes as no surprise, since Case C imposes the same strict annuitisation requirements as Case A, just deferred by 10 years, during which the freedom of fund use is limited as well.

Next, we are interested in the sensitivity of our results with respect to the underlying assumptions concerning the parameterisation of capital and annuity markets. Panel 2 of Table 3 presents utility implications of restrictive regulations under the assumption that annuities are priced based on population mortalities instead of annuitant mortalities. Mandating annuitisation reduces adverse selection in the annuity market and enables providers to price annuities using less conservative mortality assumptions, resulting in higher annuity payments. This considerably reduces the welfare losses of mandatory annuitisation, usually by more than half for all analysed restriction types if the individual does not have a bequest motive. Yet, even in this environment, welfare losses from full immediate annuitisation as well as full annuitisation at age 75 are substantial in the presence of moderate bequest motives, ranging from 23% for high-wealth individuals in Case C to 47% for low-wealth retirees in Case A. Panel 3 of Table 3 presents the results for our more pessimistic capital market parameterisation and for annuity prices based on population mortality rates. Reducing expected returns on stocks and bonds makes holding liquid financial wealth less appealing. This increases the relative attractiveness of annuities, and utility losses of mandated early annuitisation are lower under pessimistic capital market assumptions than under the baseline calibration. Variations in capital market parameters, however, have substantially less impact on utility than changes in mortality assumptions.

So far, our analysis has solely focused on fully rational individuals, which were shown to suffer substantial welfare losses from mandatory annuitisation. Yet, the discussion in Section 2 showed that real-world individuals may refrain from voluntarily purchasing annuities for behavioural reasons, despite the well-understood benefits of annuitisation. This raises the question as to whether mandated annuitisation can actually be utility-increasing for those individuals and as to how the alternative regulatory regimes perform in such an environment. In what follows, we seek to tackle this question within our rational decision making framework. To this end, we repeat our welfare analysis positing that the individual excludes annuities from the investment menu for behavioural reasons, but is fully rational otherwise. Consequently, in all cases A–C, annuities are only purchased to the extent required by our stylised regulation, and welfare is then benchmarked against an unrestricted world without annuitisation. Results are summarised in Table 4.

Table 4. Welfare implications of alternative product choice restrictions – behaviourally restricted individual

Notes: Change in utility equivalent wealth due to product choice restrictions in per cent of the initial wealth. Case A: Full mandatory annuitisation at retirement. Case B: Mandatory annuitisation of 50% of wealth at retirement, no further restrictions of use of remaining 50%. Case C: Mandatory annuitisation of remaining retirement funds at age 75, prior to that, withdrawals limited to the annual benefit of immediate life annuity purchased at the respective age. Male retiree age 65. No bequest motive: k=0, moderate bequest motive: k=2. Base case capital market parameterisation: Expected stock (bond) return: 8% (2%), return volatility stocks (bonds): 25% (0%). Pessimistic capital market parameterisation: Expected stock (bond) return: 5% (1%), return volatility stocks (bonds): 20.5% (0%). Mortality assumptions for annuity pricing: Annuitant mortalities: DAV 2004 R (year 2008) plus trend. Population mortalities: Population mortality table for German males 2004/2006. Source: Authors’ calculation.

In Panel 1 of Table 4, annuities are again priced using annuitant mortality tables. In this scenario, welfare losses are almost equal to those presented in Table 3 for individuals that include annuities in their investment menu. The differences only range between 0 and 2 percentage points. The reason for this can be seen when again looking at Figures 2 and 3. Due to high annuity prices, even fully rational investors will purchase only a small amount of annuities and only later in life. Hence, there is little difference to an individual that does not purchase any annuities.

This picture changes when assuming that annuities are priced using population mortality tables (Panels 2 and 3 of Table 4). Welfare losses for behaviourally restricted individuals with low wealth (WPR=2) are still comparable with those of their fully rational counterparts. With increasing WPRs, however, the utility impact of mandated annuitisation strongly depends on the type of restriction and on whether the individual is willing to leave a bequest. Those with a bequest motive and with higher WPRs still suffer substantial welfare losses ranging between 14 and 37% under full immediate and deferred annuitisation (Cases A and C). With mandated immediate annuitisation of only 50% (Case B), however, individuals in fact benefit from regulation, with welfare gains reaching 10% for a WPR of 10. Wealthier individuals without a bequest motive enjoy welfare gains under all regulatory regimes. Yet, Case B again generates the highest benefits for most scenarios. Here, welfare gains range from 5% for the baseline parameterisation to around 14% in the more pessimistic capital market scenario. Full immediate mandatory annuitisation (Case A) will only be preferred if individuals are very wealthy (WPR=10) and returns in the capital market are low.

Overall, we can conclude that mandated annuitisation may be beneficial for those that exclude annuities from their investment menu. Yet, as in the case of fully rational individuals, utility implications strongly depend on the type of regulation. Here, our results suggest that, in most cases, fully rational as well as behaviourally restricted individuals have similar preferences regarding the extent to which annuitisation is mandated.