The Choice Between an Annuity and a Lump Sum: Results from Swiss Pension Funds

The Choice Between an Annuity and a Lump Sum: Results from Swiss Pension Funds Monika Bütler DEEP Université de Lausanne, CEPR & CESIfo Federica Teppa CeRP Università di Torino & DEEP Université de Lausanne February 13, 2004 Abstract We analyze the choice between an annuity and a lump sum capital option upon retirement within the mandatory Swiss occupational pension system. The data analyzed clearly exhibits an acquiescence bias, meaning that a majority of retirees chooses the standard option offered by the pensions fund or suggested by the common practice. However, we also find that those who deviate from the standard option do so as predicted by economic theory. The probability of choosing the capital option shows a U shaped dependence on total capital at retirement. This finding can be well explained by a combination of differential mortality, magnitude effects, insurance aspects, investment opportunities, and the desire to leave bequests. Jel Classification: D91 Keywords: Occupational Pension, Lump Sum, Annuity, Choice Anomalies Corresponding author. Address: Monika Bütler, DEEP HEC, Université de Lausanne, BFSH1, CH 1015 Lausanne, Switzerland; email Monika.Butler@HEC.unil.ch, tel + 41 21 692 3484, fax + 41 21 692 3365. 1

1 Introduction Many funded pension plans offer a choice of withdrawal options at retirement. One polar option is a lump sum payment, another a life long annuity. The lump sum offers maximum flexibility, but may leave the individual destitute if the assets are dissipated too quickly. The annuity is the only contract that guarantees income right up to the point of death, but may unduly contrain the individual at certain times. The choice between a lump sum and an annuity at retirement is thus not an easy one. It involves knowledge about one s own (and possibly the spouse s) life expectancy and investment returns one anticipates to earn. Moreover, one needs to know whether social security and other sources of income will be sufficient to provide adequate retirement income if one lives too long. Other aspects may be equally important. Spells of bad health or other unexpected large expenditures may require enough cash at hand. Last but not least, retired people may want to leave a bequest to their children. If they die too early wealth, that is fully annuitized prevents them from doing so. The accumulation phase of fully funded pension plans is well explored and understood. The decumulation period, on the other hand, still awaits thorough analysis. This is not surprising given the relatively young age of such schemes. With the growing importance of second pillar pension plans around the world, the design of pay out options will become increasingly important. Provided the fully funded system is the main source of retirement income, the plans should guarantee a sufficient level of income as well as an adequate insurance against outliving ones assets in old age. The pay out options should also be flexible enough to cater for a wide variety individual needs in old age. There is obviously a trade off between these somewhat conflicting goals. According to theory, individuals should choose the option that guarantees the highest expected utility. Whether this is the annuity or the lump sum depends on personal characteristics (in particular mortality rates), preference parameters (such as the discount factor and bequest motives), as well as other sources of income (savings, social security), the details of the pension plan and asset market conditions. For an outside observer, mortality rates can only inferred imperfectly by relating them to gender, marital status, and wealth. The actual future value of various payment options also depends to some extent on somewhat unpredictable factors, such as future health, and investment performance. Nonetheless, as section 3 demonstrates, a number of testable predictions can be drawn from 2

economic theory. Even more important than theoretical predictions is clear evidence from the data. Do individuals really decide as predicted by theory? We use a unique sample of individuals (described in section 4) facing a choice between a lump sum payment and an annuity upon retirement in Swiss pension funds. Occupational pension schemes, constituting the second pillar of Swiss old age insurance (see section 2), are privately managed (usually by the firm), but are mandatory for all workers earning a yearly income above a certain threshold. As a consequence of the occupational pension system being mandatory and accounting for roughly 50% of retirement income, the stakes are very large, amounting to approximately 400 000 SFR(= 250 000 USD) on average. As individuals do not have a choice between different pension providers (apart from the fact that they may choose the employer), the date exhibits hardly any selection bias. 1 We show in section 5 that a large majority chooses the annuity option. The data clearly exhibits an acquiescence bias : the respondents generally choose the standard option offered by the company or follow their peers. The probability of choosing the capital option shows a U shaped dependence on total capital at retirement. This can be well explained by a combination of magnitude effects, insurance aspects, investment opportunities, and the desire to leave bequests. Moreover, the role of personal characteristics (such as gender, marital status, age at retirement, number of children) on the choice between an annuity and a (partial) lump sum payment seems to be somewhat overshadowed by other components, in particular company fixed effects. Our analysis is related to a body of literature dealing with lump sum distributions, i.e. annual flow of withdrawals from pension plans by plan participants, either upon job change or upon retirement age. The growing availability of data sources over the past decades on one hand, and the greater and greater actual and potential importance of lump sum distributions due to the passage of ERISA 2 on another hand drew increased attention to empirical research on cash-out behavior, in particular on the incidence and utilization of lump sum distributions from pension plans and targeted retirement saving accounts. A number of studies 1 This characteristics distinguishes our data set from another important field study by Warner & Pleeter (2001), where the individuals facing the choice do not constitute a random sample of military personell. 2 Employment Retirement and Income Security Act (1974), aimed at promoting private retirement savings. 3

(Atkins, 1986; Piacentini, 1990; Fernandez, 1992; Poterba, Venti and Wise, 1995; Yakoboski, 1997; Hurd, Lillard and Panis, 1998) based on information provided by the Current Population Survey (CPS) supplements on Employee Benefits, the Health and Retirement Study (HRS) and the Hewitt Associates data deliver a very consistent result: the majority of workers cash out lump sum pension settlements upon leaving their job. More heterogeneity is found when investigating how cash-outs are spent. It is important to notice however that our paper deviates from all these studies as we observe the choice between lump sums and annuities upon retirement rather than upon job change. Moreover, we do not analyze the issue of cash-outs spending, as the data at our disposal do not provide any information about it. Among this body of literature, our paper is somewhat more related to the work by Hurd, Lillard and Panis (1998), who analyze pension cash-outs by developing a theoretical framework based on the life cycle model and by estimating a reduced form probit model using data from the HRS. As already mentioned, they find that among those who took a lump sum distribution upon job separation, 54 percent cashed out. Cash-out rates are lower for large distributions and among workers that are older, well-educated, male, non-black, or earn high incomes. Moreover, the cash-out rate is higher for separated or divorced individuals and among individuals with lower incomes, particularly vulnerable to old age poverty. Consistent with the theoretical predictions, they find higher rates among individuals with a relatively short financial planning horizon or who themselves state that their chances of surviving another twenty years or so are well below average. The choice between an annuity and a lump sum has also been used to estimate personal discount rates. A particularly compelling field study in terms of magnitudes of stakes and the credibility of pay outs has recently been presented by Warner and Pleeter (2001). As part of a US military down sizing program volunteers were given the choice between an annuity over a number of years (related to previous years in service) and a one time lump sum payment, both depending on the leaver s previous salary and years of service. A large majority of the volunteers chose the lump sum although the implicit discount rate the rate at which the present value of the annuity and the lump sum were equal amounted to 17% (in nominal terms). The authors have estimated the underlying discount rates and found values of 0 30. The discount rate, however, is only one 4

factor in explaining individual choice over an annuity or a lump sum. 3 A life long annuity, for example, also offers valuable longevity insurance. As Brown (2002) has pointed out, these utility gain may be huge. Our study aims at complementing the existing literature and sheding some additional light on individual choice at retirement. We believe that the provided evidence from Switzerland one of the few countries with a relatively mature funded pension system is valuable for policy makers designing mandated pension plans. 2 The Swiss occupational pension system To understand the choice between a lump sum and an annuity within the Swiss occupational pension system, some basic background information about the Swiss scheme is indispensable. 4 Switzerland s pension system is composed of three pillars, of which the first and second are of approximately equal importance. The first pillar AHV/AVS 5 is a predominantly pay as you go (PAYG) system and aims at providing a basic subsistence level of income to all retired residents in Switzerland. The second pillar, the so called BVG/LPP 6 is a mandatory, employer based, fully funded occupational pension scheme. In 2000, on average, approximately 40% (50%) of publicly provided transfer retirement income were paid out by the second (first) pillar. This understates the importance of the occupational pension system, however, as contributing agents today can expect more than half of their combined first and second pillar income to come from the second. Important for our analysis is the fact that the first pillar scheme is relatively flat, especially in the middle and high income ranges. 3 Shane, Loewenstein & O Donoghue (2002) argue that in a perfect capital market, the choice between an annuity and a lump sum cannot be used to assess the personal discount rate. (**** Explanation ****) Rather one would estimate the underlying market interest rate in such an exercise. 4 A detailed description of all aspects of the second pillar is, however, beyond the scope of this paper. The interested reader is referred to Queissar & Vittas (2000, especially concerning institutional details) and Bütler (2003). 5 AHV = Alters und Hinterbliebenen Versicherung; AVS = Assurance Vieillesse et Survivants. 6 BVG = Bundesgesetz über die berufliche Alters-, Hinterlassenen- und Invalidenvorsorge, LPP = Loi f edérale sur la prévoyance professionnelle vieillesse, survivants et invalidité. 5

The second pillar s main goal is to maintain the pre retirement living standard together with the benefits stemming from the first pillar. 7 Upon attainment of retirement age, the accumulated capital can be withdrawn either as a monthly life long annuity or as a lump sum (or a mix of the two) provided the pension fund allows for the lump sum option (which is usually the case in defined contribution plans). Occupational pension benefits are strictly proportional to the accumulated retirement assets (retirement credits plus accrued interest). The accumulated capital K is translated into a yearly pension B using the conversion factor γ: B = γk. This conversion also applies to defined benefit plans; the fund has to make sure that enough capital is accumulated to cover the claims made based on previous income. The BVG/LPP mandates joint annuities for men, but not for women. The conversion factor is the same for everybody irrespective of gender, family status or income. Children under age 18 (or under age 25 if still dependent) of retired persons get an additional pension of 20% of the main claimant s benefit. When a retired man dies, his widow receives a benefit amounting to 60% of the previous pension, his dependent children a benefit of 20% each. These survivor benefits are not means tested. Table 1 (which is computed with most recent mortality tables) shows that this leads to sizeable differences in the MWRs with respect to marital status and gender. The conversion factor, which presently amounts to 7.2%, is determined by the Swiss Federal Council. Table 1 demonstrates that this factor together with a market interest rate of 4% delivers an average MWR close to one; with a more realistic term structure of interest rates, the average MWR clearly exceeds one. It is thus not surprising that the private market for annuities in Switzerland is relatively thin. Private insurers are simply unable to offer the same deal to their customers, especially if they are bound to face adverse selection due to information asymmetries with respect to differences in mortality rates. Benefits are fixed annuities in principle, but the law states that pension providers have 7 Apart from retirement income, the second pillar also provides insurance for disability and survivors of insured men (but not women) during the accumulation period. This aspect, however, is unimportant for the present study. 6

to adjust current old age benefits to inflation within the scope of their financial possibilities. Gender Marital R.A. r =.04 r = EJ Male Single 65 0.73 0.82 Male Married (-3) 65 1.01 1.16 Female Single 65 0.95 1.08 Female Married (no) 65 0.98 1.12 Female Married (+3) 65 1.02 1.18 Male Single 62 0.80 0.90 Male Married (-3) 62 1.08 1.25 Female Single 62 1.02 1.18 Female Married (no) 62 1.05 1.22 Female Married (+3) 62 1.10 1.27 Table 1: Money s worth ratio as a function of marital status and retirement age (=R.A.) that qualifies for full benefits. For married individuals, the number in parenthesis denotes the age difference between the spouses, or indicates the case in which no survivor benefit is available (this is the standard option for married women). As mortality differences are small between divorced, widowed and single agents, only single is reported. 3 The choice between annuity and lump sum capital at retirement: Theory When facing the choice between an annuity and a lump sum, an individual should choose the option that delivers the higher expected utility. Unfortunately for an outside observer it is not as straightforward to assess the expected utility as it seems, as a number of assumptions (apart from the equally unknown parameters of the utility function) are needed to do the comparison. Firstly, one should ideally know other sources of income than the occupational pension, notably other retirement income and private savings. Fortunately, first pillar retirement income does not vary widly across individuals covered by the second pillar. Other sources of retirement income, however, are not generally unknown. Secondly, one 7

needs to know what the lump sum if chosen is used for. The implications are very different between a lump sum that is used to guarantee a certain level of bequest and a lump sum invested in another annuity product. Thirdly, by age 60, individuals have a fairly good grasp of their life expectancy. It remains hidden as far as it is not related to gender, marital status and wealth. Nonewithstanding these objections, this section lists a number of criteria that should guide individuals in their choice as well as the testable implications derived from them. 3.1 Individual characteristics The expected return for an annuity and a lump sum depend on an individual s expected life time, his/her marital status, the presence of children under 18 (for which a substantial supplemental benefit is due), as well as his/her perceived ability to manage the pension fund in case of a one time capital payment. Because (single and married) women live longer than single men on average, the former should choose a (postponed) annuity, and the latter a lump sum capital payment. Married men should prefer an annuity due to the high value of the survivor insurance. Interestingly we find also that the implicit value of an annuity for married men and married women hardly differs. As expected lifetime is correlated with wealth (differential mortality), richer pensioners should opt for an annuity, and poorer for a one time capital payment. Richer agents, however, are also potentially more capable of managing a large fund, which offsets the advantage of an annuity for them to a certain degree. These predictions concerning mortality differences crucially hinge on the ability of individuals to assess their survival probabilities. Hamermesh (1985) has found that people are well informed about their life expectancy by the age they retire. 8 For the outside researcher, differences in survival rates may only be observed indirectly as a function of gender, family status, and to a limited degree accumulated pension wealth. 8 Hamermesh tests this conjecture by analysing responses to a questionnaire designed to elicit subjective expectations and probabilities of survival. He finds that individuals are fully aware of their expected lifetime while the subjective distribution has greater variance than its actuarial counterpart. 8

3.2 Capital market conditions and taxation of retirement income Even if the present value of the lump sum and the annuity were the same, capital market imperfections and differences in mortality rates would lead to a potential (ir)reversibility of choice: In this case, ceteris paribus, rational agents should choose the more flexible option. Although it is relatively cheap to transform the lump sum into a stream of payments for a limited time, it is a lot more difficult to get the original annuity option back as the private annuity market is plagued by adverse selection effects. On the other hand an annuity can only be translated into a lump sum if the loan can be backed up by assets (such as housing). Which of the two constraints is the more relevant is an open question. The tax treatment for the two options differs widely across cantons (the Swiss states). In most cantons a lump sum capital payment is converted into an annuity stream, using the conversion factor provided by the pension fund (equation (1)). The marginal tax rate computed from the corresponding annuity stream is then applied to the entire capital stock in case of a lump sum payment. The tax structure favors the capital option as additional income from other sources, which increases the effective marginal tax rate under the annuity option, is not taken into account for the lump sum. For married women at retirement, moreover, the tax treatment of the capital option is much more attractive as an annuity is taxed at the marginal tax rate the married couple faces. Although there are some alternative methods to impute taxes on the lump sum, the total tax bill is smaller for the lump sum in all cantons. 3.3 The role of capital and magnitude effects A large body of literature (Ainslie and Varda Haendel, 1983; Thaler, 1981; Loewenstein, 1987 among others) points out that small outcomes are discounted at a higher rate than large ones. 9 In other words, for small stakes agents generally prefer an early payment to a deferred one even in the choice implies a high discount rate. Although primarily viewed as a choice anomaly, some aspects of this magnitude effect may be explained by the impact of neglected constraints or neglected aspects in a person s utility function. Other than on a pure magnitude effects, an agent s choice between an annuity 9 See Shane, Loewenstein and O Donoghue (2001). 9

and a lump sum payment may depend on other factors: Income support: Let us first consider the case of an individual with a low level of accumulated capital. An annuity, even small, may be detrimental to the eligibility for income support 10 In most programs, wealth is only taken into account if it exceeds a certain threshold level while regular non labor income counts from the first dollar. It is thus optimal to choose the lump sum option for low levels of capital. Differential mortality: Accumulated capital is a good indicator of a person s lifetime income and social status. 11 The probability of choosing the lump sum is decreasing in capital. This effect is stronger for low levels of capital. Consumption and bequest motives: The higher the annuity, the lower the marginal utility of consumption at the given level. People might prefer to hold their pension wealth in the form of capital to be able to bequeethe it to their children (at least partially). 12 Investment opportunities (and skills): An individual may choose the capital option if he thinks he can obtain a better return than the one offered from the annuity scheme. Investment opportunities will most likely depend on the total amount to be invested, but also on investment abilities. The higher average capital stock at retirement may facilitate alternative investments especially if investment abilities are correlated with wealth. Preferential tax treatment: In Switzerland, there is clearly a tax advantage to withdraw the accumulated pension wealth in the form of a lump sum. This effect is much stronger for high and very high levels of capital. To summarize, magnitude effects and differential mortality should lead to a decreasing probability of choosing the lump sum for low and moderate levels of pension wealth, whereas the latter three factors enlisted above should lead to an increase in the likelihood of choosing the lump sum at relatively high levels of capital. Taken together, these two effects should lead to a U shaped relationship 10 Swiss case: retirees can, under certain circumstances, apply for additional support. 11 In Switzerland, a person belongs to one pension fund only by law. 12 Of course agents can save for a bequest independently from the accumulated capital at retirement, but there is the risk to die prematurely and thus leave a small amount of money. The lump sum payment guarantees a certain level of bequest. 10

between the probability of choosing the lump sum option and the total stock of capital at retirement. 3.4 Insurance aspects The insurance against longevity plus the provision of income for dependent survivors are the most urgent concerns. Obviously, a lump sum provides far less insurance than the annuity. Brown (2002) finds that in the absence of other retirement income, utility equivalent wealth for a life long annuity is approximately 50% higher than in a setting without annuity markets. More importantly, this result caries through even to people with a shorter than average life expectancy, i.e., individuals that do not necessarily benefit from an annuity in money s worth terms. He also shows that bequest motives lessen the demand for annuities to a certain degree. If one wants to insure a certain level of bequest, a partial capital withdrawal might be beneficial. Annuities also hedge individuals from the risk of inflation to a certain degree. Although the adjustment of benefits to inflation is not cast in stone in Switzerland, the pension fund is required to adjust the benefits to inflation if the financial situation allows it. In the past this has been done by almost all pension providers. 3.5 The cut off rate between the two options The cut off rate, i.e., the discount rate that equalizes the present value of the capital and the annuity option can serve as a first step to assess the trade off between the two options In money terms the cut off rate makes the agent indifferent between the lump sum and the annuity option. It is obviously a function of gender, marital status, and the age difference between the spouses. To compute the cut off rate, let us introduce the following notation: M is the main claimant,i.e., the person who has accumulated the claim to the pension system, and S is his/her spouse. The pensioner s spouse S is d years older than the main claimant. M retires at age J with an accumulated capital stock of K. 13 Upon retirement, the accumulated capital is either withdrawn as a lump sum or 13 In a defined benefit system, this is the implicitly defined capital stock that corresponds to the annuity. Note that many funds allow a partial withdrawal of capital even in a defined benefit system. 11

translated into a life long annuity using the age dependent conversion factor γ, defined as where B denotes yearly benefits 14. γ = B K In case M dies and is survived by his/her spouse S, the latter gets a survivor benefit, which is a certain fraction λ of the main benefit B. For single, divorced or widowed agents, the analysis is similar, though much simpler, as joint survival probabilities do not have to be taken into account. In virtually all Swiss pension funds, pensions are indexed to the consumer price index, so they stay (at least) constant in real terms. Often they even grow in real terms. Let us assume for the moment, that pensioners expect their real pension to grow at a real rate g. When computing the cut off discount rate we have to know the conditional probability of survival to age j for both spouses. Survival probabilities are allowed to depend on marital status, and the joint probability of survival is a function of the age difference d between the spouses. The discount rate is denoted ρ. The present value of all future benefits from retirement age on can be written as PV = 1 Ψ M J t=j ( ) t J 1 + g B 1 + ρ (Pr[M alive, S alive] + (Pr[M alive, S dead] + (Pr[M dead, S alive] λ Combining (2) with (1), we can implicitly compute the cut off discount rate ρ that makes agents indifferent between a lump sum capital payment and a life long annuity in present value terms as follows: (1) (2) 1 = 1 γ J Ψ M J ( ) t J 1 + g t=j 1 + ρ (Pr[M alive, S alive] + (Pr[M alive, S dead] + (Pr[M dead, S alive] λ (3) Note that this expression is similar to the one used in Warner & Pleeter, but is adjusted for (joint) survival and differential mortality by marital status. From equation (3) we can infer that the cut off rate ρ is: a decreasing function of the age difference d between the spouses, where d can be negative or positive. If d was positive, the probability that (s)he 14 Age and the conversion factors display a positive pairwise correlation cofficient, equal to.5976. 12

will survive the main claimant will be low and the expected length of joint survival short. 15 The cut off rate will therefore be relatively low and more likely to be below the agent s discount rate, making the lump sum option more attractive. an increasing function of the conversion factor γ (or, in other words, the generosity of the pension system). 16 An increase in the conversion factor leads to a decrease in the left-hand side of the equation. In order to let the equation still hold, the right-hand side must decrease as well, and that would imply, ceteris paribus, that the cut-off rate must increase. an increasing function of survival probabilities, which in turn are functions of gender, marital status, and socioeconomic variables (differential mortality). an increasing function of the expected annuity growth rate. The lower the cut off rate, the more likely the agent chooses the capital option as his/her personal discount rate exceeds the cut off rate. Figure 3.5 depicts cut off rates by marital status, gender, and age at retirement (only for men) as a function of the age difference between the spouses. 17 The annuity is obviously worth relatively more the younger the spouse. This effect is much stronger for men than for women, as the probability of the latter being survived by her husband is relatively small due to a higher expected lifetime for women. Interestingly, the theoretical cut off rates for married men (retiring at age 62) and married women with an average age difference of three years (as in reality) is almost equal. 3.5.1 Computing cut off rates in the data From the data, we know age at retirement, marital status 18, the rate of growth of the annuity g (usually 0), and the conversion factor γ, but not the age difference 15 Married individuals have a lower mortality rate than single or widowed ones. 16 The higher the conversion factor, the higher the value of the annuity compared to the accumulated pension wealth. A plan with a high conversion rate for a given retirement age thus offers a better deal, but this does not affect the capital. 17 For this figure we use the most recent Swiss mortality rates differentiated by gender x marital status. 18 With the exception of one company, where we assume that all agents are married as the majority of individuals at the age of retirement. 13

0.06 0.05 0.04 cut off rate 0.03 0.02 0.01 male, RA=65, married male, RA=65, single male, RA=62, married male, RA=62, single female, RA=62, married female, RA=62, single 0 10 8 6 4 2 0 2 4 6 8 10 age difference between spouses Figure 1: Cut off rates between lump sum and annuity depending on gender, marital status (no symbol = single), retirement age (RA, only for men), and age difference between spouses (negative numbers mean than that spouse is younger). For men, cut off rates are depicted for the legal retirement age 65 and for retirement at age 62, at which most companies offer the full retirement benefits. Parameters for figures: g = 0, λ = 0.6, γ = 0.072, equal tax treatment. 14

between the spouses. In computing the individual cut off rates ρ, we, therefore, use the average observed age difference in Switzerland, which is approximately three years. Note that the presence of children in education (only observed with male pensioners) is a signal for a much younger wife. Children should make annuity the preferred option, not only because they are entitled to additional benefits, but also because the survivor benefit is worth a lot more for these couples on average. 4 The data In the empirical analysis we use data collected at the individual level from 9 Swiss companies, both public and private, active in several industrial branches. They include the public railway company, civil servants, several industry firms, as well as clothing and food firms. The dataset consists of 2129 observations. 19 Each company provides data about individuals after retirement or workers who have already chosen the option of the annuity or lump-sum capital. We are given information about date of birth, marital status, number of children under 18/25 20, date of retirement, legal retirement age, yearly pension and yearly additional pension for children, total capital at retirement, lump-sum capital paid out, conversion factor 21 (γ). Most of the variables are self-explanatory. Gender takes the form of a dummy, whose value is 0 for females and 1 for males. Males and females represent 79 and 21 percent of the sample, respectively. Similarly, marital status is a categorical variable, whose value is 1 for singles, 2 for married, 3 for separated, 4 for widowed and 5 for divorced. The great majority is represented by married individuals (80%), followed by singles and divorced (7% each), widowed (5%) and separated (1%). The sample consists of individuals whose age at retirement ranges from 19 The cleaning and editing of the data has been a considerable task. Firstly, the data format provided varied widely across companies. Secondly, much of the relevant information for the project had to be imputed from other sources (regulation of pension fund) or from a combination of available data. In many cases the information could only be gathered from a personal interview with the respondible pension fund manager. 20 Children under age 18 are always eligible for additional benefits. For those over 18, but under 25, a pension is available for disabled children and those still in school. 21 In Switzerland the conversion factor is usually 60%. 15

52 to 66. Figure 2 depicts the distribution of the age at retirement for men and women. 300 250 250 200 200 150 frequency 150 frequency 100 100 50 50 0 55 56 57 58 59 60 61 62 63 64 65 66 age at retirement (men) 0 55 56 57 58 59 60 61 62 63 64 65 66 age at retirement (women) Figure 2: Distributions of age at retirement for men (left-hand side) and for women (right-hand side) The distribution of age at retirement has a triple peak profile for men and a double peak profile for women, at ages 60 and 62, and 65 (for men only). This is a result of the fact that the latter is the current legal age of retirement for men, while 62 is the legal age of retirement for women, but also the age at which many pension funds offer full benefits even for men. We notice however another important peak at age 60. This is often the lowest age for which early retirement packages are offered at relatively good conditions. The capital stock upon retirement (or the annuitized rent) is a sufficient statistics for the income during lifetime, so that all the information before retirement is redundant. The conversion factor (γ) is the factor at which is capital is translated into an annuity. The cut-off discount rate (ρ ) is the rate that should make the agent indifferent between the lump sum and the annuity option if equation (3) would hold for each observation. The variable margin is 1 for individuals who choose a combination between an annuity and a lump sum payment which is not the standard option offered by the respective pension fund. 22 On the basis of this piece of information we can infer what individuals actually choose among a 22 For these individuals, the present value of their annuity stream should exactly be equal to total capital at retirement. The corresponding cut off rates therefore provide a first estimate of the prevailing discount rate (mean cut off rate for these agents is 4.00%). 16

full annuity, a partial or a full lump-sum payment. We then build the variable choice in the form of a categorical variable, whose value is 0 for full annuity, 1 for partial lump sum and 2 for full lump sum. Only some variables are available for the complete sample, namely age at retirement, gender, total capital accumulated at retirement, fraction of total capital paid out as a lump sum, conversion factor, margin and choice. As for the other variables, the number of observations is somewhat smaller. Table 2 provides summary statistics for some of the variables we use for empirical analysis. 17

Table 2: Summary statistics for some relevant variables Variable Mean (or %) Std. Min Max # obs. 18 Age at retirement 61.85 1.98 52 66 2192 Marital status: 1782 single 7.4% 132 married 80.5% 1434 separated 0.7% 13 widowed 4.0% 71 divorced 7.4% 132 Gender (1 = male, 0 = female).795.404 0 1 2192 Children ( 18/25 y.).058.312 0 4 1691 Yearly pension (incl. child benefits) 26976 20031 0 191925 2157 Total capital at retirement ** 451870 285362 1560 3325360 2192 Lump-sum capital paid out 65016 145185 0 1089898 2192 Fraction of total cap. paid out.188.345 0 1 2192 Conversion factor (gamma).0671.0039.0372.077 2192 Cut-off discount rate.0379.010 -.0072.0539 2192 Non standard option (= 1).2806.4494 0 1 2192 Margin.1519.3590 0 1 2192 Choice.479.760 0 2 2192 (** average capital: married men = 529 631; single men = 442 569; married women = 116 303; single women = 367 995)

4.1 Individual preferences over options As mentioned above, individuals in the sample can choose among three different options: a full annuity, a partial or a full lump sum payment. Table 3 reports a number of relative frequencies of the choice variable by several demographic and socio-economic characteristics and p-values referring to χ 2 -tests of the null that the distribution of preference over the three possible options is the same across different values of a characteristic. We observe that along all characteristics the annuity is by far the most preferred option. This reflects preferences over the whole sample, where more than 60 percent of observations choose the annuity. Females choose the (full) lump sum payment more than males (29.33 percent versus 13.03 percent); the annuity payment is the most preferred option among single individuals (80.30 percent) and marital status does not seem to have a significative impact on the choice. These findings are not consistent with the predictions of the theoretical model described in Section 3. Interestingly, differences in preferences are strongly significant along the company dimension, suggesting a relevant role of company fixed effects in the personal choice. 19

Table 3: Individual preferences over options by gender, marital status and company (percentages) Characteristic Annuity Partial lump-sum Full lump-sum Total n. obs. 20 Female 61.33 9.33 29.33 450 Male 70.26 16.70 13.03 1742 p-value.000 Single 80.30 8.33 11.36 132 Married 71.55 14.02 14.44 1434 Sep. and div. 62.53 9.91 27.56 145 Widowed 71.83 9.86 18.31 71 p-value.111 PK-Manor 69.64 13.09 17.27 359 SBB 86.26 12.68 1.07 844 Thurgauer - 12.82 87.18 39 SIG 52.57 23.72 23.72 409 Kambly 33.96-66.04 53 Alusuisse 90 10-70 Unilever 9.30-90.70 43 NCR 93.33 6.67-15 ABB 57.78 19.17 23.06 360 p-value.000 Total sample 68.43 15.19 16.38 2192

We then explore preferences by company more deeply. Seven out of nine companies provide an annuity as standard option, and allow for a partial or full lump sum payment as an alternative. The remaining two companies provide a partial lump sum payment (usually a multiple of the last working year s salary) as the standard option. Table 4 shows that overall the standard option is preferred by more than 2/3 of the sample. For five companies this percentage is even bigger, reaching a maximum of 93.3%; for two companies (SIG and ABB) preferences over options are basically evenly distributed, with a slight predominance of the standard one; in only one case (Kambly) the alternative option overcomes the standard one. These figures suggest that there may be a sort of acquiescence bias driving people s choices 23. Table 4: Distribution of preferences over options by company (percentages) Company Standard Option Alternative Option PK-Manor 69.6 (annuity) 30.3 SBB 87.2 (annuity) 12.8 Thurgauer 87.1 (partial l.s.) 12.9 SIG 52.6 (annuity) 47.4 Kambly 34.0 (annuity) 66.1 Alusuisse 90.0 (annuity) 10.1 Unilever 90.7 (partial l.s.) 9.3 NCR 93.3 (annuity) 6.7 ABB 57.8 (annuity) 42.2 Total sample 71.9 28.1 5 Empirical results We start reporting (Table 5) some summary statistics of the cut-off discount rate for each of the choices actually made by the individuals in the sample. Mean values (but also maximum and minimum values) are virtually the same across 23 The expression acquiescence bias (Hurd, 1999) or status-quo bias or friendliness effect refers to a systematic bias caused by some respondents tending to agree with whatever is presented to them. 21

choices, suggesting a poor explanatory power of the cut-off discount rate. Moreover, they go in the wrong direction, as people choosing the annuity should display a higher value for the mean cut-off discount rate and, similarly, a lower cut-off discount rate should correspond to the choice of a (full) lump sum payment. Table 5: Summary statistics for cut-off discount rates Choice of individuals Mean Max Min N.Obs. Annuity.037.053 -.007 1500 Partial lump sum.039.053 -.006 333 Full lump sum.041.053 -.004 359 The determinants of choosing a (partial) lump sum payment are analyzed for two base specifications. Ordered probit estimates and marginal effects are reported in Table 6. Given the relevance of company fixed effets (see Table 3), we include them in both regressions in order to account for differences in the characteristics of the pension scheme. Moreover, pension funds could in principle, within legal limits, define new contributions and benefit structures, and this usually occurs at the beginning of the year. In order to account for a potential change in the fund s regulation, we also include dummies for year at retirement in both regressions. 22

Table 6: Determinants of choosing a lump-sum payment (ordered probit estimates and marginal effects) 23 Regression I II Coeff. t ratio Slope t ratio Coeff. t ratio Slope t ratio Expl. variables (Std) (Std) (Std) (Std) Gender (male=1).193 1.76.033 0.87.195 1.75.036 0.94.109.037.111.037 Total capital (log) -3.96 8.04-1.31 7.38-3.90 8.01-1.29 7.35.493.181.487.178 Total capital 2 (log).153 7.38.053 7.08.150 7.32.052 7.02.021.008.020.007 Age at retirement.959 1.39.305 1.27 1.38 1.90.410 1.64.691.239.727.250 Age at retirement 2 -.008 1.40 -.002 1.26 -.010 1.79 -.003 1.52.006.002.006.002 Conversion factor (γ) -72.87 3.05-22.4 2.57 23.9 8.71 Number of observations 2192 2153 2192 2153 Pseudo R 2.209.182.212.186 Company fixed effects YES YES Year fixed effects YES YES Log-Likelihood -1460.4-1080.0-1454.6-1075.7

In regression I we run a simple ordered probit with the choice made by individuals as dependent variable and control for basic background individual characteristics such as gender, stock of capital accumulated at retirement and age at retirement, and quadratic terms for the two latter variables, in order to capture a potential non monotonic relation. As expected (see Section 3.3), the stock of capital accumulated at retirement plays an important role. Both terms related to this variable are jointly significant at 5% level. 24 The capital function corresponding to regression I is depicted in Figure 3. We can see that the amount of total capital at retirement is negatively related with the probability of choosing a lump sum payment until the value of around 430,000 Swiss Francs (around 430,000 USD and around 300,000 Euro s); after that value the relation becomes positive. The other variables, gender and age at retirement, are not significant. Note that when computing marginal effects, one company (Thurgauer) drops out entirely as only the lump sum option is offered to their retirees. As a consequence, the number of observations drops from 2192 to 2153. 20 20.5 21 21.5 probit 22 22.5 23 23.5 24 24.5 7 8 9 10 11 12 13 14 15 16 log(capital) Figure 3: Capital function 24 The corresponding statistic is chi2(2)=96.50 24

Next we include (regression II) one extra variables, the conversion factor (γ in equation (1)), that departs from personal characteristics. We expect that the probability of choosing a lump sum payment is a decreasing function of this variable. The coefficient of the conversion factor indeed takes the right (negative) sign and is significant. The estimates relative to the individual background characteristics suggest that the same results from regression I hold. The main conclusion from these regressions is then the following: the role of personal characteristics on the choice between an annuity and a (partial) lump sum payment seems to be somewhat overshadowed by other components, namely company fixed effects and the conversion factor. As suggested by Table 1, the MWR for single females and married females is very close to each other, whereas it is a large difference between single males and married males. The MWR suggests that the lump sum is much more preferable to single men than for other individuals. We thus want to explore this empirically, by including marital status and a term capturing the interaction bewteen marital status and gender in the regressions. For this purpose, we distinguish only between singles and non singles, the latter including individuals who are or had been married, such as separated and divorced or widowed. Results for this specification are reported in Table 7. 25

Table 7: Determinants of choosing a lump-sum payment (ordered probit estimates and marginal effects) 26 Regression I II Coeff. t ratio Slope t ratio Coeff. t ratio Slope t ratio Expl. variables (Std) (Std) (Std) (Std) Gender (male=1).004 0.03 -.011 0.24.036 0.24 -.005 0.10.148.047.152.048 Marital status.060 0.42.013 0.28.295 1.32.072 0.99.144.046.223.076 Marital status&gender -.232 1.19 -.065 1.15.632.90.142.58.195.052.705.263 Total capital (log) -5.00 8.59-1.37 7.39-4.97 8.61-1.36 7.45.582.190.578.188 Total capital 2 (log).201 8.12.056 7.16.200 8.12.056 7.21.025.008.025.008 Age at retirement.439 0.60.172 0.76 5.79 0.71.229 0.90.730.228.816.254 Age at retirement 2 -.003 0.58 -.001 0.72 -.003 0.52 -.001 0.71.006.002.007.002 Conversion factor (γ) -92.57 1.97-26.4 1.75 47.1 15.1 Number of observations 1782 1741 1782 1741 Pseudo R 2.186.259.206.260 Company fixed effects YES YES Year fixed effects YES YES Log-Likelihood -1075.7-1037.9-979.2-1035.7

When including marital status, one company (SIG) drops because that piece of information is missing; as a onsequence the number of observations drops from 2192 to 1782. Strikingly, marital status turns out to be totally insignificant, also when controlling for the conversion factor. To explore this more deeply, we next split the sample between females and males and do the ordered probit regressions (Table 8). In the males sub-sample, we would expect a positive sign for the marital status coefficient, yet we find a negative and insignificant coefficient. It may seems that the bequest motive dominates the differential mortality motive. 27

Table 8: Determinants of choosing a lump-sum payment by gender (ordered probit estimates) 28 Females Males Coeff. t ratio Coeff. t ratio Coeff. t ratio Coeff. t ratio Expl. variables (Std) (Std) (Std) (Std) Total capital (log) -7.07 5.50 7.10 5.48-2.47 2.14-2.49 2.15 1.29 1.30 1.16 1.16 Total capital 2 (log).296 5.12.297 5.09.099 2.15.099 2.15.058.058.046.046 Age at retirement -1.99 0.86-4.27 1.69 1.06 0.93 2.34 1.70 2.31 2.53 1.14 1.38 Age at retirement 2.018 0.91.041 1.87 -.008 0.92 -.018 1.60.019.022.009.011 Marital status.008 0.05 1.03 1.90 -.205 1.60.442 0.48.157.542.129.918 Conversion factor (γ) -370.3 2.18-109.5 2.03 169.5 54.05 Number of observations 419 419 1363 1363 Pseudo R 2.346.352.214.217 Company fixed effects YES YES Year fixed effects YES YES Log-Likelihood -243.3-240.9-771.4-768.1

6 Conclusions Most private pension companies in Switzerland offer a choice between a lump-sum capital payment upon retirement or a life-long annuity thereafter. The expected return for each of these options depends crutially on an agent s expected life-time, his/her marital status, as well as the presence of children under 18 years old. We have analysed the choice between an annuity and a lump sum capital payment upon retirement by using data provided in 2000 by nine pension funds in Switzerland (**** NEW DATA TO COME ****). These decisions involve very large amounts of money. We find that the impact of personal characteristics (such as gender, marital status, age at retirement, number of children) on the individual s choice, though important, seems to be somewhat overshadowed by other components, in particular company fixed effects. This indicates a strong role for peer effects and other choice anomalies. The data clearly exhibits an acquiescence bias : the large majority of respondents choose the standard option offered by the company. The probability of choosing the capital option shows a U shaped dependence on total capital at retirement. This can be well explained by a combination of magnitude effects, insurance aspects, investment opportunities, and the desire to leave bequests. Our analysis seems to suggest that when taking financial decisions people choose on the basis of easy variables rather than of more complicated and sophisticated ones. We believe that a deeper understanding of choice upon retirement and the related distributional consequences is of great interest to academic economists and to policy makers. While the asset side of fully funded pension plans is well explored and understood, the liability side still lacks a careful analysis. Advancing our knowledge of both sides will potentially lead to more equitable and efficient policies. In order to draw more solid conclusions our data base should be enlarged: many effects are masked by strong company and year-of-retirement effects. It will be absolutely necessary to expand the database along two dimensions. First, more companies in various sectors should be included: this would enable to better control for various specific effects. Second, several years should be included as well: often the generosity of offered early retirement options depended on the performance of the pension fund (which in theory should not). 29

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