How Much Do Means-Tested Benefits Reduce the Demand for Annuities?

Transcription

1 How Much Do Means-Tesed Benefis Reduce he Demand for Annuiies? by Monika BÜTLER Kim PEIJNENBURG Sefan STAUBLI Working Paper No December 2013 Suppored by he Ausrian Science Funds The Ausrian Cener for Labor Economics and he Analysis of he Welfare Sae JKU Linz Deparmen of Economics Alenberger Srasse Linz, Ausria Corresponding auhor:

2 How much do means-esed benefis reduce he demand for annuiies? MONIKA BÜTLER SEW HSG Universiä S. Gallen, CESIfo & Nespar KIM PEIJNENBURG Bocconi Universiy, IGIER, & Nespar STEFAN STAUBLI RAND, IZA, & Nespar February 4, 2014 Absrac We analyze he effec of means-esed benefis on annuiizaion decisions. Availabiliy of means-esed paymens creaes an incenive o cash ou pension wealh for low and middle income earners, insead of aking he annuiy. Agens rade off he advanages from annuiizaion, receiving longeviy risk insurance, o he disadvanages, giving up free wealh in he form of means-esed supplemenal income. Our simulaed life-cycle model demonsraes ha he availabiliy of means-esed benefis subsanially reduces he desire o annuiize, especially for low and inermediae levels of pension wealh. In our empirical analysis we show ha he model s prediced fracion of reirees choosing he annuiy is able o mach he annuiizaion paern of occupaional pension wealh observed in Swizerland. Jel Classificaion: D14, D91, G23, J26 Keywords: Means-Tesed Benefis, Occupaional Pension, Annuiy, Life-Cycle Model We hank seminar paricipans a he Nespar Pension Workshop and various conferences for helpful commens and suggesions. Par of his research was conduced while Kim Peijnenburg was visiing he Wharon School of he Universiy of Pennsylvania, and she is graeful for heir hospialiy. We kindly acknowledge a research paper gran from he Cenre for Pensions and Superannuaion (CPS), Kim Peijnenburg acknowledges financial suppor from All Pensions Group (APG). Sefan Saubli acknowledges funding from he Ausrian Naional Science Research Nework Labor and Welfare Sae of he Ausrian FWF. 1

3 1 Inroducion Virually all indusrialized counries guaranee a cerain minimum income in old age. To do so, hey provide supplemenal benefis ha are ypically means-esed and whose eligibiliy is deermined by boh income and asses. In OECD counries means-esed reiremen benefis provide almos 22% of average earnings; approximaely 17% of individuals above age 65 claim such supplemenal benefis (OECD (2011)). In his paper we show ha he availabiliy of means-esed benefis can subsanially reduce he propensiy o annuiize pension wealh a reiremen. Because means-esed benefis guaranee a minimum income in reiremen, hey no only provide addiional free income, bu also an implici insurance agains he financial consequences of longeviy similar o an annuiy conrac. This generaes a srong incenive o cash-ou accumulaed pension wealh a reiremen even if full annuiizaion was opimal in he absence of means-esed benefis. A unique daase of individual cash-ou decisions a reiremen validaes he predicions form our life-cycle model. Yaari s (1965) seminal paper demonsraes ha a life-cycle consumer wihou a beques moive should choose o annuiize his enire wealh o insure longeviy risk. Davidoff e al. (2005) show ha posiive, bu no necessarily complee annuiizaion remains opimal even wih marke incompleeness, liquidiy consrains, as well as in he presence of beques moives and under habi formaions. However, when inernaional numbers are analyzed, i is apparen ha when given a choice, only a minoriy annuiizes volunarily even in counries in which he pre-exising annuiizaion by he public pension sysem is small. A grea amoun of lieraure has aemped o shed ligh on he annuiy puzzle. 1 reconcile wih economic heory. 2 Noneheless, he low observed annuiizaion raes remain hard o Given he size of means-esed social insurance programs in many indusrialized counries, low annuiizaion raes may no be ha surprising. Alhough he Swiss sysem sands ou somewha in erms of generosiy, is supplemenary benefi scheme nicely illusraes he incenives generaed by means-esed benefis o cash ou pension wealh. Maximal firs pillar benefis amoun o roughly $2,000 (= CHF 2,000) per monh. 3 A he same ime, here are also means-esed supplemens o 1 Adverse selecion and adminisraive loads (Michell e al. (1999), Finkelsein and Poerba (2002), Finkelsein and Poerba (2004), Rohschild (2009), and Direr (2010)) and he exisence of firs-pillar annuiies (Brown e al. (2001), Dushi and Webb (2004)) can raionalize he preference for a lump sum over an annuiy o some degree. Furher argumens agains annuiizaion include inra-family risk-sharing (Kolikoff and Spivak (1981) and Brown and Poerba (2000)), incomplee annuiy markes (Peijnenburg e al. (2012)), beques moives (Friedman and Warshawsky (1990), Bernheim (1991), Brown (2001), Lockwood (2012)), and a desire o insure agains expendiure spikes (Peijnenburg e al. (2012)). Recen work includes behavioral explanaions of individuals low annuiizaion behavior (Hu and Sco (2007), Brown e al. (2008), and Brown e al. (2012)). Benarzi e al. (2011) provide a comprehensive overview of his lieraure. 2 An excepion is Inkmann e al. (2011) who find ha a sandard life-cycle model wih reasonable preference parameers predics annuiy demand levels comparable o daa from he U.K. 3 The numbers presened in he paper are based on a pariy beween he dollar and he Swiss Franc a he ime of 1

4 firs pillar benefis ha lif he effecive minimum income o roughly $3,000 a monh. An individual wih a monhly second pillar benefi of less han $1,000 a monh, which corresponds o accumulaed occupaional pension wealh of approximaely $170,000, is always beer off wihdrawing he money upon reiremen, spending i down in he years afer reiremen and hen applying for means-esed benefis. While he incenives are clear for individuals wih low pension wealh and no oher form of wealh, for middle-income individuals here is a radeoff. The reiree weighs he benefis from aking he lump sum, free means-esed benefis afer wihdrawal, agains he disadvanages, a lower degree of longeviy insurance and a non-fla consumpion paern. We quanify he impac of means-esed benefis on opimal annuiy demand and consumpion/savings decisions using a realisic life-cycle model wih a social securiy scheme in which means-esed benefis can be claimed if income and wealh fall below a cerain level. The model also includes inflaion risk and equiy risk, and allows for differenial ax reamens of annuiy paymens versus lump sum wihdrawals. The model is calibraed o Swizerland, which is an ineresing case sudy for a number of reasons. Firs, i combines a relaively low level of pre-exising annuiizaion by he firs pillar, wih generous means-esed benefis ha exceed firs pillar benefis by roughly 50%. Second, mos individuals have accumulaed a large capial sock a reiremen hrough he mandaory occupaional pension scheme. The average Swiss reiree has a capial sock of approximaely $300,000 o $400,000 which ranslaes ino a second pillar income ha approximaely equals firs pillar benefis. Third, here is a considerable variabiliy of cash-ou decisions agains which he heoreical predicions can be compared. Büler and Teppa (2007) and Büler e al. (2012) show wih micro daa from pension providers ha he propensiy o annuiize increases in pension wealh, which is consisen wih he incenives generaed by means-esed benefis. The main conribuions of our paper are hreefold. Firs, we calibrae a life-cycle model o an exising pension scheme wih a sizeable means-esed componen. We show ha means-esed benefis have a quaniaively imporan impac on he propensiy o annuiize. The effec is especially large for agens wih a low income and wealh level. If hese reirees could no claim meansesed benefis, hey would annuiize heir second pillar pension wealh, while he opimal annuiy level is ofen zero when means-esed supplemenal income is available o hem. Second, we compare observed annuiy decisions of individuals o he opimal annuiizaion rae prediced by our model. The adminisraive daa we compiled from Swiss occupaional pension providers confirm he model s clear paern: Agens wih low pension wealh levels end o ake he lump sum while agens wih higher second pillar pension wealh annuiize more ofen. Means-esed benefis can hus provide a poenial explanaion for he low volunary annuiizaion of second pillar pension wealh and financial wealh of individuals. Third, we analyze he coss and welfare implicaions of wriing (July 2012). 2

5 differen policies for povery alleviaion. We focus on alernaive povery-alleviaion schemes ha guaranee he same (means-esed) income level, such as sricer asse es rules, a minimum income requiremen policy resricing cash-ou decisions, and mandaory annuiizaion. We find ha sricer eligibiliy ess or requiring individuals o annuiize a cerain bu limied amoun of heir pension wealh can reduce he coss of hese schemes subsanially, while no reducing welfare grealy. Our paper relaes o several sudies ha have examined he effec of means-esed social insurance programs on savings, purchase of privae insurance, and labor supply. Theoreical work by Hubbard e al. (1995) and Sefon e al. (2008) demonsrae ha means-esed welfare programs discourage savings by households wih low expeced lifeime income. Empirical evidence for his predicion is provided by Neumark and Powers (1998) and Powers (1998) using U.S. daa. Using variaion across U.S. saes in supplemenary SSI benefis, Neumark and Powers (2000) demonsrae ha generous SSI benefis reduce pre-reiremen labor supply of older men. However, he exising lieraure has largely ignored he role of means-esed social insurance programs on he decision o annuiize pension wealh. The only excepion, o our knowledge, is he paper by Pashchenko (2010) who invesigaes differen deerminans of he annuiizaion decision using a simulaion model parameerized for he U.S. In conras o her sudy, we perform an empirical analysis o validae our conjecure and show ha a life-cycle model wih means-esed benefis maches empirical annuiy decisions well. 4 In conras o many oher papers, our analysis looks a annuiy demand in mandaed fullyfunded pension plans. These schemes play a growing role in he provision of reiremen income in mos indusrialized counries. Annuiizaion in such plans is hus a more pressing concern for public policy han in volunary annuiy markes, which radiionally have a low annuiizaion rae. Furhermore, our paper is one of he few papers on annuiy demand ha employ individual level daa o explore deerminans of annuiy choices. Our daase lends iself well for esing he effecs ha means-esed benefis can have on opimal annuiy decisions. However, as he meansesed benefis are lower in many oher counries, he measured impac on annuiy decisions in Swizerland is likely o form an upper bound. The paper proceeds as follows. Secion 2 describes he life-cycle model used for he simulaions of annuiizaion decisions in he presence of means-esed benefis. Secion 3 gives an overview of he Swiss pension sysem o which he model is calibraed and which serves as an 4 Pashchenko (2010) demonsraes ha a minimum consumpion floor (implying very sringen asse es rules) reduces he paricipaion rae in volunary annuiy markes, paricularly a he boom of he income disribuion. The guaraneed income in Pashchenko (2010) is very low a only $2,663 per year (an esimae aken from De Nardi e al. (2010), which reflecs a mixure of minimum income level and value placed on differen nursing home arrangemens.) A guaraneed income level of $2,663 is subsanially smaller han he levels in counries wih a similar GDP and some U.S. saes (for example, i is $20,000 in Ausralia and $36,000 in Swizerland). More generous guaraneed income is likely o affec annuiizaion decisions for a much larger fracion of he populaion. 3

6 illusraion for he quaniaive impac of means-esed benefis. The daa used o verify he predicions of our model is presened in Secion 4. Secion 5 presens he resuls of he empirical analysis and discusses alernaive inerpreaions of a posiive relaionship beween pension wealh and he propensiy o annuiize. Implicaions for income policy in old age are discussed in Secion 6. Secion 7 concludes. 2 A life-cycle model during reiremen wih means-esed benefis and opimal annuiizaion Means-esed supplemenal benefis creae an incenive o cash ou accumulaed second pillar wealh because an annuiy, even small, is derimenal o he eligibiliy for income- or asse-esed benefis. If he combined income from he firs and second pillar is below he minimum income guaraneed by means-esed benefis, an individual can increase he presen value of his income choosing he lump sum, spending he money, and laer applying for means-esed benefis. While he incenives for individuals wih low pension and non-pension wealh are sraighforward, for middle-income individuals here is a radeoff. The reiree weighs he benefis from aking he lump sum free means-esed benefis afer wihdrawal agains he disadvanages, a decrease in consumpion once he capial is depleed and a lower level of longeviy insurance. Insiuional feaures, which are ofen specific o a counry, also influence annuiizaion decisions. Firs, in Swizerland, he eligibiliy for means-esed benefis usually depends on oal wealh and no only on pension wealh. Therefore, even for low levels of pension wealh, aking he annuiy may be opimal if non-pension wealh is high. Second, differences in axaion may eiher favor one of he wo polar opions (100% annuiizaion versus 100% lump sum) or induce a cerain opimal spli beween he wo. In he Swiss case, our illusraive example for he calibraion, he annuiy is subjec o normal income ax raes, while he lump sum is axed only once (a reiremen). Due o he differenial ax reamen he presen value of he lump sum s oal ax bill is almos always smaller han he annuiy s ax burden. Third, since annuiies are ypically no indexed o inflaion, uncerainy abou fuure prices may reduce he demand for hese annuiies. People migh be induced o keep a cerain amoun of wealh liquid o smooh consumpion due o inflaion shocks, and more equal real consumpion levels over he life-cycle. The nex secion presens a life-cycle model ha incorporaes several imporan aspecs of he annuiizaion decision, including means-esed benefis, non-pension wealh, differenial axaion of he annuiy income compared o he lump sum, and a sochasic asse reurn process in he presence of inflaion. To faciliae he analysis, we focus on single individuals. 4

7 2.1 Individual s preferences and consrains Our analysis focuses on he reiremen phase of he life cycle. There is no acive decision wih respec o he reiremen iming. A he beginning of his reiremen period he agen decides on he fracion of pension wealh o be annuiized. The amoun wihdrawn as a lump sum is subjec o an immediae ax. 5 For his enire remaining life he agen receives an annuiy income from he firs and second pillar on which regular income axes are levied. The individual decides opimally how much o consume and how o divide he remaining wealh beween socks and bonds. In each period, he also akes ino accoun he possibiliy of claiming means-esed benefis. More formally, we examine an agen during reiremen wih age = 1,..., T, where = 1 is he reiremen age and T is he maximum age possible. Le p denoe he probabiliy of surviving o age, condiional on having lived o period 1. The individuals preferences are presened by a imeseparable, consan relaive risk aversion uiliy funcion and he individual derives uiliy from real consumpion, C. Lifeime uiliy equals V = E 0 [ T =1 β 1 (( s=1 p s ) )] C 1 γ, (1) 1 γ where β is he ime preference discoun facor, γ denoes he level of risk aversion, and C is he level of dae real consumpion. Nominal consumpion is given by C = C Π, where Π is he price index a ime. A reiremen, second pillar wealh, W pw, can be ransformed ino an annuiy income, aken as a lump sum, or a combinaion of boh: W pw = W ls + W a. (2) W ls is he amoun aken as a lump sum, while W a is he par of he pension wealh annuiized. Second pillar pension wealh aken as a lump sum is subjec o a ax τ ls once.,. The ax rae is increasing n he amoun wihdrawn. Toal ne wealh a ime = 1, W 1, is he sum of afer-ax pension wealh plus non-pension financial wealh, W npw : W 1 = (1 τ ls )W ls + W npw. (3) The annuiy income, Y II, is given by Y II = W a c, (4) 5 In Swizerland, no only lump sum axes are levied bu also annual wealh axes. In he analysis we absrac from wealh axes because hese ax are quaniaively unimporan. 5

8 wih c being he conversion rae. The second pillar annuiy income provides a nominal income, while he firs pillar income is inflaion proeced. The income ax, τ i, is progressive and levied over he sum of firs and second pillar pension income. Ne means-esed benefis M equal M = max( M Y I Y II rw gw, 0) (5) where M is he guaraneed consumpion level. The applicable income for he deerminaion of means-esed benefis consiss of firs pillar pension income Y I, second pillar pension income Y II, invesmen income (wealh imes a ficiious invesmen reurn r), and a fracion g of wealh. The income numbers Y I and Y II are defined ne of axes. There are wo asses individuals can inves in, socks and a riskless bond. w is he fracion invesed in equiy, which yields a gross nominal reurn of R +1. The nominal reurn on he riskless bond is denoed by R f. The ineremporal budge consrain of he individual is, in nominal erms, equal o W +1 = (W + Y I + Y II + M C )(1 + R f + (R +1 R f )w ), (6) where W is he amoun of financial wealh a ime. If he agen receives means-esed benefis, his consumpion is always a leas as high as he guaraneed income level, M. The individual faces a number of consrains on he consumpion and invesmen decisions. Firs, we assume ha he reiree faces borrowing and shor-sales consrains w 0 and w 1. (7) Second, we impose ha he invesor is borrowing consrained C W, (8) which implies ha he individual canno borrow agains fuure annuiy income o increase consumpion oday. 2.2 Financial marke The asse menu of an invesor consiss of a riskless one-year nominal bond and a risky sock. The reurn on he sock is normally disribued wih an annual mean nominal reurn µ R and a sandard deviaion σ R. The ineres rae a ime + 1 equals r +1 = r + a r (r µ r ) + ɛ r +1, (9) 6

9 where r is he insananeous shor rae and a r indicaes he mean reversion coefficien. µ r is he long run mean of he insananeous shor rae, and ɛ r is normally disribued wih a zero mean and sandard deviaion σ r. The yield on a risk-free bond wih mauriy h is a funcion of he insananeous shor rae in he following manner: R f(h) = 1 h log(a(h)) + 1 h B(h)r, (10) where A(h) and B(h) are scalars and h is he mauriy of he bond. The real yield is equal o he nominal yield minus expeced inflaion and an inflaion risk premium. For he insananeous expeced inflaion rae we assume π +1 = π + a π (π µ π ) + ɛ π +1, (11) where a π is he mean reversion parameer, µ π is long run expeced inflaion, and he error erm ɛ π N(0, σ 2 π). Subsequenly he price index Π follows from Π +1 = Π exp(π +1 + ɛ Π +1), (12) where ɛ Π N(0, σπ 2 ) are he innovaions o he price index. We assume here is a posiive relaion beween he expeced inflaion and he insananeous shor ineres rae, ha is he correlaion coefficien beween ɛ r and ɛ Π is posiive. The benchmark parameers are presened in Secion Calibraion: Case sudy Swizerland The availabiliy of means-esed benefis obviously reduces he demand for an annuiy. The more imporan quesion is is quaniaive impac on he cash-ou decision a reiremen, especially for individuals who would have sufficien means o finance heir own reiremen. In his respec Swizerland is an ineresing case o sudy. Firs, i combines a relaively low level of pre-exising annuiizaion by he firs pillar wih a generous income guaranee exceeding firs pillar benefis by roughly 50%. Individuals whose income is below he guaranee can claim means-esed benefis. Second, as a consequence of a mandaory occupaional pension scheme, individuals wih middle and higher incomes have accumulaed a large capial sock a reiremen. The average Swiss reiree can expec a second pillar income approximaely equal o firs pillar benefis if he annuiizes his pension wealh. 7

10 3.1 The Swiss pension sysem: he firs and he second pillar Swizerland s pension sysem mainly consiss of wo pillars. The firs pillar is a publicly financed pay-as-you-go scheme, which provides a basic level of income o all reired residens in Swizerland. The second pillar is an employer-based, fully funded occupaional pension scheme, which aims o mainain he pre-reiremen living sandard in addiion o benefis from he firs pillar. I is compulsory for all employees wih annual earnings above roughly CHF 20,000. In July 2012, he CHF-$ exchange rae was CHF 1 o roughly $1.02. The firs pillar is financed by governmen revenues and a payroll ax which is proporional o labor income (wihou any upper bound). Benefis are srongly dependen on he number of years conribued, bu only o a limied degree on average labor income. In paricular, individuals whose income is high enough o qualify for he second pillar usually ge a firs-pillar income beween 90 and 100% of he maximal firs pillar benefis. The sauory reiremen age is 64 for women and 65 for men. Working beyond age 64/65 is possible, bu mos work conracs specify a reiremen age ha coincides wih he sauory reiremen age. The second pillar covers around 96% of working men and 83% of working women. As nonworking individuals are no covered, he lowes income quarile and hus he individuals wih he lowes life expecancy are only marginally included in hese schemes. Occupaional pension plans are heavily regulaed, and alhough hey ypically work as a defined conribuion sysem, far reaching income guaranees are included. Including income from he firs pillar, he arge replacemen rae of mos pension funds is approximaely 50-60% of insured income, corresponding o a ne replacemen rae of 70-80%. Income above CHF 80,000 is covered by he so-called super-mandaory par of he sysem. Alhough employers are no obliged o offer super-mandaory coverage, a large majoriy do as occupaional pensions are viewed as an imporan ool o arac qualified workers in a igh labor marke. Individuals are auomaically enrolled in boh he mandaory and super-mandaory par of he plan. They only have very limied if any invesmen choice during he accumulaion phase. Conribuions o he pension plan correspond o a cerain fracion of he covered salary (usually 7-18% depending on age) of which he employer has o pay a leas half. The capial is fully porable; when an employee sars working a anoher company, he receives all of he accumulaed conribuions (including he employer s par). The full sum has o be paid ino he new fund. The accrued reiremen capial can be wihdrawn eiher as a monhly life-long annuiy (including a 60% survivor benefi), a lump sum or a mix of he wo opions. In a minoriy of plans he cash-ou limi is equal o 50 or 25% (he legal minimum) of accumulaed capial. Depending on insurer regulaions he individual mus declare his choice beween hree monhs and hree years prior o he effecive wihdrawal dae. Many pension insurers define a defaul opion for he case when he beneficiary does no make an acive choice. 8

11 Nominal occupaional pension annuiies are sricly proporional o he accumulaed reiremen asses. The so-called conversion rae is independen of marial saus, bu depends on reiremen age and gender. In he mandaory par he law sipulaes a minimum conversion rae which is currenly 6.85%, bu was 7.2% during he period we have he daa for. This conversion rae is far more generous han he conversion rae in he unregulaed marke, which is around 5.5% for a 65- year-old single man. We find ha he acuarially fair conversion rae for a nominal single-person annuiy is 8.1%, which we calculae using nominal ineres raes and male survival probabiliies from moraliy.org. Comparing his value o he conversion facor of 7.2% used in he analysis leads o a pricing load of abou 12%. As we absrac from survivor benefis in our analysis and do no ake ino accoun moraliy differences beween single and married men, he load is overesimaed for married men (who have an annuiy ha includes survivor benefis) and somewha underesimaed for singles Means-esed supplemenal benefis in Swizerland If he oal income does no cover basic needs in old age, means-esed supplemenal benefis may be claimed as par of he firs pillar. Like in mos OECD counries, hese benefis are means-esed so ha only individuals whose income and asses are below a cerain hreshold are eligible. In Swizerland, he value of hese benefis corresponds o around 47% of average earnings, which is considerably above he average in OECD counries of 22% (OECD (2011)). Around 12% of he populaion in reiremen age receives means-esed benefis. 7 The share of benefi recipiens is increasing wih age which is consisen wih our hypohesis of spending down asses. Means-esed benefis in Swizerland are deermined by subracing an individual s income from he so-called applicable expendiures. The income used in he calculaions of meansesed supplemenal benefis is he sum of pension income from firs and second pillars, invesmen income, and earnings plus one enh of he wealh exceeding a hreshold level of CHF 25,000. The relevan annual expendiures consis of a cos-of-living allowance, a healh insurance premium, and ren or ineres paymens for he morgage. Summing up all he applicable expendiures, meansesed supplemenal benefis guaranee a gross income of approximaely CHF 36,000 for singles. As shown in Table 1, average annual means-esed supplemenal benefis, condiional on claiming, for reired beneficiaries in 2008 were CHF 9,600 for single beneficiaries. The cos-of-living 6 Pension funds are required o index pension benefis o inflaion if he financial siuaion of he fund allows for his. A presen, however, few funds are able o index pensions o inflaion mainly due o high liabiliies creaed by he high conversion facor in he mandaory par. 7 In OECD counries around 17% of he populaion above age 65 receives means-esed benefis, alhough here is a considerable variaion across counries depending on how low he eligibiliy hreshold is se. For example, in Denmark and Ausralia beween 70 o 80% of all reirees claim means-esed benefis, compared o less han 2% in Germany and Japan (OECD (2011)). 9

12 allowance, he healh insurance premium, and ren paymens are he larges caegories on he expendiure side, while ineres paymens on morgages are negligible. Because he value of a home is aken ino accoun in he calculaion of means-esed benefis, home owners rarely qualify for means-esed benefis. The main source of income, oher han means-esed benefis, are firs pillar benefis. Table Benchmark parameers The chosen parameer values for our specificaion of he life-cycle model are displayed in Table 2. Following relaed lieraure (Pang and Warshawsky (2010), and Yogo (2009)) we se he ime preference discoun facor, β, equal o Like Ameriks e al. (2011), we se he risk aversion coefficien γ o 3. We only consider individuals afer reiremen from age 65 ( = 1) o age 100 ( = 1). For all oher parameers we aim o be as close as possible o he Swiss case o faciliae a comparison of he simulaion resuls wih acual choices.the survival probabiliies are he curren male survival probabiliies in Swizerland and are obained from he Human Moraliy Daabase. 8 We assume a cerain deah a age 100. The equiy reurn is normally disribued wih a mean annual nominal reurn, µ R, of 6.5% (corresponding o a equiy premium of 4%) and an annual sandard deviaion, σ R, of 20%, which is in accordance wih hisorical sock performance. The mean insananeous shor rae is se equal o 2.5%, he sandard deviaion o 1%, and he mean reversion parameer o The correlaion beween he insananeous shor rae wih he expeced inflaion is 0.4. The parameers for he inflaion dynamics are esimaed wih daa from he Swiss Naional Bank. Mean inflaion is equal o 1.79%, he sandard deviaion of he insananeous inflaion rae is equal o 1.12%, he sandard deviaion of he price index equals 1.11%, and he mean reversion coefficien equals Pillar I annuiy income, Y I 1, is se o CHF 24,000, and is indexed o inflaion. This number approximaely corresponds o he average firs pillar income of individuals covered by occupaional pensions. The gross guaraneed income level o deermine he means-esed benefis, M, is CHF 36,000 in real erms. Under his assumpion he maximum amoun of means-esed benefis, M is CHF 12, benefis is The fracion of wealh g ha is aken ino accoun when calculaing means-esed 8 We refer for furher informaion o he websie, 9 In many cases only a fracion of he maximum means-esed benefis is paid ou, because agens sill have posiive pension wealh and/or non-pension wealh. For example, in 2008 he average means-esed benefis acually paid ou, condiional on means-esed benefis being posiive, was CHF 9, We absrac from he hreshold for wealh over which he fracion g is calculaed. Taking ino accoun he wealh hreshold would add anoher maximizaion funcion (max(0; 25, 000 W )) in he budge consrain which would complicae he numerical opimizaion procedure even more. Moreover, his assumpion has only a small effec on he 10

13 The conversion rae c used o ranslae he accumulaed capial ino a yearly nominal annuiy income is se o 7.2%, which is he rae applied o second pillar wealh for he period of our daa. The acuarially fair conversion rae for a single-life nominal annuiy would be 8.1%. However, he implici load on he annuiy, 12% of pension wealh, oversaes he average effecive load as he same conversion rae is applied for married individuals. Taking ino accoun survivor benefis, he effecive load would be much smaller, even negaive. The values aken for he progressive lump sum ax τ ls and he income ax τ Y are displayed in Appendix B. They represen he applicable ax raes of he larges Swiss ciy, Zurich. Zurich s ax burden lies in he middle of all Swiss regions. Table 2 4 Daa 4.1 Daa descripion and limiaions The predicions from our simulaed life-cycle model are compared wih adminisraive individual records from several Swiss companies. We compiled his unique daase from records provided by auonomous pension schemes as well as large insurance companies. While he former are ypically sponsored by large companies, he laer provide occupaional pension plans for small and medium sized companies. For all companies in our sample, all individual reiremen decisions for he period 1996 o 2006 are recorded. Each individual is observed only once a reiremen. The daa conain informaion on he dae of birh, he reiremen dae, annuiizaion decision, amoun of accumulaed pension wealh, conversion facor as well as company specific pension scheme informaion such as defaul and cash-ou opions. Since he amoun of means-esed benefis depends on oal wealh, informaion on non-pension wealh is imporan. Unforunaely, his informaion is no recorded in he adminisraive daa. Therefore, we uilize asse daa from he firs wave of he Survey of Healh, Aging and Reiremen in Europe (SHARE) in 2003 o esimae a disribuion of liquid and illiquid non-pension wealh separaely. We do no use a join disribuion as he correlaion is very low (correlaion coefficien: ). As Tables 3 and 4 illusrae, he disribuions of boh liquid and illiquid non-pension wealh are very heerogeneous. We will use he disribuions of liquid and illiquid non-pension wealh o calculae a weighed average of he opimal annuiizaion levels, as described in deail in secion 5.3. Table 3 resuls, given ha he hreshold is jus CHF 25,

14 Table 4 We resric he daa on annuiizaion decisions of men only for hree reasons. A number of social securiy reforms affeced women during he sample period (such as an increase in he reiremen age for women from 62 o 64 and he inroducion of child care credis). Moreover, neglecing spousal income has larger consequences for women han for men, hereby making he difference in decisions across (unobserved) marial saus more pronounced. Women also have much smaller balances in he second pillar for he birh cohors considered. Our daa usually does no record marial saus, age, or income of he spouse. We are well aware of he imporance of boh marial saus per se and socio-economic characerisics of he spouse (in paricular age and income/wealh). We expec he qualiaive impac o be similar for married and single men. Our daa span a ime period in which wives did no work much and hus he addiional pension wealh in he second pillar for married men is likely o be small. Moreover, he addiional income of he firs pillar for he spouse jus covers he addiional expendiures ha are credied agains means-esed benefis. Hence, for a given second pillar income, a married and a single man face very similar radeoff. Consisen wih his view, Büler and Teppa (2007) find lile difference in annuiizaion paerns beween married and single men for hose pension funds ha do provide informaion abou marial saus. The higher money s worh of he annuiy for married individuals (due o survivor benefis and higher life expecancy) seems o be offse by a lower demand for insurance of married couples and/or beques moives. 4.2 Summary saisics Table 5 Table 5 repors key saisics for he variables of ineres. Early reiremen, saring a age 55, as well as working beyond planned reiremen is possible. However, he average reiremen age is close o he sauory reiremen age of 65 for men. Average oal pension wealh is abou CHF 250,000. Furhermore, Table 5 reveals ha a large fracion of he beneficiaries chose a polar opion, eiher full lump sum or full annuiy. Mainly as a consequence of early reiremen adjusmens, he mean conversion rae in he mandaory par is 6.9, slighly lower han in he raed used in he life-cycle model. Figure 1 Figure 1 illusraes he relaionship beween pension wealh and he annuiizaion level of pension wealh for wealh levels below 700,000 CHF. 11 The solid line represens he fracion of reirees 11 Individuals wih higher pension wealh ofen have access o managemen pension plans ha are subjec o differen condiions. 12

15 who annuiize fully for differen levels of pension wealh. 12 As 95% of reirees choose one of he polar opions, we consider he annuiizaion as a binary decision even for he remaining 5% of he sample. Annuiizaion raes of 50% or more were se o 100%, hose below 50% o 0%. In he simulaions, he fracion of people choosing a polar opion is also very high, and of course dependen on he grid size chosen for he annuiy level. The fracion of individuals who annuiize is low for small levels of pension wealh and increases coninuously for higher levels of pension wealh. Heerogeneiy in non-pension wealh leads o some reirees choosing he annuiy, while for he res aking he lump sum is opimal. As pension wealh increases, he propensiy for reirees o ake he annuiy insead of he lump sum increases. Figure 2 Since companies can se differen defaul opions, i is ineresing o invesigae how annuiizaion levels vary wih he defaul opion. Ou of he welve companies in our sample, en companies have he annuiy as a defaul (16,514 observaions), one large company has no defaul (5,747 observaions) and one small company (25 observaions) has he lump sum as a defaul. Figure 2 shows how annuiizaion levels vary wih pension wealh for companies who have he annuiy as defaul versus all oher companies (lump sum or no defaul). The fracion of individuals who annuiize is on average 17 percenage poins higher in companies ha have he annuiy as defaul, bu as Figure 2 illusraes, he propensiy o annuiize increases wih he accumulaed pension wealh independen of he company s defaul opion. The annuiy is reaed as normal income and herefore subjec o income axes. The lump sum, on he oher hand, is axed only once and reaed independenly of oher income. Due o he differenial ax reamen he presen value of he lump sum s oal ax bill is almos always smaller han he annuiy s ax burden, especially for larger capial socks. 5 Resuls: How means-esed benefis affec annuiizaion Our resuls are organized as follows. Firs, we illusrae he impac of means-esed benefis on opimal annuiy demand using he mos basic life-cycle model. Second, we show how he opimal annuiy demand changes when inflaion and equiy risk, non-pension wealh, and axes are aken ino consideraion. Third, we compare he simulaion resuls from our model wih observed annuiizaion decisions from adminisraive daa. Finally, we discuss and es alernaive explanaions why he observed propensiy o annuiize increases wih pension wealh. 12 We calculae he values in he solid line by spliing he sample ino differen bins according o he level of pension wealh and hen calculae he mean fracion of reirees ha annuiize wihin each bin. The bins are (in CHF 1,000): , , , , ,

16 5.1 Opimal annuiy demand: The baseline model To isolae he impac of means-esed benefis, we sar wih a baseline annuiy model ha includes firs pillar benefis, bu absracs from equiy markes, axes, inflaion, and ineres rae risk. The model serves as an illusraive example ha highlighs he main mechanisms a work. Figure 3 displays he opimal consumpion levels in case he enire pension wealh is annuiized or cashedou, respecively, for wo differen levels of pension wealh. 13 The lef panel (pension wealh level of CHF 200,000) shows ha for he firs 10 years of reiremen he consumpion sream is much higher when he lump sum is aken han if he pension wealh is annuiized. Thereafer consumpion is slighly higher in he case of he lump sum compared o full annuiizaion. The annuiy income ha can be generaed by annuiizing all wealh (CHF 38,000) only marginally exceeds he guaraneed income (CHF 36,000). As a consequence, i is opimal o ake he lump sum, spend i down in he firs years of reiremen, and subsequenly apply for means-esed benefis. The righ panel illusraes ha for a higher wealh level (CHF 350,000 in he illusraion) he lump sum opion sill generaes a higher consumpion level during he firs 10 years. However, once he lump sum is depleed, he difference beween he annuiy income (CHF 49,000) and he guaraneed level due o means-esed benefis (CHF 36,000) is much higher. As a consequence, i is opimal o annuiize everyhing because he benefis from annuiizaion, consumpion smoohing and a higher insured income lae in life, ouweigh he benefis from a lump sum, receiving free wealh in he form of means-esed benefis. Figure 3 The simple example illusraes ha means-esed benefis reduce he value of an annuiy because hey replace he benefis he annuiy would have provided oherwise. The simulaions also show ha even hose individuals who sraegically choose o cash ou o qualify for means-esed benefis ake some ime (11 years in he example) o spend down heir enire pension wealh. The uiliy benefis of consumpion smoohing sill play some role in he individuals decisions. As a consequence, one would expec he number of beneficiaries of means-esed benefis o go up only laer during he reiremen period. Means-esed benefis also increase he likelihood of polar choices. The addiional benefis are highes when annuiy levels are 0%. Any annuiy income would jus reduce he means-esed benefis dollar for dollar. In a similar vein, annuiizaion is mos beneficial (in he absence of differenial axaion) when he enire capial is annuiized. A parial annuiy reduces he value of 13 In his example he opimal consumpion sraegy is o consume he enire annuiy income. As he only risk individuals face is longeviy risk, a downward sloping consumpion paern, susained by borrowing agains fuure income, would be opimal in he absence of borrowing consrains. 14

17 longeviy insurance wihou increasing he probabiliy of receiving means-esed benefis laer in life. To quanify he impac of means-esed benefis on he value of an annuiy, we compue he willingness o pay for access o an annuiy marke wih means-esed benefis. The willingness o pay is defined as he moneary equivalen of he uiliy gain from following an opimal consumpion pah in he presence of an annuiy marke relaive o an opimal consumpion pah in he absence of an annuiy marke. In a second sep, we calculae he willingness o pay for access o an annuiy marke wihou means-esed benefis. The difference in he willingness o pay beween hese wo cases measures boh he reducion in he insurance value of he annuiy and he addiional income due o means-esed benefis. We use he same baseline annuiy model as above, bu assume ha he single-life annuiies we consider are acuarially fair. 14 Table 6 summarizes he resuls. Means-esed benefis reduce he opimal annuiizaion level from 100% o 0% for reirees wih less han CHF 300,000 pension wealh (columns 1 and 2), while he willingness o pay for access o he annuiy marke is always larger in he case reirees canno claim means-esed benefis (columns 3 and 4 shows). The difference in he willingness o pay is subsanial in boh absolue and relaive erms, as shown in columns 5 and 6. For example, for a reiree wih CHF 100,000 pension wealh means-esed benefis reduce he insurance value of he annuiy by 13.5%. The fall in he insurance value is highes for reirees wih CHF 300,000 pension wealh (17%) and hen declines coninuously for higher levels of pension wealh. Table Opimal annuiy demand: The full model Table 7 displays opimal annuiy demand for differen levels of means-esed benefis using a lifecycle model ha includes equiy and ineres rae risk, inflaion and axes bu ignores non-pension wealh. We use he benchmark conversion facor of 7.2%, implying an implici load on he (singlelife) annuiy of 12%. In he absence of means-esed benefis he opimal annuiizaion level increases wih pension wealh from 40% for CHF 100,000 pension wealh o around 80% for CHF 700,000 pension wealh. Recall ha his annuiizaion is on op of an annuiy from he firs pillar (he annual firs pillar annuiy of CHF 24,000 is equivalen o a ne presen value of more han CHF 300,000). In he augmened model annuiizing 100% of pension wealh is no longer opimal, because individuals wan o keep par of heir wealh liquid o smooh inflaion shocks. Moreover, progressive raes in boh he income ax (which is levied on he annuiy) and he ax on he cash-ou, in 14 As oulined before, focusing on single-life annuiies underesimaes he araciveness of he annuiy due o neglecing spousal benefis. For singles, he acuarially fair nominal annuiy conversion rae is slighly higher a 8.1%. Based on he same parameer choices he real annuiy conversaion rae would be 6.7%. 15

18 combinaion wih a preferenial ax reamen on he lump sum, induce a shif owards a higher cash-ou rae for a given capial sock. Table 7 If means-esed benefis are available, he opimal annuiy demand falls sharply for low o inermediae levels of pension wealh. For he maximum means-esed benefis of CHF 12,000, he annuiy is no longer opimal for pension wealh below CHF 700,000. A higher uiliy level can be achieved by cashing-ou pension wealh, spending i down, and subsequenly applying for generous means-esed benefis. Wealhier reirees sill prefer o annuiize he bulk of reiremen balances because a smooh consumpion paern susained by he annuiy dominaes he receip of free wealh in he form of means-esed benefis. Table 7 also clearly demonsraes ha he availabiliy of means-esed benefis makes he annuiizaion decision basically a 0-1 decision: Individuals eiher do no annuiize a all or hey nearly fully annuiize heir pension wealh. The inuiion behind his resul is he same as in he baseline case: An inermediae degree of annuiizaion cus individuals off from means-esed benefis, bu does no give hem he full benefis of an annuiy. In a similar vein, he opimal annuiizaion level also increases wih he level of liquid non-pension. An addiional Swiss franc in non-pension wealh has he same impac as an afer-ax franc of pension wealh. 15 Means-esed benefis creae an implici ax on annuiies, as means-esed benefis are foregone by buying he annuiy conrac. 16 To quanify he implici ax, we calculae he average amoun of means-esed benefis received when an agen annuiizes opimally and compare his number o he average amoun of means-esed benefis received when an agen does no annuiize. The implici ax of means-esed benefis corresponds o he benefis forgone due o choosing he annuiy. Recall ha our analysis is resriced o male reirees. Using a uniform conversion as in he Swiss scheme has differen implicaions on acuarial fairness for singles and married individuals. The money worh of married men s annuiy is much larger han he corresponding figure for singles as spouses are eniled o survivor benefis. Moreover, here are also some moraliy differences beween single and married men. Noneheless in he absence of informaion on wheher he individual is married and on he age of he spouse, we compue he loads for single males only. Using a conversion 15 We disinguish beween liquid and illiquid non-pension wealh: Liquid non-pension wealh can be drawn down jus as easily as pension wealh leaving he opion o apply for means-esed benefis. Illiquid non-pension wealh mainly consiss of housing, which is more difficul o deplee. Many people prefer o keep living in heir own home even if hey would be beer off in financial erms by selling i. Reverse morgages have hardly been available during he period of he analysis. They also involve prey large ransacion coss. As a consequence few home owners qualify for means-esed benefis. 16 This exacly mirrors he impac of means-esed Medicaid benefis of he purchase of long-erm care insurance as analyzed in Brown and Finkelsein (2008) 16

19 facor of 7.2% leads o a prima facie pricing load of abou 12%, bu aking ino accoun spousal benefis, he annuiies are much beer value for married individuals. The compued load is hus overesimaed for married men (who have an annuiy ha includes survivor benefis) and somewha underesimaed for singles. The resuls of his analysis for wo differen levels of non-pension wealh are summarized in Table 8. Column 1 shows he gross load, which is he pricing load (again assuming single-life annuiies). Columns 2 and 3 repor he implici ax on he annuiy in absolue erms and relaive o pension wealh. The relaive implici ax is declining wih pension wealh, which is consisen wih opimal annuiizaion levels rising wih pension wealh. A comparison of panel A and B shows ha he implici ax rae is lower for individuals wih more liquid non-pension wealh, because wealhier individuals are less likely o be eligible for mean-esed benefis. Columns 4 and 5 documen he ne load in absolue erms and relaive o pension wealh. The ne load is he gross load plus he implici ax on he annuiy. We find ha due o he implici ax ne loads for individuals a he lower end of he pension wealh disribuion are subsanial. This explains why few individuals wih low pension wealh annuiize heir reiremen balances. Table Comparing opimal annuiy demand wih observed decisions Our simulaed life-cycle model predics ha annuiizaion levels increase wih accumulaed pension wealh. The daa also show a posiive relaionship beween he accumulaed pension wealh a reiremen and he fracion of individuals who choose he annuiy (see Secion 4.2). The quesion is wheher he annuiizaion paern found in he daa is quaniaively consisen wih he heoreical model. In order o calculae he opimal annuiy demand we also ake ino accoun ha individuals differ in heir liquid and illiquid non-pension wealh. We calculae a weighed average of opimal annuiizaion raes as a funcion of second pillar pension wealh levels. The weighs are derived from he empirical disribuions of liquid and illiquid non-pension wealh using SHARE daa (see Tables 3 and 4). 17 We assume ha individuals can never ransform illiquid ino liquid non-pension wealh. This raher conservaive approach, which is anamoun o infinie liquidaion coss, poenially underesimaes he incenive o spend down non-pension wealh in order o 17 The weighs depend on he fracion of agens ha fall ino a cerain caegory wih respec o he amoun of liquid and illiquid non-pension wealh. The SHARE daa do no display any correlaion beween non-pension wealh and pension wealh - he correlaions beween pension wealh and oal non-pension wealh, liquid non-pension wealh, and illiquid non-pension wealh are 0.04, 0.16, and 0.14 respecively. A possible inerpreaion for he independence is ha individuals wih low pension wealh may compensae by saving more ouside he second pillar. Alernaively, individuals wih high levels of non-pension wealh may choose o work less and hus accumulae less pension wealh. 17

20 claim means-esed benefis. 18 There are wo ways o calculae and inerpre he opimal annuiy demand: (1) he percenage of individuals who primarily op for he annuiy, i.e., hey choose o annuiize more han o cash ou; or, (2) he percenage of pension wealh invesed ino annuiies as a funcion of pension wealh. In wha follows below we focus on (1) - he percenage of individuals who choose he annuiy insead of he lump sum - because in he daa almos all individuals eiher choose full annuiizaion or zero annuiizaion. 19 Hence, we round up he opimal annuiy demand o 100%. The numbers in he case we do no round up he annuiy level o 100% are included as a robusness check. Figure 4 compares he opimal annuiizaion paern prediced by he calibraed life-cycle model wih is empirical counerpar. The solid line shows he daa: he observed fracion of individuals who ake an annuiy as a funcion of pension wealh. We firs focus on case (1) in which agens are assumed o eiher fully annuiize or no a all. The dashed line and he solid line wih squares illusrae he prediced likelihood o annuiize in he presence or absence of means-esed benefis, respecively. In boh he daa and he model he likelihood o ake he annuiy increases wih pension wealh. If means-esed benefis are unavailable, all individuals wih pension wealh of CHF 150,000 or more are prediced o choose (close o) full annuiizaion, which is clearly a odds wih he daa. The fracion of individuals who are expeced o annuiize drops dramaically when agens have access o means-esed benefis. The prediced propensiy o annuiize in he presence of means-esed benefis (dashed line) is remarkably close o he daa (solid line). Hence, he empirical annuiizaion paern in Swizerland seems o be consisen wih he proposed explanaion of means-esed benefis creaing a srong incenive o cash-ou pension wealh. The mach beween he daa (solid line) and simulaions (doed line) remains similarly close if we focus on he prediced fracion of pension wealh aken as an annuiy insead (case 2). Figure Alernaive explanaions The lieraure shows ha wealhier people end o live longer han poorer individuals (De Nardi e al. (2010)). For he U.S. De Nardi e al. (2010) find a difference in life expecancy a age 70 of 4.6 years beween he lowes and he highes income quinile. Annuiies are relaively more aracive 18 In paricular, we assume ha he 48.4% of all individuals in he daa whose illiquid non-pension wealh exceeds CHF 145,000, will never be eligible for means-esed benefis. The cuoff is CHF 145,000 since means-esed benefis will be reduced by one-enh of wealh over a hreshold of CHF 25,000 and he means-esed benefis are CHF 12,000 (0.1*(145,000-25,000)=12,000). 19 Only 5% choose a mix as shown in Table 5. In he simulaions, 60% of people choose one of he polar opions: 100% annuiizaion or 0% annuiizaion. However, due o he availabiliy of equiy, inflaion risk, and axes, i can be opimal o annuiize less han 100%. In he simulaions, 95% of people choose annuiizaion levels above 70% or exacly equal o 0%. 18