Annuity Choices and Longevity Bonds: A Developing Country Application

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1 Annuiy Choices and Longeviy Bonds: A Developing Counry Applicaion (Draf Paper. April 30, 2014) José Luis Ruiz 1 Faculy of Economics and Business, Universiy of Chile, Diagonal Paraguay 257, Saniago , Chile. Absrac We use a variable ha comes from a dynamic programming model developed by Michell e al. (1999) and Brown (2001), called Annuiy Equivalen Wealh, in order o capure he benefis of having access o he annuiy marke. We inroduce longeviy bonds as asses for insurance companies, and we expec an increase in he annuiizaion probabiliy. Keywords: Annuiies, Pensions, Welfare. JEL: G22, G23, I38, H55, J32 1. Inroducion In 1981, Chile convered is old Pay-as-You-Go sysem ino a new sysem based on individual accouns in which privae companies, called Pension Fund Adminisraors (AFPs), are in charge of collecing and invesing he mandaory conribuions from affiliaes during heir working lives. A he ime of reiremen, a person can choose eiher a pension on a phased wihdrawal in which he reiree no only keeps he conrol over he funds bu also reains he longeviy risk and bears he capial marke risk associaed wih he rae of reurn of he invesmens or as an annuiy ha will give a sream of income for he lengh of purchaser s life bu ransfers he propery of he funds o an insurance company. The annuiy proecs he reiree from longeviy risk, bu he decision o annuiize is irreversible. The normal reiremen age is 60 for females and 65 for males. Thus, he experience of more han hree decades of he Chilean privae pension sysem provides a unique experience o sudy he deerminans of annuiizaion. Whereas 1 Corresponding auhor. 1

2 annuiies are no frequenly used as pension paymen in he world, Chile has one of he highes raes of annuiizaion (Rocha and Thorburn, 2006). The longeviy risk of individuals has been underesimaed, as survival probabiliies have improved across he developed world (Ngai and Sherris, 2011). This sudy provides evidence from Chile, an emerging economy ha has developed successful public policies in he las decades (Claessens e al., 2010). We use dynamic approach o capure he benefis of having access o he annuiy marke. The way o compue hese benefis are summarized by he Annuiy Equivalen Wealh (AEW) ha a person requires o be compensaed in he case ha he annuiy markes were absen. This paper is organized in six secions, including his inroducion. Secion 2 discusses he lieraure. Secion 3 describes he daase. Secion 4 describes he mehodology o be employed. Secion 5 repors he empirical resuls and secion 6 concludes. 2. Lieraure Review Many sudies have emphasized he effec of adverse selecion on annuiies (Abel (1986), Finkelsein and Poerba (2004), McCarhy and Michell (2010)). Abel (1986) examines he implicaions for individual consumpion and beques moives. Using an overlapping generaion model in which individuals are uiliy maximizers bu are uncerain regarding he dae of deah, he shows ha an acuarially fair social securiy will increase he rae of reurn on purchased annuiies reducing he effecs of adverse selecion. Finkelsein and Poerba (2004) examine annuiy policies in he U.K. and show ha, in boh he compulsory and he volunary markes, here is srong evidence ha longer-lived individuals buy more back-loaded annuiies. McCarhy and Michell (2010) provide inernaional evidence of adverse selecion in annuiies. 2 Oher sudies have emphasized he Money s Worh Raios (MWR), calculaion of he expeced presen discouned value of payous for annuiies in relaion o he premium cos of he annuiy as a way o undersand he value of purchasing an annuiy (Michell e al 1999, Michell and Ruiz, 2011). Brown (2003) acknowledges ha annuiies are valuable longeviy insurance for individuals wih uncerain lifeimes. In his model, however, mandaing annuiies for 2 The counries sudied are he Unied Saes, he Unied Kingdom, and Japan. 2

3 all individuals would no be opimal because of he exisence of differen moraliy disribuions across groups and purchase coss. Brown and Poerba (2000) find ha he uiliy gain from annuiizaion is bigger for single individuals han for couples. As more poenial buyers are couples, his fac could help o explain he low level of annuiizaion in he counry given he effecs of adverse selecion in he case hey decide o annuiize. They also find no evidence of beques moives as an imporan variable. Using dynamic programming echniques, Brown (2001) use a measure called he Annuiy Equivalen Wealh firs used by Michell e al. (1999) o repor he uiliy value of gaining access o an acuarially fair annuiy marke. This variaion in uiliy arises from differences in marial saus, risk aversion, moraliy risk, planning horizon and healh saes. He finds no empirical suppor of beques moives. Buler and Teppa (2007) sudy he choice beween an annuiy and a lump sum using he AEW measure for Swiss pension funds. They use adminisraive records and find ha he sponsor influences he annuiy decision. They also find ha low accumulaion of reiremen asses is srongly associaed wih he choice of a lump sum. This paper is close relaed wih he idea of our sudy. However, heir sample lack of non-pension wealh and has limied individual informaion. Mackenzie (2006) recognizes ha he opimal porfolio should include some par in annuiies and some precauionary savings. Dus, Maurer and Michell (2005) examine differen alernaives for he reiremen asse decumulaion process using a risk-value approach. Here, reurn is he expeced level of benefis and risk perains o uncerainy of reaching he desired level of consumpion. They menion ha phased wihdrawal plans have he advanages of flexibiliy and beques moives, bu hey also require reirees o formulae asse allocaion and wihdrawal rules which can be complex and expose he reiree o longeviy and capial marke risk. Horneff e al. (2010) poin ou ha uiliy mazimizers will gradually annuiize he porfolio, even if reirees do no have a srong beques moives. Then, here is an annuiy puzzle given by he low rae of annuiizaion in some counries and he economic advanage of aking his decision. A pioneer proposal for Moraliy-linked securiies was inroduced by Blake and Burrows (2001). They sugges a survivor bond for hedging he longeviy risk, and his 3

4 should be issued by he governmen based on populaion moraliy. The laer was also repored by Brown and Orszag (2006). Longeviy bonds are paid according o he survival experience of a cohor (Dowd e al., 2006; Blake e al., 2006). 3. Daa We examine he empirical evidence in Chile by using he Encuesa de Proección Social (Social Proecion Survey; EPS; Deparmen of Economics a he Universiy of Chile and he Universiy of Pennsylvania, 2006), which has 16,443 respondens. This survey is unique in he Lain American economy because i includes socioeconomic, demographic, and oher informaion provided by he inerviewees. A panel of inernaional expers paricipaed in he design of he survey o ensure represenaive informaion a a naional level. This survey consiss of respondens who are 18 years and older, represening a oal populaion of abou 12.5 million people, of whom 50.9% are women and 49.1% men. Explanaory variables for pension benefis are relaed wih reiree age, gender, Marial saus, Pension Balance. Non Reiremen Wealh as higher asse people have ouside he pension sysem, lower probabiliy o annuiize we can expec. The reason is hey are able o diversify beer he asses and hen ry o keep he capial marke risk and leave a beques in case of die sooner. Anoher imporan variable is risk aversion. People who are risk-averse prefer o smooh consumpion sreams, so we expec hey will annuiize heir balances. Also, as he longeviy risk is no covered by PW, he possibiliy of running ou funds will increase he value for hem of being an annuian. This variable was also included in he Brown (2001) sudy. Using a quesion relaed o preferences for safey in he job, we creae a dummy called risk averse, wih value 2 if people choose wo conservaive opions, 1 if choose one conservaive opion, and 0 oherwise. Our hypohesis is risk-averse people prefer o smooh consumpion, so hey will value higher an annuiy. Thus, he expeced sign for changes in probabiliy of annuiizing wih respec o risk aversion is posiive. 4. Mehodology 4

5 The mehodology o be employed models choice behavior as influenced by he difference in expeced uiliy beween purchasing an annuiy and aking PW. Our objecive is o derive a measure of he annuiy Equivalen Wealh (AEW) o incorporae in an empirical model of he annuiy choice. 4.1 The Model Assuming ha individuals are expeced uiliy maximizers, i is opimal for an individual o choose an annuiy insead of a PW paymen a reiremen if E U Annuiy E U PW. Expeced Uiliy under Annuiy. If he individual chooses o buy an annuiy, he signs a conrac in which he pays an iniial up-fron sum o he insurance company, in exchange for a lifelong income annuiy sream. Then, he expeced discoun uiliy is: EU ( Annuiy) w puc ( ) (1 p) p du(0.6 C) (1 ) (1 ) (2) T age1 1 where T is he maximum possible life-span of an individual, age is he reiree s age a ime, UC ( ) represens he uiliy level defined over he consumpion in period, p is he probabiliy of remaining alive a period, he uiliy discoun rae, d is a dummy ha akes he value of one if he person is male, and represens he imporance he individual places on leaving a pension for his widow (Annuiies and PW give hem a benefi equivalen o 60% of heir husbands pension). We are assuming ha here are no children who can receive he survivorship benefi. We can see direcly from he specificaion ha a female does no leave a survivorship pension for her husband ( d 0). Consumpion sreams are deermined when he individual decides o purchase an annuiy. We will assume ha he only annuiy available is a real annuiy (he pension is adjused o he consumer s price index). Then he income sream he person will receive by purchasing he annuiy is: C C if C MPG MPG if C MPG (3) 5

6 Expeced Uiliy under PW. Under his payou opion, individuals can decide how much of he pension accrual hey will consume each period, and he amoun ha hey will save in order o increase fuure consumpion. We assume ha individuals reinves in he same AFP porfolio in which hey have heir balances as of he reiremen dae. We will solve by using dynamic programming echniques for he opimal pah of consumpion. Le U(C) represens he uiliy level defined over consumpion in period, ρ is he uiliy discoun rae, and d is a dummy ha akes he value of one when he individual is male. Then, he problem is o maximize he discouned uiliy unil he age of deah considering survivorship benefis. The maximizaion is he following: max Tage1 w pu ( c) C 1 (1 ) (1 ) (1 p ) p du(0.6 C ) (1 d) U( W ) (4) Subjec o he consrains: W is given a 0 (5) W 0 for all (6) W 1 (1 r)( W P C) (7) B P (8) 12CNU ir,, p In hese consrains, down in period, W is he AFPs balance he individual has available o draw C is he consumpion level a, S is he amoun of he PW benefi saved in order o increase fuure consumpion, P is he benefi level a and CNU i, is he capial necessary uniary o finance a uni of pension for he individual i a ime. We can define he equaion (4) as a value funcion. Then, his value funcion will saisfy he following recursive Bellman equaion: p 1 max V( W) max U ( C) V 1( W 1) (9) C C 1 6

7 The advanage of he Bellman equaion compared o solve he full maximizaion presened in equaion (4) is he fac ha he full maximizaion problem is reduced o a series of wo-period problems. The laer can be solved numerically by solving backwards from he las period. The maximizaion is subjec o he consrains in equaions (5) o (8). The sraegy followed by Michell e al (1999) and Brown (2001) was o resolve he problem in he case in which annuiies are no available and here is no beques moive. Then, is consrained o be zero. We can find he amoun in wealh ha an individual lacking access o he annuiy marke would pay for having ha access. Thus, we can find W as: V ( W * W / 0, for all ) V * (10) The specific mechanism for solving hese wo dynamic programming is presened in appendix. Following Michell e al (1999) and Brown (2001) we can define he Annuiy Equivalen Wealh (AEW) as: W * W AEW (11) W * V* is he uiliy level ha he individual reaches when he is consrained o ake he PW. Thus, AEW represens he maximum mark-up over he acuarially fair premium of an annuiy ha he individual would be willing o pay, giving he uiliy level ha could be aained wihou access o an annuiy marke. 4.2 Model Calibraion (Pending) 5. Resuls (Pending) 6. Conclusions (Pending) 7

8 References Abel, A., 1986, Capial Accumulaion and Uncerain Lifeimes wih Adverse Selecion, Economerica, 54, pp Blake, D.P., Burrows, W., Survivor bonds: helping o hedge moraliy risk, The Journal of Risk and Insurance 68, Blake, D.P., Cairns, A.J.G., Dowd, K., MacMinn, R., Longeviy bonds: financial engineering, valuaion, and hedging, The Journal of Risk and Insurance 73, Brown, J., 2001, Privae Pensions, moraliy risk and he decision o annuiize, Journal of Public Economics, pp Brown, J., 2003, Redisribuion and Insurance: Mandaary Annuiizaion Wih Moraliy Heerogeneiy, The Journal of Risk and Insurance, 70, pp Brown, J.R., Orszag, P.R., The poliical economy of governmen-issued longeviy bonds, The Journal of Risk and Insurance 73, Brown, J. and J. Poerba, 2000, Join Life Annuiies and Annuiy Demand by Married Couples, Journal of Risk and Insurance, 67, pp Buler, M. and F. Teppa, 2007, The Choice Beween an Annuiy and a Lump Sum: Resuls from Swiss Pension Funds, Journal of Public Economics 91, pp Claessens, S., Kose, M. A., and Terrones, M. E. (2010). Recessions and financial disrupions in emerging markes: A bird s eye view. Cenral Bank of Chile, Working paper no Davidoff, T., J. Brown, and P. Diamond, 2005, Annuiies and Individual Welfare, The American Economic Review, 95, pp Dowd, K., Cairns, A.J.G., Blake, D., Moraliy-dependen financial risk measures, Insurance Mahemaics and Economics 38, Dus, I., R. Maurer and O. Michell, 2005, Being on Deah and Capial Markes in Reiremen: A Shorfall Risk Analysis of Life Annuiies versus Phased Wihdrawal Plans, Financial Services Review. Lead aricle. (14) pp

9 Finkelsein, A. and J. Poerba, 2004, Adverse Selecion in Insurance Markes: Policyholder Evidence from he U.K. Annuiy Marke, Journal of Poliical Economy, 112, pp Horneff, M., R. Maurer, O. Michell and M. Samos, 2010, Variable Payou Annuiies and Dynamic Porfolio Choice in Reiremen. Journal of Pension Economics and Finance. 9, April: James, E., G. Marinez and A. Iglesias, 2006, The payou sage in Chile: Who annuiizes and why?, Journal of Pension and Finance, 5, pp Kolikoff, L. and A. Spivak, 1981, The Family as an Incomplee Annuiies Marke, Journal of Poliical Economy, pp Mackenzie, G. 2006, Annuiy Markes and Pension Reform, Cambridge Universiy Press. McCarhy, D. and O. Michell, Inernaional Adverse Selecion in Life Insurance and Annuiies. In Shripad Tuljapurkar, Naohiro Ogawa, & Anne Gauhier, eds. Riding he Age Wave: Responses o Aging in Advanced Indusrial Saes. Elsevier. New York: Springer: Michell, O., J. Poerba, M. Warshawsky, and J. Brown, 1999, New Evidence on he Money s Worh of Individual Annuiies, The American Economic Review, 89, pp Michell, Olivia S. and Jose Ruiz (2011). Chaper 7, Pension Paymens in Chile: Pas, Presen, and Fuure Prospecs. book: Securing Lifelong Reiremen Income. In Olivia S. Michell, John Piggo, and Noriyuke Takayama, eds. Oxford Universiy Press. Ngai, A. and M. Sherris, 2011, Longeviy risk managemen for life and variable annuiies: The effeciveness of saic hedging using longeviy bonds and derivaives, Insurance: Mahemaics and Economics, Volume 49, Issue 1, July 2011, Pages Rocha, R. and C. Thorburn, 2006, Developing Annuiy Markes: The Experience of Chile, Direcions in Developmen, Finance, The World Bank. Yaari, M., 1965, Uncerain Lifeime, Life Insurance, and he Theory of he Consumer, The Review of Economic Sudies, 32, pp

10 Appendix Solving he dynamic problem In his secion we add he uiliy maximizaion process we follow in order o find he annuiy equivalen wealh (AEW) for each individual. The process shows he procedure for boh pension payous. For he Annuiy: w 1 p 1VA( W 1, B, p 1) (1 p 1) p 1dwV A( W 1) VA( W, B, p) MaxU( C) c 1 (1 p 1)(1 d) bv A( W 1) Subjec o he consrains: W 1 (1 r)( W A C) W 1 0 W W PV(0.6 A) B 0(1 x) A xb 0 L, 12CNU i ir,, A Where W is he cash in he bank, A is he annuiy paymen, C is he consumpion, PV is he presen value and L is he longeviy bond paymen. For he Phased wihdrawal: w 1 p 1VP( W 1, B, p 1) (1 p 1) p 1dwV P( W 1) VP( W, B, p) MaxU( C) c 1 (1 p 1)(1 d) bv P( H 1) Subjec o he consrains: W 1 (1 r)( W P C) W 1 0 W W PV(0.6 P) B P 12CNU H W B ir,, p Where W is he cash in he bank, A is he annuiy paymen, C is he consumpion, PV is he presen value and P is he pension amoun under phased wihdrawal rule. 10

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