NBER WORKING PAPER SERIES THE EFFECT OF UNCERTAIN LABOR INCOME AND SOCIAL SECURITY ON LIFE-CYCLE PORTFOLIOS

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1 NBER WORKING PAPER SERIES THE EFFECT OF UNCERTAIN LABOR INCOME AND SOCIAL SECURITY ON LIFE-CYCLE PORTFOLIOS Raimond Maurer Olivia S. Michell Ralph Rogalla Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA January 2010 This research was conduced wih suppor from he Pension Research Council a The Wharon School of he Universiy of Pennsylvania. We are graeful for useful commens from Jason Sco and Ramu Thiagarajan. Opinions and errors are solely hose of he auhors and no of he insiuions wih whom he auhors are affiliaed. This is par of he NBER Program on he Economics of Aging. The views expressed herein are hose of he auhors and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Raimond Maurer, Olivia S. Michell, and Ralph Rogalla. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 The Effec of Uncerain Labor Income and Social Securiy on Life-cycle Porfolios Raimond Maurer, Olivia S. Michell, and Ralph Rogalla NBER Working Paper No January 2010 JEL No. G11,G22,G23,H55,J14,J24,J26 ABSTRACT This paper examines how labor income volailiy and social securiy benefis can influence lifecycle household porfolios. We examine how much he individual opimally saves and where, aking ino accoun liquid financial wealh and annuiies, and socks as well as bonds. Higher labor income uncerainy and lower old-age benefis boos demand for sable income in reiremen, bu also when young. In addiion, a declining equiy glide pah wih age is appropriae for he worker wih low income uncerainy; for he high income risk worker, equiy exposure rises unil reiremen. We also evaluae how differences in social securiy benefis can influence reiremen risk managemen. Raimond Maurer Finance Deparmen, Goehe Universiy Grüneburgplaz 1 (Uni-PF. H 23) Frankfur am Main, Germany rmaurer@wiwi.uni-frankfur.de Ralph Rogalla Goehe Universiy of Frankfur House of Finance (Uni-PF H 23), Gr D Frankfur am Main rogalla@wiwi.uni-frankfur.de Olivia S. Michell Universiy of Pennsylvania Wharon School 3620 Locus Walk, S 3000 SH-DH Philadelphia, PA and NBER michelo@wharon.upenn.edu

3 1 The Effec of Uncerain Labor Income and Social Securiy on Life-cycle Porfolios Risky labor income and pension payous are key deerminans of reiremen wellbeing and invesmen behavior over he life-cycle. In he pas, defined benefi (DB) pension plans and social securiy benefis provided a subsanial and relaively sable componen of reiremen wealh, whereas more recenly, labor marke flexibiliy has grown, along wih defined conribuion (DC) plans. As a resul, households will be required o ake on increased responsibiliy for reiremen accumulaion and decumulaion in a more uncerain world. This paper examines how consumers can opimally allocae heir saving among wo major asse classes, namely equiy and bonds, and wo ypes of reiremen asses, namely liquid saving and illiquid annuiies. We illusrae how incorporaing labor income risk as well as social securiy benefis influences opimal asse allocaion, in a realisically-calibraed dynamic lifecycle model. Our sudy exends prior lieraure by aking ino accoun life annuiies which pay a defined sream of benefis over he remaining lifeime (e.g. Cocco, Gomes, and Maenhou 2005). This work evaluaes he impac of alernaive empirical labor income rajecories, allowing for an observed invered-u-shaped age-relaed pay profile as well as volailiy around ha profile. We use his approach o assess how differences in earnings profiles and shocks may drive life-cycle invesmen behavior and he demand for annuiies. We also build on our own prior work (Horneff, Maurer, Michell, and Samos 2009a, b) which shows ha households can benefi subsanially from holding annuiies as well as capial marke asses. As demonsraed here, he paricular appeal of annuiies is ha hey offer consumers no only an invesmen reurn from he underlying asses bu also he survival credi generaed from pooling moraliy risk. 1 These papers provide insigh ino how a reasonable invesor would 1 For addiional references o he rapidly-growing lieraure on realisically calibraed discree

4 2 opimally save and inves her wealh across bonds, socks, and annuiies, aking ino accoun various levels of social securiy replacemen raes. In wha follows, we model he effec of uncerain labor income and social securiy benefi replacemen raios on life-cycle porfolios. Afer oulining he empirical framework employed, we presen resuls on opimal expeced consumpion, saving, asse allocaion, and annuiy purchases for represenaive households. We show ha higher labor income risk and lower social securiy replacemen raes will induce higher demand for sable income no only in reiremen bu also earlier in life. In oher words, individuals exposed o labor earnings risk can, o some exen, roll heir own personal defined benefi scheme by resoring o he privae annuiy marke. We also show ha a declining equiy glide pah wih age is appropriae for boh low and middle income risk workers, while, for he high income risk worker, equiy exposure rises unil reiremen. Empirical Sraegy To illusrae how differen levels of labor income uncerainy and social securiy reiremen benefis affec oucomes of ineres, we examine he case of an individual who is assumed o work from he age of 20 unil reiremen a age 65, afer which she expecs o rely on social securiy benefis, wihdrawals from liquid saving, and privaely-purchased life annuiy income. 2 The maximum assumed survival age is 100. She can inves her liquid saving in riskless bonds or risky socks, and she may also purchase immediae real fixed payou dynamic porfolio choice models, see Horneff, Maurer, Michell, and Samos (2009a, b) and Wacher and Yogo (2009). 2 For a more deailed descripion of he modeling approach see Horneff, Maurer, Michell, and Samos (2009a, b); flexible hours and endogenous reiremen ages are considered in Chai, Horneff, Maurer, and Michell (2009).

5 3 annuiies, boh before and afer reiremen. The individual anicipaes surviving from period o + 1 wih probabiliy p s, which is her subjecive probabiliy. She derives CRRA uiliy from consumpion of a single non-durable good C. The value funcion is maximized over he 1 C s argumens C,, and a according o V p E V 1 1 where ρ is he coefficien of relaive risk aversion, β is a ime discoun facor, is he share of liquid asses held in equiies, and a refers o annuiy purchases each period. 3 The household is precluded from borrowing agains fuure labor income and from shor-selling bonds, socks, and life annuiies. A opic of considerable recen ineres is how o model labor income uncerainy. 4 We posi ha each period s labor income Y is given byy exp( f ( )) PU wih P P N, where 1 f() represens a hump-shaped income profile over he life-cycle ofen used in empirical research (Cocco, Gomes, and Maenhou 2005). Here, P represens he permanen human capial componen and N allows for sochasic changes; U is a ransiory shock; σ u is he volailiy of he ransiory shock and σ n of he permanen shock. 5 In reiremen ( > K), we assume (for simpliciy) ha he individual receives consan and real social securiy benefis wih a consan benefi replacemen raio (ζ ) wih respec o final salary, expressed as Y exp f K P K, where K is he final year of work. 3 For his analysis, we assume ha he household derives no uiliy from bequess. Hurd (1989) suggess ha mos bequess are accidenal. 4 Noable prior sudies on asse allocaion ha consider uninsurable labor income risk include Campbell and Viceira (2002); Heaon and Lucas (1997); Viceira (2001); Bodie, Deemple, Oruba, and Waler (2004); and Polkovnichenko (2007). 5 The logarihms of boh N and U are normally disribued wih means zero and wih volailiies σ n and σ u, respecively. The shocks are assumed o be uncorrelaed.

6 4 Our benchmark case for an illusraive consumer ses preference parameers o sandard values found in he life-cycle lieraure: he relaive risk aversion coefficien is ρ = 5 and he discoun facor β = 0.96 (e.g. Gomes and Michaelides, 2005). Represening subjecive survival probabiliies, we apply nonlinear leas squares o fi he Gomperz force of moraliy o he 2000 Populaion Basic moraliy able for US females. To calculae he acuarial premium of a life payou annuiy, we use annuian moraliy ables and include expense loading λ of 7.2 percen, consisen wih Michell e al. (1999). The household can direcly inves in wo financial asses: riskless bonds and risky socks. The riskless real bond gross reurn is 2 percen, while he real risky sock reurn is log-normally disribued wih an expeced reurn of 6 percen and a volailiy of 18 percen as in much of he lieraure. The deerminisic age-dependen labor income funcion for an individual wih only a high-school educaion is aken from Cocco, Gomes, and Maenhou (2005). The assumed base case social securiy replacemen rae ζ of 68 percen is currenly ypical of low-wage reirees in he Unied Saes (Michell and Phillips 2006). In an alernaive scenario, we also show how oucomes would change wih a lower replacemen rae of 50 percen; his figure is consisen wih replacemen raios for low-wage earners in Japan (OECD 2009: 39). These wo alernaives are of ineres given ha Japan s curren demographic siuaion and social securiy shorfalls may well presage he fuure for he Unied Saes. The labor income volailiy parameers for he base case are σ n = 0.05 and σ u = 0.075, represening a labor income profile wih relaively low risk; here correlaions beween he sock reurns and he permanen (ransiory) income shocks are se o 0 0 n u. In he alernaive scenario, we evaluae resuls using a much higher labor income risk volailiy of four imes he base level as well as In sensiiviy analysis, we also show resuls for n

7 5 lower (ρ = 3) and higher (ρ = 8) levels of risk aversion. 6 Table 1 summarizes model parameers. Table 1 here Life-cycle Paerns of Invesmen, Saving, and Consumpion The base case invesor is one wih low labor income risk, high social securiy replacemen rae, and medium risk aversion, who faces incomplee privae markes for immediae annuiies wih high loadings. Resuls appear in Figure 1, which displays he expeced developmen of labor income, consumpion, liquid saving, annuiy purchases, and annuiy income from age 20 o 100. To generae a smooh lifeime consumpion pah, he worker saves from her 30 s o her mid-50 s so as o pay for laer consumpion. By her lae 50 s, liquid asses ouside of annuiies rise o a maximum of almos 11 imes her saring or iniial labor income. Afer ha, he invesor gradually sars drawing down asses o compensae for declining labor income; afer abou age 60, liquid asses are deployed o buy privae annuiies. From reiremen a age 65, liquid asses are depleed rapidly permiing he reiree o mainain pre-reiremen consumpion; as well, she relies increasingly on income flowing from privae annuiies, which she coninues o buy even well beyond reiremen age. In her early 80s, her liquid asses are fully exhaused because she has no beques moive; afer ha poin, he annuiy payou sream is considerable, helping mainain a smooh consumpion pah hroughou her remaining lifeime. 6 We solve he opimizaion problem by backward inducion in a hree-dimensional sae space, whereby for each grid poin we evaluae he policy and value funcions using Gaussian quadraure inegraion and cubic spline inerpolaion. For echnical deails we refer he ineresed reader o Horneff, Maurer, and Samos (2008) and Horneff, Maurer, Michell, and Samos (2009a, b).

8 6 Figure 1 here Figure 2 indicaes how liquid asses as a muliple of firs-year labor income, and saving raes are expeced o change wih age. The saving rae is defined as SRae 1 C / Income and Income refers o he flow of labor income and annuiy benefis. 7 The base case is represened by he solid line, for he low labor income risk/high social securiy replacemen rae scenario. In his safer world, he individual has lile need o save early in life: he saving rae is low a young ages and only from he mid-20 s does saving rise, wih a peak in he mid-40 s of 10 percen per year, and i becomes negaive (-5 percen) in he mid-50 s. Afer reiremen, saving raes drop preciipiously and reach a negaive -40 percen so as o smooh consumpion; he elderly older han abou age 85 have a saving rae of zero. Liquid asses grow slowly early in life, rising o around 10 imes firs-year labor income a heir peak. Figure 2 here In he riskier scenario, he social securiy replacemen rae is reduced o 50 percen, and labor income risk is four imes he base level and correlaed wih he sock marke. Here, he young adul will engage in subsanially higher saving o build a buffer agains high labor income volailiy over 40 percen per annum. Asses rise o 40 imes firs-year income by he lae 50 s. Nex, he saving rae falls, crossing he zero mark around he early 60 s; hereafer i rises again briefly jus before reiremen o offse low social securiy benefis. As we shall show nex, he money is used mainly o purchase annuiies ha provide a secondary sable income sream in reiremen. Neverheless, his individual s liquid saving coninues o rise 7 Here we repor he saving rae as SRae E( C ) / E( Income ) ; in unrepored resuls, we 1 have also compued SRae E( C / Income ) which is subsanially lower in he high risk/low replacemen rae scenario. 1

9 7 hrough he mid-50 s, due o reurns on invesmen. Afer reiremen, a 65, when he social securiy benefi begins, asses are consumed and he saving rae rajecory follows he one described earlier. Turning o Figure 3, he hree Panels illusrae how he individual will opimally allocae her oal financial wealh by age across equiies, bonds, and privae annuiies; here, oal financial wealh is defined o include boh liquid asses and he presen value of fuure privae annuiy income claims. On average, as is indicaed in Panel A, he base case individual (solid line) will opimally hold only equiies from youh o abou age 50 (apar from a few bonds early on, shown in Panel B). This is a common resul in many life-cycle sudies and occurs because, early in life, he individual s main asse is human capial which has bond-like payou characerisics. This is especially rue wih low labor income uncerainy, where her relaively safe labor income is also proeced in reiremen wih a relaively high social securiy benefi. She will opimally diversify her complee porfolio, which includes boh he presen value of her human capial (labor income plus social securiy benefis) as well as financial asses, by holding lile o nohing in bonds and insead invess enirely in equiies. Beginning abou age 55, her asse allocaion begins o include more bonds as her remaining work years dwindle. The opimal paern for privaely-purchased annuiies is illusraed in Panel C; hese play no role in he invesor s porfolio prior o he age of 59, as hey are relaively unaracive vis a vis bonds due o high loading and he use of annuian survival ables in pricing. A older ages, however, he annuiy survival credi rises above he bond rae; as a resul, annuiies crowd ou bonds. In reiremen, liquid asses are depleed o suppor consumpion and buy annuiies, which provide a secure privae income sream (assuming no bequess). From he early 80 s, he reiree is fully annuiized.

10 8 These resuls should be conrased hose generaed by he alernaive scenario wih high labor income uncerainy and low social securiy replacemen raes. 8 In general we would expec ha his consumer will need o save more, and hold more safe asses. This is borne ou in Panels A-C (dashed line), where he equiy fracion sars a zero and even in middle age remains below 30 percen; by conras he bond fracion sars ou a 100 percen and falls as he worker nears reiremen. This is because labor income no longer produces a bond-like sream of paymens ha previously pushed he young invesor ino equiies. This invesor also demands more annuiies, beginning around age 45, o help offse variable work earnings. The annuiized fracion hen rises quickly around reiremen, o help offse he now-low social securiy replacemen raes. Around age 60, he rising survival credi dominaes he annuiy pricing offses due o loads and he use of annuian moraliy ables. In all cases he ransiion o annuiies is accomplished by a subsanial movemen ou of bonds: her allocaion o bonds drops from 65 o abou 15 percen. As in he base case, he individual is fully annuiized from age 83 onward. I is also worh noing ha, around age 65 when she becomes eniled o social securiy benefis, she is no longer exposed o labor income risk. Accordingly, he sabile privae annuiy income plus he social securiy paymens permis he invesor o hold more equiies. Thus equiy exposure rises o over 40 percen, and hen i gradually declines in favor of annuiies, unil liquid savings are exhaused a age Sensiiviy Analysis 8 These are parial equilibrium compuaions, in ha lower social securiy benefi are no offse by social securiy ax cus. 9 This is because of he increasing survival credi a older ages, which raises expeced annuiy payous vis a vis equiies (Horneff, Maurer, Michell, and Samos 2009a, b).

11 9 Nex we review how resuls change across six combinaions of labor income risk levels and social securiy replacemen raes; comparaive resuls appear in Table 2. Panel A focuses on he high social securiy replacemen rae scenario and repors liquid asses, saving raes, and asse allocaion fracions, for hree workers: he low income volailiy case (he base case above), a high volailiy case (he alernaive scenario defined above), and a middle risk case (defined as σ n = 0.10, σ u = 0.20 and 0 ). Panel B indicaes he same resuls for a n lower social securiy benefi replacemen rae of 50 percen. We repor paerns for five decades of life from age 45 o 85. Table 2 here Comparing Panels A and B for all hree levels of labor income risk, i is eviden ha he Panel B individual (wih lower old-age benefis) accumulaes more liquid asses (row 6 vs row 1) by saving more early in life (row 7 vs row 2) bu she draws down her asses more quickly afer reiremen, so as o preserve her consumpion sream. Now, moving horizonally across he able, irrespecive of social securiy benefi levels, as labor income risk rises, so oo do liquid asses. For example, even by age 45, he high labor income risk individual has amassed asses five imes more due o a much higher saving rae (17.4 percen vs 8.5 percen). 10 Moving horizonally across he able, i is clear ha more labor income risk reduces he demand for equiies (rows 3 and 8), irrespecive of he social securiy replacemen rae. Similarly, higher income risk makes annuiies more aracive a younger ages, in all cases (rows 5 and 10). As seen above, a declining equiy glide pah wih age is appropriae for boh 10 In he medium labor income case, he saving rae is always lower han for he low income risk case, hough liquid asses are higher in all cases. This is due o he fac ha his medium income risk individual saves from a younger age, and a a higher rae (in resuls available on reques).

12 10 low and middle income risk workers, while, for he high income risk worker, equiy exposure opimally rises unil reiremen. Moving down he able, we noe ha lower replacemen raes promp lower equiy holdings for boh low and middle income risk workers, while bonds and annuiies become more desirable. For hose facing high labor income risk, asse allocaion paerns are less sensiive o old-age benefi levels, hough he direcion is similar. Nex we invesigae he sensiiviy of our resuls wih respec o he invesor s level of risk aversion. In addiion o he base case risk parameer ( = 5) analyzed above, Table 3 abulaes resuls for low ( = 3) and high ( = 8) relaive risk aversion levels, assuming he worker has a medium labor income volailiy (so she is exposed o risk oher han hrough he capial marke). As before, Panel A presens paerns of liquid saving and saving raes, as well as allocaions o equiies, bonds, and annuiies for he high social securiy replacemen rae; Panel B provides resuls for he lower value. Table 3 here Here, as risk aversion rises (moving horizonally across he able), liquid asses and expeced saving raes again rise (rows 1, 2, 6, and 7), irrespecive of he social securiy replacemen rae; ha is, higher risk aversion enhances he appeal of saving. Moving down he able, when social securiy benefis are reduced a a given level of labor uncerainy, higher saving raes and liquid asses are observed a younger, bu no a older, ages. Also, as we move o he righ in he able, as risk aversion rises, i is eviden and unsurprising ha he fracion in equiies falls in favor of bonds and annuiies. Going down a column, when he replacemen rae drops, again he equiy fracion falls hough i is ineresing ha a age 85, he leas risk averse consumer sill holds 15 percen of her porfolio in equiies. In all hree cases, bonds dominae a younger ages, while annuiies crowd ou bonds a older ages. Conclusions

13 11 Reiremen risk managemen is likely o become increasingly imporan wih global demographic aging, a phenomenon already requiring social securiy benefi cus in some developed naions such as Japan. This paper illusraes how increasing labor income risk and reducions in social securiy replacemen raes could influence saving, life-cycle porfolio asse demand, and purchases of payou annuiies. Our model shows ha higher labor income risk and lower social securiy replacemen raes boos saving raes early in life and liquid asses accumulaed for precauionary purposes. A more uncerain and less generous environmen also induces greaer demand for proecion in he form of sable income early in life and in reiremen. The enhanced need for safey is me no only wih bonds, bu also wih payou annuiies whereas he demand for equiies falls. Also, individuals who are more risk averse save more early in life, and hold fewer equiies. Our analysis offers several useful implicaions. For insance, financial advisers migh seek o consider possible fuure social securiy benefi cus as hey design opimal lifeime asse accumulaion pahs and porfolio allocaions for younger cliens. Also, he financial services indusry and pension sponsors would benefi by aking careful accoun of labor income risk when formulaing recommendaions for clien porfolios. Thus in he conex of our model, low and middle income risk workers will favor an equiy glide pah which declines wih age, bu for hose facing high income risk, equiy exposure would opimally be low early in life and rise unil reiremen. Moreover, for hose wih uncerain labor income, i would be desirable o purchase immediae payou annuiies early in life so as o build up a second more sable sream of income. Our work underscores he need for workers o have a way o creae heir own defined benefi plan equivalens wih privaely purchased payou annuiies.

14 12 References Bodie, Zvi, Jérôme B. Deemple, Susanne Oruba, and Sephan Waler. (2004). Opimal Consumpion Porfolio Choices and Reiremen Planning. Journal of Economic Dynamics and Conrol, 28: Campbell, John and Luis Viceira. (2002). Sraegic Asse Allocaion: Porfolio Choice for Long-Term Invesors. Clarendon Lecures in Economics. Oxford: Oxford Universiy Press. Chai, Jingjing, Wolfram Horneff, Raimond Maurer, and Olivia S. Michell. (2009). Exending Life Cycle Models of Opimal Porfolio Choice: Inegraing Flexible Work, Endogenous Reiremen, and Invesmen Decisions wih Lifeime Payous. NBER WP Cocco, João, Francisco Gomes, and Pascal Maenhou. (2005). Consumpion and Porfolio Choice over he Life Cycle. Review of Financial Sudies, 18: Gomes, Francisco and Alexander Michaelides. (2005). Opimal Life-Cycle Asse Allocaion: Undersanding he Empirical Evidence. Journal of Finance, 60: Heaon, John and Deborah Lucas. (1997). Marke Fricions, Savings and Porfolio Choice. Macroeconomic Dynamics, 1: Horneff, Wolfram, Raimond Maurer, Olivia S. Michell, and Michael Samos. (2009a). Asse Allocaion and Locaion Over he Life Cycle wih Survival Coningen Payous. Journal of Banking and Finance. 33: Horneff, Wolfram, Raimond Maurer, Olivia S. Michell, and Michael Samos. (2009b). Variable Payou Annuiies and Dynamic Porfolio Choice in Reiremen. Journal of Pension Economics and Finance. Forhcoming.

15 13 Horneff, Wolfram, Raimond Maurer, and Michael Samos. (2008). Life-Cycle Asse Allocaion wih Annuiy Markes. Journal of Economic Dynamics and Conrol, 32: Hurd, Michael. (1989). Moraliy Risk and Bequess. Economerica, 57: Michell, Olivia S. and John Phillips. (2006). Social Securiy Replacemen Raes For Alernaive Earnings Benchmarks. Benefis Quarerly, 4h Q: Michell, Olivia S., James Poerba, Mark Warshawsky, and Jeffrey Brown. (1999). New Evidence on he Money Worh of Individual Annuiies. American Economic Review, 89: OECD. (2009). Pensions a a Glance: 2009, Reiremen Income Sysems in OECD Counries. OECD: Paris. Polkovnichenko, Valery. (2007). Life-Cycle Porfolio Choice wih Addiive Habi Formaion Preferences and Uninsurable Labor Income Risk. Review of Financial Sudies, 20: Viceira, Luis. (2001). Opimal Porfolio Choice for Long-Horizon Invesors wih Nonradable Labor Income. Journal of Finance, 56: Wacher, Jessica and Moohiro Yogo. (2009). Why Do Household Porfolio Shares Rise in Wealh? Working Paper presened a he AFA 2008 New Orleans Meeings.

16 14 Figure 1: Life-cycle Asse Allocaion Paerns: Low Labor Income Risk and High Social Securiy Replacemen Rae Consumpion Ann. Income Labor Income Ann. Purchases Liquid Asses Age Source: Auhors calculaions. Noes: The Figure embodies a reiremen age of 65; replacemen rae of 68%; annuiy loading of 7.2%; moderae risk aversion (ρ = 5); volailiy of ransiory income shock = 7.5%; volailiy of permanen income shock = 5%; and correlaion of permanen labor income shock wih equiy reurns= 0 (see ex). Labor income, consumpion, liquid asses, annuiy purchases, and annuiy payous, are expressed as a muliple of firs-year labor income.

17 15 Figure 2: Liquid Asses and Saving Raes for Low vs High Labor Income Risk Levels and High vs Low Social Securiy Replacemen Raes (A) Liquid Asses (B) Saving Raes Liquid Asses Saving Rae (%) Age Age Low Labor Income Risk, High Social Securiy Replacemen Rae (68%) High Labor Income Risk, Low Social Securiy Replacemen Rae (50%). Source: Auhors calculaions. Noes: Liquid asse (held in socks and bonds) are expressed a muliple of firs-year labor income; saving raes are he percen of labor plus annuiy income saved.

18 16 Figure 3: Life-cycle Asse Allocaion for Low vs High Labor Income Risk Levels and High vs Low Social Securiy Replacemen Raes Equiy Weighs (%) (B) Bond Weighs 0 (A) Equiy Weighs Age (C) Annuiy Weighs Bond Weighs (%) Age Annuiy Weighs (%) Age Low Labor Income Risk, High Social Securiy Replacemen Rae (68%) High Labor Income Risk, Low Social Securiy Replacemen Rae (50%) Source: Auhors calculaions. Noes: Asse weighs expressed as a percen of oal wealh (liquid asses + presen value of annuiy claims).

19 17 Table 1: Behavioral and Marke Parameers Employed in Empirical Analysis σ n σ u φ n ζ ρ Low Med High Source: Auhors compilaion. Noes: σ n and σ u refer respecively o he volailiy of he permanen and ransiory income shocks; φ n is he correlaion of labor income risk wih sock reurns; ζ is he social securiy replacemen rae; and ρ is he coefficien of relaive risk aversion coefficien.

20 18 Table 2: Life-cycle Saving Raes and Porfolio Mixes for Alernaive Labor Income Risk Levels and Social Securiy Replacemen Raes Low Labor Income Risk Medium Labor Income Risk High Labor Income Risk Age Age Age (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (12) (13) (14) (15) (16) Panel A: High Social Securiy Replacemen Rae (68%) Liquid Asses (1) Saving Rae (%) (2) Equiies (%) (3) Bonds (%) (4) Annuiies (%) (5) Panel B: Low Social Securiy Replacemen Rae (50%) Liquid Asses (6) Saving Rae (%) (7) Equiies (%) (8) Bonds (%) (9) Annuiies (%) (10) Source: Auhors calculaions. Noes: Model assumes a reiremen age of 65; annuiy loading of 7.2%; moderae risk aversion (γ = 5). For he case of low labor income risk, he volailiy of ransiory income shock is 7.5%; of he permanen income shock is 5% and he correlaion of he permanen shock wih equiy reurns is 0. For he medium labor income risk case, he volailiy of ransiory income shock is 15%, of he permanen income shock is 10%; he correlaion of he permanen shock wih equiy reurns is 0. For he high labor income risk case, he volailiy of ransiory income shock is 30%, of he permanen income shock is 20%; he correlaion of he permanen shock wih equiy reurns is Invesmen weighs are compued as a fracion of oal wealh (liquid asses + presen value of annuiy claims); liquid asses are compued as a muliple of iniial labor income; saving raes are he percen of labor plus annuiy income saved.

21 19 Table 3: Life-cycle Saving Raes and Porfolio Mixes for Alernaive Levels of Risk Aversion and Social Securiy Replacemen Raes Low Risk Aversion ( = 3) Med. Risk Aversion ( = 5) High Risk Aversion ( = 8) Age Age Age (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (12) (13) (14) (15) (16) Panel A: High Social Securiy Replacemen Rae (68%) Liquid Asses (1) Saving Rae (%) (2) Equiies (%) (3) Bonds (%) (4) Annuiies (%) (5) Panel B: Low Social Securiy Replacemen Rae (50%) Liquid Asses (6) Saving Rae (%) (7) Equiies (%) (8) Bonds (%) (9) Annuiies (%) (10) Source: Auhors calculaions. Noes: Resuls are compued for he medium labor income risk case; here he volailiy of ransiory income shock is 15% and for he permanen income shock 10%; and he correlaion of he permanen shock wih equiy reurns is 0. For oher definiions see Table 2.