Lifecycle Impacs of he Financial Crisis on Opimal Consumpion-Porfolio Choice, and Labor Supply Jingjing Chai, Raimond Maurer, Olivia S. Michell, and Ralph Rogalla Sepember 2011 PRC WP2011-12 Pension Research Council Working Paper Pension Research Council The Wharon School, Universiy of Pennsylvania 3620 Locus Walk, 3000 SH-DH Philadelphia, PA 19104-6302 Tel: 215.898.7620 Fax: 215.573.3418 Email: prc@wharon.upenn.edu hp://www.pensionresearchcouncil.org The research repored herein was performed pursuan o a gran from he US Social Securiy Adminisraion (SSA) o he Michigan Reiremen Research Cener (MRRC) as par of he Reiremen Research Consorium. Addiional research suppor was provided by Nespar, he German Invesmen and Asse Managemen Associaion (BVI), he Pension Research Council a The Wharon School of he Universiy of Pennsylvania, and he Mezler Bank Exchange Professorship. Helpful commens were provided by Peer Brady, Susann Rohwedder, Mark Warshawsky, and paricipans a he 2011 Pension Research Council Conference. This research is par of he NBER programs on Aging, Public Economics, and Labor Sudies. All findings, inerpreaions, and conclusion of his paper represen he views of he auhors and no hose of he Wharon School or he Pension Research Council. 2011 Pension Research Council of he Wharon School of he Universiy of Pennsylvania. All righs reserved.
Lifecycle Impacs of he Financial Crisis on Opimal Consumpion-Porfolio Choice, and Labor Supply Absrac The direc financial impac of he financial crisis has been o deal a heavy blow o invesmen-based pensions; many workers los a subsanial porion of heir reiremen saving. The financial secor implosion produced an economic crisis for he res of he economy via high unemploymen and reduced labor earnings, which reduced household conribuions o Social Securiy and some privae pensions. Our research asks which ypes of individuals were mos affeced by hese dual financial and economic shocks, and i also explores how people may reac by changing heir consumpion, saving and invesmen, work and reiremen, and annuiizaion decisions. We do so wih a realisically calibraed lifecycle framework allowing for ime-varying invesmen opporuniies and counercyclical risky labor income dynamics. We show ha households near reiremen will reduce boh shor- and long-erm consumpion, boos work effor, and defer reiremen. Younger cohors will iniially reduce heir work hours, consumpion, saving, and equiy exposure; laer in life, hey will work more, reire laer, consume less, inves more in socks, save more, and reduce heir demand for privae annuiies. Jingjing Chai Goehe-Universiy, Frankfur chai@finance.uni-frankfur.de Olivia S. Michell Wharon School, Universiy of Pennsylvania michelo@wharon.upenn.edu Ralph Rogalla Goehe-Universiy, Frankfur rogalla@finance.uni-frankfur.de
1 Lifecycle Impacs of he Financial Crisis on Opimal Consumpion-Porfolio Choice and Labor Supply Jingjing Chai, Raimond Maurer, Olivia S. Michell, and Ralph Rogalla Workers are increasingly required o inves in invesmen-based defined conribuion (DC) accouns, and hen during heir golden years, draw down he pension asses in an orderly fashion. Such accouns can help augmen and parially replace public pension benefis, as aging economies move oward a beer-funded old-age sysem. Ye he recen financial crisis has raised fresh concerns regarding he risks o which workers are exposed o capial marke shocks in hese pension sysems: for insance, in 2008, US privae pension fund asses declined by onefourh or abou US$ 2.7 rillion (OECD 2009; Whiehouse 2010). Moreover, he subsequen economic crisis generaed rising unemploymen and falling labor earnings, wih he unforunae effec of reducing worker conribuions o boh Social Securiy and many privae pension schemes. Indeed, he US unemploymen rae of 10 percen in 2009 was double ha in 2007, wih similar high jobless raes elsewhere. These combined capial and labor marke shocks have made i much more difficul for reiremen sysems o deliver anicipaed old-age benefis. This chaper examines how households may be affeced by he dual financial and economic crisis such as he one recenly experienced. In paricular, we explore how people migh reac o hese shocks, by adjusing heir consumpion/saving paerns, invesmen/annuiizaion pahs, work hours, and reiremen paerns. Because acual responses are boh shor- and long-erm in naure, some of hese will no be observable for several decades o come; furhermore, responses are likely o be heerogeneous. Tha is, some younger workers may no reac much since hey have several decades o adjus before hey reire, whereas workers on he verge of reiremen have lile ime o adjus heir saving, work, and porfolios o offse poenial capial and labor marke losses. Furhermore, Baby Boomers reacions are likely o differ according o individuals financial wealh and human capial levels. To invesigae possible oucomes, we develop a lifecycle
2 model wih opimal invesmen, work hours, reiremen, and annuiizaion decisions, allowing for shifs in he invesmen opporuniy se and labor income dynamics. We build on wo srands of lieraure in our analysis. One srand sudies how financial marke downurns influence older workers consumpion decisions and reiremen behavior. Hurd and Rohwedder (2010) as well as Shapiro (2010) poin ou ha he recen financial and economic crisis significanly affeced near-reiremen households, which seem o have reaced by reducing consumpion and working longer. Ye Gusman, Seinmeier, and Tabaabai (2010) esimae ha reiremen will only be posponed by 1.5 monhs on average, given heir simulaions of a srucural reiremen model. Neverheless due o lack of daa, hese sudies have focused primarily on older persons near reiremen and heir shor-run responses o he recen crises. Thus hey do no explore he long-erm impac of he crisis on younger age groups, nor do hey evaluae consequen changes in asse allocaion behavior. Our chaper examines hese poins as we seek o undersand how differen age groups may adap along several dimensions, as hey reac o sock marke downurns and unemploymen risk. A second relevan lieraure has explored household porfolio choice in a discree ime life cycle model wih risky capial marke reurns and uninsurable labor income risk, asking how such uncerainy influences saving, consumpion, and asse allocaion (Cocco, Gomes, and Maenhou, 2005). This lieraure was exended by Gomes, Kolikoff, and Viceira (2008) o include flexible hours; subsequen work by Chai e al. (2011) also incorporaed flexible reiremen and Social Securiy, as well as he opion o annuiize one s wealh. A key lesson from his research is ha wellbeing is grealy enhanced when labor effor is adjusable. Neverheless, hese papers assumed ha permanen labor income shocks and risky asse reurns were independenly and idenically disribued over ime, while here is now clear empirical evidence refuing his assumpion. For insance, Guidolin and Timmerman (2008) show ha expeced sock marke reurns and volailiy vary boh over ime and across bull/bear saes. Tha
3 is, in some periods equiy reurns are characerized by persisenly low volailiy/high expeced reurns, whereas in oher periods, hey are characerized by persisenly high volailiy/low expeced reurns. Insead of focusing on sock reurns, Caroll and Dunn (1997) and Soresleen, Telmer, and Yaron (2004) esimae a regime-swiching model of labor marke earnings; hey find ha he volailiy of labor income increases in recessions and falls in expansions. In wha follows, we combine he labor and sock marke srands by modeling boh imevarying and persisen sock marke/labor income processes governed by a Markov chain for he business cycle. Here, some of he ime, asse reurns are characerized by persisen regimes wih an expansive capial marke having low volailiy/high expeced reurn; in oher periods, a conracionary marke is characerized by high volailiy/low expeced reurns. In addiion, we model he counercyclical dynamics of risky labor income using ime-varying shocks on wage raes dynamics and unemploymen probabiliies driven by he same regime-swiching process. Such a seing allows us o explore he siuaion where a financial secor crisis may also produce an economic crisis (wih a ime lag), driving high unemploymen and lower earnings. In his way, we seek o show how hese simulaneous shocks aler reiremen, work hours, and consumpion rajecories; asse allocaion paerns; and annuiy purchases of younger and elder households. In addiion, we can cleanly illusrae he long-erm impac of he financial and economic crisis on behavior well ino he fuure. While i is oo soon o acually observe how he crisis will aler long-erm behaviors, our model provides a useful se of predicions for policy purposes. Our resuls indicae ha some will be able o hedge adverse capial marke developmens hey face in he crisis, no only by alering heir asse allocaions, bu also by alering heir work hours and reiremen ages. In paricular, we find ha when hi by a financial and economic crisis, households near-reiremen mus cu heir consumpion boh in he shor-erm and also over he long-erm. Moreover, hey will have o increase heir work effor and pospone
4 reiremen. These shor-erm resuls correspond o he recen empirical findings noed above. For young cohors, shor-erm effecs differ from hose in he long-run. During he firs five years afer he onse of he crisis, young households will reduce work hours, saving, and equiy exposure, and suffer from a drop in consumpion. In he long run, however, hey will work more, reire laer, inves more in socks, consume less, save more, and spend less on privae annuiies. These predicions illusrae he key dimensions along which economic adjusmen are likely o occur, in response o he mos severe recession since he Grea Depression. The framework Labor and capial markes. We ake as a saring poin he presence of dual regimes in capial and labor marke dynamics driven by he business cycle. Accordingly, sock reurns and labor earnings are modeled as subjec o a business cycle governed by a Markov chain process ha, following he NBER classificaion, has wo saes: expansion and conracion. The variable s indicaes wheher a ime he economy is in a sae of expansion (s = 0) or conracion (s = 1). Transiion probabiliies beween he wo business cycle (BC) saes are consan over ime and BC BC defined as π P( s = j s ), (i.e., denoes he probabiliy ha a ime +1 he i, j : = + 1 = i π i, j economy will be in sae j, given ha he economy is in sae i a ime ). Hence, he probabiliy ha sae 0 (expansion) will be followed by sae 1 (conracion). The represens BC BC BC uncondiional probabiliy for sae expansion (s = 0) is given by 1 π π and BC BC for conracion (s = 1) by ( 1 π ) ( π BC π ) 1,1 2 BC π 0,1 ( ) ( ) 0,0 2 0,0 π1,1 0,0 1,1, respecively. In wha follows, we assume BC π i, j ha invesors can observe s and know he sae ransiion probabiliies a ime. Nex, we characerize wha we mean by regime shifs in he labor income process, allowing for unemploymen risk and sae-dependen wage rae dynamics. The worker faces a risk of being unemployed in he period [, + 1], where he probabiliy of unemploymen U π s is
5 sae-dependen and specified as: π U s U U i = ( π [, + 1] s = i) = wih probabiliy U π j : π π π BC i, i BC i, j The unemploymen probabiliy is lower in expansionary han in conracionary imes (i.e., π < U U 0 π 1 ). A ime, he worker mus decide wha fracion of ime (1-L ) o devoe o employmen. L sands for leisure and is measured as a percenage of available ime. In each period, if he individual is no unemployed, he receives an afer-ax disposable labor income of Y l ( 1 ) WR ( L ) E s, + 1 = ( 1 q + 1) s, + 1 1 (1) a ime + 1, where q +1 is he age-dependen deerminisic ax-deducible fracion of labor income spen on housing and oher durable goods, l is a proporional ax rae on labor income, and WR s, +1 is he sae-dependen wage rae a ime +1, (i.e., he income per hour of work effor). The wage rae dynamic process consiss of hree componens as follows: ( w + 1) Es, + 1 U 1 WR. (2) s, + 1 = exp + Here w +1 is a deerminisic age-dependen funcion of wage raes ha allows us o capure he shape of various empirically-observed earnings profiles, 1 and U +1 is a sae-independen ransiory income shock whose logarihm is independen and idenically disribued (i.i.d.) normally disribued wih mean zero and sandard deviaion σ U. In addiion, s, + 1 = s, s, + 1 a permanen labor earnings componen. The logarihm of he permanen income shock E E n n s, +1 is is drawn from a Gaussian mixure disribuion wih mean zero and sandard deviaion changing across he wo phases of he business cycle. Formally: ln( n N(0, σ ) n, i s, + 1) : = (ln( n + 1) s = i) ~ wih probabiliy N(0, σ n, j ) To capure counercyclical labor income risk, we se,,, such ha he volailiy in an π π BC i, i BC i, j. σ n,s
6 expansion (s = 0) is lower han in a conracionary period (s = 1). 2 We also allow for unemploymen compensaion paymens a ime + 1 worh a specific fracion υ (0;1) of labor U E income, (i.e., =υ Y ). Ys, + 1 s, + 1 In laer life, we ake he US Social Securiy sysem ino accoun and allow for a flexible reiremen age. According o Social Securiy rules, he worker may elec o claim Social Securiy benefis in he window [62, 70] bounded by he early reiremen age (ERA) and he lae reiremen age (LRA). The acual normal reiremen age (NRA) is se for his chaper a age 65. If he worker claims prior o he NRA, he receives a permanenly reduced benefi. Oherwise, he Social Securiy benefi is increased by he delayed reiremen credi. To capure his feaure, we calculae he afer-ax Social Securiy benefis as in Chai e al. (2009): K r ( 1 ) (1 L) exp w() ( ) K EKζ F NRA Y ( 1 q ) τ, = 1 = where F, NRA exp( g1( NRA τ )) I ( NRA) + exp( g 2 ( NRA τ )) I ( > NRA τ = τ τ ), (3). Here, we assume ha when people claim reiremen benefis hey also consume full leisure simulaneously (as in Chai e al., 2011). 3 In his way, τ is he endogenous reiremen age and ζ is he Social Securiy replacemen rae based on lifeime average earnings, and 1 L sands for he average fracion of available ime worked during he work life. The worker s average lifeime earnings level is approximaed by K = 1 ( w() ) (1 L) exp K E, where K denoes when he individual aains her K normal reiremen age under he Social Securiy rules (NRA). Reiremen benefis are axed a a rae r. I is an indicaor funcion idenifying wheher he individual reires a/prior o he NRA, or laer. F,NRA τ is a facor which depends on he NRA and he endogenous reiremen age τ. g 1 and g 2 are posiive consans. Capial markes include wo liquid asses, riskless bonds and risky socks, and illiquid deferred and immediae fixed payou life annuiies. The real bond gross reurn R f is sae-
7 independen and consan over ime, while here is a ime-varying invesmen opporuniy se in he sock marke. Given a specific sae s = i a ime, he risky real log-reurn on socks R s, + ln( 1) over he period [, +1] is drawn from Gaussian mixure disribuion wih saedependen mean µ s and sandard deviaion σ s, formally: ln( R N( μ, σ ) i i s, + 1) : = (ln( R[, + 1] ) s = i) ~ wih probabiliy N( μ j, σ j ) π π BC i, i BC i, j. (4) Each period, invesors can observe he sae of he economy a ime, bu he acual probabiliy disribuion of reurns on sock invesmens in each period depends on he (unknown) sae of he economy a ime + 1. The (sae-dependen) correlaion beween shocks o permanen earnings and sock marke reurns is denoed by φ s. In addiion o socks and bonds, he invesor can, prior o he NRA, purchase fixed payou deferred annuiies ha provide lifelong paymens commencing a he NRA. From ha poin onward, she can purchase addiional immediae life annuiies. Annuiy prices are calculaed based on acuarial principles. For a deferred life annuiy paying yearly benefis of one from NRA on, he premium is calculaed as h NRA 2 T NRA NRA 1+ m a ( NRA 1 ) a m = ( 1+ δ ) pu Rf pu Rf < NRA (5) u= m= 1 u= K 1 where a p u are he survival probabiliies based on he insurer s annuian moraliy able and δ is he expense loading facor. Accordingly, he premium for an addiional immediae life annuiy purchased afer he NRA is given by h = T 1 ( 1+ δ ) m= 1 + m u= p a u R m f NRA (6) To accoun for adverse selecion, he survival probabiliies ypically higher han hose of he overall populaion. a p u used in pricing he annuiies are
8 The consumer s life cycle problem. To explore how households migh respond o hese financial/economic and individual crises, we inegrae he decisions o opimally selec consumpion and saving, asse allocaion, work effor and reiremen age, and annuiizaion pahs over he lifecycle. We posi ha our individual faces an uncerain lifespan and can live for a maximum of T years. Her preferences are characerized by a ime addiive CRRA uiliy funcion u 1 α 1 ρ ( C, L ) = ( C ) 1 ρ L defined over he level of non-durable consumpion C and leisure L a ime. Afer reiremen, work hours are equal o zero and leisure is equal o one. The value funcion is given by: V α 1 ( C L ) ρ = + βe + 1 1 ρ p ( p V ) (7) α 1 wih erminal uiliy ( CT LT ) ρ p V =. The parameer p T denoes he subjecive probabiliy of 1 ρ surviving o ime + 1, given he consumer is alive a. The parameer ρ is he coefficien of relaive risk aversion, and β < 1 is he ime preference. Leisure preferences are governed by he parameer α. Each period, he consumer decides how o allocae her cash on hand W o bonds B, socks S, annuiy purchases A, and consumpion C. Her budge consrain is herefore: W = S + B + A + C, (8) and nex period s wealh W+1 is given by W + 1 ( S R = ( S R s, + 1 s, + 1 + B R + B R f f )(1 )(1 c ) + ( B c c ) + ( B c + S ) + Y + S ) + P + 1 + 1 + Y + 1 < NRA NRA. (9) Here, P +1 is he sum of annuiy income received from any previously purchased annuiies. Before reiremen, Y +1 represens labor income, and aferwards, i represens Social Securiy benefis. The recursive evoluion equaion for he sum of afer-ax payou claims a ime from all previous annuiies purchased can be wrien as: 4
9 P NRA + 1 = P A + h ( R ) f 1(1 R f c ) + 1 where A /h refers o he addiional annuiy paymen purchased in. 5 We preven households from borrowing agains human capial and from selling annuiies. These resricions are binding, because oherwise households would engage in highly leveraged sock posiions financed by shor posiions in bonds and/or annuiies in order o compensae for heir over-invesmen in human capial when young. Thus, in every year he opimal policy has o saisfy C, S, B, A 0. Moreover, we posi ha in order o paricipae in he sock marke, he household has o be willing and able o inves a minimum amoun in socks (as in Smeers and Chen, 2010). This amoun is se o 10 percen of he permanen labor income afer axes and housing expendiures. The individual s opimizaion problem is now o maximize uiliy as in (7) wih respec o her asse allocaion beween liquid bonds and socks, illiquid annuiies, consumpion, work hours, and he reiremen decision: C, L, S, B, A, τ [62,63,...,70] max V (10) Assuming ha he consumer knows abou he regimes governing he business cycle, here are six sae variables: cash on hand W, annuiy payous from previously purchased annuiies P, he permanen labor earnings level E, reiremen age τ, he business cycle sae s, and age. To reduce he problem by one sae variable we normalize he coninuous sae variables cash on hand wih he permanen labor earnings componen. Nex we discreize he (normalized) coninuous sae variables and solve he opimizaion problem by backward inducion. 6 Model calibraion. For he base case, preference parameers are se o sandard values in he life cycle lieraure: he coefficien of relaive risk aversion is ρ=5 and he discoun facor β=0.97. The leisure preference value α is se o 1.3. As shown in Chai e al. (2011), his se of preference parameers is able o reproduce cenral empirical facs, including he hump-shaped paern of work hours, he wo peaks in reiremen raes, he sizeable decline in consumpion a reiremen,
10 and low annuiy ake-ups of older households. The one-period survival raes p p enering he uiliy funcion are aken from he US 1996 RP-2000 populaion ables for females; he lifespan is modeled from age 20 o 100 (T=81). To esimae he business cycle ransiion marix, we ake US Gross Naional Produc (GNP) growh from he Bureau of Economic Analysis (BEA) for 1929-2006 wih Daasream daa for he years 2007-2008. 7 A conracion (expansion) sae occurs when he GNP growh rae was less han (greaer han) is sample period mean (as in Soresleen, Telmer, and Yaron 2004). In his way, we esimae he ransiion marix o be of he following form: 0.68 0.32. 8 A process wih such a ransiion marix is more likely o say in 0.32 0.68 he same sae raher han o move o he oher sae, since probabiliies p 1,1 and p 0,0 are greaer han 0.5. The deerminisic componen of he wage rae process follows Fehr, Jokisch, and Kolikoff (2006), reflecing middle-income households, and i is scaled o generae an average gross labor income of $20,000 a age 20. In wha follows, we assume an available ime of 100 waking hours per week and se he minimum leisure ime o L min =1/3, in oher words, he maximal labor supply is 2/3 of available ime. The average labor supply 1 L used o calculae Social Securiy benefis is equal o 0.4, which corresponds wih an average lifeime work effor of 40 hours per week. We follow Soresleen, Telmer, and Yaron (2004) and se he cyclical dynamic labor marke risk σ σ ) o 8.4 percen (15.9 percen) and he corresponding volailiy of he ransiory shock n, 0( n, 1 σu o 32.9 percen. 9 The unemploymen probabiliy in expansion (conracion) U periods π ( π U 1 ) 0 is se o 5 percen (10 percen). The parameer for unemploymen compensaion paymens is se o υ=60 percen. The Social Securiy benefi srucure is similar o ha in effec in he Unied Saes. The benefi replacemen rae ζ is se o 0.52 (as per Michell and Phillips, 2006); he acuarial reducion rae for early reiremen benefis is g 1 =0.0713, he delayed reiremen crediing rae is g 2 =0.077, and he normal reiremen age is 65, as in Buchinsky, Rus,
11 and Beniez-Silva (2000) and Chai e al. (2011). Social Securiy benefis are axed a a rae of 15 percen as in Gomes, Kolikoff, and Viceira (2008). 10 Housing-relaed expendiures q are modeled as in Gomes and Michaelides (2005). The annual real value-weighed marke index porfolio reurns on he NYSE, AMEX, and NASDAQ (from CRSP) from 1950 o 2008 11 are classified ino wo saes which are idenified by he GNP growh rae. Then he regime dependen parameers specifying he normal disribuion of log gross reurn are given as follows: µ 0 =6.84 percen, σ 0 =11.21 percen, µ 1 =2.12 percen, and σ 1 =20.77 percen, 12,13 equivalen o a yearly expeced gross real reurn of 1.0775 and sandard deviaion of 12.12 percen in he expansion period, and 1.0437 and 21.91 percen in he conracion phase. Here, he expansion/conracion economy ends o coincide wih a low/high-volailiy, high/low-mean regime in he sock marke. This evidence is also be found in Ang and Bekaer (2002), Gordon and S-Amour (2000), Guidolin and Timmermann (2008), and Kim and Lee (2007). The correlaion beween sock reurns and permanen and ransiory earnings shocks φ for boh cases is se o zero, consisen wih empirical evidence provided by Cocco, Gomes, and Maenhou (2005). The real riskless gross reurn for bond invesmens is R f =1.02. To price he life annuiies, fuure benefis are discouned wih he riskless reurn. The condiional survival probabiliies a p are aken from he US 1996 female annuian RP-2000 moraliy able o accoun for poenial adverse selecion in he volunary annuiy marke. The expense loading facor δ is se o 2.38 percen, a number in line wih indusry leaders such as Vanguard. Reurns on asses are assumed o be axed a 20 percen; labor earnings are axed a 30 percen following Gomes, Kolikoff, and Viceira (2008). For he average household age 55, we esimae a wealh o income raio of 9, which approximaely represens he median of he wealh disribuion. To his end, we draw on wealh daa from Gusman, Seinmeier, and Tabaabai (2010), and income daa from he SSA. Specifically, we employed he disribuion of asses by wealh deciles in 2006 for households
12 wih a leas one member born from 1948 o 1953, defining wealh as oal wealh ne of Social Securiy and defined benefi pension wealh. To esimae median labor income for households aged 55, we use SSA daa on he median income of non-married persons aged 65-69 in he year 2006. We mach labor income profiles esimaed by Soresleen, Telmer, and Yaron (2004) o his income daa and calculae he income a age 55 based on hose profiles. Moreover, we assume ha households aged 55 have no ye purchased any annuiies. Resuls Having solved he life-cycle problem for he opimal policies (consumpion, asse allocaion, work hours, saving, and reiremen behavior), nex we evaluae he disribuion of decision variables based on a Mone Carlo simulaion of 100,000 life-cycle rajecories, differeniaing beween wo general economic and financial scenarios: crisis and normalcy. Idenifying he ails of he financial/economic disribuion. Here we characerize a financial/economic crisis as one where he economy is in he conracion sae for four years in a row, and in addiion, in he firs year he sock reurn is a minus 30 percen. By conras, a normal financial and economic environmen, which we rea as he baseline scenario, is defined as one in which no addiional exogenous resricions are imposed on he sae of he business cycle or he sock marke performance. Hence, he iniial sae of he business cycle is deermined by he (uncondiional) long-run sae probabiliies and he saes in subsequen periods by he condiional sae ransiion probabiliies, while sock marke reurns are governed by he business cycle sae-specific disribuions as described above. In addiion o his general analysis using he whole simulaion sample, we are also keenly ineresed in he disribuional ails. We examine hese by analyzing subsamples of hose 100,000 life-cycles, as no all households may be affeced similarly by he business cycle; some perform excepionally well, while ohers who experience unemploymen and persisen wage
13 shocks fare far worse. Accordingly, we sipulae ha an individual suffers from a riple whammy if he experiences a financial/economic crisis a he beginning of he analysis, is unemployed in a leas wo of he firs four years hereafer, and also suffers from below firs quarile cumulaed sock marke reurns unil age 62 when he becomes eligible for Social Securiy benefis. By conras, we define a doubly forunae individual as someone ha never experiences a financial/economic crisis, is never unemployed o age 62, and experiences aboveaverage capial marke reurns o age 62 wih cumulaed sock reurns in he op 25 percenile. In wha follows, we differeniae beween he shor- and long-erm effecs of he financial/economic crisis on households behavior and wellbeing. While shor-erm effecs can be sudied using already available empirical daa, sample daa on he crisis long-erm effecs will obviously no be available for several decades. For his reason, model simulaions are he only way o make predicions abou wha fuure oucomes migh be. Of paricular ineres in his conex is how differen cohors are influenced by, and reac o, he economic/financial crisis. While over he shor run boh younger and elder cohors could be subsanially affeced by he crisis, due o heir longer remaining period of economic aciviy, younger people migh suffer less in he long run han do elder generaions. To explore his oucome, we conduc our analyses for households ha are hi by a financial/economic crisis a ages 20 and 55. For he cohor aged 20 (55), ou of he 100,000 sample pahs, we idenify 933 (979) ha qualify for he double forune scenario and 1321 (1355) ha comply wih he riple whammy scenario. Shor-erm effecs. We nex urn our aenion o he impacs of and he reacion o an economic/financial crisis over he shor run, which in his sudy we define o cover a period of a decade. Figures 1 and 2 depic he effecs for households iniially age 20 or 55 on key decision variables: expeced work hours (Panel A), consumpion (Panel B), saving/wihdrawal (i.e., labor income/social Securiy benefis afer axes and housing expendiures minus consumpion, Panel C), and sock invesmen (Panel D). Here, he solid black line presens absolue values for he
14 normal scenario (lef axis), while he bars show relaive deviaions from he base case resuls for hree alernaive scenarios: crisis (ligh grey), double forune (black), and riple whammy (dark grey) on he righ axis. Figures 1 and 2 here Shor-erm effecs for he younger cohor. In he base case scenario, he work effor of a young individual exceeds 40-hours per week, wih average work effor saring a 47 hours per week a age 20 and hen rising furher o above 51 hours in he mid-20s (Figure 1, Panel A). Long and rising work hours, combined wih a wage rae increasing wih age and experience, generae high and rising labor income. This allows he individual o increase consumpion from $9,000 a age 20 o abou $14,000 in he mid-20s (Panel B). A he same ime, periodic savings more han double from $1,600 o abou $3,700 (Panel C). A age 20, he household will on average inves abou 65 percen of liquid funds accumulaed in socks and increase his fracion over he following six years o almos 100 percen (Panel D). The young household seeks high sock fracions due o he raher bond-like naure of labor income. Ye he minimum required invesmen amoun for paricipaing in he sock marke resuls in sock fracions falling shor of 100 percen early in he life-cycle, as sufficien funds mus firs be accumulaed. Once a sufficien amoun of liquid asses has been saved, he invesor hen maximizes equiy exposure. Wih wage raes increasing even furher and invesed funds saring o generae measurable reurns, he individual can afford o enjoy more leisure by already slighly reducing work hours in his lae 20s, iniiaing he of-cied hump-shape in work effor. Boh consumpion and periodic saving increase furher o abou $17,400 and $4,100 by age 30. When we compare his baseline o a young household experiencing a financial and economic crisis a age 20, work effor proves o be virually idenical as a resul of wo offseing effecs. The crisis lowers wage raes resuling from higher unemploymen
15 probabiliies, leaving he individual less inclined o work and more likely o consume leisure (by he subsiuion effec). Ye lower income provides less consumpion opporuniy which induces greaer work effor (by he income effec). As work effor does no rise beyond base case, he individual compensaes for his income drop by reducing boh consumpion and saving. Moreover, hese reducions persis over he nex decade even if he economy evenually recovers; consumpion drops by 2 percen and periodic saving by 2-3 percen compared o he normal scenario. No ye having accumulaed financial asses, he young individual does no suffer from he 30 percen downurn in he sock marke a he beginning of he financial and economic crisis, so his sock holdings are hardly affeced, only dropping slighly (2.5 percen) in he firs wo years. By comparison, a young worker hi by a riple whammy will subsanially reduce work effor. His hours worked per week drop by almos 10 percen in he firs wo years, compared o he base case, afer which hey slowly rise again. The corresponding drop in income drives a consumpion decline of abou 15 percen over he firs four years. Periodic saving is even more affeced, dropping by more han 60 percen for a worker in his early 20s. Having so few liquid asses, he worker canno afford o paricipae in he sock marke, and overall sock fracions drop by 10-20 percen during he firs five years (from a low base). Afer four years ime, as he iniial crisis wanes, he individual srives o recover by increasing work effor above ha in he base case over he second half of he decade. While consumpion again converges oward he base case level, even a age 30, i remains abou 2 percen less han in he normal scenario. A he same ime, he household seeks o replenish accumulaed funds by saving beween 10-20 percen more han he base line invesor from he mid hrough lae 20s. Once sufficien funds have been buil up again, he household can hen afford o inves in equiies and sock holdings converge o hose in he normal scenario from he mid-20s. Finally, he doubly forunae are even inclined o work slighly more in he early-20s
16 han our base line households, which enables hem o consume abou 2-3 percen more; his is he resul of never being unemployed and no confroning a financial/economic crisis. Addiionally, hese individuals save subsanially more, which increases heir abiliy o early inves in socks. Wih above average labor income and capial marke performance, hey can reduce heir work effor even more han he baseline households in heir lae 20s, while sill being able o afford 2-3 percen higher consumpion. Shor-erm effecs for he near-reiremen cohor. Nex we urn o our aenion o he cohor looking ahead o reiremen, iniially age 55. In he baseline scenario, people reduce heir work effor ino heir lae 50s and early 60s, following he convenional hump-shape work paern. A age 55, on average, hey sill engage in near full-ime employmen, bu work hours per week gradually aper o 20 by age 65 (Figure 2, Panel A). As in he case of he younger cohors, older people who experience he financial/economic crisis mainain a virually idenical work effor pah. Figure 2 here The picure changes, however, when looking a households hi by he riple whammy. The near-reiremen cohor wih a shorer period of economic aciviy remaining mus compensae for reducions in wage raes and wealh by immediaely increasing work hours. (I will be recalled ha he younger cohor can work less, couning on a longer ime horizon over which i can recover income losses.) Consequenly, older persons work effor rises by around 10 percen relaive o he base case, and in heir 60s, he difference is greaer, abou 25 percen. Sensibly, he doubly forunae workers cash in on heir luck in boh he labor and capial markes by subsanially reducing work effor sooner. In he base case, he older cohor consumes abou $30,000 per year on average, or wo o hree imes he consumpion of households in heir 20s. This consumpion level is financed, o a large exen, by drawing down liquid financial asses (Figure 2, Panels B and C). Those older
17 persons bese by a financial/economic crisis reduce annual consumpion by around 4 percen per year from age 55 o 65, and annual wihdrawals fall by abou 2-3 percen. Those hi by a riple whammy experience subsanial and persisen reducions in annual consumpion of abou 10 percen compared o he base case. Early in he crisis, workers seek o mainain consumpion by wihdrawing almos 30 percen more from liquid asses, compared o he base case. As financial wealh was already heavily baered due o he sock marke downurn a he beginning of he crisis, hese high wihdrawals can only be mainained over a shor period. Subsequenly, wihdrawals mus be reduced by 30 percen more han he base case beween he lae 50s and mid 60s. Consumpion can only be mainained by subsanially increasing work effor. In our base case, as is ypical in life-cycle models, he fracion of financial wealh invesed in socks, around 80 percen in he mid-50s, is below ha early in working life, bu i slighly increases again oward reiremen age as he worker s exposure o labor marke shocks declines. Given a financial/economic crisis, equiy exposure falls shor of he base case value by over 20 percen during he firs four years; hereafer, afer he iniial crisis is over, sock fracions again converge. For hose hi by he riple whammy, he change in he sock fracion compared o he base case races ou an S-shape. Early in he crisis, sock allocaions drop by abou 10 percen, bu from he lae-50s i exceeds ha of base case households by abou 10 percen. Anicipaing a high probabiliy of poor sock marke performance in he following period, he household is less inclined o hold equiies over he firs years of he crisis. Laer, low remaining financial wealh provides incenives o gamble and inves more in he sock marke. Finally, doubly forunae workers have persisenly lower sock fracions over he enire period under scruiny. Having accumulaed high financial wealh allows he household o inves more conservaively. In sum, for boh younger and older cohors, he financial/economic crisis has hardly any shor-erm impac on work effor on average. Bu a subse of people fares far worse, including
18 near-reirees hi by a riple whammy who face a hosile labor marke environmen and also suffer subsanial losses in financial wealh. Since hey only have a few work years available o adjus o hese shocks, hey mus immediaely and significanly increase heir work effor afer being unemployed. By conras, hose hi a he beginning of heir work lives mus opimally reduce work hours in he less favorable labor marke environmen. The same conclusion holds for consumpion on average: he impac of he financial/economic crisis is comparable for younger versus older cohors. Ye older households hi by he riple whammy experience persisen consumpion shorfalls, which are miigaed for he younger cohor where consumpion converges o he base case level in ime. The same holds for saving a young ages and wihdrawals near reiremen. And mos sriking is he difference in household allocaions o socks. Near-reirees have already accumulaed financial wealh, and hence are more vulnerable o equiy flucuaions, while he young have accumulaed lile in he way of financial asses. For his reason, he financial/economic crisis has lile impac on he young, bu near-reirees will opimally cu heir equiy exposure by over 20 percen during he crisis. This depends on he naure of he shock, however, since near-reirees hi by he riple whammy will inves more in sock, hoping o hi high reurns. Long-erm effecs. Nex we urn our aenion o he impacs of and he reacion o an economic/financial crisis in he long run (i.e., over he remaining lifecycle). Findings are presened in Figures 3 and 4 and Tables 1 hrough 4. Figure 3 depics expeced work hours (Panel A), consumpion (Panel B), and saving/wihdrawal (i.e., labor income/social Securiy benefis afer axes and housing expendiures minus consumpion, Panel C) for he younger cohor. Again, he black line presens absolue values for he baseline or normal scenario (lef axis), while he bars show relaive deviaions from he base case for he alernaive scenarios (righ axis): crisis (ligh grey), double forune (black), and riple whammy (dark grey). Panel C disinguishes beween saving (solid black line) and wihdrawal, (i.e., negaive saving dashed
19 black line). Figure 4 presens consumpion (Panel A) and wihdrawal (Panel B) for he nearreiremen cohor. Work hours for his cohor are omied as households in his cohor will all have reired over he longer run. Tables 1 and 2 show reiremen behavior for boh cohors and Tables 3 and 4 presen heir long-erm asse allocaions. Figures 3 and 4, and Tables 1 hrough 4 here Long-erm effecs for he younger cohor. Looking a he cohor of persons firs experiencing a shock a age 20, i is clear ha paerns ha already emerged in he laer years of our shor-erm analysis of work effor coninue o persis over he longer run (Figure 3, Panel A). Our base case household in a normal scenario will gradually reduce weekly work hours from abou 50 a age 30, o around 25 by age 60. As in he shor-erm case, he longerm effecs of he financial/economic crisis on work effor are negligible. By conras, doubly forunae households reduce heir level of work effor below ha of base case households, by abou 10 percen a age 45, and 20 percen a age 55. Those hi by he riple whammy, however, mus boos work hours subsanially compared o he base case, by abou 10 percen a age 50, and 20 percen a age 60. Hence, work effor a hese ages is sill as high as ha of base case households ha are five years younger. Turning o lifeime effecs on consumpion (Panel B, Figure 3), we find ha under he normal scenario, consumpion grows o age 60 and peaks a an annual $30,500. Subsequenly, households sar o reire and subsiue less goods consumpion wih more leisure ime consumpion. 14 Doubly forunae households can subsanially increase heir consumpion level relaive o he normal scenario, by 17 percen during heir 70s and sill by 15 percen a age 90. Crisis households, however, experience a persisen consumpion reducion of 2 percen, and hose going hrough a riple whammy have 3 percen shorfalls over heir work lives. Though he laer are surely financially worse off, due o poor capial marke performance, hey can mainain much of heir consumpion by working more. Laer in life, however, hey lose his flexibiliy
20 and hence suffer from higher consumpion shorfalls, of around 10 percen a age 70. Wealh paerns are also differen. Base case households coninue o build up financial wealh unil heir 40s (Figure 3, Panel C); from heir 50s onward, hey begin drawing down asses o pay for high and sill increasing consumpion while already reducing work effor. Apparenly, as consumpion reaches is peak a age 60, so do wihdrawals wih a maximum value of $12,500 per annum. A worker who sared his work life in he crisis will save abou 4 percen less han base case households by age 30; over he nex decade, he mus boos saving o ensure sufficien financial reserves for he wihdrawal phase, so by age 40, saving exceeds ha of base case households by abou 5 percen. Laer in he life-cycle, wihdrawals are similar o he normal scenario. Doubly forunae households can afford o save less and wihdraw more han he base case household due o heir above-average labor and capial marke performance. For hose experiencing he riple whammy, obviously, he opposie is rue and hey have o save more and inves less. Table 1 depics how he younger cohor allocaes financial wealh o liquid socks and bonds, as well as o illiquid life annuiies over he life cycle. Firs, in he normal scenario, we see a ypical sock fracion pah over he life cycle. The young household is almos fully invesed in socks by age 30, and over ime he reduces equiy exposure near reiremen o well below 80 percen. Iniially, socks are subsiued by bonds which make up abou 20 percen of he porfolio by age 50. As he survival credi and, hence, he excess reurn of annuiies over bonds increases wih household age, annuiies sar o crowd ou bonds, making up abou 14 percen of he porfolio by age 70. A older ages, he individual gradually deplees his liquid financial wealh and lowers his sock fracion o 34 percen by age 80; he share of annuiies in he allocaion of overall financial wealh increases o abou half. Even a age 80, he invesor opimally holds over 16 percen of financial wealh in bonds, despie he fac ha annuiies subsanially ouperform liquid bond holdings. The reason is ha, as liquid asses are consumed,
21 i becomes more and more difficul for he household o mee he minimum requiremen on sock invesmens. Accordingly, bonds increasingly represen he only sensible liquid asse held by he household. Comparing he crisis seing o our base case scenario, we find hardly any differences, indicaing ha he long-erm effecs of he crisis on workers asse allocaions are negligible when he impac srikes young, as hese individuals lack financial asses. By conras, experiencing he riple whammy young does have a life-long impac. Young workers wih very low financial wealh have only one major asse, heir bond-like human capial, so hey are much more likely o hold more sock over heir lifeimes. In heir 60s, for example, hey sill inves over 85 percen of financial wealh in equiies. The opposie is rue for he doubly forunae households, who inves less in equiy over he whole life-cycle. Their bond-like labor income makes up a smaller par of heir overall wealh, leading hem o diversify by shifing a higher share of financial wealh ino less risky asses (i.e. bonds earlier in life and laer, annuiies). I is also of ineres o ask how he crisis shapes reiremen behavior. Table 7-2 presens he fracion of households ha reire from age 62-70 (reiring is defined by reducing work effor o below 20 hours per week). The base case seing exhibis he empirically well documened wo-peaked disribuion: over one-quarer of households reires a he early reiremen age of 62, while around half reire laer, a ages 66 and 67. By age 68, all households have reired, and on average, reiremen occurs a age 64.8. Workers sruck by he crisis a a young age have several decades o adjus, and hey make reiremen iming decisions virually idenical o hose of base case households (resuling in he same average reiremen age). By conras, young workers experiencing a riple whammy when young mus work longer o make up he shorfall: hreequarers pospone reiremen beyond he normal reiremen age, and on average hey reire one year laer han he base case scenario, a age 65.8. No surprisingly, half of he doubly forunae group reires as early as possible; 70 percen leave work prior o normal reiremen age, wice as
22 high as in he base case, which drives down he average reiremen age by more han a year (o 63.5). Long-erm effecs for he older cohor. Our base case households in he normal scenario consume abou $31,000 a age 65 on average, and reduce heir spending over he following wo decades o around $22,000. Afer ha, consumpion increases again (Figure 4, Panel A). Being exposed o a financial/economic crisis leaves households wih lower financial wealh as well as lower Social Securiy income. Consequenly, reiremen consumpion falls shor of ha of base case households by 4 percen per year. Households hi by he riple whammy close o reiremen suffer dramaically over he remaining life-ime, as consumpion persisenly drops by 11-18 percen. By conras, doubly forunae households enjoy consumpion ha exceeds base case levels by 8-15 percen. Consumpion is predominanly financed hrough consan Social Securiy income, o abou 80 percen from age 75 on. The remainder mus be suppored by wihdrawals from financial wealh ha, consequenly, exhibi he same emporal paern as consumpion, ye wih higher magniude due o he base effec (Figure 4, Panel B). Long-erm asse allocaion paerns for he older cohor appear in Table 3. Under all scenarios, sock fracions decrease over ime as he household gradually deplees liquid financial wealh, from 80-95 percen a age 65, o 24-38 percen a age 85. Bond fracions decline hrough he 60s, increase again hrough he 70s, and peak in he early 80s, when due o diminishing liquid wealh, households increasingly face difficulies o finance he minimum amoun required o paricipae in he sock marke. To ake advanage of he increasing survival credi, households gradually shif financial wealh from liquid asses ino annuiies. When combined wih he depleion of liquid asses due o consumpion-financing wihdrawals, his drives annuiy fracions up from 0.2-5 percen a age 65 o 45-64 percen a age 85. In general, compared o he base case calibraion, he allocaion o liquid asses is marginally higher under he crisis scenario and subsanially higher for riple whammy households. The asse allocaion of doubly forunae
23 households, on he oher hand, is characerized by lower sock and higher annuiy fracions. Finally, Table 4 summarizes he impac of he financial/economic crisis on reiremen paerns of he older cohor. In he baseline case, he average reiremen age is 65.1; one fifh of all households (20.6 percen) reire a he early reiremen age 62; abou half (51 percen) a age 66-67, and he remainder (5.1 percen) a age 68. In he crisis scenario, he fracion of households reiring a he early reiremen age drops by 2.4 percen, and ha of households reiring prior o he normal reiremen age of 65 drops by a mere 0.4 percen; his produces a iny increase in he average reiremen age of only 0.07 years (a lile less han a monh). Things are very differen for hose individuals who experienced he riple whammy: almos 90 percen canno afford o reire before he normal reiremen age, which drives up he average reiremen age by 1 year compared o he normal scenario. Two of five doubly forunae households reire a he early reiremen age, and hree of five reire prior o he normal reiremen age; consequenly, he average reiremen age falls by abou one year compared o he base case scenario. Under all scenarios, he laes reiremen age is 68. Conclusion Our goal was o invesigae he shor- and long-erm impacs of a combined financial and economic crisis on households a differen sages in heir life-cycles. To his end, we have developed a life-cycle model ha allows for opimal consumpion, work effor, reiremen, asse allocaion, and annuiizaion decisions, incorporaing counercyclical labor income and unemploymen risk as well as regime shifs in he invesmen opporuniy se. We show ha for young households, he financial/economic crisis will have lile impac on eiher work effor or reiremen behavior, hough hey do suffer from a long-erm decline in annual consumpion accompanied by lower saving. Sock fracions are marginally lower a he onse of he crisis, bu over he remaining life-cycle, asse allocaion does no change much.
24 Young households hi paricularly badly by he financial/economic crisis do have more response, reducing heir work effor during he crisis by up o 10 percen; laer in life, hey mus boos work hours subsanially over 20 percen a age 60 compared o he non-crisis scenario, and mus defer reiremen by one year on average. Lifeime consumpion is also lower: in heir early 20s, i is abou 15 percen less, and 5 percen less even afer age 70. The oher effec is ha young households mus save subsanially more han non-crisis households laer in life, o build up a leas some financial wealh. Low savings early in life go hand in hand wih low sock invesmen; hereafer, from abou age 40 on, equiy exposure is coninuously higher han ha of non-crisis households, while boh bond invesmens and annuiy purchases are reduced. When older persons are hi by a combined financial and economic crisis, hey are prediced o boos work effor slighly, around 0.3-1.3 percen, over he res of heir work lives. Moreover, heir average reiremen age rises slighly as well (less han one monh). The crisis is fel, insead, in more marked declines in annual consumpion, boh shor- and long-erm. Compared o a non-crisis scenario, consumpion drops by 3.5 percen before reiremen and by around 4.5 percen afer age 80. Households reduce heir asse wihdrawals by abou 2.5 percen over he shor-run and by abou 9 percen laer in life. During he immediae crisis, households reduce heir equiy exposure by more han 20 percen, on average, in favor of risk-free bonds. Over he longer run, however, invesors have a marginally higher appeie for liquid asses, boh socks and bonds, han invesors in a non-crisis scenario. Consequenly, he level of annuiizaion decreases. Those older households hi especially badly by unemploymen and sock marke shocks mus subsanially boos heir work effor, by over 20 percen in heir early 60s. Moreover, hey canno afford o reire early and mus pospone reiremen by abou one year, on average. 15 Ye hey sill experience consumpion losses of abou 10 percen in he shor-erm and abou 15 percen laer in life. While hey are able o dampen he immediae impacs of he crisis hrough