Wage Growth and the Measurement of Social Security s Financial Condition. Jagadeesh Gokhale Cato Institute

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1 DRAFT Wage rowh and he Measuremen of Socal Secury s Fnancal Condon by Jagadeesh okhale Cao Insue Aprl 26 Jagadeesh okhale s Senor Fellow a he Cao Insue. The auhor hanks Alan Auerbach, Mchael Boskn, Jeffery Brown, Lqun Lu, Donald Marron, Sco Muller, Davd Pason, Rudolph Penner, Andrew Reenmaer, Thomas Savng, Ken Smeers and semnar parcpans a he Socal Secury Admnsraon for helpful commens. The vews expressed heren are he auhor s and do no necessarly represen he vews of he Cao Insue.

2 Absrac overnmen spendng on he elderly s projeced o ncrease rapdly as he populaon ages and he baby-boomers rere. A chef concern s he connued vably of enlemen programs such as Socal Secury. Lawmakers, budge analyss, and he publc pay consderable aenon o he Socal Secury Trusees economc growh projecons because hey beleve ha hgher growh would sgnfcanly reduce he program s acuaral defc. Ths belef s valdaed by he Socal Secury Admnsraon s calculaons ha show a smaller 75-year acuaral defc when real wage growh s assumed o be faser. In recen years, however, economss have drawn aenon o he mers of measurng Socal Secury s fnancal saus over perods exendng beyond he nex 75 years. And snce 23, he Socal Secury Trusees have added esmaes of he program s fnances measured n perpeuy n her annual repors. However, sensvy analyss examnng he mpac of varous assumpons on he sysem s fnancng are no repored over he nfne erm. Frs, hs paper shows analycally ha faser wage growh may reduce Socal Secury s acuaral balance when measured n perpeuy f he declne n he rao of workers o rerees s projeced o connue beyond he frs 75 years. Second, analycally evaluaes and repors sylzed calculaons of he mpac of real wage growh and demographc change ncludng me-varyng raes of change based on offcal projecons for he US economy on Socal Secury s acuaral balance n a mul-perod seng. Thrd, uses he SSASIM acuaral model of Socal Secury fnancng o esmae he degree o whch ncreased wage growh could negavely affec he sysem s acuaral balance. These resuls rase quesons boh abou convenonal wsdom regardng how mproved wage growh would affec Socal Secury s fnancng, as well as abou how commonly used measures of Socal Secury s fnancng capure hose effecs. 2

3 1. Inroducon I s ofen argued n boh polcy crcles and he popular meda ha faser economc growh could sgnfcanly reduce Socal Secury s long-erm fundng mbalance. 1 If, as many argue, Socal Secury Trusees projecons for economc growh are unduly pessmsc, polcymakers may gnore calls for polces o reform he sysem n he belef ha faser economc growh wll bal us ou. However, Socal Secury s fnancal saus s normally analyzed under a runcaed horzon of 75 years. Does he posve assocaon of faser economc growh wh mprovemen n he sysem s acuaral balance survve under longer horzons? If no ha s, f faser economc growh fals o mprove or even worsens Socal Secury s acuaral balance over very long horzons falure o enac reforms o make he sysem susanable would be a more serous lapse han many polcymakers and budge analyss realze. The curren Socal Secury benef formula ndexes workers earnngs hrough age 6 for wage growh when calculang her average ndexed monhly wage (AIME), whch s he bass for compung Socal Secury benefs. 2 Benefs are calculaed a reremen by applyng a progressve formula o he AIME, so ha a larger fracon of pre-reremen earnngs are replaced by Socal Secury benefs for low wage workers compared o hgher earners. Pos-reremen, benefs are ncreased annually wh he Consumer Prce Index o manan her purchasng power. Each worker cohor s reremen benefs -- as calculaed when s members rere -- reflec ha cohor s hgher labor producvy and wages durng s lfeme compared o ha of 1 See, for nsance, ordon (23); Baker (1996); Weller and Rassell (2); Baker and Wesbro (1999); and Hall (25). For conrasng vews, see Penner (23); Davs (2); Bggs (2). Noe ha hs paper does no commen on he appropraeness of he wage growh projecons made by he Socal Secury Trusees or oher agences. For analyss of he Trusees projecons, see he 1999 and 23 Techncal Panel repors, as well as eneral Accounng Offce (2). 2 Ths s done o place pas earnngs on par wh curren ones by nflang he former a he rae of nomnal wage growh durng he nervenng years. Ths accouns for boh economy-wde general prce nflaon and real wage growh ha occurred durng hose years. Dsably benefs are calculaed n a smlar way, hough wh adjusmens for decreased me n he labor force. 3

4 he mmedaely precedng cohor. Thus, average benefs for succeedng cohors of rerees wll end o rse a he rae of average wages. And for each cohor, once he benef level s esablshed, s purchasng power s mananed by allowng he dollar amoun o grow a he rae of general prce nflaon. Acuaral balance s he mos promnen of a number of measures ha he Socal Secury Trusees use o assess he program s long-erm fnances. I equals he presen value of he sysem s annual ne ncome expressed as a percenage of payrolls over he measuremen perod. 3 As descrbed by he Trusees, acuaral balance s a measure of he program s fnancal saus for he 75-year valuaon perod as a whole. I s essenally he dfference beween ncome and cos of he program expressed as a percenage of axable payroll over he valuaon perod. Ths sngle number summarzes he adequacy of program fnancng for he perod. Whle he Trusees have radonally measured acuaral balance over 25, 5 and 75 years, he 75-year measure receves he mos aenon n polcy debaes. The 25 Trusees Repor projecs a 75-year acuaral defc of 1.92 percen of axable payrolls. Ths defc has a commonly appled polcy nerpreaon: When he acuaral balance s negave, he acuaral defc can be nerpreed as he percenage ha would have o be added o he curren law ncome rae n each of he nex 75 years, or subraced from he cos rae n each year, o brng he funds no acuaral balance. 4 Under hs nerpreaon, he acuaral defc ndcaes he sze of an mmedae and permanen payroll ax ncrease 1.92 percenage pons, from 12.4 percen o percen of wages up o 3 More specfcally, he Trusees measure acuaral balance over a measuremen perod as he ne value of he nal rus fund balance, he presen value of ncome, he presen value of coss, and he presen value of scheduled benefs n he fnal year of he measuremen perod. Ths las amoun s o sasfy he requremen ha he rao of rus fund asses o benef paymens n he fnal year equal 1 percen. 4 Board of Trusees (25), p. 1 4

5 he axable lm ha would be suffcen o resore he program o acuaral balance over 75 years, hough no necessarly hereafer. 5 ven how pas wages ener no he calculaon of Socal Secury benefs, s easy o undersand why many people beleve ha faser economc growh would mprove he sysem s fnancal oulook. Benefs pad o curren rerees are ndexed only o nflaon, raher han o nomnal wage growh (whch generally exceeds nflaon by he growh rae of real labor producvy). Thus, faser growh n real producvy and wages would cause an mmedae ncrease n he ax base and, herefore, n revenues, bu would ncrease benef paymens only afer a delay as workng generaons ha experenced faser wage growh rere and clam benefs n he fuure. If he ncrease n wage growh were permanen, he annual cos rae projeced benefs as a percen of he projeced ax base hrough he calculaon horzon would permanenly declne relave o a lower wage growh scenaro. Thus, cash balances relave o he payroll base would mprove n every followng year. The Trusees Annual Repor for 25 shows ha over a 75-year horzon, hs mprovemen n annual balances would carry over o an mprovemen n Socal Secury s acuaral balance. Assumng an ncrease n real wage growh from a baselne of 1.1 percen per year o 1.6 percen, he 75-year acuaral balance would mprove by.53 percenage pons, from a defc of 1.92 percen of payroll o a defc 1.39 percen. Ths analyss lends credence o he 5 I should be noed, however, ha acuaral balance s no he sole fne horzon measure used o assess Socal Secury s fnances. For example, he Socal Secury Trusees also repor measures of close acuaral balance. See he Board of Trusees (25), p. 6. The Socal Secury Admnsraon s Offce of he Chef Acuary have suggesed addonal measures, ncludng cash balances and rus fund raos n specfc years and he drecon of boh a he close of a measuremen perod. See oss (1999) and Chaplan and Wade (25). 5

6 wdely shared vew ha faser economc growh would sgnfcanly reduce Socal Secury s projeced acuaral defc. We label hs as he radonal vew. 6 In recen years Socal Secury analyss have ncreasngly focused on very long erm fnancng wh he polcy goal beng solvency ha can be susaned well beyond he radonal 75-year scorng perod ofen ermed susanable solvency. 7 The Trusees noe ha Even a 75-year perod s no long enough o provde a complee pcure of Socal Secury s fnancal condon. Overemphass on summary measures for a 75-year perod can lead o ncorrec percepons and o polcy prescrpons ha do no move oward a susanable sysem. Thus, careful consderaon of he rends n annual defcs and unfunded oblgaons oward he end of he 75-year perod s mporan. In order o provde a more complee descrpon of Socal Secury s very long-run fnancal condon, hs repor also ncludes summary measures for a me perod ha exends o he nfne horzon. 8 Proponens of longer-erm measures argue ha focusng on 75-year solvency alone can dsor polcy decsons; he 1999 Techncal Panel, for nsance, argued ha When reformers am only for 75-year balance, hey usually end up n a suaon where her reforms only las a year before beng shown ou of 75-year balance agan. 9 For ha reason, analyss have begun o calculae he Socal Secury program s fnances beyond 75 years. 1 Begnnng wh he 23 Repor, Socal Secury s Trusees have publshed daa on sysem fnancng measured over he nfne erm. The man raonale for he nfne horzon measure s ha gves he fulles vew of he oal asses and oblgaons of he Socal Secury program. The Deparmen of he Treasury noes ha 6 Alhough economc growh s a broader concep han real wage growh, he wo are generally undersood o occur concomanly, a leas n publc debaes abou Socal Secury fnancng. 7 See Advsory Councl; 1999 Techncal Panel; 23 Techncal Panel; 25 Trusees Repor; 8 Board of Trusees (25), p Techncal Panel, p For example, see okhale and Smeers (23), and Auerbach, ale, and Orzag (24). In nfne horzon calculaons, cash flows are projeced no he fuure unl he presen value sums of fuure dollar flows (benefs, axes, he ax base, and so on) become sable (asympoe o a fne value). 6

7 a 75-year projecon s ncomplee. For example, when calculang unfunded oblgaons, a 75-year horzon ncludes revenue from some fuure workers bu only a fracon of her fuure benefs. In order o provde a complee esmae of he long-run unfunded oblgaons of he programs, esmaes should be exended o he nfne horzon.. 11 Snce hen, measures of very long erm fnancng, boh for socal nsurance programs and he federal budge n general, have ganed ncreasng promnence n polcy dscussons. 12 Calculaons of long-erm fnancng measures sugges ha he radonal vew may be an arfac of calculang Socal Secury s acuaral balance under a runcaed projecon horzon of 75-years. In parcular, such lmed-horzon measures reduce he effec of a projeced declne n he worker-o-benefcary rao over he very long-erm. Under perpeuy calculaons, he concluson ha faser wage growh mproves Socal Secury s acuaral balance could be reversed when he declne n he worker-o-benefcary rao s assumed o connue beyond he nex 75 years. Ths resul arses because a declnng worker-o-benefcary rao magnfes he fuure mpac of faser wage growh on Socal Secury s cos rae and wdens he gap beween he presen value of s oulays and revenues o yeld a larger acuaral defc. Explorng he sensvy of Socal Secury s acuaral balance o ndvdual economc assumpons nvolves examnng s response o changes n one (economc or demographc) parameer a a me. However, alerng he real wage growh assumpon rases he queson of model conssency. Faser real wage growh could no occur solaed from changes n oher 11 Deparmen of he Treasury (24), p reenspan (23) dscusses he advanages of he relaed approach of accrual accounng for Socal Secury; Walker (23) dscussed one possble approach would be o calculae he esmaed dscouned presen value of major spendng and ax proposals as a supplemen o, no a subsue for, he CBO s curren 1-year cash flow projecons. Senaor Joseph Leberman (D-Conn.) has nroduced legslaon (S. 1915, The Hones overnmen Accounng Ac of 24) ha would calculae 75-year and nfne horzon ne presen value measures on a governmen-wde bass. The Socal Secury Advsory Board s 23 Techncal Panel on Assumpons and Mehods prased he Trusees ncluson of measures of sysem fnancng n perpeuy and recommended ha hey be gven greaer promnence n he Repor. 7

8 relevan economc varables. For example, faser wage growh may be he resul of echnologcal progress, whch ncreases he producvy of boh capal and labor, and could be assocaed wh hgher neres raes. In ha case, Socal Secury s (rsk free) rae of neres could also be hgher wh accompanyng effecs on acuaral balance. If he ncrease n he governmen s neres rae assocaed wh faser real wage growh were suffcenly large, bgger fuure Socal Secury oulays would receve a smaller wegh n presen-value calculaons, poenally confrmng he radonal vew. However, because neracon of faser wage growh wh a declnng worker-o-benefcary rao worsens Socal Secury s long-erm acuaral balance under a consan dscoun rae, such a worsenng may perss despe a smulaneous ncrease n he governmen s neres rae up o a lm. Wh he acuaral balance calculaon calbraed o U.S. demographcs and real wage growh, can be shown ha faser wage growh would generae larger acuaral defcs for a range of Socal Secury neres raes. Ths paper analyzes he effec of ncreased economc growh on Socal Secury solvency measured n perpeuy. 13 Usng a sylzed model, we frs show analycally ha s possble for faser wage growh o reduce he sysem s acuaral balance measure n a smple pay-as-you-go program, provded ha he rao of workers o benefcares s declnng. We hen examne hese resuls under a varey of demographc and neres rae condons. Nex, usng he SSASIM acuaral model we show ha such a declne n Socal Secury s nfne-erm acuaral balance s plausble under demographc and economc condons projeced for he Uned Saes, even 13 Admedly, a change n economc growh over he long erm would be assocaed wh changes n oher varables nvolved n measurng Socal Secury s fnancal saus -- such as wage growh, demographc change, capal reurns, and dscoun raes. Ths paper does no aemp o capure he nerrelaonshps beween hese varables n a dynamc general equlbrum seng. Raher, s lmed o examnng he mpac of hgher producvy and real wage growh on sac measures of he program s fnancal condon ha are radonally used by he Socal Secury Admnsraon and he program s Trusees. 8

9 hough he same wage growh rae would mprove he program s 75-year acuaral balance and he measure of susanable solvency. The paper closes wh a dscusson of he resuls meanng for Socal Secury fnancng and for he measures of solvency commonly appled o. 2. A Smple Model of Socal Secury Fnancng The followng bulds a sylzed model of a pay-as-you-go Socal Secury program. Inal specfcaons are delberaely smplfed for he purpose of beer communcang he core nsghs, wh ncreasng complexy and realsm added as he model s developed. Frs consder a program n whch each benefcary s pad a benef equal o a consan percenage of he average wage n ha year. The acuaral balance for such a program s heren defned as he presen value of axes mnus he presen value of benefs, expressed as a percenage of he presen value of fuure payrolls. PVTaxes PVBenefs AB. (1) PVPayroll Ths s he famlar equaon n whch he summarzed cos rae s subraced from he summarzed ncome rae. Ths sylzed measure of acuaral balance dffers from ha applyng o he rue Socal Secury program prmarly n ha excludes he nal value of he rus fund. 14 Measured n perpeuy, he presen value of axes can be expressed as PVTaxes τ w N R, (2) where 14 Acuaral balance as measured by he Socal Secury Trusees ncludes he nal rus fund balance and a requremen ha he fnal year rus fund balance be equal o 1 percen of oulays n ha year. To keep he dervaons as smple as possble, he formulaon of he acuaral balance [equaon (1)] n he ex assumes hose amouns o be zero. 9

10 τ (au) he payroll ax rae; w he average wage a me zero; N he populaon of workers a me ; a compound real wage growh facor equal o (1+g), where g equals he annual rae of real wage growh; and R an neres facor equal o (1+r), where r equals he real neres rae; The presen value of benefs s equal o PVBenefs w 1 β ρ N B R, (3) where ρ (rho) a consan replacemen rae of he average curren wage; β (bea) he worker-benefcary rao a me zero; and B a reducon facor equal o (1b) where b equals a consan percenage rae of declne n he worker-benefcary rao. The presen value of payrolls can be expressed as PVPayrolls w N R. (4) Equaon (3) shows ha he presen value of oal benefs pad a me s a funcon of a consan replacemen rae, he nal values of wages, (he nverse of) he worker-benefcary rao, and changes n he worker populaon, wages, worker-benefcary rao, and accumulaed neres beween me zero and me. For purposes of clary, he values of and B - would be greaer han 1 so long as real wages are rsng and he worker-benefcary rao fallng (g, b > ); he value of R - would be less han 1 so long as he real neres rae s posve (r>). 1

11 Noe ha equaon (3) assumes ha curren benefs are a funcon of curren wages. Tha s, here s no lag beween realzng hgher wages and hgher Socal Secury benefs. Ths relaonshp would oban f Socal Secury benefs were dependen on pas wages ndexed for wage growh hroughou a reree s lfeme. Alhough hs s no rue for Socal Secury n realy, examnng s mplcaons s helpful for developng nuon abou resuls when hs assumpon s dropped. The varables n equaon (3) affec PVBenefs n he followng ways: a hgher value of g means ha wages would be hgher n each fuure perod. Because benefs depend on conemporaneous wages by assumpon, PVBenefs would be larger. Noe ha f g were larger, each erm under he summaon sgn n equaon (3) would also be larger. Hence, he enre erm would be larger. The same s rue for PVTaxes n equaon (2). Furhermore, f he h erm n PVBenefs ncreases by x percen as a resul of an ncrease n g, so would he h erm n PVTaxes. Boh axes and benefs would, herefore, ncrease n he same proporon under a hgher value of g. Lkewse, f he worker-benefcary rao declnes (ha s, f b were larger), here would be more benefcares per worker n he fuure, mplyng a larger PVBenefs relave o PVTaxes a each gven value of g. Tha s because a change n b affecs he former bu no he laer. In conras, ncreases n he real neres rae (r) means ha fuure benef paymens, axes, and wages are all dscouned more heavly -- mplyng proporonae reducons n PVBenefs, PVTaxes, and PVPayrolls. These relaonshps are saed as Proposon 1: Assumng 1) ha he replacemen rae s consan and 2) ha curren benefs depend on curren wages: 11

12 ) An ncrease n real wage growh leads o a proporonae ncrease n PVBenefs and PVTaxes; ) A faser declne n he worker-benefcary rao ncreases PVBenefs relave o PVTaxes; ) An ncrease n he real neres rae leads o a proporonae reducon n PVBenefs and PVTaxes; and v) An ncrease n real wage growh leads o a proporonae ncrease n PVPayrolls and PVBenefs, whle an ncrease n he real neres rae leads o a proporonae reducon n boh. Usng equaons (2), (3) and (4), he acuaral balance defned n equaon (1) can be expressed as τn w AB R N N w ρβ w R 1 B R, where, for smplcy, we assume ha he oal worker populaon remans consan over me a N. The expresson for AB can be can be smplfed o 1 ρβ B R AB τ τ Ω. (5) R Equaon (5) says ha he acuaral balance s equal o he ax rae mnus he summarzed cos rae (Ω), where boh revenues and coss are expressed as a percenage of payrolls. The assumpon of a consan worker populaon bu a declnng worker-o-benefcary rao obvously mples a growng oal populaon. We nex explore he queson of he mpac of faser wage growh on he acuaral balance under several cases usng alernave paramerc assumpons, progressvely makng he model more realsc. 12

13 Case A. Consan Worker-Benefcary Rao Ths case assumes b, whch mples ha he age srucure of he populaon remans consan over me. If so, B - 1 for all fuure perods, and hs erm s elmnaed from equaon (5). Tha allows for he smplfed expresson for he acuaral balance: AB τ ρβ. (6) 1 Equaon (6) s nuvely easy o undersand: The sysem receves τ cens per worker. For o be balanced, τ cens mus be suffcen o pay benefs o he number of benefcares 1 per worker ( β ). 15 Noe ha he compound wage growh erm s also elmnaed from he expresson for AB, mplyng ha n hs smplfed model wage growh (g), does no nfluence he acuaral balance. Proposon 2: Wh an unchangng populaon srucure (b) and wh curren benefs beng proporonal o curren wages, he Socal Secury sysem s acuaral balance s unchanged n response o a change n he rae of real wage growh. Tha s, n hs smplfed seng, a Socal Secury sysem ha s nally n (ou of) balance wll reman n (ou of) balance o he same degree regardless of he rae of real wage growh. Case B: Declnng Worker-Benefcary Rao Now consder he case where b> ha s, where he worker-benefcary rao declnes over me. Frs, all oher hngs equal, hs wll reduce he acuaral balance of he sysem. Wh 15 For nsance, f he replacemen rae were 32 percen and he worker-o-reree rao were 2, he ax rae requred for a zero acuaral balance would be 16 ( ). 13

14 b>, B - [1/(1-b) ] mus be larger han Compared o he cos rae under Case A, a posve b ncreases he numeraor n he second erm of equaon (5) and makes he sysem s coss as a percenage of payrolls larger, hereby reducng acuaral balance. Proposon 3: Oher hngs equal, a faser rae of declne, b, n he worker-benefcary rao s assocaed wh a smaller (and more negave) acuaral balance. Moreover, when he worker-benefcary rao s fallng (ha s, when b>), he acuaral balance s no neural wh regard o changes n wage growh (g). If b>, hen B - >1 for each value of. In hs case, a larger value of g causes a dsproporonae change n he numeraor of he second erm n equaon (5) compared o s denomnaor, agan causng he acuaral balance o change. Proposon 4: When he worker-reree rao s declnng (b>), ncreased economc growh reduces he acuaral balance (makes more negave). A formal proof of Proposon 4 s provded n Appendx A. However, he proof s nuvely clear from equaon (5). As saed earler, B - >1 when b>. Tha means any ncrease n g mus resul n a larger ncrease n he numeraor of he second erm of equaon (5) compared o he ncrease n he denomnaor. Tha, n urn, means an ncrease n g ncreases he summarzed cos rae and reduces he sysem s acuaral balance. The nuon underlyng Proposon 4 s que sraghforward: If he populaon of rerees s growng, he populaon of workers s consan, and reremen benefs are deermned by curren wages, faser wage growh would cause benef oulays o grow faser han payrolls. 16 For nsance, f b were 2% and were 5 years, hen β - would be equal o 1/(1 -.2) 5, or

15 Fgure 1 llusraes Proposons 3 and 4 by calculang acuaral balance for a range of values of he parameers b and g. The model s desgned o be n acuaral balance n perpeuy when annual wage growh (g) s 1 percen and he rae of annual declne (b) n he workerbenefcary rao s.3 percen, roughly he rae projeced for he curren Socal Secury program over he very long erm. 17 From hs base, we aler boh he rae of declne of he workerbenefcary rao (from a low of zero percen o a hgh of.5 percen) and he rae of real wage Acuaral balance 4% 2% % -2% -4% -6% -8% -1% Fgure 1: Effec of Declnng Worker-Reree Rao and Changng Real Wage rowh on Acuaral Balance Value of b.%.5%.1%.2%.3%.4%.5% % 1% 2% Real wage growh growh, from zero percen hrough 2 percen. When he worker-benefcary rao s sable (b), changng he assumed rae of real wage growh has no effec on he acuaral balance. Wh a declnng worker o benefcary rao (b>), however, he acuaral balance (AB) declnes when real wage growh occurs faser. Fgure 1 shows ha, conssen wh Proposon 3, a hgher value of b resuls n a lower level of AB (for each gven level of g). In addon, conssen wh Proposon 4, when b>, an ncreases n g reduces AB whereas a reducon n g ncreases AB. Furhermore, AB becomes more sensve o changes n g a larger values of b. Thus, n a pure pay-as-you-go program n whch benefs are based on curren average wages, ncreased economc growh reduces acuaral balance calculaed n perpeuy so long as he worker-reree rao s declnng. 17 The seady-sae declne a he end of he 75-year perod s roughly.24 percen annually; he rae of declne n he early par of he 75-year perod, whch has a dsproporonae value n acuaral balance calculaons, s sgnfcanly hgher. 15

16 Case C: Benefs Dependen on Curren Wages and Wages Lagged One Perod Equaon (3) for PVBenefs bears an mporan dsncon from he curren Socal Secury program n ha pays benefs as a percenage of curren average wages alone whereas he Socal Secury program s benefs depend upon pas, or lagged, wages. As a resul, an mmedae ncrease n wages, and hus ax revenues, would no lead o an mmedae ncrease n benefs. Ths lag n ranslang wage growh o benef growh underles he common belef ha sysem fnancng unequvocally mproves n response o faser economc growh. Equaon (3) s re-wren below o express he curren benef as an equally weghed funcon of curren wages and wages 1 perod ago. Ths makes benefs a me a funcon of wages a me and PVBenefs w ρβ 2 1 N B R w ρβ 1 N B 1 R w ρβ N (1 + ) B R. (3a) ven (3a), equaon (5) for acuaral balance can be rewren as 1 1 ρβ B (1 + ) R 1 1 AB τ τ (1 + ) Ω. (5a) 2 2 R Wh a sable worker-reree rao (b), equaon (6) can be smplfed o AB τ ρβ (1 + ). (6a) 2 Ths expresson of he acuaral balance clarfes why many people beleve ha ncreased economc growh wll mprove sysem fnancng. Because -1 declnes as wage growh 16

17 1 ncreases, hgher wage growh reduces he cos rae, (1/ 2) ρβ (1 + rae, τ, and mproves he sysem s fnancng. Ths leads o 1 ), relave o he revenue Proposon 5: Assumng 1) a sable worker-o-benefcary rao (b) and 2) dependence of benefs on lagged wages, faser wage growh reduces he cos rae and mproves he sysem s acuaral balance. The above dscusson clarfes ha when benefs are a funcon of lagged wages, faser wage growh has a dfferenal mpac on PVBenefs and PVTaxes. Ths becomes clear by comparng equaons (5) and (5a). The obvous nex queson concerns he mpac of faser wage growh (g) on he acuaral balance when he worker-o-benefcary rao s declnng -- ha s, he sgn of he dervave dab/d when b>. Appendx B shows ha he expresson for dab/d for he case of b> can be wren as dab d ω (1 + ) ΩZ 1, (7) 1+ where Ω s he summarzed cos rae as defned n equaon (5) above and Z equals he ne ncrease n Ω arsng from a change n. (As dscussed earler, an ncrease n would lead o a larger ncrease n he numeraor of he second erm of equaon (5) compared o he ncrease n he denomnaor because each B - erm n he numeraor exceeds 1.) The erm Z n equaon (7) [whch s defned n equaon A6 n Appendx A] equals he ne ncrease n he numeraor of he second erm n equaon (5) compared o he denomnaor due o an ncrease n. The erm Z s a funcon of b, Z(b), wh he properes: () ha Z when b, wh equaly holdng when b; and () ha Z ncreases monooncally wh b. Thus, Z n equaon (7) capures he mpac of he 17

18 worker-o-reree rao on he change n he acuaral balance due o a change n he growh rae (dab/d). Wha s equaon 7 ellng us? I s smply a combnaon of Proposons 4 and 5. Proposon 4 revealed ha wh rerees formng a larger fracon of he populaon over me, faser wage growh ncreases Socal Secury s cos rae and worsens he sysem s acuaral balance. Proposon 5 shows ha under dependence of benefs on lagged wages, faser wage growh mproves he sysem s acuaral balance. Equaon 7 shows ha he change n he acuaral balance s deermned by he balance of hese opposng forces. Appendx B shows ha seng bz n Equaon (7) yelds he resul of Proposon 5, namely ha dab d Ω >. (8) Equaon (7) also clarfes ha seng b> (whch mples Z>) could change he sgn of dab/d from posve o negave by flppng he sgn of he erm n he square brackes. Tha s, a suffcenly rapd declne n he worker-o-benefcary rao could resul n Proposon 4 s effec domnang ha of Proposon 5. Tha would cause he sysem s acuaral balance o become smaller (more negave) n response o a change n he wage growh rae (g), conrary o he popular belef ha hgher wage growh mproves Socal Secury s fnances. Case D: Benefs Dependen on Wages n Several Earler Perods In pracce, curren Socal Secury benef oulays are no jus a funcon of wages one perod ago, bu of wages ofen as many as 4 perods pror. Tha s because alhough he Socal Secury benefs of hose rerng oday are wage ndexed ha s, depend on curren wages he benefs of older cohors alve oday were based on wages from several perods ago (ha prevaled n her perods of reremen) and now grow only wh prces raher han wages. For 18

19 example, Socal Secury benefs of older rerees (say, hose aged 92 who rered when hey were age 62) are deermned by he wage level of 3 perods ago whereas hose of younger rerees (say, hose aged 67 oday who rered when hey were age 62) depend on he wage level from jus 5 years ago. Appendx C shows ha f pas wages enerng he acuaral balance formula are equally weghed, he acuaral balance can be expressed as AB 1 γ ( ) N + 1 ( N + 1) ΩZ + ( ( N + 1) 1 N + 1) 1 (9) where γ () summarzes he dependence of benefs on pas wages. Agan, as Appendx C shows, he basc conclusons of Proposon 5 above would be preserved. Tha s, wheher dab/d > depends on he balance of wo opposng forces. For values of g and b where he wo forces are exacly balanced, dab/d. For oher combnaons of g and b, dab/d, meanng would be eher negave or posve. Ths yelds Proposon 6: When curren benefs are an equally weghed funcon of wages n he curren perod and N earler perods, for each gven value of gg *, here exss a value of b * b(g * ) where dab / d, wh dab / d > when b<b (g * ) and dab / d < when b>b(g * ). 18 I s obvous ha equally weghng pas wages n he acuaral balance formula s napproprae because moraly reduces he szes of older cohors whose benefs are deermned by wages furher back n he pas. Hence, acuaral balance should be calculaed usng declnng weghs calbraed o he age dsrbuon of cohor szes over me. Applyng smaller raher han equal weghs o wage levels furher back n he pas mples ha he force of Proposon 5 18 To keep he developmen of hese proposons smple, we use equal weghng of curren and pas wages n he dervaons shown n he Appendx C. However, sub-secon E below shows he resuls obaned from assumng declnng populaon weghs for wage erms earler n he pas. 19

20 (whereby acuaral balance mproves n response o faser wage growh) dmnshes relave o ha of Proposon 4 n deermnng he change n acuaral balances wh respec o a change n real wage growh. Because a larger share of oal benefs would be pad o relavely younger rerees, faser wage growh would resul n larger benef oulays more quckly. Consequenly, he combnaons of g and b values a whch dab / d would be dfferen compared o he case of equal weghng. Fgure 2 shows locus (ha s, combnaons of he wage growh rae g, and he rae of declne n he worker-o-benefcary rao, b(g)) for whch dab / d. The calculaons assume: τ (payroll ax rae)12.4%; w (nal real wage)1; N N (populaon of workers a me )1; r (neres rae)3%; ρ (benef replacemen rae)35%; β (nal worker-benefcary rao)3.33; and N (he number of pas wage perods ha ener no he benef formula)35. In Fgure 2, he locus s calculaed under he assumpon of declnng weghs for wages furher back n he pas. The weghs are calculaed based on populaon shares of hose aged 65 and older ha would arse under age-specfc condonal moraly raes for hose aged 65 and older Moraly raes provded by he Socal Secury Admnsraon are used n calculang he weghs. 2

21 .4% Fgure 2: Loc of dab/d When Curren Benefs Depend on Curren Wages And Wages In 35 Pas Perods -- Declnng Weghs Values of b (percen).3%.2%.1% dab/d> dab/d<.% Real Wage rowh Rae (percen) The dervave of acuaral balance wh respec o, dab/d, s negave for combnaons of b and g ha le n he norh eas drecon relave o he locus. Tha s, hgher wage growh would reduce acuaral balance under hese crcumsances. For wage growh raes approxmang curren raes n he Uned Saes abou 1 percen per year values of b * b(g * ) are very small abou.2 percen -- makng que lkely ha demographcs. dab / d < when b values are calbraed o U.S. Case E: Calbraon To U.S. Demographc Projecons Fgure 3 shows projeced values of he worker-benefcary rao for he Uned Saes. 2 I shows ha he rao s expeced o declne sharply durng he nex hree decades followed by a much more gradual declne afer he baby-boom generaon ransons no reremen and passes away. 2 All demographc projecons are aken from he Socal Secury Admnsraon. See hp:// (noed as of January 6, 25). 21

22 Fgure 3: Projeced Worker-Benefcary Rao and s Rae of Change (b ) n he Uned Saes Worker-Benefcary Rao Rae of Change n Worker- Benefcary Rao, b (percen) Worker-Benefcary Rao b Year Fgure 3 also shows he correspondng projeced me-varyng rae of declne (b) n he worker-o-benefcary rao. The values of b are generally que large compared o he values n Fgure 2 a whch dab / d when real wage growh equals 1 percen. Noe ha whle he worker-o-benefcary rao s projeced o declne, hs declne would ake place alongsde a growng projeced populaon n he Uned Saes. Fgure 4 shows he Socal Secury Admnsraon s projecon of he populaon of workers and ha of workers plus rerees, boh normalzed o her populaon szes n 25. Tha Fgure ndcaes ha a projeced declne n he worker-o-benefcary rao does no nvolve a sagnan worker populaon as assumed earler. Raher, boh populaons are projeced o grow n absolue sze n he Uned Saes. A declnng worker-o-benefcary rao means jus ha he fracon of he oal (and growng) populaon ha would be n he workforce s expeced o declne over he nex 75 years. 22

23 3.5 Fgure 4: Projeced U.S. Worker-Benefcary Rao, Worker Populaon, and Toal Populaons Calculaed W/B rao Toal Populaon Worker Populaon Incorporang U.S. demographc projecons no he acuaral balance calculaons (and assumng ha he rae of declne n he worker-o-benefcary rao s consan a s ermnal value beyond he year 28) yelds values for dab / d of.29 when g1.1 percen and 1.75 when g1.6 percen. The values of AB a hose wo values of g are 3.2 percen and 4.1 percen respecvely. 21 Tha s, alhough he mmedae margnal conrbuon of faser growh s posve a g1.1 percen, rapdly becomes negave as values of g are ncreased o cumulavely yeld a smaller (more negave) acuaral balance when g1.6 percen. 21 Ths sylzed model of Socal Secury fnancng excludes many deals of he acual Socal Secury program, ncludng he ncome axaon of benefs, scheduled ncreases n he normal reremen age, survvor and dsably benefs and acuaral reducons for early reremen. Is acuaral balance esmae should no, herefore, be expeced o closely approxmae he offcal esmae of he Socal Secury s Board of Trusees based on much more dealed calculaons. We regard he esmae of a 3.2 percen acuaral defc under nermedae growh and neres rae assumpons as que reasonable n comparson wh he offcal esmae of 3.5 percen. 23

24 As Table 1 shows, resrcng acuaral balance calculaons o jus 75 years would sugges he oppose concluson: A larger value of real wage growh (g) produces an Table 1: Acuaral Balance and Change n Response o Change n Producvy rowh and Dscoun Raes Real Wage Acuaral Local Dscoun Projecon rowh Balance, dab/d Elascy, Rae (%) Horzon Rae (%) AB(%) ε (algebracally) larger acuaral balance and posve values of dab / d. For example, usng he baselne dscoun rae of 3 percen and real wage growh rae of 1.1 percen, he 75-year horzon yelds an acuaral balance of jus 1.5 percen, a much smaller defc han he 3.2 percen obaned under he calculaon n perpeuy. In addon, ncreasng he growh rae o 1.6 percen per year, he 75-year acuaral balance becomes algebracally larger (less negave) 1.1 percen. Table 1 also shows ha under perpeuy calculaons, he (negave) response of acuaral balance o ncreases n wage growh raes s very large when presen values are calculaed wh smaller dscoun raes. Ths s as expeced because smaller dscoun raes ncrease he wegh on dollar flows n he dsan fuure relave o weghs on dollar flows n he mmedae fuure, makng fuure benef oblgaons larger n presen value relave o earler payroll ax-paymens. Nex, we nvesgae he mpac on acuaral balance of a slghly faser or slower declne n he U.S. worker-benefcary rao when he calculaon horzon s nfne. Fgure 5 shows he 24

25 acuaral balance for dfferen values of a parameer, γ (gamma), appled o he me-varyng values of b shown n Fgure 3. For example, γ.9 would mply a slower declne n he workero-benefcary rao over me whereas γ1.1 would mply a faser rae of declne n ha rao. Fgure 5 shows he values of AB for values of γ rangng from.9 o 1.1 and values of wage growh (g) beween 1.1 percen and 2.1 percen (ha s, values of rangng from 1.11 o 1.21). Fgure 5 shows ha a all levels of wage growh, acuaral balance s smaller (more negave) when he worker-o-benefcary rao s assumed o declne faser (γ>1). Moreover, Fgure 5 shows ha for each rae of declne n he worker-benefcary rao, here s a rae of producvy/wage growh a whch he acuaral balance s maxmzed. A γ1, he rae of real wage growh ha maxmzes acuaral balance s much smaller, only around.5 percen closer o ha under he Socal Secury Trusees hgh-cos assumpons. Under calculaons n perpeuy, ncreasng real wage growh would, accordng o he fgure, reduce Socal Secury s acuaral balance gven projeced demographc changes n he Uned Saes. 22 Fgure 5: Acuaral Balance for Alernave Raes of Declne n he Worker-Benefcary Rao and Real Wage rowh Acuaral Balance γ Real Wage rowh (percen) 22 Agan, we remnd readers ha measuremen of Socal Secury s fnances s conduced under a sac framework (see foonoe 13). 25

26 3. Wage rowh, Socal Secury Cash Flows, and Presen Value Calculaons The prevous secons resuls show ha under sylzed calculaons calbraed o feaures of he U.S. Socal Secury sysem, faser growh could worsen he nfne horzon acuaral balance. Ths resul can be explaned n a dfferen way by examnng he mpac of faser growh on Socal Secury s cash balances over me. Appendx D shows ha wh benefs parally dependen on wages from several pas perods, he acuaral balance can be expressed as: AB Cash Balance Payrolls PVPayrolls PVPayroll 1 [ τ ρβ ωγ ( ) B ] R R, (1) where ω γ () capures he mpac of pas wages levels on curren benefs, 1+g, and B1b as before (see secon 2). Equaon (1) shows ha wage growh affecs he componen erms n dfferen ways. Frs (as Appendx D clarfes), changes annual balances n every fuure year. The calculaons shown below ndcae ha under reasonable parameer choces, annual cash balances mprove wh wage growh ndcang ha he dependence of benefs on pas wages (he effec of Proposon 5 n Secon 2 above) generally domnaes n annual cash balance calculaons. Second, however, faser wage growh alers he presen-value weghs applcable o he annual balances n dfferen fuure years. Noe, ha he presen value weghs depend on he ne dscoun facor,, represenng he dfference beween he rae of real wage growh and he real neres rae. A larger value of mples a smaller ne dscoun rae. Hence, faser wage growh reduces he weghng of annual balances n he near fuure and ncreases ha on balances n he dsan fuure. The ne mpac of hese wo effecs deermnes he change n he acuaral balance. R 26

27 The crucal queson s: Wha happens o hese wo effecs of faser growh under alernave raes of declne n he worker-o-benefcary rao? Consder Fgure 6, whch shows prospecve weghed annual cash-flow balance raos when b, ndcang a sable populaon age srucure, under wo alernave values of real wage growh (g) of 1.1 percen and 1.6 percen. The sum of hese annual raos represens he acuaral balance over he perod. Increasng g from 1.1 percen o 1.6 percen ncreases (un-weghed) cash balances hroughou he fuure..5% Fgure 6: Weghed Cash Balance Raos Under Alernave Wage rowh Raes (1.1% and 1.6%) (b ; Wage-Prce Indexng) Percen of Annual Payrolls.3%.1% -.1% -.3% -.5% Fuure Year Weghed Cash Balance Rao (1.1%) Weghed Cash Balance Rao (1.6%) Tha shf n he growh rae, however, reduces he weghs, R / R on cash balance raos n he near fuure bu ncreases hose on cash balance raos n he dsan fuure. (Appendx D provdes a dealed explanaon of why hs occurs.) As a resul, despe he ncrease n early-years cash balance raos, early-years weghed cash balance raos acually become smaller. Fgure 6 shows ha, under he parameers of he calculaon, he reducon n 27

28 cash balance raos due o faser growh does no perss beyond he frs 44 years. In years 45 and laer, weghed cash balance raos are larger wh g1.6 percen compared o hose when g1.1. Those larger fuure weghed cash balance raos mprove he sysem s nfne-horzon acuaral balance ha s, he cumulave sum of weghed cash balance raos hroughou he fuure. Fgure 7, repeas Fgure 6 bu for b>, ndcang a declnng worker-reree rao. Values of b are, agan, calbraed o hose of he U.S. economy as shown n Fgure 3. Shfng from he sable demographcs of Fgure 6 o U.S. demographcs has a large frs order mpac on he acuaral balance (as noed n Proposon 3 earler)..5% Fgure 7: Weghed Cash Balance Raos Under Alernave Wage rowh Raes (1.1% and 1.6%) (b> ; Wage-Prce Indexng) Percen of Annual Payrolls.3%.1% -.1% -.3% -.5% Fuure Year Weghed Cash Balance Rao (1.1%) Weghed Cash Balance Rao (1.6%) Wh b>, annual balance raos move from nal surpluses o rapdly ncreasng fuure defcs and he ranson o defcs occurs que rapdly when he demographc ranson s especally quck as refleced by he hgh values of b durng he nex few decades (see Fgure 3). However, as s clear from Proposon 4 and equaon 1, he declnng worker-o-benefcary rao (as capured by he parameer B) acs as a drag on he mprovemen n annual cash balance raos 28

29 arsng from faser wage growh. Ths s evden from Fgure 7 n whch weghed annual cashbalance raos when g1.6 percen become larger han hose under g1.1 percen durng he early years, bu do no reman larger forever as under Fgure 6. Raher, a second crossover occurs a year-95, afer whch weghed cash-balance raos are smaller (more negave) when g1.6 percen han when g1.1 percen. I should be noed ha he change n he weghs aached o dfferen years cash balances s dencal n boh cases (Fgure 6 wh b and Fgure 7 wh b>). The dfference n he resuls sems from he dfferen me profles of cash-balance rao mprovemens rggered by he shf o faser wage growh where annual mprovemens are no as large when b> as under b. The smaller mprovemen n cash balance raos under faser wage growh leads o he declne n he nfne-horzon acuaral balance: from 3.2 when g1.1 percen o 4.1 when g1.6 percen (see he case wh a 3 percen dscoun rae and nfne horzon calculaon shown n Table 1). Thus, a declnng worker-benefcary rao mposes a demographc drag ha lms he mprovemen n annual cash balance raos and worsens he overall acuaral balance when calculaed n perpeuy. I s easy o see ha he acuaral balance would no declne f were calculaed under a 75-year me horzon. Tha s because, he larger weghed defcs beyond he ermnal year would be excluded from he calculaon. 4. Model Conssency n Evaluang he Sensvy of Acuaral Balance In hs secon, we consder he ssue of model conssency when explorng he response of acuaral balance o faser wage growh. The sandard crcsms leved agans he sensvy analyss presened n he Socal Secury rusees annual repors s ha explorng he 29

30 mplcaons of changng a sngle facor whle holdng oher npus consan s napproprae and he analyss cres ou for a general equlbrum framework. For example, faser real wage growh ha, perhaps, resuls from beer economc polces, would be accompaned by a dfferen consellaon of economc (and, perhaps, demographc) oucomes. Replcang he sac approach o analyzng Socal Secury s fnances used by mos governmen scorng agences, could be subjec o he same crcsm: Faser wage growh could be accompaned, for example, by hgher neres raes as echnologcal shocks ncreases boh labor and capal producvy. There are wo responses o hese crcsms. Frs, a general equlbrum framework requres explc specfcaon of he polces ha would be used o close he governmen s neremporal budge consran. The Trusees analyss of Socal Secury fnances mposes no such budge consran. When he objecve s o measure an exsng budge gap, general equlbrum modelng s naurally precluded: Socal Secury s presumed o connue payng scheduled benefs even hough revenues are nadequae. Second, mpendng demographc change n he Uned Saes s lkely o ncrease fuure capal nensy (a declnng pool of workers relave o he pool of rerees ownng szable wealh) would end o dampen neres rae ncreases arsng from echnologcal changes ha mprove capal and labor producvy. On he oher hand, economc agens may demand hgher reurns on savngs n an envronmen of hgher growh bu also greaer economc volaly. The sandard approach o esmang he governmen s neres rae under uncerany suggess equang o he rae of me preference (say, 1 percen per year) plus he produc of wo ems: he nverse of he degree of rsk averson and he sandard devaon of producvy growh. However, here s no consensus n he economc growh leraure on he sze of he approprae rsk averson parameer. 3

31 Here, we smply calculae he range of neres raes ha suppor an nverse relaonshp beween wage growh and Socal Secury s acuaral balance. For example, calculaons usng he sylzed model under Case E above show ha ncreasng real wage growh raes from.6 percen per year o 1.6 percen per year he acuaral balance declnes from 3. percen o 4.1 percen. However, smulaneously ncreasng he governmen s neres rae from 2.6 percen o 3.2 percen would leave he acuaral balance unchanged a 3. percen. 23 In addon o neres rae unceranes, he resuls obaned showng worsenng nfneerm acuaral balance n response o hgher wage growh depend crucally on assumng ha he declne n he worker-o-benefcary rao connues ndefnely afer he 75 h year. Of course, assumng connung declnes n he worker-reree rao for he enre fuure mples ha Socal Secury benefs would be fnanced by workers comprsng an ever smaller fracon of he populaon. 24 Alhough gradually ncreasng longevy and a gradual bu connung declne n ferly s no nconcevable for a number of decades beyond he nex 75 years, he assumpon of declnng worker-reree raos n perpeuy s dffcul o defend. 23 Under he seady sae relaonshp rρ+(x/θ), where he rae of me preference (ρ) s assumed o equal 1 percen, producvy growh rae alernaves (x) rangng beween.6 percen and 1.6 percen per year and neres rae alernaves (r) rangng beween 2.6 and 3.2 percen per year are conssen wh neremporal elasces of subsuon (θ) beween.27 and 1.. These values of θ span he range of values esmaed n he economcs leraure. However, noe ha hs relaonshp characerzes a seady sae whereas he U.S. economy s undergong a szable ranson. 24 We remnd readers ha a declnng share of he worker populaon n he oal populaon s conssen wh boh populaons growng over me. 31

32 To explore hs ssue, we calculae he nfne erm acuaral balance under alernave assumpons regardng he perod beyond 75 years for whch he worker-o-reree rao would connue o declne. In oher words, we assume b b 75 for 75 S and b for >S for alernave values of S (see Table 2). The calculaons show ha he nfne-erm acuaral balance under wage growh of 1.6 percen per year s smaller (mplyng ha he acuaral defc s larger) han ha under wage growh of 1.1 percen per year when he assumpon of b b 75 s dropped afer jus anoher 2 years beyond he nex 75 years (S>95). Thus, alhough he negave mpac of hgher wage growh on he nfne-erm acuaral balance requres he assumpon of a connued declne n he worker-o-benefcary rao, does no appear necessary o manan ha assumpon for more han a few years beyond he convenonal horzon of 75 years. 5. Smulaons Under A Dealed Model of Socal Secury--SSASIM Table 2: Infne Term Acuaral Balance Under Alernave Horzons for Connued Declne n he Worker-o- Benefcary Rao Infne Term Acuaral Balance Under S Alernave Wage rowh Rae Assumpons 1.1 percen 1.6 percen Source: 25 Socal Secury Trusees Repor, Table VI.D.4 wages bu do no capure he full deals of Socal Secury fnancng. These smple demonsraons of he mpac of wage growh on Socal Secury s acuaral balance capure he essence of he curren Socal Secury program wheren curren benefs are based on pas In hs secon we ulze he SSASIM (Socal Secury and Accouns Smulaor) model developed and mananed by he Polcy Smulaon roup. Ths model was developed durng he Advsory Councl on Socal Secury under conrac wh a number of organzaons, 32

33 ncludng he Socal Secury Admnsraon, and has been regularly updaed snce hen. 25 The SSASIM model has wo modes of calculang sysem fnancng: a cell-based acuaral mode desgned o replcae he resuls from he Socal Secury Admnsraon s acuares and a fully mcrosmulaon-based mode smlar o ha ulzed by he Congressonal Budge Offce. The resuls repored below were produced usng SSASIM s cell-based mode, hough smulaons usng he mcrosmulaon-based mode produce qualavely smlar resuls. I should be noed, however, ha resuls from he SSASIM model do no consue offcal fndngs from he Socal Secury Admnsraon s acuares and offcal esmaes may dffer. A. SSASIM Performance Relave o SSA Esmaes The Socal Secury Trusees repor resuls from sensvy analyses conduced on a number of demographc and economc facors. These facors are shfed by a pre-se amoun Table 3: Socal Secury Trusees Sensvy Analyss of Real Wage rowh on 75-year Acuaral Balance Assumed ulmae rae of real wage growh Percen of axable payroll 1.1 percen 1.6 percen Summarzed ncome rae Summarzed cos rae Acuaral balance Source: 25 Socal Secury Trusees Repor, Table VI.D.4 from her md-pon projecons o examne how ncreasng or reducng her values affecs sysem fnancng over 75 years. Table 3 repors he Trusees fndngs on he sensvy of he acuaral balance wh respec o wage growh: Increasng he ulmae rae of real wage growh from 1.1 percen o 1.6 percen ncreases he 75-year acuaral balance by.53 percen of payroll. As expeced, sysem solvency 25 For deals, see Holmer (25); 33