Working paper SUSTAINABILITY OF PENSION SCHEMES: BUILDING A SMOOTH AUTOMATIC BALANCE MECHANISM WITH AN APPLICATION TO THE US SOCIAL SECURITY

Transcription

1 206-6 Workng paper SUSINILIY OF PENSION SCHEMES: UILDING SMOOH UOMIC LNCE MECHNISM WIH N PPLICION O HE US SOCIL SECURIY Frédérc GNNON Unversy of Le Havre EDEHN Florence LEGROS ICN usness School & U Pars Dauphne Vncen OUZÉ OFCE Scences Po May 206

2 SUSINILIY OF PENSION SCHEMES: UILDING SMOOH UOMIC LNCE MECHNISM WIH N PPLICION O HE US SOCIL SECURIY Frédérc Gannon (U Le Havre) Florence Legros (U Pars Dauphne & ICN usness School) Vncen ouzé (Scences Po, OFCE) May 206 SRC We buld a "smooh" auomac balance mechansm (S M) whch would resul from an opmal radeoff beween ncreasng he receps and reducng he penson expendures he S-M obans from mnmzng an neremporal dscouned quadrac loss funcon under an neremporal budge balance consran he man advanage of our model of "opmal" adjusmen s s ably o analyse varous confguraons n erms of auomac balance mechansms (M) by conrollng he adjusmen pace hs S-M perms o denfy wo lm cases: he fla Swedsh-ype M and he fscal-clff US- ype M hese cases are obaned by assumng very hgh adjusmen coss on revenue (mplyng only penson benef adjusmen) and by choosng parcular sequences of publc dscoun raes We hen apply hs M o he case of he Uned Saes Socal Secury o evaluae he adjusmens necessary o ensure fnancal solvency hese assessmens are made under varous assumpons abou forecas me horzon, publc dscoun facor and weghng of socal coss assocaed wh ncreased receps or lower expendures Keywords: Penson scheme susanably, auomac balance mechansms, dynamc programmng JEL codes: C6, H55, H68 prevous frs verson of hs arcle was crculaed as an unpublshed paper enled "uomac djusmen Mechansms and udge alancng of Penson Schemes" (Workng Paper OFCE, December 204) We hank parcpans o h Inernaonal Workshop on Penson, Insurance and Savng (U Pars Dauphne, June 203, France), Penson enef and Socal Secury Colloquum (Inernaonal cuaral ssocaon, July 203, Lyon, France), 25h Vlla Mondragone Conference (Rome, July 203, Ialy), Inernaonal workshop on geng, Economc Uncerany, Savngs and Long-run Governance of Penson Schemes (U Le Havre, prl 205, France), Populaon gng: New Challenges for Publc Polcy Conference (Cenral Unversy of Economcs and Fnance, ejng, November 205, Chna), and 7h Inernaonal Conference on Mahemacal and Sascal Mehods for cuaral Scences and Fnance (U Pars Dauphne, March prl 206, France)

3 INRODUCION Mos governmens are relucan o reform naonal penson sysems for fear hs mgh nduce a oo hgh polcal cos In fac, he polcal debae abou he penson ssue may ofen be a source of conflcs (lanche and Legros, 2002; Marer, 2008; Weaver and Wllén, 204; Wsensale, 203) s a consequence, governemens end o procrasnae and o pospone he adopon of measures ha would guaranee solvency Of course, faced wh he nsolvency of her penson sysems, all governmens have nroduced reforms - some of hem drasc - bu whou mposng resorng forces he problem wh ad hoc reforms s ha, quong urner (2009), "(hey) have a hgh degree of polcal rsk because her mng and magnude are unknown" o avod penson sysems o depend upon choces ha polcans would no ake wllngly, governmens can nroduce specfc and mandaory rules o allow for auomac adjusmen mechansms (Ms) hese Ms conrbue o mprove solvency a any dae whou polcans seppng n, hus avodng he "need for large program changes made n crss mode" (urner, 2009) Implemenng Ms requres no only sraghforward and clear choces abou ransfers beween generaons, bu also srong socal accepance uomac alance Mechansms (Ms) may be vewed as sronger and effcen Ms securng longrun solvency Several counres (Sweden, Canada, Germany, Japan and Fnland) have adoped dfferen forms of M (Vdal-Melá e al, 2009 ; oado-penas e al, 200) In hs paper, we develop a general form of uomac alance Mechansm based on he neremporal mnmzaon of a dscouned quadrac loss funcon uldng an M requres defnng a measure of he neremporal budge balance, o fx he me horzon and o adop a crera o be opmzed Our "smooh" M (hereafer denoed S-M) reles on he use of dsoron ndces, whch makes easy o be mplemened n a realsc and praccal 2

4 prospec Smooh, gradual adjusmens replace mmedae and abrup changes, enhancng her shor-erm polcal accepance he paper organzes as follows Frs, we address he ssue of Ms: wha par do hey play n adjusng, sablzng and balancng? Second, we buld a "smooh" M, assumng a rade-off beween presen and fuure receps and expendures hrd, we apply hs M o he US Socal Secury he las secon concludes UOMIC RULES: DJUSING, SILIZING ND LNCING he Ineremporal Penson udge Consran he curren perod ( 0 ), he forecas expendures and receps a me are respecvely denoed and ssumng neglgble admnsrave coss, can be compued as follows: E0 p j, () j Ω R where R Ω s he se of rerees for perod and p, s he penson pad o each reree j j s gven by: E0w wk, (2) k Ω E where Ω s he se of employees a perod, E w, s he annual sum of monhly axable k wages pad o each employee k and τ s he payroll ax rae for perod he neremporal budge balance of he penson sysem wres: R F + + F (3) where R + r s he rskless neres facor wh r he neres rae and F he forecas 3

5 value of he fnancal asse (reserve fund) for perod Wha abou solvency? From an accounng pon of vew, he mplc lables and solvency of unfunded penson sysems can be esmaed hrough dfferen mehods In pracce, wo measures of solvency are generally used he frs s an evaluaon of he dscouned sum of receps and expendures hs valuaon approach s adoped n he Uned Saes o assess he presen value of he sysem s underfundng hs value, called "Unfunded Oblgaon", gves a fnancal (absolue) esmaon of he ax gap he US Socal Secury dmnsraon defnes as: "he excess of he presen value of he projeced cos of he program hrough a specfed dae over he sum of: () he value of rus fund reserves a he begnnng of he valuaon perod; and (2) he presen value of he projeced non-neres ncome of he program hrough a specfed dae, assumng scheduled ax raes and benef levels" he curren perod 0, he Unfunded Oblgaons compue as follows: 0 UO F ΠR Π R F (4) Sweden has oped for anoher mehod: he asse-lably approach (Seergren, 200) I defnes s penson plan as solven when: Presen value of conrbuons payable by curren workers + Value of he reserve fund Value of penson commmens owards curren generaons Hence, he Swedsh balance rao wres as an asse/lably rao Solvency ssues have been nvesgaed by Vdal-Melá and oado-penas (200) hey specfy he connecon beween he conrbuon asse and he hdden asse (smlar o he 4

6 equvalen conceps of "mplc ax on pensons" or "PYG asse" used n he leraure) o evaluae wheher usng eher of hese o comple he acuaral balance n PYG penson sysems would provde a relable solvency ndcaor he conrbuon asse can be nerpreed as he maxmum level of lables ha can be fnanced by he exsng conrbuon rae whou perodc supplemens from he sponsor, ceers parbus he ax gap rao denoed G s anoher neresng concep and a smple measure of penson scheme s nsolvency hs rao can be measured n wo ways: or G G 0 Π0R Π0R 0 F 0 Π0R + F0 Π R (5a) (5b) G measures he excess of ne-of-reserve expendures wh respec o receps measures he excess o expendures wh respec o ne-of-reserve receps hese raos can be nerpreed as mplc deb/noonal asse raos G n neresng llusraon of wo polar balancng adjusmens can be compued from hese ax gap raos: a full adjusmen operaed eher hrough receps by ndexng payroll ax on G or hrough expendures by ndexng penson amoun on G pplyng hese conceps o he US Socal Secury, Kolkoff (20) sresses ha: "Snce he sysem s $6 rllon nfne horzon fscal gap s 33 percen of he $483 rllon presen value of s axable wage base, he sysem s 27 percen ( /024) underfunded; ha s, we could mmedaely and permanenly rase he FIC conrbuon rae by 27 percen and make Socal Secury solven" or "noher way s o cu Socal Secury benefs mmedaely and 5

7 permanenly by 20 percen" 2 How he sandard uomac djusmen Mechansms (Ms) conrbue o sablzng penson schemes he general problem facng socal planners or governmens s how o adjus parameers (payroll ax rae, reremen age, penson benef calculus, penson ndex, ec) wh me dopng auomac adjusmen rules mples choosng a law of moon for parameers as a funcon of economc, fnancal or demographc varables Wh he uomac djusmen Mechansms (Ms), he nsuonal parameers are adjused accordng o predefned rules Oherwse, he changes are consdered as dscreonary decsons and are lkely o depend on he hazards of polcal choces Choosng a specfc M requres he followng acons o be aken (see osworh and Weaver, 20): legmae he adjusmen rule (equy, socal jusce or solvency), sck o one ool - one objecve rule, choose he frequency of revew/assessmen, defne he elemens on whch he adjusmen s made and fx he degree of auomacy (up o whch level he adjusmen s mandaory -no quesonng-, whch warrans credbly o he process) o conrol for penson level, four man parameers are avalable : () enef ndex : he man objecve of he benef ndex s o preserve he level of penson purchasng power (2) Conrbuory perod: elgbly for full penson requres valdang a suffcen number of quarers he conrbuory perod can be conneced o lfe expecancy (3) Reremen age: wh a gven frequency, hs age could be revsed wh new nformaons abou each cohor s changes n lfe expecancy (4) Penson-earnngs lnks: ndex rule of pas conrbuons (defned conrbuon) or pas wages (defned benef), lnk beween he amoun of he penson (replacemen rae or accumulaed-conrbuons-o-ren coeffcen) and he lfe expecancy a he 6

8 reremen, ec bou he penson-earnngs lnks, can be esablshed accordng o wo approaches: defned conrbuon (DC) or defned benef (D) In a DC penson scheme, as n Sweden, he coeffcen of converson of capal no an annuy can depend on he age and brh year hs coeffcen can be revsed o reflec he evoluon of generaon moraly ables and lfe expecancy (Lfe Expecancy Index) In he case of D penson scheme (as n US, France or Germany), a replacemen rae s used o conver average lfe-cycle wage no a penson o conrol hs replacemen rae, he man adjusmen parameer s he number of years o valdae o be elgble for full penson (maxmal value of he replacemen rae) ddonally, he legslaor can reward (bonus) long career or penalze (malus) shor career he ndex used o o gve a curren value o he pas wages n a D penson scheme or he value of he noonal accouns n a DC penson scheme conrbues o he lnk beween wages and pensons ccordng o Seergren (200), ndexng noonal penson savngs on economc growh s sablzng, snce ( ) Pensons wll grow (declne) a he same pace as average earnngs he paramerc changes nduced by he Ms can be deermned eher ex ane or ex pos In he former case, demo-economc shocks are ancpaed and paramerc changes n law are planned For example, as early as 983, US governmen launched a clear-cu longrun ex ane adjusmen devce by progressvely ncreasng he payroll axes and rasng he full penson age hs reform prevened a pendng Socal Secury crss; moreover, sll poenally guaranees an neremporal balanced budge for abou half a cenury Neherheless, as sressed by aron (20), he weakness of hs reform s ha "vrually guaraneed he reurn of defcs and a fundng gap, and he need for furher legslaon o 7

9 close " In he laer case (ex pos adjusmens), he paramerc values se by naonal legslaon evolve wh he knowledge of he saes of naure Changes aler penson formula parameers and conrbuon rae Sweden s consdered as a major poneer n adopng auomac sablzng devces relyng on Noonal Defned Conrbuons (NDC) plans n owards sronger Ms: uomac alance Mechansms (Ms) Wha happens f he adjusmens brough by he sandard Ms do no lead o enough sably? One soluon could conss n adopng a clear oblgaon of fnancal susanably n a gven me horzon: hs s precsely wha uomac alance Mechansms (Ms) are devsed for he choce of an M rases four major quesons: - How penson budge balance s defned 2? - Wha are he crera for choosng changes n curren penson law? - Wha room s lef for opmzaon? - Wha revsng frequency and wha plannng me horzon for full balancng? each perod of revson, he deal penson scheme s mng ough o be: schemes; - Frs sep (sandard Ms): seng he values of he penson parameers; - Second sep (neremporal susanably): checkng he solvency of he penson - hrd sep (M): rggerng adjusmens by reseng argeed parameers For example, o renforce he solvency robusness of s penson sysem, Sweden adoped an M n 200: a unform and permanen adjusmen of presen and fuure penson benefs gven he balance rao secures solvency (Seergren, 200) he reurn of he 2 For example, n Canada and Sweden, he M adopon "was preceded by explc legslave acons o creae an nal reference of fnancal susanably" (osworh and Weaver, 20) 8

10 "savngs" nvesed n he NDC crucally depends upon hs ndexaon (Seergren and uguslaw, 2005) Oher counres have followed Sweden and added specfc ndexaon of pensons o srenghen solvency hs s he case of Japan and Germany (Sakamoo, 203) However, we noe ha Canada has oped for a more bndng M wh a genune search for a balanced budge (Ménard and llg, 203) Fgure US Socal Secury (OSDI): expeced adjusmens by a penson reducon conraro, n he US Socal Secury, here s no M However, has o be remnded ha he US Socal Secury rus funds are no allowed o borrow hs fnancal and legal consran s a srong ncenve o plan surpluses o compensae ancpaed defcs, acng as a credble resorng force 3 he 75-year annual forecas of oard of rusees (205) 3 oard of rusees (203) explans ha: "Mananng a reasonable conngency reserve s mporan because he rus funds do no have borrowng auhory fer reserves are depleed, he rus funds would be unable o pay benefs n full on a mely bass f annual revenue were less han annual cos Unexpeced evens, such as severe economc recessons or large changes n oher rends, can quckly deplee reserves In such cases, a reasonable conngency reserve can manan he ably o pay scheduled benefs whle gvng lawmakers me o address possble changes o he program" 9

11 allows a horough analyss of solvency Noably, gves an esmaon of he year when he sysem reaches bankrupcy: 2034 for he OSI rus fund and 206 for he DI rus fund fer hs crcal year, f no correcve governmenal measures have been aken, he so-called fscal clff adjusmen oblgaon o reduce pensons o acheve a fnancal balance beween penson paymens and socal conrbuons s auomac and brual Fgure compares hese wo conrasng balancng adjusmens based on he 75 years Socal Secury admnsraon forecas publshed n June 205: he unform Swedsh-ype adjusmen vs he fscal clff US-ype adjusmen hs fgure llusraes he dffculy for lawmakers o resore solvency Swedsh-ype adjusmen mples an mmedae and permanen 55% penson decrease whereas a srong procrasnaon resuls n a fscal clff adjusmen jump wh a 25% penson decrease n 2034 and a 35% decrease n 2089 None of hese wo poenal adjusmens s realsc boh from a socal and polcal pon of vew However, he perspecve of he fscal clff s a credble hrea o adop a progressve adjusmen Hence, he dea o devse a general framework for smooh auomac balance mechansms he same fgure presens a smulaon based on he model we develop hereafer hs smulaon s based on a sngle penson adjusmen hs resul obans from an neremporal radeoffs amng a smoohng he whole adjusmen process s a maer of fac, negrang a publc preference for he presen ends o reduce hgh nal adjusmens y supposng a 2% annual rae of publc preference for he presen, he adjusmen would requre a 67% nal declne n 205 and abou 266% reducon n he long run (2090) If adjusng only by reducng pensons seems oo rough, adjusng by ncreasng payroll axes should also be consdered 0

12 2 IN SERCH OF SMOOH M (S-M) 2 Mnmzng a dscouned quadarc loss funcon Le us urn now o he buldng of a smple model 4 based on neremporal opmzaon called smooh auomac balance mechansm (S-M) smlar approach appled o reremen has been adoped by erger and Lavgne (2007) However very neresng, her approach suffers from wo shorcomngs Frsly, he adjusmen hey propose relaes solely o he conrbuon rae Secondly, he socal cos s measured by he square of he change n each perod and here s no me preference, whch dscards he possbly o monor he adjusmen lag Godnez-Olvares e al (205) enrch he approach of erger and Lavgne (2007) by proposng o esmae an M whch s based on hree parameers: he conrbuon rae, he replacemen rae and he duraon of acvy Inserng he duraon of acvy s neresng However, could be easer, nsead, o adjus wh a sandard M ha would smply seek o sasfy an objecve of acuaral farness (for example, a machng of reremen and acvy duraons) In our approach, he M s he ulmae M In conras, he dynamc opmzaon problem we ackle conemplaes wo adjusmen modes, respecvely hrough coss and/or hrough receps by usng a conngen penson ndexaon (on behalf of solvency) and a possble adjusmen of he conrbuon rae Moreover, accouns for me preference whch perms o desgn he pace of adjusmen and o conrol he magnude of he nal correcon he objecve funcon s defned as a quadrac loss funcon Quadrac cos funcons are commonly used n he analyss of moneary polcy (Svensson, 2003) hs analycal approach expresses n a sraghforward and smple way he dea of "smoohng ou" he 4 n applcaon of our model o he French PYG sysem s gven n Gannon e al (204)

13 changes n he curren legslaon For sake of smplcy, we presen a non sochasc approach of our M Our compuaons are based upon gven forecas values of receps ( ) and expendures ( ) lso, as he frs order condons are lnear, he esmaed adjusmen varables could be consdered as forecas values for he curren perod In pracce, hese varables should be revsed as he observed values and forecass would adjus wh me he forecas uncerany could be consdered by usng sochasc smulaons For example, Fujsawa and L (202) examne how he Japanses auomac balancng mechansm wll affec he ncome of he exreme elderly (people who lve beyond 00) he value of he loss assocaed o each perod s measured by: LF 2 2 ( ) + ( α ) ( ) ) α (6) where and are wo deformaon coeffcens modfyng respecvely he presen and fuure payroll ax raes (receps) and penson benefs (expendures) relavely o hose esablshed by he curren penson law Noe ha he coeffcen can be nerpreed as a penson ndex whch s, de faco, a componen of he penson rule α (respecvely α ) s he socal wegh gven o he adjusmen hrough receps (respecvely expendures) 5 ( ) and ( ) measure he relave gap wh respec o he curren legslaon hs loss funcon capures he fac ha changng parameers s cosly (boh socally and polcally) and ha, by mnmzng, he socal planner seeks o lm he amplude of changes o acheve hs goal, he socal planner ses a me horzon o mach dscouned receps wh dscouned expendures: F0 (7) Π R Π R 5 For sake of smplfcaon, hs parameer s denoed dencally as he adjusmen degree by penson 2

14 3 he opmzng program s based on a sum of dscouned losses durng perods: { } ( ) 7 s mn ) LF δ (8) where δ, assumed here -for sake of smplcy- o be consan, s he publc rae of me preference he advanage of our approach s ha only requres a publc choce of hree parameers (δ,α and ) and a long-erm forecas of expendures and receps he frs order condons are: ( ) ( ) ( ) 2 : 2 : Π Π R R ψ α δ ψ α δ (9) where he Lagrange mulpler ψ measures he socal value of he margnal slackng of he budge consran he problem s well behaved and he second order condons are checked by src quas-concavy Proposon: smooh-m can be mplemened by applyng he wo followng rules: () Esmaon of he expeced fnal adjusmen arge a me 0 : ( ) ( ) ) / Π Π R R UO α α δ α α (0) () Convergence rule o he expeced fnal adjusmen arge: ( ) ( ) ( ) ( ) ( ) ( ) Π Π R R δ δ ()

15 Proof: see appendx Our model gves a emporal key o fnance he unfunded oblgaon UO 0 From hese adjusmen processes, we deduce he forecas dynamcs of he reserve funds: F (2) R F he expeced revson of he curren levels of receps and expendures evolves approxmaely as follows wh a backward represenaon: ( ) ( ) ( ) ( ) δ δ ( r δ ) ( r δ ) (3) where g and g are respecvely he expeced receps and expendures growh raes We presen here expeced soluons In a sochasc verson, he adjusmen would nclude he revson of he expeced fnal adjusmen arge hs adjusmen rule s characerzed by he followng proprey: when > and <, hen >, e a payroll ax ncreasng, (resp <, e a penson ndex decreasng) f receps (resp expendures) growh rae s greaer han he neres rae ne of he presen preference he ncrease n he conrbuon rae (resp lower penson) s even sronger han revenue growh (resp spendng) s srong hs maxmzng problem may be compleed by addng consrans o he reserve fund level ( F > 0, for a ermnal consran or F 0 oherwse) or o he adjusmen of he conrbuon rae ( τ τ max as for example n Germany) hs S-M s ressan o me nconssency problem of choce whenever he applcaon of he adjusmen rules s mandaory In hs case, he adjusmens always apply 4

16 22 Inerpreaons In addon o denfy rules of penson ndexng and ax rae ncrease, our resuls can be nerpreed n wo oher ways: () Measurng and would allow o show how much he penson schemes are unbalanced n he long run; () Revealed preferences: reforms mply changes n legslaon he levels of expendures and receps are modfed wh respec o a prevous scenaro whou reform ssumng and o be measured wh accuracy would assocae publc decsons wh an mplc funcon of publc preferences For example, assumng ha he measure of fnancal susanably we use here s que equvalen o he asse/lably rao, hen he fla Swedsh-ype adjusmen can be nerpreed as he resul of he followng parameer choces: d (no adjusmen hrough receps) g r g (fla adjusmen) (4) hese values of parameers mply: < (5) bou he fscal clff US-ype adjusmen, he mplc values of δ sasfy : δ + for < 2034, + δ ( + r ) for 2034, + and α 2 5

17 hese values of parameers mply: for < 2034 < for 2034 Fgure 2 gves he me evoluon of he mplc values of he me prefence rae necessary and suffcen o oban a Swedsh fla adjusmen or a US fscal clff adjusmen hese values are compued wh forecas daa from he oard of rusees of he US federal OSDI (205) Fgure 2 Implc publc me preference rae 6

18 3 PPLYING HE S-M O HE US SOCIL SECURIY 3 Sensvy analyss s menoned earler, he oard of rusees of he US federal OSDI rus funds (205) publshes annual forecass wh a 75-year horzon, conemplang hree scenaros: pessmsc ( hgh-cos ), opmsc ( low-cos ) and mddle ( nermedae ) hs publcaon plays an mporan par o conrbue o he publc debae, by gvng a clear dea of he lkely survval duraon of he penson sysem In hs secon, we look a wha he use of M requres n erms of ncreased revenues and spendng cus In our compuaons, we rely on he forecas based upon he nermedae scenaro We consder several paramerc varans n, respecvely, forecas horzon, me preference, wegh of socal adjusmen hrough receps (versus expendures) Fgures 3, 4 and 5 respecvely show paramerc varans Fgure 3 Sensvy o socal weghng (α ) Fgure 3 shows he profle of and for varans n he socal wegh (gven 7

19 respecvely o receps and expendures) wh δ 0025 and 75 Choosng α s a crucal polcal decson because deermnes he share of he fscal burden beween employees and pensoners No surprsngly, he adjusmen hrough expendures s more demandng for hgh values of α Conversely, he adjusmen hrough receps s more demandng for low values of α For example, f α ends o 0, and end o, whle ends o and o 32 ha means a 0% ncrease n ax rae n he shor run ( ) and a 32% ncrease n he long run ( 75) In conras, f α ends o, and end o whle ends o 0933 and o 0734 ha means a 67% decrease n pensons n he shor run ( ) and a 266% decrease n he long run ( 75) hs case s llusraed by Fg Fgure 4a Sensvy o me preference (δ ) 8

20 Fgure 4b Sensvy o me preference: me lag (number of years) - or procrasnaon duraon - before a sgnfcan adjusmen ( ) Varaons n me preference (δ ) clearly show he consequences of posponng adjusmen mechansms (fgure 4a) Delayng adjusmen nduces very hgh adjusmen coss n he fuure he gap beween shor-run and long-run adjusmen ( or ) ncreases exponenally wh δ For example, f δ > 0%, he gap exceeds 70% for and 50% for Conversely, f δ < 2%, he gap s less han 5% for and 8% for Noe ha for weak δ ( < 075% ), adjusmen s sronger n he shor run han n he long run hs coeffcen nduces procrasnaon snce s a componen of adjusmen of he growh rae Indeed, when hs coeffcen becomes suffcenly hgh, akes several years before sgnfcan adjusmens s an llusraon (Fgs 4b and 4c), values of δ greaer han 85% requre more han en years for adjusmens hrough and above 05% as compared o weny, weny-fve and hry years for adjusmens above, 2 and 3%, respecvely 9

21 Fgure 4c Sensvy o me preference: me lag (number of years) - or procrasnaon duraon - before a sgnfcan adjusmen ( ) Fgure 5 Sensvy o me horzon ( ) 20

22 he US penson sysem performs surpluses unl 2032 (nermedae scenaro forecasng) ferward, he US governmen wll be forced o reform (ax ncrease or decrease n pensons) he longer he me horzon, he more he planner negraes mbalance hs means he adjusmens are very sensve o me horzon For a 25-year me horzon, he presen value of he unfunded fracon of he lables s low I ncreases wh he forecas horzon Increasng has wo cumulaed effecs (fgure 5): - akng no accoun a larger perod of defc ( and are larger); - dscounng more he value of he las perod ( and are larger) 32 Global analyss of a benchmark se of parameers For he followng se of parameers, α 05, δ 25% and 75, we compue he evoluon of he adjusmen coeffcens Fgure 6 uomac adjusmens and reserve fund 2

23 Fgure 7 Generaonal mpac per age he M mples an mmedae adjusmen conssng n a 4% ncrease n ax rae and a 4% decrease n penson he adjusmen gradually seles n and fnally reaches a 2% ncrease n ax rae and a 6% decrease n penson Fgure 6 represens he relave evoluon of payroll ax rae and pensons and he amoun of he reserve fund n he case where he parameers are he followng: α 05 δ 25% 75 (6) Low values of δ reduce procrasnaon hs resuls n an mmedae adjusmen hrough boh and by 4%: conrbuons ncrease by 4% whle pensons decrease by 4% In he long run, here s a connuous ncrease n ax rae and a connuous decrease n pensons over he whole 75-year perod he end of hs perod, ax has ncreased by 0% 22

24 and he pensons have decreased by 6% Durng he frs par of he perod, he adjusmen generaes a surplus hen, he reserve fund ncreases and reaches s maxmum n 2060 when he penson scheme becomes unbalanced From hs perod on, he reserve fund s used n order o fnance pensons and decreases unl he end of he perod he fund s depleed n 2085 Fgure 7 provdes he correspondng nergeneraonal analyss he upper par of he char represens he ncrease n conrbuons for varous generaons Of course, he older he generaon, he shorer he perod of conrbuons rsng In oher words, he generaon born n 950 (G950) suffers a shor perod of ncreased conrbuons (afer age 60) whle he younges one born n 990 (G990) suffers an ncrease n s conrbuons over s whole workng perod Fgure 8 djusmen prmary balance ($llon, presen value) 23

25 Fgure 9 Reserve fund ($llon, presen value) In conras, all generaons are affeced by a decrease n her pensons In erms of penson yelds, hs means he oldes generaon wll have a hgher reurn from s penson scheme han he younges one We also observe ha he reserve fund beng depleed a he end of he smulaon perod (fgures 8 and 9), oher adjusmens wll have o be made ha wll undoubedly decrease he younger generaons penson yelds CONCLUSION hs arcle has denfed dfferen ypes of M ha can be mplemened and has shown how hey conrbue o a beer solvency Sweden s he only counry ha srenghens s Ms wh an M ha ensures fnancal sably Smlarly, we propose o buld an M sarng from a dynamc opmzaon seng For a gven plannng horzon, we oban formulas ha deermne how receps and expendures mus be adjused a each perod ha 24

26 allows o consder he M chosen by Sweden as a specal case Indeed, he fla Swedshype M or fscal-clff US-ype M can be obaned by assumng very hgh adjusmen coss on revenue (mplyng only penson benef adjusmen) and choosng parcular sequences of publc dscoun raes We apply hese formulas o he fnancal balances of he US Socal Secury (OSDI program) Usng dynamc opmzaon avods brual adjusmens and hus moderaes or smoohs ou he margnal adjusmens necessary for fnancal sably he balancng adjusmen should resul n ncremenal changes Indeed, sandard Ms are hoped o lead o suffcen adjusmens and o conrbue o a beer fnancal balance he M s an ulmae safeguard seng ha should be expeced o be margnal when he oher parameers are well calbraed oo large adjusmens sugges ha a fondamenal reform should recalbrae all parameers and nclude sgnfcan and effcen Ms We suppose a fxed publc dscoun facor s regards he choce of dscoun rae, here arses an ehcal problem of dcaorshp of he presen or he fuure (Chchlnsky, 996 and 997) Fuure consderaons could be gven o adop a hgh nal dscoun ha would be gradually reduced Such choce should perm o reduce srongly he nal adjusmens and o oban laer a convergence o a fla adjusmen scheme Hence, low nal adjusmens would make he adopon of M more polcally accepable whereas he convergence o a fla adjusmen should be less cosly n erms of ner-generaonal equy n he long run REFERENCES aron, Henry J 20 Socal Secury Reconsdered Naonal ax Journal 64 (2, Par ): erger, Charle, and nne Lavgne 2007 model of he French penson reserve fund: wha could be he opmal conrbuon pah rae? Journal of Pensons Economcs and Fnance 6 (3): lanche, Dder, and Florence Legros 2002 France: he Dffcul Pah o consensual 25

27 Reforms" In Socal Secury Penson Reform n Europe, ed M Feldsen and H Seber Unversy of Chcago Press oado-penas, Mara del Carmen, Carlos Vdal-Melá, and Junch Sakamoo 200 Models of he cuaral alance of he Pay-s-You-Go Penson Sysem Revew and some Polcy Recommendaons Mmeo oard of rusees 203 he 203 nnual Repor Federal Old-ge and Survvors Insurance and Federal Dsably Insurance rus Funds oard of rusees 205 he 205 nnual Repor Federal Old-ge and Survvors Insurance and Federal Dsably Insurance rus Funds osworh arry, and Ken Weaver 20 Socal Secury on uo-plo: Inernaonal Experence Wh uomac Mechansms Workng Paper 20-8 Cener for Reremen Research (oson College) Caprea, James C 2006 uldng uomac Solvency no US Socal Secury: Insghs from Sweden and Germany Polcy bref rookng Insuons, n 5 Chchlnsky, Gracella 996 n xomac pproach o Susanable Developmen Socal Choce and Welfare 3 (2): Chchlnsky, Gracella 997 Wha s Susanable Developmen Land Economcs 73(4): Fujsawa, Yosuke, and Johnny Su-Hang L 202 he Impac of he uomac alancng Mechansm for he Publc Penson n Japan on he Exreme Elderly Norh mercan cuaral Journal 6 (2): Gannon, Frédérc, Séphane Hamayon, Florence Legros, and Vncen ouzé 204 Susanably of he French frs pllar penson scheme (CNV): ssessng auomac balance mechansms usralan Journal of cuaral Pracce (2): Godínez-Olvares, Humbero, Mara del Carmen oado-penas, and hanasos Panelous 206 How o Fnance Pensons: Opmal Sraeges for Pay-as-You-Go Penson Sysems Journal of Forecasng 35(): 3 33 Kolkoff, Laurence J 20 Fxng Socal Secury Wha would smark do? Naonal ax Journal 64(2, Par ): Marer, Park 2008 Penson Polcs: Consensus and Socal Conflc n geng Socees Rouledge Ménard, Jean-Claude, and ssa llg 203 Inergeneraonal alance of he Canadan Reremen Income Sysem Repor prepared for he Inernaonal Socal Secury ssocaon echncal Semnar on "Proacve and Prevenve pproaches n Socal Secury - Supporng Susanably", Offce of he Supernenden of Fnancal Insuons (Canada) Sakamoo, Junch 203 uomac alancng Mechansms PSS colloquum n 26

28 Lyon June Seergren, Ole 200 he uomac alance Mechansm of he Swedsh Penson Sysem Workng Paper Naonal Socal Insurance oard Seergren, Ole, and oguslaw D Mkula 2005 he rae of reurn of pay-as-you-go penson sysems: a more exac consumpon-loan model of neres Journal of Penson Economcs and Fnance 4 (2): 5 38 Svensson, Lars EO 2003 he Inflaon Forecas and he Loss Funcon In Cenral ankng, Moneary heory and Pracce: Essays n Honour of Charles Goodhar (P Mzen, Ed), vol I Edward Elgar urner, John 2009 Socal secury fnancng: uomac adjusmens o resore solvency RP Publc polcy nsue Research repor February Vdal-Melá, Carlos, and Mara del Carmen oado-penas 200 Noes on Usng he Hdden sse or Conrbuon sse o Comple he cuaral alance for Pay-s-You-Go Penson Sysems Mmeo 27 pages Vdal-Melá, Carlos, Mara del Carmen oado-penas, and Ole Seergren 2009 uomac alance Mechansms n Pay-s-You-Go Penson Sysems Geneva Papers on Rsk and Insurance - Issues and Pracce 34(2), Weaver, Ken, and lexander Wllén 204 he Swedsh penson sysem afer weny years: Md-course correcons and lessons OECD Journal on udgeng 3(3), -26 Wsensale, Seven K 203 usery vs Soldary: Inergeneraonal Conflc n he European Unon Inernaonal Journal of Humanes and Socal Scence 3 (),

29 28 PPENDIX he wo FOC express a radeoff beween ncreasng he socal cos of adjusmen and reducng he defc each perod, for a loss level gven, he radeoff beween and mples o he followng Margnal Subsuon Rae (MRS): ( ) ( ) ( ) / / gven Loss L L α α () y comparason, he slde of he budge consran for F and + F gven s such ha:, gven onsran udge c (2) where s he balance rao In case of problem of global nsolvency, n general hs rao s always greaer han he opmum, he angency of he wo curves mples: ( ) ( ) ( ) α α (3) From he FOC, we deduce ha: ( ) ( ) ( ) ( ) ) ( ) ( Π Π R R δ α α δ (4) y ncorporang hese wo expressons n he neremporal budge consran, we fnd he forecas fnal adjusmen: ( ) ( ) ( ) / ) ( Π Π R R UO α α δ α α (2)