Automtic djustment mechnisms nd budget blncing of pension schemes Frédéric Gnnon (U. Le Hvre) Florence Legros (U. Duphine) Vincent Touzé (Sciences Po - OFCE) Februry 23 Very preliminry version - Comments welcome Abstrct This rticle is dedicted to the study of the Automtic Adjustment Mechnims (AAM) used in some pension systems. The objective of the pper is twofold. First, we identify different types of utomtic djustment rules dopted (or which could be dopted) by the min developed countries nd we show how these djustments contribute to better solvency. Unfortuntely, these djustments re not suffi cient to gurntee n intertemporl blnced budget. Tht leds us to discuss the opportunity to use Automtic Blnce Mechnisms (ABM). Second, we build n exmple of ABM which would result from n optiml trdeoff between incresing the receipts nd reducing the expenditures. The ABMs obtin from the minimizing of cost function nd ensure n intertemporl budgetry blnce. We then pply this rule to Americn nd French cses to evlute the djustments necessry to ensure the finncil solvency. These ssessments re conducted under different ssumptions on forecst time horizon, time preference nd weighting of socil costs ssocited with incresed revenue or lower expenditure. Introduction In generl, governments re reluctnt to reform pension systems becuse they fer tht the reforms might induce too high politicl costs. As consequence, they tend to procrstinte nd to postpone the doption of mesures tht
would gurntee solvency. Of course, fced with the emergency of the insolvency of their pension systems, ll governments hve conducted reforms - some of them very deep - but without setting restoring forces. The problem with d hoc reforms is tht, to quote Turner (29), "(they) hve high degree of politicl risk becuse their timing nd mgnitude re unknown". To void tht the future sttes of the pension system depend on choices tht politicins would not tke willingly, two types of strtegies re used by governments: first, delegte the mngement of the pension systems to competent independent uthorities. Second, introduce new rules to llow for utomtic djustment mechnisms (AAM). These AAM would gurntee the solvency of the system t ny dte without needing politicl intervention nd eliminting the "need for lrge progrm chnges mde in crisis mode" (Turner, 29). This mens strightforwrd nd cler choices bout trnsfers between genertions nd strong underlying socil cceptnce. To void regulr nd politiclly costly d hoc reforms, Sweden hs first dopted Notionl Defined Contributions (NDC) plns in 994. Then, to reinforce the robustness of the system, it hs lunched n Automtic Blnce Mechnism (ABM) tht relies on the key rule tht every yer, the solvency of the pension system must be checked, thnks to the flexibility of the present nd future pension benefits (Settergren, 2). The return of the "svings" invested in the NDC crucilly depends on this indextion. In 983, the U.S. government hs chosen rdicl long run reform (minly by incresing the pyroll txes nd rising the full pension ge) which potentilly gurntees n intertemporl blnced budget for bout hlf century. Debt emission is not llowed for the U.S. Socil Security. This constrint plys the role of strong restoring force, since it forces to pln surpluses to compenste nticipted deficits. In Frnce, the politicl debte bout pensions issue is often source of conflicts (Blnchet nd Legros, 22). Importnt reforms hve been dopted in 993, 23 nd 27. To pcify the debte, n uthority composed of experts nd socil prtners (Conseil d orienttion des retrites) ws creted in 2. Its function is only dvisory but its lrge freedom of investigtion long with its published studies, llows it to contribute to better litercy nd socil consensus, which cn fcilitte the politicl decisions nd reduce the populist tempttions. Let us turn now to the relted literture on utomtic djustment mechnisms. Turner (29) defines the concept of utomtic djustments nd give some exmples of its pplictions to twelve high-income countries, ctegorized in five groups. First, countries with trditionl py-s-you-go (PAYG) systems with life expectncy indexing (LEI) of pension benefits: Portugl, Finlnd, Norwy. Second, countries tht hve systems with both NDC nd 2
LEI of benefits: Itly nd Polnd. Third, countries using LEI of the erliest ge t which socil security benefits cn be received: United Kingdom, Denmrk. Fourth, countries with AAM tht re tied to solvency: Sweden, Germny, Jpn, Cnd. Fifth, countries tht utomticlly djust other prmeters of their socil security systems, such s the yers of contributions required for full benefit: Frnce. Bosworth nd Wever (2) focus on the socil security utopilot by nlyzing the contrsted cses of AAM in Cnd, Sweden, Germny nd Itly, to ssess their possible implementtion in the U.S. They recll tht if semi-utomtic stbilizing mechnisms hve been used in the U.S. for the lst forty yers, true utomtic stbilizing mechnisms (ASM) re more recent. Shoyen nd Stmti (2) concentrte on the peculir role of utopilot in the NDC with n ppliction to Sweden nd Itly. Solvency issues hve been investigted by Vidl-Meli nd Bodo-Pens (2). They precise the connection between the contribution sset nd the hidden sset (similr to the equivlent concepts of "hidden tx", "implicit tx on pensions" or "PAYG sset" used in the literture) to evlute whether using either of these to compile the cturil blnce in PAYG pension systems would provide relible solvency indictor. The contribution sset cn be interpreted s the mximum level of libilities tht cn be finnced by the existing contribution rte without periodic supplements from the sponsor, ceteris pribus. The hidden sset is the present expected vlue of the hidden - or implicit - txes tht the system will pply to its prticipnts in the future, defined s contributions in excess of those tht would be needed by cpitlized system to py the sme benefits. The uthors scrutinize the Swedish "cturil blnce" to identify the elements chrcterizing these two concepts. They find tht only the contribution sset is pplied. Tht leds them to qulify the hidden sset s only theoreticl device, minly becuse its computtion requires projections of economic, demogrphic nd finncil vribles. However, interestingly enough, the U.S. dministrtion defines the hidden sset used to ssess the cturil blnce s the system s "unfunded obligtion" with perpetul horizon, or, explicitly, "the present vlue of future benefits less future contributions for current nd future prticipnts, considering tht the reserve fund dry nd tht legisltion is constnt". Cprett (26) considers the exmples of Sweden nd Germny to ddress the issue of utomtic solvency of U.S. socil security. He stresses tht, lthough correcting for longer life spns helps stbilize costs, it is not Bord of Trustees, Federl Old-Age nd Survivors nd Disbility Insurnce Trust Funds (BOT), 29, 28 Annul Report 3
suffi cient to ssure solvency t fixed contribution rte, s fertility nd popultion growth, lbor force prticiption ptterns, nd productivity growth ll ply importnt roles in long term py-s-you-go finncing. As result, Sweden dopted n ABM, wheres Germny links nnul pension indexing to chnges in the rtio of pensioners to workers supporting the system, the so-clled "sustinbility fctor". He reclls the suggestion by Steuerle nd Penner (25) to strt the process of utomtic djustments in the U.S. socil security by setting the norml retirement ge dministrtively, tking into ccount the increse of life expectncy, hence mimicking the Swedish NDC s nnuity divisor device. However, ccording to Cprett, it my be esier for the U.S. to dopt n djustment fctor similr to Germny s "sustinbility fctor". He insists tht Congress would be more likely to dopt mechnistic provision tht gurntees to future genertions of retirees the sme number of yers, on verge, in benefits s the current genertion - utomticlly. The im of this pper is to chrcterize the properties of the AAM nd to propose n ABM. Our nlysis shows how the AAM cn contribute to better solvency (ASM). We clrify the principle of Automtic Blnce Mechnism. Tht requires to define mesure of the intertemporl budget blnce (for exmple U.S. cturil blnce or Sweden blnce rtio) nd to fix the time horizon. First section defines the intertemporl pension budget constrint. The second section ddresses the issue of AAM: wht re their roles in djusting, stbilizing nd blncing? In the third section, we build "smooth" ABM, ssuming trde-off between present nd future receipts nd expenditures. The third section is dedicted to n ppliction of this ABM to U.S. Socil Security nd French defined benefit system (CNAV). The lst section concludes. 2 The intertemporl pension budget constrint The intertemporl budget blnce of the pension system writes: R F + τ w e N = p λ N + F () where R is the interest fctor, τ the contribution rte, F the vlue of the finncil sset (reserve fund) nd t ech ge, w is the verge wge, e the employment rte 2, N the size of popultion, p the verge pension nd 2 In prctice, e = ( u ) ( λ i ) where u is the rte of unemployment nd i the inctivity rte of pensioners. If we suppose rtioned job mrket by work demnd L, the unemployment rte is n djustment vrible: u = ( λ i) L L ( λ i ) L.In this cse, there is conflict ( trdeoff) between rte of retire- 4
λ the percentge of retired people. In prctice p nd d re influenced by the legisltion. We suppose tht these two prmeters nd τ cn be controlled by the socil plnner. The dynmics of the popultion is driven by simple eqution: where q is the survivl rte. We denote Γ the pyroll growth rte: Γ = λ d N N = q N (2) w e N w e N. w = the verge wge. p = is the verge pension. d = d N dependency rtio. ρ = p is the globl replcement rte. w The intertemporl blnce writes: R Γ f + τ = R Γ f + τ = R Γ f + τ = ρ d + f. w e N is e N λ N e N is the p λ N w + f e N p λ N w e + f (3) N Wht bout solvency (Bodo-Pens, Vidl-Meliá nd Skmoto, 2)? From n ccountncy point of view, there re different methods to estimte the implicit libilities nd the solvency of unfunded pension systems. In prctice, two mesures of solvency re used. The first is n ssessment of the discounted sum of revenues nd expenditures. This vlution pproch is used in the United Sttes to ssess the present vlue of the underfunding of the system. Sweden hs opted for nother method (Settergren, 2). It defines its pension pln is solvent when: Present vlue of contributions pyble by workers live tody + Vlue of the reserve fund = Vlue of pension commitments towrds genertions live tody. The generl problem of the socil plnner or the government is how to djust prmeters (τ, p, d ) with time. Adopting utomtic djusment rules mens tht lw of motion of prmeters s function of economic/demogrphic vribles is chosen. ment nd unemployment rte. 5
3 Automtic rules: djusting, stbilizing nd blncing 3. How the Automtic Adjustment Mechnisms (AAM) contribute to stbilize pension schemes 3.. Definition With the AAM, the institutionl prmeters re djusted ccording to the predefined rules. Otherwise, the chnges re considered s discretionry decisions. They re therefore subject to the hzrds of politicl choice. Choosing specific Automtic Adjustment Mechnism requires to define severl elements (see Bosworth nd Wever, 2): - Legitimting the rules ccording to the exmple "one objective, one tool." We need to identify objectives nd tools (prmeters). Min objectives concern equity, socil justice nd solvency. - Defining the frequency of review. - Choosing the elements tht will bse the djustment. - Setting djustments s ex nte bsed on expecttions (prediction-bsed) or ex post bsed on the sttes of nture. - Fixing the degree of utomticity (no questioning): the djustments re mndtory, which gurntees credibility of the process. Turner (29) shows how in prctice mny prmeters (pension, eligibility ge, etc) re indexed on chnges in the life expectncy, consumer price index or wge growth, etc. In generl, these djustments llow to reduce the gp between receipts nd expenditures, but there re not suffi cient enough to gurntee fully blnced budget. 3..2 Benefits index For ech retired people i, the pension benefit evolves ech yer s follows: p i = I p i where I is n indexing fctor. The min objective of the indexing fctor is to preserve the level of qulity of life. In generl, I corrects the increse in the cost of living nd permits to mintin the purchse power of the pension. In the pst (in some countries), I ws equl to the fctor of wge growth. In this cse, the indexing coeffi cient llows to mintin the reltive purchse power between workers nd pensioners. Generlly, indexing on the verge wge benefits to pensioners more thn indexing on the consumer price. Also, this indextion hs positive effect on the solvency becuse the gp between current wges nd pensions increses with time. However, the economic crisis my imply tht nominl wges growth be lower thn infltion. 6
3..3 Contributory period To obtin full pension requires to vlidte suffi cient number of qurters. The durtion of the ssessment period cn be connected to life expectncy. The underlying ide is to gurntee to ech genertion similr rtio: time to retire / time worked. In Frnce, the 23 lw induced n utomtic revision of the contributory period per genertion with respect to chnges in the life expectncy. 3..4 Retirement ge ("norml" or minimum) In mny countries, the reforms hve modified the lw reltive to the legl retirement ges. The minimum ge is the ge t which workers cn liquidte their pensions (for exmple, 6 y.o in Sweden). The norml retirement ge is the ge which serves s reference to define the full pension. Generlly, the djustment is not utomtic but plnned by the lw. In prctice, with given frequency, these ges could be revised w.r.t new informtions bout chnges in life expectncy for ech cohort. 3..5 Pension-ernings links In Sweden, the coeffi cient of conversion of cpitl into n nnuity depends on the ge nd the birth yer. This coeffi cient is revised to reflect the evolution of genertion mortlity tbles. In Frnce, the 993 reform plnned chnges in the pension-ernings links by incresing the reference period to compute the life cycle verge wge which is used in the first pillr pension scheme to determine the benefit. It is not n utomtic djustment but plnned one. This correction hs grdully reduced the pensions of the new genertions to retire, which could be interpreted s tking into ccount the increse in life expectncy t retirement. 3.2 Towrds Automtic Blnce Mechnisms (ABM) 3.2. Definition Wht hppens if AAM re not suffi ciently stbilizing? In 2, Sweden opted for type of ABM. The choice of n ABM rises four mjor issues: - How is defined the pension budget blnce? - Wht re the criteri for choosing chnges in current lw? - Wht room is left for optimiztion? 7
- Wht plnning time horizon for full blncing? The diffi culty is to define reference horizon nd the frequency of the utomtic djustments. As the AAM, the Automtic Blnce Mechnisms cn be determined: - Ex nte: shocks re nticipted nd chnges in lw re plnned. - Ex post: the lw evolves w.r.t to the knowledge of the sttes of nture. Chnges concern the pension formul prmeters nd the contribution rte. 3.2.2 One period horizon budget blnce: some simple exmples Cses where f = i.e. budget blnce t ech period: some simple exmples If d nd p re considered s fixed, then n utomtic djustment of the contribution rte gives: τ = ρ d. (4) If d nd τ re considered s fixed nd p = I I p with I the generl pension index nd I n index per ge, then n utomtic djustment of the pension index gives: I = τ w e N. (5) p λ I N U.S. Socil Security dopts this utomtic blncing if F =. If p nd τ re considered s fixed nd λ = ( ) γ mx λ where γ is coeffi cient of retirement dely, then n utomtic djustment by postponing retirement ges gives: τ w e N = ( ) p γ mx λ N α p mx λ N = p λ N τ w e N (6) γ = p λ N τ w e N p mx λ N If e = ( u ) ( λ i ), then τ w ( u ) ( λ i ) N = τ w ( u ) ( i ) N = 8 p λ N λ (p τ w ( u )) N
γ = λ p τ w ( u ) ( ) i λ N mx λ (7) (p τ w ( u )) N 3.2.3 T periods horizon Cses where f : the lterntives to utomtic djustment re more numerous nd it cn be interesting to pln the budget blnce on lrge number of periods. But the thorniest question is how to pln sequence of chnges in pension prmeters? Tht requires to identify n objective function. Jpn mkes predictions every 5 yers on 95-yer horizon nd computes the intertemporl solvency with respect to this horizon. From prospective point of view, the U.S. Socil Security opted for 75-yer time horizon, nd the forecsts re published nnully. The 75-yer nnul forecst of U.S. Socil Security permits thorough nlysis of the solvency. Notbly, they give n estimtion of the yer when the system reches bnkruptcy. After this criticl yer, in the bsence of corrective mesures, the federl government hs n obligtion to reduce pensions to chieve finncil blnce between pension pyments nd socil contributions. The djustment is utomtic nd brutl becuse the U.S. Socil Security does not hve the right to borrow. The cse of U.S. Socil Security budgetry rule is interesting since it must comply with rule tht prohibits debt. Therefore, this mens tht the system cn mke it if the deficit hs previously chieved surpluses. If f =, the djustment is brutl becuse the pension scheme is in bnkruptcy nd cn only py pensions t the height of its revenue, which, de fcto, mens shrp decline in pensions. 3.3 The Swedish NDC: n overlp between AAM nd ABM Sweden is only interested in working genertions live tody nd current cquired rights nd the contributions they will perform in the future. The implicit prediction horizon is the mximum life length of the younger genertion of workers. Sweden hs dopted full djustment mechnism where globl index on pension benefits is used to gurntee ech yer n intertemporl budget blnce which is estimted s n equlity between the discounted sum of current nd futur pyroll txes nd the implicit libilities net of the reserve fund. The notionl ccounts give ech individul virtul ccumulted cpitl which is mde of the sum of his contributions "virtully" revlued nnully by the rel growth rte of the verge wge in the 9
economy. Note tht the virtul cpitl is discounted t i. In fct, i is forecst of the future verge growth rte of the verge wge in the economy. This pproximtion hs been set t.6% per nnum. Wht mechnisms to blnce the pension system? Respecting the reltive stndrd of living of retirees is ensured by the indextion of pension cpitl nd the growth rte of verge wges. This implies two things: - On the one hnd, the forecst growth rte (discount rte eqution giving the bord) is ccurte. From this point of view, blncing mechnism is provided which is effective only if the relity devites from the performnce by.6% nd pensions re djusted ccordingly 3. - Secondly, the employment rte is stble. It is cler tht ny economic crisis will involve blncing mechnism consistent (ll things being equl) with the eqution. This will necessrily led to give up the indextion of pensions on the verge wge increse. This de-indextion is specificlly ctivted when the mount of resources in the system consists in the totl ssets of the reserve fund nd virtul ssets is less thn the sum of ccumulted pension rights. Sunden (29) shows the evolution of this blnce rtio from 22 to 28. This unfvorble chnge led to the downwrd indextion of pensions. The principle of this de-indextion is to ctivte the reserve fund. The interesting point is probbly wondering wht cn induce n intertemporl unblnce. In fct, t the stedy stte, the collected contributions should be equl to the sum of the promises mde by the pension pln. When dding up the mount of reserves, the mount of resources should exceeds libilities by fr. Therefore, it is necessry to hve both depressed economy nd finncil rtes of return to chieve low indextion. In ddition, wht bout the promised cturil neutrlity if one cn chnge the pensions including through the discount rte (Guérin nd Legros, 22). The chllenge of the increse in life expectncy is clerly tken into ccount by inserting n explicit conversion rte in the cturil formul for clculting pensions. They re cturilly neutrl, vrying by cohort nd ge t which the individul retires. However, since the indexing rte of pensions my vry, severl combintions exist between index nd life expectncy which give the sme conversion rte. As we hve sid very clerly this questions the strict cturil neutrlity regime. The chllenge of the size of genertions is tken into ccount by the d- 3 In pssing, in the most ncient texts, the cse of negtive difference ws not considered Sunden (998).
justment mechnism s well s the vribility of the employment rte. Lssil nd Trmo (27) show tht fertility breks my be tken into ccount by the mechnism. The Swedish model hs mjor limittion. When the economic nd finncil crisis inferred cpitl loss in the reserve fund nd reduction in the growth of revenue, the Swedish cpitl rtio fell below the criticl vlue of. The mount of pensions is reduced in order to return to blnce. But the government hs proposed to offset this by reducing txes levied on pensions. In ddition, the pension pln hs decided to spred the djustment over three yers. We cn therefore conclude tht, in cse of diffi culty, the djustment rules re modified in discretionry mnner. Another interprettion is tht the pension system is still in control nd tht the crisis hs rised diffi culties which hd not been nticipted before. 4 In serch of smoothed blncing We develop "simple" method. The objective function is defined s qudrtic loss function. Qudrtic cost functions re commonly used in the nlysis of monetry policy (Svensson, 23). A similr pproch pplied to retirement hs been developed by Berger nd Lvigne (27). But their djustment reltes solely to the contribution rte, nd the socil cost is mesured by the squre of the chnge in ech period. Moreover, they do not introduce intertemporl discount, which leves no possibility of procrstintion. Here the pproch is enhnced becuse it leves two possible djustment modes: by costs nd/or by revenues. With ABM, the djustment should result in incrementl chnges. Indeed, it is hoped tht the AAM led to suffi cient djustments nd they contribute to better finncil blnce. The ABM is n ultimte setting tht cn be expected to be mrginl. Of course, it would be nive to think tht minimizing qudrtic loss function could be suffi cient to cpture ll the problems relted to the djustment of the pension system. However, the qudrtic loss synthetizes well the will to smooth the chnges in the current legisltion. The vlue of the loss ssocited to ech period is mesured by: LF t = α (A t ) 2 + ( α) (B t ) 2. (8) where A t nd B t re two deformtion coeffi cients which modify respectively the present nd future pyroll txes nd pension expenditures reltively to those estblished by the current lw. This loss function cptures the fct tht chnging prmeters is costly (both socilly nd politiclly) nd tht minimizing it mens the socil plnner hopes to limit chnges. The socil
plnner sets time horizon T to blnce the sum of discounted receipts nd the sum of discounted expenditures: T t= A t τ t w t e t L t Π t i= R i The optimizing progrm is: min T t= {A βt LF t t,b t} s.t. T t= A t τ t w t e t L t Π t i=2 R i + F = T t= B t ρ t w t d t L t Π t i= R. (9) i + R F = T B t ρ t w t d t L t t= Π t i=2 R i The F.O.C gives: { At : β t 2 α (A t ) = ψ τ t wt et Lt Π t i=2 R i B t : β t 2 ( α) (B t ) = ψ ρt wt dt Lt Π t i=2 R i where ψ is the Lgrnge multiplier. We deduce tht: { (At ) = τ t wt et Lt τ w e L β t Π (A t i=2 R ) i (B t ) = ρt wt dt Lt α τ w e L α β t Π (A t i=2 R ) i. (). () (2) By incorporting these two expressions in the intertemporl budget constrint, we obtin: = ( ) τ T τ t w t e t L t t w t e t L t τ w e L β t Π (A t i=2 R ) + i Π t i=2 R + F i t= T ρ t w t d t L t ( ρ t wt dt Lt τ w e L α α β t Π (A t i=2 R ) + i (3) ) t= Π t i=2 R i We identify A nd B : A = B = + T t= T t= β t (Π t i= R i) 2 β t (Π t i= R i) 2 nd deduce the dynmics of coeffi cients djustment: F T Π T i= R i ( (τt w t e t L t ) 2 + α α ) (ρt wt dt L t )2 τ w e L F T Π T i= R i ( α ) α (τ t w t e t L t ) 2 +(ρ t w t d t L t ) 2 ρ w d L (4) 2
{ At = + τ t wt et Lt τ w e L β t Π (A t i=2 R ) i B t = + ρt wt dt Lt ρ w d L β t Π (B t i=2 R ) i (5) This mximizing problem cn be completed by dding constrints on the level of the reserve fund (F T > or F t t if no debt constrint) or the djustment prmeters. These results cn be interpreted in three wys: - A t nd B t cn induce prcticl implictions in terms of pension reforms. They define distnces to fixed trget in terms of pyroll txes (receipts) nd pension benefits (expenditures). - Mesuring A t nd B t would show how the pension schemes re strongly unblnced in the long run; - Reveled preferences: reforms imply chnges in legisltion. The levels of expenditures nd receipts re modified w.r.t previous scenrio without reform. Assuming A t nd B t to be mesured with ccurcy would ssocite public decisions with n implicit function of public preferences. Exmple: τ Consider sttionry economy: t w t e t L t τ w e L = Γ t = ρt wt dt Lt ρ w d L R t = R =. We β obtin the following deformtion coeffi cents: A = + B = ( Γ R ) T ( R) Γ ( R F (τ w e L / ( β R) T Γ ) ( Γ β R) 2 2T α ) (+ α h2 ) ( Γ R ) T ( Γ R ) ( R F (τ w e L / ( ( ) β R) T Γ 2T ) α α +h h ) ( Γ β R) 2 (6) with = ρ w d L τ w e L nd h = ρ w d L τ w e L. We deduce then: { At = + Γ t (A ) B t = + Γ t (B ). (7) 5 Applictions of our djustment rule 5. U.S. Socil Security As mentioned erlier, the U.S. Socil Security publishes nnul forecsts with 75-yer horizon. This forecst comprises three scenrios: pessimistic, 3
optimistic nd middle. This publiction is importnt becuse it gives cler ide of the likely survivl durtion of the pension system. In this section, we look t wht the use of ABM requires in terms of incresed revenue nd spending cuts. We consider severl prmetric vrints: - the forecst horizon; - the time preference (or degree of procrstintion); - the weight of socil djustment by revenues (vs. expenses). Figures, 2 nd 3 respectively show prmetric vrints with forecst horizons of 75, 5 nd 25 yers. The U.S. pension system performs surpluses until 232 (intermedite scenrio forecsting). After this dte, the U.S. government will be forced to reform (tx increse or decrese in pensions). The longer the horizon, the more the plnner integrtes imblnce. This mens tht the djustments re very sensitive to the horizon. For 25-yer horizon, the present vlue of the unfunded frction of the libilities is low. It increses with the forecst horizon. Thus, the need for djustments re very low (A nd B ner ) t T = 25 (Figs 3). In contrst when T = 5 (Figs 2), A nd B cn vry between 5 nd 5%. For T = 5 (Figs ), A nd B my vry up to 3% depending on the prmetric choice. Vritions of time preference (Fig x..y for β =, Fig x.2.y for β =.975 nd Fig x.3.y for β =.95) clerly show the consequences of postponing djustment mechnisms. Delying djusment induces very high djustment costs in the future. Figures Fig. x.y. (α =.25) nd Fig. xy2 (α =.5) show the profile of A nd B for vrints of the socil weighting (given respectively to revenue nd expenditure). Not surprisingly, the djustment of expenses is more demnding for high vlues of α. 4
.3 25.3 25.2 2.2 2 5 5.. 5 5.9.9 5 5 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282. α =.25 2. α =.5 β =.3 6.3 6.2 4.2 4 2 2.. 2 2 4.9 4.9 6 6 8 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 2. α =.25 22. α =.5 β =.975.3.3 5 5.2.2 5 5. 5. 5 2 25 2 25 3 3.9 35.9 35 4 4 45 45 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 3. α =.25 32. α =.5 β =.95 Figures. Time horizon T = 75 5
.3 8.3 8 7 7.2 6.2 6 5 5. 4. 4 3 3 2 2.9.9 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 2. α =.25 22. α =.5 β =.3 6.3 6.2 5.2 5 4 4. 3. 3 2 2.9.9 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 22. α =.25 222. α =.5 β =.975.3 5.3 5 4 4.2 3.2 3. 2. 2.9.9 2 2 3 3 4 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 23. α =.25 232. α =.5 β =.95 Figures 2. Time horizon T = 5 6
.3 4.3 4 35 35.2 3.2 3. 25 2 5. 25 2 5.9.9 5 5 5 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 3. α =.25 32. α =.5 β =.3 4.3 4 35 35.2 3.2 3 25 25. 2. 2 5 5.9 5.9 5 5 5 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 32. α =.25 322. α =.5 β =.975.3 4.3 4 35 35.2 3.2 3. 25. 25 2 2 5 5.9.9 5 5 22 222 232 242 252 262 272 282 22 222 232 242 252 262 272 282 33. α =.25 332. α =.5 β =.95 Figures 3. Time horizon T = 25 7
5.2 French defined benefit system (CNAV) The French system is currently in deficit, nd forecsts for 25 re rther lrmist (COR, 8th report, 2, scenrio B). We do the sme exercises to estimte n ABM. Three vrints for the horizon re performed: T = 39, T = 26 nd T = 3. Sensitivity results re similr to those obtined with the U.S. pension system. 8
.3 2.3 8 8 6.2 6.2 4 4 2. 2. 8 8 6 6 4 4.9 2.9 2 2 2 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 4. α =.25 42. α =.5 β =.3 5.3 3.2 4.2 2 3. 2..9.9 2 2 3 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 42. α =.25 422. α =.5 β =.975.3 2.3 2.2 2.2 4 4 6. 6. 8 8 2 2 4.9 4.9 6 6 8 8 2 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 43. α =.25 432. α =.5 β =.95 Figures 4. Time horizon T = 39 9
.3 9.3 8 8 7.2 7.2 6 6 5. 5. 4 4 3 3 2.9 2.9 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 5. α =.25 52. α =.5 β =.3 4.3 3 35 25.2 3.2 25 2. 2. 5 5 5.9 5.9 5 5 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 52. α =.25 522. α =.5 β =.975.3 5.3 5.2 5.2 5.. 5 5 2.9 2.9 25 25 3 3 35 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 53. α =.25 532. α =.5 β =.95 Figures 5. Time horizon T = 26 2
.3 2.3 8 8 6.2 6.2 4 4 2. 2. 8 8 6 6 4.9 4.9 2 2 2 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 6. α =.25 62. α =.5 β =.3 2.3 9.2.2 8 8 7. 6. 6 5 4 4 3 2 2.9.9 2 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 62. α =.25 622. α =.5 β =.975.3 3.3.4 2.5.2.2 2.2..5..6.4.9.5.9.2.5.2 22 27 222 227 232 237 242 247 22 27 222 227 232 237 242 247 63. α =.25 632. α =.5 β =.95 Figures 6. Time horizon T = 3 2
6 Conclusion This rticle hs identified different types of AAM tht cn be implemented nd hs shown how they contribute to better solvency. Sweden is the only country tht strengthens its AAM with n ABM tht ensures finncil stbility. Similrly s in the Swedish pension, we propose to build n ABM strting from dynmic progrmming setting. For given plnning horizon, we obtin formuls tht determine how t ech period revenues nd expenses must be djusted. Tht llows to consider the ABM chosen by Sweden s specil cse. Indeed, the Swedish ABM cn be obtined by ssuming very high djustment costs on revenue nd choosing prticulr concept of mesure of solvency. We pply these formuls to the finncil blnces of the Americn nd French systems. Using dynmic progrmming voids brutl djustments nd thus modertes or smooths the mrginl djustments necessry for finncil stbility. However, this exercise of dynmic progrmming presents mjor limit. In effect, the ABM is evluted in context where economic vribles re ssumed to be exogenous. A study of the reltionship between the fitting prmeters nd the evolution of the economy cn be nturl extension of this rticle. From mcroeconomic point of view, OLG-CGE models hve been developed to estimte the impct of Socil Security reforms in n intertemporl nd intergenertionl generl equilibrium frmework. Such models re used to "optimize" Socil Security reforms. Furthermore, dynmic microsimultion models give lot of detils on the microeconomic impcts of Socil Security reforms. References [] Brr, Nichols nd Peter Dimond, 2, "Improving Sweden s Automtic Pension Adjustement Mechnism", Issue in brief, Center for retirement reserch t Boston College, n 2. [2] Berger, Chrlie nd Anne Lvigne, 27, "A model of the French pension reserve fund: wht could be the optiml contribution pth rte?, Journl of pensions economics nd finnce, 6 (3): 233-25. [3] Blnchet, Didier nd Florence Legros, 22, "Frnce: The Diffi cult Pth to Consensul Reforms", in Socil Security Pension Reform in Europe (Mrtin Feldstein nd Horst Siebert, Eds), University of Chicgo Press. 22
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