PENSION REFORM IN BELGIUM: A NEW POINTS SYSTEM BETWEEN DB and DC

Transcription

1 PENSION REFORM IN BELGIUM: A NEW POINS SYSEM BEWEEN B and C Pierre EVOLER (*) (March 3 s, 05) Absrac More han in oher counries, he Belgian firs pillar of public pension needs urgen and srucural reforms in order o resore financial susainabiliy and inergeneraional equiy. In he las decades only small parameric changes have been made and ime has come o hink abou he fuure. Las year, a commission of academic expers has been appoined by he Belgian governmen in order o propose a new pension archiecure. his commission has proposed o implemen a pay as you go sysem based on a poins mechanism wih a risk sharing logic beween acive people and reirees. his sysem can be considered as an inermediae soluion beween B (efined Benefi) and C (efined Conribuion). he purpose of his paper is o presen he underlying principles of his sysem, o discuss is advanages and disadvanages and o address various acuarial challenges generaed by he new proposed formula. Keywords Pension reform, Social securiy, Pay as you go, Musgrave rule (*) Professor, Universié Caholique de Louvain (UCL), Insiue of Saisic, Biosaisic and Acuarial Science (ISBA) 0 Voie du Roman Pays, 348 Louvain la Neuve, Belgium, ([email protected])

2 . Inroducion As in many counries, he Belgian firs pillar of pension, based on a pay as you go mechanism and a efined Benefi archiecure, is under pressure and needs fundamenal reforms o guaranee simulaneously long erm susainabiliy and social fairness. Even if some parameric changes have been decided hese las years, no fundamenal decisions have been aken o resore he long-erm viabiliy and he global coherence of he sysem (see for insance evolder, 00). he absence of global reforms conrass a lo wih he siuaion in oher counries where fundamenal reforms emerged hese las years, such as he Noional efined Conribuion (NC) in Sweden (Holzman e al., 0; Palmer, 000; Seergren, 00), he inroducion of a susainabiliy facor in Germany ( Borsch-Supan e al., 003) of oher echniques of auomaic adjusmen (Vidal- Melia e al, 006; Knell, 00). In Belgium, however, here have been no real reforms, despie is negaive financial rend. he evoluion of he expendiure is negaively affeced no only by ageing and pappy boom (as in many wesern counries), bu also by he bad level of aciviy (see for insance he Ageing repor, 05). Neverheless, afer years of silence, an increasing poliical awareness seems finally o appear. In his conex, in 03, he Belgian governmen decided o ask a commission of academic expers o propose a new srucure for he Belgian public pensions. he resuls of his commission have been published in a repor (Commission , 04). he aim of his paper is o presen some of he ideas proposed by his commission. In paricular, we would like o address he problem of he risk sharing beween conribuors and reirees. In a classical pension archiecure, based on a B philosophy (resp. a C philosophy) all he risks are borne by he conribuors (resp. he reirees). he idea presened by he commission is o creae an auomaic adjusmen of he replacemen rae and he conribuion rae based on a sharing of he risks beween conribuors and reirees. One possible soluion in his conex is o use he so called Musgrave rule based on a modified replacemen rae. his rule is noe relaed o he gross salary, bu o he salary, ne of pension conribuions. However, oher sharing rules beween he wo generaions are possible. One of he aims of his paper is o presen various sharing rules and o measure he level of solidariy generaed by hese adjusmen echniques. We use for ha a simple deerminisic model, where he main driver is he dependence raio (raio beween he number of reirees and he number of workers). In paricular, we inroduce wo differen ways o model he impac of a change of he dependence raio on he conribuion and he replacemen raes. he firs one is based on a raio beween he change in he conribuion rae and he change in he replacemen rae. he second one

3 inroduces a convex invarian (convex combinaion beween he conribuion rae and he replacemen rae). In boh cases, B and C schemes appear o be exreme soluions for he parameers and he Musgrave rule is one of he possible inermediae sysems. Oher examples of mix beween B and C are proposed. he paper is organized as follows. Secion briefly summarizes he pension formula for he exising Belgian firs pillar for employees. Secion 3 explains he new poins sysem proposed by he commission of expers. In secion 4 we illusrae he link beween his sysem and a NC scheme. In secion 5, we develop he Musgrave rule generaing an inermediae sysem beween B and C (sysem called M efined Musgrave). his approach is generalized in secions 6 and 7. In secion 6, we define a risk sharing coefficien, comparing in case of change of he dependence raio, he impac in erms of conribuion rae and replacemen rae. In his conex we inroduce a efined Equal sharing plan where he change of he dependence raio has a same proporional effec on he conribuion and he replacemen raes. We compue also his risk sharing coefficien for he M and show ha his coefficien is no consan. We prove also ha in general his sysem is closer o B han C. In secion 7, we propose anoher approach of mixing by considering a convex combinaion beween he conribuion rae and he replacemen rae. he Musgrave rule is presened as a naural example. Secion 8 concludes he paper.. he exising efined Benefi sysem in he Belgian firs pillar he exising firs pillar of pension in Belgium is a classical combinaion of Pay-as-you-Go (PAYG) and efined Benefi (B). For insance, for employees, he pension formula is based on he average of indexed salaries; more precisely, he normal reiremen age is 65 and he amoun of pension is given by: P = 0,60.( S. h(,)) 45 = 45 where : P = pension = reiremen year S = salary of year ( wih applicaion of a wageceiling) h(, ) = indexaion coefiicien beween year and year (.) 3

4 his sysem presens many drawbacks: - financial susainabiliy is under pressure; - no ransparency; - oo many incenives for early reiremens; - no acuarial fairness. 3. A new poins sysem he pension reform s commission has proposed o move from his B framework o a new sysem having hree main characerisics: -a) PAYG financing b) benefi compuaion based on a poins sysem c) risk sharing mechanism beween B and C. In such a sysem, he pension formula is described as follows: a) during he acive career: each year, every conribuor receives a number of poins given by he raio beween his own salary and a reference salary, fixed each year. he reference salary could be for insance he mean salary of he economy: n S = S r where : n = number of poins for year (3.) S = individualsalary of year S r = reference salary of year b) he oal number of poins accumulaed a reiremen age by a pension paricipan, for a career of M years, is given by: N = n = M (3.) For example, when M=45, somebody earning each year exacly he reference salary, will obain exacly 45 poins a reiremen. he oal number of poins is herefore a sor of meric of he lengh of he career, correced of course by he level of salary. 4

5 c) he pension a reiremen age is given by he following formula: P = N. V. ρ where : N = oal number of poins V = value of he poin ( in ) ρ = acuarial coefficien he value of he poin V is fixed every year aking ino accoun simulaneously differen goals o combine. I should ensure a susainable individual pension based on an adequae replacemen rae, while providing a relaive sabiliy o he conribuion rae. ifferen poliical choices can be made concerning he risk sharing beween conribuors and reirees. his poin will be addressed in deail in secion 5. he acuarial correcion mus ake ino accoun he reiremen age and he lengh of he career (oal or parial acuarial neuraliy) and is based on life expecancies. (3.3) d) afer reiremen, he pension is indexed, aking ino accoun he evoluion of he salaries and he susainabiliy of he regime: P = P. h. η + where : h = indexaion coefficien η = susainabiliy facor (3.4) As a firs simple example of deerminaion of he value of he poin, consider a arge in erms of replacemen rae for a represenaive agen ( B philosophy). Le us assume an affiliae wih a salary equal each year o he reference salary ; in order o obain a full pension we ask his affiliae o work during a reference period denoed by N*. We don apply in his case any acuarial correcion (ρ = ) and he pension (3.3) becomes: P = N *. V he value of he poin can be fixed by reference o a replacemen rae : (3.5) P =. S r (3.6) he value of he poin is hen : V r.s = N * (3.7) 5

6 For a replacemen rae of 60% and a reference period for he career of 45 years, he value of he poin is hen equal o.33 % of he reference salary. 4. Comparison wih a NC scheme here are clear analogies beween his poins sysem and a Noional efined Conribuion scheme (NC). In a NC scheme (see for insance Holzman e al.,0), he pension can be wrien (assuming a reiremen age of 65): P =..S. g(,) a 65 = 45 where : P = pension = reiremen year S = salary of year (wih ceiling) (4.) = conribuion rae g(, ) = revalorizaion based on noional raes a 65 = annuiy price a reiremen age I is easy o see ha formula (4.) can be seen as a paricular choice of he general poin formula (3.3). Inroducing in formula (4.) he reference salary, we obain: S r P =... (g(,).s ) a r 65 = 45 S If we assume, as usual in NC sysems, ha he revalorizaion coefficiens are in line wih he increase of he mean salary, we can wrie: So finally: he value of he poin is hen: g(,).s 65 r = S r r P =..S.N a V.S = a 65 r he replacemen rae for a reference salary is no consan anymore bu given by: 6

7 .N = a Beween B and C: he Musgrave rule he poin sysem presened in secion 3 is a very flexible archiecure and can be modelled using various calibraions. he key quesion is how o fix he value of he poin and how o adap auomaically he sysem o exogenous shocks. We have already proposed wo ways o define he poin (formula (3.7) in a B philosophy and formula (4.) in a NC conex). In a B framework, here is an absolue guaranee for he reirees (fixed replacemen rae) and he conribuors mus suppor he risks; in a C framework, here is an absolue sabiliy for he conribuors (fixed conribuion rae) and he replacemen rae is adjused. he poins sysem can exend his dualiy by allowing many oher mechanisms of risk sharing beween reirees and acive workers. In order o model he demographic risk, le us assume an iniial sable siuaion ( denoed by sae ) composed only of reprenaive agens ( same salary and same career) receiving a pension based on a replacemen rae ( wih 0 < < ) and a conribuion rae. We denoe by he dependence raio (raio beween he number of reirees and he number of conribuors). he sysem is hen given by he wo equaions : - budge equaion :.P =.S - pension equaion: P =.S he equilibrium beween he parameers is obained when he following classical condiion is fulfilled: =. (5.) Accordingly o formula (3.7), he value of he poin is given by : V r.s = (5.) N* Suppose now ha he sysem moves o anoher sage characerized by anoher dependence raio denoed by. We will ofen assume ha > (ageing of he populaion). We wan o define he new parameers and, sill linked by : =. a) in a B scheme, he replacemen rae has o remain consan and he conribuion rae mus 7

8 increase ( risk is only borne by he conribuors) : = = =. b) in a C srucure ( for insance NC ), he conribuion rae has o remain fix and he replacemen rae will decrease ( risk is only borne by he reirees) : = = =. c) Musgrave (98) has proposed anoher invarian leading o a form of sharing of he risk beween he wo generaions. Le us define he Musgrave raio as he raio beween he pension and he salary ne of pension conribuions : P M = = S ( ) ( ) In a B srucure, he Musgrave raio increases when he dependence raio increases: In a C srucure, he Musgrave raio decreases : M = = ( ) ( / ) M = =. ( ) ( ) In he Musgrave rule, called here M ( efined Musgrave),we wan o sabilize his coefficien : (5.3) (5.4) (5.5) M = M = M (5.6) In his philosophy, he new replacemen rae can be easily obained using (5.) : = = M ( ) ( ) M so : = (5.7) + M. By using (5.) again, he conribuion rae becomes :.M = (5.8) + M. We can also compare old and new values of he wo parameers : 8

9 a) replacemen rae: M = = + M. / ( ) +. =. +.( ) In a C scheme, he new replacemen rae was given by : In a B scheme, he replacemen rae remains consan : (5.9) =. (5.0) = (5.) We can obain he following rule, showing ha efined Musgrave can be seen as an inermediary beween efined Benefi ( no influence of he dependence raio on he replacemen rae) and efined Conribuion ( full influence of he dependence raio ) : Propery 5.. : If he dependence raio increases ( > ) and if he iniial conribuion rae 0 < <, hen we have he following inequaliy: >. >. + ( ) (5.) Or: B M C > > Proof: (i). > + ( ) is a direc consequence of: > (ii). >. + ( ) or: >.( + ( )) Or: >. ( ) =.( ) Or: < 9

10 b) conribuion rae: /..M = = + M. / + =.. +.( ) In a B scheme he new conribuion rae was given by: =. In a C scheme he conribuion rae remains consan: = hen we have he following propery similar o propery 5.. : Propery 5.. : If he dependence raio increases ( > ) and if he iniial conribuion rae 0 < <, hen we have he following inequaliy: <. <. + ( ) (5.3) Or: Proof: (i) <. + ( ) C C M B = < < Or: + ( ) < Or: < (ii). <. + ( ) is direc consequence of: +.( ) > Remark ha, if he populaion is geing younger raher han ageing (i.e. < ), he order relaions given in properies 5. and 5. are reversed. Formulas (5.) and (5.3) show ha he efined Musgrave approach can be seen as an inermediary beween B and C in erms of conribuion raes and replacemen raes. In a M scheme, he wo raes move ogeher in opposie direcions (increase of he conribuion rae and 0

11 decrease of he replacemen rae).conribuors and reirees are affeced by he demographic risk. able summarizes he hree choices (B, C, and M). ABLE : Conribuion rae and replacemen rae formula in B, C and M Conribuion rae Replacemen rae Value of he poin efined Benefi = = =. efined Conribuion efined Musgrave V.S = V = N * = = =. V = V. =. +.( ) =. +.( ) = R V V. +.( ) Example 5.: Le us assume an iniial seady sae characerized by he following parameers: - iniial dependence raio: = iniial replacemen rae: = iniial conribuion rae : = 0.40 x 0.50 = 0.0 hen able gives for various values of he new dependence raio he new conribuion rae and replacemen rae in he hree srucures ( B, C and M) : ABLE : numerical comparison beween B, C and M =0,5 =0,35 =0,45 =0,50 =0,60 B C M

12 6. Risk sharing coefficien he defined Musgrave mechanism can be considered as an inermediae scheme beween B and C. We can develop a whole family of inermediae soluions beween B and C where a change of he dependence raio is no suppored only by he reirees (C) or only by he conribuors (B) bu is shared beween he wo groups. In order o inroduce his family, we sar from a seady sae given by he equilibrium equaion (5.). A change in he dependence raio generaes new values for he conribuion rae and he replacemen rae, sill soluions of he equaion: We inroduce he following noaion: =. (6.) = ( + λ ) = ( λ ) he parameers λ represen he relaive changes in he wo raes. Equilibrium relaion (6.) gives he following relaion beween hese parameers: ( ).( ) (6.) + λ = λ (6.3) We can also inroduce a risk sharing coefficien, comparing he effors suppored by he conribuors and he reirees: λ ρ = (6.4) λ If his coefficien is equal o, he risk is equally shared by he wo generaions. We compue firs he values of hese new parameers in he hree sysems inroduced in secion 5. a) In a B scheme, we have by definiion: λ = Equaion (6.3) gives he oher parameer: 0 + λ = or: λ = (6.5) he risk sharing coefficien is hen: ρ = + (6.6)

13 b) In a C scheme, we have by definiion: λ = Equaion (6.3) gives he oher parameer: 0 = ( λ ) or: λ = (6.7) he risk sharing coefficien is hen: ρ = 0 (6.8) c) In a M scheme, i comes, using able : - for he conribuion par: =. =.( + λ ) +.( ) ( )( ) λ =.( ) or: + - for he replacemen rae: =. =.( λ ) +.( ).( ).( ) or: λ = + he risk sharing coefficien in a M scheme is : λ ( ).( ) +.( ) ρ = =. λ + ( ).( ) = = For naural values of he conribuion rae ( < 0.5), his sharing coefficien is higher han, showing ha in a efined Musgrave, conribuors made a bigger effor han he reirees ( sysem closer o B han C). In example 5. ( = 0. ), his coefficien is equal o 4. Le us remark ha in a efined Musgrave, his coefficien depends on he conribuion rae. herefore, successive applicaions of his rule will change he value of he risk sharing coefficien (along wih he change in he conribuion rae). So a defined Musgrave canno be considered as a sysem wih a consan risk sharing coefficien. (6.9) 3

14 Apar from hese hree sysems, we are now able o develop oher sharing rules. d) For insance, a naural candidae is characerized by a risk sharing coefficien equal o. We could call his rule E (efined Equal sharing). In his case, we have: λ = λ = λ hen equaion (6.3) becomes: ( + λ ) =.( λ ) or: λ = + In his case, using formula (6.) he new conribuion and replacemen raes are respecively given by: = = (6.0) (6.) e) In general, we can characerize a pension scheme by of is level of solidariy beween reirees and conribuors, summarized by he coefficien ρ. A value of ρ > ( resp. ρ <) generaes more effor from he conribuors ( resp. he reirees), he B and he C being he wo limi echniques. he parameers are hen soluion of he wo equaions: he soluion is given by: ( + λ ) = ( λ) λ = ρ. λ λ( ρ ) = + ρ. λ( ρ ) = ρ. + ρ. he conribuion and replacemen raes become: =.( + ρ). + ρ. =.( + ρ). + ρ. (6.) (6.3) he C, B and M frameworks seen before are paricular cases of hese general formulas for risk sharing coefficien ρ respecively equal o ρ = 0; ρ = + ; ρ = ( ) /. 4

15 Example 6. Using he same assumpions as in example 5., able 3 compares he effec of he risk sharing coefficien on he conribuion rae and he replacemen rae ABLE 3: numerical comparison of he conribuion rae and he replacemen rae for various values of he risk sharing coefficien ρ=0 (C) =0,5 =0,35 =0,45 =0,50 =0, ρ= ρ= (E) ρ= (M) ρ= ρ = (B) A convex invarian he Musgrave rule can also be revisied using a convex combinaion beween he replacemen rae and he conribuion rae and asking his combinaion o say consan in case of a demographic shock. his inerpreaion will allow us o consider again a whole family of inermediae schemes beween 5

16 B and C. he efined Musgrave is based on he following invarian ( cf. equaion (5.5)): his relaion can be wrien : or : M = M = + M. M M. +. = + M + M + M or: α. + ( α). = α (7.) his las relaion shows ha in a M, a convex combinaion of he conribuion rae and he replacemen rae has o remain consan. he coefficien α of he combinaion being equal o: α = = + M + In example 5., his coefficien α is equal o 0.6, showing once again ha M is closer o B han C. In general, he convex parameer α of a M will be greaer han 0.5 if: > + or: + < or by using (5.): < + < + Relaion (7.) allows us o generalize he M approach by choosing oher values of he convex coefficien α. I is already easy o see ha a B scheme corresponds o he case α = and a C scheme o he case α =0. In general, a convex invarian risk sharing will be based on he following rule: where he coefficien α is chosen beween 0 (C) and (B). α. + ( α). = consan (7.) his coefficien α can be seen as a measure of he imporance given o he reirees; α being he measure of he imporance given o he conribuors. In case of a demographic shock, he new conribuion and replacemen raes become hen soluions of he following equaions : α. + ( α). = α. + ( α). =. 6

17 So we obain he new raes as funcion of he convex coefficien : =. α + α + ( α). ( α ). α + ( α). =.. α + ( α). For insance, if α = 0.5 ( equal weigh beween conribuion rae and replacemen rae ), we obain: + =. + + =.. + he following propery gives a link beween his convex parameer α and he risk sharing coefficien ρ inroduced in secion 6 (formula (6.4)): Propery 7.. : he risk sharing coefficien ρ given by (6.4) and he convex parameer α given by (7.) are linked (7.3) (7.4) by he relaion: α ρ =. α Proof : he replacemen rae expressed in erms of he risk sharing coefficien ρ is given by ( 6.3): (7.5) =.( + ρ). + ρ. On he oher hand, he replacemen rae in erms of he convex parameer α is given by (7.3): So he equivalence condiion is : =. α + α + ( α). ( α ). α + ( α ). ( + ρ) = α + ( α ). + ρ which gives afer simple compuaions : α ρ =. α he same developmen wih he conribuion rae generaes he same relaion. Remark: Relaion (7.5) shows ha if we look a a pension sysem on a muli period model wih successive changes in he dependence raio and herefore successive applicaions of he auomaic adjusmen, 7

18 he wo coefficiens α and ρ canno remain simulaneously consan across ime, apar from he wo limi siuaions of a B or a C. For insance, a M scheme is characerized by a consan α =, (see (7.)), bu is risk sharing coefficien given by (6.9) will change on ime + M ogeher wih he conribuion rae. On he oher hand, he E sysem is defined by a consan risk sharing coefficien ( ρ =) ( 6.), bu is convex parameer will change on ime (given by : α = ) Conclusion NC and classical B social securiy sysems can be seen as exreme soluions in he risk sharing beween reirees and conribuors. he Musgrave echnique (using a replacemen rae expressed in erms of salaries, ne of pension conribuions) is an inermediae soluion ha has been considered in he proposiion of reform based on a poins sysem for Belgium. his approach seems o bring more solidariy and equiy beween he generaions han in a pure B or C scheme, where only one generaion bears he risk. However, his Musgrave sysem is bu one example of mix beween B and C and is based on a solidariy level ha can be challenged. In his paper, we inroduce wo ways o exend hese hree sysems ino a coninuous family of sysems wih an auomaic adjusmen mechanism based on some consrain. In secion 6 we propose a firs family based on he inuiive reques of a fixed raio beween he variaion of he conribuion rae and he variaion of he replacemen rae; in secion 7 we inroduce a convex mix beween he replacemen rae and he conribuion rae. he Musgrave rule is a paricular case of his las philosophy. hese differen formulas allow he Sae o decide he level of solidariy o be injeced in he social securiy. In his paper we have considered only a deerminisic model on wo periods of ime. Fuure exension will examine sochasic models wih more han wo periods and he sabiliy issue of hese adjusmens. 8

19 References Borsch-Supan, A., A.Reil-Held and C.B.Wilke (003) How o make a defined benefi sysem susainable: he susainabiliy facor in he German Benefi Indexaion formula. iscussion paper 37/003, Mannheim Insiue for he Economics of Aging Commission (04) Un conra social performan e fiable, hp://pension040.belgium.be/fr/ evolder, P. (00) Perspecives pour nos régimes de pension légale. Revue Belge de Sécurié sociale»,4,p isney, R. (996) Can we afford o grow older. he MI Press, London European Commission (04) he 05 Ageing Repor, European Economy 8/04 Holzmann, R., E. Palmer and. Robalino (0) Non-financial efined Conribuion Pension schemes in a changing Pension world, Vol., Washingon.C., World Bank Knell M. (00) How auomaic adjusmen facors affec he inernal rae of reurn of PAYG pension sysems. Journal of Pension Economics and Finance, 9(),-3 Musgrave, R. (98) A reappraisal of social securiy finance. Social Securiy financing, Cambridge, MI, p OEC ( 04) OEC Pensions Oulook 04, OEC Publishing Palmer, E. (000) he Swedish pension reform model: framework and issues. Social Proecion iscussion Paper (), World Bank Seergren, O. (00) he Auomaic Balance Mechanism of he Swedish Pension Sysem: A Non-echnical Inroducion, Wirschafspoliische Blaer, 4,

20 Vidal-Melia,C., M.C. Boado-Penas, and J.E. evesa-carpio (006) Auomaic Balance Mechanisms in Pay-as-you-go Pension Sysems, he Geneva Papers on Risk and Insurance- Issues and Pracice, 34(),