Using Acuarial Mhodologis o Analys Chins PAYG Pnsion Sysm Jing Xu Insiu for Financial and Acuarial Mahmaics (IFAM), Dparmn of Mahmaical Scincs, Univrsiy of Livrpool, Livrpool L69 7ZL, UK. E-mail: sgju2@livrpool.ac.uk María dl Carmn Boado-Pnas (Corrsponding auhor), Insiu for Financial and Acuarial Mahmaics (IFAM), Dparmn of Mahmaical Scincs, Univrsiy of Livrpool, Livrpool L69 7ZL, UK. E-mail: Carmn.Boado@livrpool.ac.uk Absrac This papr provids wo acuarial balanc mhodologis o analys h Chins conribuory PAYG pnsion sysm in h urban ara. Firs, w us h Swdish acuarial balanc sh mhodology o analys h solvncy of h Chins pnsion sysm basd on vrifiabl facs. W compar his wih h US acuarial balanc indicaor modl ha aks ino accoun h dmographic and conomic scnario in h long run. This is h firs sima of solvncy and susainabiliy lvls of h Chins PAYG pnsion sysm. Boh mhodologis show ha h Chins pnsion sysm in is currn form is nihr susainabl nor solvn. Finally, h papr provids som advic on h paramric rforms ha should b undrakn o rsor h financial halh of h sysm basd on our analysis. JEL Classificaion: D83, E62, H55, J11, J26 Kywords: Acuarial analysis, Aging, PAYG, Public pnsions, Susainabiliy, Transparncy 1
Using Acuarial Mhodologis o Analys Chins PAYG Pnsion Sysm 1 Inroducion Pay-As-You-Go (PAYG) pnsion sysms rquir a balanc bwn h bnfis paid o h pnsionrs and h conribuions mad by h aciv workrs. Th dclin in friliy ras and h incras in longviy will conribu o a subsanial incras in h ag dpndncy raio, and his will rais srious concrns for h susainabiliy of PAYG pnsion sysms. This is a worldwid problm, and many Europan counris hav alrady akn sps o solv i. Mos counris hav also carrid ou som paramric rforms. For ampl in Ialy h normal rirmn ag has incrasd from 60 o 65 for mn and from 55 o 60 for womn whil h indaion of pnsion paymns has bn modifid in ordr o rduc hir ra of incras. Grmany has also inroducd pnalis for arly rirmn 1. As sad in Holzmann al. [10], counris such as Swdn, Poland, Ialy and Lavia hav undrakn som srucural rforms by changing h formula o calcula hir iniial pnsion from a Dfind Bnfi (DB) o a Noional Dfind-Conribuion (NDC) pnsion sysm. In h manim, som counris, among ohrs, Swdn, Grmany and Japan, hav dcidd o s up an auomaic balanc mchanism (ABM) according o an indicaor 2 ha rflcs h financial halh of h sysm. In Asia 3, h siuaion prsns a grar challng. Th spd of aging for Asia is much fasr han Europ. According o UN daa, h dpndncy raio 4 for Europ will dcras from 2.9 in h arly 2010s o 1.5 in 2050s, whil for Asia, h dpndncy raio will drop from h currn 6.4 o 2.4. Japan, on of h counris suffring from h mos svr aging problm, has akn som masurs by incrasing h rirmn ag from 60 o 65, and also sing up an ABM h modifid indaion 5 ha is applid o boh h rvaluaion of conribuion bass and pnsions in paymn.according o Moon [17], Souh Kora has dcrasd h rplacmn ra from 60% o 50% and is currnly schduld o fall furhr o 40% by 2028. Also, hy ar considring ransfring o an NDC schm and sing up an ABM [4]. A h sam im, Vinam, is considring o ransfr from PAYG DB o parially fundd Dfind Conribuion (DC) [8]. Pnsion sysms in counris such as Thailand and India, ha ar no widly covrd in h naional scal, hav conducd many rforms and rcnly hy boh plan o chang o h fundd-dc sysm. In som formr Briish colonis, such as Singapor or Malaysia, h Cnral Providn 1 Daild pnsion rforms for Europan counris can b found in Whiford and Whihous [34]. 2 S Vidal-Mliá al.[32] for mor dails on ABMs. 3 Daild pnsion rforms rgarding Asian counris can b found in Holzmann al. [9]. 4 Dpndncy raio is h raio of conribuors o h pnsionrs. 5 Th modifid indaion aks ino accoun improvmns in lif pcancy and populaion dcrass. S Sakamoo [22] for mor dails. 2
Fund (CPF) is a compulsory comprhnsiv savings plan dsignd o fund mainly rirmn and halhcar. Th CPF was no a good soluion givn arly wihdrawals. Currnly in Singapor, h rirmn ag will incras from 64 in 2015 o 65 in 2018 whil h conribuion ras incras by 1.5% as sad in Ashr [1]. Malaysia has incrasd h conribuion ra from an iniial 10% o 23% and also s rsricions for arly wihdraws, s [31]. China suffrs from h aging problm mainly du o h on child 6 policy which was pursud in 1980s [12], [13]. This policy ld o a sharp dclin in h friliy ra from 6.11 in h 1950s o 1.63 in h 2010s, and as a rsul, a dcras in h dpndncy raio for China from 7.2 conribuors financing ach pnsionr in h 1980s o 2.5 in 2010 according o UN daa [6].China has rid o solv h problm by dcrasing h rplacmn ras in urban aras from 77% o 45% in h las dcad and currnly is considring incrasing h pnsion ag from 60 o 65, and ransfring h pnsion sysm o NDC [19], [7], [36].Howvr, no acuarial balanc analysis has bn carrid ou so far o valua h ral financial halh of h sysm. Thus, som acuarial balanc analysis for China is ndd o rval h sysm s ru solvncyand susainabiliylvl. Th aim of his papr is o giv h firs sima of h solvncy and susainabiliy lvl of h Chins conribuory PAYG pnsion sysm in h urban aras (for h vry firs im, according o h auhors knowldg) using wo acuarial balanc mhodologis. Th papr also provids som discussion of h paramric rforms which could b mad o h currn Chins PAYG pnsion sysm basd on our rsuls, in ordr o mak h sysm solvn/susainabl in h long run. Following his inroducion, h papr is srucurd as follows. Scion 2 provids a dscripion of h Chins pnsion sysm. Scion 3 inroducs h Swdish acuarial balanc sh and US acuarial balanc indicaor mhodologis in dail, and compars h wo mhodologis. Scion 4 analyss h Chins PAYG pnsion sysm following h mhodology of h acuarial balanc sh. This scion also includs a dscripion of h daa usd and main assumpions, oghr wih a comparison wih h Swdish acuarial balanc sh and a discussion of paramric rforms basd on h rsuls. Scion 5 analyss h Chins PAYG pnsion sysm following h US acuarial balanc. This scion also conains a dscripion of h daa usd and h main assumpions mad, oghr wih a comparison wih h US acuarial balanc and discussion of possibl paramric rforms basd on h rsuls. Th final scion concluds. 2 Th Chins Pnsion Sysm Sinc h bginning of Chins conomic rforms in h arly 1980s, h Chins urban pnsion sysm has also undrgon a sris of rforms. Th pr-rform sysm isd only in h sa and urban collciv scors and was a pur PAYG sysm wihin ach nrpris. Afr h 1997 pnsion rform, pnsion pools sprad o provincs and all urban workrs wr pcd o paricipa rgardlss of ownrship (Shao and Xu [28]). Fundd individual accouns wr sablishd in 1995 o incras h porabiliy of h 6 On child policy is a compulsory policy whr ach Chins family can only hav on child. Sinc Novmbr 2013, h 'on child policy has bn rlad and, as a rsul, ach family can hav a maimum of wo childrn. 3
pnsions for rdundan workrs who lf sa-ownd nrpriss (SOE) during h conomic rforms in h mid-1980s. Howvr, h sysm did no work in h way i was inndd. Bcaus of h larg-scal SOE rsrucuring, many laid-off workrs wr givn immdia pnsions a qui young ags (vn a 40) which broadly mpid h individual accouns as h adminisraion usd h rvnus o pay h pnsions of currn rirs. Thn, in ordr o solv h mpy accouns problm, h PAYG Naional Accoun was sparad 7 from h Fundd Individual Accoun by h Sa Council Documn o. 42 in 2001. In h manim, h conribuion ra also changd many ims sinc h sablishmn of h wo accouns. And rcnly du o h aging problm and mpy accouns, h Chins govrnmn is considring incrasing rirmn ag from 60 o 65 and many prs on h Chins pnsion sysm, Oksann [19] and Dorfman al. [7] and Zhng [36],ar proposing h chang of h currn pnsion sysm o an NDC on in h fuur. Th currn Chins urban compulsory pnsion sysm consiss of wo pars 8 : h firs par is a PAYG-DB yp Naional Accoun and h conribuion ra for his accoun is 20%. Th scond par is a fully-fundd-dc yp Individual Accoun and h conribuion ra for his accoun is 8%. Each accoun's fund was originally oprad sparaly. This papr focuss on h Urban PAYG Naional Accoun, no only bcaus h conribuions o his, accouns for h largs proporion of h oal conribuions, bu also bcaus h problm par of his accoun is rood in h origin of h whol Chins pnsion sysm. Fng [11] and Chng [35] sa ha h problms of h Chins pnsion sysm ar no causd by h us of PAYG bu by h paricular paramr valus. By sing an appropria ra of conribuion, pnsion paymn, and rirmn ag, h problm in PAYG pnsion sysm can b solvd. Th formula o calcula h iniial pnsion of h Chins DB PAYG Naional Accouns is prssd as: 1+ WI P( + A, ) = Y( 1) A 1% (2.1) 2 whr is h arlis ag of nry ino h pnsion schm, A is h numbr of conribuion yars, Y ( 1) is h avrag salary for all h conribuors in h sysm a yar ( 1), and WI is h wag ind for popl who rir a yar. Th formula o calcula h Wag Ind is: A y( + A, k) WI = (2.2) Y A whr y( + A, k) is h salary a yar ( k) for individuals who rir a ag + A. Th Wag Ind is an indicaor usd o masur h rlaiv wigh of ach individual k=1 ( k) 7 Daild informaion on pnsion rform in China is includd in Oksann [19] and Saldi [23]. 8 Chins social scuriy sysm includs: Pnsion, Mdical Car, Unmploymn, Disabiliy, and Marniy & Childcar. Each sysm opras indpndnly. And hr ar wo accouns in h Pnsion sysm (Naional Accoun & Individual Accoun). 4
conribuion bas wih rspc o h avrag conribuion bas of h oalworking populaion. 3 Mhodologis o calcula h financial halh of h pnsion sysm 3.1 Th Swdish acuarial balanc sh mhodology Th acuarial balanc shof a PAYG pnsion sysm is h financial samn lising pnsion sysm s obligaions owards conribuors and pnsionrs oghr wih h amoun of asss ha back up hos liabiliis [27]. Th main aim of h acuarial balanc sh is o giv a ru and fair viw of h pnsion sysm s solvncy, by comparing h asss and liabiliis vry yar. Compiling an acuarial balanc sh givs ransparncy ino h pnsion sysm a h sam im ha i incrass h confidnc of conribuors and pnsionrs in h sns ha promiss of paymn may b raionally rspcd. Th acuarial balanc sh was firs dvlopd and applid in Swdn a yar 2001, hrafr h Swdish govrnmn has publishd an acuarial balanc sh vry yar in is Orang Rpor [27]. This balanc sh lads o an raordinary lvl of ransparncy. To kp h sysm solvn, Swdn also s up an Auomaic Balanc Mchanism (ABM) basd on h Solvncy Raio (SR) which mrgs from h acuarial balanc sh. This ABM is riggrd whn h SR is blow 1 9. Afr ha, som auhors sard o compil h acuarial balanc shs for pnsion sysms of ohr counris. Boado-Pnas al. [3] compild h acuarial balanc sh for Spain from 2001 o 2006 and analysd h SR. In Japan, Takayama [30] also usd h acuarial balanc sh o analys h proposd rforms in h pnsion sysm. Th srucur of h acuarial balanc sh is shown in Tabl 1: Tabl 1: main nris on h balanc sh of a pay-as-you-go sysm Asss Liabiliis Financial and ral asss Liabiliy o pnsionrs Conribuion ass Liabiliy o conribuors Accumulad dfici Accumulad surplus Toal asss Toal liabiliis Sourc from Boado-Pnas al. [3] Th sysm is solvn, if Toal asss Toal liabiliis. This implis ha h accumulad dfici mus b nil or ngaiv, and h paricipans in h sysm would hav rasonabl pcaions ha h promiss of paymns may b rspcd, wihou h sponsor of h sysm (h Sa) having o mak non-sauory conribuions. Howvr, if Toal asss < Toal liabilii s or h accumulad dfici is posiiv, hn h pnsion sysm is parially solvn (insolvn), and h promiss of h paricipans migh b parially brokn wihou h sponsorship of h Sa. A dscripion of h main nris in h acuarial balanc sh is providd blow. 9 Daild informaion for h Swdish ABM can b found in Appndi 2. 5
Liabiliis o Pnsionrs Liabiliis o pnsionrs ar calculad as h prsn valu of currn and fuur pnsions for currn pnsionrs. Th formula o calcula liabiliis o pnsionrs is: w A 1 r V P A k A ka& + + + + + A+ k k=0 P A+ k ( + A + k, A+ k a & + A+ whr w is h maimum ag a which popl can surviv, h rirmn pnsion for h pnsionrs agd ) = (3.1) + is h amoun of + is h numbr of pnsionrs agd ( + A + k), and & k is h lif annuiy for popl agd ( + A + k). Liabiliis o Conribuors Liabiliis o conribuors ar calculad in a prospciv mhod 10 as h diffrnc bwn h prsn valu of fuur pnsions and fuur conribuions. Th formula o calcula liabiliis o conribuors is prssd as: whr yar, P A), k Fuur pnsions 64444444 74444444 8 6444444 Fuur conribuions 7444444 8 A 1 A 1A k c V = P( ), && + A k + ka( + A), k + ky( + k), k=0 k=0 =1 θ (3.2) ( + is h amoun of fuur pnsion for conribuors who agd ( + k) a + k is h numbr of conribuors agd ( + k) a yar, and & ( + A k is h lif annuiy a h rirmn ag for popl agd ( + k) in yar. Conribuion Ass a ), Th novl nry on h PAYG acuarial balanc sh is h conribuion ass (CA) dfind by Srgrn [24] and [25], Srgrn and Mikula [26] and h liraur of Swdish Social Insuranc Agncy. Th formula o calcula h CA is prssd as: CA=TD C =(A A ) C Whr TD is h urnovr duraion and is h im pcd o pass from whn a monary uni nrs h sysm as a conribuion unil i lavs in h form of a pnsion. I is also h diffrnc bwn Ar and A c. Th formula for TD 11 is shown in Appndi 1. C is conribuion rvnu a yar A r is h avrag wighd ag for h pnsionrs (wighd by h amoun of annual pnsions considring h ag-bnfi profil), and A c is h avrag wighd ag for h conribuors (wighd by h amoun of ral conribuions considring h ag-arnings profil). 10 This mhod is usd du o h DB naur of h Chins PAYG pnsion sysm. For mor daild informaion s Boado-Pnas al. [5]. 11 Daild informaion can b found in Boado-Pnas al. [5] and Srgrn and Mikula [26]. 6
3.2 US acuarial balanc indicaor mhodology Plamondon al. [20], was a firs amp a concpualising h acuarial balanc of h PAYG sysm. Afr ha, Boado-Pnas al [3] and Billig and Ménard [2] dscribd h diffrn yps of acuarial balanc for h PAYG pnsion sysms, including h Swdish NDC modl. According o hs auhors, h main mhodology 12 usd o compil h acuarial balanc in nonfinancial DB sysms could b dscribd as an aggrga accouning projcion modl ha compars h spnding on pnsion wih h incom from conribuions. In h Unid Sas, an annual acuarial balanc has bn compild sinc 1941 [29].This balanc is dscribd as bing h bnchmark for DB sysm. I basically involvs using h forcas dmographic scnario o drmin h fuur voluion of h numbr of conribuors and pnsionrs according o h ruls of h pnsion sysm. Th acuarial balanc indicaor masurs h sysm's financial susainabiliy 13 by masuring h diffrnc in prsn valu, discound a h projcd yild, bwn spnding on pnsions and incom from conribuions, aking ino accoun ha h lvl of financial rsrvs a h nd of h im horizon rachs a magniud of on-yar pndiur. This valu summariss h sysm s financial dfici or surplus for h 75-yar horizon. Th formula o calcula Acuarial Balanc (AB) Indicaor is as shown as follows: Prsn valu of Conribuions Prsn valu of bnfis 6444444 44 744444444 8 6444444 74444444 8 74 74 74 (1+ gh) (1+ λh) ( TF74) TF0 + y0 θ B0 R =0 h=1 (1 rh) + =0 h=1 (1 rh) h=1 (1 rh) AB = + + + 74 74 (1+ gh) (1+ gh) y0 y0 1444444 =0 2 h r 4 =1 (1 444444 h) + 3 1444444 =0 2 h r 4 =1 (1+ 444444 h) 3 Prsn valu of payrolls Prsn valu of payrolls 144444444444 244444444444 3 Summarizd Incom Ra 1444444444444 2444444444444 3 Summarizd Cos Ra (3.3) Whr TF 0 dnos h valu of asss in h rus fund a h bginning of h priod, θ is conribuion ra a, y 0 dnos h conribuion bas a yar 0, dnos h numbr of conribuors in yar, g is h annual ral wag growh ra, r is h projcd yild ra on rus fund asss, B 0 dnos h avrag pnsion in yar 0, R dnos h numbr of pnsionrs a yar, and λ is h annual ral indaion ofpnsions. 12 Th mos commonly usd mhodologis for making projcions of spnding on pnsions or analysing h susainabiliy of pnsion sysms ar: aggrga or growh accouning modls, micro-simulaion modls, gnral quilibrium modls and indirc modls. On his aspc s h paprs by Lfbvr (2007) and TEPC (2007). 13 Idnifying h diffrnc bwn h concps of solvncy and susainabiliy is no immdia. According o Knll al. (2006), h rm susainabiliy has many dfiniions hough i almos always rfrs o h fiscal policis of a govrnmn, h public scor or h pnsion sysm. On of h mos widly accpd dfiniions in h ara of pnsions is ha of a posiion whr hr is no nd o incras h conribuion ra in h fuur. 7
If AB 0, hn h sysm is susainabl for h n 75 yars. And, if AB < 0, h sysm is unsusainabl. 3.3 Diffrncs bwn h wo mhodologis Th Swdish acuarial balanc sh mhodology and h US acuarial balanc indicaor mhodology ar wo diffrn yps of mhodology o analys h financial halh of h pnsion sysm in h long run. Th Swdish modl is basd on vrifiabl facs, and h drivaion of h conribuion ass is from a sady sa: hus no dmographic or conomic projcions ar mad in his modl. On h ohr hand, h US modl is highly dpndn on h projcions 14 of dmographic and conomic srucurs in h n 75 yars. Th srucurs of h wo acuarial balancs ar diffrn as wll. Th Swdish acuarial balanc sh follows h srucur of h radiional accouning balanc sh whil h US modl is mor lik a financial profil showing h calculaion of h acuarial balanc indicaor. Also h Swdish acuarial balanc sh uss SR as an indicaor o analys h long-rm solvncy lvl of h pnsion sysm and consruc an ABM basd on his SR. Th US uss h acuarial balanc indicaor o calcula how much h currn conribuion ra should incras for h sysm o b susainabl for h n 75 yars. Tabl 2 shows h diffrn characrisics of boh modls. Ownsourc Tabl2:Comparison bwn h US and Swdish modls Swdn Basdonvrifiablfacs Assumpions of a sady sa Srucurofaccouningbalancsh SolvncyRaio US Projcionsforn75-yars Projcionsonpnsionvariabls Morafinancialprofil AcuarialBalancIndicaor 4 Analysis of h Chins PAYG pnsion sysm using h Swdish acuarial balanc sh mhodology - Daa, rsuls and proposd paramric rforms This scion shows firs a dscripion of h daa and assumpions mad o compil h Chins acuarial balanc sh following h mhodology of Swdish acuarial balanc modl, andscondly h rsuls of an acuarial balanc sh for China oghr wih a comparison wih Swdish acuarial balanc sh during h sam priod of sudy. A snsiiviy analysis isalso providd o show how h numbr of conribuory yars affcs h solvncy of h Chins pnsion sysm. Finally, som proposals for paramric rforms ar givn basd on our rsuls. 14 Th US acuarial balanc involvs projcions of h main variabls in h pnsion sysm, such as annual wag growh ra g, yild ra on rus fund asss r, indaion of pnsions, λ, and numbr of conribuors and pnsionrs. 8
4.1 Daa and assumpions for h Chins acuarial balanc sh Th ffciv rirmn ag 15 in China is 53 [14], Financial Asss daa is akn from [16], Conribuion Rvnus ar from [15]. Toal numbr of conribuors ar akn from [15]. I is assumd ha h disribuion of h numbr of conribuors pr ag group follows h sam ag disribuion as h numbr of urban mployd workrs. Disribuion of urban mployd popl pr ag group is basd on [18]. Toal numbr of pnsionrs ar basd on [15]. Disribuion of pnsionrs pr ag group follows h sam disribuion for urban popl agd ovr 53. Disribuion for Urban popl agd ovr 53 pr ag group is akn from [18]. Th oal avrag monhly wag daa for currn workrs ar from aional Burau of Saisics of h Popl s Rpublic of China from yar 2007 o 2012. Wag disribuion pr ag group is akn from h Minisry of Human Rsourcs and Social Scuriy of h Popl s Rpublic of China. Th moraliy abls w usd ar basd on [5]. I is assumd ha onc individuals nr h labour mark, hy conribu hroughou hir working livs wih 100% dnsiy. Th discoun ra for fuur pnsions and conribuions should b consisn wih h on of h conribuion ass, and his ra is assumd o b 0%. I should b nod ha h sysm s SRs dpnd on h rlaion bwn asss and liabiliis and no h ac amoun of asss and liabiliis. Salaris ar kp consan in ral rms pr ag group. W assum ha h numbr of conribuion yars is on avrag qual o 33 in h normal cas 16. I is assumd ha graduas of Junior Scondary School sar working a h ag of 16, of Snior Scondary School a h ag of 18, and of Univrsiy and boyond a h ag of 22. And h daa on Educaional Aainmn for Urban Employd Prsons by s, proporions of fmal mployd prsons in urban ara, and proporion of unmployd womn for h rason of Do Houswork in h urban ara, which ar rquird o calcula h oal conribuions, ar obaind from China Populaion and Employmn Saisics YarBook 2008-2013 [5]. 4.2 Rsuls of Chins acuarial balanc sh and comparison wih Swdn This scionbuilds an acuarial balanc sh for China for h priod 2007-2012 and compars h rsuls wih hos using h Swdish acuarial balanc sh for h sam priod. A snsiiviy analysis for diffrn conribuion yars of h Chins acuarial balanc sh is givn. Rsuls for h Chins acuarial balanc sh 15 In China, h ffciv rirmn ag dos no coincid wih h sauory normal rirmn ag which is 60 for mn and 50 for womn. 16 This assumpion is mad following h advic of prs of Chins pnsion sysm, w go h advic a yar 2014. Lgal rirmn ag for mn (60) and for womn (50) ar usd o calcula h oal conribuion yars. 9
Th rsul of Chins acuarial balanc sh from yar 2007 o 2012 for h normal cas scnario is shown in Tabl 4 17. Th numbr of conribuory yars is assumd o b qual o 33 in his scnario. From Tabl 4, w can s ha h SR for China is always around 0.4 from yar 2007 o 2012, which mans h oal liabiliis ar mor han doubl oal asss. This implis ha h Chins pnsion sysm is qui insolvn. Tabl 4: Th Balanc sh for h Chins pnsion sysm a 31 Dcmbr ach yar. All h nris ar as a proporion of GDP, o mak i asy for comparison bwn diffrn counris, and bwn diffrn pnsion sysms (DB vrsus DC). Conribuion Yars =33 2007 2008 2009 2010 2011 2012 Ass(% of GDP) Financial ass 2.30 2.60 3.14 3.49 3.75 4.22 Conribuion ass 58.84 61.10 67.91 68.90 72.81 76.73 Accumulad dfici 84.28 84.28 93.96 111.00 109.30 113.79 Loss for h priod 0.00 9.68 17.04-1.70 4.49 11.14 Toal asss 145.42157.66 182.06 181.70 190.35 205.88 Liabiliis(% of GDP) Liabiliy o pnsionrs 64.15 69.76 80.67 83.25 84.54 90.63 Liabiliy o conribuors 81.27 87.90 101.39 98.44 105.81 115.25 Toal liabiliis 145.42157.66 182.06 181.70 190.35 205.88 Funding, solvncy and liquidiy Indicaors Raio of (in)solvncy 0.420 0.404 0.390 0.398 0.402 0.393 (asss/liabiliis) Dgr of funding(%) 1.58 1.65 1.73 1.92 1.97 2.05 (financial ass/liabiliis) Liabiliis o conribuors/ 55.9 55.8 55.7 54.2 55.6 56.0 liabiliis(%) Own sourc 17 Du o h pnsion daa for China a yar 2013 is no availabl currnly, h analysd priod for China is from 2007 o 2012. 10
Figur 1: Evoluion of h Solvncy Raio for China from 2007 o 2012 Own sourc Also, Figur 1 shows ha h SR dcrass during our priod of analysis, wha maks h problm vn mor srious if no masurs ar akn. Th voluion of oal asss, oal liabiliis and accumulad dficis for h Chins PAYG pnsion sysm is givn in Figur 2. W can s ha, boh asss and liabiliis ar incrasing during h priod 2007 o 2012, bu h oal liabiliis incras a a highr ra han oal asss, causing an incrasing h amoun of h accumulad dfici. 11
Figur 2: Evoluion of asss, liabiliis and accumulad dficis for Chins pnsion sysm Own sourc Comparison of solvncy lvls bwn China and Swdn Figur 3 show a comparison of h lvl of conribuion asss and oal liabiliis, accumulad surplus/dficisand SR bwn China and Swdnfrom 2007 o 2012. W can s ha gap bwn conribuion asss and liabiliis is dcrasing for Swdn, Figur 3(a) and 3(b), bu his is no h cas for China whr his gap rprsns 170% of h GDP in 2012. As shown in,figur 3(c), China accumulad a larg amoun of dfici which maks h SR lowr han on (S figur 3(d)) whil Swdn is managing o kp a small dfici for som yars and an SR always around 1 18. 18 Th SR is around 1 givn ha, following Srgrn (2001), if for som rason h solvncy raio is lss han 1, h ABM is riggrd. This consiss basically of rducing h growh in pnsion liabiliy ha is, h pnsions in paymn and h conribuors noional capial. 12
Figur 3: Comparison bwn Swdn and China from 2007 o 2012 (a) Conribuion asss and oal liabiliis for Swdn (b) Conribuion asss and oal liabiliis for China (c)comparison of Accumulad surplus/dficis bwn Swdn and China (d) Comparison of SRs bwn Swdn and China Own sourc. Th Swdish rsuls ar basd on h annual "Orang Rpor" 2008 o 2013, s Srgrn [27]. Snsiiviy analysis for Mor conribuion yars and Fwr conribuion yars This scion provids a snsiiviy analysis for diffrn numbrs of conribuory yars. Du o h lack of accura daa for conribuion yars w ar inrsd in how h numbr of conribuory yars migh affc h SR undr h currn ruls of h Chins pnsion sysm. Tabl 5 show h diffrn assumpions mad wih rspc o h numbr of conribuion yars dpnding on h nry ag o h labour mark and h numbr of non-conribuions yars. W can s ha undr h scnario of mor conribuory yars h oal numbr of conribuion yars is qual o 35, and h popl who join h sysm a h ag of 16 will hav a non-conribuory priod of 7 yars. Th prssion o calcula h oal numbr of conribuory yars undr diffrn scnarios is givn in Appndi 3. 13
Tabl5: Diffrn assumpions for conribuory yars Normal Mor conribuion yars Fwr conribuion yars Enry working Ag Non-conribuion Priods a diffrn sar working ag 16 10 7 15 18 5 4 7 22 3 2 5 Toal Conribuory Yars 33 35 29 Tabls 6 and 7 show h rsuls of acuarial balanc shs undr h scnarios of Mor conribuion yars and Fwr conribuion yars. Tabl6: Balanc sh for h Chins pnsion sysm a 31 Dcmbr ach yar undr Mor conribuion yars scnario Conribuion Yars =35 2007 2008 2009 2010 2011 2012 Ass(% of GDP) Financial ass 2.30 2.60 3.14 3.49 3.75 4.22 Conribuion ass 60.05 62.29 69.13 70.03 73.76 77.61 Accumulad dfici 88.68 88.68 98.93 116.98 115.51 121.21 Loss for h priod 0.00 10.26 18.04-1.46 5.70 12.20 Toal asss 151.02163.82 189.24 189.04 198.71 215.23 Liabiliis(% of GDP) Liabiliy o pnsionrs 64.15 69.76 80.67 83.25 84.54 90.63 Liabiliy o conribuors 86.87 94.07 108.58 105.78 114.18 124.60 Toal liabiliis 151.02163.82 189.24 189.04 198.71 215.23 Funding, solvncy and liquidiy Indicaors Raio of (in)solvncy 0.413 0.396 0.382 0.389 0.390 0.380 (asss/liabiliis) Dgr of funding(%) 1.52 1.59 1.66 1.85 1.89 1.96 (financial ass/liabiliis) Liabiliis o conribuors/ 57.5 57.4 57.4 56.0 57.5 57.9 liabiliis(%) Ownsourc 14
Tabl 7: Balanc sh for h Chins pnsion sysm a 31 Dcmbr ach yar undr h Fwr conribuion yars scnario Conribuion Yars =29 2007 2008 2009 2010 2011 2012 Ass(% of GDP) Financial ass 2.30 2.60 3.14 3.49 3.75 4.22 Conribuion ass 55.95 57.95 64.22 64.74 68.27 72.31 Accumulad dfici 76.44 76.44 85.79 102.11 101.67 105.80 Loss for h priod 0.00 9.35 16.31-0.44 4.13 9.24 Toal asss 134.69146.34 169.47 169.90 177.82 191.57 Liabiliis(% of GDP) Liabiliy o pnsionrs 64.15 69.76 80.67 83.25 84.54 90.63 Liabiliy o conribuors 70.54 76.58 88.80 86.65 93.28 100.94 Toal liabiliis 134.69146.34 169.47 169.90 177.82 191.57 Funding, solvncy and liquidiy indicaors Raio of (in)solvncy 0.432 0.414 0.397 0.402 0.405 0.399 (asss/liabiliis) Dgr of funding(%) 1.71 1.78 1.85 2.06 2.11 2.20 (financial ass/liabiliis) Liabiliis o conribuors/ 52.4 52.3 52.4 51.0 52.5 52.7 liabiliis(%) Own sourc Th rsuls of h snsiiviy analysis show ha h Chins solvncy raio kps qui sabl undr h diffrn scnarios, ha is around 0.4, which again indicas h insolvncy of h sysm undr h diffrn scnarios analysd. Also i can b obsrvd in Figur 4, ha h highr h numbr of conribuion yars h lowr h solvncy raio. Th rason bhind his rlaionship is ha h formula o calcula h iniial pnsion for h Chins PAYG pnsion sysm oghr wih h conribuion ra s by h Chins auhoriis ld o a sysm ha is no acuarially fair or nural according o Quissr [21]. In ohr words, h inrnal ra of rurn (IRR) 19 for h pnsion sysm is highr whn w pand h numbr of conribuory yars 20. Howvr, h rplacmn ra dcrass du o h dcras in h numbr of yars of conribuions, ha is, fwr conribuion yars lad o a lowr iniial pnsion. 19 Th formula o calcula IRR for pnsion is in Appndi D. 20 I should b nod ha whn discussing SR undr diffrn numbr of conribuory yars, h rirmn ag is assumd. In raliy, i is vry hard o mak h rirmn ag consan whil h numbr of conribuory yars changs. Th only way o do his is conrolling h nry ag ino h sysm and his is hard o apply. 15
Figur 4: Rlaionship bwn Conribuion Yars and Solvncy Raio 4.3 Paramric rforms basd on acuarial balanc sh for China Th rsuls of h Chins acuarial balanc sh calculaions show ha h currn Chins PAYG pnsion sysm is only parially solvn, and ha hrfor som paramric rforms should b undrakn immdialy o improv h sysm s solvncy lvl in h long-rm. This scion proposs som paramric rforms for h currn Chins PAYG pnsion sysm o achiv solvncy. Hnc, for ampl, in ordr for h Chins pnsion sysm o achiv solvncy hrough an incras in h conribuion ra (CR), his ra would hav o go up by 16%. Furhr, h Rplacmn Ra (RR) for Naional Accouns would hav o dcras o 10% 21, h indaion of pnsions ( λ) dcras by 45% or h rirmn ag incras o 66. Obviously som or mos masurs akn in isolaion ar unfasibl. Tabl 8 shows h ffc, via h SR, of diffrn combinaions of paramric soluions akn wo a a im. 21 Th oal Rplacmn Ra (Individual Accoun and Naional Accoun) should b 22%, as h rplacmn ra for h Individual Accoun in 2012 is 12%. 16
Tabl 8: (In)Solvncy raio (SR) for h Chins pnsion sysm afr changs in paramric masurs RR Rirmn Ag Im 31% 22% 18% 0% -10% -20% 53 60 63 = 0.393 0.539 0.649 0.393 0.455 0.539 0.393 0.613 0.790 5% 0.533 0.758 0.938 0.533 0.626 0.758 0.533 0.946 1.372 CR 10% 0.703 1.046 1.346 0.703 0.841 1.046 0.703 1.497 2.742 15% 0.914 1.444 1.963 0.914 1.119 1.444 0.914 2.590 9.869 31% 0.393 0.455 0.539 0.393 0.613 0.790 RR 22% 0.633 0.766 0.539 0.913 1.265 18% 0.770 0.948 0.649 1.175 1.744 0% 0.393 0.613 0.790-10% 0.455 0.747 1.007-20% 0.539 0.956 1.386 Own sourc Th SRs wihin h rang [0.9, 1.1] ar highlighd in h abl. A possibiliy o rsor solvncy if hr paramric masurs wr akn simulanously scuring a rplacmn ra of 50% would b a rirmn ag of 60, an incras of h CR of 6%, and a h sam im a dcras in h indaion of pnsions by 10%: 5 Analysis of h Chins PAYG pnsion sysm using h US acuarial balanc indicaor mhodology - Daa, rsuls and proposd paramric rforms Firs, his scion ss ou h daa usd and assumpions mad o calcula h acuarial balanc indicaor for China following h US mhodology. Scondly h rsuls for h Chins acuarial balanc indicaor oghr wih a comparison wih US is givn. A snsiiviy analysis of h Chins acuarial balanc indicaor undr hr diffrn dmographic scnarios (pssimisic, normal and opimisic) is also providd. Finally, som proposals for paramric rforms of h Chins pnsion sysm ar givn basd on our rsuls. 5.1 Daa and assumpions for h Chins acuarial balanc indicaor Annual ral wag growh ra g, h annual ral indaion of pnsions λ, and projcd yild ra r for h Chins pnsion fund ar assumd o kp consan a h las 20 yars avrag ras. Th projcd daa on h populaion of China is from [6]. 17
Th projcions undr Normal Scnario follow h srucur of Mdium Varian (Mdium friliy, normal moraliy, normal inrnaional migraion) in [6]. A snsiiviy analysis for Opimisic scnario and Pssimisic Scnario rgarding Chins AB is providd. Th projcions undr Opimisic scnario assum h numbr of conribuors and pnsionrs rmain consan as from h bginning of h priod of sudy, sinc an aging problm will lad o a much lowr dpndncy raio in h fuur, h opimisic scnario kps h dpndncy raio consan as in h currn yar. Whil h projcions undr h Pssimisic Scnario assum ha h numbr of conribuors follows a Low Varian (Low friliy, normal moraliy, normal inrnaional migraion) srucur and h numbr of pnsionrs follows High Varian (High friliy, normal moraliy, normal inrnaional migraion) srucur [6]. This assumpion will giv us a pssimisic scnario wih h numbr of conribuors dcrasing and of pnsionrs incrasing rapidly in h n 75 yars. 5.2 Rsuls of Chins acuarial balanc indicaor and comparison wih US Th calculaion and rsuls of h Chins AB ar shown in his scion, oghr wih h rsuls of h AB for h US a h sam yar for purposs of comparison. Tabl 9 shows h calculaion of AB in Normal Scnario for China and compars i wih h US, for h priod from 2012 o 2086. Tabl9:Elmns of h75-yar acuarial balanc 2012-2086. Prsn valu a January 2012. Ims China US (RMB in billions) (Dollar in billions) 1 Incom from conribuions for n 75yars 717977 45198 2 Spnding on pnsions for n 75 yars 2027633 56477 3=1-2 Iniial dfici basd on n 75 yars -1309656-11278 4 Trus fund asss a sar of priod 2190 2678 5=3+4 Opn group unfundd obligaion -1307466-8601 6 Ending arg rus fund 95982 501 7=5-6 Rsuls for h priod -1403448-9101 8 Aggrga conribuion bass 3589883 341465 9=(1+4)/8 Summarizd incom ra 20.06% 14.02% 10=(2+6)/8 Summarizd cos ra 59.16% 16.69% 11=9-10 Acuarial Balanc(AB) -39.09% -2.67% 12 Yar of firs dfici 2025 2012 13 Rsrv fund hausd(yar) 2034 2033 Ownsourc Th AB for China a yar 2012 is -39.09%, which mans ha h currn CR in China should b immdialy incrasd by 39.09% o mak h Chins PAYG pnsion sysm susainabl, and hrfor h CR in China should b 59.09%. A h sam im, h AB for h US in 2012 is qual o -2.67%, maning ha h US only nds o incras h CR 18
o 15.91% o mak is pnsion sysm susainabl ovr h n 75 yars. As a rsul, h currn Chins PAYG pnsion sysm is qui unsusainabl compard o ha of h US hough China will hav wo mor yars han h US for h rsrv fund o b hausd, and h yar of firs dfici is 13 yars lar han for h US. I should b nod ha, iniial dfici (or surplus) in our abl is h diffrnc bwn h prsn valu of oal incom from conribuions for n 75 yars and h prsn valu of oal spnding on pnsions for n 75 yars. This is diffrn from dfici (or surplus) for ach yar, for ampl, h firs yar ha pndiur on pnsions cdsh incom from conribuions for China is yar 2025, whr h incom is 3569 billion RMB and spnding 3925 RMB. As for yar 2012, h incom from conribuions cds spnding on pnsions, gnraing a surplus of 1004 billion RMB in yar 2012 for h Chins pnsion sysm. Snsiiviy analysis for Chins acuarial balanc indicaor Tabl 10 shows h calculaion of h Chins AB undr hr diffrn scnarios. As mniond, undr h opimisic scnario h numbr of conribuors and pnsionrs rmain consan as in yar 2012. Undr h pssimisic scnario is assumd ha h numbr of conribuors follows a low varian and h numbr of pnsionrs a high varian Tabl10:Elmns of h 75-yar acuarial balanc 2012-2086 for China undr diffrn scnarios. Prsn valu a January 2012. Uni: RMB in billions Ims Opimisic Normal Pssimisic 1 Incom from conribuions 948870 717977 536258 2 Spnding on pnsions 1092022 2027633 2071472 3=1-2 Iniial dfici -143152-1309656 -1535214 4 Trus fund asss a sar of priod 2190 2190 2190 5=3+4 Opn group unfundd obligaion -140962-1307466 -1533024 6 Ending arg rus fund 57170 95982 106616 7=5-6 Rsuls for h priod -198132-1403448 -1639640 8 Aggrga conribuion bass 4744349 3589883 2681290 9=(1+4)/8 Summarizd incom ra 20.05% 20.06% 20.08% 10=(2+6)/8 Summarizd cos ra 24.22% 59.16% 81.23% 11=9-10 Acuarial Balanc(AB) -4.18% -39.09% -61.15% 12 Dpndncy Raio a yar 2086 3.08 0.82 0.42 Own sourc In h Opimisic Scnario, whn h assumd dmographic srucur is kp consan for h n 75 yars as in 2012, h AB for China is only -4.18%, compard wih -39.09% for h normal scnario. Howvr, h AB for China in h Pssimisic Scnario is qual o -61.15%. Alhough h AB changs a lo undr diffrn scnarios, h summarisd incom ra is mor or lss h sam, hus h major chang of AB coms from h summarizd cos ra, i.. h prsn valu of fuur pnsions ndd o b paid and h nd arg pnsion fund as a prcnag of h prsn valu of conribuion bass. 19
And vn in h cas of an Opimisic Scnario wih a sabl dmographic srucur h Chins pnsion sysm is no susainabl. Th dpndncy raio a h nd yar for ach scnario is prsnd a h boom of h abl. As pcd, h dpndncy raio is highs in h opimisic, and lows in h pssimisic scnario. Sinc h aging problm is h mos imporan problm for h fuur of h Chins PAYG pnsion sysm, his snsiiviy analysis only considrs h diffrn scnarios for dmographic srucur changs. Furhr rsarch is rquird for macroconomic variabl changs, considraion of which is byond h scop of his papr. 5.3 Paramric rforms basd on h acuarial balanc indicaor for China Sinc h AB for China indicas ha h currn Chins PAYG pnsion sysm is no susainabl undr all h scnarios, som paramric rforms nd o b implmnd immdialy o mak h sysm susainabl in h fuur. Tabl 11 provids h paramric rforms and hir simad rsuls basd on h Normal Scnario. If paramric rforms wr undrakn ach in isolaion, hn h CR should b incrasd by 16%. Anohr possibiliy would b a dcras in h indaion on pnsions by 10.51% or an incras in h rirmn ag o 66. Howvr, h wo paramric masurs could b undrakn simulanously, o mak a rlaivly smooh rform, as shown in Tabl 11. Tabl11:Paramric soluions of wo paramric rforms simulanously for h Chins acuarial balanc indicaor. RR Rirmn Ag Im 31% 25% 20% 0% -1% -2% 62 64 66 = -39.0% -27.7% -18.1% -39.0% -15.3% -1.4% -5.3% -3.0% 1.3% 10% -29.1% -17.7% -8.1% -29.1% -5.3% 8.6% 4.8% 7.0% 11.3% CR 15% -24.1% -12.7% -3.1% -24.1% -0.3% 13.6% 9.8% 12.0% 16.3% 20% -19.1% -7.7% 1.9% -19.1% 4.7% 18.6% 14.8% 17.0% 21.3% 31% -39.0% -15.3% -1.4% -5.3% -3.0% 1.3% RR 25% -27.7% -8.4% 2.7% -0.4% 1.5% 4.9% 20% -18.1% -2.7% 6.2% 3.7% 5.2% 7.9% 0% -5.3% -3.0% 1.3% -1% 5.0% 6.4% 8.9% -2% 11.0% 11.8% 13.3% Own sourc Highlighd bos ar h rsuls for h AB wihin h rang [-8%, 8%] 6 Conclusions This papr uss wo acuarial balanc mhodologis o analys h Chins PAYG pnsion sysm. Firs w compil h acuarial balanc sh for h Chins DB PAYG pnsion sysm basd on h vrifiabl facs, no h projcion daa, following h Swdish acuarial balanc sh modl. Th rsuls show ha h oal liabiliis of h currn Chins PAYG pnsion sysm ar mor han doubl is asss, which implis 20
ha h sysm is qui insolvn. And h Solvncy Raio (SR) kps dcrasing during h priod w analysd. From h snsiiviy analysis for h numbr of conribuion yars, w find ha h Chins solvncy raio dcrass whn h numbr of conribuory yars incrass. Som paramric rforms o rsor h solvncy and susainabiliyof h Chins pnsion sysm ar providd using h Swdish acuarial balanc sh. Th rsuls show ha i is mor pracical o ak wo rforms oghr han applying ach on individually. In addiion, if hr masur ar akn oghr, w can vn incras h currn Chins oal RR o 50% as h world sandard lvl, by incrasing h CR by +6%, dcrasing h indaion on pnsions by 10%, and a h sam im incrasing h rirmn ag o 60. Th US prsns an acuarial balanc indicaor (AB) in is annual pnsion rpor, which analyss h susainabiliy of h pnsion sysm basd on n 75 yars projcions of dmographic and conomic srucurs, and i is a qui diffrn mhodology from h Swdish acuarial balanc sh. This papr also analyss h Chins PAYG pnsion sysm using h US framwork. Th rsuls show ha h AB for China is qual o -39.09%, whil AB for US a h sam priod is only -2.67%. Th rsuls following paramric rforms basd on h Chins acuarial balanc indicaor ar also givn, A possibl combinaion of a paramric rform following h US framwork would b o incras h CR by 10% and a h sam im dcras h indaion of pnsions by 1%. Finally, as a rsul, no mar undr which modl, h solvncy lvl or susainabiliy lvl of h Chins PAYG pnsion sysm is qui low 22. Som paramric rforms nd o b undrakn immdialy o mak h sysm solvn or susainabl in h long-rm. Acknowldgmns: This projc has rcivd funding from h Europan Union s Svnh Framwork Programm for rsarch, chnological dvlopmn and dmonsraion undr gran agrmn no 318984-RARE. Maríadl Carmn Boado-Pnas is graful for h financial assisanc rcivd from h Spanish Minisry of h Economy and Compiivnss (projc ECO2012-36685) and h Insiu and Faculy of Acuaris (IFoA). Prliminary vrsions of his papr wr prsnd a h Prspcivs on Acuarial Risks in Talks of Young rsarchrs (PARTY) in January 2015 and a RARE Sminar a h Univrsiy of Livrpool in 2014 and a h 18h Inrnaional Congrss on Insuranc: Mahmaics & Economics (IME 2014) in Shanghai (China) in July 2014. W ar graful o sminar paricipans and spcially o BingwnZhng and Junichi Sakamoo for hir valuabl commns and Pr Lawrnc for his English suppor. Any rmaining rrors ar nirly 22 In addiion, SR for Spain a yar 2006 is 0.7 according o Boado-Pnas al. [5] whil h SR for China a yar 2007 is 0.4. And AB for Spain a yar 2010 is -14% according o Vidal-Mliá whil h AB for China a yar 2012 is -39%. No mar which modl, h rsuls for China ar consisnly wors compard o Spain. 21
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Appndi 1: Th Formula for Turnovr Duraion (TD) Th formula of TD is as blow, s Boado-Pnas al. [3] and Srgrn and Mikula [26]: Pay ou duraion, p 6444444444 74444444444 r Pay in duraion, p 8 644444444 744444444 c 8 w A 1 A 1 k && + A+ ka + A+ k(1+ g) + ky( + k),1( k + 1) k=0 k=0 = + A w A 1 A 1 k + A+ k(1+ g) y( + k),1 + k k=0 k=0 = ( 14 A 1) + p 4444 244444 3r ( 14 + A 1 p ) 4444 244444 c3 Avragwighd ag of pnsionrs, A r Avragwighd ag of conribuors, A c TD (A1.1) + (A1.2) whr w is h maimum survival ag for h whol populaion, is h ag ha popl in h sysm sar o work, A is h numbr of conribuion yars, y ( + k),1 is firs salary in ral rms for popl agd ( + k), and a & + A+ k is h lif annuiy for popl agd ( + A + k). I can b inrprd in an inuiiv way ha on avrag hr will b TD yars of annual conribuions coming ino h sysm bfor h pnsion commimns incurrd his yar hav o b paid ou as bnfis. Appndi 2: Th ABM in h Swdish pnsion sysm According o Vidal-Mliá al. [32].h solvncy raio usd in Swdn has a doubl purpos: o masur whhr h sysm can fulfill is obligaions and o dcid whhr h ABM should b applid. ABM is a s of prdrmind masurs sablishd by law applid immdialy as rquird according o SR, s Vidal-Mliá al. [32]. Onc SR is lss han 1, a balanc ind will b applid o pnsion paymns and o h conribuors noional pnsion capial insad of h incom ind. Th formula o calcula h balanc ind a yar, h firs yar whn SR is lss han 1, is: BI = I I + i SR (A2.1) + i 1 In h yar +i, h BI is qual o: I = (A2.2) i + i BI + i SR + ibi+ i 1 = I+ i SR + i I+ i 1 i=0 Th prssion for h incom ind for h yar is: 25
1/3 u 1 CPI 4 CPI 1 I = ki 1 (A2.3) u 4 CPI 1 CPI 2 Whr, u = Y/, Y is h oal pnsion-qualifying incom wihou a ciling limiaion, for prsons agd 16-64 in h yar, afr dducion of h individual pnsion conribuion. is h numbr of prsons agd 16-64 wih pnsion-qualifying incom in h yar. CPI 1 is h consumr pric ind for Jun of h yar. And k is h adjusmn facor for rror in simaion of u 1. Appndi 3: Calculaion of conribuion yars Th formula o calcula h oal numbr of conribuion yars is as follows: A = M + W 22 =16 22 =16 ( R m [( R w c A ) M c A )(1 W ) + ( ) W ] W s s s (A3.1) whr A dnos h oal numbr of conribuion yars undr diffrn scnarios. M is h proporion of mal conribuors in h oal working populaion. is h ag ha popl sar o work. R m is h lgal rirmn ag for mal workrs. c A is avrag non-conribuion priods for popl who sar working a ag. M ar h wighs of mal workrs who sar working a ag. W is h proporion of fmal conribuors in h oal working populaion. R w is h lgal rirmn ag for fmal workrs. W s ar h wighs of fmal workrs who sop working afr marriag 23. s is h avrag ag whn fmal workrs sop working afr marriag. W ar h wighs of fmal workrs who sar working a ag. Appndi 4: Inrnal Ra of Rurn for h pnsion sysm Th Inrnal Ra of Rurn (IRR) summariss h rlaionship bwn conribuions and bnfis rcivd during h lif cycl. Th IRR is dfind as h paramr I of h compound capialisaion law ha allows h qualiy bwn h flow of conribuions and h pnsions. Th formula o calcula IRR for pnsion is: 23 Th prssion of his daa appard in China human rsourcs and social scuriy yarbook as Raio of unmploymn of womn for h rason of Do Houswork. 26
+ A w 1 C = = (1+ IRR) = + A+ 1(1+ P IRR) (A4.1) Whr C is h conribuion a yar, P is h pnsion a yar, w is h maimum survival ag. 27