Workng Papers n Socal Insurance 2001:3 Comment to The Englsh Translaton of The Legslaton on the Automatc Balance Mechansm Ole Settergren The Natonal Socal Insurance Board
OLE SETTERGREN THE NATIONAL SOCIAL INSURANCE BOARD, SWEDEN ole.settergren@rfv.se, 2001-09-18 COMMENT TO THE ENGLISH TRANSLATION OF THE LEGISLATION ON THE AUTOMATIC BALANCE MECHANISM Enclosed s an unoffcal translaton of the legslaton on the so-called automatc balance mechansm of the new Swedsh publc penson system. It s not a translaton of the government bll that presented the proposed legslaton that parlament adopted n May of ths year. The bll explans both more generally and more n detal how the law wll work. Further the bll also comments the reasons and as well as the foreseen alternatves to the automatc balance mechansm. The balance mechansm s a part of the legslaton governng the ndexaton of pensons and (notonal) penson captal. As long as the balance mechansm s nactve the ndexaton of pensons notonal penson captal s based on the growth n average ncome. Snce the growth n average ncome normally wll devate from the systems nternal rate of return ths ndex mples that labltes may grow faster than assets, or vce verca. If and when labltes should exceed assets, the bass for ndexaton s automatcally swtched to an approxmaton of the system s nternal rate of return, thus automatcally adjustng penson levels as well. The penson level s automatcally reestablshed, as s growth n average ncome as the bass of ndexaton, as soon as ths s possble wthout undermnng the fnancal balance of the system. Only hstorc transactons are used to calculate the lablty and the assets. The valuaton of assets s performed by a new concept, expected turnover duraton. The automatc balance mechansm secures the fnancal stablty of the new penson scheme wth a fxed contrbuton rate. The fnancal burden from a negatve turn out of all potental rsks of the penson scheme are, f fnancally requred, dstrbuted through the ndexaton of (notonal) penson captal and pensons. Examples of rsk factors are; fertlty, labour force partcpaton, mortalty, the return on buffer fund captal and changes n ncome and mortalty patterns. In most analysed scenaros, the balance mechansm secures that the buffer fund s not empted. In some scenaros the buffer fund wll be empted but the fund wll never go nto severe long-term defct. To handle a stuaton wth a temporary negatve buffer fund the funds have been enttled to fnance oblgatons by borrowng. For more nformaton about the balance mechansm n Englsh see The Automatc Balance Mechansm a non-techncal ntroducton,, Wrtschafts Poltsche Blätter 2001/4 also on the web ste of the Natonal Socal Insurance Board, www.rfv.se. 73
OLE SETTERGREN 2001-07-11 Englsh, unoffcal, translaton of the legslaton on The Automatc Balance Mechansm Chapter 1 5 a For each year the Government shall determne a balance rato. Ths rato shall show the relatonshp between the contrbuton asset of the pay-as-you-go system, wth the addton of the reported market value of the assets of the Frst, Second, Thrd, Fourth and the Sxth Natonal Penson Fund, and the penson lablty of the pay-as-you-go system at the end of the second year precedng the applcable year for the balance rato, hereafter referred to as the balance-rato year. By contrbuton asset s meant the value of the contrbutons to the pay-as-you-go system multpled by the average number of years elapsng from the tme when penson credt s earned to the tme when the penson s dsbursed (turnover duraton). By penson lablty s meant the total penson commtment of the pay-asyou-go system. 5 b Penson contrbutons are calculated as 1. the average ncome of the second-fourth years precedng the balance-rato year, multpled by 2. the estmated relatve annual change n ncomes n the second-ffth years precedng the balance-rato year. In calculatng the relatve change n ncomes, the annual change n the general prce level n the same perod from June to June shall be deducted. The resultng value shall thereafter be adjusted by the change n the general prce level from June two years precedng the balance-rato year to June of the year mmedately precedng the balance-rato year. Turnover duraton s calculated as the medan of the turnover duratons for the thrd, fourth, and ffth years precedng the balance-rato year. The penson lablty s calculated for the second year precedng the balance-rato year, as the sum of 1. penson balances calculated n accordance wth Chapter 5, 2, 2. the value of penson credts for the ncome-replacement penson, such value to be calculated n accordance wth Chapter 4, 2 6, 3. penson dsbursements for each age group n December, multpled by the estmated number of remanng dsbursements of an average penson for the same age group, and adjusted by the nterest-rate factor specfed n Chapter 5, 12, second paragraph, and 4. the estmated value of future dsbursements of the supplementary penson to ndvduals who have not yet begun to receve such a penson. The Government may publsh addtonal regulatons for the mplementaton of the statutory provsons concernng the calculaton of the balance rato. The calculatons are to be performed by the Natonal Socal Insurance Board 5 c 74
If the balance rato for a partcular year s less than 1.00, the Government shall determne a balance ndex to be used for certan calculatons n accordance wth ths statute. A balance ndex shall thereafter be determned for each year untl such tme as sad ndex shall equal or exceed the ncome ndex. In the ntal calculaton of the balance ndex for such a perod, the balance rato shall be multpled by the ncome ndex for the same year. For each succeedng year of the perod, the balance ndex as thus calculated shall be multpled by the rato between the ncome ndex after year end and the ncome ndex pror to year end and thereafter by the balance rato applcable after year end. Chapter 5 6 If the ncome ndex changes between the applcable year for a recalculaton n accordance wth 4, or, f no such recalculaton s to be made, between the year n whch the ncome ndex was determned and the year thereafter, the penson balance shall be recalculated to reflect ths change. For years for whch a balance ndex s determned, the calculaton shall reflect ths ndex nstead of the ncome ndex. The calculaton shall be performed after the penson credt for the mmedately precedng year has been determned and after the recalculaton has been performed n accordance wth 4. 75
Formula for calculatng the balance rato 1. The balance rato, BR, s calculated as CA( t 2) + F( t 2) BR( = D( t 2) CA ( = C( T ( C( + C( t 1) + C( t 2) C( CPI( t 3) C( = 3 C( t 3) CPI( [ T ( t 1), T ( t 2), T ( 3) ] T ( = medant t 1 3 CPI( CPI ( t 1) (1.0) (1.1) (1.2) (1.3) where t CA F D C T C T CPI = calendar year f the varable refers to flows, end of calendar year f the varable refers to stocks = contrbuton asset = buffer fund, the aggregate market value of the assets of the Frst-Fourth and the Sxth Natonal Penson Funds. By market value s meant the value whch n accordance wth Ch. 6, 3, of the Natonal Penson Funds Act (2000:192) and Ch. 4, 2, of the Sxth Natonal Penson Fund Act (2000:193), s to be shown n the annual reports of these funds = penson lablty = smoothed value for the contrbuton to the pay-as-you-go system = smoothed value for turnover duraton = contrbutons to the pay-as-you-go penson system, n accordance wth accountng practce. = turnover duraton = consumer prce ndex from June 2. The average retrement age, R, s calculated as R( = where R ( t P ( ) G ( R () t = 61 R () t = 61 P () t G () t P () t G () t, R rounded off to nearest whole number (2.0) = age at end of year t for persons born n the same calendar year, or age group = the oldest age group for whch pensons have been granted n year t = total of pensons granted monthly n year t to persons n age group = annualzaton dvsor n year t for age group 76
3. Turnover duraton, T, s calculated as Tt () = ID() t + OD() t (3.0) 3.1 Pay-n duraton, ID, s calculated as ID() t = Rt () 1 = 16 E () t L () t ( Rt () 0,5) Rt () 1 = 16 E () t L () t (3.1.1) E() t E 1() t + + N () 1() ()1() t N E Rt t + t E() t =, for ERt () 1() t = (3.1.2) 2 N () t Rt () 1 L () t = L () t h () t for = 17, 18,..., Rt () 1 där L () t = 1 (3.1.3) 1 16 N () t h () t = for 17, 18,..., R(-1 N ( t 1) = 1 (3.1.4) where E N ( = the sum of 16 % of penson-qualfyng ncome calculated n accordance wth Ch. 2 of the Natonal Income Replacement Penson Act (1998:674) and 16 % of penson-qualfyng ncome calculated n accordance wth Ch. 3 of sad act = number of ndvduals n age group who at any tme have been credted wth penson-qualfyng ncome or mputed ncome and who have not been regstered as deceased 3.2 Pay-out duraton, OD, s calculated as OD() t = Rt () = Rt () 1 ( Rt () + 0,5) 1,016 L () t ( Rt () + 0,5) Rt () = Rt () L ( = L ( he (, L ( Rt () + 0,5) 1,016 L () t 60 = 1 (3.2.1) (3.2.2) P ( he ( = för = 61, 62,..., R( (3.2.3) P ( + Pd ( + 2 Pd ( where R( P ( = age of the oldest person recevng a penson n year t = total penson dsbursements n December of year t to age group 77
Pd ( t Pd ( ) = total monthly penson dsbursements to persons n age group made n December of year t-1 and ceasng n year t = total monthly pensons to persons n age group wth pensons granted n year t and ceasng to be dsbursed n year t 4. Penson lablty, D, s calculated as D ( = AD( + DD( (4.0) AD ( = K( + E( + ATP( (4.1) R( DD( = = 61 Ge ( + Ge ( t 1) + Ge ( t 2) P ( 12 (4.2) 3 Ge () t = Rt () j= ( Lj t Lj+ 1 t ) 1 () + () 1.016 2 j 1 L () t (4.3) where AD = penson lablty n regard to penson commtment on whch dsbursement has not yet commenced (penson lablty to economcally actve ndvduals) DD = penson lablty n regard to pensons currently beng dsbursed (penson lablty to retred persons n the pay-as-you-go system) K = total penson balances n accordance wth Ch. 5, 2, of the Natonal Income Replacement Penson Act (1998:674) E = penson credt for ncome-replacement penson n accordance wth Ch. 4, 2 6, of sad act ATP = estmated value of the Natonal Supplementary Penson and so-called Basc Income Replacement Penson for persons who have not yet begun to receve these two pensons Comment on the Formula for Calculatng the Balance Rato The proposed method of calculatng the contrbuton asset and the penson lablty nvolves a numercal approxmaton of a contnuous calculaton and s based on assumptons whch nclude the followng: brths and deaths of ndvduals are evenly dstrbuted throughout the applcable year, contrbuton revenue and penson dsbursements are evenly dstrbuted throughout the applcable year. The calculaton s performed for age groups, not by calendar tme. The calculaton s based on a steady state wth respect to the earnng of penson credt and the dsbursement of pensons. 78
1.0 The balance rato for year t. The estmated assets and labltes of the penson system at the end of the second year (t-2) before the balance-rato year can affect the ndexng of the penson lablty at the end of the year (t-1) before the balance-rato year. Ths shft of one year s necessary n order to avod any element of forecastng n the calculaton of the assets of the system. 1.1 In order to acheve a smaller standard devaton n the contrbuton asset, the latter s calculated on the bass of smoothed values for contrbuton revenue and turnover duraton. 1.2 The smoothng of contrbuton revenue s acheved by calculatng the average contrbuton revenue for the three most recently ended calendar years at the tme of the calculaton and by projectng ths revenue one year ahead. The projecton s lnked to the calculaton of the ncome ndex. Ths s acheved by usng the underlyng data (defned n a dfferent manner) and nflaton rate for the same years n projectng smoothed contrbuton revenue as are used n the recalculaton of the penson lablty. 1.3 In order to calculate the turnover duraton for a partcular year, t s necessary n prncple to determne the penson credt of every ndvdual. The penson credt for the year t-2 has not been determned for all ncome earners n the autumn of t-1, when the balance rato for the year t s to be calculated. For ths reason, the smoothed value for the turnover duraton for year t s based on the years t-1, t-2, and t-3. For ths purpose the medan s consdered preferable to an arthmetc mean. Snce turnover duraton s ndependent of the general development of ncomes and prces, there s no need to make a projecton for the value of turnover duraton. 2.0 In order to estmate turnover duraton n accordance wth the proposal, there must be a dvson nto penson-credt-accumulaton duraton and penson-dsbursement duraton. For ths purpose an average retrement age s calculated annually. The average retrement s a mean, weghted by penson captal, of the ages at whch pensons are ntally dsbursed. The proposed calculaton means that the supplementary penson and the ncome-replacement penson can be treated n the same manner. Furthermore, the calculaton means that any correlaton between amount of penson and age at dsbursement wll be taken nto consderaton. In order to facltate the calculaton of turnover duraton, the estmated age of retrement s rounded off to the nearest whole number. It s estmated that n so dong the maxmum roundng-off error n turnover duraton wll be 0.2 year. Ths means that the maxmum roundng-off error n the calculaton of the contrbuton asset wll be approxmately 0.5 %. 3.0 79
Turnover duraton can be dvded nto two segments. One s the weghted average tme durng whch penson credt s earned and accumulated, IT; the other s the weghted average tme durng whch pensons are dsbursed, UT. IT s calculated n accordance wth 3.1.1-3.1.3 by frst computng a mean value for the penson credt earned by each age group durng the year of measurement. Thereafter, a calculaton s made of the proporton of total accumulated penson credt that each age group would have earned, on the bass of the calculated mean, n an actuarally normalzed collectve. The term age group refers to persons born n the same year who have receved penson credt at any tme. IT could have been calculated more smply and drectly by basng t solely on the change n penson credt earned durng the year of measurement. The reason why the more complcated calculaton method was chosen was that t results n a smaller standard devaton. 3.1.1 The rato ndcates the average tme n years, weghted by penson credt earned, from when penson credt s earned untl pensons are ntally dsbursed. The average penson credt earned for each age group, PR (, s multpled by the normalzed number of persons nsured, L (, n the age group. The product ndcates the penson credt that would be earned by an actuarally normalzed collectve. The share of each age group, multpled by the tme remanng untl the ntal dsbursement of pensons, R ( 0, 5, s added together wth that of all other age groups. Ths sum s dvded by the total penson credt of the actuarally normalzed collectve. The calculaton of the tme durng whch penson credt s earned s based on the assumpton that retrement occurs at an exact age that s, the brthday on whch the ndvdual reaches the retrement age n accordance wth equaton 2.0. The deducton of 0.5 s made to take account of the fact that penson credt on average s earned at md-year. Durng the phase-out of the Natonal Penson System, whch for ths purpose wll contnue through 2018, t wll be possble to earn penson credt under that system as well as the new, reformed penson system. However, the calculaton of turnover duraton s based on the assumpton that penson credt earned s equal to 16 % of the contrbuton base. Ths means that n regard to the earnng of Natonal Supplementary Penson credt, turnover duraton s treated on the same bass as the earnng of penson credt under the reformed rules. Thus, no consderaton s gven to the fact that a porton of the contrbuton base conssts of Natonal Supplementary Penson credt and that ths penson credt wll normally dffer n amount from 16 % of the contrbuton base. Thus, durng the phase-out of the Natonal Supplementary Penson, there wll be a rsk of error n estmates of turnover duraton. However, the margn of error wll be qute lmted and wll rapdly dmnsh. 3.1.2 E () t s the penson credt of each age group earned n year t by each person who has earned penson credt at any tme n year t or earler. 3.1.3 80
L ( s the estmated normalzed number of ndvduals of age who at any tme have receved penson credt n year t. 3.1.4 h ( descrbes the change durng year t n the number of ndvduals n age group who at any tme have been credted wth penson qualfyng ncome or mputed ncome. 3.2.1 The rato ndcates the average tme n years, weghted by the amount of penson, from ntal penson dsbursement untl fnal penson dsbursement. The estmated normalzed penson for each age group, (, reduced to take ( () 0.5) account of the norm 1.016 Rt+, s multpled by the tme durng whch the age group has receved a penson, ( Rt () + 0.5). Ths duraton of dsbursement, weghted by the normalzed penson amount, s summed for all age groups. Ths sum s dvded, n turn, by the sum of all normalzed penson dsbursements. The calculaton of dsbursement duraton s based on the assumpton that retrement occurs at an exact age n other words, on the brthday when the ndvdual reaches the retrement age n accordance wth equaton 2.0. The addton of 0.5 s made n order to account for the fact that pensons on average are dsbursed at md-year. 3.2.2 L ( may be taken as a relatve number of ndvduals n age group, weghted by the amount of ther penson, who receve a penson n year t. L thus consttutes an economc lfe-expectancy table specfc to the penson system. L s the result of a chaned multplcaton of economc death rates. 3.2.3 he shows the change n penson dsbursements to age group durng year t as a consequence of death (or revocaton of retremen. Based on penson dsbursements and not on the mortalty of ndvduals, the calculaton reflects the relatonshp, f any, between penson levels and mortalty. In certan cases penson amounts wll be granted and dsbursements wll cease n the same year because the nsured ndvdual des or (revokes hs/her retremen durng that year. On average, such penson dsbursements wll have taken place for half a year and thus carry half the weght of amounts dsbursed before the year of measurement. To correct for ths factor, ther weght s doubled n the calculaton of he. 4.0 The penson lablty can be dvded nto a commtment to persons who have not yet begun to receve a penson, SA, and a commtment to persons who are already recevng a penson, SP. 4.1 L 81
The penson lablty to persons who have not yet begun to receve a penson conssts of the total of all penson balances at the end of year t (PB). Ths total penson balance has been recalculated by adjustng t for the change n the ncome or balance ndex between year t+1 and year t and for the factors of actuaral gans and costs of admnstraton. The amount should be ncreased by the penson credt earned durng year t and not ncluded n the penson balance (PB) at the end of year t. Furthermore, untl the end of 2018, the penson lablty should be ncreased by the estmated amount of supplementary pensons (ATP), ncludng the so-called ncomereplacement penson, to persons who have not yet begun to receve ther pensons. 4.2 The penson lablty to persons who are already recevng a penson s calculated as the sum of penson dsbursements to each age group n December, multpled by 12 and the expected average number of remanng years n whch the penson s to be dsbursed. In order to smooth out temporary varatons n average (economc) lfe expectancy, the number of remanng years s measured as a mean of the De measured for the three most recent years. 4.3 De s the economc annualzaton dvsor, an estmate of the expected average remanng tme for whch a penson s to be dsbursed to each age group. Indvdual penson amounts are proportonal to the dsbursement profle whch results from economc adjustment ndexng by the norm of 1.6 %. In addton, ths profle s weghted accordng to the lfe-expectancy table calculated specfcally for the penson system n equaton 3.2.2 (by calendar tme), dvded by the same populaton, L, at the outset of the calculaton perod. Ths rato reflects the estmated normalzed dstrbuton of penson dsbursements over dfferent ages. Note that even on the frst age group s affected by economc-adjustment ndexng. The calculaton n whch De s used s performed at year end; thus, dsbursements after year end wll be ndexed once even for the youngest age group. Ths explans the exponent gven to the norm of 1.016 n equaton 4.3. 82