Pension Reform through Voluntary Opt-Out: The Czech Case *

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1 JEL Classfcaton: H31, H55, G23 Keywords: penson system reform, opt-out, penson fund Penson Reform through Voluntary Opt-Out: The Czech Case * Robert JAHODA Jí ŠPALEK: both: Faculty of Economcs and Admnstraton, Masaryk Unversty, Brno (jahoda@econ.mun.cz), (spalek@econ.mun.cz) Abstract The mportance of long-term publc fnance sustanablty n the context of current fnancal crss s stll seen as one of the basc factors of economc stablty. Demographc development resultng n hgher percentage of people n retrement age versus economcally actve people s one of the man rsks. There s a growng pressure on expendtures of age-related systems. For ths reason the penson scheme reforms are major ssue n advanced countres. Whle some countres have chosen strctly regulated approach towards penson reform, some have gven ts ctzens a choce whether to stay n the old system, or whether to swtch to a new one. Such a decson s very complex and whenever the choce was mplemented, many more workers swtched to a new system than was expected. In our paper, we present a mcro-based smulaton model for the Czech Republc that allows us to model the ndvduals swtchng decson usng several economc and behavoral factors wthn an old (PAYG DB) and new (FDC) systems. It allows us to estmate the proporton of people who would opt-out to a funded pllar. Our results ndcate that under the assumpton of ratonalty and long run predctablty of most parameters, only a small fracton of populaton would choose the mult-pllar scheme. However, ths concluson holds only under a full ratonalty. Once we relax ths assumpton, a wde range of swtchng strateges become vable. Therefore, the expectatons that the swtch wll be popular cannot be based only on economc factors, but must also ncorporate behavoral aspects, such as the rsk of averson. 1. Introducton Publc penson schemes n developed countres are among the most mportant exstng redstrbutve programs. Ther am s to provde a long-term securty of ncome for ndvduals n the stuatons when they are no longer ganfully employed. Due to the crcumstances of ther creaton, the resultng systems were mostly based on pay-as-you-go (PAYG) scheme. It was admnstratvely smpler and more transparent for an ndvdual to base the penson system on the defned benefts (DB) desgn, where the fnal penson depends on the wage profle. Other retrement schemes were also created a fully funded (FF) scheme based on the rule of defned contrbutons (DC), where the fnal penson depends on nvested sum as well as on nvestment returns. Extenson of the socal state n the second half of the 20th Century together wth a steeply growng lfe expectancy and a shft n the exstng demographc pattern led to the changes n orgnally small old-age penson plans nto the most mportant expendture tem of publc budgets. At the end of the 20th Century fnancng of these * We would lke to thank O. Schneder and anonymous referees for helpful comments and suggeston. Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

2 plans appeared to be unsustanable and the governments had to respond to the stuaton by ntroducng reforms. Ths process dd not progress at the same pace. Not a sngle country proposed anythng lke a unversal model of the reform, whch could (wth mnor modfcatons) be coped and transferred from one country to another. Old-age penson system n the CR evolved n a manner smlar to some developed countres. In the frst half of the 20th Century a great varety of dfferent schemes came nto beng (n the sense of settng redstrbuton rules) for dfferent groups of persons (employees). Subsequently, under the Communst rule, they were extended and ntegrated nto a sngle unversal old-age penson scheme. Reforms whch were to respond to the deteroratng demographc stuaton were launched only after the transformaton of the centrally planned economy (CPE) to the market economy began (poltcal economy of penson reform n the Czech Republc durng the s can be found n Müller, 2002), whereas reforms n developed countres gradually started n the 80s (for detaled summary see Immergut, Anderson, Schulze, 2006). One of the objectves of the Czech penson system reform n the last two decades has been to address the ssue of long-term sustanablty of the scheme. Government used to tackle ths problem usng manly parametrc modfcatons of the exstng scheme. The 1966 reform attempted to stablze the system s budget and to re-ntroduce the mert prncple and dversfcaton of fundng. Klmentová (1998) dscusses man changes n the Czech penson system untl Even whle the reform n 1996 was beng mplemented, the demographc developments quckly rendered t nsuffcent. However, the more systemc reform whch would enable a greater nterventon n the exstng system and generate alternatve penson pllar schemes lacked a poltcal consensus n the long run development of the penson system. A step towards consensus was the so-called Bezdk Commsson n 2005 whch was set up by the government to explore potental mpacts of poltcal partes proposals of a systemc reform of the old-age penson scheme. The Commsson (Bezdk et al., 2005:88) hghlghted dfferences n the poltcal partes proposals, but t has not led to any further convergence n penson reform agenda and thus the Czech Republc stll reles on a classcal PAYG system wth a neglgble mpact of funded (prvate and voluntary) pllar. Our paper dscusses effects of an hypothetcal penson reform n the Czech Republc that would ntroduce the voluntary funded pllar and allow to opt-out from the exstng purely PAYG and government run system. It s not our objectve to dscuss the necessty or rsks of ths pllar. Instead, we focus on the method used for people choosng to opt-out from the mandatory nsurance. The focal pont of our contrbuton les n fndng an answer to the queston how many people wll opt-out of the FDC pllar when they are allowed. Solvng ths problem can help n fndng the sutable transformaton method of the exstng one-pllar system nto a two-pllar one (the pllar of the voluntary supplementary penson nsurance, called the thrd pllar s not dscussed here). Ths problem had already been dealt wth by Ježek n the Czech Republc (see Ježek, 2003), who compared the dfference between replacement rato (penson as a percentage of the preretrement wage) one can expect from the already exstng PAYG DB system and replacement rato one could get f they took part n FDC system. Our approach dffers from the Ježek s one manly n 3 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

3 two aspects. Frst, we use updated estmates of man economc varables used n the model. Second, we attempt to evaluate the mpact of rratonal decson of an ndvdual. Ths s not the case of nether our or Ježek s model as our ndvdual s strctly ratonal. However, our model tests the possble stuaton of repercusson, where the ndvdual (for a number of reasons dscussed below) does not behave ratonally. The Ježek s approach results (compared to ours) lead to the concluson that swtch s more benefcal for larger group of people. Some reasons for ths dfference are dscussed n the Concluson. The frst part of the artcle (Secton 2) wll ndcate phases of the reform where optng- out could be ncorporated and what factors nfluence an ndvdual to opt-out. The followng part (Secton 3) formalzes the nfluence of the factors dscussed n the prevous part usng a mathematcal mcro-smulaton model. In the next part (Secton 4) we perform senstvty analyss whch purpose s to demonstrate how ndvdual s decson to opt-out changes accordng to the set of defned factors. Our results ndcate that under the assumpton of ratonalty and long run predctablty of most parameters only a small fracton of populaton would choose the mult-pllar scheme. However, ths concluson holds only under a full ratonalty. Once we relax ths assumpton, a wde range of swtchng strateges become vable. Therefore, the expectatons that the swtch wll be popular cannot be based on economc factors only, but must also ncorporate behavoral aspects, such as the rsk of averson. 2. Pure Opt-Out and a Degree of Freedom of an Indvdual n Its Partcular Areas In 1975 the Great Brtan was one of the frst countres where people could choose to opt-out of the state-guaranteed pllar when they were not members of a contracted-out occupatonal scheme. In ths stuaton they can jon the FDC pllar admnstered by the prvate sector. Schulze and Moran (2006:60) say: Employers had the possblty of contractng-out of SERPS, thereby recevng a rebate of the state penson contrbuton, f the occupatonal scheme they offered guaranteed benefts at least equal to the SERPS. Two terms to contract-out and to opt-out (and all ts dervatves such as contractng-out or optng-out) have been used n the smlar context. We understand the term to opt-out n the same manner,.e. the choce of an ndvdual not to be nvolved, not to partcpate n somethng. Optng-out from the basc penson scheme s therefore further nterpreted as a maxmum freedom of an ndvdual to decde whether to partcpate n the emergng second pllar. The opposte approach, n whch a person has no choce to nfluence hs/her part n the second pllar, s called the state-controlled transformaton. The state controlled transformaton means that the state takes away the opton of personal choce and mplements the approved form of the reform. We argue that a real transformaton (systemc reform) usually conssts of several steps and the state has a possblty to provde an ndvdual wth a choce n some areas, whle other areas are strctly controlled. The systemc reform than could provde the followng areas where a varyng degree of freedom could be appled: (1) freedom to jon the FDC pllar, (2) the percentage of the opt-out rate, (3) the choce of a penson savngs provder to accumulate penson assets, ncludng a selecton of the trade offs between gans and rsks, (4) the choce when to retre and when to start drawng pen- Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

4 son benefts from the FDC system, (5) the choce what to do wth the penson assets upon retrement. Although the overall outlne of the reform usually les somewhere between the pure opt-out and state-controlled transformaton, Palacos, Whtehouse (1998) showed that both pure opt-out and state-controlled transformaton varants have been appled. 1 Due to the spread of ntroducng the contrbuton based schemes nto penson systems n the world, large volume of studes concernng the topc can be found. Most of them deal wth the pros and cons (benefts and costs) of ntroducng such a scheme. (In the case of CR see e.g. Kredl, 1998; Kubalík, Zbol, 2000, Bezdk, 2001 or Ježek, 2003). But as we stated before, the purpose of our artcle s dfferent. We work wth an assumpton that the second pllar wll be ntroduced n the CR (the decson has been made). The focal pont of our contrbuton les n fndng a sutable method of how to transform the exstng one-pllar system nto a two-pllar one. Smlar approaches to ours are appled only for rather small part of the populaton. There are nspratonal studes by Rchard Dsney and Carl Emmerson (Dsney et al., 2001 or Emmerson, 2001) for the UK. Sgnfcant debate s devoted also to 401(k) program n the U.S.A. (see Mller et al., 2009). But most of these studes usually take the form of ex-post analyss of who has opted-out stemmng from demographc prncples. We argue that our approach s nnovatve n respect of ex ante analyss based on ncome, rather than on demographc prncple. 3. Factors Affectng Jobholder s Opt-out The ndvdual s decson about optng-out can be smplfed by comparng the loss of penson ncome that an ndvdual wll not be pad from the exstng PAYG system wth the penson ncome from the FDC pllar. We assume that ndvdual wll opt-out f the followng condton s satsfed: 2 PAYG PAYG FDC PAYG P P P P * RI where P FDC s the opted-out ndvdual penson from the FDC system, P PAYG s the loss of penson from the exstng PAYG n case of ndvdual s opt out and RI we call the ratonalty ndex. Furthermore, we assume that the decson s made n partcular year (20 n our model) and only by ndvduals who are currently (n the year mentoned above) on the labor market. The Secton 3.1 presents mcro smulaton model of proft and loss of penson benefts from the subsequent pllars. In the followng Secton 3.2 we dscuss the parameters whch could be taken nto account by an ndvdual when evaluatng the advantages of optng-out. Therefore our analyss could take two forms. Frst approach could be based on ratonal assessment of fnancal advantages of a new arrangement. 1 They menton Argentna, Colomba or Peru as examples of pure opt-out varant and Bolva, Kazakhstan or Mexco as examples of (pure) state transformaton. For more comprehensve overvew of current penson schemes n the OECD countres see OECD (2004). 2 Ths model and the followng ones are descrbed n greater detal n the Appendx. Our model s smlar to the one used by Dsney, Palacos, Whtehouse (1999), who examne the welfare consequences of partal shft from a publc unfunded scheme to a prvate scheme both from an ndvdual and a macroeconomc perspectve n the UK. The earler analyses based on the same model of ndvdual responses to prvatzaton of the socal securty system n the USA can be found n Gustman, Stenmeer (1995). 312 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

5 But we argue that n realty people do not make a decson only on the bass of fnte amount of fnancal parameters. Ther decson makng process mght be more complex and may nvolve more nputs. Therefore we use a second approach where the ratonalty ndex s ntroduced to the model. The ndex suggests that ndvdual may choose to opt-out even f that would result n (not a large) drop n hs overall penson amount. Ratonalty ndex and overall nfluence of ndvdual s (r)ratonalty n the decson-makng s further dscussed n the Secton The Model Assessng Advantages of Optng-out of the PAYG System The Model of Penson from the FDC Pllar To calculate the penson whch an opted-out ndvdual receves from the FDC system, some smple fnancal-mathematcal relatonshps can be appled. Snce the FDC model s characterzed by full equvalence, t must be true that what s saved n the system s later drawn from the system n the form of penson benefts. For the sake of smplcty, we assume that an ndvdual draws a lfe annuty from the FDC system. Based on the equvalence prncple, an ndvdual s penson equals: where FDC P f W, cr, r, v, n, n FDC W s the gross wage durng the savng phase, 1 2 crfdc s the contrbuton rate to the FDC pllar, r the real apprecaton rate of penson savngs, v s the adjustment of pad out penson, n 1 s the length of ganful employment and n 2 s the lfe expectancy of the average ndvdual of partcular age cohort at the moment of retrement Loss of Penson from the PAYG Pllar By optng-out the ndvdual accepts the fact that hs/her ncome from the pay- -as-you-go system wll drop. Ths drop ( P PAYG ) s gven by the formula: 1 PAYG PAYG OPT OUT h FDC FDC P P * I f W, cr, r, rr, RA, ncp f n, n, cr, cr, where P PAYG s the orgnal (non-opted-out) penson, I s the share of opted- OPT OUT -out penson from PAYG on total (potental) PAYG penson, r h and rr are the reducton lmts for calculatng the percentage-based assessment, RA s the statutory retrement age and ncp characterzes the defnton and method of ncluson of non- -contrbutory perods. The symbol FDC n denotes the savng perod n FDC system of the ndvdual, cr s the orgnal rate pad to the PAYG and the coeffcent characterzes the penson reducton from the PAYG system n case of optng-out. 3 8 In our model we assume that the reducton wll be proportonal to the extent of optng-out and wll be unform for everybody. It means that the coeffcent s assumed to reach a unt value. Alternatvely, we could suppose that the coeffcent wll (1) change n tme, or (2) vary accordng to the ndvdual s ncome, and (3) be dfferent for a person durng varous stages of hs/her lfespan. In ths perspectve our model does not nvolve any alternatve scenaros. The system of accrued penson rghts reducton s one part of swtchng condtons and should be decded poltcally. Over restrcton mght be the way to reduce transformaton costs of the transton. Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

6 Parameters estmatng the development of labor productvty, nflaton rate, number of employees and gross natonal product (GNP) are crucal macroeconomc data and they appear practcally n all models. Projected development of these parameters has been manly taken from the Fnal Report of the Executve Team. As we expect that a dfferent macroeconomc development wll not sgnfcantly nfluence the decson-makng about optng-out, we do not derve alternatve macroeconomc framework. Another sgnfcant parameter whch s taken for granted wthout further dscusson s the contrbuton rate (cr). The value of 21% (old-age pensons) has been used n our models nstead of the total 28% current contrbuton rate (21% nstead of 28% correspond to the fact that 73.5% of penson s expendture n 2008 represented old age pensons, the rest belonged to dsablty, wdow, wdower and orphan pensons whch are not matter of ths artcle smlar concept can be found n Ježek, 2003:521). All other comparsons are related to the contrbuton rate whch has been determned n ths manner. 3.2 What Influences the Antcpated Penson from the PAYG DB and FDC Pllar Level and Development of Wages (W ) The overall mpact s examned for 200 model ndvduals who represent partcular ncome percentles (0 for men and 0 for women). For ths reason t s also mportant to nclude projectons of changes n ncome dfferentaton nto the actual calculaton of wages of the ndvdual W n a gven ncome percentle. 4 Pensons from the FDC pllar are affected by the earnngs durng the whole ganful employment, whle n the DB pllar the earnngs taken durng the relevant perod (last 30 years) are decsve. That s why ncome dfferentaton may nfluence the level of penson from both systems. In our model we expect the ncome dfferentaton measured by the decle rato of wages to be at the level 3.5 n the year Accordng to OECD (2009a) statstcs the ndcator falls between 3.0 and 4.0 n vast majorty of countres, wth some countres reachng the level of 5.0 (Hungary, USA) and n some countres, on the other hand, the level of 2.0 (Belgum, Sweden, Fnland, Denmark). The model senstvty analyss dd not reveal any major nfluence of the ncome dfferentaton development. That s why ths analyss was not dscussed n the follow- -up text any longer. Although, ths does not affect the fact that wage dfferentaton development may nfluence the further evoluton of PAYG DB system. The patterns modelng the wage development together wth the wage projecton untl the year 2050 can be found n the Appendx. Furthermore, t s assumed that a person s ncome moves around a certan unchanged ncome level (approprate ncome percentle) through the whole career. Average wage growth s taken from the data provded by the Team of Experts. The data are based on assumed wage growth n EU countres together wth the speed of convergence of the Czech economy wth the EU countres. 4 Source s a publcaton of the Czech Statstcal Offce about wage dfferentaton n 2008 (CSO, 2009) and also the data acqured from our models. 5 Ths means that n 2050 the wage of the nnth ncome decle s 3.5 tmes hgher than the wage of the frst decle. 314 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

7 3.2.2 Opt-out Contrbuton Rate n the FDC Model (cr FDC ) The level of contrbuton rate n the FDC system naturally determnes the extent of optng-out. It can be generally assumed that the level of ths rate may vary n the course of the workng career and so cr FDC represents a vector of rates rather than a sngle concrete value. The model enables us to express the advantages of optng-out for a contrbuton rate varant. Concrete values of opt-out percentage are essentally nfluenced by the macroeconomc framework of the reform. It can be assumed that optng-out s largely determned by the ablty of the state or publc fnances to cover the cost of such changes. Kredl (1998:39) assumed present value of the mplct penson debt 6 for the statutory penson age 65 between 180 and 230% GDP. Later IPD calculatons (see MLSA, 2004:91, Bezdk et al., 2005:17 or MLSA, 2008:70) have decreased ts level towards % of GDP. Introducton of FDC pllar wll nduce transformaton of the IPD nto explct debt. It s hard to say what the extent of such transformaton wll be, as t s nfluenced by the set condton of such swtch. One can say that one of the most mportant factors are: the opt-out contrbuton rate, number of people who opted-out to FDC or system of reducton of penson rghts from PAYD DB. In our artcle we set the opt-out contrbuton rate at 6%, snce we beleve that such transformaton would not pose serous problems wth fnancng the transformaton costs of transton Estmated Return on the Penson Portfolo and Its Volatlty (r) Generally, a hgher apprecaton of assets n the FDC pllar wll lead to a hgher extent of optng-out. The crucal queston s what wll be the real apprecaton of assets n the FDC. Can we apply hstorcal experence to ts estmate? Accordng to the study of the London Busness School (cted from ABM AMRO, 2007:5) the average annual return for the global stock markets durng the past 0 years (ncludng renvested dvdends) was about 5.8%, 1.6% for bonds and only 1% for publc securtes. Captal markets are characterzed by a consderable volatlty. The above mentoned study (ABM AMRO, 2007:7) clams that volatlty reducton, whch may be reached by a convenent structurng of the portfolo, results n a drop n ts average return. The latest London Busness School study admtted the fall n the real return on the global ndex for equtes to 5.2% caused by the fall n captal markets n the years 2007 and 2008 (Dmson, Marsch, Staunton, 2009:43). However, t has attracted attenton to the fact that the man part of the aver-age return s beng generated from renvested dvdends, captal apprecaton s of lower mportance. The European Commsson represented by the Economc Polcy Commttee (EPC) agreed that a long-term real rate of return of 3% wll be assumed for calculatons of mpacts of populaton ageng (EPC and EC, 2005). Ther senstvty tests of models worked wth alternatve rates of 2% or 4%. We consder the possblty that an ndvdual can save money n three varous funds n hs/her lfetme. 7 We have dubbed them Growth, Balanced, and Conservatve. The Growth fund wll have the hghest average return but t s lnked wth 6 Defnton of IPD and ts measurement s not the subject of ths artcle and can be found e.g. n Holzmann, Palacos, Zvnene (2004) 7 The dea s based on the current state of the Slovak penson system. Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

8 Table 1 Projected Real Apprecaton Rates n the FDC Model Accumulaton of assets fund type growth balanced conservatve (max. 15 years before retrement) 15 to 7 years before retrement 7 years before retrement Rate of return durng annuty drawng Basc varant 4.5% 3.2% 2% 2% Varant wth hgher return rates Varant wth lower return rate Source: Authors. 5.5% 4.2% 3% 3% 3.5% 2.2% 1% 1% a hgher volatlty. To decrease t, the ndvdual has to transfer hs penson assets nto a fund wth lower volatlty (balanced or conservatve) at certan pont pror to retrng. These funds generate a lower rate of return. We test the ndvdual s senstvty to changng volatlty by means of varants wth dfferent level of proftablty. We treat the admnstratve costs (annual charges) of penson savng provders as asset-based and we set the level at 1% of the assets value annually. 8 The mpact of dfferent average rate of return r on the choce of optng-out s evaluated by usng the senstvty analyss. We wll suppose that penson savngs provders wll acheve ether hgher or lower rate of return on penson assets. Projected values of the alternatves are summarzed n the Table 1 together wth the values of the basc varant Adjustment (Valorzaton) of Pad-out Penson Benefts (v) In a consstently equvalent FDC model the method of adjustment of pad out annutes does not play any role. The retree wll get back hs/her assets at the same level; what wll change s the dstrbuton of assets n tme. Let us suppose that pad out pensons from both systems are adjusted accordng to the same rules. Snce the rule of FDC penson adjustment cannot nfluence the net present value of pensons pad n future, we can employ the adjustment rule from the PAYG DB pensons even for FDC pensons. We do so to compare the FDC penson wth the loss of penson n PAYG DB. The same method was appled by Ježek (2003:518). (See formula (9) and () n Appendces) Duraton of the Savng/Insurance Perod (n 1 ) and Non-contrbutory Perods wthn Savng/Insurance Perod (ncp) When projectng the duraton of savng perod (FDC) or nsurance perod (PAYG DB), t s vtal to estmate non-contrbutory nsurance perods (e.g. duraton of study, unemployment, chldcare or sckness). Non-contrbutory perods of nsurance affect the calculaton of partcular penson benefts both n the PAYG DB and 8 Many knds of charges can be appled by penson funds. These charges dffer across the countres and penson funds. Whtehouse (2000:13, 28) uses charge rato for overall mpact of charges on penson savngs. For selected Latn Amerca countres he found that the charge rato les between 13.5 and 26%. In our model the value of the charge rato equals 18.3% (for the ndvdual 40 years before retrement). For measurement of overall mpact on the level of annuty we can use Money worth rato (MWR). Accordng to James, Vttas (2000:26) MWR s mostly between 0.8 and For CR Ježek (2003:521) uses MWR = 0.. In our model the value of the MWR equals (for the male who has just retred). 316 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

9 Table 2 Influence of Non-Contrbutory Perods (ncp) n the PAYG DB System Duraton of nsurance n years men women unsex Average nsurance perod Insurance perod wthout ncp Share of ncp on average nsurance perod 18.7% 22.5% 20.7% Source: Holub (2009:486) the FDC system. Whle ncp s consdered as an nsurance perod wthn PAYG DB, FDC model does not compensate for t. Non-contrbutory perods n the Czech penson system have been examned by Holub, Conclusons from hs research are summarzed n the Table 2. Accordng to the Table 2 above, the average length of nsurance les between 30.7 years (women wthout ncp) and 44.4 years (men wth all ncp). The future duraton of nsurance wll be nfluenced by: (1) advancement of the retrement age (+), (2) ncrease n the length of educaton (-), (3) ncrease n mpact of unemployment perods whch dd not have any sgnfcance pror to 1989 (-), (4) gradual elmnaton of generous ncp recognton n exstng PAYG DB system (-). Unfortunately, we are not able to precsely qualfy the parallel nfluence of the above mentoned factors on the total nsurance (PAYG) or savng duraton (FDC). Therefore, n our models we count on constant length of the savng perod (40 years) whch s consdered n both the PAYG DB and n the FDC models and whch s dentcal for both men and women. Further on we suppose that the non-contrbutory perod proporton throughout the ganful employment wll be on average %, both for men and women. Alternatvely we are gong to test the FDC model for the mpact of shorter (ncp = 0% both for men and women) or longer (ncp = 20% both for men and women) non-contrbutory perods, whch can be nterpreted n several ways: (1) the mpact of rasng the retrement age, (2) the mpact of changng the approach towards non- -contrbutory perods n the PAYG DB pllar, (3) the mpact of takng nto account the non-contrbutory perod n the FDC pllar f the state chooses to pay the contrbutons to the FDC pllar n certan cases, (4) the mpact of not consderng chldcare perods as nsurance perod Duraton of the Payout Annuty (n 2 ) and Retrement Age (RA) Duraton of the payout annuty s equal to lfe expectancy (LE) upon retrement and n ths respect crucally depends on precse retrement age (RA). Factor (RA) appears n two forms n both models. The retrement age s stpulated by the law and our models work prmarly wth 65 years. Where possble and approprate we have also made estmates for 67 years. However, LE depends more on the real retrement age rather than on the statutory retrement age. On average people retre before they reach the statutory RA. Based on the exstng development we have ncluded an arbtrary projecton of devaton from the statutory and real retrement age. In 2007 t was equal to 1.2 years for men and 1.33 years for women. Smlar dfference can be observed n other years as well. For the sake of smplcty the parameter has been fxed at 1 year. A potental development of LE n the CR s ndcated n the Table 3. Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

10 Table 3 Potental Development of Lfe Expectancy at the Age 65 n the CR Year Source of data MALES FEMALES UNISEX 2006 CSO EPC and EC A Bezdk B Bezdk Notes:(1) UNISEX data are calculated as weghted arthmetc mean (where avalable) for males and females. (2) 2065A calculated as current lfe tables for the year (3) 2051B calculated as generaton lfe tables for persons born n Source: CSO (2007); EPC and EC (2008); Bezdk et al. (2005). Accordng to the Czech Statstcal Offce (CSO, 2007) the lfe expectancy n 2006 for 65 year-old males was 14.8 years, and for females 18 years. Accordng to the recent development n European countres t can be sad that the LE of 65 year- -old persons ncreases every decade by one year (see OECD, 2009b). At the moment nothng seems to suggest that ths trend could change and that the LE wll not ncrease by further 4 5 years n the comng 50 years. 9 Our projectons of the LE are based on the lfe tables of the Czech Statstcal Offce (CSO, 2007). We assume that the LE of a 65 year-old person ncreases by 0.1 year every year. Usng ths rule the LE of a 65 year-old person, regardless of sex, wll be 20.8 years n 2050, whch s 0.7 year less than EPC and EC (2008) projecton. The LE of a 65 year old-person s 22.3 years for the year 2065, whch s a year less than correspondng demographc projecton by Burcn, Kuera (2004). To test the senstvty n case of optng-out, we have used other two varants of lfe expectancy. The longer varant prolongs the LE, whle the shorter varant shortens t. Departure of both varants from the base projecton wll be 0.7 year n The same concept was used by the EPC and EC (2008) whch tested a varant of ncreased lfe expectancy at brth by one year by 2060 compared to the baselne projecton. In our model nstead of usng sex-specfc lfe expectances we use unsex lfe expectancy as such practce better reflects the shape of newly launched captalzng pllars n EU (e.g. Hungary, Poland or Slovak Republc for basc descrpton of ther penson systems see OECD, 2009c). Indvdually appled varants of LE are graphcally represented n the Fgure 1, full fgures are presented n the Appendx on the journal web page System of the Income Redstrbuton n Pad Out Pensons (rh, rr) Penson systems play mportant re-dstrbutve role as well. The redstrbutve functon of the Czech system s captured by three factors the basc ncome level, whch s unform for all pensoners, and two reductons lmts that nfluence ncome- -related part of the penson. We assume that adjustment of three basc parameters allows us to model future ncome redstrbuton wthn the frst pllar. The basc varant assumes that the current level of the basc amount, the frst and the second reducton lmts are fully adjusted accordng to the nflaton rate and partally (75%) 9 Lfe nsurance companes base ther calculatons of lfe annutes on a converson of current (cross-sectonal) lfe tables nto generaton (cohort) tables, whch ncreases the lfe expectancy by about 5 years (Bezdk et.al., 2005). 318 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

11 Fgure 1 Unsex Projectons of Lfe Expectancy at the Age of 65 Usng Correcton Coeffcents modfed (longer) modfed (basc) 18 modfed (shorter) unmodfed (based on CSO) Source: CSO (2007); own modfcaton. Table 4 Provson for a Growth n Real Wage n Indexaton of Parameters n the Frst Pllar a Basc amount Second Frst reducton of penson reducton Basc varant 75% 75% 75% Redstrbutve varant 140% 60% 0% Dfferentaton varant 0% 75% 150% Note: a Partcular varants lead n the long run (2050) to smlar replacement rato of average wage earner. Varants manly dffer n change of the equvalency between contrbutons and benefts. Whle the Redstrbutve varant decreases ncome dfferences among ndvdual pensons, the Dfferentaton varant does the opposte. Source: Authors. accordng to an ncrease n real wages. Together wth ths varant, two addtonal varants are tested. One of them s called Redstrbutve, n whch the present redstrbuton role of pensons s strengthened. Dfferentaton varant allows for a gradual weakenng of ncome redstrbuton. Projectons of the adjustment method are summarzed n the Table Behavoral Factors that Influence the Decson of an Indvdual to Opt-out In addton to the above mentoned factors whch are relatvely easy to quantfy a host of other factors wll nfluence an ndvdual n hs/her decson-makng about optng-out. Some of them are related to the above mentoned, others are qualtatve (behavoral) and so they are dffcult to quantfy. The followng secton descrbes some of the most relevant factors. When assessng the advantages of optng-out we rely on the ratonalty of an ndvdual. Thaler, Benartz (2004) argue that we should consder ndvduals bounded as ratonal. The problem soluton s a hard one even for an economst and ndvduals may not be able to evaluate the entre range of aspects nfluencng opt- -out. There are a number of behavoural factors that can nfluence opt-out decson, the most decsve are: Indvdual s preferences regardng dversfcaton of the penson portfolo. A decson of an ndvdual to opt-out wll be also affected by hs/her personal preferences for the dversfcaton of the penson portfolo. It can be characterzed as postve nsurance benefts from dversfcaton (Brugavn, Dsney, 1995). On Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

12 the other hand, these benefts may not offset the transacton costs of entry to the prvate schemes (Dsney et al., 2001). Wth regard to the outlook of the Czech penson system t can be expected that ndvduals wth a hgher ncome wll tend to dversfy. Lack of or naccuracy of avalable nformaton due to an nsuffcent or naccurate presentaton from the government, deceptve (msleadng) campagns of opposng poltcal partes, or the nfluence of nfluental nterest groups (such as promoton of penson savngs provders). Rsk averson. Persons wth a strong rsk averson can choose to reman n the frst pllar, because they thnk that the FDC pllar s too rsky. Rsk averson can be hgher n older persons who approach the retrement age (they dstrust prvate penson savng provders due to recent experences). On the other hand, Dusek, Kopecsn (2008) show that nherent rskness of often-reformed publc PAYG systems s comparable to rsks assocated wth prvate systems. Influence of leadng members of the communty on the decson of an ndvdual. (Demonstraton or hallo effects when a person mtates the decson of others who are n a dfferent ncome bracket or belong to a dfferent age group. Sometmes there s a trend towards famly decsons, f the household head decdes for all household members. All these nfluences can result n consderable dfferences between the fnal number of opted-out persons and our presented estmates. Thanks to ther certan contradctory character, t s not possble to accurately predct ther overall effect. As we stated above, we have ntroduced these factors nto our model as Ratonalty ndex (RI). For the purpose of subsequent senstvty analyss we use three basc values of RI. The basc varant presumes no other than pure fnancal (or ratonal) factors and RI = 1. But ndvduals could be motvated to opt-out even when ther gan from FDC pllar s less than the loss from PAYG. For that case we use RI = 0.95 (we call such varant a low rsk averson ). On the other hand, Palacos, Whtehouse (1998) argue that for people (especally low-ncome workers) the future (small) gan from swtchng to FDC would not overcome the cost of the decson (nformaton cost, charges and rsk). For that varant we use RI = 1.05 (we call such varant a hgh rsk averson ). 4. Results of Opt-out Smulaton In the prevous secton we have dentfed the seres of varables used n our models. Ths secton s dedcated to the results of modelng the advantages of optng- -out. 11 Frst the basc alternatve s modeled, based on the above mentoned assumptons about values and development of ndvdual parameters. The remanng secton specfes the outcomes of values assumed by partcular parameters. We should stress that senstvty of the opt-out advantages to a change n (settng) these parameters s consdered more sgnfcant than any concrete values (advantages for gven groups of persons). The basc varant of parameters settng s summarzed n the Table 5. The assumpton s confrmed by the case of Slovaka, where many more persons decded to opt out than estmated. Potental consequence can be a recent reopenng of the second pllar, whch represents a marked change of the proposed system. 11 The detaled presentaton of results s avalable on the journal web page. 320 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

13 Fgure 2 For Whch Income Percentle It Is Advantageous to Opt-Out (basc varant) Source: Authors. Income percente 0 Females Males years to the retrement age lmt Table 5 Basc Varant of Assumpton about Further Development of Sgnfcant Parameters 1 Real return rate (n %, after deductng admnstratve costs) Phase of penson assets creaton fund type Phase of growth balanced Conservatve penson assets wthdrawal Development of unsex lfe expectancy at 65 years Share of non-contrbutory Males Females perods n FDC (from the total of 40 years of ganful employment) % % 4 FDC contrbuton rate (opted 6% out of PAYG DB) 5 Allowance for the growth Second Basc amount of penson Frst reducton n real wage for ndexng some reducton parameters n the frst pllar 75% 75% 75% Source: Authors. Although there are several possbltes how to analyze the nfluence of above factors, we present our results usng one graph. For more detaled analyss we refer to fgures and tables n Appendx, addtonal nformaton s avalable from the correspondng authors upon request. The presented Fgure 2 shows for whch ncome percentle t s advantageous to opt-out, dependng on the number of years remanng to the retrement age lmt. Advantages are shown separately for males and females. As seen from the Fgure 2 and Table 6, under basc settng optng-out s advantageous only for a relatvely small group of persons. It s only applcable to men and especally to women n the hghest ncome percentles. The fgure shape suggests that the advantages of opt-out for ndvdual percentles vary accordng to the number of years before retrement. However ths dependence s not lnear. The number of persons for whom t s advantageous to opt-out drops frst. Wth the ncreasng tme perod of a person to the retrement age t starts to grow. 12 It s understandable that a maxmum number of people for whom the opt-out s cost-effectve s found n the youngest age bracket. 12 It s manfested by the fact that the frst ncome percentle for whch t s advantageous to opt-out s decreasng. Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

14 Table 6 Growth (+) and Drop (-) n the Gross Replacement Rate of the Opted-Out Penson n Comparson wth the Non-Opted-Out Penson for Some Income Percentles [% of the pre-retrement wage] W Males Females W W W W W Source: Authors. Among man reasons whch determne such shape can be found: (1) The convergence of the Czech economy to the EU countres results n a faster wage growth n the frst years of the modeled perod (real growth of average wage n 2015 s 2.8%, contrary to 2.1% n 2050). Ths causes hgher IRR of the PAYG DB pllar compared to FDC and subsequently results n the constant (or slghtly decreasng) number of ndvduals who would opt-out. The nfluence of the convergence s substantal manly wth ndvduals who swtch 1 to 15 years before retrement. Wth the perod closer to the year 2050 ths argument s fadng. (2) The lower real rate of return (FDC) makes the opt-out curve rather flatter for people who swtched a few years before ther retrement. The advantage of long term savngs belongs only to young and mddle age generaton. (3) Growng lfe expectancy lowers pensons from the FDC pllar. Ths fact does not envsage drect nfluence of the penson from PAYG DB model. However, n realty ths mght be one of the man factors n the long run. Such argument may explan why the opt out curve declnes qute gently for people swtchng 30 to 40 years before ther retrement. Smlar shape of the opt-out curve for countres whch ntroduced FDC pllar can be found n Palacos, Whtehouse (1998). Whle our opt-out curve predcts the number of ndvduals who would opt-out, Palacos and Whtehouse present real shares of opted-out ndvduals n total. To show the nfluence of the factors, we perform the senstvty analyss. In the followng secton we present the results only for the parameters whch have a remarkable mpact on the opt-out rate. Other graphs showng varous aspects of optng-out can be found n the Appendx. The most nterestng s the dfference n the total replacement rato for the males accordng to tme to retrement (total opted- -out pensons mnus non-opted-out penson). The Fgure 3 compares the two replacement rates and the results are presented separately for three wage levels. Ths graph mght be seen as a comparson of the reform scenaro wth the no-reform scenaro. But the reader should be aware of the fact that results for the no-reform strategy are only approxmate, as we are not able to antcpate the (poltcal) settng of the PAYG DB pllar n the long run. The fgure logcally complements the presented fgure showng the (ds)advantage rate of optng-out for selected ncome percentles. If optng-out s mandatory for all, ths fgure llustrates varyng ncome dstrbuton of penson benefts n connecton wth the opt-out. 322 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

15 Fgure 3 Dfference n the Total Replacement Rato for Males Accordng to Tme to Retrement Source: Authors. Dfference (%) W Average wage W Senstvty of Results n the Basc Varant of Parameters to a Gradual Change n the Followng Parameters Real Rate of Return If the estmated rate of return grows as compared to the basc varant, (by 1% n all phases) the number of persons for whom the opt-out s advantageous grows slghtly. The proporton certanly ncreases n tme (t means that the opt-out s best for the young who wll retre n 30 or more years). By contrast a decreasng rate of return (by 1% aganst the basc varant), whch corresponds to the varant wth a lower rate of return of assets (see Table 1) leads to a stuaton where a number of opted-out persons s neglgble. Thus t can be concluded that wth a declnng assets apprecaton, the number of opted-out persons decreases sgnfcantly (see Fgure 4) Lfe Expectancy Regardng the lfe expectancy we ran the senstvty tests only for FDC pllar (PAYG DB pllar beng fxed). The mpact of lfe expectancy on the proporton of opt-outs s then unambguous the shorter the lfe expectancy at 65, the more jobholders wll opt-out from the frst pllar. The effect of ths parameter s promnent: the number of persons who opt-out grows by 5% for each year by whch the lfe expectancy s lower. Smlar prncple apples when the lfe expectancy ncreases. Due to the fact that changes n the lfe expectancy nfluence PAYG DB penson also, we can conclude that mpact of ths factor s rather mnor (see Fgure 5) Duraton of Non-contrbutory Perods n the FDC Extenson of the perod of nactvty results n the drop of the number of people who would opt-out (for detaled results see Fgure 6). If we suppose that women wll be nactve for the perod of 20% (nstead of % n the basc varant) of ther workng lfe, the opt-out becomes dsadvantageous. If we suppose that a jobholder has no perod of nactvty n the course of hs/her workng lfe, the advantage of opt- -out wll be more promnent (especally for males opt-out s advantageous for almost of half of them). The rules for nactvty perods are set by the state and they drectly nfluence the advantage of opt-out for people who are at or slghtly above the average wage. Indrect reducton of non-contrbutory perod can be regarded as Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

16 Fgure 4 Opt-Out Rate n Men and Women wth Dfferng Apprecaton Rate Income percente Hgher return varant Source: Authors. Males Females years to the retrement age lmt Lower return varant prolongng statutory penson age an ndvdual has to work longer wth the same PAYG DB penson and ncreases FDC penson Effects of the Real Wage Growth n Indexaton of Some Parameters of the Frst Pllar Frst pllar settng and parameter ndexaton (see Table 4) play an mportant role for the degree of optng-out n varous groups of persons. If the frst pllar was Income percente Males Females years to the retrement age lmt Fgure 5 Opt-Out Rate n Men and Women for Dfferent Lfe Expectances Income percente Shorter varant Source: Authors. Females Males years to the retrement age lmt Income percente Longer varant Males Females years to the retrement age lmt Fgure 6 Opt-Out Rate of Men and Women n Case of Dfferent Non-Contrbutory Perods Income percente Hgher level of nactvty (20% ncp) Females Source: Authors. Males years to the retrement age lmt Income percente Zero nactvty (0% ncp) Females Males years to the retrement age lmt 324 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

17 Fgure 7 Proporton of Opted Out Males and Females for a Varous Settng of the Frst Pllar Income percente Dfferentaton varant Source: Authors. Males Females years to the retrement age lmt Redstrbutve varant markedly redstrbutve, the number of persons who opt-out would ncrease. Ths growth would be accompaned by a slght drop n the replacement rato as well as by a lesser degree of penson dstrbuton (see Fgure 7). On the contrary, a low degree of penson redstrbuton n the frst pllar would not change the proporton of opted- -out persons very much (n comparson wth the basc varant) Senstvty to Indvdual Ratonalty Indvdual ratonalty seems to be the most mportant factor whch nfluences the number of opted-out persons (for detaled results see Fgure 8). We have set the level of ratonalty ndex (RI) to 0.95 and 1.05 respectvely. Ths settng s rather arbtrary. In our vew the wdth span of RI s qute narrow for persons below the age of 50. (We mght menton that the probablty that a person at the age of 60 des before reachng retrement age s hgher than 5%). Ths mght be supported by the fact that no one can predct the level of penson from PAYG DB n the 15 year horzon. Narrowng nterval for the two levels of RI s nfluenced by the way we have appled RI n the model. If we used RI only for the fractonal penson whch resulted from the opt- -out, t would make the nterval narrow even for the persons who are just before ther retrement age. Hgh senstvty to RI factor can gve a partal answer to the ques- Income percente Females Males years to the retrement age lmt Fgure 8 Proporton of Opted-out Males and Females for a Varous Settng of the Ratonalty Index Income percente Males years to the retrement age lmt Source: Authors. Basc Hgh rsk averson Low rsk averson Income percente Females Basc Hgh rsk averson Low rsk averson years to the retrement age lmt Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

18 ton why more Slovaks opted-out than t had been predcted by model calculatons (MPSVR SR, 2007). It may be rather surprsng that the varant low rsk averson s ncreasng the number of the opted-outs up to 0% n case of age cohorts swtchng just before ther retrement. As a result of later retrement age, n case of swtchng, the number of ndvduals wllng to opt-out s decreasng. Ths s a consequence of the fact that the ratonalty ndex s applcable to the total amount of PAYG DB penson. It may lead to a stuaton that the ndvdual who s swtchng a couple of years before the retrement s facng the lower loss of PAYG DB than corresponds to 5% RI nfluence. In such case the ndvdual always opts-out, gnorng the mpact of other parameters. The test could be modfed as to compare only potental losses from the PAYG system and potental gans from the FDC system n the case of opt-out. If ths s the case, the rsk averson curves n the Fgure 8 would converge more closely to the basc varant opt-out schedule. However, we beleve that ndvdual choce would be based more on comparng the total value of penson, not ncremental losses and gans even though t may lead to paradoxcal results for ndvduals few years before ther retrement Conclusons Experence from the countres whch have carred out the penson system reform shows that the decson about the form of penson system s prmarly poltcal. When analyzng expectatons of penson scheme expendture n 17 OECD countres, Schneder ponts out that the nfluence of economc factors on occurrence of penson reforms s unconvncng. He follows that governments do react to expectatons of ncreasng penson expendtures, but they are unmoved by the level of [current] penson expendtures (Schneder, 2009:305). In our artcle we start from a smple proposton that the decson about the move toward the captal pllar n the Czech Republc has been done. Our objectve then was to formulate the way how to carry out the transformaton. We dfferentated between the opt-out form, when ndvdual can decde whether and how to partcpate n the reform, and the form of state controlled transformaton, when all decsons on the shape of transformaton are gven by the state on behalf of an ndvdual. Our paper then focused on the ssue of the proporton of the Czech populaton who wll decde to opt-out from PAYG DB to FDC when they are allowed. Our analyss s based on mcro-smulaton model n whch we compare penson of the ndvdual whose penson s opted-out wth the penson of the same ndvdual n case (s)he stays only n the PAYG DB penson pllar. In the year 20 only around 20% to 30% of men wth hghest salares (resp. 8% to 12% for women) would opt-out to a mult-pllar scheme. Ths result s vald only under the assumpton of ratonalty and long run predctablty of most parameters. Our results are consstent wth the calculatons made by Bezdk Commsson whch clamed that approxmately 50% of men and less than % of women wll opt-out (see Bezdk et al., 2005:23 and 37). 13 For example, worker on the 20th percentl and 5 years pror retrement would lose by 50% more n the PAYG than he/she would gan n the FDC system. Therefore, when comparng gans and losses, he/she would probably never consder optng-out. However, hs/her penson would fall after opt-out by 1.3% only: a loss he/she can easly choose to gnore. 326 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4

19 The senstvty analyss showed that the rate of real return of the penson assets s the most nfluental parameter. Hgher apprecaton rate make opt-out more favorable for more than 70% of the men and almost 50% of the women who are enterng labor market. Smlar analyss for the Czech Republc was made by Ježek (2003). Hs results do not clearly show the number of people who would opt-out, as the outcome of hs model s the so-called swtchng wage. It states from whch wage level t would be proftable for an ndvdual to opt-out n the year In all analyzed varants he shows that the level of swtchng wage s lower than the basc varant n our model. Our model shows smlar results only when the varant where the penson funds realze hgher real rate of return of penson actves s appled. Ths example mples that the dfference between Ježek s and our results s manly gven by the set-up of parameters. Relaxng the condton that the ndvdual s decson s done only under strct ratonal arguments nduces that opt-out mght be favorable for sgnfcantly larger proporton of the populaton. Therefore, based on full ratonalty we suppose that number of people who wll opt-out wll be hgher than predcted by Bezdk Commsson or by our calculaton. We beleve that our estmates are supported by the Slovak Republc s experence. Ther frst calculatons underestmated the real number of people who have opted-out. We argue that such rratonal behavor can be explaned by two arguments: (1) n case when long run fnancal sustanablty of the frst pllar (PAYG DB) s unpredctable or unwarrantable, t mght be wse for everybody to dversfy the future penson, (2) ndvdual thnks of penson savngs as personal assets whch may be nherted, whereas future penson from PAYG DB mght be rather uncertan. 14 The queston s whether t s possble to mplement such behavoral factors nto mathematcal model. We should also ask what the consequences of an ndvdual s rratonal decson mght be n the reform as far as the opt-out s concerned. The more persons opt-out, the hgher share of mplct penson debt s transformed nto explct debt. Ths mght cause problems n a publc debt management. To what extent are these problems crucal so that the concept of transformaton usng opt-out can be refused? The vtal factor for ths decson s the level of the opt-out nsurance rate, because hgher nsurance rates wll enlarge the problems and vce versa. Even f the problem of transformaton costs has been put asde n our analyss, we beleve that the realzaton of the way of transformaton we are suggestng would not cause serous problems to the Czech publc fnance, not even n the stuaton n whch a larger number of people than estmated n the model would opt-out. Moreover, the model showed the fact that potental decrease n pensons by some ndvduals s not of such extent whch would make the state solve the outcomes by some systemc measures. A more rgd (controlled) transformaton, wth no voluntary opt-out and wth strct age lmts for swtch to the new system along the lnes of reforms n Poland or Chle mght decrease uncertanty durng the reform and mght lmt the scope for rratonal decson by ndvduals. However, the government s able to lmt uncertanty and rratonalty only f t can correctly predct developments of man economc and 14 Ths argument mght be supported by Dušek, Kopecsn (2008:342) who proved that the polcy rsk of the PAYG system n three central European countres (Hungary, Slovaka and the Czech Republc) can be substantal. Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no

20 demographc parameters and then commt tself to a consstent reform polcy over a longer term. The recent Czech experence warns that these condtons for consstent government polces mght be too strct. If so, we cannot clam that the controlled transformaton s more approprate than the opt-out verson. In such case t s mpossble to predct the reform strategy whch would lead to a more effcent outcome. APPENDIX Models Used n Our Analyss 1. PAYG DB Model Calculaton of the new acknowledged penson s done by usng the current practce n the CR (accordng to Secton of the Act No. 155/1995, Coll.). The equatons (1) (5) also uses Bezdk (2005), the phlosophy of the calculaton can be found n MLSA (2008:94 96). PAYG P BA PA (1) PA n1 * ar * CB (2) CB PAB * rr max(0, PAB rh )*( rr rr ) max(0, PAB rh )*( rr rr ) (3) PAB Y 1 Y 1 ABk * ky1mn(30, Y11986) jk mn(30, Y 11986)*12 w j, W j 1 wj (4) W j Y 1 AB PAB WY 1 (5) 12 (1) Penson s composed of two elements (a dual component structure): BA basc amount (flat rate) and PA a percentage-based assessment based on the nsured perod and earnngs acheved. (2) The amount of PA depends on personal nsurance perod ( n 1 40 ), enttlement ( ar 1, 5% ) and personal calculaton base ( CB ). (3) Personal calculaton base s gven by personal assessment base and reducton lmts ( rr1, rr2, rr3, rh1, rh 2 ). (4) Personal assessment base depends on annual bases ( AB k ) wthn the reference perod; annual bases are adjusted by the coeffcent of the growth of the general Y 1 assessment base ( wj ). jk 328 Fnance a úvr Czech Journal of Economcs and Fnance, 59, 2009, no. 4