The impact of increased life expectancy on the level pension

Transcription

1 Alanic Review of Economics 1s Volume The impac of increased life expecancy on he level pension Alleiddine AYED ZAMBAA Faculy of Economics and Managemen of Sfax, Tunisia Revisa Alánica de Economía Volumen

2 Alanic Review of Economics 1s Volume Absrac This paper proposes an overlapping generaion model along he lines of he papers by Fani and Gori (2008). Is objecive is o sudy he effec of demographic shocks on he level pension respecively in he PAYG and funded sysem wihin he conex of increased life expecancy a long-run. Resumen En ese rabajo se propone un modelo de generación de superposición en la línea de los rabajos de Fani y Gori ( 2008 ). Su objeivo es esudiar el efeco de los shocks demográficos sobre la pensión nivel, respecivamene, en el reparo y sisema de capialización en el conexo del aumeno de la esperanza de vida al largo plazo. Key words: life expecancy, pension sysem, overlapping generaion model JEL Classificaion: H55, J13 Revisa Alánica de Economía Volumen

3 Alanic Review of Economics 1s Volume Inroducion The quesion of reiremen has been he subjec for some ime, an imporan and special aenion from economiss. Thus, he recen changes in demographics and pensions echnical lead differen economiss o focus on debae PAYG/ funded. This debae focuses mainly on hree poins which are respecively differences in reurns and risk, impac on savings and economic growh and sensiiviies demographic shocks. The laer will be he ineres of our. Blanche (1999) disinguished wo ypes of demographic shock. The firs shock focuses on he populaion growh rae. The second shock is relaed o he increase in life expecancy. More specifically, we are ineresed in he effec of his second ype of demographic shocks on he level pension. The increase in individual life expecancy a all ages is a recen populaion even in human hisory. Indeed, during he firs half of he 20h cenury, i was obained as a resul of a sharp decrease in infan moraliy raes, which helped make seady gains in life expecancy a birh. Afer he Second World War, he main conribuion came from he decrease in moraliy afer 60, lenghening life expecancy in old age period. These gains in life expecancy a older ages have brough people ino he era of longeviy. There is ample saisical evidence ha indicaed he rend of increased life expecancy will influence asse reurns in funded sysem and herefore he level of pension received by he pensionner will reduce in he coming decades according Abel (2003). In fac, Zhang and Lee (2001), Miyazao (2010) and Beesma e al. (2011) noed ha his ype of demographic shocks in he funded pension sysem resuls in regression of reurns on annuiies. Similarly, Aliparmakov (2013) showed ha funded pension sysems are far from immune o his phenomenon of increased life expecancy. In oher words, his phenomenon leads conribuors o receive over ime lower pension levels for he same amoun of accumulaed reiremen savings. In he same, Thomas e al. (2014) indicae ha he level pension in he case of funded will decrease in he nex wo decades because of he arrival a he reiremen of he baby-boom generaion. On he oher hand, Devolder (2007) have noiced ha he increase of life expecancy affecs an equivalen manner he level pension in he wo ypes of pension sysem since each ype of reiremen sysem consiues a ransfer of income from asses o he pensioners. Bu, in our paper, we sudy his problem hrough an approach of overlapping generaion along he lines of he papers by Fani and Gori (2008). The res of he paper is organised as follows. Secion 2 describes he model. Secion 3 analyses how he increased of life expecancy affecs he level pension in he PAYG sysem. Secion 4 sudied his impac in he case of funded pension sysem. Secion 5 concludes. Revisa Alánica de Economía Volumen

4 Alanic Review of Economics 1s Volume The model Our model is inspired by he paper of Fani and Gori (2008) in which agens live wo periods. Each individual born in consume successively c and c 1. In his model, i assumes ha he old individuals survive o he second period wih a probabiliy. Thus, he funcion of ineremporal uiliy of he represenaive agen is given by he following expression: U ln( c1, ) ln( c2, 1) (1) Where is he subjecive discoun facor Each worker receives wage income a he compeiive rae w and pays a proporional ax on income from work, which is used o finance he pension sysem. Thus, he budge consrain of he individual in he firs period is wrien as follows: c s w ( 1 ) (2) where s is he level of saving in he firs period and is he conribuion rae. In he second period, individuals reire and heir consumpion is ensured by heir savings from he previous period plus he accrued ineres a rae r 1 on he one hand, on he oher hand he pension benefis P 1. Hence, he following equaion of he budge consrain in he second period: c 1 1 r 1 The objecive of he individual is o maximize is ineremporal uiliy and o choose he equilibrium disribuion of ne income beween he savings ha serve for consumpion during reiremen and consumer spending in he firs period. The resoluion of he programme of he represenaive agen allows us hen o wrie he expression of he saving as follows: s s P 1 w (1 ) P 1 1 (1 )(1 r 1 ) (3) (4) This model supposes he exisence of infiniy of firms having he same producion funcion and producing a homogeneous unique produc. The producion is assured by means of he labor ( L ) and physical capial ( K ) according on he echnology producion of Cobb-Douglas following: Revisa Alánica de Economía Volumen

5 Alanic Review of Economics 1s Volume Y AK L (5) 1 A is a parameer of produciviy is a elasiciy of physical capial 1 is a elasiciy of labor In his model, here is a oal depreciaion of capial a he end of each period and ha he producion is sold a uni price. This brings us o he following condiions of maximizaion profi: r Ak 1 1 (6) w ( 1 ) Ak (7) Wih k K L 3. The impac of he increase of life expecancy on pension level in he PAYG pension sysem In a PAYG sysem, he conribuions of he workers ransmied o he reirees during he same period. Therefore, he pension spending a is limied by he oal conribuions. Then, he balance of PAYG pension in each period according is he following formula: P w ( 1 n) (8) Using he balance of PAYG pension in equaion 4 allows us o obain he following expression: s w (1 ) (1 n) w 1 (1 )(1 r 1 1 ) (9) A equilibrium in he marke for goods and services, he saving is equal o he invesmen on he one hand; on he oher hand, even he invesmen of period is equal o he capial sock of he nex period. These wo condiions ha brings us o: ( 1 n) k 1 s (10) Revisa Alánica de Economía Volumen

6 Alanic Review of Economics 1s Volume Insering equaion 10 ino equaion 9 and use equaions 5 and 6 deermine he dynamic equilibrium sequence of capial: (1 ) (1 ) A k 1 k (11) (1 n) (1 ) (1 ) Seady-sae occurs when k remains consan over ime. We herefore find ha he seady sae value of k is given by: 1 k 1 (12) (1 ) (1 ) A (1 n) (1 ) (1 ) Afer he deerminaion of he seady sae of he sock of capial, we focalize in he deerminaion of he level pension a long-run. For his, we combine equaions 6, 7 and 12 o obain: (1 ) (1 ) A (1 n)(1 ) A (1 n) (1 ) (1 ) P PAYG (13) 1 From equaion 13, we visualize ha he increased life expecancy can cause wo differen effecs on he level pension a long-run. The firs effec is he decrease of he level pension because he higher number of pensioners in he fuure. The second effec is posiif of he pension level by a rise wage rae due an increased sock of capial per-capia. The second effec is mos imporan ha he firs effec because he posiive relaionship beween PAYG pension and wages. 4. The impac of he increase of life expecancy on level pension in he funded sysem We consider anoher ype of pension sysem which is he funded pension sysem ha consiss for an individual o conribue oday for his fuure reiremen. In he period of reiremen, each pensioner receives he mass of he conribuions paid during he period of aciviy which is raised by he ineres rae. In fac, he balance of funded pension can hen be wrien as: P w (1 r ) (14) 1 Revisa Alánica de Economía Volumen

7 Alanic Review of Economics 1s Volume Inegraing equaion 14 ino equaion 7, we obain herefore: w ( 1 ) w 1 s (15) follows Under he funded pension sysem, he equaion of capial accumulaion is expressed as ( 1 n) k s w. Thus, he exploiaion of he capial accumulaion equaion and he wo 1 equaions of wage and saving leads us o obain he dynamics of he capial sock: (1 ) A k 1 k (16) (1 )(1 n) Therefore, he seady-sae of capial sock in he long erm is of he following form: (17) k (1 ) A (1 n)(1 ) 1 1 Subsequenly, combining equaions 6, 7 and 17 in order o deermine he level of pension a long-run: 2 1 P funded 2 1 (18) (1 ) A (1 ) A (1 n)(1 ) From equaion 18, in he funded pension sysem, he cos resuling from he increase in life expecancy is suppored by reirees hrough a reducion in pensions. Thus, when a person affiliaed o a funded pension, he accumulaed capial hrough he sum of conribuions and heir reurns in sock marke is convered regular pension, known as ren. The calculaion of he pension will be based on he expeced lifespan for affiliaes a he ime of reiremen, so ha he level pension will auomaically decrease as conribuors live longer. 5. Conclusion This paper presens a simple overlapping generaion model wih an increase of life expecancy. Almos all heoreical models exising in he lieraure aemp o show ha he increase in life expecancy affecs an equivalen manner he level of pension in he PAYG and funded sysem. Revisa Alánica de Economía Volumen

8 Alanic Review of Economics 1s Volume However, his paper reaches a differen resul, based on he work of Fani and Gori (2008) bu mainaining a generaional approach o compare he effec of he increasing life expecancy on he pension level in boh ypes of pension sysem. We show ha he funded pension sysem is more affeced han he PAYG sysem by he risk of increasing life expecancy. The resul is mainly due o he sharp decline of yield funded yield because he number of reirees growing more rapidly han he number of conribuors. Thus, our conribuion leads o a resul differen from he work of Devolder (2007), in which he increase of life expecancy in feriliy leads o more reduce he level of pension in he case of funded pension han he PAYG sysem. Revisa Alánica de Economía Volumen

9 Alanic Review of Economics 1s Volume Reference Abel A. (2003), The Effecs of a Baby Boom on Sock Prices and Capial Accumulaion in he Presence of Social Securiy. Economerica, vol.71, n 2. Aliparmakov N. (2013), Is here an alernaive o he pay-as-you-go pension sysems in Serbia?. Economic annals, vol.58, Issue 198, pp Beesma R.J, Bovenberg A.L and Romp W.E (2011), Funded pensions, inergeneraional and inernaional risk sharing in general equilibrium. Journal of inernaional money and finance, vol.30, n 7, pp Blanche D. (1999), Le déba répariion capialisaion : un éa des lieux. Reraie e épargne, pp Devolder P. (2007) Managemen of a pension fund under moraliy and financial risks. Insurance : mahemaics and economics, vol.41. Gori L. and Fani L. (2008), Longeviy and PAYG pension sysems susainabiliy. Economics Bullein, vol.10, n 2, pp 1-8. Miyazao N. (2010), The opimal size of Japan s public pensions: An analysis considering he risks of longeviy and volailiy of reurn on asses. Japan and he world economy, vol.22, n 1, pp Thomas A., Spaaro L. and Mahew N. (2014), Pension funds and sock marke volailiy: An empirical analysis of OECD counries. Journal of financial sabiliy, vol.11, pp Zhang J. and Lee R. (2001), Moraliy decline and long-run economic growh. Journal of Public Economics, vol.80, n 3, pp Revisa Alánica de Economía Volumen