IS THERE A LINK BETWEEN PENSION-FUND ASSETS AND ECONOMIC GROWTH? - A CROSS-COUNTRY STUDY

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1 5th June 2005 IS THERE A LINK BETWEEN PENSION-FUND ASSETS AND ECONOMIC GROWTH? - A CROSS-COUNTRY STUDY E Phlp Davs * and Yu-We Hu ** Brunel Unversty and NIESR London Abstract: Debate over superorty of penson fundng over pay-as-you-go lnks notably to the queston whether fundng mproves economc performance suffcently to generate addtonal resources to meet the needs of an ageng populaton. To address ths ssue, we desgn a modfed Cobb-Douglas producton functon wth penson assets as a shft factor, and nvestgate the drect lnk between penson assets and economc growth employng a dataset coverng up to 38 countres, usng a varety of approprate econometrc methods. We fnd postve results for both OECD countres and Emergng Market Economes (EMEs), wth consstent evdence for a larger effect for EMEs than OECD countres. Key words: Penson funds, economc growth, producton functon, panel estmaton JEL Classfcaton: G23, O16, C33 * E Phlp Davs s Professor of Economcs and Fnance, Brunel Unversty, Uxbrdge, Mddlesex, UB8 3PH, Unted Kngdom (emal e_phlp_davs@msn.com, webste: He s also a Vstng Fellow at the Natonal Insttute of Economcs and Socal Research, an Assocate Member of the Fnancal Markets Group at LSE, Assocate Fellow of the Royal Insttute of Internatonal Affars and Research Fellow of the Penson Insttute at Cty Unversty, London. ** Yu-We Hu s a doctoral research student at Brunel Unversty (emal: Yu-We.Hu@Brunel.ac.uk). The work was undertaken as part of a project on the Economcs of Pensons across OECD countres and Emergng Market Economes. Ths paper s a large expanson of the earler conference paper presented at the CCISSR Forum 2004, th June, Bejng Unversty, Bejng. The deas and concepts developed n ths paper have benefted from suggestons from Jagjt Chadha, Andros Gregorou, John Hunter, Estelle James, Kul Luntel, Chrs Martn, Norma Sephuma, Harry Verbon and partcpants n semnars at Brunel Unversty and Tlburg Unversty. Thanks are also gven to Mukul Asher and Gregoro Impavdo for assstance n fndng penson data. They are of course not responsble for the authors errors.

2 2 Introducton The current global demographc shft toward populaton agng, largely reflectng rsng lfe expectancy and declnng fertlty (Munnell 2004) has led many countres across the world to re-evaluate ther penson systems. Typcally, they swtch wholly or partally from unfunded systems, e.g. pay-as-you-go (PAYG) to funded systems, wth reform n Emergng Market Economes (EMEs) often supported by World Bank fnance (Holzmann and Hnz 2005). Gven the funded nature of many new penson schemes, penson fund assets have ncreased across many countres. Lookng frst at OECD countres, n 1980, UK penson assets were equvalent to bllon US dollars (21.5% of GDP), whereas n 2000 these two fgures had ncreased to bllon US dollars (79% of GDP) (OECD 2003). The trend was smlar n most other OECD countres. Table 1 shows that as of 2000, total penson fund assets across our selected advanced OECD countres were US$12 trllon. The US as the bggest penson market accounted for just above half of the total wth Japan and the UK followng. In terms of penson assets relatve to GDP, the Netherlands had the largest rato at 149% of GDP, whle ths fgure for New Zealand, at 0.69%, was the smallest across OECD countres. As regards data for EMEs shown n Table 2, Chle s the country whch poneered reform towards prvate funded pensons and ts experence s often cted to justfy funded penson reform; n that country penson funds grew from zero n 1980 to 60 per cent of GDP as of The bggest EME penson markets were, however, Sngapore and Malaysa whch adopted publcly managed funded Provdent Fund penson systems n the 1950s. Other EMEs wth sgnfcant penson assets nclude Brazl and Mexco. Total penson assets across our selected EME countres n 2002 were US$ 280 bllon, whle the average penson asset-gdp rato was 12 per cent, much less than that of OECD countres whch was 42 per cent. Gven demographc trends and the structure of funded schemes, t s vrtually certan that penson funds wll contnue ther rapd expanson durng the comng decades. In ths context, a key ssue n penson reform s whether such a shft from PAYG to fundng s largely a matter of reallocaton of the fnancal burden of ageng (wth the rsk of a generaton payng twce), or whether fundng mproves economc performance suffcently to generate at least some of the addtonal resources requred to meet the needs of an ageng populaton. There are several aspects to ths queston. One s whether fundng leads to an ncrease n savng whch permts hgher captal formaton. A second s whether, ndependently of the mpact on savng, there are favourable effects of fundng on the functonng of captal and labour markets, for example va acceleraton of fnancal development, generatng n turn a more effcent allocaton of captal. A thrd s whether, followng from these effects, a drect mpact of fundng on growth can be dscerned. Whereas there s qute extensve work on fundng s effect on savng and on fnancal development (Hu (2005a), Davs and Hu (2005), Davs (2005)), the drect role of penson funds n economc growth has been lttle examned. Is penson-fund growth postvely assocated wth economc performance? And f so, how long wll ths postve mpact contnue? In ths paper, we seek to provde nsght nto these questons wth both a theoretcal model and related emprcal work for most OECD countres and selected EMEs. The paper s structured as follows. Secton 1 provdes a bref lterature revew on the ssue of whether and how penson fund growth may mpact on economc performance. Secton 2 deals wth the model specfcaton, whch s derved from the Cobb-Douglas producton functon, and vews penson fund assets as a shft factor, an dea developed from McCoskey and Kao (1999) and Arests et al (2004). Data and varables are dscussed n Secton 3. In Sectons 4, we

3 3 test our data s statonarty by usng unt root tests and fnd varables to be I(1), mplyng a need to allow for contegraton. In Secton 5, our frst econometrc work s conducted wth the help of contegratng dynamc OLS (DOLS) model, whch we consder most approprate for the queston n hand. Complementng ths, n Secton 6, we follow the dynamc heterogeneous estmaton procedures desgned by Pesaran and Smth (1995) to look at the average long run relatons and allow for cross country heterogenety. In Secton 7, we move to country-by-country co-ntegraton tests, nvestgatng whether there s a long run relatonshp between penson funds and economc growth and agan allowng agan for cross country heterogenety. Impulse responses of output per capta to penson assets n the related Vector Error Correcton Models (VECM) are calculated as well as varance decompostons. In each case we assess results wth and wthout a tme trend, whch may capture other nfluences on the producton relaton such as structural reform. Summarsng the results (see Table 11), a strong and postve relaton s found n the contegratng dynamc OLS panel model between penson assets, output and captal, wth larger effects of penson assets on output for EMEs when a tme trend s ncluded. Panel contegraton coeffcents usng mean-group dynamc heterogeneous models agan fnd a postve and sgnfcant average long run relatonshp between penson assets and output, agan notably for emergng market economes. Country-by-country contegraton tests typcally fnd a contegratng relatonshp between the I(1) varables penson assets/gdp, the captal stock per capta and output per capta. Impulse responses n the related VECM wth and wthout the trend show that a rse n penson assets typcally boosts output per worker, and durng a 25-year perod, the effect typcally remans postve. Sgnfcantly larger effects are found for EMEs than OECD countres. 1. Lterature revew Whereas there s some evdence of a small postve effect of penson-fundng on household savng (Kohl and O Bren 1998), the relevant varable for economc growth s natonal savng whch largely determnes nvestment 1, as would be predcted by a standard Solow (2000) growth model. James (1998) argues that one man advantage of World Bank mult-pllar model of penson reform s that natonal savng as well as personal savng could be boosted. But any postve effect of penson fund growth on personal savng could be offset at the level of natonal savng by the mpact on publc fnances of the costs nvolved n the transton to a prvately funded system (Holzmann 1997), as well as the costs of tax subsdes to personal savng. A key aspect of ths ssue s hence how penson-reformng governments fnance exstng socal securty oblgatons. If the government tres to fnance the mplct penson debts by publc debts, then publc savngs would decrease, so the overall natonal savng rate mght be unchanged or even fall. There s conflctng emprcal evdence on ths pont. Schmdt-Hebbel (1999) estmated that penson reform n Chle rased the natonal savng rate. Gven the dffculty of pnnng down how the penson reform was fnanced n Chle, he consdered three cases,.e. fscal contracton-based fnancng of penson reform at the levels of 100%, 75% and 50%. On balance, he suggests that between 10% and 45% of the rse n natonal savng could be explaned by penson reform, wth the remanng beng explaned by structural reform, e.g. tax reform etc. Lopez-Murphy and Musalem (2004) study 50 countres and fnd that natonal savng s boosted where penson funds are the result of a mandatory penson programme, but not when they are voluntary. On the other hand, Samwck (1999), workng wth a panel of 1 Whereas such relatons can be weakened by nternatonal captal flows, the extensve lterature on the Feldsten-Horoka puzzle shows that domestc nvestment contnues to be strongly related to domestc (.e. natonal) savng.

4 4 countres, found that no countres except Chle experenced an ncrease n gross natonal savng rates after penson reform towards non-payg systems. He ncluded control varables such as the log of per capta ncome, per capta ncome growth, the prvate credt to ncome rato, demographc ndcators and the urbansaton rate to avod omtted varables bas. Furthermore, Bosworth and Burtless (2004) found that OECD countres that seek to prefund socal securty oblgatons such as Japan and the US ncur offsettng ncreases n government borrowng that agan offset any dfference n natonal savng. Gven the doubt about a lnk of penson reform to natonal savng, we consder t mportant to focus on some alternatve channels for pensons to affect growth, va mproved economc effcency and resource allocaton. The lnk between penson funds and captal market development has been wdely analysed n the recent lterature, as revewed n Davs and Hu (2005). Both prces and quanttes of long term fnancng may be favourably affected, whch may n turn rase productve nvestment and mprove resource allocaton. Focusng on emergng market economes (EMEs), Walker and Lefort (2002) argue that penson funds can decrease the cost of captal va three channels. The frst channel s more developed captal market resultng from penson reforms, thus makng the ssung of securtes cheaper. Secondly, even allowng for short-term performance evaluaton (Davs and Stel 2001), the expected nvestment tme horzon of penson funds s longer than that of ndvduals and frms, thus reducng the term premum. Thrd, the equty rsk premum s reduced due to penson funds poolng and professonal management. Both the term premum and rsk premum s reducton mght lead to a decrease n the average cost of captal, whch spurs nvestment. In addton, they gve some evdence that penson funds reduce securty prce volatlty, mplyng a lower rsk premum for ther panel of emergng market economes, although an opposte result s found by Davs (2004) for G-7 countres. Turnng from prces to quanttes, Catalan et al (2000) gve evdence that contractual savng nsttutons, e.g. penson funds, postvely Granger-cause equty market captalsaton as well as value traded, whle Impavdo et al (2003) and Hu (2005a) fnd a postve relatonshp between contractual savng assets and bond market captalsaton/gdp. In sum, the current lterature suggests a postve relaton between penson fund growth and fnancal development, see also the survey n Davs (2005). Gven t s wdely consdered that fnancal development s postvely assocated wth economc growth (Levne and Zervos 1998; Beck and Levne 2004), then penson funds mght enhance economc growth va ther mpact on fnancal development, ndependently of an effect on natonal savng. Penson funds may also boost economc growth va mproved corporate governance (Clark and Hebb 2003; Myners 2001) 2. Clark and Hebb (2003) dentfy four drvers whch facltate penson funds corporate engagement, whch they see as foreshadowng the so-called Ffth Stage of Captalsm. The frst drver s the wdespread use of ndexaton technques n the penson funds ndustry, whch hnders ext va sale of shares n underperformng companes whch are n the ndex. The second drver s the ncreasng demand by owners for more transparency and accountablty, partcularly after the Enron, Worldcom and Parmalat scandals. Thrd, there s penson funds pressure to undertake socally responsble nvestng (SRI). Fourth, pressures to humanze captal wth socal, moral and poltcal objectves extend penson funds smple concerns for rate of return. A postve mpact of penson fund actvsm on corporate performance at the frm level s well 2 The effectveness of penson funds postve mpact on corporate governance has been challenged by Orszag (2002) and emprcal works n the US such as Del Guerco and Hawkns (1999).

5 5 documented, although emprcal work s largely focused on the US 3. But our concern n ths paper s whether penson fund growth s a potental engne of economc growth va ts effect on corporate performance at the macro level, an ssue whch s gnored or dsmssed by most current pensons research. An excepton s Davs (2002, 2004) who argues that complementary studes at the macro level are needed, because effects of governance ntatves from nsttutonal nvestors may go wder than the target frms to the whole economy. Ths s because unaffected frms have natural ncentves to mprove ther performance so as to avod the threat from penson fund actvsm n the future (Marsh 1990). Therefore, f a sgnfcant proporton of frms, whether drectly affected and ndrectly affected by penson fund actvsm, tend to mprove ther performance, the overall effect mght be hgher economc growth and productvty for the whole economy. Consstent wth ths, Davs found nter ala that nsttutonal holdng of equty s related to a boost to Total Factor Productvty (TFP) and n R and D. Besdes the ssue of corporate governance, labour market performance s relevant. It s well known that due to the weak lnk between penson contrbutons and benefts under defned-beneft PAYG systems, there s a tendency towards earler retrement and job mmoblty. For example, over the postwar perod, there was a very sharp fall n partcpaton rates for those men over state penson age (65+) n EU countres (Dsney 2002). One contrbutng factor was the dsncentves mbedded n publc penson systems (Blondal and Scarpetta 1998). In addton to the penson system s mpact on labour supply, Dsney (2003) argues that the dstortonary tax component of publc penson contrbutons can also affect labour demand f the employee can pass through the burden of penson contrbuton to consumers for example va product prces, because product demand falls and producers mght consder reducng the demand for labour. In vew of such problems, James (1998) suggests that the close lnkage between benefts and contrbutons, n a defned-contrbuton plan s desgned to reduce labour market dstortons. In consequence, economc growth mght be ncreased, e.g. due to a hgher labour partcpaton rate after penson reform. Such effects mght be smaller where defned beneft funded schemes predomnate. Lookng at the drect lnk of growth to penson reform, most extant studes have focused on Chle. Holzmann (1997) found a postve relatonshp between penson reform and economc growth. Wth the smple Solow resdual specfcaton of TFP, t was found that mprovng fnancal market condtons followng the penson reform sgnfcantly postvely affected TFP. But ths model suffers from low t values whch mght result from multcollnearty between ndependent varables, e.g. the unemployment rate and stock market ndex. Meanwhle, Schmdt-Hebbel (1999) reached the concluson that penson reform n Chle boosted prvate nvestment, the average productvty of captal and TFP. One sngle regresson was estmated to obtan the coeffcents of parameters, then these coeffcents are used to calculate the rse of each varable attrbuted respectvely to structural reform, (e.g. tax reform) and penson reform. In all, he concluded that penson reform n Chle had a postve mpact on the prvate nvestment rate, average productvty of captal and the TFP growth rate. For example, penson reform contrbuted to per cent of the 1.5 per cent ncrease n TFP growth rate, whle per cent of the total 13 per cent rse n prvate nvestment rate was attrbuted to penson reforms wth the remander beng explaned by structural reform. Emprcal work whch nvestgates the drect lnk between penson fund growth and economc growth at a transnatonal level s qute scarce to our knowledge, although Davs (2002 and 2004) wth a dataset coverng both penson funds and lfe nsurance companes, looked at the relaton between nsttutonalsaton and economc performance at the macro level. Although 3 See Wahal (1996), Smth (1996), and more recent work by Wokdtke (2002) and Coronado et al (2003) for estmates of the mpact of penson actvsm on corporate performance at the frm level.

6 6 hs results are, as noted, consstent wth hgher TFP, he fnds no drect effect of the proporton of equty held by lfe nsurers and penson funds on GDP growth. Agan, Davs (2004) usng a dataset of 16 OECD countres and a standard Levne-Zervos (1998) specfcaton for fnance and growth does not fnd a postve drect lnk between nsttutonalsaton (lfe nsurance and penson assets/gdp) and growth per se. On the other hand, usng the technque developed by Hurln and Venet (2003) and Hurln (2005), Hu (2005b) shows that Panel Granger Causalty tests do ndcate homogeneous causalty from penson assets to GDP growth n 38 countres as well as n the subgroups OECD (18 countres) and EMEs (19 countres). Reverse causalty s weaker, and notably for emergng markets there s no strong evdence that GDP growth homogenously causes penson assets. Takng nto account the above lterature revew, ths paper seeks to contrbute to the current growth and pensons lterature n three areas. Frst, we desgn a modfed Cobb-Douglas producton functon wth the ncluson of penson assets as a shft factor. Second, we employ a set of dfferent econometrc methods to test the model on data for up to 38 countres, whch ncludes a contegratng dynamc OLS estmator for the man panel results and also the dynamc heterogeneous models desgned by Pesaran and Smth (1995) to look at the average long run relatons between varables, allowng for cross country heterogenety. Thrd we drectly lnk penson assets to economc growth n a co-ntegraton relatonshp on a country-by-country bass and nvestgate the extent to whch they are correlated n the long run as well as the mpulse responses and varance decomposton n the related Vector-Error-Correcton Model. 2. Model specfcaton The Cobb-Douglas producton functon s wdely used n the economc lterature: Q 1 = AK β L β (1) where A s technology, K s the captal stock and L s the labour force. Generally, the Cobb-Douglas functon s specfed as shown n Equaton (1). But n ths study, we modfy the functon slghtly so as to facltate our analyss of the mplcaton of penson fund assets for output Q. In addton, n vew of our panel analyss, we use a double subscrpt on ts varables. Q = A ( P ) ( K ) ( L ) (2) λ β 1 β t, t, t, t, t, where: : tme seres dmenson; t: cross secton dmenson; Q: aggregate output, proxed by GDP; A: state of technology; P: penson funds, proxed by penson fund assets/gdp; K: captal stock 4 ; L: labour supply, proxed by total populaton; λ : elastcty of aggregate output wth respect to penson fund assets; β : elastcty of aggregate output wth respect to the captal stock. Equaton (2) suggests that aggregate output s affected both by technology A and penson fund assets P, whch act as shft factors, as well as captal K and labour L. Note that the model does 4 Captal stock s calculated based on the perpetual nventory method. Consstent wth Luntel and Khan (1999), we used 8 per cent of deprecaton rate and averaged frst 3-year growth rate to obtan the ntal captal stock.

7 7 not assume penson fund growth rases savng trends n natonal savng wll be captured by the captal stock varable, to the extent external balance s mantaned. In effect, we test whether owng to better resource allocaton, ncentves etc., penson fund growth makes the captal stock more productve. Arests et al (2004) and McCoskey and Kao (1999), among others, use the smlar specfcaton,.e. a generalsed Cobb-Douglas producton functon wth relevant addtonal varables such as urbanzaton rates or the nature of the fnancal system set as shft factors nto the standard functon. Technology may then be specfed as follows: t, t A = e α + γ + ε (3) t, Ths specfcaton s n lne wth McCoskey and Kao (1999), where α s the ntercept, t s the tme trend and ε s the resdual term. Specfyng the state of technology n ths way assgns each of our country sample wth the country-specfc ntercept and tme trend (allowng for heterogenety across countres that mght relate to factors such as structural reform) and also ntroduces a stochastc element,.e.ε nto the model as ndcated n Equaton (5) below. Replacng technology A n Equaton (2) by ts expresson n terms of t as shown n Equaton (3) gves α+ γt+ ε, t λ β 1 β t, ( t, ) ( t, ) t, Q = e P K L (4) Then, normalsng by L t, and takng logs from both sdes n Equaton 4, we have Q L K t, t, t t, e α + γ + = ε ( Pt, ) λ ( ) β t, Lt, * α + γ t+, t * t, = ε ( t, ) λ ( t, ) β Q e P K LnQ = α + γ t + λ LnP + β LnK + ε (5) * * t, t, t, t, where Q K Q = and K = * t, * t, t, t, Lt, Lt, γ = λ + ω1, λ = λ + ω β = φ + ω 2 and 3 Q s output per worker and * t, K s captal per worker. The model shown n Equaton (5) s * t, the standard formulaton of Swamy s Random Coeffcent Model (RCM) (Swamy and Tavlas 1995) where we can allow for heterogenety across countres n terms of tme (t), penson fund assets (LnP) and captal per worker (LnK). We vew ths model as approprate n that penson fund assets mpact on output mght show marked dfferentals across countres. Followng the model above, we regress captal per worker (CPW) and penson fund assets/gdp (PFAGDP), whch are K* and P n Equaton 5 respectvely, on output per worker (OPW) or Q*, usng varous econometrc technques. We estmate wth and wthout the tme trend (t) whch may capture other nfluences on producton relatons such as structural reforms. Followng Arests et al (2004) we do not nclude some of the standard varables typcally entered n cross-sectonal cross country growth regressons such as years of schoolng, as well as corrupton, socal captal, nequalty and rule of law. On the one hand, t would not have been feasble to buld an annual tme seres for these varables. Furthermore, we consder that a generalzed producton functon estmated s the approprate specfcaton for the ssue n hand and usng panel data wth fxed effects and a tme trend (n some specfcatons) wll capture

8 any relevant dfferences n growth performance across countres. 3. Data and varables 8 Before descrbng estmaton, we outlne ssues n data constructon and unt root tests. Regardng the calculatons of Q* and K* we use standard macro-economc data from the World Development Indcators 2003 (WDI) database. The captal stock s derved by the perpetual nventory method. Consstent wth Luntel and Khan (1999), we used an 8 per cent deprecaton rate and averaged the frst 3-year growth rate to obtan the ntal captal stock. Penson fund asset data were collected from a varety of sources. For OECD countres, OECD (2003) and Davs and Stel (2001) are the man sources, but some are expanded and updated by checkng fnancal statstcal reports n ndvdual countres, e.g. Natonal Fnancal Statstcs for the UK data and Insttute of Penson Research and Nkko Fnancal Intellgence, Inc for the Japan data. For Latn Amercan countres, the webste of Federacón Internaconal de Admnstradoras de Fondos de Pensones (FIAP) (Internatonal Federaton of Penson Fund Admnstratons) n Chle provdes penson data up to the year end of 2003 on many Latn Amercan countres. For South Asan countres and South Afrca, penson data are largely compled ndvdually by searchng local central banks Fnancal Bulletns, although ASEAN Socal Securty Assocaton s webste was used to update recent penson data on some Southeast Asan countres. Regardng the data observaton perod, n general, for captal per worker and output per worker we have data for years between 1960 and But penson data are an excepton. For OECD countres, e.g. the UK, the US, we have data rangng from 1960s to 2002, whle for many EMEs, e.g. Brazl, the data avalable are relatvely lmted. See Appendx 1 for detals of the varables across our 38 countres. 4. Panel unt root test Before proceedng to formal panel regresson analyss, the frst step s to examne our data s statonarty. 4.1 Specfcaton of tests There are a number of ways to test panel data s statonarty (Maddala and Wu 1999; Baltag 2001). In ths study, n order to check our results robustness, we use three dfferent but commonly quoted tests,.e. one desgned by Levn, Ln and Chu (2002) (hereafter LLC), one by Im, Pesaran and Shn (2003) (hereafter IPS), and last one by Hadr (2000). Consder the followng model yt, = ρyt, 1 + Xt, δ+ εt, = 1,... N : t = 1,... T (6) where y s our varable of nterest; X s a vector of exogenous varables, ncludng fxed effects and/or a tme trend, or smply a constant, based on the modelers assumptons. ε t, are 2..d. (0, σ ). As customary, t proxes tme, whle proxes country. ε The prncpal dfference between LLC and IPS s the assumpton made on ρ. LLC proposes that ρ = ρ, mplyng the coeffcent of lagged dependent varable n Equaton (6) s the same

9 9 across countres, whle under IPS, ρ s allowed to vary across countres. Gven that n our sample, both OECD countres and EMEs are ncluded, we put more emphass on the latter test,.e. IPS (2003), n that there mght be heterogenety across countres. Both LLC and IPS tests are an extended verson of tme seres Augmented Dckey-Fuller test (ADF) nto the context of panel data. The formulaton s as follows: p y = βy + ρ y + X δ + ε = 1,... N : t = 1,... T (7) t, t, 1, j t, j t, t, j= 1 LLC tests the null hypothess of β =0, whle IPS s testng that of β =0 for all. In addton, for the IPS test, t-bar statstcs s used, whch are formed as a smple average of the ndvdual t statstcs for testng β =0 n Equaton 7, namely t bar N 1 NT = N t T = 1 (8) Both LLC and IPS are commonly used n the current emprcal lterature for panel data. It has been argued, however, that they both suffer from the lack of power (Hadr 2000). In other words, the null hypothess of a unt root tends to be accepted or not rejected unless there s strong evdence to the alternatve, one form of type II error (Davdson and MacKnnon 1993; Greene 2003). Therefore, t s suggested to test a null of statonarty as well as a null of a unt root. One well-known test for the null of no unt root s that proposed by Hadr (2000). Hadr testng s a resdual based Lagrange multpler (LM) test. Consder the model, y = r + β t+ ε (9) t, t, t, where rt, = r t, 1 + µ t,, a random walk. The LM statstc s formulated as follows: LM = 1 N 1 N T T 2 t= 1 2 σ ε S 2 t, (10) where S =, j and t, t j= 1 ε 2 1 N T 2 ε t, σ = NT = 1 t= 1 ε ε, j s the estmated resdual from Equaton (9), t, S s the partal sum of resduals, whle s the estmate of the error varance. Hadr s resdual-based LM test for the null of statonarty s promsng n that t ncreases the power of testng for the null of a unt root. One problem assocated wth Hadr (2000), however, that lke LLC (2003), t assumes the homogenety of coeffcents of ρ = ρ n Equaton (6). As we mentoned earler, n our study, we use a dataset coverng both OECD countres and EMEs; therefore, an assumpton that ρ vares across sectons mght be more approprate. 4.2 Results for panel unt root tests Table 3 presents the results of the panel unt root tests. For the log of the penson assets to GDP 2 σ ε

10 10 rato (PFAGDP) our results, under all three testng approaches, are n favour of non-statonarty n levels, and statonarty n frst dfferences, mplyng that PFAGDP s an I(1) varable. Regardng the log-levels of output per worker (OPW) and captal per worker (CPW), under IPS and LLC, the null hypothess of non-statonarty could not be rejected for ths panel of 38 countres. But after frst dfferencng, the null hypothess of non-statonarty s rejected and the alternatve hypothess of statonarty be accepted. Ths s consstent wth our assumpton that OPW and CPW are also I(1) seres. By employng the Hadr (2000) test, however, we could reject the hypothess of no unt root under both levels and frst dfferences. After second dfferencng, OPW and CPW become statonary, as the null of statonarty could not be rejected. Ths s ntrgung and mples that OPW and CPW are I(2) varables f only based on Hadr. But, t s worth notng agan that Hadr (2000) assumes a common unt root process, whch as we have motoned earler s less relevant n ths study. Therefore, together wth other two testng procedures, we beleve PFAGDP, CPW and OPW are all non-statonary and I(1) varables. 5. Dynamc OLS estmaton 5.1 Econometrc specfcaton In ths secton, we seek to dentfy the relaton between penson assets and output n the context of our theoretcal model by usng the dynamc OLS (DOLS) contegratng panel estmator. In panel data, Kao (1999) fnds that the ordnary least squares (OLS) estmator s based, n that the t-statstcs dverge so the nference s not relable. The fully modfed OLS (FMOLS) estmator s argued to be able to correct such bas n certan cases. The FMOLS was frst proposed by Phlps and Hansen (1990), and extended to the context of heterogeneous panels by Pedron (1997), and then developed further n Phlps and Moon (1999). Based on the smulaton results from the Monte Carlo experments, Kao and Chang (2000), however, prove that under both contexts of homogeneous and heterogeneous panels, dynamc OLS (DOLS) s superor to fully modfed OLS (FMOLS) and other OLS estmators. The advantages of DOLS over FMOLS are no requrement for ntal estmaton and non-parametrc correcton 5. The DOLS model, used n our paper and followng Stock and Watson (1993) s as follows: t, t, t, t, j= n n Y = α + βx + γ X + ε (11) where and t are country and tme ndces as conventonal. Y t, s the dependent varable,.e. log output per worker (OPW). X t, s a vector of explanatory varables,.e. log penson fund assets/gdp, and log captal per worker (CPW). X t, s the frst dfference of X t,, thereby ntroducng dynamc structure nto the equaton. The coeffcents of X t, gve the accumulatve/total effects. In addton, the length of leads and lags for X t, has to be defned. The ncluson of these nusance parameters n Equaton 11 means we can obtan coeffcent estmates wth satsfactory lmtng dstrbuton propertes (Kao and Chang 2000; Kao et al 1999). As mentoned by Kao and Chang, however, t s dffcult to choose the optmal length of leads and lags, whch s a major drawback of the DOLS estmator. But, the practce s to use 1 and/or 2 leads and lags. 5 We also consder DOLS to be more approprate than system Generalsed Method of Moments (GMM) of Arellano and Bover (1995), snce GMM s most approprate when N s large and T s small (Bond 2002). But n our dataset, nether s the case; for example, we only have data coverng 38 countres, whle observatons range from 5 years to 35 years.

11 Emprcal results Results are gven n Tables 4a and 4b, where our man focus s on the sgn, sze and sgnfcance of the varable LPFAGDP, the log of the penson fund assets/gdp rato, whch ndcates the shft n the producton functon. As noted above, t s arbtrary to choose the length of leads and lags n the DOLS model, but the practce s to use 1 or 2 leads/lags (Mark and Sul 2002, and Kao et al 1999). In ths paper, n order to check the robustness of DOLS model as n Pelgrn et al (2002), we used both 1 lead/lag and 2 leads/lags. We splt our dataset accordng to two dmensons,.e. OECD/EMEs, and wth trend/no trend. Use of a trend s consstent wth McCoskey and Kao (1999) where they use a tme trend to dentfy the potental benefcal effect of technologcal advances on growth over tme, as well as structural reform not related to pensons. In addton, as we have noted earler, the varable captal per worker (CPW) s not statonary even after frst dfferencng based on Hadr test, whch mght be due to the presence of a determnstc trend. Therefore, the specfcaton wth a trend utlsed here mght be able to deal wth ths ssue. In order to allow for our data to have a determnstc trend as well as to allow for the potental effect of technologcal advances, we specfed a model wth a trend as well as wthout both n ths secton and for the Mean-Group and Johansen results reported below.. As regards the coeffcent of LPFAGDP, n Table 4a where we used 1 lead/lag of the dynamc terms, fve out of sx estmates are sgnfcant and postve as expected, coverng all three country groups. In Table 4b where we used 2 leads/lags, results are smlar. In each case, for the All-countres estmaton, the estmate wthout the trend s postve and statstcally sgnfcant, whle the estmate wth the trend s nsgnfcant, suggestng heterogenety, whch s manfest when the tme trend s ncluded. All the EME and OECD estmates are postve and sgnfcant. Meanwhle, the tme trend term tends to be postve and sgnfcant under all cases. It mples that technologcal advances and structural reforms over tme mprove the relaton of captal and labour to output. Its ncluson means the penson varable s not proxyng an omtted trend. The estmates for LCPW are very satsfactory, n that all are statstcally sgnfcant at 1 per cent, and postve at the range of Fnally, the adjusted R-square ratos are qute hgh n all cases. Note that dfferences n the sze of the coeffcents between the 1 and 2 lead/lag specfcaton may relate largely to the dfference n country composton, where the former uses data from 37 countres, the latter from 33. As regards the sze of the LPFAGDP coeffcents, they are n each case smaller when the tme trend s ncluded, mplyng that there are techncal and structural changes that the trend s capturng, whch s otherwse ncorporated n the penson assets varable. But as noted, for OECD and EME groups and for each lag specfcaton, the coeffcents are sgnfcant and postve wth the trend as well as wthout t. Ths parameter measures the total or cumulatve effect of penson assets on output. Therefore, t mples that a one percent ncrease n LPFAGDP rases LOPW by a mnmum per cent under the case of OECD-wth trend, and a maxmum per cent under the OECD-no trend as n Table 4b. Comparng the OECD and EME results, the OECD penson varable tends to be larger when the trend s omtted but smaller than n EMEs when the trend s ncluded, where the latter results are more plausble. One would expect larger coeffcents for EMEs, as s generally the case throughout our results, ncludng the Mean-Group and Johansen regressons reported below. Such a fndng s consstent wth economc convergence theory (Sala-I-Martn 1996),.e. poor countres are expected to grow faster than rch countres, as well as recent emprcal results by Beck and Levne (2004) and Beck et al (2000) mplyng fnancal development s more benefcal to economc growth n EMEs.

12 12 The basc results are estmated by unbalanced-panel GLS wth fxed effects and cross secton weghts. To check robustness, we sought to re-estmate wth the Seemngly-Unrelated Regresson (SUR) technque, whch allows for correlatons n the error terms. Ths was not feasble for the All or the EME group, because many of the observaton seres were too short. However, as shown n Tables 4a and 4b, t s apparent that for the OECD group, usng SUR does not change the parameter estmates for LPFAGDP markedly, mplyng that our result of a clear shft effect n the producton functon from penson fundng s a robust one. 6. Dynamc heterogeneous models In vew of the possblty that the mpact of penson funds on economc growth may vary across countres, and also consstent wth the suggeston of McCoskey and Kao (1999), we n ths secton seek to look further at the long run relatonshp by employng dynamc heterogeneous models. Pesaran and Smth (1995) present a number of dfferent estmaton procedures for estmatng a dynamc panel data model across heterogeneous countres, namely the mean group estmator, aggregate tme-seres estmator, pooled mean group estmator and cross-secton estmator. Due to other approaches lmtatons 6 as well as data avalablty, we use only the mean group estmator n ths secton, nvestgatng the average long run coeffcents. 6.1 Mean group estmator specfcaton The dynamc model we use n ths secton s specfed as follows: * * * LnQ, t α + γ t + ϕ1 LnQ, t 1 + λ1 LnPt + β1 LnK, t + ε, t = (12) Equaton 12 s the standard formulaton of a dynamc heterogeneous panel model, consstent wth Pesaran and Smth s (1995) specfcaton. However, wth the consderaton of savng degree of freedom, we nclude only one lag of the dependent varable on the rght hand sde of the functon rather than addng lag one of all ndependent varables lke the autoregressve dstrbuted lag (ARDL) estmaton used by Pesaran and Smth (1995). Pesaran (1997) and Pesaran and Smth (1999) argue that the use of the ARDL estmaton procedure has advantages over the fully-modfed (FM) OLS estmator desgned by Phlps and Hansen (PH) (1990) for tme seres co-ntegraton relatons, e.g. n that the tests based on PH method have a clear tendency to over-reject n small samples and also show larger bas. Based on the mean group estmaton procedure, we ran regressons for each ndvdual country, then averaged across countres usng two methods to obtan the average long run coeffcents. Accordng to the frst method, the long-run elastctes of LnQ* wth respect to LnP and LnK* can be calculated usng the formula, ϕ β η = λ 1 ϕ and ξ = β 1 ϕ respectvely. λ, and are the estmated values of the correspondng parameters n Equaton (12). Then the average long-run coeffcents n terms of LnP and LnK* can be computed as 6 For example, the pooled estmator assumes that the coeffcents are homogeneous across sectons, an assumpton whch we wsh to ease here.

13 N 1 1 η = N η and = N = 1 N = 1 13 ξ ξ respectvely. The second method, as presented by Pesaran and Smth (1995), mantans that the average long-run coeffcents can also be calculated usng the means of short-term coeffcents, namely η = λ 1 ϕ and ξ = β 1 ϕ where N 1 ϕ = N ϕ, = N = 1 N 1 λ λ and β = N = 1 N 1 β The sgnfcance levels or t-values of η and ξ were calculated by followng the formulas, η t value η = and se( η ) computed as the square root of the varance of (Smth and Fuertes 2004). 6.2 Emprcal result = 1 ξ t value ξ = respectvely, where the standard errors were se( ξ ) η and ξ dvded by the number of groups Results for ndvdual country coeffcents wth a tme trend are gven n Appendx 2, where we ran the regresson n Equaton 12 on 16 countres 7 ndvdually,.e. 11 advanced OECD countres and 5 EMEs. The coeffcents of LCPW and LPFAGDP measure the short-run effects on output, whle these coeffcents dvded by one mnus lag one of output LOPW(-1) measure the long run effects on output. Not surprsngly, results vary across countres. The general pattern, however, s clear. The mpact of the captal per worker rato s generally postve, n 15 out of 16 estmates, ndcatng the postve mpact of captal accumulaton on output, and s sgnfcant n 7 cases. Regardng the penson assets/gdp rato, 11 out of 16 estmates show a postve sgn, although some are nsgnfcant. Meanwhle, the long run effect of LCPW (the rato of the coeffcent on LCPW to one mnus the coeffcent on LOPW(-1)) s generally around 1, and the penson asset varable s usually around 0.1. The average short-run coeffcents for all explanatory varables are gven n the bottom-rght corner of Appendx 2. A one per cent ncrease n penson assets leads to an mmedate rse n output by per cent, whle captal s contrbuton s larger at per cent. The average lagged dependent varable s Further justfed n our approach by the dfferentals across countres as revealed n Appendx 2, we followed the approach noted above by Pesaran and Smth (1995) to assess the long run relaton between output, penson assets and captal. Results, accordng to the mean-group estmators usng Methods 1 and 2 are summarzed n Tables 5a, 5b and 5c. As n Secton 5, we ran three separate regressons by country groupngs,.e. all 16 countres, 11 OECD countres and 5 EMEs. Table 5a presents results for the ARDL wth tme trend, based on all 16 countres, whle Table 5b s based on 10 countres, excludng Canada, Japan, Malaysa, South Afrca, Sweden and Swtzerland. We dropped those countres snce most of coeffcent estmates (at least 3 out of 4 estmates) for those countres are not sgnfcant (See Appendx 2 for detals). Therefore, ther presence mght dstort our results from the mean-group estmators. One of the 7 22 other countres were excluded due to the small number of observatons.

14 14 reason penson assets ratos are nsgnfcant n those countres mght be the smple ARDL model we specfed. However, n order to keep the specfcaton consstent across countres, and to follow the methodology by Pesaran and Smth (1995), we retan t n ths secton. Fnally n Table 5c we show correspondng results for all 16 countres wthout the tme trend. Results n Table 5a are satsfactory and encouragng, as all estmates under the two methods and three groups are postve, ndcatng a postve average long run relatonshp between penson assets, captal stock and output. For example, for OECD countres, a one per cent ncrease n the captal stock rases output by per cent under method 1 and per cent under method 2. These two estmates are qute close to each other. In fact, t s ths estmaton robustness that leads us to use the smplfed model compared wth Pesaran and Smth (1995). Concernng the log of penson assets/gdp, we fnd that All countres and EMEs have hghly sgnfcant coeffcents, wth the long run effect beng around three tmes larger n EMEs than n the All country average. Note however, that ths s strongly affected by the result for Chle, wthout whch the EME result would be smlar to that from DOLS set out n Secton 5.2. Whereas the estmates for OECD countres under both methods n Table 5a are not sgnfcant, as noted above, some country by country results feature largely nsgnfcant coeffcents. In order to address ths problem, we excluded those countres, and the subsequent results are presented n Table 5b. We stll have the expected sgns and all the LPFAGDP varables are now sgnfcant and postve. The effect s, unsurprsngly, larger for EMEs than OECD countres as well as than All countres. The thrd set of results n Table 5c are for the equatons wthout the trend. Here we fnd that for all 16 countres, there s a sgnfcant and postve effect of LPFAGDP, thus supportng the result wth trend. The coeffcents are larger than wth the tme trend for OECD countres, but reflectng the result for Chle, they are smaller for All countres and EMEs. The EME coeffcents are agan consstently larger than for OECD countres. 7. Co ntegraton test As noted n Secton 4, penson fund assets, captal per worker and output per worker are all I(1) varables, then we may be nterested n whether they are co-ntegrated,.e. whether there exsts a long run relatonshp between them. We address ths ssue n ths secton on a country-by-country bass to allow for heterogenety, as well as calculatng panel estmates of the contegratng coeffcents. A co-ntegratng relatonshp captures the long run or equlbrum relatonshp between non-statonary,.e. I(1) varables. If varables are non-statonary, partcularly n the case of tme seres data, but the common resdual terms are statonary,.e. I(0), then we say these varables are co-ntegrated and economc theory as set out n Secton 2 suggests forces whch tend to keep such seres together, and do not let them drft too far apart (Banerjee et al 1993). In addton, f varables are co-ntegrated, our estmates are super-consstent. In other words, our estmates are not only consstent, but also converge to ther true values more quckly than normal (Davdson and MacKnnon 1993). 7.1 Specfcaton In ths paper we employ the VAR-based contegraton test (Vector Error Correcton Model) usng the methodology developed by Johansen (1991 and 1995). The specfcaton s as follows:

15 y t = A L) y t 1 t 15 ( + ε (13) where A ( L ) = A 1 + A A L k k 1 yt s a k-vector of I(1) varables,.e. OPW, CPW and PFAGDP n ths paper. L s the lag operator, and the lag order s selected based on a range of nformaton crtera,.e. AIC (Akake nformaton crteron) and SC (Schwarz nformaton crteron). Generally, the suggested lag order s 2 years, although n some cases t extended to 3 years. If Equaton (13) s wrtten as VAR format, then we have y t = Γ( L) y + Πy + ε (14) t 1 t k t where Γ = ( 1 A1... A ), = 1,... k 1 ' Π = 1 A... A ) or Π = α β ( 1 whereα s the speed of adjustment from short run devaton to long run equlbrum, and β ' s the contegratng vector, whch thus represents the long run coeffcents. Based on Granger s representaton theorem, the Johansen VAR-based contegraton test s to frst estmate the Π matrx from an unrestrcted VAR and then test whether the restrcton suggested by the reduced rank of Π - the number of contegratng relatons - s rejected. 7.2 Results for Contegraton test Ths secton presents the estmaton results for the Johansen contegraton test. Agan, we consder two slghtly dfferent specfcatons,.e. one wthout a trend and the other wth trend. We group our sample nto OECD countres and EMEs, whch n turn are estmated separately. Tables 6a and 6b gve results of our frst specfcaton,.e. wthout a trend. In most cases, the Trace and Maxmum-Egenvalue statstcs ndcate a co-ntegratng relatonshp between our varables, and the null hypothess of non-contegraton s rejected at ether the 5% or 10% level. Note that the sgns of coeffcents are opposte to those of the mpact of the varable on LOPW because the equatons are normalzed n the form 0 = LOPW - a 1 LPFAGDP - a 2 LCPW As shown n Table 6a, n only two of eleven OECD countres,.e. Canada and Swtzerland s the sgn of coeffcents on LPFAGDP postve, mplyng a negatve relatonshp between penson assets growth and economc output n the normalzed contegratng relaton. For all the other countres, however, the sgn s negatve, as expected. For almost all of these countres, penson fund growth has a statstcally sgnfcant and postve relatonshp wth output per worker, the extent of whch vares from 0.04 for Sweden to 0.27 for Germany. The small sze of the postve effect n Sweden could also be due to the restrcton of Swedsh s ATP scheme from equty nvestment and state management of the fund (Davs 2003). Regardng the other regressor,.e. LCPW (captal per worker), our estmates are satsfactory, as all coeffcents are negatve, mplyng a postve lnkage between economc output and the captal stock across OECD countres. In addton, the estmates of coeffcents of LCPW are qute close to each other; for seven out of eleven countres, t s between , mplyng a comparable producton functon relatonshp among developed OECD countres. All estmates except n Canada, Sweden and Swtzerland, are less than 1, consstent wth our model n

16 16 Secton 2, whch suggests that the β -elastcty of aggregate output wth respect to captal should not be greater than 1. Results for EMEs are gven n Table 6b. All coeffcent estmates for LPFAGDP except for Malaysa are negatve. Therefore, a benefcal effect of pensons on growth s also found across EMEs. For example, for Chle, one per cent ncrease n penson assets can contrbute to economc growth by 0.14 per cent; ths complements fndngs by Schmdt-Hebbel (1999), who shows that per cent of the 1.5 per cent ncrease n total factor productvty (TFP) n Chle n the 1980s and 1990s was attrbuted to penson reform. As for LCPW, one out of fve countres, South Afrca, shows an ncorrect postve sgn. For the other four countres, however, the sgn s negatve, consstent wth our fndngs earler. In other words, n these countres, growth n the captal/labour rato accompanes a rse n economy wde productvty. Tables 7a and 7b show the comparable results for the contegratng vector wth trend. Vrtually all of the Trace and Maxmum Egenvalue tests show contegraton. The results are broadly comparable; n Table 7a we have 8 out of 11 results showng a postve effect of LPFAGDP on output per capta, whle for LCPW t s 9 out of 11. In Table 7b we have 3 out of 5 wth a postve effect of penson fund assets on output per head, and n 4 out of 5 cases for LCPW. Note that as shown n Secton 7.3 below for the mpulse responses, even where the contegratng vector has a wrong sgn, the dynamcs may be such as to generate a long-term postve effect of penson assets on output. As regards the trend, among eleven OECD countres, sx show a negatve coeffcent, whch mples (gven normalzaton) that technologcal advances over tme enhance economc growth. The same fndng s obtaned by McCoskey and Kao (1999), where sx out of eght OECD countres are dentfed to have a postve and sgnfcant trend. Smlar results are found for EMEs (Table 7b) where three out of fve countres show sgnfcant trends enhancng economc growth. To complement our country-by-country analyss, we derved the panel co-ntegraton coeffcents n Table 8 by averagng the ndvdual coeffcents from the above ndvdual regressons. The formula for β s as follows: panel n = 1 β panel = n β (15) β panel s the panel coeffcent, β the coeffcent for ndvdual countres, and n the number of countres concerned. T-values for the panel co-ntegraton were calculated by followng the formula, t β, panel = n t β = 1 n (16) t β, panel s the panel t-values, and t β the t-value for ndvdual countres. Agan, our sample countres are grouped nto All, OECD countres and EMEs. When estmatng OECD and EMEs, we consder two scenaros,.e. Panel 1 and Panel 2. In Panel 1,