Partially funded social security and growth

Bethencourt, Carlos; Kunze, Lars; Perera‐Tallo, Fernando Article — Published Version Partially funded social security and growth Metroeconomica Provided in Cooperation with: John Wiley & Sons Suggested Citation: Bethencourt, Carlos; Kunze, Lars; Perera‐Tallo, Fernando (2024) : Partially funded social security and growth, Metroeconomica, ISSN 1467-999X, Wiley, Hoboken, NJ, Vol. 76, Iss. 2, pp. 297-310, https://doi.org/10.1111/meca.12484 This Version is available at: https://hdl.handle.net/10419/319317 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Received: 17 November 2023 - Revised: 15 August 2024 - Accepted: 16 August 2024 DOI: 10.1111/meca.12484 ORIGINAL ARTICLE Partially funded social security and growth Carlos Bethencourt 1 |Lars Kunze 2 |Fernando Perera‐Tallo 1 1 Departamento de Economía, Universidad de La Laguna, Tenerife, Spain 2 Department of Economics, TU Dortmund, Dortmund, Germany Correspondence Lars Kunze, Department of Economics, TU Dortmund, Dortmund 44221, Germany. Email: [email protected] Abstract This paper investigates the relationship between economic growth and the degree of fundedness of a social security system in an overlapping generations model with family altruism. It is shown that the relationship between the degree of fundedness and economic growth is inverted U‐shaped so that a gradual increase in funding may harm growth if bequests are not operative within the family. Our findings put some caution on the conventional view that a higher degree of funded social security is beneficial for growth. KEYWORDS family altruism, growth, social security JEL CLASSIFICATION D9, H3, I2, O4 1 | INTRODUCTION Pensions are financed by both the pay‐as‐you‐go and the funding principle in many countries. In recent years, however, due to rapid population aging and slow economic growth, a shift towards more funding could be observed with a corresponding increase in the share of private pensions in total pension spending (OECD, 2019). For example, the share of public old age spending in GDP among OECD countries increased from 4.9% in 1980 to 7.4% in 2019 whereas the corresponding share of mandatory and voluntary private spending almost tripled from 0.6% in 1980 to 1.7% in 2019. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2024 The Author(s). Metroeconomica published by John Wiley & Sons Ltd. Metroeconomica. 2025;76:297–310. wileyonlinelibrary.com/journal/meca - 297 The transition from an unfunded pension system towards a fully funded one has recently received much attention in the economic literature. However, most of the existing theoretical work is concerned about transitional issues between both pension schemes (e.g., Gyárfás & Marquardt, 2001) or focusses on the comparison of funded versus unfunded social security systems and their performance with growth and other outcomes (e.g., Docquier & Paddison, 2003; Kaganovic & Zilcha, 2012). With respect to economic growth, the general finding of these studies is that a fully funded social security system is superior to an unfunded scheme as it provides better incentives for human capital accumulation. Moreover, the growth effects from either an existing unfunded or an existing funded social security system are well documented, see, for example, Lambrecht et al. (2005) and Maebayashi (2020) for the case of an unfunded system and Zhang (1995) and Kunze (2012) for the case of a fully funded system. 1 However, none of these studies analyze how changes in the degree of fundedness affect economic long‐ run growth in a model with both a funded and an unfunded component. To close this gap is the aim of the current paper. The scarce empirical evidence on the relationship between pension reform towards more funding and economic growth, however, turns out to be mixed. Davis and Hu (2008) find a positive effect of pension savings on output for both OECD countries and Emerging Market Economies whereas Zandberg and Spierdijk (2013) and Altiparmakov and Nedelkovic (2018) find no significant effects on economic growth for OECD and non‐OECD countries or countries in Latin America and Eastern Europe, respectively. Papers focussing on the effects of pension reforms on aggregate savings find that countries with pay‐as‐you‐go pensions tend to have lower aggregate saving rates than countries with funded pensions, see, for example, Samwick (2000) and Bailliu and Reisen (1998). Finally, Bijlsma et al. (2018) find a significant impact of pension assets on growth for sectors that are more dependent on external financing. These generally mixed findings are somewhat confirmed by some casual inspection of Figure 1which uses data from the OECD Social Expenditure Database (SOCX) 2 and shows the degree of fundedness, calculated as the share of mandatory and voluntary private old age spending in total old age spending, and annual GDP growth rates for OECD countries from 1980 to 2020. If at all, these data point to a weak non‐linear relationship between the degree of funding and economic growth. To interpret these findings, this paper addresses the question how an increase in the degree of fundedness of an existing pension scheme with both a funded and an unfunded component impacts on economic growth depending on preferences with regard to altruism and technology. Using an overlapping generations model with family altruism and homogenous households, as has been formalized by Lambrecht et al. (2006), where private investment in human capital of children is the engine of growth, we consider a unified social security system in which different social security plans are represented via certain degrees of fundedness and which comprises the cases of an unfunded and a fully funded pension scheme as special cases (as in Park (2018)). In contrast to the conventional view that a fully funded system is superior to an unfunded one with respect to economic growth, the current paper demonstrates that the relationship 1 Note that the focus of this paper is on the impact of a higher degree of fundedness on privately‐financed human capital formation. Therefore, we do not deal with the issue of public versus private education funding. Kaganovich and Zilcha (1999), for example, analyze the relationship between a pay‐as‐you‐go pension programme and growth when both private and public spending finances education. 2 See https://www.oecd.org/social/expenditure.htm. 298 - BETHENCOURT ET AL. between the degree of fundedness and economic growth may be inverted U‐shaped if bequests are not operative within the family. In response to a gradual increase in funding individuals substitute private savings for educational spending as a result of a lower pension benefit from the unfunded part of the social security system. If this direct effect through lower educational spending dominates the positive general equilibrium effect resulting from higher capital accumulation and therefore a higher return to education, a gradual increase in the degree of fundedness reduces growth. When bequests are operative, however, our results are consistent with previous results in the literature as a higher degree of fundedness is beneficial to growth. In this case individuals substitute voluntary savings for consumption spending to provide a larger amount of bequest to their offspring which in turn increases aggregate savings and capital accumulation. Our results add to the ongoing debate regarding the desirability of a transition from a pay‐as‐you‐go social security regime to a fully funded one by providing an additional argument against a higher degree of funded social security, based on a possible negative effect on economic growth, thereby corroborating the conclusions of the most recent literature on this topic. Westerhout et al. (2022), for example, study the optimal balance between pay‐as‐ you‐go and funding in view of recent trends, as for example, low economic growth and increased capital market volatility, and conclude that it may be wise to halt the shift towards more funding. Similarly, Lin et al. (2021) show that reforms of unfunded systems outperform the transition to a funded system in many aspects, for example, a higher GDP in the long run, which in turn provides an explanation of why a shift to a funded system is rarely observed. The remainder is organized as follows. The next section introduces the model and derives the growth effects of a higher degree of fundedness when bequests are either operative or not. FIGURE 1 Share of mandatory private and voluntary private old age spending in total old age spending and annual GDP growth rates for OECD countries from 1980 to 2020. Source: Own calculations, OECD Social Expenditure Database (SOCX). [Colour figure can be viewed at wileyonlinelibrary.com] BETHENCOURT ET AL. - 299 2 | THE MODEL We consider an overlapping‐generations model in which parents have an altruistic concern and care about the disposable income of their children. 3 Population size Ntis assumed to grow at a constant rate n, so that a new cohort of identical individuals is born in each period, that is, Nt¼ ð1þnÞNt−1. 4 Each individual lives for three periods: During childhood individuals are educated by their parents and do not make any economic decision. In the second period of life, each individual gives birth to 1 þnchildren and inelastically supplies htefficiency units of labor, her endowment of human capital depending on her parents' spending on education. She receives the market wage wtand a non‐negative bequest btfrom her parents. Income is spend on consumption ct, private education ð1þnÞetand savings st: It≡ð1−τÞwthtþbt¼ctþ ð1þnÞetþstð1Þ where τis the contribution rate to the pension scheme. During old‐age, each individual allocates the return to her voluntary savings Rtþ1stplus the benefit from the pension scheme θtþ1, to second period consumption dtþ1and to give a non‐negative bequest btþ1to her ð1þnÞ offsprings: dtþ1¼Rtþ1stþθtþ1−ð1þnÞbtþ1ð2Þ where Rtþ1is the interest factor at tþ1. The government runs a unified social security system which is parametized by the intensity ϕ∈½0;1�of fundedness. Hence, the portion ϕτ of individual contributions is invested as mandatory savings whereas the remaining share ð1þnÞð1−ϕÞτis used to pay retirement benefits to the currently old individuals. Consequently, the case ϕ¼0 corresponds to an unfunded social security system while ϕ¼1 implies a fully funded one. The main focus of this paper is to study how a shift in the degree of fundedness towards a more funded pension scheme (a higher ϕ) affects long run growth depending on assumptions with regard to preferences and technology. 5 3 The model is a generalization of Lambrecht et al. (2005) and Kunze (2012), who study the growth effects of a pay‐as‐ you‐go and a fully funded pension scheme, respectively. The main idea of the family altruism model is that parents care about the economic success of their children, which is measured by the children's lifetime income. See the aforementioned papers and references therein for further details and empirical evidence. 4 Note that we follow the most closely related literature (see Kunze, 2012; Lambrecht et al., 2005; Park, 2014) and assume that fertility choice is exogenous. An analysis of the case with endogenous fertility is left for future research. In this case, however, the model would no longer be analytically tractable. 5 Such a unified framework has been considered by Park (2014,2018) in the context of a neoclassical growth model. Moreover, the case ϕ¼0 corresponds to the model in Lambrecht et al. (2005) whereas the resulting model with ϕ¼1 has been analyzed by Kunze (2012). These two papers focus on the growth effects resulting from changes in the contribution rate τ. With operative bequests, Lambrecht et al. (2005) find that a higher contribution rate reduces long run growth whereas there is a growth maximizing size of τin Kunze (2012). By contrast, with inoperative bequests an increase in τis neutral to growth in Kunze (2012) while there is a growth maximizing size of τin Lambrecht et al. (2005). Consequently, for a given degree of fundedness, that is, ϕ∈ð0;1Þ, there should be a growth maximizing size of τwhen bequests are inoperative (where the positive growth effect becomes less likely the higher ϕ), whereas there will either be a negative growth effect or a growth maximizing size of τwhen bequests are operative (the magnitude of these effects again depending on the level of ϕ). 300 - BETHENCOURT ET AL. A balanced social security budget thus requires θtþ1¼ ð1−ϕÞð1þnÞτwtþ1htþ1þϕRtþ1τwtht:ð3Þ The human capital of an individual in period tþ1 is a function of the private investment in education, et, and the parent's human capital, ht: htþ1¼Deδ th1−δ t¼Deδ thtð4Þ where Dis a scale parameter, 0 <δ<1 is the elasticity of the education technology with respect to private educational spending and et≡et=htprivate educational spending per unit of human capital. Individual preferences are assumed to be logarithmic and depend on first and second period consumption and on the disposable income of the adult children: Ut¼ ð1−βÞln ctþβln dtþ1þγln Itþ1ð5Þ where 0 <β<1, γdenotes the degree of altruism towards own children and Itþ1¼ ð1−τÞwtþ1htþ1þbtþ1:ð6Þ Each individual maximizes utility (5) subject to the constraints (1), (2), (6) and the non‐ negativity of bequests btþ1≥0 by choosing ct,et,st,dtþ1and btþ1. The first order conditions determining optimal savings, private educational spending and bequest are 6 : ∂Ut ∂st ¼−1−β ct þβRtþ1 dtþ1 ¼0ð7Þ ∂Ut ∂et ¼−ð1þnÞð1−βÞ ct þγð1−τÞwtþ1Dδeδ−1 th1−δ t Itþ1 ¼0ð8Þ ∂Ut ∂btþ1 ¼−ð1þnÞβ dtþ1 þγ Itþ1 ≤0ð ¼ 0 if btþ1>0Þ ð9Þ Inserting Equations (7) and (8) into (9) gives ð1−τÞwtþ1Dδeδ−1 th1−δ t≥Rtþ1ð10Þ When bequests are operative, Equation (10) holds with equality and the rate of return to private education equals the interest rate. With inoperative bequests, however, the rate of return to private education exceeds the interest rate. 6 Note that the focus of this paper is on the case in which the funded share of public pensions does not fully crowd out private savings. An analysis of the case in which voluntary savings are zero is left for future research. BETHENCOURT ET AL. - 301 In every period t, firms produce a single output good according to a Cobb–Douglas production function combining physical capital Ktand human capital Ht: Yt¼AKα tH1−α tð11Þ where 0 <α<1 denotes the capital share. Profit maximization gives the usual marginal productivity conditions: wt¼ ð1−αÞAKα tH−α t¼ ð1−αÞAkα t;Rt¼αAKα−1 tH1−α t¼αAkα−1 tð12Þ where kt¼Kt=Htis the physical to human capital ratio. In equilibrium, the market clearing conditions for the capital, the labor and the good market are: Kt¼Nt−2st−1þϕτwt−1ht−1Nt−2ð13Þ Ht¼Nt−1htð14Þ Yt¼Nt−1ðctþstþ ð1þnÞetþϕτwthtÞ þ dtNt−2ð15Þ Inserting the old's budget constraint (2) into the good market equilibrium condition, Equation (15) becomes dtþ ð1þnÞIt¼ ð1þnÞð1−ϕτð1−αÞÞAkα thtð16Þ 2.1 | Inoperative bequests In a first step, we study the growth effects of an increase in the degree of fundedness (an increase in ϕ) when bequests are inoperative in period tþ1. Then, Equations (9) and (16) give Itþ1¼ ð1−τÞwtþ1htþ1¼ ð1−τÞð1−αÞAkα tþ1htþ1ð17Þ dtþ1¼ ð1þnÞðαþ ð1−ϕÞτð1−αÞÞAkα tþ1htþ1ð18Þ Combining Equations (7), (8) and (12) we obtain e1−δ t¼γδD βα ðαþ ð1−ϕÞτð1−αÞÞktþ1ð19Þ For a given stock of capital ktþ1, a higher degree of fundedness reduces educational spending. At the same time a lower effective contribution rate from the unfunded social security system, that is, ð1−ϕÞτ, may have a positive impact on ktþ1through voluntary savings. This raises the question whether a higher degree of fundedness is beneficial to or harms growth when bequests are inoperative. 302 - BETHENCOURT ET AL. From the non‐negative bequest condition (10) and (19) we can derive an upper bound on the social security contribution rate so that bequests are inoperative if the following inequality holds τ≤β−αðβþγÞ ð1−αÞðβþγð1−ϕÞÞ ≡χð20Þ Consequently, the case with inoperative bequests occurs if the contribution rate is not too large, that is, 0 <τ≤χ, which further implies that, by assumption, individuals are not too altruistic as χ>0⇔γ<ð1−αÞβ=α. Using Equations (4) and (19) gives ktþ1htþ1¼αβ δγ 1 αþ ð1−ϕÞτð1−αÞethtð21Þ which in turn allows us to determine individual savings stand consumption ct(from Equations (13), (7) and (18), (21)): st¼αβ δγ ð1þnÞ αþ ð1−ϕÞτð1−αÞetht−ϕτð1−αÞAkα thtð22Þ ct¼ð1þnÞð1−βÞ β αþ ð1−ϕÞτð1−αÞ αktþ1htþ1¼ð1þnÞð1−βÞ δγ ethtð23Þ Plugging Equations (22) and (23) into (1) and solving for etgives et¼ð1−ð1−ϕÞτÞð1−αÞ Bðτ;ϕÞAkα tð24Þ where Bðτ;ϕÞ ¼ ð1þnÞ�1þ1−β γδ þαβ γδ 1 αþ ð1−ϕÞτð1−αÞ�:ð25Þ The dynamics of the physical to human capital ratio ktwith inoperative bequests result from combining Equations (19) and (24) �δγD αβ ðαþ ð1−ϕÞτð1−αÞÞktþ1�1 1−δ ¼et¼ð1−ð1−ϕÞτÞð1−αÞ Bðτ;ϕÞAkα tð26Þ which converge monotonically towards a steady state �k;e�. 7 To assess the growth effect of increasing the degree of fundedness of the social security system when bequests are inoperative, we first derive the long‐run physical to human capital ratio k. It is obtained by rearranging Equation (26) in steady state: 7 Note that Equation (26) can be rearranged so that ktþ1¼Ckαð1−δÞ twith αð1−δÞ<1, which in turn ensures convergence towards a unique steady state. BETHENCOURT ET AL. - 303 k¼ αβ γδDðαþ ð1−ϕÞτð1−αÞÞ �ð1−ð1−ϕÞτÞð1−αÞA Bðτ;ϕÞ�1−δ!1 1−αð1−δÞ ð27Þ Using Equations (24) and (27), the growth factor of the economy, which equals g¼htþ1=ht¼Deδ, can then be derived as g¼D�ð1−ð1−ϕÞτÞð1−αÞA Bðτ;ϕÞ�αβ γδDðαþ ð1−ϕÞτð1−αÞÞ�α�δ 1−αð1−δÞ ð28Þ Further inspection of Equations (20) and (28) reveals: Proposition 1. If parents are not sufficiently altruistic towards their child, that is, γ <ð1−αÞβ=α, then bequests are inoperative and a higher degree of funded social security is beneficial for growth if β< ~ β≡ð1þγδÞαð2−αÞ ð1−αÞð29Þ If β > ~ β, however, there exists a growth maximizing degree of funded social security b ϕ so that a higher degree of fundedness lowers growth if the initial degree is already sufficiently large �ϕ>b ϕ�. Furthermore, if β>β≡ð1þγδÞðτþ ð1−τÞαÞðτþ ð1−τÞð2α−α2ÞÞ ð1−αÞðτ2ð1−αð1−αÞÞ þ αð1−ατÞ þ ατð1−τÞÞ > ~ βð30Þ then b ϕ is at a corner and increasing the degree of funded social security always reduces growth. Proof. The logarithmic derivative of ∂e1−αð1−δÞ=∂ϕhas the same sign as the function ΨðκÞ ¼ xð1−αÞ3κ3þακð1−αÞð3−2αÞ þ α2ð2−αÞ� −βð1−αÞð1−αÞ2κ2þακð1−αÞ þ α� with x¼1þγδ and κ¼ ð1−ϕÞτ. This function increases from Ψð0Þ ¼ −αðαxðα−2Þ þ βð1−αÞÞ to ΨðτÞ ¼ xðτþ ð1−τÞαÞτþ ð1−τÞ2α−α2ÞÞ −βð1−αÞτ2ð1−αð1−αÞÞ þ αð1−ατÞ þ ατð1−τÞ� 304 - BETHENCOURT ET AL.