Do pensions foster education? An empirical perspective

ABSTRACT The paper examines the effect of population ageing on public education spending. On the one hand, ageing is expected to have a negative effect on education, as an increasing number of retirees results in ‘intergenerational conflict’ and, hence, the condemnation of education expenditure. On the other hand, ageing, in combination with pay-as-you-go pension systems, offers incentives for the working-age generation to invest in the public education of the young in order to ‘reap’ the benefits (that is, higher income tax/contributions) of their greater future productivity. Empirical evidence derived from the application of a fixed effects approach to panel data for OECD countries shows that the increasing share of elderly people has a non-linear effect on education spending. This indicates a certain degree of intergenerational conflict. Nevertheless, we find that future population ageing, which reinforces the mechanism linking public education and pensions, reflects positively on education expenditure. Furthermore, by disaggregating total education expenditure by educational levels, we observe that this effect is led by levels of non-compulsory education, probably as a reflection of the direct connection to labor productivity.


Introduction
The welfare state has been extending its action from mere monetary transfers for poverty reduction to wider programmes, such as providing basic social goods (education and health) and income substitution programmes, such as pensions, with a high insurance component. Interestingly, in a way this process leads to the gradual substitution of private intergenerational transfers from the public sphere. Government intervention in this case goes beyond intra-generational redistribution, introducing intergenerational redistribution. Indeed, two of the most important policies are public education and pensions, which focus directly on both sides of dependency (children and the elderly).
In particular, the size of public pensions in OECD countries in 2012 was on average 7.6% of GDP and expenditure on public education was on average 5.5% of GDP. 1 Parallel to this, population ageing is becoming an issue of increasing concern, especially as the generations of "baby boomers" reach retirement age, putting considerable pressure on current payas-you-go (PAYG) pension systems. More specifically, in 2012 the old age dependency ratio for the average of OECD countries was 22.4% and it is expected to be 43.4% by 2040. The driving forces behind population ageing are the decreased fertility rate -preceded by the post-war "baby boom" -and increased life expectancy. Among other things, the latter is a result of better-quality services due to technological progress in the healthcare system. The former can be seen as a result of the increasing opportunity cost for women to have children in developed economies. 2 Both processes -demographic change and the extension of the welfare state -seem to be related, as shown by the convergence of both literature strands. The relation between economic and demographic variables is mediated either by a household's reactions to exogenous changes and/or changes in preferences and social norms. 3 Hence, the investigation of intergenerational transfers implies considering, more or less explicitly, hypotheses about the motives for private transfers and government intervention, which go from forward and backward altruism to strategic behaviour or, following the recent investigations on endogenous preferences, they can be due to reciprocity. 4 The political economy literature also meets the literature on intergenerational transfers and population change by investigating the link between forward and backward intergenerational transfers in the absence of altruism. This link is quite intuitively present in the family but to a lesser extent in government action.
Back in the late seventies, scholars had already discussed the existence of the link between forward and backward public intergenerational transfers by answering the question why selfish generations choose to transfer resources to future generations. Pogue and Sgontz (1977) argue that the design of the PAYG pension system creates the appropriate incentives to invest in public education because it enhances the income of the future working generation. Following the same argument, Konrad (1995) explains that, even in the absence of altruism, the working-class cohorts are willing to pay for public education only if they can "reap" gains by taxing the results of higher productivity in the future.
A few years later, in a game theoretical framework Rangel (2003) investigates the possibility of sustaining a system of public forward and backward intergenerational transfers. He uses the concept of a sub-game perfect equilibrium in order to investigate, in the context of selfish generations, the ability of non-market intergenerational arrangements to invest optimally in forward and backward 1 For the data sources, see Table 9, Appendix B 2 In Galor and Weil (1996), this is forced by a higher increase in female wages with respect to household income.
Other potential channels are the increase in human capital investment per child and the quantity-quality trade-offà la Becker [Becker et al. (1990); Galor and Weil (2000)] 3 Doepke and Tertilt (2016) point out the need to incorporate changes in family structure in dynamic macroeconomic models. 4 Michel et al. (2006) for a survey on forward and backward altruism in the context of neoclassical growth models; Laferrere and Wolff (2006) for a survey on the motives for private transfers; and Fehr and Schmidt (2006) for a detailed survey on altruism and endogenous preferences (others regarding preferences).
transfers. With the help of simple trigger strategies (STS) in a repeated voting setting, he concludes that the provision of education for the younger cohort is optimal and sustained only when it is linked to sufficiently large transfers to the older cohort. 5 Furthermore, Kemnitz (2000), using an overlapping generations (OLG) model -where the determination of intergenerational transfers is decided in a context of representative democracy -, shows that the demographic transition achieves a better backward (pensions) and forward (education) redistribution of public funds. 6 This study points out the impact of the political influence of the working population over the political power of retirees. According to Kemnitz, population ageing, accompanied by the specific structure of the PAYG pension system, stimulates the working generation to invest in education in order to provide future pension benefits for themselves. Gradstein and Kaganovich (2004) reach similar conclusions, having a slightly different intuition. According to their OLG model, as the old population grows there should be two antithetical effects on public education expenditure. On the one hand, there is a growing number of retirees who want to minimize the amount spent on education. On the other hand, there are working-age agents who foresee that they are going to live longer because of the increase in longevity. In addition, they realize that the increased number of retirees makes the pay-as-you-go system less generous in terms of spending per retiree. Having anticipated these facts, they will react by investing more in education in the current period in order to take advantage of the future higher productivity of currently young people. In this way, they pursue an increase in future tax revenues and endeavour to ensure a higher return on their savings in order to deal with the increased fiscal needs of a prolonged retirement period.
The authors find that, even in the absence of altruistic linkages, the second effect is stronger and therefore the ageing process has a positive impact on the amount spent on education.
The main purpose of the present paper is to conduct an empirical investigation of the effect of a changing demographic environment on public education spending. To our knowledge no empirical work exists that tries to test for the theoretical predictions arising from the aforementioned studies [Kemnitz (2000), Gradstein and Kaganovich (2004)]. This is what we attempt here, and what could be considered as the value added to the existing literature. Using panel data from OECD countries we suggest that, considering the projected worsening of population ageing in the future, the structure of the PAYG pension system provides incentives to the working-age generation to support educational transfers towards the young generation even in the absence of altruism. Decomposing total education spending by level of education, we notice that only the non-mandatory educational levels benefit from future population ageing. This is mainly due to the fact that there is space for political intervention in favour of enhancing future labour productivity.
Concerning the impact of current population ageing on public education spending, most studies focus on testing the so-called "generational conflict" hypothesis. According to this hypothesis, the increasing political power of the elderly changes the allocation of public resources, shifting more resources towards the older cohort and fewer to the younger one. In his studies, Poterba (1997Poterba ( , 1998 argues that, in the case of the US, the effect of gerontocracy on education outlays per 5 As Boldrin and Montes (2005) stress, financing only public education is not sufficient to restore economic efficiency because in order to do so an additional intergenerational trade arrangement is needed. 6 As shown in Appendix B Figure 2, parallel to population ageing there is an increasing trend for education and pension spending per student and retiree, respectively. child is negative. Nonetheless, Ladd and Murray (2001) contest the approach of Poterba (1997) by suggesting that the use of local government instead of state-level data weakens the negative effect of the share of the elderly on per-student education or even makes it insignificant. Harris et al. (2001) try to reconcile these two studies using a panel data set at the school district level. While they find a negative effect of a growing elderly population, the magnitude of the impact is far more moderate compared to the state-level model of Poterba (1997). Later on, Grob and Wolter (2007) and Borge and Rattso (2008) use state-level data for the Swiss Cantons and local governments in Denmark, respectively. Both studies find evidence in favour of the "generational conflict" hypothesis.
However, as shown in Krieger and Ruhose (2013), there is only partial evidence when the hypothesis is examined on the panel data of OECD countries. 7 Following a similar analysis, we extend the generational conflict hypothesis in order to account for potential non-linear effects. The results show that current population ageing appears to be negatively related to education expenditure, although it seems to be dependent on the level of total pension spending.
The remainder of this paper proceeds as follows. Section 2 presents data and methodology. In the section 3 and 4 we investigate the generational conflict hypothesis. Section 5 and 6 analyze the impact of the projected population ageing on education expenditure in total and per level of education, respectively. In the last section we provide our conclusions and suggest some topics for future research.
2 Data and Methodology

Data
We use panel data for 31 OECD countries and yearly observations over the period 1996-2012. 8 The choice of the annual base analysis is partially justified by the empirical evidence provided in Appendix B Figure 3. This figure shows that education spending fluctuates on a yearly basis in contrast with pensions that vary over a longer period, which is necessary for pension reform.
In Table 1, we summarize the main descriptive statistics of the variables that we use in our model. 9 The first two variables according to Table 1 are used as dependent variables and represent the total education spending as a percentage of GDP (TES) and per-student spending (ESPS), respectively. 10 A closer look at Table 1 and Table 8  Definitions and sources of the variables can be found in Table 9 in the Appendix B. 10 Total general (local, regional and central) government expenditure on education (current, capital, and transfers), expressed as a percentage of GDP. It includes expenditure funded by transfers from international sources to government. student spending, the differences between countries are bigger than the differences within countries (over years). The next two variables are the total (TPS) and per-retiree pension spending (PSPR).
We incorporate the pension outlays in order to check the potential link with education expenditure.
The demographic variables (PRODR, ODR, PopEduc, Fertility) describe the projected old dependency ratio 17 years in the future (2013-2029), the current old dependency ratio, the population of official age for education and the fertility rate, respectively. First, the projected old dependency ratio is employed to examine the effect that future ageing has on current education expenditure. The underlying hypothesis here is that the working-age cohort, realizing the forthcoming demographic crisis, chooses to invest in education in order to preserve its pension benefits in the future. Therefore, it is expected that the effect of the projected old dependency ratio will have a positive effect on education spending. Second, the current old dependency ratio is used to test the hypothesis that there is a conflict over public resources between generations because of the increasing political power of the elderly. Third, the young population of official age for education is used to control for the size effect, namely that a larger proportion of pupils/students could mean a higher budget allocated to education. Finally, we have the fertility rate that is used as a proxy for the proportion of parents in the voting population. Parents are expected to push for more spending on public education as their children benefit directly from a higher quality of education services. 11 The macroeconomic variables GDP per capita (GDPpc) and real GDP growth (RGDPgr) are used as control variables. The former variable is an indicator of the level of economic development in a country and the latter is used as a control for the business cycle. In addition, we include two fiscal variables, tax revenues (TaxRev), total social expenditure (TotSocExp) and social expenditure not including retirement spending (SocExp), in order to control for the size of the government and the generosity of the welfare state. Tax receipts include taxes on income, profits and capital gains and social security contributions. Respectively, social expenditure includes survivors and incapacityrelated benefits, health, family, active labour market programmes, unemployment, housing and other social policy areas.
The variable MYS (Mean Years of Schooling) illustrates the average number of years of education received by people aged 25 and older. This variable tries to capture the quality of the educational system as referred in Molina-Morales et al. (2013). It is assumed that the more you study the better your educational level. In addition, we use three institutional variables, globalization index (GI), index of voice and accountability (VAI) and index of economic freedom (EFI). 12 The first one shows how globalised a country is at the political, economic, cultural and social level. The underlying hypothesis is that the more open the economy is, the more countries are engaged in the "race to the bottom", reducing their spending and taxes in order to be more competitive vis a vis the rest of the world. The second index captures perceptions of the extent to which a country's citizens are able to participate in selecting their government, as well as freedom of expression, freedom of association, and a free media; in general, the variable captures the level of democracy in a country. It is expected that a higher level of democracy will lead to higher education spending. Finally, the last index includes assessments on commercial policy, government tax load, government intervention in the economy, monetary policy, foreign investment and capital flow, foreign activity, financial activity, 11 The fertility rate variable appears only in the per-student model specifications.  salary and price control, property rights, and black market regulation and activity. Here too, it is expected that a higher degree of economic freedom leads to a larger amount spent on education policy.
Furthermore, we include in our model a dummy variable (Left) that accounts for the political ideology of the governing party. The dummy variable takes 1 when the government is either left-wing or social-democratic and 0 otherwise. It is predicted that left-wing governments are more fervent toward redistribution through social policies and education in order to favour their electoral base that lies among poorer social layers [Castles (1989); Busemeyer (2007)]. In addition, as it is shown empirically, left-wing governments favour more generous spending packages on social policies and therefore on education [Roubini and Sachs (1989); Kontopoulos and Perotti (1997)].
Finally, we show in Table 1 the descriptive statistics of pre-primary (PPES), primary (PES), secondary (SES) and tertiary (TERES) education spending and the population of the official age (ppoap, poap, soap, toap) for these levels of education, respectively. These variables are used in order to investigate the effect of projected ageing per level of education (see Table 5).

Methodology
Our empirical approach complements the existing evidence on the determinants of public education spending at a cross-national level [Castles (1989); Busemeyer (2007) Krieger and Ruhose (2013)]. These studies identify a set of variables that explains most of the variation in public education expenditure. Nevertheless, we extend the literature by focusing on the demographic transition and adding into the model variables that capture the current and future demographic features, such as current, projected old dependency ratio and fertility rate.
In order to choose our estimation strategy we conduct some diagnostic tests. Primarily, we have to decide between pooled OLS -which takes into account both between and within variation -and Random Effects (RE) which consider that the differences across countries have a significant influence on the dependent variable. In order to decide, we use the adjusted instead of the simple Breusch and Pagan (1980) Lagrange multiplier (LM) test. It might be the case that, in the presence of first-order serial correlation, the simple LM test by Breusch-Pagan 1980 too often rejects the correct null hypothesis of no random effects. Therefore, we have to conduct some complementary tests: the Baltagi and Li (1995) test for first-order serial correlation and the Baltagi and Li (1991) joint test for serial correlation and random effects. 13 According to the outcome of these tests, the Ho hypothesis that the variance of the random effect is zero or that there are no individual effects in the model is rejected. Therefore, in the presence of country-specific characteristics (individual) heterogeneity, we have to decide between using random or fixed effects. Thus, we apply the test introduced by Hausman (1978), which leads us to a strong rejection of the null hypothesis that random effects provide consistent estimates or that there is no correlation between the error term and the independent variables. Therefore, the test indicates use of the fixed effects method that produces a consistent estimator. This method takes into account the within variation (over time) 14 and controls for the unobserved characteristics that remain constant over the years and that might 13 These tests show that both serial correlation and random effects are present. 14 The test for time fixed effects reveals that no time fixed effects are needed in our specification of the model. affect public expenditure on education, like culture heritage or religion, etc. 15 Additionally, we conduct a series of other diagnostic tests: the modified Wald test for heteroscedasticity by Baum (2001); Frees (1995) and Pesaran (2004); cross-sectional dependence tests; and serial correlation test or the test for autocorrelation by Wooldridge (2002). 16 These tests first show that the idiosyncratic errors are heteroscedastic, meaning that the variation of the errors across countries is not constant. Second, there is contemporaneous correlation, namely the errors between countries are correlated, and third there is a first-order autocorrelation in errors within countries.
As mentioned in Cameron and Trivedi (2010), ignoring cross-sectional dependence and correlation of errors over time can lead to systematic bias and thus to erroneous results.
Therefore, we have to use estimation methods that allow us to conduct consistent estimations in the presence of AR(1) autocorrelation within panels and cross-sectional correlation and heteroscedasticity across panels. For that purpose, we use an estimator (SCC) introduced by Hoechle (2007), that produces Driscoll and Kraay (1998) standard errors for the estimated coefficients using fixed effects. In our specification of this estimator, the error structure is assumed to be heteroscedastic, autocorrelated up to one lag and correlated between the countries. As mentioned in Hoechle (2007), Driscoll-Kraay standard errors are robust to very general forms of cross-sectional and temporal dependence when the time dimension is large enough. Additionally, their particular technique to estimate standard errors does not impose any restrictions on the number of countries, which can be even bigger than the number of periods. Finally, the implementation of Driscoll and Kraay's covariance estimator works for both balanced and unbalanced panels (Cameron and Trivedi, 2010).
All the above properties make this estimator suitable for our panel data. At this point we should emphasize that, by using this kind of aggregate data model, we might be facing the usual problems of endogeneity. One potential problem might be the reverse causality between education spending and the old dependency ratio. In this case, higher education spending 15 As referred in Castles (1994), cultural heritage and the tradition of Catholicism can play an important role in public expenditure on education. The countries that have Catholicism as their predominant religion might have to spend less on education of children as the Catholic Church undertakes a large part of the children's education. 16 The latter is in addition to the previous Baltagi-Li test, as we saw above. 17 Later, in the regressions, we "break" the total social expenditure into two variables, total retirement spending (TPS) and the rest of social expenditure (SocExp).
could negatively influence the fertility rate and in the long run may essentially lead to a higher old dependency ratio. Nevertheless, we can argue that the impact of education on the fertility rate is not straightforward. On the one hand, more educated women tend to have fewer children [Becker et al. (1990); Galor and Weil (1996)]. On the other hand, as discussed in Esping-Andersen and Billari (2015), recent studies on some OECD countries point to a reversal of the negative relationship between education and fertility. In addition, one can argue that more educated people tend to live longer, increasing the old dependency ratio. However, it is plausible to assume that both of these effects (decreased fertility and prolonged life expectancy) take place in the long run -after one generation -rather than in the short period examined in this study. Regarding the control variables, similarly there could be other reverse causality problems. For example, education spending might have a positive effect on tax revenue. The same counterargument as before regarding the time frame can be used here. In addition, the main effect of education would be on personal income tax revenues rather than on general tax revenues. Hence, the potential endogeneity problems of our analysis seem to be limited.
The general answer to the potential endogeneity problems is to reduce the causality claims that we can make, due to the nature of the data and the difficulty to use the instrumental variables technique to tackle the endogeneity problems properly. In the end, the main goal of the empirical analysis of aggregate data models is to point out interesting connections and test theoretical predictions and hypotheses.

3
Generational conflict: The effect of current population ageing on education spending We begin our analysis with the impact of the current population ageing on public education expenditure. As discussed above, the increasing percentage of old people in the population has a negative effect on educational spending, the generational conflict hypothesis. In order to test whether there is conflict in relation to fiscal resources between the generation of people over 65 years old and the generation of young people, we employ the old dependency ratio (ODR). In general, an increase in the old dependency ratio has two opposite effects on education spending. On the one hand, there is a negative effect on education spending due to the increased number of old people that put greater pressure on fiscal resources (generational conflict). On the other hand, there is a positive effect derived from the link between pensions and education. The working-age generation, realizing that the increasing number of old people makes the PAYG system less profitable and unsustainable, decides to invest in the education of young people in order to boost their productivity and consequently the revenues from taxing their income in the future.
As we can see from the Table 2, the effect of the ODR on total education spending (TES), without controlling for total social expenditure and for the institutional indices, is positive and statistically non-significant (regression 1). However, when we take into account total social expenditure, the effect of the ODR on education spending becomes negative, as expected by the "generational conflict" hypothesis (regressions 2 and 3). The reason for running the model sequentially and starting without including total social expenditure is the plausible strong relationship between education spending and total social expenditure. It is reasonable to expect people to vote for social packages as a whole (pensions and education). For instance, if voters are willing to support an extended welfare state, they might also be willing to support higher education spending. However, if we do not take into account social expenditure then, as our results show, the ODR can absorb these effects. A closer look shows that a 1% increase in the ODR generates a 0.037% reduction in total education expenditure (regression 3). However, the old dependency ratio has a negative and not significant effect on education spending per student (regression 5 and 6). Regarding the performance of the control variables, it seems that the level of economic development (GDPpc) has a positive and significant impact only on per-student spending (regression 4, 5 and 6). Moreover, as it is obvious, education spending is not affected significantly by the business cycle (real GDP growth). In addition, the level of fiscal resources (tax revenue) has the expected positive sign for total spending on education but they only weakly affect the level of education spending per student. Next, the size of the welfare state represented by total social expenditure has an important positive impact on both measures of education spending. 18 The variable used as an approximation of education quality, the mean years of schooling (MYS), has no significant influence on education. Left-wing governments have a non-important influence on education spending. Finally, the fertility rate, which reflects the interest of young parents in education spending, has a very strong and positive influence on per-student spending. A higher fertility rate means more children per couple and that makes young parents more willing to "push" for a higher level of educational expenditure. We could call that the "political power of parents" hypothesis.
In regard to the institutional variables in Table 2, globalization index (GI), Voice and Accountability Index (VAI) and Economic Freedom Index (EFI) have the expected effects. The first one has a negative sign, reflecting the "race to the bottom" hypothesis that claims that more globalised countries engage more actively in competition with other countries and, hence, aim to lower the level of public spending in order to be able to lower taxes and become more competitive. The second index has a positive effect on both measures of education spending, showing that a higher level of democracy promotes the expansion of the public education system. The Index of Economic Freedom shows that the process of economic liberalization has encouraged higher spending on public education.
In this section, we find only partial support for the generational conflict hypothesis, since the old dependency ratio has a significant and negative effect only on total education spending rather than on education spending per student. This result gives us a hint that there might be something more complicated in the relationship between population ageing and education spending that we need to examine further.

Generational conflict and the link between pensions and education
One way to investigate further the relationship between current population ageing and education spending is to check for possible non-linear effects. One can claim that it is plausible to assume that the impact of population ageing on education expenditure depends on the scarcity of fiscal resources. 19 For instance, the effect of the old dependency ratio on education spending might depend on the level of total retirement expenditure. Thus, we need to disentangle the effect of retirement spending from the effect of total social expenditure on educational outlays. In order to do so, we "break" total social expenditure into two parts, social expenditure (survivors and incapacityrelated benefits, health, family, active labour market programmes, unemployment, housing and other social policy areas) and retirement spending (public pensions). In this way, we are able to interact retirement spending with the old dependency ratio in order to capture potential non-linearities in the relationship of population ageing and education expenditure. In addition, we obtain the direct effect of retirement spending on education expenditure in order to test whether there is a direct link 18 The social expenditure used for these regressions also includes retirement spending. 19 It is shown in the Appendix A Tables 6 and 7, that the effect of population ageing on pensions expenditure depends on the scarcity of fiscal resources and after a certain point reduces the amount spent per retiree.
between these two public policies. 20 As we can see from the regression 1 of the Table 3, total retirement spending has a positive but non-significant effect on total education spending, and the new variable for social expenditure is strongly significant and positive. In addition, we do not observe any significant evidence in favour of 20 As suggested by Kemnitz (2000), in contrast with the negative predictions for the social security system due to higher life expectancy and lower fertility, the demographic transition has beneficial effects on both education and pensions. According to his theoretical model, in a steady state equilibrium there is higher investment in per capita human capital and a higher contribution rate to the social security the generational conflict. However, in the regression 2, where the interaction term between the old dependency ratio and retirement spending is taken into account, we can observe that the individual effect of both variables becomes significant and, additionally, the interaction term is significantly negative. In technical terms, this means that the effect of the old dependency ratio on total education outlays is non-linear and depends on the level of total retirement expenditure. 21 More specifically, the effect of the old dependency ratio on education is positive until a certain level of total retirement spending (TPS=8%). When the level of retirement expenditure exceeds 8% of GDP, then the effect of the old dependency ratio on total education outlays becomes negative.
As we already mentioned in the previous section an increase in the old dependency ratio has two opposite effects on education spending. There is the negative effect of the generational conflict due to the increasing number of elderly and the positive effect derived from the link between pensions and education. Therefore, when retirement spending is low, the former effect is dominated by the latter and hence the net effect on education expenditure is positive. This effect is a result of the choice by the working-age generation to invest public resources in education in order to ensure their future pensions. However, when the total expenditure on retirement is quite high, the former effect dominates the latter, and hence the net effect on education is negative. This outcome reflects the fact that, when there are limited fiscal resources, an increase in the political power of the elderly is translated into a decrease in education expenditure, because the old generation tries to appropriate more public resources in their own favour.
Similarly, after a certain point (ODR=26%), the effect of increasing spending on retirement has a negative effect on total education spending. For example, when the ODR is equal to its mean value (21%), in our sample the effect of an additional percentage point of total retirement spending on total education spending is 0.07%. However, when the ODR is higher, for instance 30%, then the effect on education is -0.06%. The theoretical intuition behind this result can be derived from the generational conflict hypothesis. Thus, when the old cohort is politically stronger (higher ODR), an increase in total retirement spending is financed out of the same public resources that are used for education expenditure.
Furthermore, as we can see from Table 3 (regression 4), the same interaction effect is present in the case of education spending per student. The effect of total retirement spending depends on the level of the old dependency ratio. However, in this case the effect of total retirement spending on education becomes negative at the point where the level of the ODR is 37%, which is the maximum value that the ODR takes in our sample. Likewise, the effect of the old dependency ratio becomes negative only after the level of total retirement spending is above 11 % of GDP. Therefore, the negative impact of the interaction terms takes place only at a very high level of the old dependency ratio and retirement spending, respectively. This evidence is in favour of the generational conflict hypothesis that claims that there is competition for fiscal resources between young and old cohorts.
21 Isolating the effect of the ODR and TPS on total education spending, we obtain the expression below: T ES = 0.1141 * ODR + 0.3760 * T P S − 0.0144 * ODR * T P S In order to obtain the effect of the old dependency ratio on total education spending, we take the derivative of TES with respect to the ODR: ∂T ES/∂ODR = 0.1141 − 0.0144 * T P S In the same way, we can obtain the derivatives with respect to TPS.
In other words, the increasing share of old people (retirees) has a negative impact on education expenditure per student. However, we show that the effect of generational conflict is non-linear rather than linear, as it is highlighted in the past literature.
Last but not least, in regressions 5 and 6 we present the effect of retirement spending per retiree on education and the interaction of retirement spending with the old dependency ratio, respectively.
It is obvious that there is no interaction between the old dependency ratio and average spending per retiree (regression 6). Hence, the impact of retirement spending per retiree and the impact of the old dependency ratio on education do not depend on each other. As we can see from Table 3, it seems that the higher the average spending on retirees, the higher the education expenditure per student.
The intuition behind this result is that an increase in education spending per student as a result of an increase in average pensions is financially backed by the working-age generation because, for them, this is a way to secure their future pensions. Moreover, this is an indication that pensions and education are positively linked. More specifically, an increase of $ 100 in average pensions results in an increase of $ 6.5 in education spending per student. For the same reason a one percentage point increase in the old dependency ratio enhances education spending with $37.5 per student.
After focusing on the current old dependency ratio, we find that there is competition for resources, at least after a certain level of total retirement spending. Therefore, it is plausible to claim that the current population ageing, is more related to generational conflict than to the positive link between pensions and education. The latter is quite intuitively associated with the future rather than the current population ageing. The working-age voters worry more about the future than the current old dependency ratio for the simple reason that they receive their pensions in the future. Hence, it is interesting to investigate the effect of the future population ageing on education spending. This is what we attempt in the next section, where we employ instead of the current the projected old dependency ratio.

The impact of the projected population ageing on education spending
In this section, we estimate the effect of the projected old dependency ratio on education spending.
According to the theoretical predictions of Kemnitz (2000) and Gradstein and Kaganovich (2004), the process of future population ageing achieves a better forward (education) redistribution of public funds. More specifically, population ageing, alongside the specific structure of the PAYG pension system, provides the appropriate incentives to the middle-aged generation to make an investment in the education of the young generation. This has a positive effect on pension benefits by broadening the tax base or the pie available for redistribution, due to the increased productivity of more educated labour in the future.
In contrast with the previous sections where we use the old dependency, here we employ the estimated projections of the old dependency ratio in order to capture the effect of future population ageing through the link mechanism between pensions and education. The main difference between the two demographic variables is that the latter does not capture the generational conflict and therefore it is only expected to have a positive impact on education expenditure. The middle-aged voters respond to the increase in the projected old dependency ratio by supporting a more generous redistribution towards education. In this case there is no generational conflict, because future population ageing does not concern the current old generation and therefore they do not "fight" for public resources now. As we can see from the Table 4, the projected old dependency ratio brings about the expected positive impact on both total level of education spending and spending per student. A closer look reveals that a one percentage point rise in the proportion of old people in the future ceteris paribus generates a 0.021 % increase (regression 1) in total education spending and a $52 rise in per-student expenditure (regression 2). These results are in contrast with the negative impact that the old dependency ratio has on education spending in Table 2 (regressions 4 and 6). These differences are mainly attributed to the absence of the negative impact of generational conflict on education spending. Comparing the magnitude of the effect of ODR in Table 3 (regression 5) and the magnitude of the impact of PRODR in Table 4 (regression 4), once again we can observe the absence of the generational conflict in the latter.
In addition, as expected, a higher number of students increases the public spending in education as a percentage of GDP. Furthermore, a one percentage point increase in the fertility rate that captures parental willingness to support education brings about roughly a $1300 increase in education expenditure per student (regression 2). In general, most of the control variables in these specifications of the model behave as expected by the literature. The political ideology seems to have only a weak role in the determination of education expenses. More specifically, left-wing and socialdemocratic governments tend to spend more per student than their ideological opponents. As in the previous section, the level of the welfare state (excluding pensions) and economic development have a positive and very significant impact on per-student spending. Finally, institutional indices have significant effects in the expected direction. Furthermore, in Table 4 the main results do not change when, instead of using total social expenditure, we introduce the level of total retirement spending separately from the rest of the social outlays (regression 2 and 3). Also, the effect of the projected old dependency ratio remains the same when we use retirement spending per retiree, which also has a positive impact on education spending per student, providing further evidence in favour of the positive link between education and pensions (regression 4). This result is similar with the result of regression 5 in Table 3 The above findings are consistent with the main theoretical outcomes of Kemnitz (2000) and Gradstein and Kaganovich (2004). More specifically, in order to interpret the results, one can argue that the working-age generations, realizing the severe consequences of the ageing process for their retirement benefits, decide to exploit the current set-up of the PAYG pension system. Thus, they react to an increasing projected old dependency ratio by investing in the education of young people "today" in order to boost the labour productivity and consequently the revenues from income tax "tomorrow". Hence, in this way the fiscal resources generated from the investment of the working-age cohort in education now, will be used to pay for their pensions in the future.
6 The effect of the projected population ageing on disaggregated levels of public education In this section we go one step further by investigating which educational levels are the driving forces behind the impact of future population ageing on total education expenditure. Moreover, we examine to what extent they are affected by demographic transition that acts through the link mechanism between pensions and education. We investigate the effect of population ageing on public education per level (pre-primary, primary, secondary and tertiary). In order to estimate the effect of the projected population ageing, we employ the same model as in Table 4 (regression 1). In this specification of the model, among other variables we control for total level of social expenditure (pensions plus other welfare expenditure) and the proportion of pupils/students per level of education. The dependent variables are spending by education level measured as a percentage of GDP.  Freedom Index (EFI). Constant is included but not reported.
As the Table 5 shows, spending on non-mandatory, pre-primary and tertiary education is positively affected by the increasing percentage of the elderly. In contrast, the impact on the mandatory, primary and secondary educational level is significantly negative and insignificantly positive, respectively. One can argue that an increase in the projected old dependency ratio raises the future welfare state fiscal requirements (pensions and other social expenditure) as the number of beneficiaries increases. Hence, enhancing the productivity of the current and future generations as an attempt to obtain additional resources (tax revenues) can be considered as the main reaction of the working-age population to handle the forthcoming fiscal sustainability issues of the welfare state. Thus, in order to boost current and future productivity, voters decide to support investments in the non-mandatory levels of education and those more related to productivity, pre-primary and tertiary education. In our opinion, the investment in non-mandatory education takes place only because there is a space for political intervention. In other words, increasing the quality of the non-compulsory educational levels may have a larger positive effect on the participation rate of these educational levels than on participation in mandatory education.
More specifically, investment in pre-primary public education can positively affect the productivity of young parents (especially young mothers) by supporting them with such a time-consuming process as child-raising. Therefore, improving the quality of pre-primary education could eventually lead to an increase in productivity. However, in the case of primary and secondary education, the mandatory character of participation prevents such an investment from being beneficial for the productivity of current workers. Regarding the productivity of future workers, there is a positive impact from the projected population ageing on higher education spending. Consequently, one can expect that this could bring about an increase in participation in tertiary education and eventually lead to a future working generation with enhanced skills and productivity. In other words, as mentioned above, working-age voters, on considering their future public benefits, choose to support investments in higher education in order to boost the productivity of the young generation and "reap" the benefits from increased income tax in the future.

Conclusions
The share of the elderly in the population of many developed countries is rising as the demographic transition unfolds. Much attention has been paid by economists to the implications of this trend for major public policies like social security (pensions) and education. Yet another issue of growing concern is the impact on the allocation of public funds among the different generations. Children and the elderly are both on the side of dependency as main beneficiaries of social spending. Therefore, a conflict of interests may arise between generations.
First, we test the "generational conflict" hypothesis, according to which the increased number of old people is expected to push for more pension and less education expenditure. As is shown, the generational conflict effect is present but depends on the level of total pension spending. Thus, when the level of total retirement spending is low and there are more public resources available, an increase in the old dependency ratio will have a positive effect on education spending due to the positive link between pensions and education. However, when total retirement spending is quite high, an increase in the old dependency ratio has a negative impact on education spending, reflecting the struggle between generations for limited public resources. Hence, an increase in the current population ageing translated into political power of the older generation -that supports pro-pension policies -seems to have a negative impact on both total and per-student education spending.
Second, the main focus of this paper is the positive relationship between public pensions and education in a changing demographic environment. More specifically, we test the theoretical hypothesis -arising from the studies of Kemnitz (2000) and Gradstein and Kaganovich (2004) -that population ageing achieves higher forward (education) reallocation of public funds. Our results show that, indeed, the projected (future) old dependency ratio has a positive impact on education expenditure and operates via the link between education and pensions. The specific design of the PAYG pension system creates the appropriate incentive to invest in education. The intuition behind the link is that the working-age generation, realizing the higher life expectancy and the increasing number of retirees, invests more in public education "today" in order to derive some benefits in the form of higher contributions (income tax) for pensions "tomorrow". Therefore, even in the absence of altruism, middle-aged voters would be in favour of a public education programme as a way to improve their pensions thanks to an increase in the productivity of future workers. This could have some policy implications in the face of the imminent demographic crisis of PAYG-financed pension systems. Educational expenditure can be seen as a complement or an alternative pre-funding device to the long-discussed transition to a capitalization system.
Moreover, by disaggregating education expenditure by level of education, we try to examine whether there is a different impact of future population ageing on each educational level. The results show that there is a positive effect only on non-mandatory (pre-primary and tertiary) education spending. Our interpretation of this outcome is that investment in non-compulsory education only occurs because there is space for political intervention in order to increase the participation and consequently the productivity of the current and future working-age generation.
The important lesson we learn from this study is that population ageing affects the working-age and the elderly generations differently. While the current population ageing increases the number of retirees that are opposed to education spending, the current and especially the future projection of population ageing stimulate -through the positive link of education with pensions -the working-age generation to support expansionary education policy.
Further research is needed on both the empirical and the theoretical side. On the theoretical side, the reasons behind the private transfers and the interaction with the public transfers -introduced by welfare state programmes -needs further investigation. On the empirical side, along these lines, the strong positive effect of fertility on education spending per student -that we find here -could be analyzed as an indication of the political power of parents driven by altruism or other motivations.
these demographic variables in order to test the "elderly power" and the "fiscal leakage" hypotheses.
Second, we include as control variables four macroeconomic indicators: GDP per capita (GDPpc), real GDP growth (RGDPgr), interest rate (Intrate) and trade openness (Openc). Third, we add two variables related to the labour market: unemployment (Unemp) and union density (Un.Den.).
Fourth, we include political variables: type of government (G.T.) and government party (G.P.). 25 In addition, in order to fit a two-way FE model, we include time fixed effects, µ t . In this way, we control for time effects in order to capture any unexpected variation or special events that may affect the dependent variable. Finally, c is the constant, γ is the coefficient vector, α i represents the unobserved country-specific characteristics and i,t is the idiosyncratic error term.
From Table 6 we can see that the total pension expenditure is affected positively by all the demographic variables except of projected old dependency ratio. This result can be attributed to the size effect; the higher number of old people means more total expenditure. However, the effect of the same demographic variables on the pension spending per retiree is negative and significant only for the current and projected in the future old dependency ratio. These outcomes are in favour of the "fiscal leakage" hypothesis. The high current and projected in the future old dependency ratio make the pay-as-you-go system less profitable for the currently working voters who push for less generous pensions. It is interesting to notice here that, when we include part of the working-age voters in our demographic variable (ODR+55), the negative effect is moderated (regression 4). This can be attributed to the fact that the working-age voters close to retirement age will not claim less generous pensions, even though the profitability of the system is lower because they are about to retire. Constant is included but not reported. 25 The former is a variable that takes values that represent five different types of government starting from the strongest type (=1, single party majority) to the weakest type (=5, multi-party minority). The latter represents the ideological spectrum of the government cabinet (also known as Schmidt-Index) and goes from the hegemony of right-wing and centre parties (=1) to the hegemony of social-democratic and other left-wing parties (=5).
Extending the scope of the aforementioned empirical literature we examine the presence of nonlinear effects in our model. As far as we are concerned, the only study from the empirical literature on political economy of the social security that considers the non-linear effect of ageing on socialspending patterns is the one undertaken by Lindert (1996).
First, in order to check for non-linear effects, we test which specification fits our data better with the help of simple scatter-plots of Figure 1. We check for non-linear effects concluding that the cubic regression model fits the data better than the quadratic or the linear one.   As we can see from the Table 7, the effect of the population ratios (ODR and ODR(+55)) on retirement spending per retiree is non-linear (regressions 2 and 4, respectively). More specifically, the effect of the ODR on retirement spending per retiree can be analysed through its cubic regression model. A change in the ODR from 13 to 14 % has a negative impact (-1.201) on pension expenditure, ceteris paribus. 26 The negative impact of the ODR on generosity of the system can be observed until the level where the ODR=23 %; however, the magnitude of the effect decreases gradually from 13 to 23. This direction of the effect is clearly in favour of the "fiscal leakage" hypothesis; the generosity of the PAYG pension system decreases with a larger share of elderly people in society.
As we can observe after this point (ODR=23 %), a change in the old dependency ratio from 23 to 24 has a positive effect on pension and this effect holds until the point where the ODR=28 %. The demographic transition in this range (23 to 28) has a positive effect on pension generosity and that is in favour of the "elderly power" hypothesis. However, beyond the point where the old dependency ratio is 28, we observe again the negative impact of a change in the ODR on pension generosity, and the magnitude of the effect increases as the old dependency ratio increases, even beyond our data range. The intuition behind these results can be as follows. The initial increase in the number of retirees puts pressure on the pension system and therefore has a negative effect on it. However, as the old dependency ratio grows, it reaches a certain point (ODR=23 %) where the elderly acquire considerable political power in order to influence the government to favour more generous pensions. 26 The range of the variable old dependency ratio in our data is from 13 to 33% and for ODR(+55) is from 26 to 57 %, respectively.
It seems that they manage to cancel out the negative effect on the PAYG pension system from the increasing number of old people. Nevertheless, after a certain point (ODR=28 %), the number of retirees is too big to be counterbalanced by the political power of the elderly. Similar interpretation applies to the other demographic proxy variable (ODR(+55)).
Hence, our empirical findings provide an indication that population ageing has a non-linear effect on pension expenditure per retiree and therefore both effects are present. Thus, the outcome and the strength of both effects depend on the proportion of old people. Hence, when the old dependency ratio (or ODR(+55)) is at a very high level, the "elderly power" effect is dominated by the "fiscal leakage" effect.   Figure 3: In those graphs we can see the difference between the variation of the total education and pension spending. Unlike the pensions that are clustered over periods of 4 to 5 years (period needed for a pension reform), education seems to vary on an almost annual basis.