سالمندی، بودجه های دولتی، بازنشستگی، و رشد

We analyze the short and long-run effects of demographic ageing – increased longevity and reduced fertility – on per-capita growth. The OLG model captures direct effects, working through adjustments in the savings rate, labor supply, and capital deepening, and indirect effects, working through changes of taxes, government spending components and the retirement age in politico-economic equilibrium. Growth is driven by capital accumulation and productivity increases fueled by public investment. The closed-form solutions of the model predict taxation and the retirement age in OECD economies to increase in response to demographic ageing and per-capita growth to accelerate. If the retirement age was held constant, the growth rate in politico-economic equilibrium would essentially remain unchanged, due to a surge of social-security transfers and crowding out of public investment.

The prospect of “graying” populations in many developed economies raises concerns about the sustainability of economic growth. According to these concerns, rising old-age dependency ratios translate into growing tax burdens while generous pension and health care benefits crowd out public investment spending for infrastructure or education, with negative effects for capital accumulation and productivity growth. However, the demographic transition has been ongoing for a while – developed economies have experienced a marked decrease in fertility and increase in longevity for several decades – without producing clear evidence that this transition has caused a fall in per-capita growth. Rather to the opposite, Barro and Sala-i-Martin (1995) find in growth regressions that both a decrease in the fertility rate and an increase in longevity are associated with higher growth rates.1 The evidence is similarly mixed as far as government budgets are concerned. While the GDP share of transfers to the elderly has increased, the share of public investment does not show a clear trend in most countries, see Figs. 1 and 2.23 Moreover, most developed countries have started to increase the retirement age or tighten the conditions for early retirement, reducing the pressure on social-security taxes.To interpret this data and gauge likely future developments, we develop a tractable model to analyze the effects of demographic ageing on government budgets and per-capita growth. Building on a standard overlapping generations setup with private and public capital formation sustaining endogenous growth, our framework features two demographic driving forces – fertility and longevity – and a number of economic and political choices. In their role as economic agents, households in the model take prices, taxes, public investment, the retirement age and retirement benefits as given when choosing consumption, savings, and labor supply. In their role as voters, households choose among office motivated parties that offer policy platforms comprising labor income taxes, the expenditure shares for intergenerational transfers and public investment (reflecting spending components of central importance for developed economies), as well as the retirement age. The political process lacks commitment, and elections take place every period. Policy choices in the model are of different concern to young and old voters: the exposure of households to labor income taxes changes over the life cycle; the old benefit from social-security transfers to their group but are hurt by an increase in the retirement age; and only the young benefit from the returns to public investment. When evaluating the policy platforms on offer in the political arena, voters therefore disagree as to which platform should ideally be implemented. We model the resolution of the ensuing conflict under the assumption of probabilistic voting, reflecting a small degree of randomness in voters' support for a party. In equilibrium, vote-seeking parties propose a policy platform maximizing average welfare of all voters, and changes in the economic or demographic environment give rise to a gradual adjustment of the policy instruments. Policy choices do not only affect economic outcomes. Absent commitment, they also affect, indirectly, future policy decisions. In addition to the “economic” repercussions of their policy choices, voters internalize the “political” repercussions, reflected in the equilibrium relationship between future state variables and policy choices. We assume that only fundamental state variables enter this equilibrium relationship, excluding artificial state variables of the type sustaining trigger strategy equilibria. While we agree that the existence of intergenerational transfers or public investment may also owe to reputational arrangements, we focus on the Markov perfect equilibrium in order to identify the fundamental and robust forces that shape the size of these programs, and therefore growth.4 Under standard functional form assumptions, we characterize the politico-economic equilibrium in closed form.5 Changes in the demographic structure affect the equilibrium allocation both directly and indirectly, by inducing policy changes. The direct effect of changes in fertility and longevity works through modified private savings and labor-supply decisions which in equilibrium manifest themselves in faster capital accumulation. Indirectly, demographic ageing affects growth because it alters the relative political power of the old and the effect of later retirement on aggregate labor supply. At the same time, higher longevity increases the political support for public investment. To quantify the equilibrium implications of demographic ageing, we analyze calibrated versions of the model representing a rich OECD economy, a rich European OECD economy, the United States, and Japan. For each of the countries and country blocks, the model predicts that the forecasted demographic changes give rise to a continued increase of the GDP share of social-security transfers, a slightly higher GDP share of public investment, a strong increase of the retirement age, and a rise in per-capita growth. In particular, annual per-capita growth is predicted to accelerate by approximately 35 basis points toward the end of the century. Importantly, these findings hinge on the assumption that both fiscal policy and the retirement age are endogenous. With constant policy instruments, the growth rate would increase more strongly than in politico-economic equilibrium. With endogenous tax rates and budget shares but a fixed retirement age, the per-capita growth rate would essentially remain stuck at its current level in the medium run and increase only slightly in the long run, due to a surge of social-security transfers and – most importantly – crowding out of public investment. The central predictions of the model are robust to a variety of changes in the modeling assumptions. In particular, the results do not change if capital income taxes in addition to labor income taxes are introduced or if the balanced-budget assumption is relaxed. The results are also robust to replacing the endogenous-growth specification by one of exogenous growth. In the model, the political process does not internalize the long-term benefits of public investment because these occur beyond the lifetimes of even the youngest voters. As a consequence, the exact specification of productivity growth has no effect on the evolution of the policy instruments and the government budget shares in politico-economic equilibrium. Moreover, as we show, it does not have a strong effect on the evolution of output per capita in the medium run either. While broadly consistent with the evidence, the model predictions contradict the common view among policy makers that the political process will implement measures to raise productivity in order to “outgrow” the burden imposed by demographic change.6 According to the model, demographic ageing indeed induces the political process to raise public investment in order to foster productivity growth. However, the main positive growth effects arise directly while the net effect of endogenous policy on growth is negative. Our work relates to the literature analyzing the effects of government policy on growth, see Barro (1990), Jones et al. (1993) or Glomm and Ravikumar (1997) for a review. Our contribution relative to these papers lies in modeling the determinants of policy and linking fertility and longevity to growth.7Galor and Weil (1999), Cervellati and Sunde (2005) and Soares (2005) analyze the growth effects of demographic change due to its impact on private savings and education decisions, and Hazan (2009) introduces private retirement decisions in a model of human capital accumulation. Our model complements these papers by modeling the role of policy and its determinants in politico-economic equilibrium, and by focusing on the ongoing demographic transition in developed economies rather than historical developments. Our work also relates to politico-economic models of redistribution and growth. Alesina and Rodrik (1994), Persson and Tabellini (1994) and Krusell et al. (1997) argue that inequality depresses growth because anticipated redistributive taxation reduces the incentive to accumulate, or because higher inequality pushes the median voter's preferred level of public investment and taxes beyond the growth-maximizing level. Relative to these papers, we focus on inter- rather than intragenerational conflict, consider a larger set of policy instruments available to policy makers, and focus on the implications of fertility and longevity on growth. Our analysis therefore sheds light on the equilibrium size and composition of the government budget, and it emphasizes how demographic ageing affects both this composition and growth.8,9 Like Bellettini and Berti Ceroni (1999) and Rangel (2003), our paper analyzes the choice of productive versus redistributive public spending in an overlapping-generations model. In these papers, voters support public investment even if they do not directly benefit from it because a trigger strategy links investment spending to the provision of public pensions in the future. Our model adopts a different perspective. Rather than emphasizing complementarities between investment spending and transfer payments, it focuses on the conflict over the size of these two spending components, and how the resolution of this conflict is shaped by fertility and longevity. The model also differs from these papers in that it features political and economic choices, embedded in the standard growth model. This allows us to model the macroeconomic consequences of population ageing in a rich setting without having to sacrifice analytical tractability. Gradstein and Kaganovich (2004) argue that public investment might rise in response to increased longevity. Our model incorporates the mechanism underlying Gradstein and Kaganovich's (2004) argument. In addition, it features a role for fertility, the retirement age, a second government spending component that competes for funding, and – central to our analysis – growth effects of policy. The remainder of the paper is structured as follows. Section 2 describes the model and characterizes the allocation conditional on policy. Section 3 solves for the politico-economic equilibrium and analyzes its properties. Section 4 contains the analysis of the short and long-run effects of demographic ageing on government budgets and macroeconomic outcomes, in particular the growth rate. Section 5 concludes.

We have presented a rich, yet tractable framework to analyze the impact of demographic ageing on economic growth. Building on a standard overlapping-generations model, our framework combines various channels discussed in the literature and referred to in the political debate. On the one hand, it captures the implications of rising longevity and falling fertility in general equilibrium, including adjustments in the savings rate, labor supply, factor prices and capital deepening. On the other hand, it captures responses by the political system, in particular adjustments of the size of the government budget and its composition between investment and transfer spending as well as changes in the retirement age. Calibrated versions of the model predict that annual per-capita growth in rich OECD economies will increase by roughly 30–35 basis points during the 21st century, with the positive direct growth effects of demographic ageing partly being reversed by the consequences of endogenous policy responses. The model predictions support the view that rising longevity paired with falling fertility increases the GDP-share of social-security transfers, with negative implications for growth. However, they do not support the common view that rising social-security transfers crowd out productive public investment (as a share of GDP). Crowding out only results in an extreme scenario where the political process adjusts tax rates and the composition of government spending, but not the retirement age. In the more plausible scenario where the political process adjusts instruments along all three margins, both social-security transfers and public investment as a share of GDP rise, and the increase of the former is much more moderate than with a fixed retirement age. These results are robust to changes in the specification of the source of economic growth. Throughout the paper, we have assumed that the government runs a balanced budget, excluding government deficits and debt. This assumption is not very restrictive. In our model, unlike in Bassetto and Sargent (2006) who assume commitment, public under-investment cannot be overcome by letting voters finance investment expenditures out of government debt. For lack of commitment implies that the economic equivalence of social-security and debt policies largely extends to the political sphere.34 We have also assumed that longevity and fertility are exogenous. While this assumption is useful for the purpose of studying the long-run effects of demographic ageing on growth, there are clearly potential feedback effects from government budgets to demographics, for example via investments in public health (see Hall and Jones, 2007). With endogenous fertility, the demographic structure would turn into an endogenous state variable, rendering an analytical solution of the policy game considered in the present paper infeasible. The magnitude of the feedback effects introduced by endogenous fertility would depend on assumptions, among others, about the direction of altruistic linkages between parents and children (Boldrin et al., 2005). We leave an analysis of these feedback effects for future research.