امنیت اجتماعی، آموزش عمومی و ارتباط رشد-نابرابری

We study how the relationship between economic growth and inequality depends upon the levels of funding of two of the largest government programs, public education and social security. We do this in the context of an overlapping generations economy with heterogeneous agents where the government collects a tax on labor income to finance these programs. We show that in our model an increase in government spending on social security reduces income inequality and can have a non-monotonic effect on growth. When the initial level of social security funding is low, as is the case in most poor economies, then its increase will enhance growth. When its funding level is high as is typical for developed countries, we show that its further increase can slow down growth while reducing income inequality. These results obtain regardless of whether the increase in social security funding is financed by a tax increase or by cutting the public education budget. We also find that the effects of increasing the level of public education expenditures or the overall size of the government budget (holding the budget composition fixed) are characterized by similar non-monotonic growth–inequality relationships.

The relationship between income inequality and economic growth has been studied extensively in recent years. One of the first contributions to this literature is a model by Galor and Zeira (1993) which studies inequality within a paradigm of human capital driven growth. They show that in the presence of credit constraints on human capital investments high initial inequality may be harmful to long-run growth, while redistribution may have a positive effect. In a similar framework, Maoz and Moav (1999) argue that income redistribution can have a positive or adverse effect on growth depending on whether the distortionary effect of higher taxation is dominated by a pro-growth effect due to relaxing of a credit constraint on human capital investment for some individuals. Galor and Moav (2004) generalize the analysis by comparing the human capital driven growth to the early stages of industrial development, when the lion's share of growth was due to physical capital accumulation. They argue that at the early industrial stage high inequality was conducive to growth because the rich have a higher propensity to accumulate physical capital, whereas at later stages associated with an increasing role of human capital high inequality may be an impediment to growth according to the aforementioned credit constraints argument. The effects of inequality on growth are also investigated in the political economy literature, exemplified by Persson and Tabellini (1994), as well as the literature on the political economy of public expenditures (such as Saint-Paul and Verdier, 1993 and Alesina and Rodrik, 1994) which typically postulates a political mechanism that determines public policy as a function of the income distribution, while public policy in turn affects economic growth. Most of the papers in this literature find a monotonic relationship between inequality and the level of redistributive taxation, and between the tax rate and growth. According to Aghion et al. (1999), who summarize the bulk of this literature, the predictions of these papers are “impressively unambiguous, since they all suggest that greater inequality reduces the rate of growth.” Our paper is related to this literature through our focus on how growth is affected by public policies. We depart from the political economy literature in two ways. First, we take all public policy measures as exogenous and study implications of changes in public policy on growth and income inequality. Second, we study two redistributive government programs, pay-as-you-go (PAYG) social security and public education and their individual and combined effects on growth and inequality in a general equilibrium framework. In contrast to the political economy literature, we find a complex and non-monotonic relationship between public policies and growth. Moreover, the inequality–growth relationship turns out to be non-monotonic as well. The implications of each of these programs (separately) for long-run growth as well as income inequality are addressed in a large and growing body of theoretical literature. The effects of public provision of education on growth and/or income distribution have been explored by Glomm and Ravikumar (1992), Eckstein and Zilcha (1994), Benabou, 1996 and Benabou, 2002, Fernandez and Rogerson (1996) and many others. This literature supports the view that public education enhances both growth and equitable distribution. The literature on the growth effects of PAYG social security programs includes, among others, Feldstein (1974), Hubbard and Judd (1987), Laitner (1988), Pecchenino and Utendorf (1999), Docquier and Paddison (2003), and Lambrecht et al. (2005). The most common threads in this literature are that PAYG social security, while reducing inequality, is harmful to growth.1 In this paper we aim to contribute to the literature which studies how the growth–inequality relationship is influenced by government policies. In many of the dynamic general equilibrium models of redistribution and growth (e.g. the seminal paper by Persson and Tabellini, 1994) tax revenue is distributed in cash. Here we study this relationship in a growth model where the government has access to two instruments for redistribution. We focus on public funding for education and PAYG social security since in many countries they are the two largest items in the government budget and since both of these programs are redistributive, at least in intent (one of them in kind and the other in cash), and are believed to have significant impact on economic growth. Moreover, the relative size of these two expenditures varies fundamentally across countries, with poor countries typically having very small, if any, social security programs, and it is thus compelling to investigate the growth and distributional effects of changes in the absolute and relative size of these to programs. This paper aims to show that in the presence of these two redistributive instruments, the growth–inequality relationship turns out to be more complex than predicted by conventional theory and may in fact depend on a country's composition of public expenditures. We employ a Diamond-type overlapping generations model of physical and human capital accumulation populated by family dynasties where individuals derive utility from the stock of human capital of their offspring and where this altruistic motive varies across individuals. Human capital of a child is produced using effective labor of the parent and public education expenditures as inputs. The government also makes lump-sum social security transfers to the old. All government expenditures are financed with a labor income tax and the government budget is balanced in each period. Our model predicts that the general equilibrium growth–inequality relationship is dependent on the absolute and relative sizes of the social security and public education budgets as well as on technology and preference parameters. Moreover, we show that this relationship is, in general, non-monotonic in the transfer policy parameters. We study the comparative dynamics effects of increased social security funding in the context of two policy experiments. The first is a permanent marginal expansion of the social security program while keeping the public education funding rate fixed, thereby requiring an increase in the overall tax burden. In the second policy experiment, motivated by a political requirement to keep the overall tax burden from rising, the marginal expansion of social security funding occurs at the expense of shrinking the share of public education funding in the budget. Under both experiments we show that the effect of increasing social security funding on the growth–inequality relationship is non-monotonic. Such an increase unambiguously reduces inequality, but the effect on growth can be positive if the initial social security funding level is low, and negative otherwise. In particular, if at the outset of the experiments social security program is very small or non-existent, then its introduction or expansion can accelerate growth. This can be true even if social security expands at the expense of public education funding (our second policy experiment) because of the critical effect higher social security payments have on private investment in education in our model: it allows individuals to reduce their work time and devote more of it to the education of their children. Our analysis depends crucially on the feature of our model that the public education input is complemented by a private input, effective parental time. It is believed that private parental inputs at a pre-school stage as well as parent's time spent helping the child in school related activities such as homework, reading and field trips play a fundamental role in the formation of human capital. The relationship of these parental inputs to public education inputs has been explored by Houtenville and Smith Conway (2003). Heckman (1999) emphasizes the need to study “the crucial role of families [and firms] in fostering skill and the variety of abilities to succeed in the modern economy”. Benabou (1996) stresses the complementarities between public and private inputs in human capital formation and studies their implications for growth and inequality. In this paper we take these complementarities between public and parental inputs as given and explore their implications for the growth–inequality trade off. Glomm and Kaganovich (2003) have shown that when there is complementarity between public and private inputs in education a reallocation of funds from public education to social security budget can lead, due to a positive income effect, to increased private input in education. This effect is particularly strong in low income families, therefore such a reallocation of public funds is progressively redistributive. An important implication of our analysis is showing that despite the role of public education funding as an engine of economic growth, this effect can be non-monotonic: an increase beyond a certain level can have an adverse growth effect. An increase in public education funding, especially if it occurs at the expense of social security funding, can lead in our model to a net retirement income loss of the relatively poor individuals. If they place sufficiently high priority on their own consumption when old, this will compel them to substantially increase labor force participation and therefore to spend less time helping their offsprings learn. This reduction in private investment in children's education can result in lower aggregate human capital in the economy, despite the increased public school input. The overall result can be a decline in growth. The combination of the two insights outlined above leads to a more complex growth–inequality relationship than suggested by standard models of income redistribution. Our result of a non-monotonic effect of fiscal policy on the growth–inequality relationship contributes to the growing understanding of the non-monotonic nature of relationships observed in the wider literature studying fiscal policy effects on economic outcomes. Barro (1990), for example, shows in a simple model of public investment in infrastructure that the long-run growth rate is a non-monotonic function of the size of government. Kaganovich and Zilcha (1999) study the impact of reallocating public funds between social security and public education. They find that the growth rate of an economy is a non-monotonic function of the relationship between the sizes of social security and public education budgets; and that, in particular, when a social security program is marginally expanded from a relatively small size, this may speed up growth, while the reverse is true when the size of the social security program is big. Lambrecht et al. (2005) likewise show that under certain conditions increasing social security payments can increase economic growth by allowing larger private expenditures in human capital accumulation; moreover, for some parameter values they obtain a non-monotonic relationship between social security funding and growth. Glomm and Kaganovich (2003) who focus on implications of public education funding for income inequality, find that the relationship between the level of such funding and the degree of inequality can too be non-monotonic. It is important to emphasize that our analysis treats the growth–inequality relationship in the context of a general equilibrium co-movement response to exogenous policy changes, rather than as a causal relationship where one of the characteristics, e.g., initial inequality, is treated as exogenously given, as in the aforementioned seminal paper by Persson and Tabellini (1994). We are aware of several papers which study the co-movement of growth and income inequality caused by a change in one public policy. Karni and Zilcha (1989) find that the introduction of fully funded social security has a simultaneous effect of decreasing growth and increasing inequality along the entire general equilibrium path. Eckstein and Zilcha (1994) prove that imposing mandatory schooling funded by the government simultaneously raises long-term growth and income inequality. Benabou (1996) characterizes the growth–inequality relationship as a function of the degree of decentralization of education funding. Viaene and Zilcha (2003) who model creation of human capital as a sum of components due to public and home schooling, consider the simultaneous effect of technological improvement in schooling technologies on growth and inequality. They find that while the growth effect is unequivocally positive, the effect on inequality may be positive or negative depending on whether the improvement occurs in the public or home sector. All these papers, however, consider only one dimension of public policy and they do not obtain the non-monotonic effect of policy on growth–inequality relationship which we are able to demonstrate in the presence of public education and social security programs.2 In Section 2 we lay out details of this model and define the dynamic competitive equilibrium with the government programs, while in Section 3 we solve the model and derive the relationships characterizing the equilibrium dynamics. Section 4 presents the comparative dynamics results on growth, inequality, as well as on the growth–inequality relationship. In Section 5, we conclude that the aforementioned policy effects on growth and inequality are not absolute but do depend on an economy's composition of public expenditure. In particular our model suggests that growth–inequality relationship is positive for countries where social security transfers dominate public education expenditures (typically the wealthy economies), while for countries where public education expenditures are larger than social security payments (typically the poor countries) it may be non-monotonic and depend upon prevailing preference parameters. An Appendix to this paper contains the proofs of the main technical results of Section 4.

In this paper we have presented a model in which the government funds two programs, public education and social security. We showed in our model that increasing the funding of social security unequivocally reduces income inequality. This result obtains when public education funding is held constant and also when the increase in social security funding comes at the expense of public education. We then showed that the effect of increasing social security funding on economic growth and hence on the growth–inequality relationship depends on the prior social security funding level and on technology and preference parameters in a complex manner. We argue that similar policy experiments such as increasing public education funding (while holding social security taxes constant) or increasing overall taxation (holding the composition of government expenditure constant) also yield non-monotonic growth–inequality relationships depending on absolute and relative funding levels. An additional, closely related, dimension of individual decisions and public policy is fertility—indeed, it is believed to have played a critical role in the process of transition to human capital driven growth (see e.g., Galor, 2005). The “quantity–quality trade-off” that accompanied the trend of increasing investment in human capital during the demographic transition is therefore an important part of the picture that we analyze. While we focus on the essential role of a dedicated parental time in a child's education assuming that fertility is fixed, an introduction of endogenous fertility would add the dimension of quantity–quality trade-off to the opportunity cost of education in terms of parent's labor supply. It can be argued (see, e.g. Zhang and Zhang, 1998), however, and empirically observed that when a policy creates a negative income shock for parents, both trade-offs would work in the same direction: lower parental investment in children's human capital and disproportionately so by lower income parents. This means that while the introduction of endogenous fertility into the model would be likely to give rise to additional interesting insights into the growth–inequality relationship, it appears that they would be in the same spirit, but probably stronger, as those offered by our model. On the other hand, the robustness of our results would be more of an open question if parental altruism with regard to children's human capital was allowed (unlike in our model) to correlate across generations. The evolutionary implications of such a theoretical possibility would be of much interest for a future research.