مرگ و میر درون زا، سرمایه انسانی و رشد اقتصادی

We consider growth and welfare effects of lifetime-uncertainty in an economy with human capital-led endogenous growth. We argue that lifetime uncertainty reduces private incentives to invest in both physical and human capital. Using an overlapping generations framework with finite-lived households we analyze the relevance of government expenditure on health and education to counter such growth-reducing forces. We focus on three different models that differ with respect to the mode of financing of education: (i) both private and public spending, (ii) only public spending, and (iii) only private spending. Results show that models (i) and (iii) outperform model (ii) with respect to long-term growth rates of per capita income, welfare levels and other important macroeconomic indicators. Theoretical predictions of model rankings for these macroeconomic indicators are also supported by observed stylized facts.

Countries differ dramatically in the way they finance their educational systems. Education can be provided through public funds, through private funds, or a combination of the two. As reported in the Education at a Glance (OECD, 2003), a number of countries in 2000 had public education shares close to 100%, such as Norway (98.7%), Turkey and Portugal (98.6% each), Finland (98%) and Sweden (97%). Of the 36 OECD and non-OECD countries covered in this study, 19 countries (53%) financed at least 90% of their overall educational expenditures through public spending in 2000. In contrast, a number of countries put a larger responsibility on the private provision of education. Among those, Chile has gone the furthest with a private education share of more than 46%. Other countries in the above dataset with large private education shares include South Korea (41%), Indonesia (36%), Jamaica (35%), and the United States (32%). Overall investment in education, through its effect on the stock of human capital, has long been identified as a source for long-run growth in an economy (see, for example, Rebelo, 1991). In this broad category, a number of studies have specifically stressed the importance of public investment in education in further enhancing the growth performance of the economy (Glomm and Ravikmar, 1992, Glomm and Ravikmar, 1997, Boldrin, 1992 and Benabou, 1996). Given the trade-off between public and private financing in education, the question arises how different degrees of public (versus private) involvement in the production of human capital affect welfare, long-term growth, and other indicators of economic performance. Furthermore, budget components like public education spending must compete with other budget items such as internal and external security, infrastructure expenditures, and debt servicing, to name a few. One of the fastest growing budget components of many countries is public health expenditure. World Bank (2001) data show that between 1972 and 1999 the share of public health expenditure in total public spending has increased twofold or more in many countries. Over the 1972–1999 period, the average annual growth rate of the public health expenditure share was 1.7%.2 Just like the market for education, the provision of health services can also be linked to a number of positive externalities, which in turn explain the large public involvement in the health sector. One such externality that has not been sufficiently recognized in the literature is the impact of public health spending on longevity: Increased levels of public health expenditures are most likely to be positively associated with higher life expectancy (Lichtenberg, 2002). In addition to the individual benefits of living longer lives, increased life expectancy may confer important growth effects. These effects arise since increased longevity produces stronger incentives to invest in physical and human capital as these long-term assets yield high returns only later in life (Chakraborty, 2004). Importantly, since public spending on education competes with public spending on health, a second trade-off exists that, like the first one between public and private education shares, may matter for the long-term growth rate of the economy as well as its level of welfare. In this paper, we study the trade-off between public and private spending on education in a model with uncertain lifetimes and endogenous growth. To this end, we construct a three-period overlapping generations model in which survival of an individual in the third period is uncertain. Thus, like Chakraborty (2004), we model adult mortality rather than infant or child mortality. The probability of survival depends on her own health as well public health spending. To the extent that good (poor) health and consequent higher (lower) longevity generates (dis)incentive for private accumulation of human capital, public health expenditure plays an important role in generation of human capital, thereby affecting long-run growth. However, the more the government spends on health, the less it can spend on public education, adversely affecting future human capital. Since human capital accumulation is the engine of growth in this model, differences between public spending on health and education on one side and public and private spending on education on the other constitute the two fundamental trade-offs in our model that generate important growth and welfare consequences. This paper connects two different strands of the growth literature. One of them focuses on government spending on education assuming certainty with regard to the length of the life of each individual (Glomm and Ravikmar, 1992, Glomm and Ravikmar, 1997, Boldrin, 1992, Benabou, 1996 and de la Croix and Doepke, 2004). Glomm and Ravikmar, 1992 and de la Croix and Doepke, 2004 focus on the effect of private and public provision of education on long-term economic growth and income inequality, while Glomm and Ravikmar (1997) discuss different forms of productive public expenditures and their effects on long-run growth.3Boldrin, 1992 and Benabou, 1996, on the other hand, focus on endogenous determination of public policies in a political economy setting. The other, more recent strand of the literature, deals with uncertain lifetimes in models with endogenous growth mechanism but abstracts from government spending on education. Chakraborty (2004) treats mortality as endogenous and argues that a decline in adult mortality has a multiplier effect on growth, generating either a ‘poverty trap’ or a ‘stagnation to growth’ dynamics with endogenous growth. Blackburn and Cipriani (2002) use a discontinuous (step-function) endogenous survival function to explain the existence of multiple development regimes in which the survival of an agent into old age depends upon her inherited level of human capital. In Birchenall (2004) higher consumption growth and increased public health expenditure enable an economy to escape a high child-mortality Malthusian equilibrium by reducing child mortality from infectious diseases. In Kalemli-Ozcan et al. (2000) a lower mortality raises human capital investment and strengthens long-run growth because the return from such investment are typically earned over a longer time horizon. The effect of a change in adult mortality, however, is analyzed as a comparative statics exercise. The objective of the paper is to examine the relative macroeconomic performance of alternative educational funding strategies when public spending on education and health gives rise to budgetary tensions. For this reason, we analyze three distinct model scenarios. We begin with the analysis of a model with both public and private education expenditures (the benchmark model) followed by two alternative specifications: One with only public investment in education (the public education model) and one with exclusive private provision of education (the private education model). Except for the differences in funding education, all models share identical taste, technology, and policy (tax) parameters. Our main results are as follows. First, longevity is highest in the private education model, followed by the benchmark model. Second, with regard to long-run growth, interest rate, and human-to-physical capital ratio, the benchmark and private education models generate similar values, all of which are higher than the corresponding values in the public education model. Third, with respect to welfare, the private education model ranks highest, followed by the benchmark and the public education models. Fourth, we compare the benchmark to the public education model for an optimally chosen tax rate (in a second-best sense). We show that the welfare ranking of two regimes depends on the (exogenous) relative size of government spending on education and health. For high levels of public spending on education relative to health, the public education model is welfare superior, while the reverse is true for low public education spending. Finally, we show that the observed stylized facts support the theoretical model rankings for several macroeconomic indicators. The conclusions drawn from our analysis add to our understanding of the link between longevity, growth, and welfare. The better performance of the benchmark and private education vis-à-vis the pure public education model has an intuitive explanation. In a world with limited government resources, a country is better off if the government can concentrate its scarce resources on fewer budget items (here: full health coverage, but limited role in education) instead of spreading itself thin on too many budgetary needs (here: full provision of both health and public education). Note that our simulation results reveal that the macroeconomic performance ranking of the public education model can be reversed, but only for very high levels of taxation that exceed those found in most countries in our sample. The paper unfolds as follows: Section 2 lays down the basic model framework and the characterization of the competitive equilibrium. The three models are analyzed in Sections 3, 4 and 5, respectively. Section 6 provides a numerical comparison of the three models including welfare analysis when tax policy is endogenous. Section 7 concludes.

We incorporate dual public spending on education and health in a general equilibrium overlapping generations framework in which individuals have lifetime uncertainty. Private decisions regarding saving and expenditure on child’s education depend crucially on the incentive effect generated by better health and therefore higher longevity. Health accumulation depends on public funding on health alone, while the accumulation of human capital depends on both private and public funding. We analyze three different models. In the benchmark model, the most general form of human capital accumulation function is used requiring both private and public spending. In the public education model, the government is the sole provider of education, while private individuals are the sole providers in the private education model. The implications of these three models shed important light on policy issues such as the welfare maximizing mix of public versus private spending on education. By combining ‘productive’ government spending with endogenous length-of-life effects we can investigate not only the long-run (steady state) growth and welfare implications for three different education regimes, but also the short-term (transitional) growth impact of variable longevity.24 Another novel assumption of this paper is the simultaneous inclusion of two productive government investments (education and health) and their specific roles in generating and sustaining long-term growth under lifetime uncertainty. An important result of the paper is that the public education model produces results that are inferior to both the benchmark and the private education model with regard to a number of macroeconomic indicators. For a fixed income tax rate, long-run growth, interest rates, and the ratio of human-to-physical capital are all lower in the public education model than in the other two models, while longevity and welfare are highest in the private education model and lowest in the public education model. The poor performance of the public education model has its root in an income tax rate that is too low relative to its optimal level. In other words, the public education model cannot perform properly if the government cannot raise the funds needed to run both a public health and a public education system. This simple intuition is validated when we endogenize the income tax rate: Welfare-maximizing tax rates are on average more than three times higher in the public education model compared to the benchmark model. In addition, a comparison of welfare levels based on second-best tax rates reveals that the welfare ranking of benchmark versus public education model depends on the (exogenous) relative size of government spending on education and health. For high levels of public spending on education relative to health, the public education model is welfare superior, while the reverse is true for low public education spending. Our results point to an interesting policy implication. Faced with a given technology and a level of taxation that is too low relative to its optimal size, a government that cares about longevity, welfare, and long-run growth should encourage private participation in funding of education, thereby freeing up public funds for the provision of health care and related services.