سرمایه گذاری سلامت، انباشت سرمایه فیزیکی، و رشد اقتصادی

This paper analyzes the effect of health investment, and hence of health capital, on physical capital accumulation and long-run economic growth in an extended Ramsey model with an Arrow–Romer production function and a Grossman (1972) utility function. The paper concludes that economic growth is related to both the health growth rate and the health level. While growth in health capital always facilitates economic growth, the gross effect of health level on the rate of economic growth depends on how it affects physical capital accumulation. If the negative effect of health on economic growth through its influence on physical capital accumulation is not taken into consideration, then health level has a positive effect on the rate of economic growth by improving the efficiency of labor production. However, since health investment may crowd out physical capital investment and thus influence physical capital accumulation, excessive investment in health may have a negative effect on economic growth. Empirical tests of these theoretical hypotheses using panel data from individual provinces of China produce results that are consistent with our theoretical conclusions.

In recent decades, the ratio of health spending to GDP has surged in developed country. For example, health spending accounted for only 4% of GDP during the 1930s in the United States. However, the ratio increased to 13.1% during the 1990s and to 14.5 during the 2000s (Tang & Zhang, 2007). Why does the ratio of health spending to GDP increase with economic growth? How does the increase of health spending affect physical capital accumulation and long-run economic growth? The relationship between health spending, physical capital accumulation and long-run economic growth has received a great deal of attention. This paper focuses on the fundamental macroeconomic relationship between health investment/spending, physical capital accumulation, and long-run economic growth. By extending traditional growth models to allow for the consideration of health generation, we study the dynamics of physical capital accumulation and health level, and their effects on long-run economic growth through an economic growth model featuring the Arrow–Romer production function and the Grossman (1972) utility function. The paper contributes to the existing literature on health and growth in two respects: first, we study the effect of health spending/investment and health level on physical capital accumulation and economic growth and find that economic growth is related to both the growth rate of health and the level of health. We also find that the gross effect of health level on the rate of economic growth depends on how it affects physical capital accumulation. If the negative effect of health investment/spending on economic growth through its influence on physical capital accumulation is not taken into consideration, then the health level has a positive effect on growth by improving the efficiency of labor production. However, since health investment may crowd out physical capital investment and thus influence physical capital accumulation, excessive investment/spending in health may have a negative impact on economic growth. We test these theoretical hypotheses empirically using a panel data from individual provinces of China and obtain results consistent with our theoretical conclusions. Second, we find that introducing health level into an economy may lead to the existence of a development trap in the Grossman–Arrow–Romer model, in which case growth will persist only in an economy where initial capital exceeds a certain level, otherwise the economy will get into a negative-growth trap. Thus, countries that differ in their initial states may develop and grow in different ways. As we note below, there is an extensive body of literature, both empirical and theoretical, focusing on the effect of health on economic growth and development. Most of these papers argued that health, as a type of human capital similar to education, will facilitate economic growth by improving labor productivity. However, since better health can provide an individual with additional utility from the consumption of other goods, health will differ from other forms of human capital at least in one respect, that a person purchases medical services not only as human investment but also to maintain “good health,” just as Grossman (1972) emphasized. Therefore, if “health” is a normal good, then health level and/or health investment/spending will continue to increase in the process of economic growth and may crowd out physical capital investment and thus harm economic growth in the long run. This characteristic of health has been noted by Baumol (1967) and van Zon and Muysken, 2001 and van Zon and Muysken, 2003. In a Lucas (1988) endogenous growth model with health investment, van Zon and Muysken, 2001 and van Zon and Muysken, 2003 analyzed this effect of health on economic growth and concluded that a slowdown in growth can be explained by a preference for health that is positively influenced by a growing per capita income, or explained by an aging population, and growth may virtually disappear in countries with high rates of decay of health, low productivity of the health-sector, or high rates of discount. In an Arrow–Romer (Arrow, 1962 and Romer, 1986) endogenous growth model with health investment, this paper considers the effect of health on economic growth in a setting in which health enters the production function as human capital, but also appears as a service in the individual's utility function. Given these assumptions, health level must increase as income increases, similar to van Zon and Muysken, 2001 and van Zon and Muysken, 2003. On the other hand, since higher health level requires higher health investment/spending, an increase in health level may reduce physical capital investment when output is constant. Therefore, increases in health level may harm economic growth if the contribution of health capital to production is insufficient. We test the positive effect of health investment on economic growth using a panel data from individual provinces in China. Our empirical results show that the negative effect of health investment/spending on economic growth is determined by the ratio of health investment/spending to physical capital stock and is statistically significant. In addition, in the case of Arrow–Romer production function, due to the spillover effects of physical capital in the economy, health level may have a spillover effect on economic growth by influencing the returns to physical capital and hence physical capital accumulation. As a result, a development trap may exist in the Grossman–Arrow–Romer model. This result is different from van Zon and Muysken, 2001 and van Zon and Muysken, 2003. During the last 20 years, especially after 2000, a large number of studies were produced that investigated the theoretical relationship between health and growth. A pioneering analytical study in this field is Grossman (1972). However, his study focused on the provision of health services from a microeconomic demand perspective and ignored the possible interaction between health and the process of physical capital accumulation, education investment as human capital, and knowledge accumulation as the driving force behind economic growth. Barro (1996) first studied in a theoretical framework the macroeconomic effects of health as one of the most important components in human capital. In a three-sector neoclassical growth model that incorporated a concept of health capital as well as schooling capital, Barro analyzed the effect of health capital on schooling capital and physical capital and the interaction between these three factors, and further discussed public policy implications in the cases of health services as a publicly subsidized private good and as a public good. By adding a health accumulation function to the Cass–Koopmans optimal-growth model, Muysken, Yetkiner, and Ziesemer (1999) also investigated the growth implications of health as another component of human capital similar to education. Compared with Barro's (1996) static analysis of the impact of exogenous parameters on the steady state, Muysken et al. (1999) further analyzed the impact of optimal health care expenditure on steady-state growth and transition dynamics. However, Barro (1996) and Muysken et al. (1999) only concerned with the effect of health on economic growth through its influence on labor productivity, and neither considered the impact of health services on economic growth through utilities. Extending the Lucas (1988) endogenous growth model to include health investment and taking into account that health services can provide utility, van Zon and Muysken, 2001 and van Zon and Muysken, 2003 discussed the macroeconomic effects on economic growth of health human capital deriving from health investment. Compared with Barro (1996), in addition to the effect of health on labor productivity, van Zon and Muysken, 2001 and van Zon and Muysken, 2003 also considered three other channels through which health influences economic growth: 1) health increases education human capital accumulation; 2) health services increase an agent's utility; and 3) health improvement increases longevity and thus leads to an aging population. While the first two effects of health on labor productivity and education human capital accumulation tend to facilitate economic growth, the last two effects suggest that health investment may exceed the optimal amount when the marginal contribution of health investment to growth equals the marginal cost to growth. This will crowd out too much physical capital investment and harm physical capital accumulation. Accordingly, health investment may in the end impede the progress of economic growth. By introducing the effects of skill-driven technological change (henceforth SDTC) into van Zon and Muysken, 2001 and van Zon and Muysken, 2003, in an endogenous growth model that integrates SDTC, human capital accumulation through formal schooling, and health capital accumulation, Hosoya, 2002 and Hosoya, 2003 investigated the relationships among economic growth, average health level, labor allocation, and population longevity. Compared with van Zon and Muysken, 2001 and van Zon and Muysken, 2003 and Hosoya, 2002 and Hosoya, 2003, this paper also considers the growth effect of health entering the utility function of the individual. Different from the analyses in van Zon and Muysken, 2001 and van Zon and Muysken, 2003 and Hosoya, 2002 and Hosoya, 2003 which extended the Lucas (1988) endogenous growth model, we study the effect of health investment on growth in an extended Arrow–Romer (Romer, 1986) endogenous growth model. Given this difference, in addition to the negative effect of health on long-run growth, we find that introducing health into the Arrow–Romer endogenous growth model may lead to the existence of a development trap, which implies that growth will persist only in an economy with the initial capital above a certain level. In order to explain the real world situation in which rich countries may end up with higher capital, better health, and higher consumption than poor countries, the existence of multiple steady states and of development trap are also important issues in the literature that explores the relationship between health and economic development. Chakraborty (2004) and Bunzel and Qiao (2005) introduced endogenous mortality risk into a two-period overlapping generations model to study the effect of health measured in mortality on economic growth and confirmed the existence of multiple steady states. Hemmi, Tabata, and Futagami (2007) studied the interaction between decisions about financing post-retirement health shocks and precautionary saving motives, and demonstrated that, at low levels of income, individuals choose not to save to finance the cost of post-retirement health shocks. However, once individuals become sufficiently rich, they do choose to save to finance the cost of these shocks. Therefore, this change in individual saving behavior may also give rise to multiple steady-state equilibria and will lead to a development trap. In our paper, we also find the existence of a development trap. However, while the development trap results from multiple steady-state equilibria in Chakraborty (2004), Bunzel and Qiao (2005) and Hemmi et al. (2007), in this paper it is the instability of the steady state that leads to the existence of a development trap, so that countries with different initial states will find themselves in different growth states and the difference between them will be increasing. In the theoretical literature on health and economic growth, there are many other studies that focus on the effect of health in terms of mortality, longevity and fertility on long-run economic development and demographic change (Issa, 2003, Kalemli-Ozcan, 2002, Lagerlof, 2003, Morand, 2004 and Tamura, 2006). The effect of health improvement (by means of longevity, thus leading to an aging population) on economic growth has also aroused the attention of economists in recent years (Aisa and Pueyo, 2004, Aisa and Pueyo, 2006 and Tabata, 2005). Other economists analyzed the effect of longevity on economic growth (Ehrilch and Lui, 1991, Jones, 2001, Zhang et al., 2001 and Zhang et al., 2003). In addition, the status of education and skilled human capital is also considered to be an important channel through which health affects economic growth. Some authors focused on this topic in a theoretical framework (Kalemli-Ozcan et al., 2000 and Howitt, 2005; etc.). Since these studies have little relation to our paper, we do not review this literature in detail. In the literature related to health and economic growth, the empirical studies that examined the relationship between health and income growth or productivity can be classified into three main categories (Jamison, Lau, & Wang, 2005). The first comprises historical case studies that may be more or less quantitative (Fogel, 1994a, Fogel, 1994b, Fogel, 2002, Sohn, 2000 and Strauss and Thomas, 1998). These studies indicate that nutritional improvement is the main force that enhances health capital improvement and hence economic growth in the long term. The second category is characterized by many “micro” studies, which involve either household surveys that include one or more measurements of health status along with other extensive information, or the assessment of the impact of specific diseases. Strauss and Thomas (1998) provided a major review (considerably updated by Thomas, 2001), while Savedoff and Schultz (2000) surveyed methods used in the household studies and summarized findings of recent analyses from five Latin American countries. Recent studies include Liu, Dow, Fu, and Akin (2003) on China and Laxminarayan (2004) on Vietnam. This literature further confirmed that health is positively associated with productivity at the micro level and they are consistent with our assumption that health improvements will enhance labor productivity. The third category, which is much closer to the empirical analysis in this paper, is comprised by a large number of macro analyses of health and growth that mainly rely on cross-national data to assess the impact of measures of health at the national level on income growth rates or investment rates. Cross-country studies go back at least to the first of the World Bank's World Development Reports (WDRs) on poverty (Hicks, 1979, Wheeler, 1980 and World Bank, 1980), with their findings having been suggestive of the importance of health but not definitive. However, more recent studies examined the economic growth effects of health, measured in life expectancy, adult survival rates, adult mortality rates or other indices and all confirmed that health is positively related to growth (Barro, 1996, Bhargava et al., 2001, Bloom and Williamson, 1998, Lorentzen et al., 2005, Mayer et al., 2001, McDonald and Roberts, 2006 and Sachs and Warner, 1997). Bloom, Canning, and Jamison (2004); Bloom, Canning, and Sevilla (2004) surveyed the results of 13 related studies that mostly reach similar quantitative results, and compare them to their own estimation results which come from regressing residual productivity (after accounting for physical capital and education) on health measures in a panel of countries, showing that a one-year increase in life expectancy raises output by 4%. Using a somewhat similar technique, Jamison et al. (2005) estimated that the elasticity of GDP with respect to the adult survival rate is 0.5. Arora (2001) investigated the influence of health on the growth paths of ten industrialized countries (Australia, Denmark, Finland, France, Italy, Japan, Netherlands, Norway, Sweden, and the United Kingdom) using long time series data starting as early as 1870. The causal relationship between economic growth and health was also examined. The results have notably shown that health contributes to economic growth permanently but the same does not hold for the effect of economic growth on health. Casas (2000) surveyed many recent empirical studies on the relationship between health and growth to establish the link between income and health and to find the determinants of health, with a particular focus on Latin American and Caribbean countries. In particular, he discussed the econometric evidence regarding the long-term impact of health on economic growth using cross-country or time series approaches. Compared with the above empirical literature, the empirical analysis in this paper has two distinctive characteristics. First, instead of studying the relationship between economic growth and health measured in life expectancy, adult survival rates, adult mortality rate or other health indices, this paper tests the relationship between economic growth and health investment measured in medical devices and equipment (medical beds). Second, we investigate not only the positive effect of health investment on economic growth represented by the effect of health investment on the per capita growth rate, but also the negative crowding-out effect of health investment that is represented by the effect of the ratio of medical devices and equipment to the physical capital stock on per capita growth rate. The rest of the paper is organized as follows: in Section 2 we present our theoretical model and analyze the relationship between health investment, physical capital accumulation and growth. Section 3 is the empirical analysis testing these theoretical results. In Section 4 we present our conclusions.

In this paper, by extending traditional growth models to allow for health generation, we analyzed the effect of health investment and hence of health level on physical capital accumulation and on long-run economic growth in an economic growth model with an Arrow–Romer production function and a Grossman (1972) utility function. We also tested our theoretical results empirically using a panel data from individual provinces of China and the results of our empirical analysis are consistent with our theoretical conclusions. In the theoretical discussion we indicated that: first, in the short-term, the rate of economic growth is related to both the growth rate of health and the level of health. The growth of health always improves economic growth, but whether the health level improves economic growth depends on whether the productivity effect of health dominates the crowding out effect of health investment on physical capital. If the former dominates the latter, then the health level improves economic growth, and vice versa. In the long run, the trend of increasing health level as the economy grows leads to a slowdown in economic growth. Second, we also find that introducing health into an economy may lead to the existence of a development trap in the Grossman–Arrow–Romer model, so that growth will persist only in the economy with the initial capital above a certain level, otherwise the economy will find itself in a zero-growth or/and negative-growth trap. In the empirical part of the paper we mainly focused on the short-term effect of health level and the health investment growth rate on economic growth. Examining the experiences of 28 Chinese provinces over 25 years in a panel data setting we find that (i) the health growth rate (GPCMB) has a positive and significant impact on economic growth; (ii) health level (PCMB) has a positive and most significant association with economic growth; (iii) the ratio of health to physical capital stock has a negative and significant relation to the rate of economic growth. Thus, it is uncertain whether or not the per capita health level has a positive effect on economic growth. It depends on the relationship between physical capital and health level. All of these results are consistent with our theoretical predictions.