رتبه بندی درآمد و همگرایی با سرمایه فیزیکی و انسانی و نابرابری درآمد

This paper presents an overlapping generations model with physical and human capital and income inequality. It shows that inequality impedes output growth by directly harming capital accumulation and indirectly raising the ratio of physical to human capital. The convergence speed of output growth equals the lower of the convergence speeds of the relative capital ratio and inequality, and varies with initial states. Among economies with the same balanced growth rate but different initial income levels, the ranking of income can switch in favor of those starting from low inequality and a low ratio of physical to human capital, particularly if the growth rate converges slowly.

This paper presents an overlapping generations model with income inequality originating from innate ability, and endogenous accumulations of physical and human capital, in the presence of spillovers from average human capital. It focuses on three related questions. First, how does growth interact with income inequality when investments in physical and human capital are endogenously chosen? Second, how does the economy converge when income inequality adjusts in one dimension and the ratio of physical to human capital adjusts in another? Third, and foremost, can catching-up and even overtaking in income ranking occur among economies sharing the same balanced growth rate but starting from different levels of per capita income? With the two-dimensional adjustment mechanism, our model sheds light on these questions as follows. Due to the spillovers from average human capital, the earnings of children increase with the earnings of their parents at a diminishing rate within families, and regress to the intragenerational mean value of earnings over time. Thus, income inequality converges to its long-run level. If inequality is initially high, then the growth rates of average human capital and average output are initially low, given an increasing and concave function describing the education technology. The resulting high ratio of physical to human capital further impedes output growth under the standard assumption of diminishing marginal products. Moreover, the increased ratio of physical to human capital tends to raise the wage rate per unit of effective labor but lower the interest rate, thereby tending to accelerate growth in average human capital relative to growth in average physical capital in transition. Eventually, the ratio of physical to human capital converges to its long-run level. The speeds at which income inequality and the ratio of physical to human capital converge differ from each other in general in this model. Along the balanced path, the lower of the two speeds sets the convergence speed for the growth rate of output per capita. Outside the balanced path, the convergence speed of the growth rate varies over time, depending on the gap between initial and steady states in terms of income inequality and the ratio of physical to human capital. If initial inequality and the initial ratio of physical to human capital are all conducive to (harmful for) economic growth, they reinforce each other for an extra push (drag) compared to cases without inequality or without an adjustable ratio of physical to human capital. The high (low) growth rate can remain above (below) normal for generations, particularly when the growth rate converges slowly. Consequently, the ranking of income levels per capita can change among economies sharing the same balanced growth rate but having different initial states, in favor of those starting with low inequality and a low ratio of physical to human capital. This paper differs from the existing literature on capital accumulation and income distribution in some important ways. The existing models typically describe their dynamics by a one-dimensional locus, without the joint evolution of income inequality and the ratio of physical to human capital that we consider here. For example, many of them focus on capital accumulation, and bypass the issue of income inequality by assuming representative agents (e.g. Lucas, 1988). Those that also consider the interaction between growth and income inequality assume either one type of capital or a constant ratio of one type of capital to another (e.g. Tamura, 1991, Glomm and Ravikumar, 1992, Eckstein and Zilcha, 1994, Persson and Tabellini, 1994, Benabou, 1996 and Zhang, 1996). These extended models usually find a negative effect of income inequality on output growth as in our model. But unlike our model, they could not capture the indirect negative effect of income inequality on output growth via raising the ratio of physical to human capital. Also, the convergence speed of the growth rate in the existing studies with a one-dimensional adjustment mechanism is constant (e.g. Barro and Sala-i-Martin, 1992 and Ortigueira and Santos, 1997). However, the empirically estimated convergence speed of the growth rate of per capita GDP varies across samples for different times or different regions, with the OECD countries converging faster than other countries, as seen in Barro and Sala-i-Martin (1992), Mankiw et al. (1992), and Bernard and Jones, 1996a and Bernard and Jones, 1996b.1 Some recent studies show varying speeds of convergence over time and across sectors, by noting the role of technology change. Eicher and Turnovsky, 1999 and Eicher and Turnovsky, 2001 obtained that result by using a two-sector growth model with accumulations of both physical capital and knowledge, where the sectoral technologies are of the non-scale type, due to Jones (1995). With productivity shocks in a neoclassical growth model, Den Haan (1995) showed that a given cross-section of income levels cannot be expected to converge in the same manner at every point in time and for every set of countries. In contrast to these studies, we obtain varying speeds of convergence by considering the distribution of income and the accumulations of physical and human capital. In our model, if the convergence speed of output growth is equal to the convergence speed of income inequality, public programs designed to mitigate inequality through spreading skills to the whole population, such as public schooling, can accelerate the convergence of both inequality and output growth. Thus, the reason the OECD countries converge faster than others may arise from their greater provision of public education according to our model. Finally, the existing growth models with a one-dimensional locus only allow partial catching-up in income levels among economies sharing the same balanced growth rate, in the absence of country-specific shocks and multiple equilibria. For example, in the neoclassical or endogenous growth models without inequality, the partial catching-up could occur when an economy starts with relative abundance in human capital or effective labor. On the other hand, incorporating inequality into a growth model with only one type of capital, the partial catching-up could occur when an economy starts with low inequality. In the real world, however, income ranking changes from time to time, arising from miraculous growth in some countries along with stagnant development in some others (see e.g. Abramovitz, 1986, Lucas, 1993 and Jones, 1997). Our model captures this pattern of income ranking change for economies that share the same set of preferences and technologies but start from different income levels. The rest of the paper is organized as follows. Section 2 introduces the model. Sections 3 and 4 provide analytical and numerical results, respectively. Section 5 concludes.

This paper has developed a two-sector growth model with life-cycle saving, human capital investment, and income inequality, where global convergence is achieved through adjustments in both inequality and the ratio of physical to human capital. The results of this two-dimensional adjustment mechanism have gone well beyond a simple sum of those in the one-dimensional adjustment cases. We have shown that higher inequality has not only a direct negative effect on output growth through decelerating growth in average human capital, but also an indirect negative effect through raising the ratio of physical to human capital. The increased ratio of physical to human capital raises the wage rate per unit of effective labor and reduces the interest rate, thereby tending to encourage human capital accumulation in transition. Eventually, the ratio of physical to human capital converges to its steady state level. The convergence of inequality hinges on the presence of spillovers from average human capital. On the balanced path, the convergence speed of output growth is equal to the lower of the convergence speeds of inequality and the ratio of physical to human capital, whereas in transition the convergence speed of output growth varies with initial conditions and over time. In particular, when inequality convergence sets the pace for output growth to converge, the convergence speed depends on education regimes, and can thus explain why the OECD countries that have provided better public access to education have converged faster than other countries. Finally, rapid or stagnant growth can occur so that income ranking can alter in short horizon among economies that share the same balanced growth path, complementing approaches that may generate income ranking change by considering country-specific uncertainties, country-specific technologies or multiple equilibria. The policy implication of this result is positive: poor countries can catch up with, or even overtake, their rich counterpart by reducing inequality and promoting human capital formation.