Abstract
In this study, we develop a model of overlapping generations where adults make decisions on consumption, fertility, and their personal education. We show that under the assumption of exogenous mortality, there are multiple steady states with club convergence occurring when mortality is sufficiently high. If mortality is sufficiently low, there will be a unique, stable steady state, and the economy will converge to a “good” steady state irrespective of where it starts from. Under the assumption of endogenous mortality with “threshold effects,” we find that club convergence will occur if the threshold is sufficiently high; conversely, a low threshold can help the economy to steer clear of the underdevelopment trap.
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Notes
See Galor (2005) for a survey of the related literature.
Studies concentrating on the effects of the mortality of old agents on economic growth can also be found in Hu (1995), Kalemli-Ozcan et al. (2000), Zhang and Zhang (2001), Boucekkine et al. (2002; Boucekkine et al. (2003), Zhang et al. (2003) and Miyazawa (2006). The impact of the mortality of children on economic growth has also been analyzed by Ehrlich and Lui (1991), Cigno (1998), Kalemli-Ozcan (2002), Hazan and Zoabi (2006) and Azarnert (2006).
A wealth of studies exists on the quality-quantity trade-off of children during the process of economic development. In de la Croix and Doepke (2003; de la Croix and Doepke (2004), for example, overlapping generations models were developed to study the role played by the fertility differential in the linkage between growth and income inequality.
See also Zhang and Zhang (2001); however, Hazan and Zoabi (2006) challenged the conventional wisdom on the quality–quantity trade-off of children by arguing that an increase in longevity would not only raise the returns to human capital investment in children but also the returns to fertility, since each child would live longer.
The traditional studies on fertility issues have usually assumed that parents make decisions both on fertility and on their level of educational investment in their children. The dynamic transition of the economy is governed by the human capital accumulation function, which is positively correlated to parental human capital (see de la Croix and Doepke 2003; de la Croix and Doepke 2004). Under this setting, the children of skilled parents remain skilled, and there is no social intergroup mobility; hence, the composition of the labor market in the next period is determined by the fertility choices of skilled and unskilled parents in the current period. Note that Azarnert (2004) showed that if the spillover effect of human capital was considered in this setting, this would result in the upward mobility of the offspring of unskilled parents. In this paper, we assume that parents make both the fertility choice and their own decisions on education, depending on the mortality rate with which they are faced.
The impact of endogenous mortality on economic growth was examined by Chakraborty (2004), in which mortality was dependent on health capital augmented by public investment, with Fig. 1 showing the existence of a positive correlation between life expectancy at birth and log per capita gross national product.
Since there is no health capital in our model, we assume that mortality is dependent upon capital per worker, reflecting the fact that mortality is lower in developed countries due to higher public health investment (such as better sanitation) than in developing countries; however, there are other ways of endogenizing life expectancy. For example, Castello-Climent and Domenech (2006) assumed that life expectancy was dependent on parental human capital.
Although our model is based on Kimura and Yasui (2007), the focus in this paper differs from theirs, with several necessary modifications having been included. We extend the Kimura-Yasui model by including the probability of survival from adulthood to old age and adding adult consumption into the utility function in order to study the impact of life expectancy on economic growth. As we will see later, the ratios of skilled workers and unskilled workers to the adult population as well as the law of motion of capital per worker will then depend on the life expectancy.
Note that a higher σ is required for a higher x in order for this inequality to hold. Let σ represent the situation when equality holds with x = 1. That is, \(1=-\frac{1-\alpha }{\alpha }\eta (1)\ln \big({1-\mathop \sigma \limits_- } \big)\). Then, a sufficient condition for this inequality to hold for any x is that \(\sigma >\mathop \sigma \limits_- \).
Note that \({v}'\left( x \right)<0\).
As we shall see in the next section, the first case corresponds to the situation where there is a high mortality rate, while the third case corresponds to the situation where there is a low mortality rate.
To explain the existence of the underdevelopment trap, Azariadis and Drazen (1990) assumed that the “threshold effects” of total factor productivity would generate multiple equilibria. Similar step functions were adopted by studies on different issues; see, for example, Galor and Tsiddon (1997) and Vidal (1998).
Note that similar dynamic behavior will also occur if \(\mathop k\limits^- \left( {x_D } \right)<k^\# <k_M^\ast \left( {x_B } \right)\).
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Acknowledgements
The author would like to thank two anonymous referees for their helpful comments and suggestions. The financial support provided by the Program for Globalization Studies at the Institute for Advanced Studies in Humanities at the National Taiwan University is gratefully acknowledged (grant number: 95R0064-AH03-03). Any errors within the paper are the author’s responsibility.
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Chen, HJ. Life expectancy, fertility, and educational investment. J Popul Econ 23, 37–56 (2010). https://doi.org/10.1007/s00148-008-0202-y
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DOI: https://doi.org/10.1007/s00148-008-0202-y