امید به زندگی، بازنشستگی و رشد درونزا

In this paper I address the links between life expectancy, retirement age and economic growth. I build a finite horizon OLG model with exogenous retirement in which human capital accumulation drives endogenous growth. The return on individual investment in human capital depends positively on the remaining active years. Postponing retirement age raises the return and investment in human capital, and the proportion of working individuals, thus increasing the sustainable growth rate. Increments in life expectancy do not increase the growth rate by themselves, but reduce it: optimal investment in human capital is not affected and the proportion of retirees becomes larger. Therefore, increases in life expectancy lead to higher growth rates only if they are accompanied by simultaneous increments in the working period.

‘Life expectancy alone is one of the strongest explanatory variables of growth in GDP’, World Health Organization. In this paper I address the issue of how life expectancy and retirement age are linked to economic growth. To this end I build a finite horizon OLG model with exogenous retirement in which human capital accumulation drives endogenous growth and which I solve numerically. The issue of the effects of the reduction in mortality rates and the resulting increases in life expectancy upon economic growth rates has recently been addressed in the literature through both empirical and theoretical studies. Concerning empirical studies, the hypothesis that the reduction in mortality rates has caused higher levels of investment in human capital and, therefore, augmented growth rates is partially supported for various economies. Thus, Kalemli-Ozcan et al. (2000) show an increase in life expectancy at birth along with an increase in average numbers of years of schooling in England. They claim that after averaging across lower income countries, there is apparently a connection between increases in life expectancy at birth and increases in gross secondary school enrollment that is positively connected with higher growth rates observed.1Rodrı́guez and Sachs (1999) also show a positive relationship between life expectancy and growth for the case of Venezuela. Preliminary data from Latin American and Caribbean countries show that GDP growth is statistically associated with life expectancy: for instance, estimates based on data from Mexico suggest that for any additional year of life expectancy there will be an additional 1% increase in GDP 15 years later. ( World Health Organization, 1999, Box 1.2, p. 9). Barro and Sala-i-Martin (1995) estimate for a sample of 97 countries that a 13-year increment in life-expectancy would increase the per capita growth rate by 1.4% per year, although they also find some exceptions. 2 Malmberg (1994) gives another exception: higher growth was achieved when middle-aged persons were numerous, whereas increases in dependent age groups led to lower per capita growth in Sweden. A common result in most theoretical studies which include some sort of human capital is that an increase in life expectancy lengthens the period needed to recover investment in human capital, which translates into higher returns on individual education or human capital investment. This augmented return will give rise to higher levels of investment in human capital which in turn will raise growth rates. Ehrlich and Lui (1991) show in a three overlapping generations model how improvements in longevity lower fertility, thus raising educational investment and long term growth. In a similar setup Meltzer (1995) obtains that mortality reductions may favor economic growth by increasing educational investment. Kalemli-Ozcan et al. (2000) show in an overlapping generations model à la Blanchard–Yaari that if mortality drops, life expectancy increases, so that an augmented life horizon to enjoy the return on human capital investment gives rise to higher schooling (human capital investment), although growth is not affected as the growth rate in their model is identically equal to zero. In a similar setup, Hu (1995) simulates that the projected population aging in the US is likely to increase the growth rate of output by approximately 0.4%. In this case, the interpretation is that population aging increases saving, and thereby capital accumulation. In a slightly modified model, Hu (1999) reaches the same result: demographic changes leading to population aging can have a positive growth effect on the economy because they induce an increase in human capital investment. De la Croix and Licandro (1999) also take the Blanchard–Yaari model as the starting point. They build an economy in which there is no physical capital (an AH economy), and where individuals accumulate human capital as a function of the optimal length of the schooling period that they choose. The effect of lower mortality rates upon growth turns out to be ambiguous as three effects follow: (i) individuals die later on average, thus the depreciation rate of aggregate human capital decreases: (ii) agents tend to study more because the expected flow of future wages has risen, and the human capital per capita increases; but (iii) the economy consists of more old agents who completed their schooling a long time ago. The first two effects have positive influence on the growth rate, but the third a negative one. 3 A similar result can be found in Reinhart (1999), but this time through a different channel as only physical capital is assumed. In a Blanchard–Yaari type model he shows that longer life expectancy generates higher growth: if the mortality rate goes down, individuals discount the future less so that savings (and physical investment) increase, thus raising the growth rate. Futagami and Nakajima (2001), however, obtain the opposite result. In a finite horizon OLG model (again, without human capital), they show that higher life expectancy increases growth: even though higher life expectancy causes a lower savings rate (for a given growth rate), in equilibrium the growth rate must be higher because the growth rate has a strong positive effect on the savings rate. Uhlig and Yanagawa (1996) pose a different issue, but one can use their OLG model with only physical capital to answer the question that I am dealing with here. 4 By simulating their model it can be shown, nevertheless, that an increase in the number of periods of life (and/or the number of active periods) might result either in higher or in lower growth rates depending on the parameterization of the model. 5 The model that I use here draws on Nerlove et al., 1993 and Echevarrı́a and Iza, 2000: a finite horizon OLG model in which individuals are allowed to invest in human capital, and into which the economy's productivity or knowledge enters as an externality in the stock of human capital with which individuals are endowed at birth and in the individual production of human capital. The private return on individual investment in human capital at any age before retirement depends positively on the remaining active years. Consequently, postponing the retirement age raises the return and investment in human capital; additionally, the proportion of working individuals in the society is enlarged. Therefore, the sustainable growth rate becomes higher. Increments in life expectancy at birth do not increase the growth rate by themselves, however, but reduce it: the optimal investment in human capital is not affected and the proportion of retirees becomes larger. This is in line with a commonly accepted view: if life expectancy increases, the ratio of retirees (dissavers) to workers (savers) goes up, so the aggregate saving rate falls and so do accumulation in physical capital and growth. In short, increases in life expectancy at birth cause higher growth rates only if they are accompanied by simultaneous increments in the working period. In the light of this simple model, I believe that the theoretical reasoning often used in the literature to explain how a higher life expectancy gives rise to a higher level of economic growth through human capital arguments must be rephrased. When one considers infinite horizon models à la Blanchard–Yaari, for instance, there is usually no room for retirement age. Therefore any increase in life expectancy represents an enlarged working period, thus increasing the return on human capital investment. But when finite horizon economies are considered instead, the existence of a retirement age becomes essential to characterize the return on human capital investment. Increments in life expectancy by themselves do not necessarily cause changes in human capital investment. The growth rate might even turn out to be lowered as explained above. The argument might perhaps be right for models in which there is no retirement (so that the last active period coincides with the last period alive) and for less developed economies in which retirement takes place late in individuals’ lives (because they keep on working as long as they are physically capable). In this case, improvements in food and health conditions lead to higher life expectancies and longer working periods. The paper is organized as follows. Section 2 sets up and solves the model: the individual problem (Section 2.1), the aggregates of individual choices (Section 2.2), the production side (Section 2.3), and the characterization of the steady state growth rate (Section 2.4). Section 3 sets out and discusses the values assigned to the parameters in the model. Section 4 shows the results for the benchmark model (Section 4.1), and presents some sensitivity analyses (Section 4.2). Section 5 concludes. A mathematical appendix is included at the end of the paper (Appendix A).

In this paper I address the issue of how life expectancy and retirement age are linked to economic growth. I start from empirical evidence and theoretical literature that shows a positive correlation between life expectancy at birth and per capita growth rate. I build a finite horizon OLG model in which human capital accumulation drives endogenous growth. The return on individual investment in human capital depends positively on the remaining active years. Consequently, postponing retirement age raises the return and investment in human capital; additionally, the proportion of working individuals in the society is enlarged. Although the working population also becomes older on average (which tends to reduce the average human capital in the economy), the sustainable growth rate becomes higher. Increments in life expectancy at birth do not increase growth rate by themselves, however, but reduce it: the optimal investment in human capital is not affected and the proportion of retirees becomes larger. In short, increases in life expectancy at birth cause higher growth rates only if they are accompanied by simultaneous increments in working period. I believe that the theoretical reasoning often used in literature to explain how a higher life expectancy gives rise to a higher level of economic growth through human capital arguments must be rephrased. When one takes infinite horizon models à la Blanchard–Yaari, there is no retirement age. Therefore any increase in life expectancy represents an enlarged working period, thus increasing the return on human capital investment. But when finite horizon economies are considered instead, the retirement age becomes essential to characterize the return to human capital investment. Increments in life expectancy itself need not cause changes in human capital investment. Even the growth rate might turn out to be lowered, as explained above. The argument might perhaps be right for underdeveloped economies in which retirement takes place late in individuals’ lives (because they keep on working as long as they are physically capable). In this case, improvements in food and health conditions lead to higher life expectancies and longer working periods. 27 Given the crucial role played by the retirement age, I strongly believe that a promising line for further research would be one which would endogenize the retirement age (e.g. Boucekkine et al., 2002) as there is empirical evidence that workers choose their retirement to some extent in response to, for instance, social security incentives. (See Coile and Gruber (2000) for the US case and Gruber et al. (1999) for several countries’ economies.)