اثرات طول عمر و تحریف در آموزش و پرورش و بازنشستگی

This article studies the impact of longevity and taxation on life-cycle decisions and long run income. Individuals allocate optimally their total lifetime between education, working and retirement. They also decide at each moment how much to save or consume out of their income, and, after entering the labor market, how to divide their time between labor and leisure. The model incorporates experience–earnings profiles and return to education function that follows evidence from the labor literature. In this setup increases in longevity raises the investment in education—time in school—and retirement. The model is calibrated to the US and is able to reproduce observed schooling trends of the last century. It also reproduces the increase in retirement, as the evidence shows. Simulations show that a country equal to the US but with 20% smaller longevity will be 25% poorer, mostly because of the impact of life expectancy on human capital formation and retirement. In this economy labor taxes have a strong impact on the per capita income, as it decreases labor effort, time at school and retirement age, in addition to the general equilibrium impact over physical capital.

One of the most impressive facts of the twentieth century is the large increase of educational attainment of the adult population. In 1990, the median schooling of a male aged 25 years in the US, according to estimations in Gustavus and Nam (1968) based on Census Data, was 6.8 years. By 2000 it had jumped to more than 12 years (Jones, 2002). Even more dramatic is the rise of longevity in the same period. By the beginning of last century life expectancy at birth was, on average, less than 48 years, according to the National Vital Statistics Reports (2002). One hundred years later it was estimated to be 77 years. Although most gains were related to reduction of child mortality, the increase of adult longevity in the same period is very significant. The life expectancy of a man aged 20 years in 1900 was 42.8 years, but in 2000 a man of the same age is expected to die 57.8 years later, a 15 years variation. These two facts may not be unrelated. Greater longevity allows for extension of the population working life and, consequently, an increase in the present value of the flow of wages of a given investment in education. Higher returns to education in turn induce individuals to stay longer in school, increasing average human capital of the population, with a potential effect on long-run income. At the same time, the number of years individuals expend at retirement increased continuously in the previous century. Lee (2001) calculates that the expected period of retirement increased from 2.6 years for the cohort born in 1880 to 13.1 years to the cohort born in 1930. Moreover, labor force participation for man aged 65 and over went from 58% in 1930 to only 16% by 1985 (Kalemli-Oczan andWeil, 2004). In principle this fact does not contradict the link between life expectancy and schooling, as working and retirement lives could have increased with the longevity. However, Gendell and Siegel (1992) estimate that age at final retirement has fallen by 4 to 5 years since 1950, for both man and woman. Median age of retirement for men fell from 66.9 years in 1950–1955 to 62.6 in 1985–1990. More years at school and younger retirement age can only mean shorter career length, something at odds with the idea that longevity influences schooling because it increases the period one can enjoy the return to education investment. In this paper we develop a model that reconcile the above facts. Individuals allocate their total lifetime between education, working and retirement. They also decide at each moment how to divide their time between labor and leisure and how much to save or consume out of their income. The labor/leisure choice is key for the retirement decision. In order to explain, however, why people stop working completely at a certain age and do not spread evenly leisure, the model incorporates experience–earnings profiles that mimics the evidence from the labor literature (e.g., Heckman et al., 2003, among many). At a given moment of a worker life, productivity growth slows down or decreases, so that labor supply falls continuously up to a point when the marginal gain of working is smaller than that of leisure and then individuals leave the labor market for good. In this model, increases in longevity raises investment in education and retirement life, everything else constant. We are then able to explain in an unified framework these two life-cycle observations. The model is simulated after it was calibrated to US observations. We reproduced qualitatively and quantitatively the main facts. Moreover, if productivity in late periods of life decreases faster today than in the past—something that one may infer from estimations across different decades—in addition to rising retirement life we obtain that retirement age falls with longevity. This is so because agents prefer to work more intensively when they are young and relatively more productive, increase savings, and retire earlier.We believe that this article extends and improves the previous literature in many respects. First, as said before, we reunite in a single model two strands of the literature that studies separately, in the context of development and growth, the impact of longevity on schooling and retirement. In Soares (2005), Enrlich and Lui (1991), Kalemli-Oczan et al. (2000) and Boucekkine et al. (2002) longer lives become by definition longer career span and retirement is non-existent. That may be a good hypothesis for the seventeenth and eighteenth century Europe, the period examined by Boucekkine et al. (2003), but certainly not for the US after 1950. Kaboski (2003) allows working life to vary with longevity, but he treats career spans exogenously and calibrate it to the US observed path.1 As opposed to some of the studies above, in our framework schooling and human capital have level effects on per capita income, not permanent growth effects. The evidence in Bills and Klenow (2000) and Krueger and Lindhal (2000) does not favor the latter, nor externality due to human capital. Moreover, the model generates rising schooling as a steady state result, in contrast to Jones (2002). A second literature that relates to ours investigates the links between longevity and retirement. Kalemli-Oczan andWeil (2004) show that exogenous decreases in the probability of death, which allow people to better plan saving for old age, generate longer retirement life. This is a different explanation than ours, which relies on the income-effect due to the longevity-schooling channel and declining productivity, on the individual level, at old age. Their model also incorporates labor–leisure choices, but there is no education decision. As our taxation exercises show, these two dimensions are closely linked. In a sense, our explanation also relates to that in Graebner (1980) that says that technological change leads to retirement because the learning of old people is slower, making then obsolete in periods of faster innovation. In our model there are different learning rates for young and old people, the latter being smaller. However, one needs also longevity effects to explain higher retirement life in the dimension observed in the past. Not to mention, of course, schooling expansion. Finally, we also study the long-run impact of human capital, physical capital and labor taxation. The many decision dimensions—e.g., labor, schooling and retirement—and two sectors of production of our model constitutes a rich general equilibrium environment to explore the transmission mechanisms of public policy. For instance, most articles that use overlapping generations framework ignore labor–leisure decision (e.g., Davies and Whalley (1991); Heckman et al., 1998a, 1998b), reducing the impact of labor tax on human capital in the presence of tuition costs.2 We show that in this framework, labor taxes and taxes on tuition have significant impact on schooling and retirement decision, and hence on income. As opposed to Stokey and Rebelo (1995) and Hendricks (1999) in our model, by construction, taxation do not have growth effect but only level effect. This is similar to Trostel (1993) that, however, ignores life cycle effects as he uses a dynastic framework. It also contrasts with Lucas (1990), who suggests that life cycle effects are not relevant in analyzing the aggregate effects of taxation. Results in this article show that they are qualitatively and quantitatively important.We believe that this article extends and improves the previous literature in many respects. First, as said before, we reunite in a single model two strands of the literature that studies separately, in the context of development and growth, the impact of longevity on schooling and retirement. In Soares (2005), Enrlich and Lui (1991), Kalemli-Oczan et al. (2000) and Boucekkine et al. (2002) longer lives become by definition longer career span and retirement is non-existent. That may be a good hypothesis for the seventeenth and eighteenth century Europe, the period examined by Boucekkine et al. (2003), but certainly not for the US after 1950. Kaboski (2003) allows working life to vary with longevity, but he treats career spans exogenously and calibrate it to the US observed path.1 As opposed to some of the studies above, in our framework schooling and human capital have level effects on per capita income, not permanent growth effects. The evidence in Bills and Klenow (2000) and Krueger and Lindhal (2000) does not favor the latter, nor externality due to human capital. Moreover, the model generates rising schooling as a steady state result, in contrast to Jones (2002). A second literature that relates to ours investigates the links between longevity and retirement. Kalemli-Oczan andWeil (2004) show that exogenous decreases in the probability of death, which allow people to better plan saving for old age, generate longer retirement life. This is a different explanation than ours, which relies on the income-effect due to the longevity-schooling channel and declining productivity, on the individual level, at old age. Their model also incorporates labor–leisure choices, but there is no education decision. As our taxation exercises show, these two dimensions are closely linked. In a sense, our explanation also relates to that in Graebner (1980) that says that technological change leads to retirement because the learning of old people is slower, making then obsolete in periods of faster innovation. In our model there are different learning rates for young and old people, the latter being smaller. However, one needs also longevity effects to explain higher retirement life in the dimension observed in the past. Not to mention, of course, schooling expansion. Finally, we also study the long-run impact of human capital, physical capital and labor taxation. The many decision dimensions—e.g., labor, schooling and retirement—and two sectors of production of our model constitutes a rich general equilibrium environment to explore the transmission mechanisms of public policy. For instance, most articles that use overlapping generations framework ignore labor–leisure decision (e.g., Davies and Whalley (1991); Heckman et al., 1998a, 1998b), reducing the impact of labor tax on human capital in the presence of tuition costs.2 We show that in this framework, labor taxes and taxes on tuition have significant impact on schooling and retirement decision, and hence on income. As opposed to Stokey and Rebelo (1995) and Hendricks (1999) in our model, by construction, taxation do not have growth effect but only level effect. This is similar to Trostel (1993) that, however, ignores life cycle effects as he uses a dynastic framework. It also contrasts with Lucas (1990), who suggests that life cycle effects are not relevant in analyzing the aggregate effects of taxation. Results in this article show that they are qualitatively and quantitatively important.We believe that this article extends and improves the previous literature in many respects. First, as said before, we reunite in a single model two strands of the literature that studies separately, in the context of development and growth, the impact of longevity on schooling and retirement. In Soares (2005), Enrlich and Lui (1991), Kalemli-Oczan et al. (2000) and Boucekkine et al. (2002) longer lives become by definition longer career span and retirement is non-existent. That may be a good hypothesis for the seventeenth and eighteenth century Europe, the period examined by Boucekkine et al. (2003), but certainly not for the US after 1950. Kaboski (2003) allows working life to vary with longevity, but he treats career spans exogenously and calibrate it to the US observed path.1 As opposed to some of the studies above, in our framework schooling and human capital have level effects on per capita income, not permanent growth effects. The evidence in Bills and Klenow (2000) and Krueger and Lindhal (2000) does not favor the latter, nor externality due to human capital. Moreover, the model generates rising schooling as a steady state result, in contrast to Jones (2002). A second literature that relates to ours investigates the links between longevity and retirement. Kalemli-Oczan andWeil (2004) show that exogenous decreases in the probability of death, which allow people to better plan saving for old age, generate longer retirement life. This is a different explanation than ours, which relies on the income-effect due to the longevity-schooling channel and declining productivity, on the individual level, at old age. Their model also incorporates labor–leisure choices, but there is no education decision. As our taxation exercises show, these two dimensions are closely linked. In a sense, our explanation also relates to that in Graebner (1980) that says that technological change leads to retirement because the learning of old people is slower, making then obsolete in periods of faster innovation. In our model there are different learning rates for young and old people, the latter being smaller. However, one needs also longevity effects to explain higher retirement life in the dimension observed in the past. Not to mention, of course, schooling expansion. Finally, we also study the long-run impact of human capital, physical capital and labor taxation. The many decision dimensions—e.g., labor, schooling and retirement—and two sectors of production of our model constitutes a rich general equilibrium environment to explore the transmission mechanisms of public policy. For instance, most articles that use overlapping generations framework ignore labor–leisure decision (e.g., Davies and Whalley (1991); Heckman et al., 1998a, 1998b), reducing the impact of labor tax on human capital in the presence of tuition costs.2 We show that in this framework, labor taxes and taxes on tuition have significant impact on schooling and retirement decision, and hence on income. As opposed to Stokey and Rebelo (1995) and Hendricks (1999) in our model, by construction, taxation do not have growth effect but only level effect. This is similar to Trostel (1993) that, however, ignores life cycle effects as he uses a dynastic framework. It also contrasts with Lucas (1990), who suggests that life cycle effects are not relevant in analyzing the aggregate effects of taxation. Results in this article show that they are qualitatively and quantitatively important.The article is organized as follows. In the next section we present the model and briefly discuss the hypothesis of exogenous life expectancy. Section 3 discusses calibration and measurement issues. Results concerning the link between education and retirement, in the one side, and longevity, in the other, are presented in Section 4 while sensitivity analysis, focusing mostly on distortions are presented in Section 5. Section 6 concludes.

In this paper we have studied a finite life economy in which higher life expectancy explains increases in schooling and retirement, and plays an important role in the determination of longrun income. This role could only arise because of the hypothesis of finite life and the Mincerian formulation of human capital, which seem to us the most realistic assumptions. When calibrated to the US experience during last century we reproduced education levels, and showed that a 20% difference in longevity, everything else constant, would lead to a 15% gap in per capita income. The mechanism of the model that allows for retirement are, in addition to the labor–leisure choice, an experience profile that mimics the parabolic shape estimated by studies in the labor field. As productivity decreases or slow down at old age, at certain point of life the marginal gain of working is below that of leisure, and people leaves the job market. Longer lives allows people to enjoy proportionally larger retirement. If, on top of that, productivity profile jumps up so that young people learn relatively faster, or if it decreases faster at old age, we obtain that retirement age falls, replicating the evidence. The sensitivity analysis and tax simulations showed that life-cycle aspects are very important to the study of public policy and the allocative effect of taxation. Once schooling and retirement decisions are incorporated to the analysis, and career span is finite, labor taxation and, in a lesser extent, human capital taxation have significant effects on the long-run level of per capita income and on variables such as labor supply, retirement and physical capital investment. The literature on the physical capital taxation, however, is much more extensive than that on human capital taxation, although there are important exceptions, most of them using endogenous growth models. One possible reason is that taxation on human capital in many models is neutral, as it decreasesits return but also the cost of being out of the labor market. However, our results show that if there are any other costs imposed on the acquisition of education which are not proportional to wages (e.g., tuition), the long-run impact of any form of taxation on human capital—either direct on tuition or indirect on wages—is relevant.