The Impacts of Population Aging on Saving, Capital Formation, and Economic Growth

The evolving population aging scenarios of the industrialized countries can be attributed to two major demographic dynamics: the declining fertility and fast aging population. The increasing old age dependency ratio, decreasing young dependency ratio, and shrinking share of working-age population in the aging economies generate substantial impacts on individual as well as aggregate consumption, saving and employment. Because retired people save less, an aging society with increasing proportion of retirees would experience a decline in aggregate savings, which in turn leads to lower capital formation and reduces economic growth. This paper focuses on the effect of population aging on aggregate saving, physical capital formation, and economic growth in Japan. The current study theorizes the effect of aging demographic dynamics on savings and capital formation. Taking into account the effects of population dynamics, saving, and capital formation together, this paper steps further in examining the implications of population aging for economic growth and discusses policy implications for the aging economy.


Introduction
The evolving population aging scenarios of the industrialized countries can be attributed to two major demographic dynamics: the declining fertility and fast aging population. The increasing old age dependency ratio, decreasing young dependency ratio, and shrinking share of working-age population in the aging economies generate substantial impacts on individual as well as aggregate consumption, saving and employment. Since retired people save less, an aging so-gether with the latest population projection made by National Institute of Population and Social Security Research (IPSS), Japan. Figure  is the historical data adopted from Statistical Bureau of Japan and to its right is the forecasted series taken from National Institute of Population and Social Security Research, Japan. In this graph, a data labeled with suffix "H" signifies historical data (e.g., POPH) and data labeled with suffix "F" represents forecasted series.
The left panel of Figure 1 indicates that Japanese aggregate population had reached its climax around 2010. However, the working age population, people with age 16 to age 64, had already reached its peak circa 1995 (see AGE1564H in the right panel). The right panel of Figure 1 also shows that the number of young-age population (AGE0014) has been shrinking rapidly while the old-age people (AGE65up) has increased rapidly between 1950 and 2010. The size of old-age population will continue to increase up to the time circa 2050 and decline  Various studies have examined the implications of these evolving demographic dynamics in Japan. Some addressed aging effect on saving behavior (Horioka [1]; Iwaisako and Okada [2]); others focused on its labor market effects (Ito [3]; Ogawa et al. [4]), and some others investigated overall macroeconomic effects of population aging in Japan (e.g. Muto et al. [5]). Razin et al. [6] and Bloom et al. [7] investigated the implications of population aging on social welfare and old-age health care. Of all these published works, one issue that has not been fully investigated is the effect of demographic transition on capital accumulation and its consequence on labor productivity and economic growth.
Therefore, the current paper wishes to bridge the gap and focuses on the macroeconomic effect of population aging on capital formation and economic growth in the aged economy.
It is recognized that capital accumulation enhances overall quality of the nation's workforce and thus contributes to economic growth and national competitiveness. The effect of aging population on capital formation is an issue worth exploring. In order to have a better understanding of the dynamic interactions among various macroeconomic variables, this paper use Japan as an example to explore the effects of population aging on national saving, and thus national saving on capital formation and economic growth.
This research adopts data from National Tax Agency of Japan, Penn World The remainder of this paper is organized as follows. Section 2 reviews previous literatures of population aging, saving and economic growth. Section 3 illustrates the specification of theoretical model and methodology employed in this study. Section 4 presents the major findings of this work and discusses policy implications drawn from this study. Section 5 draws conclusions from this study and presents extension to discuss policy implications from this research.

Literature Reviews
The research interest of this study focuses on the effects of demographic struc- to support that hypothesis. Higgins [10] found that youth dependency ratio and old dependency ratio are significant determinants of saving rate in a sample of 100 countries. Higgins' investigation coincided with much of the prior literatures surveyed in Ando and Modigliani [9] and Horioka [1] in which demographic transition has substantial effects on national savings rates in Japan and United States, so that it predicted that Japan's saving rate would decline sharply in the coming decades due to rapid population aging. However, Iwaisako and Okada [2] argued the monotonic trend of population aging alone can't explain the nonlinear movement in Japanese household saving rate, though household saving rate showed accelerated decline after the economic crisis in 1997-1998 as We have reviewed the literature on the effects of population aging on national saving; we proceed to review literatures exploring the correlation between saving and economic growth. The acknowledged theoretical investigation of the effect of saving on economic growth dated back to Harrod [13], Domar [14] [15], and Solow [16]. Given that aggregate output is the function of physical capital and labor inputs, these models proposed that economic growth depends on saving rate and that higher saving rate contributes to higher economic growth. In the exploration of source of economic growth, the extended model incorporated one demographic variable, population growth rate, and investigated the effect of population growth on economic growth. However, in these growth models population growth rate is assumed to be positive and constant. Neither a negative growth rate of the population, nor a shift in the age structure is considered in these models. Over the later decades, studies of economic growth model have extended previous works by taking into account additional factors, such as technology, human capital, urbanization, institutions, openness to international trade, and geographic factors, in the determination of economic growth. 2 Most recent development in growth theory, the endogenous growth theory whose pioneer studies are Romer [24], Lucas [25], and Rebelo [26], considers saving rate as one of the key determinants of economic growth. It predicts that an increase in the saving rate will lead to a permanently higher growth rate.
However, these empirical studies on the relationship between economic growth and savings have not reached unanimous conclusion, due to their difference in the methods, periods of study, and countries being selected for studied. Miller rates, while the effect of old-age population on saving is less conclusive. For example, Braun et al. [32] found the Japanese demographic factors account for the decline in Japan's national saving rate in the 1990s. Bloom et al. [33] demonstrated the demographic dividends of the working-age population for economic growth. Li et al. [11] examined the effects of demographic structure on economic growth by using 29 provincial panel dataset in China and found that the old age dependency ratio has a positive effect on savings, investment, and economic growth rate. Bloom et al. [7] argued population aging will lower labor force participation and savings rates, which leads to decline in economic growth.

Model Specification and Methodology
According to Harrod [13], Domar [14] and Solow [16], saving is a key driver to economic growth. The current study investigates the effects of population aging on economic growth based on the idea of the life-cycle hypothesis of Modigliani where t Y is aggregate output or gross domestic product (GDP); A denotes a "Hicks-neutral" technological progress. The input factors, t K and t N , represent physical capital and labor, respectively. α and 1 α − are the partial production elasticities of physical capital and labor and they are also the shares of physical capital and labor in income. Economic growth is determined by the growth of three elements: technological progress (A), physical capital ( t K ) and labor input Taking natural logarithms of (2) and calculating the first difference, one obtains growth rate of output per capita: Equation (3)  In Solow's model, saving contributes to the accumulation of the physical capital stock which increases the labor efficiency of production. However, the saving rate in Solow's model is assumed to be constant over time. According to life-cycle hypothesis (LCH) individual saving varies with age; the empirical data from "Family Income and Expenditure Survey" of Japan also shows that saving and consumption is age-dependent. As a result, it would be confidently to take household head as a representative individual in the economy and relate his/her age to income and expenditure at different ages. Figure 2 illustrates the profile of income and expenditure of the average household at different ages in 2018. The figures shown in Figure 2 are yearly average of monthly income and disbursements per household of various age groups in 2018, which is adopted from Japanese Family Income and Expenditure Survey of Two-or-more-person Households. 4 Although income and expenditure may differ across years due to economic fluctuations, both series reveal a common pattern across age groups. That is, both income and expenditure are hump-shaped which increase with ages up to age 55 and decline thereafter. A young representative household The data series is available at: https://www.e-stat.go.jp/dbview?sid=0002070011.  Comparing with other years, 2018 is the year that people save more out of their income. However, the saving behavior of a typical household head at different ages shows similar saving pattern across years. Moreover, young people tends to have a higher APS than the middle-aged and the elders. In 2018, the young cohort (age 34 and less), though has the lowest income comparing to the other middle-age cohorts, has the highest saving rate which is 34.2%. When people approaches retirement age of 55, APS increases slightly and then drops sharply around age 60. In 2018, the APS for the retiree cohort (age 60 -64) is only 9.1%, whereas the APS of this age cohort is less than 3% in the previous three years.
From the Japanese household survey data one observes that both household's income and expenditure reveal an inverted U-shape. One also notices that the Japanese household saving rates decrease with age, up to the middle-age around age 50 -54, and then increase while approaching to the brink of retirement age  Rewrite Equation (4), one obtains saving per capita ( t t S N ) which is a function of relative share of each age group to total population ( it t N N ). That is, Furthermore, saving rate per capita can also be expressed as a function of relative age composition of each age group to total population: In order to capture the impact of demographic structure change on saving rate, one can express aggregate saving rate, t s , alternatively as: Equation (7) states that aggregate saving rate is the sum of two products: age-specific saving rate ( it s ) and share of age i 's income to aggregate income ( it where 0 1 it β < < and Income per capita can also be written as a function of the population's age structure: where t Y is GDP (total income), t N is total population, it Y is total income by age i , it y is the average income of age i cohort, and is the number of ( ) population growth rate (n) and the second is the saving rate (s). In Solow's model both rates are assumed to be constant and exogenously given. In this paper both rates are assumed to be determined by demographic transition and vary over time as population structure changed. The behavior of saving rate in this model has been illustrated in (7), here we introduce the determination of population growth rate at time t: where b t is the crude birth rate and d t is the crude death rate; both b t and d t are determined independently from contemporaneous economic factors. As a consequence, n t is the net rate of increase in total population at time t. There is no immigration in this specification.
The model system used in this study consists of four equations which are summarized as followings:

Empirical Estimation and Simulations
It has been shown that population aging alters age composition of the population which in turn affects labor supply and physical capital formation. This section investigates the dynamic correlation among population age structure, saving, capital accumulation, and GDP growth. In the demographic aging process, the size of labor force in the economy shrinks as the age structure of total population changed. Moreover, according to the life cycle hypothesis, people at old age save less than the middle ages. Therefore, the empirical model includes demographic factor in the context of saving, capital accumulation and economic growth estimation.
The simulation exercise uses the medium variant population projections, 2016-2065, made by National Institute of Population and Social Security Research in Japan as baseline population input for calibration. 6 Model calibration and validation has been conducted for years 2016 to 2065.
Based on the LCH, old-age people save less than that of the prime-age working population. As a result, one would expect that increasing share of old age population in the economy would lead to a decline in average saving per head. Figure   4 illustrates the time path of the simulated scenarios of GDP, capital stock, aggregate saving ( t S ), saving per capita ( t t S N ) and the corresponding growth of American Journal of Industrial and Business Management  Figure   4), which do not conform to the prediction based on the LCH proposition.
However, as population aging evolves both the rate of change in aggregate saving and per capita saving decrease remarkably. One notices that both rates of change in aggregate and per capita saving decrease drastically, drop from roughly 28% to 5% in 10 years. After 10 years, both rates keep decreasing, though only decrease mildly, and then stagnate around 1% in the long-run. The simulated results also indicate that saving rate ( t t S Y ) also decreases with population aging ( Figure 5). The simulated saving ratio declines from 0.205 in 2018 to 0.18 in 2065, and stagnates around that rate in the long-run. Therefore, on significant finding of this paper is that the simulated results from this paper confirm that population aging will lead to a decline in the saving rate and saving out of current income, not the aggregate level of saving predicted by LCH.
The baseline model indicates that, absent from any counteracting force to deter the effects arising from population aging, per capita output growth and hence the living standard per capita (1st row in Figure 4) in Japan will experience modest decline in the decades to come. Given these alarming scenarios, we are interested in exploring possible policy measures that can be used to mitigate this alarming development.
This paper considers two different saving behaviors of the aging economy and their effects on GDP growth: 1) Being concerned about the reduction in future income, people may save more while they are still working. Therefore, the first experiment considers an increase in saving rate of all age groups. 2) While all age groups may increase their savings, which age group's saving has the most prominent effect on GDP growth?
The effects of increasing saving rates of all age groups have positive effect in promoting output growth ( Figure 6). However, the effect of continuous increases   per annum by 1% yields more prominent effect than a one-time increase of 3%.
However, in order to enjoy the long-run fruit of improved GDP growth, resulting from saving increase, people has to endure a short-run suffering of declined economic growth. The simulated scenarios in Figure 6 show that there is approximately a five-year period of downfall in growth rate due to increased savings before people can enjoy higher economic growth.
Current savings inject to future capital stock and hence increase future economic growth. However, which age group's saving has contribution that is more noticeable than the other age groups? The young workers? The middle-age working group? Or the late middle-age working group? This paper conducts a simulation on the effects of increasing savings in four age groups: the young workers aged 20 -24; the prime age cohort of the labor force aged 35 -39 and 45 -49, and the group who is nearing retirement, namely, workers aged 60 -64.
The simulated results in Figure 7 indicate that a same percentage increase in the saving ratio of the prime working-age population generates most impressive effects on GDP growth than that of the other age groups. This result may not be surprisingly because income of this cohort is higher than that of the other age cohorts, so that the volume of income saved injects more to capital stock and yields more output in the future. Therefore, our model shows that a continuous increase in saving rates generates obvious effects on capital formation and output growth, especially for the prime saving age cohorts (Figure 7).
Population aging leads to a reduction in the working age population and a increase in the dependent elder population. Although the demographic development of population aging inevitably leads to a reduction in future economic growth, the shrinking volume in labor force may countered by improvement in productivity. A final experiment of this paper considers the effects of technological  advancement or productivity growth on economic growth in the aging economy.
The simulation experiments consider a one-time jump of technology and continuous improvement of production technology. Comparing the scenarios of baseline and alternative productivity advancement hypothesis, it is noticeable that a steady continuous technological advancement can produce prominent improvement on GDP growth than that of either one-time technological jump or no productivity progress cases (Figure 8).

Discussions and Policy Implications
This study explores the impact of population aging on saving and physical capital accumulation in Japan. The effect of population aging on economic growth has been investigated via two channels, the labor productivity channel and labor supply channel. The current study concentrates on the first channel that illustrates how population aging affects the capital accumulation, capital intensity and multi-factor productivity. This study also performs various hypothetical experiments trying to identify factors that can be used to compensate for the negative effect of declining labor supply resulting from population aging.
The life-cycle hypothesis maintains that an individual's life time income and Moreover, the growth effects of total factor productivity are larger than the effects of saving rate in the future. 7 In view of the LCH, it comes as no surprise that the impacts of saving rate of young age and old age population are small.
In the current study, we distinguish between the young, prime and old age populations according to LCH. The results imply that the ongoing aging process is expected to adversely affect the economy. Though the growth effects of separate saving rates are small, the overall higher saving rates of all age groups have the potential to give rise to economic growth. Measures to encourage continuous increase in saving rate of the prime age population or whole economy can mitigate the adverse effects of population aging on GDP growth.
Labor shortage due to population aging is a challenge to economic growth in the aging economy. From the demographic prospective, this challenge is the result of falling fertility and lengthening of longevity. To mitigate the adverse im- welfare, such as increases in child care facilities and make direct subsidies or tax rebates to child bearing, and wish these measures may work to increase fertility.
However, parenting involves many unforeseeable opportunity costs and requires both mental and physical perseverance to raise the young siblings; government policy encouragement may not produce enough incentive to increase fertility.
Even if the government could effectively promote the fertility rate, its effect to economic growth can only be effective sixteen years later when the newborn siblings grow up and are suitable to undertake physical works. Therefore, a more reasonable measure to mitigate the challenge is to improve the labor market efficiency to increase labor force participation rate and to create old-age friendly employment environment so that encouraging re-entry of the healthy retirees to the labor market. Additional policy measures to postpone the mandatory retirement age can also be used, so that the healthy elders can stay longer in the labor market.
Another important policy measures in the aging economy is to improve total factor productivity to counter the adverse effect on economic growth arising from shrinking labor input. The simulation experiments in this study have shown that increase in total factor productivity has more prominent effect on economic growth than encouraging saving and capital formation. Policy measures that encourage research and development (R&D) to promote innovation and technological progress may be the most useful and viable measures to mitigate the adverse effect of population aging on economic growth. Moreover, increasing human capital formation is also an important policy measure because it improves labor quality and productivity, so that the adverse "volume" effect of population aging on labor force can be partially offset by the improvement in the labor productivity.