In many developed countries, fertility rates are in decline and longevity is increasing. While greater longevity is cause for celebration, a growing elderly population increases the overall demand for expanded social security programs, particularly those pertaining to long-term care services. By considering and measuring the care burden per capita, we show that an increase in the fertility rate can improve household utility, even though it reduces the wage rate. The findings of this analysis imply that improvements in the fertility rate are desirable, as it eases burdens relating to long-term care services, as well as those relating to public pension plans.
In many developed countries, fertility rates are declining and longevity is increasing. On the face of it, greater longevity is cause for celebration; however, a growing elderly population also increases demand for expanded social security programs, particularly those pertaining to long-term care services. It is very important that society, at the very least, meets the demand for minimum necessary long-term care services for the elderly.
Let us take a look at actual data showing what and how much individuals consume, by age, in Japan and the United States, two highly developed countries.
ducted by Japan’s Ministry of Internal Affairs and Communications.
These figures show that in both Japan and the United States, elderly people spend more on healthcare services than those in any other age group. For all goods except those in the clothing and footwear, transportation and communication, and education categories, consumption by elderly people in Japan is somewhat lower than but approximating that of people in their forties. In the United States, elderly people spend less money than 35 - 44-year-olds on apparel and services, education, tobacco products and smoking supplies, and personal insurance and pensions, but more than 35 - 44-year-olds on reading and cash contributions, and about the same on other goods.
Thus, when considering the problems posed by an aging population, it is very important for us to bear in mind differences between elderly people and the general population, in terms of the kinds of things they consume. Groezen, Meijdam, and Verbon [
However, not all elderly people can purchase sufficient long-term care services; economically disadvantaged elderly people who cannot save enough money to buy the services they need are forced to depend on government services. A full 90% of spending in the elderly nursing system in Japan is financed not just by insurance premiums paid by individuals over 40 years of age, but also by public funds from the national and local governments; users are charged for only 10% of the costs. Even so, because their savings cannot adequately cover expenses in their old age, many elderly people cannot purchase even the most essential of long-term care services (hereafter, “minimum necessary long-term care services”). Many believe that for these individuals to receive the minimum necessary long-term care services, the government should finance all related costs by using tax monies.
The provision of minimum necessary long-term care services requires the hiring of a sufficient number of long-term care workers. Long-term care workers must receive wages equal to those of workers in the business sector, because if the wages of long-term care workers are lower, no workers will choose to work in the long- term care sector. Thus, the government must work to make the wages of long-term care workers on par with those of business workers, by using tax-rate adjustments―just to provide elderly individuals with minimum necessary long-term care services. This, however, increases the tax burden on the working generation, in a society in which the number of children (and therefore the number of future caregivers and taxpayers) is decreasing.
As the number of children in a society increases, the per-capita tax burden drops; however, wage rates decrease, as does the capital-labor ratio. The combination of these two factors prompts us to ask whether there is a case in which, although an increase in the number of children lowers the average wages, it also decreases the per-capita burden of long-term care services, such that there is an overall improvement in the utility level. Furthermore, since an increase in the number of children reduces the per-capita tax burden―thus allowing individuals to increase their amounts of consumption―could this improve the utility level? The present study aims to explore these possibilities by using a simple overlapping generation model and considering fully the current, relevant issues.
A considerable body of literature relates to the care industry. Scholars such as Sandmo [
Nevertheless, although many scholars have analyzed the problems inherent in the care industry, few other than Groezen, Meijdam, and Verbon [
The remainder of this paper is organized as follows. The model and a numerical example are presented in section 2, and section 3 summarizes our discussion and presents topics that require further study.
In this section, we develop an overlapping generational model. Here, it is assumed that the lifetime of a household is divided into three periods: a youth period, a working period, and a retirement period. After some uncontrollable amount of consumption in the first period of life, in the second period, households of generation t work; bear
ber of required long-term care workers,
workers in competitive firms, and others are employed as long-term care workers. The total number of workers
in firms,
long-term care workers into the total number of workers in the firm, the number of workers in firms becomes
Firms produce consumption goods. In each period, the capital stock is the sum of households’ savings in the
preceding period:
average values.) The capital stock lasts for only one period and has zero scrap value in the subsequent period.
The initial capital stock (
Each of them owns
In each period, the Cobb?Douglas technology is employed for production, using two inputs: physical capital
The government imposes a care tax
equally them. The budget constraint for this system is
workers; the government adjusts the care-tax rate to ensure that the wage rate of care workers is comparable to
that of firm workers. The adjusted care tax endogenously becomes
rate of care workers equal to that of firm workers. The equated wage rate is defined as
workers to the tth generation people is
number of care workers becomes
kers, the ratio of firm workers becomes
The firm workers and care workers have the same utility function. For analytical convenience, we assume the utility function to be additively separable and logarithmic, as follows:
Where X = L or H,
tion
The budget constraints become
where
comes
optimal savings also become identical. Using the optimal savings, the wage rate and the optimal savings become constant:
where
utility function:
By differentiating equation (4) with respect to
Thus,
what is more, since
The condition of equation (7a) implies that an increase in the number of children per household can increase the wage rate, if the opportunity-cost rate of bearing a child is sufficiently high.
Next, let us focus on the effects of an increase in the number of children on the household’s steady-state utility level. These effects can be calculated by differentiating the indirect utility function with respect to n:
where
The condition of equation (9) implies that an increase in a household’s number of children can increase its utility level, if the opportunity-cost rate of bearing a child is sufficiently high; this implies children are relatively valuable.
A comparison of the condition of equation (7a) with that of equation (9) shows that:
because
Let us now focus on the relationship between the number of children and household utility. The first term of the right-hand side of equation (8)―which implies the effects of an increase in the number of children on the individual disposable income rate―becomes positive(negative) if the number of children is less(more) than
The level of utility depends not only on the wage rate, but also on the disposal rate―the latter of which can be directly increased through a decrease in the burden of care that stems from an increase in the number of children. However, the wage rate can be only indirectly increased by an increase in the disposal rate that stems from an increase in the number of children. Thus, while an increase in the number of children tends to reduce the wage rate, it also tends to increase the utility.
The variables are given as reasonable parameters, and we explicitly present the situation in Japan. We present in
According to the exogenous variables in
this model (
National Lifestyle” (2007), the cost of raising a child is JPY13.02 million, and the additional costs of a second child are JPY10.52 million. The cost of raising 1.41 children is directly calculated as a weighted average: JPY12.00 million. The opportunity cost of raising children is JPY227.32 million3. In this case, the total direct and indirect cost of raising children becomes JPY239.32 million, which represents 27.42% per child of a house- hold’s total income (male university graduates: JPY342.60 million; female university graduates: JPY276.45 million) (“Basic Survey on Wage Structure,” 2003). This implies
Exogenous Variable | Value |
---|---|
Preference to consume in the working period ( | 0.54 |
Preference to consume in the retirement period ( | 0.46 |
Capital share rate ( | 0.3 |
Labor share rate ( | 0.7 |
Number of children per household | 1.29 |
Necessary number of long-term care workers per surviving elderly persons | 0.04 |
Variable | Value |
---|---|
0.03 | |
0.97 | |
?0.03 | |
23.47 | |
0.05 |
A comparison of the values of
It is generally accepted that in Japan, the demand for long-term care workers will drastically increase in the future. If the necessary number of long-term care workers per person aged 65 were to increase to 0.1, we would
have
grown 10-fold relative to present figures, an improvement in the fertility rate would definitely increase the utility level but nonetheless reduce the wage rate, assuming that the cost of raising children remains the same as that at present
In this study, we analyzed the effects of an increase in the number of children on an economy where having a sufficient number of care workers is ensured. An increase in the number of children can reduce the wage rate but increase household utility, even if the burden per capita of caring for the elderly was sufficiently small. A nume- rical example for the case of Japan was also calculated; that example implied that the government should support households in having more children―through the provision of subsidies or other supports―so as to ease the burden of long-term care services provision that is placed on the working generation. This applies not only to long-term care services, but also to the pressures being placed on public pension plans (e.g., Groezen, Leers, and Meijdam [
To analyze the effects of an increase in the number of children on household utility when only the minimum necessary long-term care services are produced, we examine the exogenously given number of children per person. Under normal conditions, however, the number of children per person is a household choice variable; as such, it is not exogenously given. Thus, we should consider a model where a household endogenously choose sits number of children, and the government supports it through child allowances or similar instruments; under such conditions, households could increase their number of children, if they so desired.
Financial support for this study was provided through a Grant-in-Aid for Scientific Research (No. 25380370). The author is grateful to Professor Hirobumi Akagi (Meijyo University) for helpful comments. Any remaining errors are the author’s responsibility.