Adult age starts at age 20 for households without a college degree, and at age 22 for households with a college degree. The age of retirement is set to 65 for all households. The investor dies with probability one at age 100. Prior to this age we use the mortality tables of the National Center for Health Statistics to parameterize the conditional survival probabilities, r for j = 1,…T. We set the discount factor B to 0.96, and the coefficient of relative risk aversion 7 to 5. In variations of the benchmark case, we also consider investors who are extremely impatient with B = 0.80, comparatively risk-tolerant with 7 = 2, and extremely risk-averse with 7 = 10.
To estimate the labor income process we follow CGM (1998). Here we briefly describe the data and estimation method.
The estimation controls for family-specific fixed effects. To control for education the sample is split into three groups: households without high school education, a second group with high school education but without a college degree, and finally college graduates. This sample split is intended to accommodate the well-established finding that age profiles differ in shape across education groups (Attanasio 1995, Hubbard, Skinner and Zeldes 1994). For each education group the function f (t, ~t) is assumed to be additively separable in t and Zit. The vector Zit of personal characteristics, other than age and the fixed household effect, includes marital status and household composition. Household composition equals the additional number of family members in the household besides the head and (if present) his spouse.
Ideally one should also control for occupation. Using PSID data this is problematic because from the 1975 wave onwards the majority of the unemployed report no occupation, and are categorized together with people who are not in the labor force. But modelling unemployment as a switch in occupation is inappropriate as the possibility of unemployment through layoff is one of the main sources of labor income risk. We explore this in greater detail in Section 4 below.
Next-period liquid and retirement wealth are then given by:
where fu is a binary variable which equals zero until the investor pays the fixed cost of entering the stock market and equals one thereafter, and — it+г is the return on the portfolio held from period t to period t + 1:
Here a^t is freely chosen when fu = 1, and equals zero when fu = 0.
After retirement (t > К), the problem takes the same form except that retirement wealth no longer accumulates. Instead, it is annuitized and provides riskless income A(W^). After-tax labor income (1 — 9)Yit in (9) and (10) is replaced by A(W^).
We model a system of mandatory saving for retirement in the following simple way. During working life the individual must save a fraction, W, of current labor income as retirement wealth. Under this assumption disposable labor income, Yt, is given by:
The amount WYt is added to retirement wealth, denoted by. During working life retirement wealth is illiquid; the individual cannot consume it or borrow against it. At age К retirement wealth is rolled into a riskless annuity, so that the individual receives in each of the retirement years the annuity value corresponding to W^. This assumption of riskless annuitization affects the portfolio choices of older investors. An interesting extension of our work would be to allow investors to choose between riskless and variable annuities.
We will consider several alternative systems governing the investment of retirement wealth during working life. In the first system the individual is forced to hold retirement wealth in riskless assets. This implies that W^ = B|?, where B|? is the dollar amount of retirement wealth investor i has in riskless assets. In alternative systems retirement wealth is partially or fully invested in risky assets, but the allocation remains constant over time and is not controlled by the investor. We interpret this as the social security administration managing the individual’s retirement account. For this reason the fixed cost of investing in stocks applies only to investments outside the retirement account.
We let t denote adult age. The investor is adult for a maximum of T periods, of which he works the first К. For simplicity К is assumed to be exogenous and deterministic. We allow for uncertain life-span in the manner of Hubbard, Skinner and Zeldes (1994). Let r denote the probability that the investor is alive at date t + 1, conditional on being alive at date t. Then, investor i’s preferences are described by the time-separable power utility function:
where Си is the level of date t consumption, 7 > 0 is the coefficient of relative risk aversion, and B < 1 is the discount factor. We assume that the individual derives no utility from leaving a bequest.
If the household is constrained from borrowing to finance risky investments, the solution may be a corner at which the portfolio is 100% risky assets. If labor income is risky but uncorrelated with risky financial assets, then riskless asset holdings are still crowded out but less strongly; the portfolio tilt towards risky assets is reduced (Viceira 1997). If labor income is positively correlated with risky financial assets, then risky assets can actually be crowded out, tilting the portfolio towards safe financial assets.
Under the assumption that income shocks are uncorrelated or only weakly correlated with stock returns, these results suggest that households who expect high future labor income—discounted at some appropriate rate and measured relative to financial wealth—should have the strongest desire to hold stocks. In a life-cycle model with a realistic age profile of income, the discounted value of expected future income increases relative to financial wealth in the very early part of adulthood, but peaks fairly early and then declines as workers approach retirement. This suggests that fairly young (but not the very youngest) households are the most likely to be affected by borrowing constraints that limit their equity positions. While empirical evidence on household portfolio allocation is fragmentary, a few recent empirical papers have found that household portfolios over the life cycle have hump-shaped equity positions, and U-shaped positions in safe assets, consistent with the message of the theoretical literature (Bertaut and Haliassos 1997, Heaton and Lucas 1997b, Poterba and Samwick 1997).
Two different sorts of constraints are potentially relevant. First, a household may be unable to borrow at the riskless interest rate to finance equity investments (Con-stantinides, Donaldson, and Mehra 1998). Second, a household may face fixed costs of equity market participation; if these fixed costs exceed the benefit of participation, the household may hold no equities (Abel 1998). These constraints may affect different households differently. The first constraint is particularly likely to bind on a household whose unconstrained optimal equity position is particularly large, while the second constraint is particularly likely to bind on a poor household with little total wealth. These different sorts of households may be differentially affected by a Social Security reform that alters portfolio constraints.
During the past few decades, American households have begun to display increasing financial sophistication and awareness of rates of return on alternative investments. At the same time the implicit rate of return on contributions to the Social Security system has declined as the system has matured; and this rate of return is projected to decline further in the 21st Century in response to unfavorable demographic trends (Geanakoplos, Mitchell, and Zeldes 1998). Unsurprisingly, politicians and the public have become interested in the possibility of moving to a privatized system in which retirement contributions earn market-based rates of return.
Unfortunately, it is not straightforward to compare alternative retirement systems. Three important issues affect the comparison and invalidate simple rate-of-return calculations. First, the return on the current system is low in part because of the overhang of unfunded liabilities. Past generations have received a gift that must be paid off before the economy can enjoy the steady-state benefits of any new system. Second, capital income taxation puts a wedge between pre-tax and after-tax rates of return. Welfare calculations should take account of the tax revenue generated by capital accumulation (in some systems, this tax revenue is forgiven and private retirement accounts earn higher pre-tax rates of return). Third, returns on alternative financial assets can differ if these assets have different risk characteristics. A valid comparison of rates of return must adjust for risk.
The greatest legacy a child would have from his parents in particular and the nation in general is education. It is surely an investment to man. Among other things, if quality education is given to the recipients, higher levels of attainment would be achieved and the education industry would attract high rate of recognition.
Environment for learning must be stable and should there be positive changes, it then shows that meaningful learning is taking place. Such changes must mean that classrooms are adequate and reflect the standard specified. Class size must the stipulated number, every child should have the opportunity of owing a chair and a table and be comfortable during lessons.
Facilities need to be maintained regularly to ensure a longer life span. If facilities are well secured, vandalism by the community will not occur. Enough funds are indispensable if standard specifications are to be implemented.
a. Average class size for both public and private secondary schools exceeded the stipulated number of students as approved by the National Policy on Education. Federal and state Ministries of Educations and UNESCO, However, students are more in the public than in the private schools.
b. The urban and rural schools exceeded the maximum number of student in the class as approved by the National Policy on Education, Federal and state Ministries of Education and UNESCO. A high average class size was recorded in the urban schools than the rural schools.
c. There are more furniture in the urban schools than in the rural schools. It is pertinent to note here that most schools in rural areas have still not conformed with the approved 4 seater bench and tables but still have their normal table and chair per student. However, following the result still, not every child has a chair and a table. Moreso, most of the public schools still maintain the one table and chair per student.
d. The major factor militating against implementation of standard specifications in both public and private schools is insufficient fund for the provision of facilities.
The maintenance practice carried out in the public/private urban and rural schools is mainly the curative type.