# The Human Capital Effect

Imagine that labor income Y_{2} is now available in the second period as well. Then, the impact of interest income tax on saving may be modified. The second period budget constraint is rewritten as

With the interest income tax, the lifetime budget constraint is now rewritten as

I

Since interest income tax reduces the discount rate for future labor income, the present value of labor income increases; namely, through the presence of t_{s}, the present value of future labor income Y2/(1+r) is modified to Y_{2}/[1+r(1 — t_{s})], which increases with t_{s}.

This effect raises current consumption while reducing saving. This is called the human capital effect. Note that current labor income Y_{1} is not affected by interest income tax. Considering the relation s = Y_{1} — c_{1}, current consumption and saving move in the opposite direction.

# The Cobb-Douglas Utility Function Revisited

For example, with regard to the Cobb-Douglas utility function, current consumption depends upon the present value of labor income. When labor income occurs only in period 1, this value is independent of the interest rate; thus, the interest rate does not affect labor supply. The substitution effect completely offsets the income effect. However, if labor income appears in the second period as well, the interest rate is included in the discount rate for future labor income. As a result, owing to interest income tax, the after-tax interest rate evaluates second-period labor income more than before, raising the present value of labor income and hence stimulating current consumption. In other words, even if we assume the Cobb-Douglas utility function, or a separable utility function, interest income tax has a depressing effect on saving.

Mathematically, suppose that the Cobb-Douglas utility function is again given as

Then, considering Eq. (8.13), it is now optimal to allocate income between c_{1} and c_{2 }as follows:

Thus, the saving function is now given by

which is a decreasing function of interest income tax, t_{s}. If Y_{2} = 0, the saving function is given as (8.12), which is independent of interest income tax, t_{s}. In contrast, if Y_{2} is positive, an increase in t_{s} raises the present value of Y_{2}, stimulating c_{1} and depressing s.

Generally speaking, a reduction of interest income tax may promote capital accumulation. Since the substitution effect offsets the income effect to some extent, the overall effect is ambiguous.

Boskin (1978) pointed out that for the US economy, the substitution effect is likely to dominate the income effect; thus, a reduction of interest income tax could stimulate capital accumulation. Although empirical studies after Boskin’s paper have not necessarily supported his conjecture, we can obtain a similar result if we incorporate the human capital effect into the analysis appropriately. See the advanced study of this chapter for a more detailed analysis.