B3.2 The Effect on Savings
Let us investigate the impact of tax reform on savings. A reduction of T1 directly increases an individual’s saving. However, if r > n, the decrease in T1 reduces T and hence indirectly reduces her or his saving. However, considering (9.B50), we have
Hence, the direct effect of T1 is always greater than the indirect effect of T1: An individual’s saving is raised irrespective of the sign of r-n. The lump sum tax reform (T1 ! T2) increases the saving of the existing younger generation j + 1 and the future generation.
This may be called the (permanent) tax timing effect. This tax reform imposes a tax liability later in the life cycle. As a result, taxpayers tend to increase their saving early in the life cycle in order to meet the additional tax liability later in the life cycle.
The impact of this tax reform on generation j’s saving depends upon whether a member of generation j anticipates this tax reform in period j or not. If an individual of generation j does not anticipate the reform, her or his saving is unaffected by the tax reform. If she or he anticipates the reform, an increase inTJ2+1 raises Tj and hence increases sj. This may be called the (temporary) tax timing effect.
Because of the tax reform, the saving function of future generations moves upward. Hence, the tax reform stimulates capital accumulation during the transition path. The new long-run equilibrium capital/labor ratio, kL1, is greater than the initial long-run equilibrium ratio, kL0. Thus, the tax reform (T1 ! T2) stimulates capital accumulation in the long run.
If a member of generation j anticipates the tax reform, generation j’s saving is greater than the level indicated by the initial saving function. This leads to an extra initial capital endowment to generation j + 1. Thus, generation j’s extra saving stimulates capital accumulation during the earlier transition process. Note that this temporary tax timing effect disappears in the long run.
B3.3 The Welfare Effect of Tax Reform
We now explore the welfare aspect of tax reform during the growth process. Let us examine the effect of tax reform on the utility of each generation j + i, uj+j (i = 0, 1,2, ...). If the tax reform is to increase T2 and reduce T1 from period j + 1 on, uj definitely decreases. This is because of the direct tax reform effect.
Moreover, if a member of generation j does not anticipate the tax reform, uj reduces further. The effect on the future generation j + i (i = 1,2, ...) depends upon the tax postponement effect and the temporary and permanent tax timing effects. If r > n, the tax postponement effect is favorable for the future generation.