3.2  Alternative cases

In this section we consider the impact of varying our underlying assumptions. Not surprisingly, the aggregate excess burden is most sensitive to the discount rate.

3.2.1  Compensated Labour Supply Elasticity

We re-estimate the results (reported in Table 2) with a range of elasticities between 0.2 and 0.5.

For higher elasticities, a number of the balanced budget simulations do not have solutions.[10] This is because projected government expenditure exceeds the revenue-maximising tax rate for some simulations.[11] In comparing the relative efficiency of the financing strategies, it is necessary to exclude the simulations for which there are no balanced budget solutions. This biases the median statistics downwards.[12] Importantly, the extent of the bias will be worse for balanced budget, underestimating the savings from tax smoothing reported in Table 2.

Source: Authors’ estimates

3.2.2  Labour Supply Functional Form

If the compensated labour supply is not linear, the welfare cost equation takes a different form. As an alternative, we model a constant elasticity labour supply where the relationship between labour supply and the wage rate is given by . The corresponding deadweight loss function is:

(2)

Source: Authors’ estimates

We can see from these results that the potential overestimate of the excess burden from assuming a linear labour supply curve is minimal (at least at an elasticity of 0.3). In fact, the saving over balanced budget is actually estimated to be larger in the constant elasticity case.

3.2.3  Expenditure profile

In the absence of rapidly increasing per capita health and superannuation costs, the question of how best to finance public expenditure would be much less important. The tax profiles associated with the balanced budget and tax smoothing strategies would be less distinct. For this reason, we consider alternative expenditure paths (low and high growth in health and education) and compare the results with those under the base case.[13] Figure 5 illustrates the sensitivity of the expenditure profile, and the tax smoothing tax rates, to variations in the real per capita expense growth.

The difference in median tax rates is marked. Under the high growth scenario, expenditure grows throughout the entire projection period to reach 42% of GDP in 2050/51. With low expenditure growth, public spending peaks at just under 35% of GDP before beginning a slow decline around 2040.

Source: Authors’ estimates

Figure 5 – Median tax smoothing tax rates for various expenditure paths

Source: Authors’ estimates

Table 4 demonstrates the effect that these alternative expenditure profiles have on deadweight losses. Under the high growth assumption, the adjustment to taxes under a balanced budget strategy is more severe which tends to favour the tax smoothing strategy. On the other hand, low expenditure growth requires a smaller adjustment to taxes. However, even under the low growth scenario the benefits of tax smoothing remain significant.

3.2.4  Discount Rate

We re-estimate the results (reported in Table 5) with a range of discount rates between 1.5% (that is, 0% real) and 7.2%.

Unsurprisingly, the deadweight loss savings associated with tax smoothing are highly sensitive to the discount rate, and reduce quite sharply as r increases. However, we are sympathetic to the arguments of Caplin and Leahy (2000) and others who maintain that individuals discount the future too much and that governments should employ a lower discount rate for the purposes of welfare analysis than individuals would choose in determining their utility from future consumption. This result is derived from changes in individuals’ preferences as they age (changes that individuals do not anticipate). Therefore, for the purposes of policy analysis, we would tend towards applying a lower, rather than higher, discount rate than our base case.

Source: Authors’ estimates