3  Results

3.1  Base case

We begin by analysing the balanced budget scenario. The first thing to note about the stochastic modelling is that even in the absence of risky portfolio returns, volatility in the tax base (GDP growth) has a very strong impact on the volatility of tax rates (see Figure 2). This volatility largely results from the decision not to use the balance sheet to absorb short-run volatility in the tax rate. If the gross debt target were relaxed somewhat this volatility would decline substantially (see Davis, 2001, for an example of banded debt targets in a stochastic environment).

Figure 2 – Balanced budget tax rate

Source: Authors’ estimates

Due to the initial stock of debt, the government needs to run operating surpluses in order to maintain net debt as a constant share of output. The rising expenditure profile requires the median tax rate to increase from the current tax rate of 32% to 41% of GDP by 2050/51 with a 10% probability of the tax rate exceeding 50% at the end of the projection period.

Figure 2 can be compared with the distribution of tax rates under a fifty-year tax smoothing strategy (see Figure 3). The median tax rate is much smoother, only rising slowly through time. The gentle increase reflects the fact that government expenditure is expected to reach and then maintain a higher level for the foreseeable future.[9]

Figure 4 demonstrates the extent of the asset accumulation that occurs under tax smoothing. By assumption, gross liabilities remain at a constant share of GDP implying that the median financial asset portfolio reaches around 107% of GDP in 2051/52. Note also the large variation in net debt levels under different simulations. This volatility is a function of both the size of the asset portfolio and the underlying volatility in returns. Despite this volatility, the two financing strategies generate distributions of tax rates that are quite similar in breadth.

Figure 3 – Tax smoothing (fifty-year moving window) tax rate

Source: Authors’ estimates

Figure 4 – Tax smoothing net debt

Source: Authors’ estimates

Table 1 compares the present value of deadweight loss associated with the two financing strategies. In each case, the deadweight loss is a large percentage of current GDP. These estimates are broadly in line with previous calculations by Browning (1987) and emphasise that the welfare costs of taxation are significant.

However, our estimates of the welfare savings from tax smoothing are higher than previous studies. Using the fixed horizon approach consistent with previous studies, we estimate that tax smoothing generates present value savings of 5.5% of GDP over a balanced budget strategy. This compares with previous estimates of between 0.03% of GDP and 1.0% of GNP. The main reason for this difference lies in the excess return that we assume over the government’s cost of borrowing.

It would not make sense to implement a fixed horizon tax smoothing strategy in practice. Hence the remaining tax smoothing simulations are conducted on a moving horizon basis. Under our base assumptions, we estimate the welfare savings from tax smoothing to be 2.9% of 2000/01 GDP or approximately $3.3 billion. Furthermore since we are applying a 50-year moving window and the expenditure increase is persistent, a substantial pool of assets remains at the end of our assessment period. Thus the benefits of tax smoothing are underestimated substantially since, by construction, those assets would be used to partially fund another fifty years of higher expenditure.

Source: Authors’ estimates

To see how significant this underestimate might be, consider the following rough calculation of the deadweight losses outside the projection period (essentially assuming that expenditure has converged to a long-run rate). The median balanced budget tax rate in 2050/51 is 40.6% compared with 33.9% for tax smoothing with assumed future nominal growth in GDP of 2.8% p.a., thus we have:

DWL Savings ≈ DWL difference * discounted annuity increasing at GDP growth rate

While this underestimate is significant, the rest of the paper is restricted to fifty-year simulations. This is due to the availability of forecast demographic and expenditure paths, and to allow easier comparison with earlier studies of deadweight losses.