2  Analytical framework

2.1  Efficient public finance

Economic efficiency is usually defined in terms of welfare. In the area of public finance, a key source of excess burden is taxation. Due to their involuntary nature, taxes create incentives for taxpayers to substitute away from taxed activities toward activities that are not taxed, or are taxed at lower marginal rates. If the taxed activities would otherwise be worthwhile, the substitution reduces welfare. It follows that society would benefit if taxes were levied in a way that minimises the welfare costs of taxation.

Barro (1979) first demonstrated that governments should minimise the excess burden associated with taxation by smoothing tax rates over time. This result arises because welfare costs are thought to increase (decrease) by more than the proportionate rise (fall) in the tax rate. While Barro constructed his argument in a deterministic framework, Lucas and Stokey (1983) and then Bohn (1990) demonstrated that the tax smoothing result generalised in a stochastic environment to smoothing tax rates over time and across states of nature. Bohn (1990) highlighted the role for financial instruments in insuring against state-contingent shocks to the primary balance.

The implication for fiscal policy is that, by smoothing taxes, the government can minimise the present value of deadweight losses. We follow Browning (1987) in approximating the deadweight loss function by:

(1)

τ _t is the marginal rate of labour income tax; Y_t the aggregate labour income at time t; and ε the compensated net-of-tax wage elasticity of labour supply. With a discount rate r, the present value of the excess burden, , is used to assess the relative efficiency of alternative financing strategies.

Our theoretical approach is to estimate H(τ) with aggregate data. Browning (1987) notes that, if all households are confronted with the same marginal tax rate and had the same labour supply elasticity, this approach will yield accurate results. However when marginal tax rates and/or elasticities differ, this approach will understate the excess burden. The degree of understatement increases with the dispersion in marginal tax rates and/or elasticities.

Furthermore we treat all income as labour income. This also biases our excess burden estimates downwards because marginal deadweight losses for capital income taxes are thought to be higher than for labour income taxes. We use the ratio of total taxes to GDP (that is, an aggregate average tax rate) as our measure of the marginal tax rate. This too biases down our estimates since the aggregate marginal tax rate is higher than the aggregate average tax rate.

Equation (1) may give estimates that overstate the true welfare cost. First, Browning’s partial equilibrium approach assumes that the marginal value product of additional hours worked, and therefore the gross wage rate, is constant. The degree to which this assumption biases the results depends on the elasticity of the marginal product curve relative to the labour supply elasticity. Browning argues that the demand elasticity is high relative to the labour supply elasticity. It follows that the degree of overstatement is small.

Second, if the actual compensated labour supply curve is convex instead of linear, then the excess burden measured using equation (1) overstates the true excess burden. An alternative approach is to use a compensated labour supply function that exhibits constant wage elasticity. Whether a constant elasticity specification over or understates the true welfare cost is unclear. The available evidence provides little basis for determining an appropriate form for compensated labour supply. For this reason, we test the sensitivity of excess burden estimates to changes in the functional form.

2.2  Modelling methodology

While in theory it is efficient to smooth the burden of taxes over time, in practice, and with few exceptions, governments do not tend to follow strategies that resemble tax smoothing (Alesina and Perotti, 1994). One hypothesis that might be formed from this observation is that the quantitative benefits of smoothing taxes are insignificant. Alternatively, one might suppose that there is something in tax smoothing that renders it impractical or economically costly in practice. We consider the former issue in Section 3 and leave the latter to Section 4.

Previous estimates of the welfare costs of alternative financing strategies, in the face of demographic-related expenditure growth, have found the gains of tax smoothing over balanced budget to be insignificant. In a study for the United States, Cutler et al (1990) write, “the change in the present value deadweight loss between 1990 and 2060 is 1% of 1990 GNP” (page 49). In a similar study for Denmark, Jensen and Nielsen (1995) find that the difference in the present value of deadweight losses between the two strategies “accounts for only about 0.03% of GDP in 1993” (page 17). For New Zealand, Dahanayake (1998) estimates that “the maximum gain of tax-smoothing [using a 40-year fixed horizon] over balanced-budget is only about 0.87% of projected [2007/08] GDP”.[4]

While our modelling approach is similar to these previous studies there are some important differences:

• Endogenous Labour Supply - we make total hours worked endogenous to account for the substitution effect of taxes on labour supply. This adjustment is implicit in Browning’s formulation of the excess burden but is overlooked by other studies.
• Moving Horizon - we employ a moving-horizon (fixed smoothing period length) in our tax-smoothing simulations.[5] This has the effect of generating a rising tax rate over the next fifty years, irrespective of the financing strategy.
• Stochastic Productivity Growth - we model labour productivity growth as a stochastic process. This has the effect of making nominal GDP growth and tax revenue stochastic, while maintaining the LTFM’s hypothesised negative relationship between population ageing and economic growth.
• Government Investment in Risky Assets - we assume that the government invests primary surpluses in assets that are expected to earn returns in excess of the government’s cost of borrowing. Importantly, this excess return is not without risk since returns are modelled stochastically. The risk/return properties of the financial portfolio are allowed to vary with the government’s choice of asset allocation.

Other aspects of our approach are more conventional. For example, we start by assuming that the government’s expenditure profile is exogenous. This assumption is partially relaxed later in the paper. The expenditure profile is obtained from Treasury’s LTFM (see Woods, 2001, for an overview of that model). Tax rates are determined using deterministic GDP forecasts rather than stochastic ones. This avoids making the unrealistic assumption that the government has perfect foresight. Finally, for the tax smoothing scenarios, the tax rate is determined as the rate that is expected to return net debt to its initial level (relative to GDP) at the end of the smoothing period.[6]