Measures of Efficiency and Welfare

In the process of raising revenue and redistributing income, taxes generate distortions to behaviour which mean that the full economic cost of raising an additional dollar of tax revenue is greater than a dollar. This can be measured by the marginal cost of funds (MCF), or deadweight loss (DWL), or excess burden of tax concepts. Finding empirical measures of these concepts for income taxes and transfers is not straightforward however, and typically requires a variety of assumptions about individuals' behaviour and/or application of microsimulation modelling techniques.[8] The New Zealand Treasury (NZT) does not currently have such a model and hence must assess the efficiency and welfare impacts of taxes using simpler methods.

Key components of such modelling are methods to account for the fact that different individuals may have differing preferences and face different, non-linear budget constraints that influence their labour supply and other responses to income taxation. These cannot readily be factored into tax policy evaluations without a fully specified model. However the existing literature provides a number of guiding principles.

Firstly, an approximation for the excess burden for a linear income tax is proportional to the square of the marginal tax rate.[9]The New Zealand tax system is much more complex than the simple linear case, with several tax thresholds and rates, giving rise to a piecewise-linear budget constraint. Also, means-tested transfer payments such as Working for Families, WfF, lead to non-convexities in the budget set. However, the simple ‘square of the tax rate’ approximation points to the need to recognise that the efficiency losses associated with increases in marginal tax rates are non-proportional. Secondly, the labour supply literature has identified a number of groups that might be expected to be especially responsive or unresponsive to changes in effective tax rates. Thirdly the literature on tax avoidance responses by taxpayers also points to some key margins likely to give rise to efficiency losses, such as divergences between the relevant personal and corporate tax rates or the impacts of progressive personal income tax scales on income splitting among taxpayers.

Since the abbreviated welfare function includes both the average income level and the degree of equality (one minus the degree of inequality), it can be used to provide a simple comparison of different tax structures, as captured by their impacts on mean incomes (efficiency) and on equality. For example, a tax change that involves an increase in inequality (either the Gini or the Atkinson index) from 0.2 to 0.25, implies a proportionate change in equality of (0.75 - 0.8)/0.8 = -0.0625. As a result, for social welfare, W, to improve, the tax change must also be associated with an improvement in mean incomes of at least 6.25 per cent. If efficiency gains are unable to generate such an improvement, the tax policy would be evaluated as harming social welfare. This evaluation depends on the inequality measure used and, in the case of the Atkinson index, the aversion to inequality, ε, and hence cannot be made without first specifying the relevant value judgement.

The abbreviated social welfare function can also be used to measure the ‘welfare premium’ associated with a particular tax or tax change. The welfare premium is the welfare in excess of that arising from a (hypothetical) proportional tax which raises the same revenue. In the present context, with a tax and transfer system in place, we can think of the proportional system as applying to taxes plus transfers. That is, the welfare premium compares the welfare of the current tax-transfer system with one in which current tax revenue net of transfers is distributed in proportion to pre-tax-and-transfer income. Lambert (1993) showed that the welfare premium, P, can be measured as:

Or, normalising by mean income:

where I is the chosen inequality index, such as the Gini or Atkinson measure, that is compatible with the abbreviated social welfare function. However, this exercise also assumes that mean income is unaffected by the fiscal changes.

One issue for policy advice emerging from the above concerns the question of whether the methods of generating social welfare changes in association with tax changes, such as those derived from microsimulation models, provide a suitably transparent and reliable method of evaluating reform. Given the need to value leisure and model labour supply and other responses, specify utility and social welfare functions, and make inequality aversion judgements, such methods can appear to policy-makers as too opaque or unreliable. An alternative approach would be to seek to measure efficiency aspects, for example via excess burden approximations, and inequality aspects of tax reforms separately, but which identify the trade-offs and value judgements required for policy choices.

For example, Figure 1 shows a trade-off between efficiency and inequality outcomes of two alternative hypothetical policies compared to the status quo, for differing inequality aversion judgements (represented by Index1 and Index2). For such comparisons to be useful requires a suitably comprehensive efficiency measure and an inequality measure that is not too sensitive to the particular choice of index.

Figure 1 - Equity-Efficiency Trade-offs

In Figure 1, Policy 1 could involve a reduction in a top marginal rate that improves efficiency but at the cost of reduced equality (relative to the status quo; the size of the reduction depending on inequality aversion). Policy 2 - such as an increase in a social welfare transfer - could involve the opposite choice - improved equality and worsened efficiency. The impact of inequality aversion on the equality outcomes, captured by Indices 1 and 2, need not be the same for both policy options.