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1 Introduction

The concept of the excess burden arising from the introduction of a tax or a tax change - loosely speaking the excess of the welfare loss over the extra revenue raised - is central in public finance analysis. In discussions of tax efficiency (in economic rather than administrative terms), the excess burden and associated concepts are crucial.[1] Yet there have been few attempts to measure excess burdens in New Zealand. And all previous attempts to measure the excess burden of income tax have been at a high level of aggregation.

The present paper reports estimates of welfare changes and the marginal welfare cost of income taxation for a wide range of income and demographic groups in New Zealand, in the context of simple income tax policy change. The results are obtained using enhancements to the NZ Treasury's behavioural microsimulation model, Taxwell-B. The database used is the 2011/12 New Zealand Household Economic Survey. Taxwell-B uses discrete hours modelling to examine the labour supply responses of all individuals to an income tax and benefit change. The discrete-hours specification, whereby individuals have the choice of working only a discrete number of hours levels, involves the assumption that utility functions have both deterministic and random components. This gives rise to a probability distribution for each individual over the available hours levels, which takes the multinomial logit form. This is particularly helpful in modelling labour supply because the econometric estimation of preference functions overcomes the endogeneity issues which plagued earlier attempts to estimate labour supply functions, in view of the fact that hours worked and the marginal tax rate faced are jointly determined in a piecewise-linear tax structure. Furthermore, by allowing the parameters of utility functions to depend on a wide range of characteristics, it allows for the considerable extent of population heterogeneity that exists. Added to this is the fact that estimation requires only net (after tax and transfer) incomes of individuals at the discrete hours levels used. It therefore allows the full complexity of the tax and transfer system to be considered.

The existence for each individual of a frequency distribution over hours levels, combined with the fact that budget constraints are highly nonlinear, means that convenient analytical expressions for the required welfare changes are not available. This paper applies the method devised by Creedy and Kalb (2005) for the deterministic case with nonlinear budget constraints, extended to deal with the stochastic utility case by Creedy, Herault and Kalb (2011).

Previous estimates of marginal welfare costs and excess burdens for NZ are discussed in Section 2. Section 3 briefly summarises the method used to compute welfare changes. The main results for a tax change involving a 5 percentage point increase in all marginal income tax rates are presented in Section 4. Marginal welfare costs are reported for a range of demographic and income groups. Section 5 goes on to examine an overall evaluation of the tax change using a social welfare function expressed in terms of money metric utility. Brief conclusions are in Section 6.

First, it is useful to summarise briefly the concepts used throughout the paper. For an individual taxpayer, the concepts of welfare change are the equivalent and compensating variations, EV and CV respectively. The former, EV, is the maximum amount of money the individual would be prepared to pay, after the tax change, to return to the old prices. The latter, CV, is the minimum amount of money needed to return the individual to the pre-change indifference curve, at the new prices (or new net wage rate in the case of an income tax change).[2]

The associated tax burden, or deadweight loss, concepts are the excess burden (EB) and marginal excess burden (MEB), evaluated using either the EV or CV. Where these measures are based on the equivalent variation, the marginal excess burden is simply given by MEB=EV-MR, where MR is the actual change in (net) revenue. In the case of the compensating variation, this is complicated by the fact that MEB=CV-MR*, where MR* is the revenue change allowing for the individual's behaviour after compensation has been paid (allowing individuals to return to their initial indifference curve at the new prices).[3] In view of this extra complication, the approach taken here is to base measures on the equivalent variation.[4]

The marginal welfare cost, MWC, is then defined as the marginal excess burden per dollar of extra revenue, MEB/MR. Attention is given here to the EV and the associated MWC concepts, which are unambiguously defined for individuals. However, aggregate values, for particular groups, are also reported.[5]


  • [1]The welfare measurement does not account for administrative costs, avoidance costs, compliance costs, enforcement and rent-seeking costs.
  • [2]As is conventional in the public finance literature, the welfare changes are defined to be positive where a loss is concerned. A negative EV, indicating a welfare gain, arises when relevant tax rates are reduced. In the present paper, as with all the estimates mentioned in the following section, government expenditure is not included in individuals’ utility functions.
  • [3]Of course, the hypothetical compensation itself is not part of the net revenue calculation.
  • [4]The two measures are equal only for truly marginal changes, or where there are no income effects, but of course most tax changes are non-marginal.
  • [5]The associated concept that receives considerable attention in analyses of optimal taxation and expenditure is that of the marginal cost of funds, MCF, which is simply equal to 1+MWC. It is the MCF (at the aggregate level) that is important when considering the question of the 'optimality' condition regarding public expenditure, and the question of raising additional tax revenue to finance a government project. The value judgements behind an optimal position (the ‘first-order conditions') necessarily depends on the views of the government, viewed as the ‘decision taker'. They can be expressed as follows. The perceived value of an additional unit of public spending is referred to as the marginal value of public funds, MVPF, and is of course expected to exceed 1: a dollar or public expenditure produces more than a dollar's worth of ‘public services'. The MWC of the tax-financed funds is valued by the government using the concept of the marginal social value, MSV: this reflects the weight attached by the decision taker to the welfare cost imposed on taxpayers. For example, if the extra tax revenue is raised by high-income taxpayers and the decision taker attaches little value to their loss of welfare, the MSV is relatively low. The optimality condition can be expressed as MCF=MVPF/MSV.
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