1 Introduction

The aim of this paper is to show how the change in income tax revenue - at individual and aggregate levels - as a consequence of a marginal rate change can be decomposed into several effects. The decomposition is useful for revenue forecasting purposes and in contexts where revenue changes form one component of a larger economic model. First, in elasticity terms there is the obvious ceteris paribus positive revenue effect of a rate rise which depends (at the individual level) only on the tax structure: this is the partial elasticity of revenue with respect to the relevant tax rate. Second there is a negative effect arising from behavioural responses. This latter effect can itself be divided into two multiplicative influences. The elasticity of taxable income - the response of taxable income to a change in the marginal net-of-tax rate (one minus the marginal rate) - captures the net effect of all incentive effects associated with the marginal rate change.[1] In addition, the tax revenue elasticity - the elasticity of tax revenue with respect to a change in income - determines the consequent effect on revenue of the behavioural response.

The recognition of two basic effects of a rate rise is not of course new. Reference has long been made to 'tax base' and 'tax rate' effects of rate changes and, for example, behavioural and 'mechanical' effects of an increase in the top marginal tax rate in a multi-rate structure were distinguished by Saez (2004).[2] However, when discussing revenue changes resulting from marginal rate changes, the literature on the elasticity of taxable income has not identified the specific role of the revenue elasticity. The latter is the central concept in the literature on 'fiscal drag', which is concerned with the extent to which the non-indexation of tax thresholds leads to increasing average tax rates over time.[3] In this context, the change in gross income is considered to be exogenous and any consequent feedback disincentive effect on income arising from the change in the average tax rate is ignored. Indeed, at the individual level the literature concentrates on changes which do not involve a movement across tax thresholds, which would otherwise lead to a change in the marginal tax rate.[4] Hence, in addition to the partial elasticity of revenue with respect to the relevant tax rate, one elasticity concerns the way tax revenue changes in response to exogenous income changes while the other elasticity measures the extent to which income declared for tax purposes adjusts when the income tax rate varies.[5]

The revenue elasticity is concerned only with the nature of the income tax structure itself and, when considering aggregation over individuals, the form of the income distribution. The elasticity of taxable income is concerned with a wide range of behavioural adjustments associated with tax rate changes, captured in a single measure. Hence there is no direct connection between the two elasticity concepts. It is shown below how the revenue elasticity has a clear role at the individual level in influencing the change in tax resulting from a rate change. In considering aggregate revenue over all individuals, changes are shown to depend on the revenue elasticity at the arithmetic mean income level within each tax bracket in a multi-rate income tax structure. The restriction of previous analyses to the top marginal rate also involves a substantial simplification. The present paper extends the treatment to deal with changes resulting from any tax rate, and thereby also deals with simultaneous changes in all tax rates.

Section 2 explores the precise relationships among the various elasticities, namely partial elasticity, the individual tax revenue elasticity, the individual elasticity of taxable income and their combination to determine the elasticity of tax revenue with respect to a change in the marginal tax rate. In view of the ubiquitous nature of the multi-step tax function, results are given for this case. Section 3 looks at aggregation over individuals when a single marginal rate changes in a multi-rate tax structure. A diagrammatic method of illustrating the various components is also devised. To illustrate the orders of magnitude involved section 3 applies the aggregate analysis to the New Zealand income tax system. This provides a convenient 'natural experiment' since the New Zealand government's May 2010 Budget involved changes to all marginal income tax rates whilst holding all thresholds constant. The analysis concerns only the effects on income tax revenue, and it is worth recognising that, to the extent that the elasticity of taxable income captures some shifting towards sources which attract lower marginal rates, it does not deal with the potential full consequences for tax revenue. Brief conclusions are in Section 4.