1 Introduction

The 'elasticity of taxable income' (ETI), the response of taxable income to variations in the net-of-tax rate, 1 - τ, was proposed by Feldstein (1995) as a way of capturing the combined impact of various economic responses to changes in marginal income tax rates. The elasticity not only captures all responses to a change in the tax rate in a simple reduced-form specification, it provides, under certain conditions, a convenient method of calculating the welfare effects of tax changes.[1] It is thus a crucial component of any investigation of the potential revenue effects of proposed income tax changes. It has also been used, for example by Diamond & Saez (2011), to determine an optimal top marginal tax rate.

There has been a plethora of empirical estimates of the elasticity, mainly for the US and using a variety of methods. However, as the review by Saez et al. (2012) points out, estimation presents a number of challenges. In particular, they state that, 'in order to isolate the effects of the net-of-tax rate, one would want to compare observed reported incomes after the tax rate change to the incomes that would have been reported had the tax change not taken place. Obviously, the latter are not observed and must be estimated' (2012, p. 18).

This paper has two main objectives. First, it examines the use of instrumental variable regression methods. It is argued that the standard instrument for the net-of-tax rate - the rate that would be applicable post-reform but with unchanged income levels - may be unsatisfactory in contexts where there are substantial exogenous changes in taxable income.[2] This is in addition to acknowledged problems associated with controlling for income changes as part of the regression specification. Two alternative tax rate instruments are proposed. The approach advocated here to deal with the challenge posed by Saez et al. involves estimating the dynamics of taxable income for a panel of taxpayers, using data over a period that involves no tax changes.[3]

The parameters derived from this procedure are then used to construct hypothetical (or counterfactual) post-reform incomes that would be expected in the absence of reform. From the resulting probability distribution of income for each taxpayer, two alternative net-of-tax rate instruments may be obtained. One instrument is based on the tax rate each individual would face if their income were equal to expected income, conditional on income in the previous two periods and knowledge of the process of relative income dynamics. The preferred alternative uses the form of the conditional distribution of income for each taxpayer to obtain an instrument based on their expected tax rate.

The second objective is to use the proposed new instruments to estimate the elasticity of taxable income in New Zealand, using information about taxable incomes for a sample of taxpayers before and after the income tax rate changes in 2001. This reform provides an especially useful context in which to examine the performance of the three instruments, given the nature of that reform and the availability of suitable data to estimate income dynamics.

Following a brief review of existing estimates obtained using instrumental variable and other methods in section 2, section 3 summarises the basic instrumental variable specification. Section 4 compares some key properties of the standard instrument and the two proposed alternatives. The construction of these alternatives is described in detail in Section 5. Section 6 applies the various instruments to a tax policy change in New Zealand in 2001 and discusses the resulting estimates of the elasticity of taxable income. Brief conclusions are provided in section 7.