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2.2  Tax Rate Definitions

This sub-section defines the key tax rates used in this paper. At the individual taxpayer level most personal income tax systems specify a ‘schedule' of statutory marginal tax rates (MTRs) that describe the increase in tax liability associated with an additional dollar of income across different income ranges.[5] In typical progressive income tax systems these statutory MTRs rise in ‘steps' with income.

Effective marginal tax rates (EMTRs) refer to the de facto increase in tax liability associated with increases in incomes. These are affected by both the statutory MTR and other aspects of the tax code, such as eligible deductions against tax, that affect the taxpayer's tax liability as income rises. Common examples are the withdrawal of tax exemptions or social welfare payments in association with changes in income, and additional taxes (such as supplementary ‘war taxes') that are related to income tax liabilities. The EMTRs reported in this paper do not take into account the impact of withdrawal of social welfare payments, but they do include the impact of tax exemptions and additional taxes.

As we discuss below, the New Zealand income tax and transfer system has at various times: (i) set different marginal tax rates for earned and unearned income; (ii) used income-tested exemptions, benefits and rebates, such as Family Tax Credits; and (iii) adopted additional income-related taxes such as social security tax and tax deductions associated with family-owned trusts or companies. In addition, legislative changes to levels of tax-exempt income, even where these exemptions are not directly income-related, can nevertheless move taxpayers into different income tax brackets, and hence the EMTRs that they face, on a given gross (pre-exemptions) income.

Consider a simple tax schedule with only one (non-zero) marginal tax rate, t1, and where no tax is liable on incomes below an initial tax-exempt level, a, such that:

T(y) = t1[y - a],         for y > a         (1)

where t1 is the statutory marginal tax rate, T is total tax paid on income, y, and a is the tax exempt income level. If, in addition, the level of the tax-exempt income, a, is reduced at rate v per unit of income as income rises above ya (where ya > a), then, for y > ya, the effective marginal rate is given byt1 + v, until a = 0. Further, for given income levels, a decision to increase the level of a that leads to y < a, will reduce the taxpayer's EMTR from t1 to zero. The individual's average tax rate (ATR) for the schedule in (1) is then given by:

T(y)/y = t1[y - a)]/y         for y > a.         (2)

Hence the ATR in (2) must be less than the marginal rate, t1, if a > 0. An equivalent effective average tax rate (EATR) - that takes into account any transfer payments (‘negative taxes') received - can also be lower than the ATR, depending on the size of the transfers received relative to the individual's income level.

Where individual or household level data are available it is common practice to use effective marginal or average tax rates of personal income tax to test for behavioural responses. These can generally be calculated from tax schedule and other information of the sort described above. When working at the aggregate level, however, the choice of an aggregate equivalent to individual marginal tax rates is not straightforward and, empirically, is often limited by data availability.

A commonly used aggregate tax rate is the so-called ‘implicit' average tax rate, R/Y or IATR, based on data for aggregate tax revenue (R) and an aggregate income measure (Y). A marginal equivalent, or dR/dY, is also sometimes calculated. These ‘implicit' rates are widely recognised as unsatisfactory proxies for their conceptual equivalents, but are readily calculated from generally available data. As Myles (2009b, p.34) notes such an aggregate average or constructed marginal rate “probably does not [reflect] the rate that any particular economic decision maker is facing”. This is because the IATR is likely to include changes in the income tax base in response to the ‘true' EMTR, and hence the IATR measure is not independent of income. Such independence is required to reliably measure the response of income to an exogenous marginal tax rate change.

However, Barro-Sahasakul (1983) established the conditions under which aggregate equivalents of individual MTRs can be constructed from individual values. They showed that the correct form of aggregation depends on how taxes affect consumption, and the question of interest. For example, is the investigator interested in the response of income, or of consumption, or of something else, to changes in marginal tax rates? They show that a consumption-share weighted aggregate of individual MTRs provides the correct aggregation of individual MTRs, under certain assumptions about individual's utility functions.[6] Empirically, since individual income data are more readily available than consumption data, they propose an (individual) income-weighted average as a proxy.[7] It is this income-weighted average marginal tax rate (hereafter labelled ‘AMTR'), that we focus on below; see Barro and Sahasakul (1983, pp.426-7) for more details.

In later sections we present evidence for New Zealand on the Barro and Sahasakul income-weighted AMTRs from 1907 (the earliest date for relevant income data). We also report data on the top statutory MTR, and the top EMTR taking account of other taxes added to, or abated with respect to, the personal income tax. First, since the nature of the personal income tax structure has changed substantially over the years, the next sub-section outlines some of its key features.


  • [5]The legal and economic issues surrounding the definition and measurement of ‘income’ for tax purposes are not explored here.
  • [6]For some purposes, such as measuring tax impacts on employment or unemployment, a taxpayer-weighted aggregation may be more appropriate.
  • [7]This consumption or income weighting can be based on a geometric, rather than arithmetic, mean if consumption or income responses to tax rates are expected to take a constant elasticity form.
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