Appendix 3: Method for Calculating EMTRs
EMTRs can be calculated with the following algebraic approach, which was developed by Ivan Tuckwell and Matthew Bell of the New Zealand Treasury [Treasury, 1999; Nolan, 2002, pp. 17-21].
The net benefit is abated against gross non-benefit earnings. Thus when a family earns an extra dollar in gross non-benefit earnings the total gross income (which includes the gross benefit) does not rise by the full dollar because of the benefit abatement.
The gross benefit abatement (rb) equals the net benefit abatement (rB) divided by one minus the marginal tax rate on benefit income (tB).
(1) rb > = rB / (1 – tB)
In this paper it is assumed that the change in the tax on gross non-benefit earnings is the marginal personal income tax rate on earnings (t) multiplied by the change in gross income. (However, in practise beneficiaries’ non-benefit earnings are generally taxed under a withholding tax regime (secondary tax) at 21 percent.[20]) Further, the tax on the gross abated benefit and the non-benefit earnings are calculated separately as the tax rate applying to the benefit income may differ from the tax rate applying to non-benefit earnings. Differences in the tax rates applying to benefit and non-benefit income occur when a beneficiary’s annual gross benefit income is below a personal income tax threshold and non-benefit earnings increase total gross income above the threshold. For instance, under the current personal income tax scale, such a difference would occur if a beneficiary receives a gross benefit below $9,500 along with non-benefit income that increases total gross income to above $9,500. In a couple, total gross income is the total of gross non-benefit income and one half of the gross benefit income.
The change in gross income (yG) is one minus the gross benefit abatement.
(2) Δ yG = 1 – rb
The change in disposable income (yD) is the change in gross income multiplied by the changes in tax liability (t) and Family Assistance abatement (rP) minus the ACC earners’ account levy.
(3) Δ yD = Δ yG (1 – t – rP) – ACC
The EMTR is one minus the change in the disposable income.
(4) EMTR = 1 – Δ yD
Notes
- [20]The secondary tax is a withholding tax, so excessive tax withheld during the year is returned when taxes are reconciled at the end of the income tax year.
