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5.3 Decomposing Changes in the AMTRs

The variations in the AMTR over the period can be decomposed into changes to the tax system, changes in average income levels, and changes to the income distribution. The impact of each of these varies across the period. This section attempts to identify the most significant impacts in different time periods.

The AMTRs changed only slightly during the period 1907 - 1916, due to minor changes in both tax rates and income distribution. In 1914 the multi-slope scale was introduced. It did not have a large impact on the AMTR, however, as the tax rates remained low and there were many unaffected non-filers.

In 1917 effective marginal tax rates were increased substantially (by around 3 times at the lower end of the income distribution and up to 8 times at the upper end). The increase included the addition of a ‘special war tax'. In addition, abatement of the general exemption was introduced. As a result the AMTR increased from 0.5% in 1914 to 3.0% in 1917. It increased further to 4.5% in 1920, solely as a result of increasing incomes which moved people into higher tax brackets (the tax system did not change). From 1922 to 1924 tax rates were reduced slightly, but the AMTRs continued to rise due to increasing incomes shifting the distribution towards higher income tax brackets.

It was not until 1925, however, that post-WWI tax rates fell more significantly, with the top marginal tax rate dropping from 29% in 1924 to 22.5% in 1925. Thereafter the AMTR generally rose slowly over the remaining '20s and '30s, except for a relatively large rise (compared to previously) between 1930 and 1932. This largely reflected tax schedule changes in 1931.[17] In the same year, total income dropped by 5% and the income distribution was skewed downwards. The net effect of these changes was an increase in the AMTR from 3.3% in 1930 to 5.5% in 1931.

From the mid-1930s to the early post-WWII years, AMTRs rose rapidly and did so again from the mid-1970s until the early 1980s. In between, the roughly 30 year period from the mid-1940s to mid-1970s reveals a steady upward trend the AMTRs, punctuated by a brief decline from 1951-54 and the sharp fall in 1961-63.

The especially rapid rise in the lead-up to, and during, WWII largely reflects tax system changes: mainly tax rate and threshold changes designed to raise additional revenue. In 1936 tax rates were increased substantially (the top marginal rate on earned income increased from around 43% in 1935 to 65% in 1936), and increased again in 1939 plus an “additional tax” at 15% to finance the war effort (War Expenses Act 1939). In 1942 social security was increased to 12.5% and the additional tax was increased from 15% to 33.3%. Combined with an upward movement in incomes, these changes generated a rise in the AMTR to 27% in 1942 and 30% by 1945.

Unsurprisingly, the sharp drop in the AMTR in 1946 captures the reduction in social security and the additional ‘war' tax to 10% and 15% respectively in the aftermath of the war. However, as noted above, upward movements from 1948 are interrupted by reductions in 1951-54 and 1961-63. Both appear to arise mainly from legislated increases in exemptions. The large drop in 1962-63 reflects both increased generosity of exemptions (they rose from 46% of total gross assessable income in 1961, to 56% in 1963) and across-the-board upward shifts in MTRj thresholds in 1962.

The upward trend in the AMTR was interrupted briefly in the early-1970s and halted sharply in 1982 - well before the major economic and tax reforms of the mid-1980s. As with the AMTR declines in 1962-63, the decline in AMTR from 1982-84 is associated with increases in the tax thresholds at most income levels (but a new higher top rate) and some schedule simplification in 1984. The major reforms involving a reduced top rate did not become effective until 1988-89 when the top MTRj was reduced from 66% in 1987 to 48% in 1988 and 33% in 1989.

Further insight into the time-series pattern of AMTRs, and the role of different components, can be obtained by considering the relationship between personal income not subject to income tax and the AMTR. Figure 7 shows cross-plots of the AMTR with the estimated income share of non-filers. It also shows the share of income (of filers) that is tax-exempt - where the latter is added to the former in Figure 7. Increasing exemptions push more taxpayers into tax-free status (when an initial zero tax rate exists) as well as reducing positive MTRjs for others.

The Figure shows the time-series from 1922 (top left corner) to 1983 (bottom right corner) with dashed lines joining annual observations.[18] The non-filers' share reaches zero (in 1958) and therefore tracks the horizontal axis thereafter. The non-filers' income share reveals a clear negatively-sloped, and non-linear, relationship with the AMTR, - the correlation with the AMTR is -0.91 (1922-58). The relationship of the AMTR to exemptions is more complex. Though the combined ‘non-filers plus exemptions' share in Figure 8 reveals a negative slope, for exemptions alone the correlation with the AMTR is +0.76 (1922-58) but -0.93 (1959-83). That is, as AMTRs generally rose over time, and non-filing became less common (to 1958), exemptions tended to replace non-filing as the preferred means of keeping tax rates low or zero on lower income earners. After 1958 however, when PAYE was introduced, exemptions tend to decline over time in association with rising AMTRs.

Figure 7 - AMTRs and tax exempt/non-filed income, 1922-1983
Figure 7 - AMTRs and tax exempt/non-filed income, 1922-1983.

Of course, in any given year the share of income that is exempt from tax depends on a variety of underlying factors including income growth, tax schedule changes and so on. With some years involving tax schedules with many different MTRjs and thresholds, a formal decomposition into income changes and tax system changes cannot readily be made. However, it is useful to consider year-to-year changes to all non-zero MTRjs in the tax schedule since this provides one indicator of changes in the tax structure other than exemptions. We take a simple unweighted mean of all non-zero tax rates in the personal income tax schedule for each year - using effective marginal rates rather than statutory rates.[19] These are plotted against the AMTR for 1922-83 in Figure 8.

Figure 8 - Cross-plot of AMTR and non-zero EMTRj average, 1922-1983
Figure 8 - Cross-plot of AMTR and non-zero EMTR<sub>j</sub> average, 1922-1983   .

This reveals that the rise in the AMTR occurred largely in association with a rise in the ‘average' non-zero MTRj that each individual faced in the tax schedule from around 1931 (bottom left corner), until around 1942-45 but not thereafter. That is, for the post-WWII period, increases in the AMTR are not generally associated with changes to the tax schedule that raised MTRjs, though this does not of course preclude changes in thresholds that meant a given MTRj applied at higher or lower income levels. In essence, by the 1940s, top (and other) MTRs had reached sufficiently high levels, that they tended to remain around those levels or fall back in subsequent years.

Though these broad patterns over several years are revealing they do not indicate the extent to which each annual change in the AMTR reflects its various components. To apply that here, for the 1907-2009 period, first consider a simplified two-rate step function involving two tax rates, t0, t1, where t0 = 0, and t1 > 0. For this simplified case the change in the AMTR, dM, can be broken down into:

dM = w1dt1 + t1dw1 + dt1dw1 + { w0dt0 + t0dw0}         (8)

where w1 is the income weight of taxpayers facing t1 (= 1- w0), and the term in curly brackets is zero (t0 = dt0 = 0). The income weights are affected by tax thresholds that determine the MTRjs applicable at different taxpayer income levels. Of course the NZ personal income tax schedule involves a more complex structure of several (sometimes many!) non-zero tax rates. Nevertheless it is useful to approximate the exact specification in (8) using the annual ‘unweighted average' of the non-zero MTRjs, in the schedule, as shown in Figure 8. Thus (8) becomes:

dM = w'1dt'1 + t'1dw'1 + dt'1dw'1 + R         (8')

where t' is the simple average of non-zero MTRjs in the schedule, w' is the income weight of all taxpayers facing a non-zero MTRj, and R is a residual - capturing the omitted components involving changes in each non-zero MTRs relative to the average t'1, changes in associated tax thresholds, and changes in income shares relative to w'1.

Using (8') to decompose changes in AMTRs (dM) for each year during 1907-83 gives the following correlation matrix where pre- and post-1940 correlations are examined separately - Figure 9 suggests a different relationship after around 1940.

Table 4 - Correlation matrix of AMTR changes
1907-40 1941-83
w’1dt’1 t’1dw’1 dt’1dw’1 w’1dt’1 t’1dw’1 dt’1dw’1
t’1dw’1 0.19 - - -0.15 - -
AMTR 0.85 0.24 0.51 0.34 0.08 0.27

It can be seen that both changes in the share of taxable in total income, t'1dw'1, and changes in ‘average' non-zero MTRjs, w'1dt'1, are positively correlated with annual changes in the AMTR. However changes in the taxable income share have a much smaller correlation at 0.24 versus 0.85 (pre-1940) and 0.08 versus 0.34 (post-1940). The positive cross-correlation between, w'1dt'1 and t'1dw'1 reveals that this has a larger effect on the AMTR than the change in the income weight, t'1dw'1.

These correlations therefore reinforce the view that, at least to around 1940, the annual AMTR changes were largely associated with changes in the set of non-zero EMTRjs - both directly and via the associated change in income weights (due to dt'1dw'1). By themselves change in the income weighting (between taxed and untaxed incomes) within the AMTR calculation had relatively little impact. After 1940 changes in average non-zero tax rates are still important but other factors (hidden within the residual in equation (8')) appear to be more important.

The data underlying these correlations can be seen in Figure 9, which plots the annual change in the AMTR (right-hand axis) and the unweighted average non-zero EMTRjs (left-hand axis). This reveals that for many years the EMTRjs remain relatively constant (generally because statutory rates are unchanged), while the AMTR changes - because of changes to income levels/distribution, changes in thresholds, exemptions etc. Nevertheless, many of the largest changes in the AMTR are associated with substantial changes in statutory or effective marginal tax rates such as in 1925, 1936, 1940-42, 1946 and the 1970s.

Figure 9 - Changes in unweighted averages of EMTRjs and AMTRs, 1922-1983
Figure 9 - Changes in unweighted averages of EMTR<sub>j</sub>s and AMTRs, 1922-1983   .


  • [17]For example, the statutory MTRjs were approximately doubled across the income distribution and the tax-free threshold was reduced; a 30% additional tax was added to the final tax bill; social security tax was introduced at 1.25%; and a supplementary 33.33% tax was applied to unearned income.
  • [18]1983 is the last year for which we can conduct this exercise due to the switch to IRD unit record data thereafter.
  • [19]That is, social security, additional taxes/discounts and exemption adjustments are included. Using statutory rates yields similar results.
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