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Average Marginal Income Tax Rates for New Zealand, 1907-2009 WP 12/04

Appendix 4: Estimating Non-filers' Incomes

An important issue in the measurement of AMTRs is the inability of tax-return-based data in the NZOYBs to capture the incomes of those not required to furnish tax returns - expected to be significant for low income earners during the early part of the 20th century. This Appendix briefly outlines how we quantify the size of income of non filers not adequately captured by NZOYB data. This provides suitable income weights to attach to those income earners who effectively face a zero personal income tax rate.

The approach used to estimate non-filer income follows three stages.

1. Estimate the number of potential non-filers

The total number of employees, from the long term data file at the Statistics New Zealand's (SNZ) website,[25] was used as a proxy for the total number of individual income earners. The number of individual taxpayers from the NZOYB was subtracted from total employees to produce an estimate of the total number of non filers.

2. Estimate the average annual income of non-filers

A distribution of the population by income, from NZ censuses, was used to estimate the average annual income level of non filers - which are predominantly low income earners. The 1926 census was the first to include a question on incomes, and we were able to source a count of the population by income from that census onwards. Through the first half of the 20th century in New Zealand, income tax returns were not required to be completed for those earning under a certain income (£300 in 1926). Fortunately, census data on income over this period focused on ranges of income that were close to this low income exemption. For instance, the 1926 census asked respondents to indicate their annual income from the following ranges.

Income ranges used in the 1926 census
No income < £52 £52 - £155 £156 - £207 £208 - £311 £312 - £363 > £363

Aggregate tables by income and age were obtained for the 1926, 1936, 1945 and 1951 censuses. From the aggregate tables, we ignored those under the age of 16 and those who indicated they did not earn any income ie, we aimed to count only those most likely to be making work and investment decisions. Furthermore, for the purpose of estimating the average income of non-filers, people earning over the low income exemption were also excluded in our calculation. The weighted average income of non-filers was estimated by multiplying the mid-point of each income bracket (deemed to include non-filers) by the corresponding weight each selected bracket contributed to the total of the selected population. Table A3 presents our estimated average income of non-filers from the 1926 census and the corresponding weights used to derive it.

Table A3 - Estimated average income of non-filers from 1926 census data
Income bracket Under £52 £52 to £155 £156 to £207 £208 to £311
Weight of selected population by income bracket 11.30% 38.30% 20.10% 30.20%
Midpoint £26.00 £103.50 £181.50 £259.50
Weighted average income £158

3. Calculate total income of non-filers

The estimated average income above was multiplied by the estimated number of non-filers, giving total income generated by non-filers. This total income can then be used to increase the weight associated with the lowest income group's contribution to the AMTR calculation. However, as noted in the NZOYB, some low-income earners, despite not being required to file a tax return, still furnished returns and were captured in the NZOYB income data. As a result, the income recorded in the NZOYB under the lowest income bracket was subtracted from our estimated total non-filer assessable income to avoid any double counting.

Table A4 outlines the process of calculating total assessable income of non-filers. Unsurprisingly, the estimated number of non-filers, and in turn income, was considerable in 1926. As income rose over time in general, a smaller number of taxpayers fell into the non-filer group leading to a lower amount of non-filer income.

Table A4 - Estimated non-filer income
Income year Tax payers Number employed Estimated non filers Estimated average income of non filers Estimated total income of non filers Assessable income within non filer income bracket Additional income for AMTR calculation
  (A) (B) (C)=(B)-(A) (D) (E)=(C) x (D) (F) (G)=(E)-(F)
1926 43910 563718 519,808 £158 £81,931,267 £4,162,525 £77,768,742
1936 80530 587712 507,182 £84 £42,818,313 £20,118,237 £22,700,076
1945 310926 628471 317,545 £101 £31,945,578 £25,217,000 £6,728,578
1951 452,890 730,868 277,978 £96 £26,632,198 £15,790,000 £10,842,198

To estimate non-filers in years between censuses we follow the approach of Barro and Sahasakul (1983) who suggest that the proportion of non-filer income to total income fluctuated during different economic conditions, such as the depression in the 1930s. They show, as expected, that there is a higher proportion of non-filer to total income during the depression for the U.S. (Barro and Sahasakul, 1983, Table 1), while the proportion decreased in years of greater prosperity during the 1920s. Barro-Sahasakul also use the ratio of personal income to nominal GNP to estimate the relevant no-filer to filer income ratio for earlier years.

We follow the same approach here and extend estimates based on census years. Using our estimates for non-filer incomes in 1926, 1936, 1945, and 1951, aggregated personal income is found by adding the non-filers adjustment to total (filers') assessable income. Using the ratio of this total personal income to GNP for the four census years, we extend this ratio linearly to fill in all other years. Personal income for missing years is then found by multiplying this ratio with annual GNP. Finally non-filer income is obtained by subtracting the assessable from the total personal income.

The above approach (using the personal income to GDP ratio) produces a generally increasing ratio of filer to total assessable income from 1926 to 1951 (0.347, 0.707, 0.919, 0.963). However between 1945 and 1951, this produces an estimated negative amount of non-filer income in some intervening years. To interpolate between 1945-51 we therefore interpolate linearly between the filers/total income ratios of 0.919 and 0.963. From 1958 the introduction of PAYE taxation renders the non-filers adjustments unnecessary for subsequent years.

While this approach undoubtedly involved various inaccuracy (of unknown magnitude) it is likely to be more accurate as a method of filling in missing years between the census, and before 1926, than taking simple linearly interpolated averages. The resulting time-series for the ratio of filers-to-total personal income and the breakdown of filer and non-filer incomes are given in Figures A2 and A3 respectively.

Figure A3 - Ratio of filers-to-total personal incomes, 1907-1958
Figure A3 - Ratio of filers-to-total personal incomes, 1907-1958   .
Figure A4 - Decomposition of total personal income into filers/non-filers, 1907-195
Figure A4 - Decomposition of total personal income into filers/non-filers, 1907-195.

Notes

  • [25]Long-term labour market statistics can be found here: http://www.stats.govt.nz/browse_for_stats/economic_indicators/NationalAccounts/long-term-data-series/labour-market.aspx
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