The general conclusion must be that the statistics arising from the imposition of the super-tax have tended to raise new problems rather than to solve old ones. UNIVERSITY OF LONDON. A. L. BOWLEY. NOTE I INCOME BETWEEN £160 AND £7001 Computed Numbers of Abatements allowed on Incomes of The abatement allowed on incomes not exceeding £400 is £160 throughout the period; thus a person with an income of £390 would pay tax on £230. In 1897-98 the abatement on £400-£500 was £100; in subsequent years, £150. The abatements on incomes of £500-£600 and £600-£700 were £120 and £70 from 1898-99. The tax was 8d. in the pound in 1897-98, 1898-99, 1899-00; 1 shilling in 1900-01; 1s. 2d. in 1901-02; 1s. 3d. in 1902-03; 11d. in 1903-04; 1s. in 1904-05, 1905-06, 1906-07; 1s. on unearned and 9d. on earned income in 1907-08; 1s. 2d. on unearned and 9d. on earned income in 1908-09, till the present date. 1 46th and 56th Reports of the Commissioners of the Inland Revenue. ? Fiscal year beginning April, 1897. No abatements on incomes above £500 till 1898-99. The numbers are obtained by dividing the total amount admitted for abatement in each class by the maximum (£160, £150, £120, or £70) that can be allowed; but in fact it is supposed that some people do not claim the maximum (since it may involve more trouble to claim for the whole amount than for part) and therefore the average divisor is somewhat too large and the numbers too small. Sir H. Primrose (the chairman of the Board of Inland Revenue) in 1906 thought that the deficiency "might be at least as much as 25,000 (3 per cent) in 1903-04. For the same date he thought that the addition of 10% to the numbers, for those who were entitled to abatement but did not claim it, would not " be an excessive estimate." He did not, however, commit himself to such large additions. It is to be noticed that the numbers of abatements, which had shown little movement in the years 1892 to 1897, advanced rapidly as the rate of tax increased to its maximum (1s. 3d.) in 1902–03; since then the growth in the class under £400 has been only about 2% per annum. A further considerable increase occurred in the numbers in the higher classes when the rate on earned incomes was made 3d. and subsequently 5d. less than on unearned; in claiming this differentiation it was easy to claim abatement also; but the growth since 1908 has been slight. It seems that the great part of the group who did not claim in 1903 must now be included, and that instead of adding 13% we should add much less, say 6%. The number of incomes between £160 and £700 in 1911-12 was almost certainly between 850,000 and 900,000, and probably near 880,000. This view is confirmed by Pareto's Law of Grading. The numbers for 1909-10 are complete: there were still a small number of returns to come in for subsequent years: thus it is supposed that another 100 persons will have to be added to the next table. number of persons whose income is greater than x units per head; A and a are constants to be determined from the data. In the case where a = 1.5, average income between £x, and z2 1. If we take 880,000 persons as having incomes between £160 and £700 it is found that a = 1.5 gives a good fit and that log A Below £700 the relation between the abatements and numbers is precisely that expected, the defect in the first line being due to non-claiming of the full abatement (Note I). But the income and number above £5000 is too small, and the total income should be £810,000,000 instead of £478,000,000. 2. From examination of the super-tax statistics it is found that a = 1.5 and log A = 9.618 gives a very good fit from £5000 to £55,000 and then gives numbers in excess; thus: The number below £700 is impossibly large. Diagram II shows that these dilemmas cannot be escaped, for the vertical heights of marks do not depend on any assumed value of A, and the horizontal positions (calculated from formula (v) where a is taken to be 1.5) would only be microscopically affected by any other reasonable value of a. 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 LOGARITHMS OF INCOMES A The more developed form of Pareto's Law, N = .10-**, (x+b)a where b and c are additional small constants, is found, after several trials, not to get over this difficulty. In the diagram the marks show the numbers of persons at each income, whereas it has been usual to show the aggregate numbers above an assigned income when this formula has been used. The marks show the actual numbers of abatements, whereas the slant line is drawn for the corrected numbers of incomes. NOTE IV DEATH DUTY STATISTICS Computed from the 56th Report of the Commissioners Number of estates of various values: 1. Actual. Average, passing at death, for the years 1907-08 to 1912-13, which is very nearly the same as the number in 1912-13. |