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    "source_key": "britannica_1926",
    "source_title": "Encyclopaedia Britannica (1926)",
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    "chunk_id": "1926:income tax:5ea1007a8790",
    "title": "INCOME TAX",
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    "verified_text": "war provides a fertile soil for taxation, and a tax on income has been adopted during and since the world war in some countries which had hitherto rejected this form of direct taxation, long the sheet anchor of british finance. i. the united kingdom the british tax has been developed gradually in detail, reflect- ing at various stages in its history the growth of opinion, equality and justice, until to-day it is a financial instrument of great intricacy, subtlety and power. none the less the broad scheme of the law has remained unchanged in many essential charac- teristics for nearly a century. flexibility is provided by the annual re-enactment of the whole income tax code through the medium of the continuation clauses in the yearly finance act, which serves also as the medium for amendments, extensions and declarations of the construction of the law. the salient characteristics of the tax may be grouped under eight heads. —_ scope.—the tax extends, broadly speaking, to all income aris- ing in the united kingdom by whomsoever it may be enjoyed, and to all income accruing to persons residing in the united kingdom without regard to the place where it may arise. the tax walks, so to speak, upon the two legs of origin and residence. it therefore leads to the problems of double taxation. pro- visions for relief against this defect, resting upon the principle of division of the total tax between the two taxing jurisdictions, exist as respects income liable both to united kingdom tax and tax in any of the british dominions overseas, except in the case of the irish free state, where the relief is based upon the prin- ciple of charging tax only in the country of residence. further provisions for double taxation relief also exist as respects profits on shipping. one code of laws applies, generally speaking, to individuals, partnerships, companies and other bodies of per- sons. in the main the tax is a tax on the incomes of individuals, nearly 90% of the total actual income brought into charge being distributed among individuals who are actually resident in the united kingdom. administratively, the tax is levied under five separate cate- gories or schedules of income. but this is a matter of machinery only, and the tax borne by individuals is in reality only one tax on the total income of the individual, and not, as is often thought, a series of taxes on the separate sources of his income. definition of income.—in respect of the ownership of lands, houses, etc., in the united kingdom, the measure of income is the annual value, which means broadly the rent at which the property is let, or is worth to be let by the year (the tenant bearing his usual rates and taxes), less certain statutory deduc- tions for repairs, and an average cost of additional expenditure on repairs, maintenance, insurance and management. in respect of the profits on occupation of land in the united kingdom, the measure of profit is made on a conventional basis, which assumes profits bearing a fixed relation to the annual value of the land occupied. to-day that relation in the case of land used mainly for the purposes of husbandry is one of equality, and in other cases it is a relation of one-third of the annual value. no definition is necessary in the case of interest on public funds. income from dominion and foreign securities (other than public debts) or from foreign and dominion stocks, shares and rents is normally liable on the full amount of the income, less charges which must necessarily be met abroad. a420 there remain the two main classes: income from trades or professions and income from employments. here the broad rule is that the income to be charged is the excess of the gross receipts over the expenses incurred wholly, necessarily and exclusively in earning the profits or income in question. the british income tax, in the words of one of the judges, “ is a tax on income,” and this is strictly construed by the exclusion from the scope of the tax of profits which are in the nature of capital gains; and in this respect the british system is strikingly different from that in force in the united states of america. in consequence, the law prohibits, in arriving at profits for income tax purposes, any deductions in respect of capital charges, lost capital or losses unconnected with the business. provision is, however, made for a deduction from the statutory profits liable to tax of an allowance in respect of the depreciation of machinery or plant. computation of the statutory income-—the amount of income liable to be taxed fer any year of assessment (a year running from april 6 to the subsequent april 5) may be, but frequently is not, equal to the amount of income earned or received by the taxpayer in the year. this arises from the great variety of rules which govern the computation on various bases of the statutory income of different classes, for instance, income from trades and professions or from dominion and foreign stocks, shares and rents was charged on an average of the three preceding years. employments and income from interest on public debts or from dominion and foreign securities are charged on the basis of the year of assessment. in other cases an average of five years is used. proposals were, however, made to parliament in 1926 for sweeping away some of this medley of differ- ent bases, and for substituting in the case of profits from trades and manufactures, mines, railways, iron works, gas works and water works, etc., and of income from dominion and foreign securities and possessions, a uniform base of the profits of the year preceding the year of assessment. differentiation.—more than a century of agitation passed before this feature of the income tax was established in 1907. at first it was effected by a reduction of the normal rate of tax in favour of earned income. to-day the differentiation is granted by deducting from the earned income an allowance of one-sixth of that income subject to a maximum deduction of £250. graduation.—this ts the principle of levying a heavier percentage upon large incomes than upon small. from the inception of the tax graduation in some form or other has figured among its characteris- tics. during the last half of the 19th century graduation was effected on small incomes by a scale of abatements which from ig0g to 1g18 was continuously developed and widened. to-day graduation is effected as follows: the total of the statutory income from various sources having been ascertained, the amount of any earned income allowance is deducted therefrom. from the balance, called assessable income, there is then deducted an aggregate of various personal allowances and deductions (¢.g., for self or self and wife, children, housekeeper, dependent relatives, ctc.), leaving a balance constituting the taxable income. tax is calculated upon this taxable income by charging the first £225 thereof at half the standard rate and the remainder thereof at the standard rate. from the amount of tax so arrived at there is deducted any relief, expressed in terms of tax, due in respect of life insurance premiums or dominion tax. if the system of graduation stopped at this point, the relevant curve would rise steeply until incomes in the neighbourhood of £2,000 were reached, but after that point it would flatten rapidly. in order to continue graduation an additional duty of income tax called super-tax is charged on any individual whose total income from all sources for the preceding year, as computed for income tax, cx- ceeds a fixed sum which stands at £2,000. for administrative rea- sons this additional tax is assessed and collected separately from income tax, but it is only a part of the scheme of graduation for the direct taxation of incomes exceeding a fixed amount. the super-tax therefore continues the process of graduation by imposing an addi- tional rate of tax on successive sections of the total income ahove £2,000. the effect of this system as a whole is to levy an effective rate of tax on each f of the total income of an individual, rising gradually from a fraction of a penny in the £ until the rate closely approaches a maximum rate represented by the sum of the standard rate of income tax and the highest rate of super-tax. the following table of the amount of income tax and super-tax and the effective rate of tax per £ of income on specimen incomes clearly illustrates the graduation of the tax in the case of married couples without children for the year 1926-7. it shows how the effective rate rises in the case of earned income from 2d. in the £ for a total income of £300 by gradual stages up to 9s. 73d. in the £ on an earned income of £150,000. the rate for uncarned income rises from 2% for an income of £250 to 9-73 to one of £150,000. plotted on a graph, these effective rates fall upon a very smooth line un- broken by any abrupt jumps. income tax income tax and super-tax married couples without children, 1926-7 if income all ‘' invest- ment ’’ income if income all ‘‘ earned ’’ income total income tax income tax oe (including | effective | (including | effective super-tax, if rate super-tax, if rate any any £ t) -s.. akes cl : eae es ee dc: . 250 2. «10-0 25 300 2 10 o 2 7 10 o 6 350 6 13 4 a 12 10 0 83 {00 10 16 8 65 17 10 0 10} 500 19 3 4 9 32 i0 oo| 1 33 600 32 10 o| i i 52 10 o| i 9 700 49 3 4/1 5 72 10 © | 2 i 800 65 16 8| 1 re 92 10 0} 2 4 g0o0 82 10 o| i 10 p12. 16° 0. |'-2 6 1,000 oo. 3. 4.12 oo 142 10-6: |-2 8 1,250 140 16 8 | 2 3 18210 0 | 2 it 1,500 182 10 0 | 2 5 232 10 oq | 3 i 2,000 282 10 0| 2 ~~ io a32> 10> 0: 3 4 2,500 go be eg. 23 0,3 £72 3,000 s20; 15: ord 6 o|3 # i0 4,000 80r 5 0} 4 o oo! 4 3 5,000 i1,t13 15 o] 4 53 oo} 4 8 6,000 1463 15 0; 4 10} o15 oo} 7,000 1638 ts. o25 3 oo; 5 5 8,000 2213-15 oo} ss 63 o| 5 8 9,000 2,613 15 o|} § 93 o| 5 i! 10,000 3,013 i5 o| 6 o% o | 6 13 15,000 5.138 1§ 0] 6 10 o|6 i! 20,000 7,388 15 o|] 7 44 o19 25,000 9,763 15 o|7 92 o| 7 30,000 12,138 15 o| 8 i o;| 8 40,000 17,138 15 o| 8 7 0] 8 50,000 22,138 15 0] 8 104 o! 8 100,000 : 5 o1g 5 oo] 9 150,000 o| 9 75 @-|-9 collection of the tax.—perhaps the most famous characteristic of the british tax is the principle of collection at the source. seligman has called it, “ perhaps the chief cause of the success of income tax.” it dates from as early as 1803. under this principle the tax is obtained, whenever it is possible to do so, by deducting it before the income reaches the person to whom it belongs. the formal assess- ment is accordingly laid, wherever this course is possible, on each source of income by itself and on persons who are debtors in respect of income belonging to other persons. power is given to the payer of income to deduct the appropriate tax from the payments made to the ultimate proprictors of that income. for instance, a limited liability company is assessed to tax at the standard rate on the whole of its profits, without reference to their ultimate destination. on paying interest to its debenture holders, or dividends to its share- holders, the company is entitled to deduct and retain the amount of tax appropriate to the interest paid or dividend distributed, and the investor thus receives his interest or dividend subject to this deduc- tion of tax. it is estimated that approximately two-thirds of the net yicld of the tax is collected at the source. whether the tax charged in respect of any income brought into assessment is collected by deduction at the source or not thus de- pends upon the ultimate proprietorship of the income assessed. so far as the person charged is not the ultimate proprietor, the tax is collected by deduction at the source; so far as he is, the tax is col- lected directly. he chief classes of income in respect of which the tax is collected directly are the profits from trade of individuals, whether sole or partnership traders; the like profits of limited liabil- ity companies so far as they are not distributed to shareholders, debenture holders, etc.; profits from the occupation of land; income from professions and most employments; income from dominion and forcign securities and possessions not paid through agents in the united kingdom; income from certain interest, discounts, etc. the income of individuals upon which tax is collected directly is charged in the assessments, as far as possible, at the respective half standard and full standard rates on the taxable income, that is on the balance of the assessable income remaining after deduction of the personal allowances and deductions due. as the total income of any individual taxpayer may be made up of a number of separate items, on some of which tax is borne by deduction at the source at the full standard rate, and on others of which tax is collectible directly, adjustments are in numerous cases necessary in order to restrict the total tax payable to the amount proper to the actual circumstances of the individual concerned under the scheme of graduation and differentiation already described. these adjustments are made as far as possible when dealing with tax collected directly, any balance being dealt with by repayment of tax. they are greatly facilitated by the fact that personal statements of total income are rendered income tax annually by almost every individual taxpayer, for purposes of either income tax or super-tax. with the exception of tax collected at the source on interest on public debts and on income from foreign dividends, etc., which is paid at or shortly after the time of payment of the income from which the tax is deducted, income tax contained in the main assess- ments for the year is due and payable on or before jan. 1 in the year of assessment; tax contained in additional assessments signed after that date is payable on the day after the date of signature. to this general rule there are, however, some other important exceptions. the bulk of the tax charged on income from the ownership of prop- erty, tax charged on any individual or firm in respect of lands occu- pied for husbandry, or tax charged on any individual or firm in re- spect of a trade, profession or vocation, and of most employments, is payable in two equal instalments, the first on or before jan. 1 in the year of assessment, and the second on or before the following july 1. railway companies in england and ireland pay tax on their profits in four quarterly instalments, on or before the 20th june, sept., dec. ad march. manual wage earners assessed half-yearly pay tax in respect of each half-year. tax in respect of employments under the crown is deducted (usually quarterly) at the source. administration.—in this sphere there is a striking division of authority. the original basis of income tax administration is modelled to a certain extent on provisions in the land tax acts of the 18th century. the main conception in 1806, as well as in 1842, was that of a temporary impost to be assessed and collected locally with a minimum of interference by the exchequer. the responsi- bility for assessment and collection of a very large part of the tax was laid upon the local bodies of commissioners possessing certain prop- erty or other qualifications. benches of these local or district com- missioners were and are still appointed for certain cities and bor- oughs and for parts or all of a geographical county. the individual commissioners are entirely unconnected with and independent of official control. each body has its own clerk. the commissioners were also empowered to appoint assessors of taxes and collectors of taxes. except as respects profits from commercial, financial and pro- fessional activities, the assessor was charged with making the assess- ment of tax; in the case of the income arising from the activities mentioned this duty was laid upon a body of commissioners known as the additional commissioners. on the main body of the local or district commissioners distinguished by being known as the general commissioners, fell the statutory duty of signing and allowing assessments made either by the assessor or the additional commis- sioners and of hearing and determining appeals against such assess- ments. fitted into this scheme was the officer of the crown, known originally as the surveyor of taxes, and to-day as h.m. inspector of taxes. in law his part was primarily to safeguard the interests of the revenue with strictly defined rights of intervention and objection at various stages of the formal procedure jaid down by the statues, even in the early years this broad scheme was honeycombed with exceptions which have grown rather than diminished with the pas- sage of years. certain assessments for instance are hived off under the single jurisdiction of a body known as the special commissioners of income tax, each of whom, still independent of the revenue authority, is appointed by h.m. treasury. this body performs all the duties of district commissioners in northern ireland; it makes all the assessments on railway companies and on their officials; the assessment of foreign and dominion dividends paid through agents in the united kingdom is under its care; it is also solely charged with the whole of the administration of the super-tax. then there are commissioners for the various public departments of state who are charged with making all assessments on official salaries, etc. the bank of england and the national debt commissioners also act as commissioners for assessment of individual salaries, etc., paid by these bodies and those of the bank of england are also responsible for the assessment of the profits of the bank. again all assessments on manual weekly wage earners which are for a half year only are made by h.m. inspector of taxes. the taxpayer normally charged by the district commissioners may, if he wishes, elect to be dealt with by the special commissioners and even if he allows his assess- ment to be made by the district commissioners, he may take an appeal against that assessment to the special commissioners. during the past 50 years income tax grew so much in importance and complexity that its efficient administration compelled a con- siderable development of the methods of administration. the high graduation of the tax rests very largely upon the factor of the total income from all sources of the taxpayer. as business and finance have grown in complexity, the sources of individual incomes have ramified accordingly, necessitating close and continuous inter- communication between various parts of the country. the scheme of administration originally laid down having made no adcquate provision for inter-communication between the various bodies of commissioners, this defect has been almost of necessity filled by the development of the official organisation of the inspectorate of taxes, functioning under the direction of the board of inland revenue. in practice, therefore, to-day the inspector of taxes carries out, with the full concurrence of the various bodies of commissioners, most of the duties that are vitally essential to the smooth-working efficiency of the machinery of administration. nevertheless, the key functions of the district commissioners have been preserved throughout. in a2i the absence of any detailed accounts or other evidence, it is the additional commissioners who determine the amount of the assess- ment upon business profits; even more important, the general com- missioners still retain their appellate functions and so stand in an independent and impartial position between the taxpayer and the representative of the revenue. rates and yield of tax.—during the three years preceding the war, 1911-3, the normal rate of tax was is. 2d. in the £ and the net produce of each penny of the rate was round about £3,000,000. at that time the exemption limit stood at £160 and out of some 19,000,000 of occupied persons only 1,200,000 were within this scope of the tax. in 1915-6, the exemption limit was reduced to £130. notwithstanding the depreciation in the value of money it remained at that level until 1920. in 1920-1, when the system of differ- entiation and graduation was radically altered in accordance with the recommendations of the royal commission on the income tax of 1920, the effective exemption limit was raised to £135 of assessable income, or £150 in terms of earned income. under the influence of the change in the price level and the consequential movement of wages the total number of individuals within the scope of the tax rose in 1919 to 7,800,000, but it had fallen in 1925-6 to 4,200,000. the standard rate of tax was changed on six occasions between 1914 and 1925. the peak rate of 6s. in the £ stood for the four years from 1918-9 to 1921-2 inclusive. i[t was reduced to §s. in 1922, to 4s. 6d. in 1923 and to 4s. in 1925. the statutory tncome of persons liable to tax amounted in 1913-4 to {951,000,000 and the net tax collected in that year amounted to {43,500,000. these figures relate to the whole of the united kingdom of great britain and all ireland. for 1924-5, the total statutory income of persons liable to the tax for the new united kingdom of great britain and northern ireland was estimated at {£2,300,000,000. in 1924-5 the exchequer receipt was nearly £274,000,000; in 1925-6 the exchequer receipt was £259,000,000 and it was estimated that the collection in 1926-7 would amount to £255,000,000. the preceding figures relate to income tax alone and do not include the yicld of the super-tax. prior to the war the point at which lia- bility to this tax commenced was {5,000. incomes below that figure were exempt from this impost. in 1914 the exemption level was reduced from £5,000 to £3,000. in 1918-9 the scope of the tax was altered to include all incomes exceeding {£2,500 and in 1920-1 further extension was made by the alteration of this limit to £2,000, before the war the rate of super-tax was 6d. for every £ of the amount by which the total income exceeded £3,000, although, as noted, no liability arose unless the total income exceeded £5,000. a graduated scale was introduced in 1914-5, increased in weight in i91§ and 1918, until it reached the peak rates in 1920, when it ranged from is. 6d. in the £ for every £ of the first £500 of the excess over £2,000, to 6s. in the £ on every £ of income above £30,000. a reduced scale! of rates of tax came into force in 1925-6. in the year before the war only 14,000 persons were liable to this tax. in 1924-5, the number of individuals charged had risen to 90,000. a similar and even greater increase marks, of course, the annual yield of the tax. from £3,250,000 in 1913-4 the year’s collection had grown to £68,500,000 in 1925-6. these figures may be completed by noting that during the 10 years from 1916-7 to 1925-6 inclusive, the british taxpayer paid £2,768,000,000 in income tax and £493,000,000 in super-tax, making a total of £3,261,000,000. this burden was borne in addi- tion to £1,280,000,000 in the form of excess profits duty and cor- poration profits tax, each of which was levied upon business profits before the income tax and super-tax were due to be computed. ill. the british dominions taxation according to faculty, that is, direct taxation based upon the principle of ability to pay, so early established in great britain, was naturally carried overseas to the various british possessions. it is not therefore surprising to find income taxes firmly established to-day in south africa, in the provinces and protectorates there as well as in the union, in canada, where also there are provincial income taxes as well as the dominion tax, australia, where a similar widespread use of the tax is made, new zealand, india and in most of the west rate in the £ so, 0k 1qon the first £2,000 of the income. nil on the next £500 (to £2,500) ; : i we & on the next £500 (to £3,000) on the next £1,000 (to £4,000) on the next £1,000 (to £5,000) on the next £1,000 (to £6,000) on the next £1,000 (to £7,000) on the next £1,000 (to £8,000) on the next £2,000 (to £10,000) on the next £5,000 (to £15,000) on the next £5,000 (to £20,000) on the next {10,000 (to £30,000) on the remainder (above £30,000) cit gr ae oe ga ga net 422 indian islands. naturally also there is a strong family resem- blance between the various income tax systems, most of them having been strongly influenced by british law. income is usually defined broadly but comprehensively, but there is a general absence of the schedular arrangement of the british tax. broadly speaking, the year preceding the year of assessment is favoured as the basis of computation of the income to be charged. the minimum amount of income exempted from tax varies, but personal allowances to the taxpayer, his wife and children are general. graduation of the tax is a common feature, and the device of an additional tax, or super-tax, is freely adopted. in some dominions, graduation is extended also to companies. the methods of graduation range from simplicity to formulae of great complexity. differentiation in favour of earned income is found, but is not widely favoured. taxation at the source is a frequent feature, especially in respect of dividends paid by companies. the rates of tax vary widely, as may be expected from the range of budget requirements of communities of dif- ferent populations and varying degrees of wealth. asa rule, the income tax in the british dominions overseas is one tax levied upon the base of the total income, irrespective of the nature of the components of that income. in this respect, the british tradition is followed. iii. some european countries latin countries.—in latin communities, a more complex sys- tem of income taxation is commonly found. there the develop- ment of the income tax as a fiscal instrument has been slower, and has met with much greater opposition. the influence of the ancient taxes in france of the real estate tax (contribution fonciere), the door and window tax (contribution des portes et fenetres), the business tax (pafentes) and the personal property tax (contribution personelle et mobiliere) led to the introduction by caillaux, shortly before the world war, of an income tax, in the form of seven schedular taxes on income, combined with a general income tax on total income. under this system, the schedular income taxes (impets cedulaires or impets sur les revenus) are but lightly linked together. different rates may be, and often are, imposed under the several schedules; each sched- ule may have its own scale of personal abatements or reliefs; each may have its own rules for the computation of income. in france, the seven schedules cover buildings and land, agricul- ture, dividends, interest, etc. (again divided into four sub- groups), industrial and commercial profits, salaries and pensions, professional earnings and mining. kach of the seven schedules has its own method of assessment, usually its own particular allowances, and its own special rate of tax. the general income tax (pimpet general sur le revenu) is steeply graduated. belgium, on introducing an income tax into her fiscal system in 1919, followed the same method of schedular taxes combined with a general income tax. here, there are three schedular taxes, on income from real property, income from investment of personal property and, lastly, income from trade business or profession or employment. agricultural profits are included under the third schedule. for the first two schedules there is the same flat rate, but for the third, the rate of tax is graduated according to the amount of income. the general income tax is also graduated. in spain and italy similar systems prevail. an income tax, designed to measure and to tax the almost infinite variations of methods by which men seek the means to satisfy their wants can never be simple, but the schedular sys- tem adds complexity to complexity. moreover, so far as the rates of tax are differential, they tend to affect the ordinary incidence of an income tax, and sd to set up reactions upon economic effort which defy measurement. there is also a strong tendency to regard the schedular income taxes, not as personal taxes but as real income taxes, a contradiction in terms which is at present proving a grave obstacle to the development of a satisfactory solution of the problem of double taxation. bibliography.—j. c, stamp, british incomes and property (1916); s. dowell, the acts relating to the income tax, 8th ed., rev. by j. e. piper (1919); e. r. a. seligman, public finance (1926). income tax see also report of departmental committee on the income tax, with appendix, cd. 2575 and 2576 (1905); report of the select committee on the income tax, no. 365 (1906); report of royal commission on the income tax, cmd. 615 (1920); finance act, part 2, income tax (1925); commissioners of inland revenue (annual reports); fin- anctal statements presented to the house of commons by the chancellor of the exchequer (annual). (w. h.c.) iv. the united states although taxes on gains and profits derived from personal ability as distinguished from property—so-called ‘‘ faculty ’’ taxes—were employed in the american colonies before the middle of the 17th century, no successful use of the general income tax was made in the united states until the civil war; and the income taxes then adopted were soon thereafter repealed, or fell into practical disuse. the demand for effective income taxation, however, showed great vital- ity. it kept moribund income tax laws on the statute books in sev- eral states; led to abortive experiments with the tax, particularly in the ‘forties and ‘nineties; and finally in 1909 resulted in the adoption of a federal excise tax ‘‘ with respect to the carrying on or doing business ’’ by corporations, equivalent to 1% of the annual net in- come over and above $5,000. this proved to be in substance an effective income tax. ; state income taxes.—in 1911 the state of wisconsin adopted a general income-tax law applicable to individuals, partnerships and corporations. the practical success of this tax encouraged other states to adopt similar laws or to vitalise the administration of un- successful income-tax laws already on the statute books; and al- though a few states either repealed or rejected the tax, about one- third of the statesin 1925 had income taxes. the adoption of income taxes by the states has been largely for the purpose of replacing the unsatisfactory personal-property tax (particularly on intangible personal property) and the so-called corporation franchise tax. the newer state income taxes are gencrally administered by state or cen- tral authority, but provide for the return of a substantial portion of the tax to the county or local governments. there is an increasing tendency to assess the tax on the basis of the federal income-tax return and an effort is made by apportionment devices to exempt in whole or in part business or corporation income derived from prop- erty located and business transacted outside the state. jurisdictional questions and multiple taxation thus constitute fundamental prob- lems. the .various state income taxes differ considerably in their exemptions and rates, but in general the rates are much lower than in the federal tax, the highest rates—in s. carolina—being one- third of the federal rates. however, the combined federal and state taxes represent a serious burden on the larger incomes. federal income tax.—the foundation for the federal system of income taxation was laid by the ratification on feb. 25 1913 of the sixteenth amendment to the constitution, which pro- vides :-—— that congress shall have power to lay and collect taxes on in- comes, from whatever source derived, without apportionment among the several states, and without regard to any census or enumeration. | the development of the federal income tax is suggested in the accompanying tabular statement. under the revenue act of 1926 the income tax carries exemptions of $1,500 for single individuals, $3,500 for heads of families and $2,000 for cor- porations. under the personal income tax there is a further specific exemption of $400 for each child under 18 years and for every dependent incapable of self-support. individuals are subject to a split normal tax of 13% on the first $4,000 of tax- able income, 3% on the next $4,000 and 5% on the remainder; and to a surtax ranging from 1°% of the net income between $10,000 and $14,000, to 20% on the net income in excess of $100,000. corporations are subject to a flat rate of 133%. (since jan. 1 1926). earned income (to the extent of $20,000) is taxed 25° less than unearned income, all incomes of $5,000 or less being considered as earned. net income is defined as all income and gains “ from whatever source derived,” excluding cer- tain specified classes of income and less certain specific deductions. the most important characteristic of the federal income tax is its striking productivity, the elasticity of which is illustrated in the table. the present exemptions are high compared with similar exemptions allowed in other countries, and only a small proportion of the population is directly affected by the tax. a large proportion of the tax is collected in the industrial or urban states and is thus marked by some unfortunate class and sec- tional characteristics. compared with similar taxes of other countries the rates on small and moderate incomes are low, while the rates on the larger incomes were until the year 1925 unusually index numbers federal income tax personal income tax —_—_— | 2 _____,____ ee total number of returns! per cent number of returns to population total net income 357,598 437,036 4,425,114 5,332,760 6,662,176 7,698,321 0-37 0-43 4°27 5°03 6-28 6-94 $3,900,000,000 | $6,298,577,620 | $15,924,639,355 | $19,859,491,448 | $19,577,212,528 | $24,840,137,364 total tax yield . : f $28,253,535 $173,386,694 | $1,127,721,835 | $1,269,630, 104 $7 19,387,106 $663,651,505 average tax individua 79.01 $396.60 $254.85 $238.08 $107.98 $86.21 average rate of tax:— ieee $1 ,000-$2,000 a3 i-19 % 0-87 zo 0-81 % 0-49 %% incomes $5,000—-$10,000 00-61% a384 % slo, 2-90 “ 2-04% incomes $25,000-$50,000 ses 1-41 % 13-32% 12°13 %% 11-53% 7°97 % incomes $100,000-$150,000 - 3°48 % 33°68 % 33°12 % 32-00 “o 19°85 °% incomes $1,000,000 and over ne 11-09 % 64°65 % 64-87 % 63°59 0 23°53 ‘0 general average rate : 0°725% 2°75 % 7-08 % 6:39 %5 3°67 % 2-67 % normal rate $4,000 and under 1% 2% 6% 4 %o 4% 4% normal rate over $4,000 ; of 2% 12 8 zo vo 8% maximum surtax ee 135 65 % 65 % 65 % 50% incomes under $5,000:— per cent of total returns 36-60 89°17 87-67 92-10 91-87 per cent oj total net income returned 9:92 59°00 56-14 2°37 66-29 per cent of total tax i-e5 12:84 10-16 12-90 12-21 incomes over $100,000:— per cent of total returns. - i-54 o-10 o-le 0-035 0-056 per cent of total net income returned 29°47 6:22 5:9 2-37 3:67 per cent of total tax 73:11 41-66 42:77 28-11 31-76 personal exemptions:— to individual $3,000 $3,000 $1,000 $1,000 $1,000 $1,000 to head of family $4,000 $4,000 $2,000 $2,000 2,500? $2,500? for each dependent i 23 $200 $200 $100 $..00 corporation taxes 1913 1916 1918 1919 192! 1923 total number of returns 316,909 341,253 317,579 320,198 356,397 398,933 returns showing taxable in- come a a rr 188,866 206,984 202,061 209,634 171,239 233,339 returns showing no taxable income ; 128,043 134,269 115,518 110,564 185,158 165,596 total net income $4,714,000,000 | $8,765,900,000 | $8,400,000,000 $9,412,000,000 $4,336,000,000 $8, 322,000,000 elie as vel , ae $43,127,740| $171,805,150 $653,198,483 $743,535,888 $366,443,621 $937, 106,798 var profits and excess profits tax yield z co $2,505,565,939 | $1,431,805,690 $335,131,811 ae _total tax yield . $43,127,740 $171,805,150 | $3.158,764,422 | $2,175,341,578 $701,575,432 $937,106,798 grand total— individuals and corporations $71,381,275 $345,191,844 | $4,286,486,257 | $3,444,971,682' | $1,420,962,538 | $1 ,600,758,303 1 returns reporting net income in excess of personal exemptions. * for net income of $5,000 and over, this exemption was reduced to $2,000, high. from the technical standpoint, the striking characteristics of the federal tax are: the high ratio of surtax to normal tax; the marked difference in the normal tax applicable to individ- uals and corporations respectively; the taxation of gains from the occasional sale of capital assets, at a flat rate of 123%; its failure, largely because of constitutional limitations, to reach interest on municipal bonds and other tax-free securities; the small use of “ stoppage-at-source ” (whereby the normal tax is withheld and paid direct to the government by payers out of payments due to corresponding payees) ; and the credit accorded for income and profits taxes paid to foreign countries on income derived from sources therein. the tax law is extremely complex, largely owing to the taxa- tion of capital gains and to certain “ cushions” or relief pro- vistons designed to protect the tax-payer against hardship; but the law has been simplified in a measure by the repeal of the excess-profits tax and of many of the special war provisions such as allowances for amortisation, inventory losses and the like. this has been accompanied by a movement away from cen- traliscd administration of the tax, and by a steady reduction in the rates. nevertheless, complexity, centralisation and high surtax rates still cause excessive delay in the audit of the larger returns. the interpretation of the law has been much improved by the creation in 1924 of a board of tax appeals (an extra- administrative tribunal whose decision is final unless modified by the courts), and by giving local revenue agents the power to audit and settle the smaller cases. the american tax reveals a gradual approach to the british position on capital gains and losses, which are taken into account at a special rate of 124%. bibliography.—e. r. a. seligman, the income tax (1914); k. k. kennan, income taxation (1910); d. o. kinsman, the in- come tax in the commonweaiths of the u.s. (1903); r. m. haig (ed.) i the federal income tax (1921); g. e. holmes, federal taxes (1926 ed.); treasury department, regulations 65 (1924); bureau of the census, digest of state laws relating to tuxation and revenue (1922); prentice-hall, federal tax service (annually); commerce clearing house, federal tax service (annually); corporation trust co., lzucome tax service (annually); national income tax magazine (monthly); bull. ef national tax assn. (monthly), (t. s. a.) index numbers.—the phrase index number is some- times applied to any series in which a chosen term is written as 1900 and the other terms expressed as percentages of it. the earlier and more general use is, however, consonant with the following definitions:—“ an index number [is] a number adapted by its variations to indicate the increase or decrease of a magnitude not susceptible of accurate measurement ” (edge- worth, economic journal, 1925, p. 379); “index numbers are used to measure the change in some quantity which we cannot observe directly, which we know to have a definite influence on many other quantities which we can so observe, tending to increase all or diminish all, while this influence is concealed by the action of many causes affecting the separate quantities in different ways” (bowley, elements of statistics, 1920, p. 196). thus index numbers are applied to the measurement of the general movement of prices, cost of living, wages, production, consumption, employment, etc. the data from which index numbers are formed consist of records of particular quantities at two or more dates or places and information about the relative importance of these quantities in a general measurement. in constructing an index number to measure the movement of any defined magnitude it is necessary to decide on the choice of the scparate quantities, on their relative importance, on the period or place to be taken as base, and on the formula of compilation. thus, in the statist index number the objective is the measurement of the change of 424 wholesale prices in the united kingdom, 45 commodities are selected and regarded as of equal importance, the period 1867-77 is taken as base and the average price in that period of each commodity is equated to 100, the terms in each series of prices are expressed as percentages of that average (‘‘ price-relatives ’’), and the simple average of the 45 relatives in any year form the index number for that year. a distinction is drawn, but not by all writers, between two classes of index numbers: (a) where, as in the definitions quoted above, the object is to measure the movements of a magnitude without specific reference to any pre-determined application, e.g., the purchasing power of money in general (‘‘ indice mone- taire ’’) as concelved by jevons, the variation of prices and the value of currency since 1782 (1865); (b) where the measure- ment is to be applied to a defined group, e. g., the changes in the cost of a quantitative standard, such as is used in a cost of living index (“indice budgetaire’’). many index numbers, however, are intermediate between these classes, and much of the analysis of the form and content of the numbers is appropri- ate to both. thus, in all cases of price measurement, only those commodities can be included which are measurable in a defined and unchanged unit, and for which the price can be ascertained, and (unless the geometric mean is used) a base period in which each price is equated to 100 must always be selected. (a) in the measurement of the purchasing power of money in general it is argued that the prices of all commodities, not sub- ject to regulation or monopoly, are equally significant. theo- retically the problem is one of pure sampling, and the precision of the result in any year is directly proportional to the square root of the number of independent terms included and inversely proportional to the mean dispersion of these terms from their average in that year. in practice, the terms are not completely independent, for the prices of related commodities influence one another, and the precision is thus reduced. also, the greater the interval from the base year, the greater tends to be the dispersion and the smaller the precision. in periods when prices are changing rapidly, as in the years 1914 to 1923, the dispersion is usually considerable and the measurement loses accuracy. there are three types of averages applicable to price-relatives: their arithmetic mean as described above for the statist index number; the geometric mean of the same numbers, that is the nth root of their product if there are n commodities; and the harmonic mean, which is the reciprocal of the arithmetic mean of the reciprocals. thus, for two commodities whose prices were 6d. and rod. in the base year, and 1s. and 2s.1d. in any other year, the price-relatives are 200 and 250, their a.m. is 225, their g.m.is v¥ (200 x 250) = 223-6, their h.m.is1+4(agg+a59) = 222-2 if the latter year is taken as 100, the relatives in the original base year are 50 and 4o, the a.m. is 45, and 45:100= 100:222:2. the h.m. of the “ forward ” relatives gives the same measurement as the a.m. of the “ backward ” relatives; or, if the comparison is between two places the h.m. of the relatives when the first is taken as base gives the same measurement as the a.m. when the second is so taken. . these statements are more readily expressed algebraically. write p;, pe... for the prices in the first year (or place), and e pi, pe... for the second. write 100 ss ait+d)... i where a= “ee is the a.m. of the price-relatives.1 then zd=o, the geometric mean, g= ¥ (rire...) and *“nilog g=z log a(i+di)=n log a+-zd— 32d?... =n log a—4ns?, approx. where s is the standard deviation of the dis- persion of the relatives each divided by a, and mean d3, etc., are neglected. hence a= gel*?=g(1+}s\"), approx. if s is small. also the harmonic mean, har+—2-=na+2(1+d)4 1such an expression as zv is to be read vitve+. . .+vn where n is the number of similar terms. index numbers ee ashx-3(1-d+e\" —...)=h(i+s\"), aporox. “ h=g(ri—3s*), and ¥ ah=g, approx. thus, if s is small a, h, g differ little from each other, but a>g>h. if gis the correct measurement a exaggerates a rise and underestimates a fall (since 1oo—a<100—g), while h has the opposite effect. the g.m. of a and h is very nearly g. for the statist index number in 1913 (1869-79 base period), a=85:0, g=8o-9, h=76-5, s’=-104. as regards precision of sampling a may be written as a 1 i) =a (i +:053) = 85 £4-4, if the 45 correlated entries are taken as equivalent to 36 independent (statistical journal, p. 316, mar. 1926). in this case the standard error attributable to sampling is about the same as the difference between a and g. _a general change in the relation of currency to its use tends to affect all prices in the same proportion, and “ if other disturbing causes may be considered proportional to the ratio of change of price they produce in one or more commodities, then all the individual variations of prices will be correctly balanced off against each other in the geometric mean ”’ (jevons, investiga- tions in currency and finance, 1884, pp. 121-2; see also bowley, economic journal, 1921, p. 202). the geometric mean is there- fore considered appropriate to this problem. it has the ad- vantage that it gives less importance to extreme measurements than does the arithmetic mean. it has the further advantage that the comparison by its use of any two years is independent of the choice of the base vear (see below). (b) the method generally used in the more objective problem of measuring the change of cost of a fixed aggregate of goods is as follows: the quantities of defined commodities which are pro- duced or consumed in a year, or exported or imported, or are purchased in a week by a family, are estimated and the prices per unit are ascertained in a base year or period and also in the year to which the measurement is to refer. this budget of quantities is valued at the base year prices and again at the prices of the year in question; the latter total expressedi as a per- centage of the first gives the required index number. the com- putation is often effected by writing down the relative expenili- ture (quantity & price) on each commodity in the base vear, applying to each the percentage that its price in the second year forms of that in the first, and adding the products. this sum (divided by the total of the base year’s relative expend- itures) gives the same index number as before. cost of living index numbers are computed by this method. in this form the index number appears as a “ weighted average,’”’ where the weights are the relative expenditures and the things weighted are the price-relatives. from the theory of weighted averages it is known that considerable roughness in the weights has little effect on the result. it may also be regarded as an average of price-relatives which form a sample of a larger group than that included, and thereforce—as under (a)—its precision depends on the square root of the number of independent relatives and, inversely, on their dispersion about their average. write q:, q... for the number of units of quantities, pi, ps . . . for the pricesin the base period,pi,pe... for those in the year in question. then ef) =q,p:+q2p24+ ... 1s the total expenditure in the first year, and f2= qipitqpe+. .. is the total expendli- ture in the second year. then the index number ts i1= 100k2+ e}. now write q:pi=llfi, q.pe=he...., with h+h+...=1. write toopp=mpi, roops=rep’s.. ., sothatr, re... are the price relatives. then the new index number is hrn+hrm+...= (qi piritq2poret- om )+ ey = 1oo(qipit qope-f oe eck \\+ r= the weighted geometric mean, gi= ¥ (mm... ) where ntm+...=n,so that n logg=n, log m+n log re+. ... the ‘nglish board of trade, for its index number of wholesale prices, uses a similar form in which, if for example ni is the weight assigned to cereals, r\"1 is replaced by 1% %e1x... ton factors where 1), 2-1. . are price relatives of nm, different quotations of cereal prices. when ni, no... are once chosen the comparison between any two years a and b is independent of the base year; index system—india for if the price ratios for the years are written %, .f... and g ..and g,, gp are the resultant means, then log a= ig log gp—log ga=ni(log pri—log am) no(log pre—logarm)+ .. . =m log apti--ne log apret. .., where abt, ab¥2...are the ratios of the prices of the year b to those of the year a, and the prices in the base year do not enter. if with similar notation the arithmetic average is used, we have ap+aa=(niptitnipte+ 2.) (nati ne ate+. . .), in which no corresponding elimination takes place. the weakness of this method is that, when we make a com- parison between two years or two places, the relative expendi- tures generally differ and each scheme appears to have an equal claim to be included. this difficulty may be met theoretically by computing the index twice, first with the expenditures in year or place a and then with those in b and averaging the result. for comparison between places this method is applied, but it is seldom that the necessary ‘‘ weights’ can be obtained for more than one year, and till there is a further census of pro- duction or a new collection of working class budgets the double computation cannot be made. further, if the weights are avail- able for three years or places, a, b and c, the index for b in reference to a multiplied by that for c in reference to b does not by any weighted average formula give that for c in reference to a (+100), as it should. this so-called “ condition transitive ” is not satisfied by any formula that is symmetrical with regard to weights. write ,q:, .qe... and pi, .pe. .. for quantities and prices in a, and lq, bqa. oy bp1, pls aes in be the be forward . index number is i,=1ootaqr,piez.qi-.p: and the “ backward ” index number is i,=1002,qi-bp:+2,qi-ap:. the geometric mean v¥v 1,xi, is prof. irving fisher’s ‘ ideal index number ” (the making of index numbers, 1922, p. 220). the arithmetic average, 4(i,+i.) and the form ip:=1002}(.q:+1q))-.pi1+ ~2(,q0:++q:)api, may be conveniently used. the three forms of average may be expected to give nearly identical results. i;, in which the quantities at the two dates are averaged, is per- haps the simplest in idea. each average lies between i, and i,, and is greater than i, if an increase of prices of a commodity above the general increase from year a to a later year b is cor- related with a relative decrease of the quantity purchased, as may be expected if there is a possibility of substitution of one com- modity for another without any general change of standard (bowley, statistical journal, 1919, pp. 343 seq.). in their measurement of the change of import or export index prices from year a to the consecutive year b, the board of trade uses the formula i, and for comparison with the next year c by, ble. p> porppi dd orel t . : —-—— —_~——. which d t l the formula 1 s o.. s.oep: which does not equa z qieep: ° ° ° ld 1005 o1-.pi obtained by direct re-valuation of the c quanti- ela ties by the a prices and, if there is a very rapid change of quan- tities and prices, may differ considerably from it. this is an example of the ‘‘ step-by-step ” or “chain” method of index 2 qrapi pa soirak’s number of quantity of trade (prices constant), and roo is an index = pqirnpi az aqral is the index number of value of trade. the product of these measurements of price and quantity is the index of value (x 100). since no form of index number satisfies all the conditions which can properly be laid down (see e.g., gini, in afefron, 1924, pp. 8r and 134), on the one hand we must select the form most suited for a particular purpose, on the other we can only expect precision when different relevant forms give approximately the same result, for which the conditions are that the dispersion of prices from their average should be small and the number of constituent elements should be considerable. sce cost of living: prices. (a. l. bo.) index system: see office appliances. numbers. note that from a to b, 100 425",
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