National Income in the United Kingdom and the United States of America

The Review of Economic Studies, Ltd.

National Income in the United Kingdom and the United States of AmericaAuthor(s): Richard StoneSource: The Review of Economic Studies, Vol. 10, No. 1 (Winter, 1942-1943), pp. 1-27Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2967492 .

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National Income in the United Kingdom and the United States

of America." 2

I. INTRODUCTION.

The purpose of this paper is to draw attention to the statistics of national income and expenditure in the United States of America which are now being prepared in the Department of Commerce of that country. With the help of these figures the development since I929 of certain aspects of the American economy will be shown. Recent movements in America will be compared with movements in the United Kingdom and for this purpose the new quarterly statistics for America will be used to enable us to trace the turnover to total war down to the second quarter of this year. The paper will be concerned mainly with money value figures unadjusted for changes in prices since the data for such an adjustment in the detail in which they would be required are not at present available.

II. THE DEFINITIONAL PROBLEM.

Since any attempt to compare the structure of two economies is a hazard- ous business I should like to make clear my own attitude to the problem at an early stage. In setting out tables of national income and expenditure there are two problems which it is important to keep separate. I shall call these respectively the economic and the logical problem. The economic problem is concerned with what it is we wish to measure and what conventions it is convenient to follow in the treatment of the items entering the tables. For example in what follows I shall operate mainly with two income concepts. The first, the net national income at factor cost, is intended to measure the net incomes of the factors of production and is by definition equal to the current value of goods and services produced by the factors of production of a given country valued exclusive of net3 indirect taxes; it is also equal to expenditure on consumption plus government expenditure on goods and services plus net additions to capital at home and abroad, all valued at market prices less net indirect taxes.

The second concept is that of private disposable income which is a measure of the aggregate disposable money income available to a given country. It is equal to the earnings of the factors of production less any income public authorities may receive from property plus any transfer incomes received by the private from the public sector of the economy. Private disposable income

I This paper was read before the Manchester Statistical Society on 28th October, 1942. I am indebted to the Society for permission to republish it here.

2 I should like to express my gratitude to Dr. M. Jahoda who, in spite of many other pre- occupations, was kind enough to work out most of the calculations on which this paper is based.

3 Net indirect taxes means the excess of indirect taxes over subsidies.

I



2 THE REVIEW OF ECONOMIC STUDIES

may, for certain purposes, conveniently be further divided into private personal and private impersonal income.

These two main concepts are useful for different purposes. The net national income at factor cost is a measure of the total net income of the factors of production and its constituents show how income is distributed between different factors. Similarly, the constituents of the net national output show how much of this income was generated in different branches of economic activity, while those of the net national expenditure show the forms in which current output goes to satisfy the needs of the community. Private disposable income on the other hand is concerned not with various ways of classifying current output, but with the receipt and disposal of all receipts which reach the private sector of the economy as income, irrespective of whether or not they are gained as a result of productive activity.

In order to define these concepts precisely, it is necessary first to decide on the treatment of a large number of items. Once the treatment of any item is decided upon it must of course be applied consistently throughout the tables. The two concepts of income define different things; they are not merely alternative ways of defining the same thing.

In many cases, at any rate in the present state of knowledge and perhaps inevitably, these questions of treatment must be settled on some conventional basis convenient for the purposes in hand. As an example I will take the case of compulsory contributions to social insurance. Since these are compulsory they may reasonably be regarded as a form of tax. They may further be treated either as direct or as indirect taxes. In the British White Paper' employees' contributions paid out of income are treated as direct taxes while employers' contributions are considered as a business expense, and are treated as an indirect tax. The employers' payments could however have been treated as in effect an addition to wages and salaries which in turn is paid as a direct tax to the social insurance fund. There is no obvious reason for regarding one method as right and the other as wrong, and any choice made must be arbitrary. It may be of course that for some particular problem one method will lead to more useful results than another.

We have so far assumed that these payments are to be treated as analogous to some sort of tax. This is not necessary. Above, I stressed their compulsory nature; but I might have stressed the fact that they are a method of meeting what is in fact a real cost of industry and from this point of view are analogous to workmen's compensation premiums. These are not commonly regarded as taxation. We might therefore decide to treat social security payments as an insurance transaction like workmen's compensation premiums.

Having decided to do this we have still a further decision to make. The payments might be regarded merely as a business expense in which case they would not be part of anyone's income or' they might be regarded as an addition in kind to wages and salaries. Again there is no obvious reason for regarding one method as right and the other as wrong.

1 An Analysis of the Sources of War Finance and an Estimate of the National Income and Expenditure in 1938, 1940 and I941. Cmd. 6347. Aprfl, I942.



NATIONAL INCOME IN THE U.K. AND THE U.S.A. 3

This brings me to the second kind of problem; the logical problem. Let us suppose we have decided to treat employers' contributions as an indirect tax. As such, they are a business expense and are to be deducted from business receipts before profits are arrived at. They also form no part of wage and salary incomes. Looked at from the expenditure point of view they are a charge against the market value of goods and services before income is reached. This is not to say that they are necessarily passed on to the consumer, only that they must be met out of the market value of the goods. Accordingly if we measure expenditure at market prices then these payments along with other indirect taxes must be deducted in order that our expenditure may be at factor cost and therefore equal to the sum of factor incomes. There is no convention or convenience about this; it follows unambiguously from the original decision.

I hope this one example will be sufficient to illustrate the nature of the two kinds of problems. In the practical work of income measurement the formulation of reasonable and appropriate conventions and the consistent application of the consequences of these conventions throughout the tables of income and expenditure, presents an almost unending problem.' What I have called the economic problem clearly becomes of greater and greater importance as the analysis is extended to cover a number of countries with different institutional arrangements.

In the present case if a comparison is to be fair and useful it is important that the economic conventions adopted shall be the same for both countries. Quite apart from practical difficulties this is not altogether a straightforward matter. For example suppose that two countries made different institutional arrangements in respect of the health insurance of employees. One country required that contributions be paid into a government fund, the other that a policy be taken out with an insurance company. If all payments were made by employers and we agreed to treat those of the first country as analogous to indirect taxes and those of the second country as business expenses not taking the form of supplements to the income of employees, then we might so arrange matters that the national incomes of the two countries were unaffected by the different institutional conditions. But when we come to tax payments, the position would be different in the two countries. If the difference between the countries applied not only to health insurance but also to a large number of other important transactions it might be extremely difficult or practically impossible to make a sensible comparison of tax burdens. Little however is known of these difficulties. Probably the best way to find out about them would be to attempt the construction of income and expenditure tables for a country like the U.S.S.R. where institutions are very different from those of capitalistic countries like this country and the United States.

1 logical problem may reach a considerable degree of complexity especially where an elaborate arrangement of income and expenditure tables is adopted. Mr. Meade and I made an attempt to set out the general principle on which the solution depends in an article appearing in the Economic Journal for June-September, I94I (see sectipn VIII, pp. 227-230). We hope to supplement this method by a rather different approach as follows: Consider the universe of all balance sheets whether of a current or capital nature for, say, the United Kingdom which in the abstract may be considered to exist for any one period whether or not they are in fact ever written out. What then are the laws for combining these balance sheets into meaningful and consistent aggregates ?




In what follows I have done my best to arrange the American tables on the same basis as those given in Cmd. 6347. Nevertheless, it must be remembered that there are innumerable possibilities for minor discrepancies. Thus, it is important that comparisons should not be pushed too far in view of the difficulty of insuring that small component items are estimated on the same definitional basis.

III. THE NEW AMERICAN QUARTERLY ESTIMATES.

In a recent paper' I endeavoured to arrange the annual estimates of the Department of Commerce on the same basis as was adopted in the British official estimates. The tables given below2 attempt as far as possible to do the same for the new quarterly estimates published in the Survey of Current Business.3

Between I939 and the second quarter of this year the net national income of the United States on the definitions here employed has risen in money terms by over 6o per cent. Although prices have risen as well this represents a considerable rise in real output. At the same time government expenditure on goods and services connected with the war has risen from nearly 3 to nearly 4I milliard dollars, and taxes have also risen though as a percentage of private disposable income they are at the moment low by British war time standards. This is hardly surprising since it took this country a considerable time to raise taxation to its present high level. But while taxation has risen relatively slowly, private savings, and in particular personal savings, have increased with enormous rapidity until in the second quarter of this year they reached an annual rate of some 23 milliard dollars or about I9 per cent of private disposable income. Consumers' expenditure at current market prices have risen since 1939 but under the impact of war are now beginning to decline. As might be expected, most of the fall is taking place in the purchases of durable goods. Estimates are also available4 of consumers' expenditures at constant prices, s.e. after correction for changes in the value of money. Taking I939 as IOO, a peak of II7 was reached in the second quarter of I94I. The level at the second quarter of this year was 107, a decline of about 9 per cent from the peak. Looking at these figures, it is evident that the American public has responded magnificently to the requirements of total war.

Under normal conditions, as will be seen in the following section, the annual rate of private disposable income current in the second quarter of this year, i.e. I20 milliards, might be expected to have been associated with an expenditure for private purposes of some 88 milliard dollars at factor cost. The level of such expenditure in fact reached was about 65 milliards. In this period, therefore, an annual rate of 55 milliards went to the government by way either of taxes paid out of private incomes or loans. Of this 55 milliards, 23 milliards may be regarded from the experience of the period I929-4I as abnormal and attributable

I See Economic Journal, June-September, 1942, pp. 154-175.

2 See Appendix I below. 3 See S.C.B., August, I942, pp. 14 and 15.

4 See S.C.B., August, I942, Table 5, line II, p. 14.




to the war. This is one measure, though there are others, of the diversion of the American economy to war.

IV. SOME PEACE TIME RELATIONS IN THE AMERICAN ECONOMY.

The following analysis attempts to answer two questions. First, what is the normal relation between income on the one hand and expenditure on consumption, tax payments and saving on the other ? Second, to what extent have the combined endeavours of the people and the government succeeded in disrupting this relationship in the transition from a peace to a war economy ? At the same time I shall analyse the other side of the balance sheet and endeav- our to show the way in which the payments of rent, profits, wages, etc., vary as income varies.

It is evident that the statistics appropriate to this purpose could be defined in a number of ways, each of which would enable us to answer certain questions. There is therefore nothing unique about the following method; it is adopted because for present purposes it is convenient. The basic income concept used is what I have called private disposable income defined as the net national income at factor cost plus transfer payments miinus miscellaneous income from public property, etc. Looked at another way it is equal to personal incomes before deduction of direct taxes, etc., plus private impersonal incomes.

We must now ask: what is the correlative of this income concept on the expenditure side of the account ? The answer, as may be seen by analogy from the right-hand side of Table II of Cmd. 6347, is that the expenditure side may be divided into (a) personal expenditure on consumption, (b) private tax payments and (c) private savings. In the present application, consumption will be taken at factor cost, taxes will relate to the total of direct and indirect taxes other than those paid by public authorities themselves' and private savings will be taken equal to private net investment at factor cost plus loans to public authorities. As in the case of consumption, indirect taxes on net investment are treated as part of tax payments and therefore not included in savings as here defined.

The advantage of this procedure is that the sum of consumption and net investment at factor cost is a measure of the command over current labour and equipment currently being exercised by the private sector of the economy. The remainder of private disposable income goes either by way of taxes or loans to finance the expenditure of public authorities. The residual expenditure of public authorities not met in this way is met out of income from public property which does not form part of private disposable income. Tax payments by public authorities to themselves are simply a piece of intergovernmental accounting and could clearly be omitted from both sides of the public authority account. Throughout this section indirect taxes2 are to be understood net, i.e. after the deduction of subsidies.

1 Since the period covered here extended over the years I929-4I, it was impossible to make use of the improved method of allocating indirect taxes discussed in Appendix II below. This information which relates only to the last three calendar years became available after most of the computing work had been completed.

2 For a discussion of -certain complexities surrounding the treatment of indirect taxes see Appendix II below.




Diagram I below shows for the United States over the period since I929 the relation between private disposable income and the three variables defined above.' The diagram shows the normal peace time relation between the variables at a point of time located in the middle of I94I. It is not to be supposed from this diagram that apart from a time trend, which has been removed, consumption in all circumstances depends on nothing but income. Consumption would clearly be affected by variations in the rates of taxes but over the period, until recently at any rate, it would appear that the effect of such variation as there has been can be subsumed in the time trend. Again consumption would doubtless be affected by changes in the distribution of incomes but it would seem that over the period the variation in this distribution in so far as it did not take the form of a trend, must have been very highly correlated with the deviations of income from its trend. For otherwise it would not be easy to explain the high correlation between the deviations of income and consumption from their respective trends.2

DIAGRAM I.

U.S. $000,000,000.

I20

4 10y04W 90 4.

70 40

Tas at4on 60

50

40

0 10 20 30 40 60 60 70 $0 90 100 11 /0X ?rLvafe oisposale rcorne

The data and equations on which this diagram is based are set out in Appendix III below. 2 See Appendix III below for a further discussion of this point.




It will be seen that over the period i929-4i the observed points lie close to the calculated curves. But in time of war, when other factors are operative, this is not to be expected. For at such times the government requires to increase its share of the current services of labour and equipment. In part this can be achieved without dislocation of normal civil habits simply by increasing output. But for total war this is not enough. It is essential that as income and output increases the public should not continue to increase their expenditure as they normally would, but should increase it less or even diminish it. This will leave a larger part of the increased income for taxes and savings. Taxes go straight to the government but savings may be devoted to increasing private capital equipment. In time of war it is not possible to maintain all forms of capital equipment let alone increase them. A larger part of savings must go to finance government loans. Indeed not only the whole of savings but also a considerable part of normal depreciation allowances may well be required for the finance of government loans.

DIAGRAM II.

U.S. $000o,000,000.

100

90 mo~~~~~~~~~~~~~~~~~~In

70 '~~~~~~~~~~~~~~~~Taeaaoan 1 420 11 / ~~~~~~~~~~~~~ ~ ~~autRrt Hl

4~~~~~~~4 60

50~~~~~~~~~~~~~~~~~~~3

40

0 / 332Consuomptiotia'n2

not Unvestme/le

at factor cot

0 10 20 30 40 50 60 70 80 90 100 110 1;0

Private aisposable Lacoec

Accordingly we may measure the diversion of resources to war purposes by the extent to which in time of war the relationships shown in diagram I are




DIAGRAM III.

U.S. $000,000,000.

10

90

0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~40 36

40

30

20

t0

10 20 30 40 ,0 60 80 90 ?itw&to atspo3Alie Lrncomne

disrupted. If the community is to finance its war effort not only by an i'ncrease in output but also by a reduction in civil demand, then we should expect consumptilon to fall below the level it would have reached under -peace conditions had the larger war time level of income been achieved. Again consumption plus taxes might be expected to fall but to a less extent since taxes themselves are likely to increase. It will be seen from diagram I that these movements have recently been taking place.

This way of looking at the matter does not take directly into account the fall in capital development which takes place in war time. Accordingly in diagram Il the data have been rearranged. The curve this time shows the level of consumption and net investment at factor cost associated with given levels of income measured along the abscissa. It will be seen, by comparing the observed points on this diagram with those in diagram I, that this sum was absolutely less than consumption alone 'in the second quarter of 1942. This means that net investment had become negative; that is, not only were there no net additions to private capital but there was even some decline.

flThe data and equations on which this diagram is based are set out in Appendix IV below.




So far we have considered what happens when private money income is increased; so much is spent on consumption, so much on taxes and so much is saved. Turning to the other side of the account we may now enquire how much of this additional expenditure will generate income in the form of wages, profits, rent and so on. This is shown in diagram JJJ.1 Here private money income is subdivided into (a) wages, salaries, etc., and social security benefits, (b) profits and (c) rent and interest including federal debt interest. It will be seen that the points lie close to the lines though in the case of wages and profits there is some indication of time lags. 2 It is now possible to say how far an additional dollar of private outlay will generate incomes of different kinds. From the equations in the appendix these can be seen to be:

Cents Wages, etc. .. .. 55 Profits, etc. .. .. 38 Rent, interest, etc. .. 7

IOO

V. A COMPARISON OF THE DISPOSAL OF PRIVATE INCOMES.

C-Y T -* Y S Y

U.K. I U.S.A. U.K. U.S.A. U.K. U.S.A.

I9383 o.69 0.77 0.22 o.i8 0.09 0.05

I939 .. 0.75 .. 0.I7 .. o.o8

I940 o.6i 0.72 0.27 o.i8 O.2 0.IO

I94I 0.53 o.68 0.33 0.2I 0.I4 O.II

I94I: I .. 0-7I .. 0.2I .. o.o8 II . . o.6g .. 0.2I .. 0.1O

III . . o.67 .. 0.22 .. O.II IV .. o.63 .. 0.2I .. o.i6

I942: I .o. .62 .. 0.22 .. O.i6 II . . 0.59 .. 0.22 .. 0.I9

The data and equations on which this diagram is based are set out in Appendix V below. 2 See Appendix III, last paragraph. 3 In the case of the United States the improved method of allocating general indirect taxes

set out in Appendix III below was used in this and the two following tables. Had my original assumption been adopted, the ratio for I938 would have been 0.75, o.ig and o.o6. A certain amount of seasonality exists in the quarterly figures and this has not been removed. See Appendix VII below. In view of the alrangement of the American data, direct taxes have been taken equal to the sum of personal payments and impersonal liabilities in each country. See Appendix VIII below.



to THE REVIEW OF ECONOMIC STUDIES

When we consider this country it is unfortunately impossible to present so complete an analysis. The reason is that as yet' no data are available which can satisfactorily be adjusted to the definitions adopted in Cmd. 6347 or in the American figures above. I shall confine myself therefore to a comparison of certain proportions for the period since I938. These proportions will relate to the ratios of consumption (C), taxes (T), and savings (S) to private disposable income (Y) as defined in Appendix III below. 2

From this table it can be seen that in the United States the proportion of private incomes devoted to consumption at factor cost is now falling fast, having been abnormally low in the past three quarters. Taxes, on the other hand, have been rising slowly but savings have risen extremely fast in the last three quarters and as a proportion of private incomes are now higher than they were in this country in I94I.

At this point it is worth for a moment turning to peace time. It will have been noticed from the table that between I938 and I94I the proportion of private disposable income devoted to consumption fell while that going to savings rose in the United States. This was a period of rising income and these movements were the normal concomitant of this prosperity. With the help of the equations on which diagram I is based we can calculate the hypothetical level of savings which under the conditions of the period of observation might be expected to accompany a good level of income and employment. This level of income we might put at I25 milliard dollars. The value for S in I94I for this value of Y is I7.5 milliards. This figure may be taken to represent the level of private savings which might have been expected had income been at the level assumed. To my mind its very magnitude goes a long way to explain- ing why such a high level of income was not in fact reached. For such a level to be reached it would be necessary for private investment, voluntary or involuntary, plus the deficit of public authorities to absorb this level of saving. And for such a level to be maintained it is necessary that voluntary additions to private fixed capital and stocks should together with net borrowing by public authorities absorb such a sum. Over the period the deficit of public authorities averaged some 3 milliards and it would have been more likely to fall than to rise had trade been very good. This leaves I4.5 milliard dollars to be absorbed annually by private net investment at home and abroad. At five dollars to the pound even, this is nearly ?3,000 millions. Is it surprising that such a level was not achieved let alone maintained ? Yet this, or something like it, is the figure which the propensities of the American economy would have demanded at that time were a high level of income and employment to be achieved. In I929, a year of relatively high activity, net investment as here defined3 was at the level of 9 milliard dollars.

I See Appendix VI for a discussion of the problems of defining the tax burden.

' See Economic Journal, loc. cit. items 65-64-57.

3 It is hoped that this deficiency will be remedied in the not-too-distant future as a result of researches which are being conducted by the writer under the auspices of the National Institute of Economic and Social Research.



NATIONAL INCOME IN THE U.K. AND THE U.S.A. I

IV. A COMPARISON OF THE PROPORTION OF RESOURCES DEVOTED TO

DIFFERENT PURPOSES.

This comparison may be made on either of two bases. First we might take the proportion of current resources, i.e. the net national income at factor cost, devoted to the different purposes. Second, in time of war when net investment may be expected to become negative, it is convenient to express the amount of resources devoted to different purposes as a proportion of resources used for current purposes, i.e. the sum of consumption and government expenditure on goods and services each at factor cost. This method was adopted for the war years in Section B of Cmd. 6347.

I shall consider the first method first.

Proportion of the Net National Income at Factor Cost devoted to various purposes.

Government Net Consumption goods and investment

services

U.K. U.S.A. U.K. U.S.A. U.K. U.S.A.

I938 0.75 o.8i o.I8 o.I8 0.07 O.OI

I939 .. 0.78 .. o.i8 .. 0.04

I940 o.66 0.75 0.52 o.I8 o.078 0.07

I94I 0.57 0.70 o.62 0.22 -O.I9 o.o8

I941 I .. 0.72 .. 0.20 .. o.o8 II . . 0.72 .. 0.20 .. o.o8

HI .. 0~~.69 .. 0.22 .. 0.09 IV o 0.67 0| o.26 | 0.07

I942: I .. o.65 .. 0.32 .. 0.03 II o.. .6o .. 0.4I .. -0.01

These ratios are based on the definitions set out, in the second method of Appendix II below. The discrepancy' has been spread pro rata over the three items and no attempt at a further adjustment for seasonal variation has been made.2

The second method yields the following table: See item I7, table I, Appendix I below.

2 See Appendix VII below. The reason is that the seasonalities given there are derived from series based on my original assumption regarding the allocation of general indirect taxes.



I2 THE REVIEW OF ECONOMIC STUDIES

Proportion of the Sutm of Consumption and Government Goods and Services devoted to each of these purposes.l

Consumption Government Goods and services

U.K. U.S.A. U.K. U.S.A.

I938 o.8i o.8i 0.I9 O.I9 I939 .. o.8i .. 0.19 I940 0.56 o.8i 0.44 0.I9

I94I 0.48 0.76 0.52 0.24 I94I: I .. o.78 .. 0.22

III | . 00.78 0.22 III .. ~~~~~0.76 .0.24

IV .. 0.72 .. 0.28 1942: I o. .67 ..0.33

II . 0.59 .. 0.4I

These figures may be interpreted as follows. Each year the community spends a certain amount of money on current goods and services unconnected with the provision of new capital equipment. So much is spent on consumption goods at factor cost and so much more on government goods and services at factor cost. The amount spent in this way is in a prosperous peace time year less than the total national expenditure since net additions are being made to the stock of capital. In war time on the other hand the amount so spent may well be larger than the total national expendit-ure since the stock of capital is being depleted; partly by insufficient maintenance which releases the factors normally engaged on this work for government service; partly by the sale without replacement of stocks of goods which makes possible the maintenance of a certain standard of consumption with a smaller call on the services of current factors than would otherwise be necessary; and partly by the sale of overseas assets which makes possible the purchase of essential imports without the necessity of diverting home factors into producing exports necessary to pay for them.

The proportion of the national expenditure devoted to consumption and government goods and services can be seen from the previous table. In the case of the United Kingdom it was 0.75+0.I8=0.93 in I938 and 0.57+o.62=I.I9 in I94I. The comparable figure for the United States just exceeded i.00 in the second quarter of this year. It is hardly to be expected however that it will reach so high a figure as I.I9 since as can be seen from Table I of Cmd. 6347 this total was reached only by large realisations of overseas assets or borrowing from abroad. It is evident that we cannot all borrow from abroad (net) at the same time.

1 The figures in the final column of this table differ from those given in row (8) of the table in the Economic Journal, loc. cit., p. I57 partly on account of revision and partly because of the assumption there adopted that the whole of the item " other business taxes " should be deducted from consumption. This assumption is here replaced by the calculations in Appendix II.



NATIONAL INCOME IN THE U.K. AND THE U.S.A. I3

VII. PROBLEMS AND PROSPECTS.

A word may be in place about the reliability of the kind of e3timates I have been describing. If we measure the net national income simply by adding up incomes we may arrive at a figure which is adequate for many purposes although its margin of error is as much as 5 or 1O per cent. If, however, we add up all forms of final expenditure defined in such a way that their sum should be equal to the sum of incomes we shall have a further check on our first figure. This check will be stronger if in addition we can measure directly the items in other tables, such as the table of private disposable income and outlay, which have some but not all of their items in common with the net national income and expenditure. For the new information derived from such additional measure- ments will impose certain restrictions on the numerical values which can be considered reasonable in the first table.'

The information at our disposal for checking purposes will be still further increased if it is possible to estimate the items in several tables not merely for one but for a number of years. For if this can be done we can discover whether or not a discrepancy appearing in one year recurs fairly consistently in other years.

Another point worth bearing in mind in thinking of the reliability of these estimates is that we are normally interested in the reliability of aggregates composed of large numbers of independent estimates. Each of these may have a large relative- error but if its absolute error is small compared with the total, the relative error of the total may be small. For example, suppose an aggregate of 4,000 is composed of 400 independent estimates of items each of io. Suppose further that the error curves of these estimates may be supposed to be roughly normal and that measures analogous to the standard deviations of these error curves may in all cases be put at IO. This means that the chances may be taken as roughly 2 to i that in each case the truth lies between o and 20, a degree of inaccuracy seldom met with in practice. The margin of error of the aggregate may then be taken as roughly equal to:

V400. I02 = 200 that is a relative error of only 5 per cent. The absolute error of the total is, as might be expected, much larger than that of any of the component items but its relative error is very much smaller. This example is purely illustrative and ignores certain complications that arise in practice.

It must also be remembered that in many cases we are concerned not with the absolute level of a particular series but with the differences between successive years or quarters. The reliability of these differences is normally greater than that of the original series since a large part of the error in each year of the series will usually be common to the two values to be compared.

The value of national income and expenditure estimates in time of war is too well-known to call for comment. In conclusion I should like to describe a use they might have in peace time. This is only one of many uses but, it seems to me, an important one.

1 See Review of Economic Studies, Summer, 1942, pp. III-125, for a further discussion of this question.



I4 THE REVIEW OF ECONOMIC STUDIES

As in war time, the estimates could be used to provide a background for general economic policy. It is admitted on all sides that one of the great curses of highly industrialised countries in the twenty years before the war was the curse of unemployment. National income estimates taken together with information on the occupied population, unemployment, hours of work and the like would enable us to form some opinion of the level the national income would attain if involuntary unemployment were eliminated. This would be a*measure of the level which expenditure at factor cost would have to attain if full employment was to be achieved. It would also be possible to estimate the probable level of consumers' expenditure and the projected expenditure of public authorities on goods and services. The balance would give us the required value of additions to capital at home and abroad necessary to achieve the given level of income. If, at the same time, some such body as the often proposed National Investment Board were to collect information on projected capital development by industry and commerce, it would be possible to see if the two sides of the account were approximately equal. If the sum of the expenditures was larger than the estimated income it would mean that an attempt by the community to spend so much money would be likely to generate an inflationary boom, and it would be appropriate to consider means of damping down certain branches of activity. If, on the other hand, the estimated expenditures were less than the estimated income, it would mean that some involuntary employment would be likely to exist and it would be appropriate to consider measures for stimulat- ing expenditure of one kind or another. If estimates of this kind could be reviewed continuously in peace time and were used to direct policy it should prove possible, with a little experience, to prevent the appearance of unemployment on a serious scale since the position would be kept continuously under review and it would be possible to act before it got seriously out of hand. This is not the place in which to consider what kinds of action would be appropriate. London. RICHARD STONE.




APPENDIX I. The following tables are based on data given recently in the Survey of Current Business.,

This is the first time that official quarterly estimates of all the items in the tables have made their appearance. The estimates given below are arranged in a similar manner to the annual estimates for the period 1929-41 which were set out recently in the Economic Journal. 2 These figures in turn were intended to be broadly comparable with the official estimates of this country.3

Apart from the necessity for regrouping some of the items due to the form of presentation of the quarterly data, two changes of definition have been made in what follows compared with the annual estimates.

First, the item " capital outlays charged to current expense " has been transferred from income to depreciation. The treatment which I gave previously has been changed since, as I now understand the position, these outlays are on the whole better not regarded as part of income. This correction also involves that they are not regarded as an item of saving. I understand however that some part at any rate both of this item and also of other business reserves may reasonably be regarded as part of income. Accordingly the figures given below probably underestimate slightly the level of income. To date the error involved cannot be very large.

The second change is necessitated by the regroupings of the data in the quarterly estimates. In these, it is impossible to separate " personal savings " from " savings of unincorporated business other than agriculture." The latter has therefore been included with the former. It is evident that any line between the two would unavoidably be rather arbitrary.

The tables show the seasonally adjusted annual rate in each quarter.4 This enables the trend of each series to be gauged without the disturbance of seasonal variations in units which are familiar from the study of annual data.

In a footnote to the article in the S.C.B. it is stated that " all concerned wish it understood that quarterly estimates so soon after the event are necessarily more approximate than usual annual series."

Notes on particular items in the Tables. These notes are intended to set out the logical basis of the items in the tables and to supple-

ment those given by me in a recent paper (cf. Economic Journal, June-September, I942, Pp. 170-5). Further particulars of the statistical basis of the quarterly estimates are to be found in S.C.B., August, 1942, PP. 15-17.

TABLE I. I. E.J. items i and 5. 2. E.J. items 2 and 4(a). Excludes federal debt interest. 3. E.J. item 3. In the quarterly estimates S.C.B. gives only the sum of this item and " other

business taxes " (cf. item 15 below). Annual estimates are, however, available and it is thus possible to divide the total for each quarter into its two components without fear of much inaccuracy. Figures arrived at by this method are shown in the table.

4. E.J. item 4(b). 5. E.J. item 7. It is stated in the S.C.B. note on this item that the series must be regarded as

tentative and approximate at the present time. 6. E.J. item 8. 7. E.J. items 9 and io. 8. The difference between the sum of items I to 7 and an estimate of the net national income

made in a way which seemed to minimize the risk of rounding off and other errors. The method, illustrated by 1941 figures, is as follows:

U.S. $ooo,ooo,ooo (I) National income (S.C.B., August, 1942, table 4, line i, p. I4) .. .. .. 94.7

Plus (2) Imputed rents (writer's estimate: see note to E. J. item i (b) ) .. .. .. I.6 (6) Corporation income and excess profits taxes .. .. .. .. .. 6.9 (4) Inventory revaluation adjustment .. .. .. .. .. .. .. 3.2

Less (S) Social security contributions of employers .. .. .. .. .. .. (6) Federal debt interest .. .. .. .. .. .. .. .. .. -. (7) Net national income at factor cost .. .. .. .. .. .. .. 97.2

Apart from revisions, (7) differs from E.J. item 12 by the exclusion of E.J. item 6.

1 See " National Income and the War Effort-First Half of 1942," S.C.B., August, 1942Z PP. 10-17.

2 See Economic Journal, June-September, 1942, pp. 154-175. 8 See Cmd. 6347, April, 1942. 4 But see Appendix VII below.



THE REVIEW OF ECONOMIC STUDIES

TABLE I.

United

States

of

America

Net

National

Income

and

Expe-nditure

U.S.

$ooo,ooo,ooo

I939

11939

1940

1940

I94I

I94I

I942

1942

x

IIIii IV

I

11

IIIIV

I

II

III

IV

I

II

III

IV

x.

Net

rents

and

entrepreneurial

income

I.

.

.

4.4

I4.6

14.9

15.6

14.8

15.3

15.2

15.0

15.9

15.3

i6.5

i8.0

19.7

21z.6

19.0

22.6

23.0

2.

Dividends

and

interest

.

7.1

7.7

8.2

8.5

7.9

8.2

8.2

8.4

8.5

8.3

8.4

8.6

8.9

9.3

8.8

9.3

8.9

3.

Corporate

income

and

excess

profits

taxes

..

.

1.2

1.2

i.6

2.0

I .51

2.0

2.4

3.2

3.6

2.8

5.2

6.8

7.6

8.o

6.9

8.8

9.2

4.

Corporate

savings

.

..-0.3

0.2

0.9

0.9

0.4

0.9

1.2

1.2

1.7

1.2

2.1

2.8

2.7

2.6

2.6

2.7

2.0

5.

Inventory

revaluation

adjust-

ment

..

.

.-0.4

0.4

-0.4

-o.8

-0.3

-0.4

-

-0.4

-o.8

-0.4

-2.0

-2.8

-3.6

-4.4

-3.2

-2.8

-2.8

6.

Salaries

and

wages

.

..42.9

43.3

44.4

46.6

44.4

47.0

47.8

49.3

5I.9

49.0

55-

59.7

63.3

66.5

61.3

70.9

75.3

7.

Other

labour

income .

..

2.8

2.8

2.4

2.4

2.5

2.4

2.4

2.4

2.0

2.4

2.0

2.4

1.6

i.6

1.9

1.6

i.6

8.

Discrepancy

.

.

.

0.1

-0.11

0.1

-0.1I

-

0.2

-

0.1

-

0.2

0.1

-0.2

0.3

0.1

-0. 1

-0.2

-0.2

9.

Net

national

income at

factor

cost

..

.

.67.8

70.1

72.1I

75.1

71.2

75.6

77.2

79.2

82.8

78.8

88. i

95.3

100.5

105.1

97.2

112.9

117.0

io.

Consumers'

expenditure:

a

Durable

goods

..

.

6.9

6.9

7.0

7.5

7.11

8.o

8.xi

8.o

9.0

8.3

I0.9

11.1

10.4

8.8

10.3

7.3

6.5

b

Non-durable

goods

and -

services

..

.

.55.3

56.0

56.8

57.6

56.4

58.

58.9

59.6

60.5

59.4

63.5

66.1i

69.3

69.4

67.1

74.9

73.9

i i.

Government

expenditures

for

goods

and

services:

a

War

.

.

.

1.2

1.4

1.4

i.6

1.4

i.8

2.0

2.6

4.8

2.8

6.7

9.0

12.1

17.0

11.2

27.3

40.8

b

Other

federal

.

..

4.0

4.7

4.6

4.2

4.4

4.5

4.6

3.7

3.7

4.1

4.7

3.7

3.9

4.2

4.11

3.5

3.7

c

State

and

local

.

..

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.2

8.2

8.2

8.2

8.2

8.2

8.o

12.Private

gross

investment

at

home:

a

Construction

.

..

3.7

3.8

3.9

4.0

3.9

4.1

4.4

4.5

5.0

4.5

5.3

5.4

5j.6

5.5

5.5

4.6

3.7

b

Producers'

durable

equipment

4.9

5.1

5.3

6.2

5.4

6.3

6.3

6.6

7.2

6.6

8.3

8.8

9.9

8.5j

8.9

7.6

6.8

c

Net

change

in

business

in-

ventories

.

..

0.4

-0.4

0.7

2.7

oS8

2.0

0.4

I.9

2.8

1.8

2.3

3.2

3.8

4.9

3.6

3.1

2.8

d

Domestic

output of

monetary

gold

and

silver

..

.

0.2

0.3

-

0.3

0.1

0.1

0.4

0.1

0.4

0.3

-

0.2

0.4

0.1

0.2

0.1

0.1

Less

1 3.

Depreciation:

a

Depreciation

and

depletion

charges

.

.

.

-6.4

-6.4

-6.4

-6.4

-6.4

-6.4

-6.4

-6.4

-6.8

-6.5

-6.8

-6.8

-7.2

-7.2

-7.0

-7.6

8-84

b

Other

business

reserves

.

-o.8

-o.8

-o.8

-o.8

-o. 8

-o. 8

-o.8

-o.8

-i.2

-.9

-I.2

-1.6

-i.6

-2.0

-i.6

-2.0

-4.0

c

Capital

outlays

charged

to

current

expense

..

.

-o.8

-o.8

-o.8

-o.8

-o. 8

-o. 8

-o.8

-I.2

-1.2

-1.0

-1.2

-i.6

-2.0

-2.4

-i.8

-2.4

-3.2

14.

Net

change in

foreign

claims..

0.7

o.6

0.7

1.0

o.8

1.7

1.5

1.2

1.3

1.4

1.0

0.7

1.3

0.9

0.9

0.6

0.5

Less

15.

Other

business

taxes .

..-7.2

-8.o

-8.4

-8.8

-8. i

-8.4

-8.8

-9.2

-9.6

-9.0

-10o.0

-10.4

-io.8

-ii.6

-10.7

-12.0

-12.4

i6.

Social

security

contributions of

employers

.

.

.

-1.2

-1.2

-1.2

-1.2

-1.3

-1.2

-1.2

-1.2

-T.6

-.1.3

-x.6

-i.6

-i.6

-2.0

-1.7

-2.0

-2.0

17.

Discrepancy

..

.

.-1.4

o.6

1.0

-0.3

-

-2.1

0.3

1.5

0.2

-

-2.0

0.9

-1.2

2.8-

1.7

0.2

i8.

Net

national

expenditure

at

factor

cost

..

..

.67.8170.1

72.1

75.1

71.2,75.6

77.2,7Q9.2,82.8

78.81

88.i,

95.3

100.5

105.1

97.21

112.9,

117.01




TABLE

II.

United

States of

America

Private

Disposable

Income,

Expenditure

and

Savings

U.S.

$S??,?O0,000

1939

I939

1940

I940

I941

I94I

1942

I942

I

II

III

IV

I

II

III

IV

I1I11

II1

1IV

I

II

III

IV

Ig.

Personal

private

income:

a

Net

rents

and

entrepreneurial

income

..

.

..

14.4

I4.6

14.9

15.6

I4.8

I5.3

I5.2

I5.0

I5.9

I5.3

I6.5

I8.0

19.7

21.6

19.0

22.6

23.0

b

Dividends

and

interest

..

8.I

8.7

9.2

9.5

8.9

9.3

9.3

9.5

9.6

9.4

9.5

9.7

IO0

10.4

9.9

10.4

IO I

c

Salaries

and

wages

..

..

42.9

43.3

44.4

46.6

44.4

47.0

47.8

49.3

5I.9

49.0

55.8

59.7

63.3

66.5

6I.3

70.9

75.3

d

Other

labour

income..

..

2.8

2.8

2.4

2.4

2.5

2.4

2.4

2.4

2.0

2.4

2.0

2.4

I.6

i.6

I.9

i.6

I.6

e

Other

transfer

payments

.

2.3

2.3

2.4

2.2

2.4

2.4

2.5

2.6

2.3

2.4

2.3

2.2

2.2

2.0

2.2

2.1

i.8

f

Discrepancy

..

..

..

3

0.1

0I

0.4

-

0.2

-

0. I

-

0.2

0. I

-0.2

0.3

-0.2

-.I

-0.2

-0.2

20.

Impersonal

private

income

..

o.5

i.8

2. I

2.I

I.6

2.5

3.6

4.0

4.5

3.6

5.3

6.8

6.7

6.2

6.3

8.7

8.4

~~~~~~~9i

8o88.

628

86I08 I01 =O-

ii. 12.

21.

Private

disposable

income

71.3

73.4

75.5

78.8

74.6

79.1

8o.8

82.9

86.2

82.3

91.5

98.6

103.8

IO8

100.5

I6

120.0

22.

Consumers'

expenditure

..

62.2

62.9

63.8

65.I

63.5

66.5

67.o

67.6

69.5

67.7

74.4

77.2

79.7

78.2

77.4

82.2

80.4

23.

Direct

taxes,

etc.:

a

Personal

direct

tax

payments

2.2

2.3

2.4

2.5

2.4

2.5

2.5

2.6

2.7

2.5

2.9

3.2

3.3

3.5

3.2

5.4

5.6

b

Social

security

contributions

of

employees

..

..

o.8

o.8

o.8

o.8

0.7

o.8

o.8

o.8

o.8

o.8

o.8

o.8

I.2

o.8

0.9

o.8

1.2

c

Impersonal

direct

tax

liabili-

ties

I..

..

..

..

.2

1.2

I.6

2.0

I.5

2.0

2.4

3.2

3.6

2.8

5.2

6.8

7.6

8.o

6.9

8.8

9.2

24.

Savings

a

Personal

..

.

(5 7)

(5.I)

(6.4)

(8.o)

(6.3)

(6.7)

(6.8)

(7.8)

(8.9) (7 7)

(8.2)

(IO4)

(I3 I)

(19 5)

(I2.7)

(I9.3)

(24.2)

b

Impersonal

..

..

-0.7

o.6

0.5

0.1

0.I

0.5

I.2

o.8

o.9

o.8

o.1

-

-0.9

-i.8

-o.6

-0.i

-o.8

25.

Discrepancy

.

.

.

-0.1

0.5

-

0.3

0.1

0.1

0.1

0.1

-0.2-

-0.1

0.2

-0.2

-0.1

-

-0.3

0.2

26.

Private

expenditure,

taxes

and

savings

..

.

.

7I.3

73.4

75.5

78.8

74.6

79.I

8o.8

82.9

86.2

82.3

91.5

98.6

103.8

io8.i

I00.5

ii6.i

120.0

l~~~~~~~~~~~~~~~~~~~~~~~~~

1



THE REVIEW OF ECONOMIC STUDIES

TABLE

III.

United

States of

America

Private

Savings,

Net

Investment

and the

Deficit of

Public

Authorities.

U.S.

$S??,o.?,?.?

I939

1939

1939

1940

194I

1941

I942

1942

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

27.

Personal

savings

and

savings

of

unincorporated

business .

..

5.7

5.3I

6.4

8.o

6.3

6.7

6.8

7.8

8.9

7.7

8.2

10.4

I3.'

I9.5

12.7

I9.3

24.2

28.

Corporate

savings

..

..

3

0.2

0.9

0.9

0.4

0.9

1.2

1.2

1.7

1.2

2.1

2.8

2.7

2.6

2.6

2.7

2.0

29.

Inventory

revaluation

adjustment

-0.4

0.4

-0.4

-.8

-0.3

-0.4

-

-0.4

-o.8

-0.4

-2.0

-2.8

-3.6

-4.4

-3.2

-2.8

-2.8

30.

Private

savin

.

.

50

57

6.9

8.i

6.4

7.2

8.o

8.6

9.8

8.5

8.3

10.4

12.2

17.7

12.I

I9.2

23.4

31.

Private

net

investment at

home. .

1.2

o.8

1.9

5.2

2.2

4.5

3-5

4.7

6.2

4.8

6.7

7.6

8.9

7.4

7.8

3.4

-2.2

32.

Net

change in

foreign

claims . .

0.7

o.6

0.7

I.O

o.8

I.7

1.5

1.2

I.3

1.4

I.0

0.7

I.3

0.9

0.9

o.6

0.5

33.

Deficit of

public

authorities

.

.

4.2

4.2

3.3

2.0

3-5

3.2

2.8

I.3

1.9

2.3

2.5

1.4

3.o

6.6

3.4

13.2

25.I

34.

DiSCrepanCy

..

..

..

-1.1

0.1

1.0

-0. I

-.I

-2.2

0.2

1.4

0.4

-

-1.9

0.7

-1.0

2.8

-

2.o

35.

Private

net

investment

at

home

and

abroad

plus

the

deficit

of

pubLc

authorities..

..

..

s.

7 5

6.9

8.i

6.4

7.2

8.o

8.6

9.8

8.5

8.3

10.4

12.2

17.7

12.1

I9.2

23.4



NATIONAL INCOME IN THE U.K. AND THE U.S.A.

TABLE

IV.

United

States of

America.

Income,

Deficit

and

Expenditure

of

Public

Authoties

U.S.

$000,0o0o.00

1939

I939

1940

1940

1941

1941

1942

1942

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

36.

Direct

taxes,

etc.:

a

Corporate

income

and

excess

profits

taxes

.

.

.

1.2

1.2

i.6.

2.0

1.5

2.0

2.4

3.2

3.6

2.8

5.2

6.8

7.6

8.ol

6.9

8.8

9.2

b

Direct

personal

taxes:

i

Federal

..

..

o.8

o.8

o.9

o.9

o.9

I.0

1.o

I.

1.1

1.0

I.5

i.6

I.7

z.8

I.6

3.8

3.9

ii

State

and

local

..

..

1.4

I.5

1.5

i.6

1.5

I.5

1.5

I.5

i.6

I.5

1.4

i.6

I.6

1.7

I.6

I.6

1.7

c

Social

security

contributions of

employees

..

..

..

o.8

o.8

o.8

o.8

0.7

o.8

o.8

o.8

o.8

o.8

o.8

o.8

1.2

o.8

0.9

o.8

1.2

37.

Indirect

taxes,

etc.:

a

All

other

business

taxes

..

7.2

8.o

8.4

8.8

8.I

8.4

8.8

9.2

9.6

9.0

IO0

IO4

Io.8

iI.6

IO.7

12.0

12.4

b

Social

security

contributions of

employers

..

..

..

1.2

1.2

1.2

1.2

I.3

1.2

I.2

1.2

I.6

13

I.6

I.6

I.6

2.0

17

2.0

2.0

38.

Deficit

..

..

..

..

4.2

4.2

3.3

2.0

3.5

3.2

2.8

I.3

I.9

2.3

2.5

1.4

3.0

6.6

3.4

13.2

25.1

39.

Income

plus

deficit

..

..

I6.8

17.7

17.7

17.3

I7.5

i8.I

I8.5

I8.3

20.2

I8.7

23.0

24.2

27.5

32.5

26.8

42.2

55.5

4o.

Transfer

payments:

a

Federal

debt

interest

..

..

.

1.0

1.0

1.0

r.o

.

1.

1.1

.1

1.1

1.

J.j

11.1

.1

11.1.LI

1.2

b

Other

transfer

payments

.

2.3

2.3

2.4

2.2

2.4

2.4

2.5

2.6

2.3

2.4

2.3

2.2

2.2

2.0

2.2

2.1

I.8

4I.

Governmentexpendituresforgoods

and

services:

a

War

.

..

.

..

1.2

1.4

1.4

i.6

I.4

i.8

2.0

2.6

4.8

2.8

6.7

9.0

I2.1

17.0

11.2

27.3

40.8

b

Other

federal

..

.

.

4.0

4.7

4.6

4.2

4.4

4.5

4.6

3.7

3.7

4.11

4.7

3.7

3.9

4.2

4.1

3.5

3.7

c

State

and

local

..

..

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.3

8.2

8.2

8.2

8.2

8.2

8.2

8.o

42.

Total

expenditure

| I6.8

r7.7

17.7

17.3

17.5

I8. I| i

58.

I8.3

20.2

18.7

23.0

24.2

27.5

32.5

26.8

42.2

55.5




9. The sum of items i to 8. roa. E.J. item 3I(a). Annual estimates of the flow of durable goods taken from the survey

contained in S.C.B. for April, I942, and adjusted for government purchases. Interpolation was based on an index of the retail sales of durable-goods stores. In extrapolating into I942

it was assumed that only 25 per cent of passenger-automobile sales were to consumers. rob. E.J. item 3I(b). Annual estimates of the flow of non-durable goods taken from the same

source as io(a) and interpolated by retail sale of non-durable goods stores. Services based on an unpublished index prepared by the Bureau of Foreign and Domestic Commerce.

iI. E.J. item 32. I2a. E.J. items 33 (a) and (b). These quarterly figures were published in S.C.B., May, 1942.

b. E.J. item 33(c). It is stated in the S.C.B. note on this item that the data for making the 1942 extrapolation are far short of adequate.

12C. E.J. item 33(d). 12d. E.J. item 33(e). I3a. E.J. item 34(a). It is stated in the S.C.B. note on this item that the quarterly interpola-

tions should be regarded as approximate only. b. E.J. item 34(b). c. E.J. item 6. Transferred to this side of the table (see p. I 7 above).

14. E.J. item 35. 15. E.J. item 36. See note to item 3 above. i6. E.J. item 37. I7. See note to item 8 above. It seems probable that the rather large discrepancies in some of

the quarters are due to the difficulty of interpolating the components of item 12 and especially item 12(C).

I8. The sum of items IO to I7.

TABLE II.

iga. See item i above. b. Sum of items 2 and 40(a). c. See item 6 above. d. See item 7 above. e. Transfer payments other than federal debt interest. E.J. item 46. f. The difference between the sum of items ig(a) to (e) and 20 and an estimate of private

income made in a way which seemed to minimize the risk of rounding off and other errors. The method, illustrated by 1941 figures, is as follows:

U.S. $ooo,ooo,ooo (i) Net national income at factor cost (see line (7) in the note to item 8 above) 97.2

Plus (2) Transfer payments (sum of items 40(a) and (b) below) .. .. .. 3.3

(3) Private disposable income .. .. .. .. .. .. .. .. 00.5

20. Sum of items 23 (c) and 24 (b) below. Since the contribution of the impersonal private sector is the same on each side of this table, the sector makes no contribution to the discrepancy.

21. Sum of items I9 and 20. Differs from E.J. item 48 apart from revisions of the figures by the inclusion of item 20 above and of E.J. item 55 which is here treated as part of personal income and savings.

22. See item io above. 23a. E.J. item 50.

b. E.J. item 51. c. See item 3 above.

24a. Obtained by difference but found reasonably consistent with an independent quarterly series prepared by the Securities and Exchange Commission. Sum of E.J. items 54 and 55.

b. Sum of E.J. items 56 and 58. 25. See note to item I9(f) above. 26. Sum of items 22 to 25. See note to item 2I above.

TABLEt III. 27. See item 24 (a) above. 28. See item 4 above. 29. See item 5 above. 30. Sum of items 27 to 29. Equal to E.J. item 59 less E.J. item 57. See note to item 8 above.



NATIONAL INCOME IN THE U.K. AND THE U.S.A. 2I

31. Sum of items I2 and 13 above. 32. See item 14 above. 33. Difference between item 42 and the sum of items 36 and 37 below. 34. Difference between item 30 and sum of items 3 I to 33. It can be seen that this item tends to

move in a similar way to the discrepancy shown in item I7. In putting all the error into this side of the table, I have in effect assumed that the estimates of consumers' expenditures are accurate compared with those of the investment items. This may not be true.

35. Sum of items 3I to 34. See note to item 30 above.

TABLE IV. 36a. See item 3 above.

b. i and ii. See item 23(a) above. c. See item 23 (b) above.

37a. See item IS above. b. See item i6 above.

38. Difference between item 42 and sum of items 36 and 37. See item 33 above. 39. Sum of items 36 to 38. 4oa. E.J. item 70(a).

b. See item ig(e) above. 41. See item i i above. 42. Sum of items 4o and 4I.

APPENDIX II.

In the S.C.B. for nugust, 19421 an attempt is made to allocate indirect taxes, other than those specifically on consumption goods, to the components of the national product. Since for my purposes it is necessary to make this allocation on the same basis in each country, I shall set out what seem to me to be the admissible solutions to this problem.2

It is convenient to distinguish between specific indirect taxes which are levied on a single commodity, such as the tobacco duty, and general indirect taxes which fall, possibly in varying degrees, on the whole of output. Examples of this class are, on the definitions employed in this paper; employers' contributions to social insurance, compulsory premiums paid under war risks insurance schemes and local rates.

Although not perfectly general, it is unlikely that any of these taxes have a very marked effect on relative prices and for this reason it might be convenient to regard them as direct taxes paid out of income rather than as indirect taxes to be deducted from the sales proceeds of output.3 If this treatment were adopted there would clearly be no problem of allocation since only specific indirect taxes would be left to be deducted from expenditure.

Let us suppose however that we decide not to do this and so require to know the principles on which the allocation should be made. There are two quite distinct concepts which we may wish to measure. First, we may wish to determine the proportion of current factors of production used in producing investment goods (whether or not these be for the replacement of assets currently used up) and the remaining proportion of current factors used together with capital equipment in industries producing consumption and government goods and services. Second, we may be interested in the proportion of current factors used to produce additions to the stock of capital on the one hand and to produce other goods and services including all capital goods necessary for replacement purposes on the other.

If it is the first alternative that we are interested in then it is necessary first to distribute depreciation allowances, etc., between gross investment and the remaining part of the gross national expenditure at market prices less specific indirect taxes (assumed to fall only on consumption) and then to allocate general indirect taxes over these two parts of output. If we are interested in the second, then we must simply allocate general indirect taxes between net investment and the remainder of the net national expenditure at market prices less specific indirect taxes (assumed to fall only on consumption).

This distinction may be made clearer by an example. In it I shall assume, for want of information, that where any allocation is to be done in the case either of depreciation allowances or of general indirect taxes it may be done pro rata.

1 p. 15 statistical note to table I. 2 1 am indebted to Mr. J. M. Fleming who, I think, was the first to see the correct line of

approach here and to Mr. Meade for discussions on these questions. $ For a further discussion of the implications of this treatment in the case of social security

contributions, see pp. 2 and 3 above.




In my original calculation" it was necessary to make an assumption about the distribution of " other business taxes " between the specific and general categories. I assumed that they were all specific, realising that this was probably not the case but thinking that anyhow the equations would not be greatly affected whatever plausible assumption was made. Information which has more recently become available2 enables a better estimate to be made for recent years. It is stated that in order to deduct what I have called general indirect taxes from war expenditures the procedure was to allocate all indirect taxes other than those specifically on consumption to war expenditures in the ratio of these expenditures to national product. It is not stated how national product is defined in this context but it is to be presumed that it is after deduction of specific indirect taxes since otherwise consumption would bear an undue share of general indirect taxes. If therefore we write:

Is = specific indirect taxes on consumption Ig = general indirect taxes I = Is + Ig = total indirect taxes P national product W =war expenditures a = general indirect taxes falling on war expenditures

then w

a -' g(p I)

I = Ig + Is and therefore

a(P-I) Ig W-a

For I394 in milliards of dollars a = 0.7 P = I 19.5 I = I0.7 W = II.2

So that Ig = 7.3

and Is = 3.4

For 1939 and 1940 Ig was 6.2 and 6.8 while Is was I.9 and 2.2 respectively. My assumption was evidently not a good one. But in peace time this was not of great import-

ance since the greater part of Ig had also to come off consumption. Let us now return to the two methods. For I941 in milliards of dollars we have at market

Consumers' expenditure .. .. .. .. .. .. 77.4 Government expenditures for goods and services .. .. 23.5 Gross investment .. .. .. .. .. .. I9.I

Less Depreciation allowances, etc. 1.. .. .. .. - 0.4

Net national expenditure at market prices .. .. .. o09.6

Deducting specific indirect taxes and spreading depreciation allowances pro rata we obtain:

Consumers' expenditure .. .. .. .. . 67.4 Government expenditures for goods and services .. .. 21.4

Gross investment .. .. .. . .. .. 17.4 Net national expenditure at market prices kss specific indirect

taxes I06.2

It is not to be supposed that government expenditures are in fact likely to bear so large a proportion of depreciation allowances: the assumption is made here for purposes of illustration. It is moreover an assumption that can be corrected by the original compilers of the estimates.

From these figures we have to deduct general indirect taxes and employers' contributions to social security. We obtaln:

1 See Appefndices III and IV. atistical note to table L I See S.C.B., August, 1942, P. 15, staitclnetoabeI




U.S. $ooo,ooo,ooo Proportions

Consumers' expenditures .. .. .. 6I.7 o.635 Government expenditures for goods and

services .. .. .. .. i9.6 0.202 Gross investment I.. .. .. .. 5.9 O.I63

Net national expenditure at factor cost .. 97.2 I.000

These ratios show, on the assumptions made, the proportion of current national resources used in (i) producing capital goods including additions to stock (I6.3 per cent), (ii) co-operating with certain capital equipment to produce consumers' goods and services (63.5 per cent), and (iii) co-operating with certain capital equipment to produce goods and services bought by the government (20.2 per cent). It is evident that these ratios would be unaffected had we decided to treat general indirect taxes as direct taxes and transferred them accordingly to the other side of the account.

Now for the second method. We begin with consumers' expenditure at market prices less specific indirect taxes, government expenditures for goods and services at market prices and net investment at market prices; and from these we deductpro rata general indirect taxes. We obtain:

U.S. $ooo,ooo,ooo Proportions

Consumers' expenditure .. .. .. 68.3 0.703 Government expenditures for goods

and services .. .. .. .. 21.7 0.223 Net investment .. .. .. .. 7.2 0.074

Net national expenditure at factor cost .. 97.2 I.000

These ratios show on the assumptions made the proportion of current national resources devoted in the case of consumption not only to producing consumers' goods and services but also to maintaining the capital equipment necessary for maintaining this current output; and in the case of net investment to producing new capital goods and maintaining the capital necessary to do this at the current rate.

If net investment is negative, i.e. if gross investment is less than depreciation allowances then in principle a share of general indirect taxes requires to be subtracted algebraically, i.e. added. The effect of this will be to show that the running down of capital equipment at factor cost is less than it is at market prices, a result which is clearly correct.

The ratios obtained by this method are also unaffected by the decision to treat general indirect taxes as direct taxes.

APPENDIX III. The following equations show

C = expenditure on consumption at factor cost T = direct and indirect taxes, etc., met out of private incomes, S = private personal and impersonal savings less indirect taxes on net investment

in terms of private disposable income (Y) and time (t). The constants in the equations were obtained by the method of least squares from the annual data for the period I929-4I. t was set at o in 1935.

The simplest form of equation used was C = all + a12Y + a13t T = a2l + a22Y + a23t S = a3. + a32Y + a33t

Since C + T + S - Y, it follows that a,, + a., + a3l a,, + a.3 + a32 = o and that aL2 + a22 + a32 = i. The values obtained for the constants are:

all = I0.78 a1, o.6039 a1L o.6348 a2l = 3.22 a22 0.1309 a23 = o.6826

a3l = - I4.00 a32 0.2652 a.3 0.0478

1 In view of the way in which the American data are presented, it has been necessary to take personal direct taxes on a payments basis and impersonal direct taxes on a liabilities basis. See Appendix VIII below.




If, for the sake of illustration, these equations are regarded as an adequate description of the observations, they indicate, among other things (a) that an additional dollar of private money income is divided between C, T and S in the proportions o.60, 0.I3 and 0.27 respectively; and (b) that over this period quite apart from fluctuations in income, taxes had a tendency to rise through time and that this rise took place mainly at the expense of consumption.

In fact, however, these equations, though fitting the data tolerably well, can be improved by the addition of a term in y2. With this addition they may be written in the form

C b1L + b12Y + b13Y2 + b14t T b2l + b22Y + b23Y2 + b24t S b3l + b32Y + b33Y2 + b34t

Here bl, + b21 + b3l = bl3 + b23 + b33g = b4+ b24 + b34 = o while b12 + b22 + b82 = I. The values obtained for the constants are:

bl = - 2.42 b12 = 1.0054 b13 0.002887 b,4 = - o.6235 b2l = i8.64 b22 - 0.3378 b23= 0.003370 b24 = o.6693 b3l = - i6.22 b32- 0.3324 b33 0.000483 b34 =- 0.0458

From this it can be seen that the addition of terms in Y2 does not greatly modify the coefficients of t.

This addition however which gives a considerably improved fit to the data means that an addition to Y is no longer distributed between C, T and S in the same proportion at all levels of Y. The change in C accompanying a change in Y, t being held constant, is given by

DC9 - y= b12 + 2b13Y

Using this equation and similar partial differentials for T and S with respect to Y the following table is obtained:

Y DC AT AS milliard DY aY DY dollars

50 0.72 0.00 0.28 75 0.57 0.17 0.26

100 0.43 0.33 o.24

These values show that the proportion of an wadditional dollar of Y which is laid out on C diminishes with income; that the same is true to a very much less marked extent in the case of S; and finally that the proportion going to T rises sharply with income.

There are at least three things to be said, in connection with these figures if their limitations are to be clearly understood.

(i) The inclusion of a term y2 implies that each dependent variable is related to Y by a curve having the form of a parabola. This is obviously not an ideal assumption though it may give reasonable results over a fairly wide range of values of Y. A disadvantage of this assumption is, for example, that the estimated value of C will reach a maximum as Y increases, though in fact this is most unlikely to happen. This maximum will be reached at the point where

y= 2b2

- 174 (appr.) Further, the calculated value of T reaches a minimum at the point where

y _ _S b22

2b23

- 50 (appr.) This is clearly unsatisfactory since it is not to be expected that tax payments in fact rise

with every fall in Y below 50. Thus, while the simple equations used are adequate for a general description of the data it must be borne in mind that their form is not ideal.

(2) The coefficients in the equations were obfained so as to give the best fit in a least squares sense to the data over the period 1929-41. Since the fit obtained is very good, it is to be presumed that other factors which might be supposed to affect C, T or S were either highly correlated with Y over the period or remained constant or changed slowly so that their variation could be subsumed in the trend factor. This raises two questions. First, at other times and particularly at the present time, other factors, such as tax rates, may vary quite independently of income and cause, say, C to take a different value at any given level of income, from the one derived from the




equation. Second, other factors, of which the distribution of income may be an example though little is known on this point, clearly affect the relation of C to Y but may be supposed normally to be highly correlated with Y apart from a trend factor. If the distribution of incomes had not been highly correlated with income over the period I929-41 then either its independent variation must be unimportant, which on general grounds is unlikely, or its variation must have been small so that it can be subsumed in the trend factor. Fqr if neither of these facts were the case over the period it would have been impossible to express 'C in terms of Y and t with a high degree of accuracy.

It can be seen therefore that in so far as previously existing correlations of this kind are broken down in the future it may turn out that the partial differential of C with respect to Y is different from the value given by the equation since to some extent this may really be the differential of C with respect to Y and the distribution of income, the relation between the last pair of variables having been stable over the period of observation.,

Returning to the question of independent variables other than Y and t which may be supposed to influence C, it may wvell be that the equation of normal relationship is slightly affected numerically by the inclusion of the latter part of I94I, since at this time the progress of the war may have introduced new factors.

(3) I have chosen to study the relationship between certain variables because they enable certain relations to be seen simply and are adequate for my particular purposes. For other purposes it might be important to define both income and expenditure differently and to make allowance for time lags which, though small, undoubtedly exist and which I have entirely neglected.

APPENDIX IV. The following equations show

C = expenditure on consumption at factor cost V = net investment at home and abroad at factor cost

(B + T) = loans to public authorities plus direct and indirect taxes, etc., met out of private incomes

in terms of private disposable income (Y) and time (t). The constants in the equations were obtained by the method of least squares from the annual data for the period i929-4i. t was set at o in I935.

The form of equations used was C = bl, + b,2Y + b13Y2 + bl4t V = b4l + b42Y + b43Y2 + b44t

(B + T) = brj + b52Y + b53Y2 + b54t Since C + V + B + T _ Y it follows that bj + b4l + b5l = b13 + b43 + b5s =b,4 + b44 + b54

=o and that b12 + b42 + 52 = I. The- values obtained for the constants in the equation for C have already been given: those for V are

b4l = - I7.70 b42 = 0.2785 b43= o.ooooo6 b44 = - 0.0853

From this information the values of b.1, b52, b53 and b54 could be obtained by difference. Further, since the constants in the equation for T are known, those for B could be obtained by difference.

The sums (bl, + b4l), (b,2 + b42), (b,3 + b43) and (bl4 + b44) are the coefficients of an equation expressing the value of outlay at factor cost for private purposes in terms of Y and t; while the sums - (bll, + b4l), I - (b12 + b42), - (bl3 + b48) and - (b,4 + b44) are the coefficients of an equation expressing the sums going to public authorities (whether from taxes, etc., met out of private incomes or loans) in terms of Y and t. This division of Y is shown ih diagram II for a point of time located in the middle of I94I.

Some of the limitations of this kind of equation were set out at the end of Appendix III.

APPENDIX V, The following equations show

R = net rents, royalties and interest payments including federal debt interest. P = profits of corporations and unincorporated- business. L = wages, salaries, other labouir income and transfer payments other than

federal debt interest in terms of private disposable income (Y) and time (t). The constants in the equations were obtained by the method of least squares from the annual data for the period I929-4I. t was set at o in I935.




The form of equation used was R Cll+ C12Y + C13t p = C21 + C22Y + C23t L = C31 + C32Y + C33t

Since R + P + L Y it follows that cll + c21 + c31 = c13 + c23 + c33 = o and that C12 + C22 + C32 = i. The values obtained for the constants are

C11 = 3.96 C12 = 0.0709 C13 0.27i6 C21 - - II-49 C22 = 0.3799 C23 0.0297 C31 = 7.53 C32 = 0.5492 C33 = 0.2419

These equations fit the observations closely. They show that over this period, trend influences apart, the expenditure of an additional dollar generated income in the forms R, P and L in the proportions 0.07, 0.38 and 0.55 respectively. These proportions were moreover independent of the level of income.

The concept of private disposable income (Y) differs from the net national income at factor cost in that it excludes miscellaneous income from public property and includes transfer payments. Strictly therefore the proportions just given do not relate to marginal factor shares. They may however be taken as fairly close approximations of these since in the figures taken from the Department of Commerce, miscellaneous income from public property is zero throughout the period while transfer payments vary hardly at all apart from a slight upward trend. It is of interest therefore to note that there is no evidence that the shares of R, P and L are constant at different levels of income as is shown by the fact that the constants c1,, c2H and c3L are not near to zero. Setting t = o the following shares are obtained.

Y R P L milliard Y Y dollars

50 0.15 O.I5 0.70 75 o.12 0.23 0.65

100 0.II 0.27 0.62

Some of the limitations of this kind of equation were set out at the end of Appendix III.

APPENDIX VI. As here defined the tax burden, or better perhaps the gross tax burden since no account is

taken of the uses to which the taxes are put, is measured by the ratio of taxes paid out of private incomes to the total of such incomes. This procedure does not count as part of the burden taxes on goods bought by the government or payable on government income from property. This omission can be seen to be reasonable from the fact that such taxes are equivalent only to intergovernmental transfers which could be struck out from both sides of the consolidated account of public authorities. Put another way, if the government only raises from the private sector enough money to pay the cost of the factors employed in providing the goods and services it buys, then the indirect taxes in the market value of these goods and services are self-financing.

The correctness of this result can be seen from an example' from which, on the simplified assumptions employed, can also be deduced the appropriate income concept if it be desired to treat the total revenue as the numerator of the proportion of private incomes going in taxes.

Consider a simple economy in which the only forms of expenditure are consumption and the purchase of goods by the government. Further suppose the whole of government purchases to be financed out of indirect taxes. There are no transfer payments, government income from property direct taxes or government deficit.

Let C = personal expenditure on consumption at factor cost G = government expenditure on goods and service at factor cost

= the rate of indirect taxation supposed to be levied pro rata on the factor cost of all output.

From the conditions of the problem it can be seen that the tax burden is G

C + G

1 For which I am indebted to Mr. Meade.




The amount of taxes is (C + G)t while the expenditure to be financed is G(i + t). Hence, since these must be equal

_G

The amount of tax paid by the private sector is Ct since these are taxes paid in respect of consumption. Ct = G. Private incomes are equal to C + G. Henice the formula already adopted gives the correct result namely

Ct G C + G C + G

If it be desired to put (C + G)t as the numerator of this expression then the denominator must be multiplied by (I + t), i.e. incomes must be taken not at factor cost but at market prices. These simple relationships no longer hold if we pass to more complicated economies.

The method adopted here of measuring the tax burden, namely the ratio of taxes paid out of private incomes to private incomes themselves, appears to be consistent. It is not however unique since it depends on the definition of direct and indirect taxes. I shall not pursue this matter here.

APPENDIX VII.

The quarterly data given in the tables of Appendix I above are stated to be at seasonally adjusted annual rates. In calculating the quarterly changes in certain ratios and, in particular, the ratio of private savings to private disposable income, it became apparent that the method of seasonal adjustment used was of a kind which did not fully allow for the trend of the series. As a result the savings ratios took the form of a saw edge rising throughout each calendar year and dropping abruptly between the fourth and first quarters. In order to calculate smooth series for the diagrams it seemed desirable to remove this residual seasonality.

Since these residual seasonalities may be useful to other workers in this field, I set them out below. They were obtained by the median link relative method from the data for the quarters of 1939, 1940, 194I and the first quarter of 1942.

Residual seasonality. I II III IV

Y 1.013 1.003 0.992 0.993 C 1.02I I.002 0.991 o.986 T 1.017 1.001 0.999 0.983 S o.9o8 0.957 1.031 I.I05 L 1.0ig 0.997 0.992 0.993

APPENDIX VIII.

The phrases ' tax liabilities " and " tax accruals " perhaps need some explanation. Tax liabilities may be understood in two senses. The first " estimated tax liabilities ' in the case of, say, income tax means the liability at current tax rates which will finally have to be met in respect of the possession of current income. This will be different from current payments in so far as (a) these payments are in respect of assessments based on a higher or lower past income, (b) the fluctuations in payments throughout the year do not correspond to the fluctuations in incoiie5 and (c) the rate of tax at which current payments are being made is different from the current rate of tax. This is the most useful sense I think in which the term is used.

This concept must be distinguished from final or true tax liabilities which makes allow ance for the fact that tax in respect of the income of a given period may finally be levied at a rate different from that current in the period.

Similarly there are two forms of tax accruals which are respectively the excess of the first or the second kind of tax liabilities over tax payments in a given period.

In a tax system in which both the period of collection and the lag in assessment are one year, true tax accruals summed over the whole of the past through this year will be equal to this year's tax liabilities. This is obvious, since if true tax liabilities, row (I) say, are to date a, b, c, d, e then tax payments row (2) say, are o, a, b, c, d and the sum of the differences (i) - (2) is identically equal to e. The amount c would eventually flow into the tax authority even if no tax were levied in respect of income earned after the current period.

14 Vol. 9/10



Documents

National Income in the United Kingdom and the United States of America