I. FUNCTIONAL SHAREIrving B. Kravis
II. SIZEStanley Lebergott
The distribution of income has been a focal point in the study of economics since the time of Adam Smith. At first, the emphasis was almost exclusively on the functional distribution—that is, the division of income among the factors of production. For Smith and many of his successors in the development of economic thought, including Ricardo and Marx, the distribution of income among the suppliers of labor, land, and capital was the key indicator of the relative welfare of different groups in society. Rents represented the income of agricultural proprietors; profits, the income of commercial and industrial entrepreneurs; wages, the income of laborers.
Even before the end of the nineteenth century, more attention began to be given to the distribution of income by size—in terms of individuals, families, or other consumer units. This was made more and more relevant by the blurring, particularly in the United States, of the sharp lines between various economic classes. Quantitative studies of the size distribution were encouraged by the growing availability of data from income tax returns and, subsequently, from modern sample surveys.
It is true, of course, that the direct identification of social groups with particular types of income can no longer be made so readily as in the past. In the United States in 1950, for example, over half the interest, dividends, and rents received by urban consumer units went to units headed by employees (Kravis 1962), and during the period between the two world wars the top 1 per cent of income receivers obtained about a third of their income in the form of employee compensation (Kuznets 1953). However, the significance of the dispersion of various types of income among all socioeconomic groups can easily be exaggerated. Income units headed by clerical, sales, and blue-collar workers received about 90 per cent of their incomes in the form of wages and salaries. The salaried-managerial group were the only employees for whom property incomes were important; in 1950, for example, they received about a fifth of their incomes in the form of rent, interest, and dividends. Property incomes are also important for the self-employed and the not-gainfully employed. Thus, it remains true that a given shift in the functional distribution is still likely to affect certain socioeconomic groups in the population favorably and others unfavorably.
Even if sources of income for individuals or families were more thoroughly mixed than in fact they are, an analysis of the functional distribution would still be an important step toward an explanation of the size distribution. This is true as long as the income of any individual or family depends, at least to a major extent, upon the supplies of the various factors that he or it is able to offer on the market and if the conditions underlying demand and supply differ from one factor of production to another.
However, our interest in the study of factor shares need not be limited to the implications for particular groups in society. We may be interested in measuring changes in the productivity of individual factors of production. Or we may wish to know how the division of returns to current effort and returns to accumulated assets has altered over time. In both instances, our understanding of the historical processes of the society would be enhanced even though every person might contribute some of each factor.
Finally, the historical trend of factor shares has sometimes been used in efforts to explain other significant aspects of the economy. For example, Kalecki (1954) has used the percentage of entrepreneurs’ markup over direct cost as an index of the degree of monopoly, and Weintraub (1962) has used the entrepreneurs’ markup over the compensation of employees as a basis for explaining and predicting changes in the level of prices.
The empirical study of income shares
The study of the trends in the functional distribution of income is handicapped by the fact that the nature of the components of income for which we have data has not been determined by the requirements of economic analysis but, rather, by the legal and institutional arangements of our society. Each factor share found in the national accounts, as maintained, for example, in the United States by the Department of Commerce, differs significantly from its corresponding theoretical concept. The “rent” of national accounting is the “rental income of persons” and does not represent a scarcity return either on the indestructible resources of nature or on specific factors temporarily fixed in quantity. A significant part of it may be regarded as a reward for entrepreneurial activity. It does not, however, include the net income on all leased property, but only the portion thereof received by persons; the net income on real estate owned by businesses is not counted as rent, but as part of corporate profits or unincorporated business income. Corporate profits also include explicit or computed interest received by firms, and the income of unincorporated enterprises contains not only rent and interest but also the return for the labor of the proprietor. Even employee compensation cannot be regarded as a pure return to current effort in a modern economy such as that of the United States, where substantial resources have been invested in the education and training of the labor force.
A threefold division of national income
Accepting for the moment the accounting framework used for national income purposes, a threefold division of income into employee compensation, entrepreneurial (unincorporated) income, and property income (rent, interest, and corporate profit) is perhaps most relevant to the study of functional shares. Data for the United States cast in these terms are set out in the form of average shares for overlapping decades in Table 1. Employee compensation rose in two long swings, from 55 per cent in 1900-1909 to 67 per cent in the 1930s, and then again to 70 per cent by the decade beginning in the mid-1950s. It is possible to view the record as a generally upward trend—interrupted only by the swelling of profits and the corresponding diminution of the wage share during the war prosperity of the second decade of the century, and more seriously, by the contraction of profits and the unusually large and temporary expansion in the wage share during the great depression of the 1930s. (For an analysis of cyclical changes which finds that the labor share is inversely correlated with changes in the level of economic activity, see Burkhead 1953.)
The bulk of the increase in the share of employee compensation came at the expense of entrepreneurial income, which declined from 24 per cent to 15 per cent, and then to 12 per cent. The upward trend in wages, or total employee compensation, and the decline in entrepreneurial income have their beginnings in the nineteenth century. E. C. Budd (1960) has estimated that the share of wages in private income rose from about 43 per cent in 1869-1870 to about 48 per cent in 1909-1910.
The long-run rise in the employee share and the decline in the entrepreneurial share of income reflect two other important and interrelated trends in the nation’s economic structure—the change from an agricultural to an industrial country and the shift out of self-employment into wage and salary employment. The proportion of persons engaged in agriculture declined from more than half of the work force in 1870 to less than 40 per cent at the turn of the century, and to 7 per cent in the early 1960s, while the proportion of wage and salary employees rose from 58 per cent in 1870 to 64 per cent at the turn of the century, and to about 85 per cent in the 1960s (Budd 1960; Survey of Current Business, July 1963).
It should not be inferred that managerial employees were the main beneficiaries of the rise in employee compensation. On the contrary, the share of corporate officers dropped from around 4 per cent in the 1920s and 1930s to around 3 per cent
|Table 1 - Distributive shares in U.S. national income, 1900-1963 (averages of percentage shares for individual years in overlapping decades)|
|DISTRIBUTIVE SHARES||PROPERTY SHARE, VARIOUS CONCEPTS|
|Entrepreneurial income||Total property sharebb|
|Employee compensation||Farm||Nonfarm||Corporate profits||Interest||Rent||Totala||Interest, rent, and corporate profits||Asset basis||Labor basis||Proportionate basis|
|a. Details may not add to total because of rounding.|
|b. Final stages of estimation carried out in terms of aggregates for decades.|
|c. Not available.|
|Sources: 1900-1909 to 1930-1939: Johnson 1954, p. 178. Johnson’s estimates were based on data of U.S. Office of Business Economics, National Income 1951; Kuznets 1941; King 1930; National Industrial Conference Board 1939. 1929-1938 to 1949-1963: derived from U.S. Office of Business Economics, Narionaf Income 1954; U.S. Office … 1958a; Survey of Current Business, July issues for 1957-1964.|
in the 1940s and 1950s (Kravis 1959, p. 920). Even allowing for a substantial understatement of the actual earnings of this group, it seems unlikely that its share has been expanding. It is, of course, possible that the income share of corporate managerial employees below the officer level has been rising.
The share of property income (interest, rent, and corporate profits) hovered around a level of 21 or 22 per cent until the depression decade of the 1930s. At that time the share dropped by three or four percentage points, and it has since remained around a level of 18 or 19 per cent. This relative stability of the property share has, however, been the result of offsetting shifts in its components, particularly interest and corporate profits. In 7 out of the 11 decade-to-decade changes in Table 1, the interest and corporate profits shares move in opposite directions, describing about one and one-half long cycles during the half century or more. (The interest and corporate profit shares move in the same direction in only 2 out of the 11 decade-to-decadal changes; in the other 2 instances, one of the shares remains unchanged.) There was a peak in the profits share and a trough in the interest share during the prosperity of World War i, a profits trough and interest peak in the depressed 1930s, and high profits and low interest shares in the prosperous 1940s and 1950s. This seesaw relationship between a return based on a fixed claim and one representing a residual share contrasts with the decline in the rent share from 9.0 per cent in 1900-1909 to around 3.3 per cent in 1934-1943 and ensuing periods. In a sense, this reduction in the rent share plays an important role in producing the relative stability of the property share. Compared with those of most previous decades, the recent levels of the profit share tend to be higher by a large number of percentage points than the interest share is lower, and were it not for the fact that the rent share has been only one-half or one-third of its former levels, the property share would have risen. (For a discussion of the decline of the rent share, see Kravis 1959, pp. 921-923.)
The growing importance of corporate profits in the composition of property incomes adds significance to the changes in the allocations of corporate profits to dividends, taxes, and retained earnings. Unlike the other property shares, allocations to taxes and undistributed profits may create a substantial gap between profits earned by corporations and income actually paid out by them to income receivers in the form of dividends. The record for the period since World War I is shown in Table 2.
Well over half of the relative rise in corporate profits from the 1920s and the 1930s has been
|Table 2 -Percentage share of corporate profits in U.S. national income, 7979-7963|
|Before fox||After tax||TAXES||DIVIDENDS||UNDIS-TRIBUTED PROFITS*|
|*Includes inventory valuation adjustment. It should be noted that the shares of corporate profits shown differ somewhat from those in Table 1, mainly because different sources and methods were used in deriving the figures.|
|Sources: 1919-1938: Kuinets’shares of corporate dividends and corporate saving (1959, p. 217) in national income, adjusted so as to include the federal corporate income and excess profits taxes as shown by Schuller (1953, p. 312). 1929-1963: U.S. Office of Business Economics, National Income 1954; U.S. Office … 1958a; Survey of Current Business.|
accounted for by the increase in tax liability. The share of dividends in the national income has actually decreased. The implication is that property income has declined relative to labor income in terms of income actually paid to income recipients (personal income) even more than it has in terms of income earned (national income).
The employee share in individual sectors
When the behavior of shares in individual sectors and industries of the U.S. economy is examined, we find that the employee share tends to conform to the movement of the employee share in the economy as a whole (see Table 3). The typical pattern is an initial decline, with the trough most often coming in the 1940s, and then a swing upward, the share for the final period exceeding that for the initial one. There are, however, some important exceptions. The corporate sector as a whole and several industries, including manufacturing and mining, have higher employee shares at the beginning than at the end. The initial share in each of these cases is high because of the impact of the great depression; in some instances, periods of two or three years are found in the early 1930s when the employee share exceeded 100 per cent (that is, the compensation of employees was actually greater than the income originating, owing to negative profits). For the last four entries in the table, the U-shaped pattern of the share movements is inverted; there is a peak in the middle of the period, which falls most frequently in the 1944-1953 decade.
The trend in other countries
The available evidence for other countries seems to indicate that the broad pattern of the movement in shares is similar to that of the United States. (See Table 4.) At least from the second decade of the twentieth century the share of employee compensation has increased mainly, though not entirely, at the expense of the entrepreneurial share. The property share also has tended to decline, not only after World War II, as in the United States, but after
|Table 3 - Shares of employee compensation in income originating in U.S. national economy and in various sectors, 1929-1963 (averages of percentages for individual years in overlapping decades)|
|Per cent of income devoted to employee compensation|
|Sources: U.S. Office of Business Economics, National Ineome 1954; U.S. Office…1958a; Survey of Currant Business.|
|Private economy (exc. gov′t.)||61.1||58.8||59.3||60.7||63.2||65.4|
|Private business (exc. gov′t. and households)||62.6||60.0||58.8||60.3||63.3||66.0|
|Agriculture, forestry, and fisheries||18.4||16.8||16.3||16.6||18.5||20.3|
|Wholesale and retail trade||76.9||66.3||59.6||62.6||69.6||73.8|
|Finance, insurance, real estate||31.8||32.0||29.0||28.6||29.8||32.3|
|Of which: Finance and insurance||(89.0)||(81.2)||(73.8)||(69.8)||(70.7)||(73.9)|
|Households and institutions||73.3||75.2||80.7||79.6||70.5||66.6|
|Table 4 - Factor shares in national income, selected countries and periods|
|Employee compensation||Unincorporated business||Property income||Total*|
|*Details may not add to total because of rounding.|
|Sources: Canada, Goldberg 1964, p. 205; other countries, Kuznets 1959.|
World War I as well. Kuznets, upon whose work these generalizations are based (1959, p. 49), thinks it most likely that the property share tended to remain stable in most countries between the third quarter of the nineteenth century and World War I.
The influence of the accounting framework
The trends in shares analyzed in the preceding sections may be challenged both on statistical and on conceptual grounds. Statistically, the quality of the data becomes worse as we go back in time. For the United States, they are generally accepted as reasonably accurate for the period since 1929, somewhat less reliable for 1919 to 1929, and subject to wide margins of error for the first two decades of the century. The basic estimates for the two early decades were in some instances derived by estimating methods that make them unsatisfactory for the determination of relative shares; for some industries, for example, entrepreneurial earnings were extrapolated backward according to the movements of total wages (Lebergott 1964). Some of the errors that have been pointed out exaggerate the tendency toward a rising wage share and others to understate it, and it is difficult to judge their net effect. The figures in Table 1 relating to the first two decades must therefore be regarded with great reserve.
The share figures are affected not only by the methods of estimation but more fundamentally—at least for recent decades—by the accounting framework under which they were produced. While there is, on the whole, widespread agreement upon the methods of social accounting, some issues which may affect the income share estimates remain controversial (Conference on Research …1958, especially the papers by G. Jaszi, R. T. Bowman and R. A. Easterlin, and E. C. Budd; Kravis 1957). In addition, even some of the conventional procedures that are followed may have won agreement more on the ground of statistical convenience than on that of conceptual adequacy. We are faced with the question, therefore, of whether the trend in shares that we have observed—particularly the rise in the wage share—would persist if the issues concerning accounting methods had been resolved in another way. The effects of some of these factors, such as the shift of certain activities from households to the market, the omission from the national accounts of the returns on certain types of property (namely, property owned by government and durable goods other than residences owned by consumers), and the exclusion from the estimates of interest on government debt and the inclusion of the compensation of government employees, have been discussed elsewhere (Kravis 1962). Effects of changes in tax laws and in regulations governing depreciation allowances and the practice of using historical rather than replacement-cost depreciation have also been studied (Brown 1963).
The outcome of these studies is that the factors commonly cited as limiting the usefulness of national accounts data for the study of income shares are not of sufficient quantitative importance to throw into question the major trends in the threefold division of income. The marked rise in the labor share and the decline in the entrepreneurial share are hardly affected. At worst, a little doubt is cast upon the persistence of the decline in the property share in the 1930s. If we impute returns to property owned by government, especially military property, or if we place the method of computing depreciation on a more consistent basis, much or all of the diminution in the property share is offset. On the other hand, if we exclude government completely, or if we use replacement-cost depreciation, the original result remains unaffected.
|Table 5 - Distributive shares in U.S. personal income, 1909-1963 (averages of percentage shares for individual years in overlapping decades)|
|NATIONAL BUREAU DATA||COMMERCE DEPARTMENT DATA|
|a. For 1909-1918 to 1924-1933 includes government transfer payments. From 1929 on, personal contributions for social insurance were deducted from labor income. Division between wages, salaries, and transfers not available until 1929.|
|b.Details may not add to total because of rounding.|
|Sources: 1909-1938, derived from Creamer 1956, pp. 116-123; 1929-1963, derived from U.S. Office of Business Economics, National Income 1954; U.S. Office . . . 1958a; Survey of Current Business.|
|Wages and salaries Transfers||64.4||61.5||63.8||65.6||66.4||67.6||68.0|
A threefold division of personal income
For some purposes it may be preferable to consider distributive shares in income received by households rather than in income produced by the nation —that is, shares in personal rather than national income. The U.S. data are set out in this manner in Table 5.
For the period preceding 1929, transfers and corporate taxes, which constitute the most important differences between national and personal income, were of smaller quantitative significance, and the shares in personal income were not far different in magnitude and direction of change from the shares in national income. After 1929, however, government policies brought about an expansion of both transfer payments and corporate taxes, and the share of property in personal income declined sharply, whereas its share in national income remained roughly constant. The relative importance of corporate profits in property income rose, while the share of corporate profits allocated to dividends (see Table 2)—the only part of corporate profits that enters into personal income—fell. The gap between the property share in earned income and in income actually paid out to income recipients was further widened by a rise in corporate saving; undistributed profits have amounted to 2 or 3 per cent of the national income in recent decades. (For a discussion of the impact of the accounting framework, see Kravis 1962.)
A twofold division of income
Although the threefold division into labor, entrepreneurial, and property shares is as far as the usual accounting records of the economy can carry us, it is necessary to attempt to divide entrepreneurial income into its labor and property components if we are to probe some questions that arise: Has the increase in the share of labor been attributable mainly to the shift from self-employment in the proprietorship form to employment under the corporate form of business organization? What has happened to the share of income representing returns to the current efforts of persons engaged in economic activity (i.e., what we shall call the “total labor” share) as compared with the share representing the return on past accumulations of wealth (i.e., what we shall call the “total property” share)?
Of course, if all or virtually all entrepreneurial income could be considered as a reward for the labor of the entrepreneur, the answer to these questions would be very simple. In that case, our findings would be that the relative shares of labor and property in the national income have remained almost constant for more than half a century, except for a shift in favor of labor in the years around 1930.
The difficulty with this view is that it implicitly assumes that the returns upon the assets of unincorporated enterprises have been zero or negligible. These assets form a substantial, albeit declining, share of total private wealth. In 1958, unincorporated businesses and farms accounted for 18 per cent of the nation’s total tangible assets; in 1900, they accounted for 35 per cent (Goldsmith & Lipsey 1963, p. 43). Therefore, the assumption about the rate of return earned by these assets is critical to an evaluation of the property share in entrepreneurial income.
One possible assumption is that the rate of yield on entrepreneurial property may be imputed from the rates observed in the market place for similar types of property. We have made some very rough calculations along these lines, distinguishing only between farm real property, farm nonreal property, and tangible assets of nonfarm unincorporated businesses. For farm real property, rents were estimated on the basis of rents on rented farm land. For farm nonreal property, the interest rates on farm mortgages were taken as the rate of return, and for unincorporated businesses the rate of return was taken to be the same as that for manufacturing corporations. (The methods followed are largely those used by Johnson 1948, with the aid of data from Brownlee & Conrad 1961; National …1939; Stigler 1961; U.S. Bureau … 1960; U.S. Department of Agriculture, Agricultural Statistics.) When the entrepreneurial property shares calculated in this fashion are added to the other property shares (interest, rent, and corporate profits) to obtain what may be called the total property share, the results are as shown in column 9 of Table 1. This will be referred to as the “asset basis” for estimating the property share in entrepreneurial income.
The asset basis regards the return to entrepreneurial labor as the residual component of entrepreneurial income. It seems just as logical—and has the sanction of at least occasional practice—to calculate the labor component directly and to regard the property portion as the residual return. This can be done by assuming that the annual value of the labor of a proprietor is equal to the annual earnings of a hired worker. Since there are wide differences in annual earnings from one industry to another, the labor earnings of entrepreneurs in different industries should be estimated separately. In our rough estimates, however, only two “industries” are distinguished—farm and non-farm. The figures produced by this approach, the “labor basis” for splitting up entrepreneurial income, are presented in column 10 of Table 1. (The sources are U.S. Office of Business Economics, National Income 1954; U.S. Office …1958a; Survey of Current Business. For the years before 1929 they are Kuznets 1941; Creamer 1956; King 1930; National Industrial Conference Board 1939; Douglas 1930; U.S. Bureau of the Census 1960.)
The difficulty with both the asset basis and the labor basis is that they tend to concentrate the effects of fluctuations in the entrepreneurial share upon one or the other component. It may be more realistic to argue that when the entrepreneur commits his labor and capital to an enterprise, he is taking the risk that he will get much less than the market rates of return on both the labor and capital in the hope, of course, that he will get much more. Since the two types of input are jointly committed, both should be allowed to share in the ups and downs of entrepreneurial income. In this approach to the allocation of entrepreneurial income, the ’ labor” reward of entrepreneurs is computed as in the “labor” basis and the “property” reward as in the “asset” basis, and the two are adjusted proportionately so as to make their total conform to actual entrepreneurial income. We have labeled this the “proportionate” basis. In our actual computations entrepreneurial property returns were assumed to bear the same ratio to rent, interest, and corporate profit as entrepreneurial assets bear to all other tangible assets. The resulting total property share shown in column 11 of Table 1 differs in level but not in direction of movement from the share that is produced when the asset method is employed to derive the property component in the “proportionate” method calculations.
The calculations in the last four columns of Table 1 indicate that the general pattern of movement is similar for these four ways of measuring the property share. In the first decade or two of the century—the period for which the data are least reliable—there is a slight rise in the property share, however measured. There follows a decline that becomes more marked with the depressed 1930s; after the 1930s, however, little if any of this decline is recovered. The amplitude of the decline from the 1920s to the ensuing decades is, however, substantially greater for the total property share, regardless of the method by which it is estimated, than for the simple (interest, rent, and corporate profits) property share. This result would follow even from the addition of a constant percentage of the declining entrepreneurial share to the near-constant simple property share. For this not to be the outcome, the imputation would have to allocate a rapidly rising fraction of entrepreneurial income to property. As we have seen, in other business sectors, in recent decades at least, the property share has tended to fall rather than to rise.
All in all, the evidence thus points to an increase in the share of national income attributable to current human effort. This may either be the result of a structural shift brought about by, or at least coinciding with, the great depression, or it may be the result of longer-run tendencies. The latter view is plausible if we regard the property shares as having been artificially depressed by the great depression. Had it not been for the unprecedented collapse of incomes, the property share might have shown a smoother and more continuous decline from the second or third decade of the century to the most recent decade. Obviously, this is not a trend that can continue forever, but it requires explanation.
Reasons for decline in property share
The distribution of income among the factors of production is the net result of the operation of the whole intricate clockwork of the economy. Nothing less than a full set of equations setting out the general equilibrium of the system could be certain to include all the elements at work, and even in this approach it would be difficult, if not impossible, to take full account of shifts in resources, tastes, and technology, any of which may affect factor shares. The practical problem therefore becomes the familiar one of seeking to identify the key elements affecting the movement of relative shares. The literature on this subject, which has been growing apace in recent years, has in common only this tacit agreement on a search for the key variables. There has not even been agreement on what it is that has to be explained. Some writers, brushing aside the government and unincorporated business sectors, have found a striking constancy in relative shares and have sought to explain that. Others have found that it was an increase in the employee share that had to be explained. Nor has there been agreement, not even within either group, on the selection of the key variables that affect the constancy or movement of relative shares.
The explanations that have been advanced may be classified into three categories, according to the nature of the key variables selected: structural, factor-oriented, and aggregative.
Structural explanations. The structural approach attempts to explain the movement in overall income shares in terms of changes in some basic characteristic of the economy, such as shifts in the relative importance of different industries, alterations in the bargaining power of labor and/or employers (monopoly power), and variations in the size of firms.
In general, any intersectoral shift which changes the relative importance of sectors with either very high or very low, or with rapidly rising or rapidly falling, employee shares will have an impact on the over-all share.
We have already had occasion to mention two such shifts that are often cited in attempts to probe the sources of the increase in the share of employee compensation in the national income—the growth in the importance of the government sector (with an employee share of 100 per cent) and the decline in the importance of unincorporated business (with a below-average employee share in the 35-45 per cent range). Sometimes one or both of these sectors are omitted from the analysis, but the conceptual simplicity thus obtained is purchased at a high price. The functioning of factor markets in determining relative shares can hardly be explained satisfactorily if employers of significant amounts of the factors are left out. In 1962, for example, nearly 20 per cent of total employee compensation was paid by the nonbusiness sector and nearly 40 per cent by the nonbusiness and noncorporate business sectors combined.
A number of writers have analyzed the effects upon relative shares of changes in the importance of different sectors of the economy. Kuznets (1941, pp. 241-250), Denison (1952), Johnson (1954), and Budd (1964), working with different periods during the past half century, have produced results which indicate that changes in the industrial composition of employment and income have tended somewhat to increase the share of labor. It seems clear, however, that the rise in the employee share cannot be explained away in terms of sectoral shifts. This conclusion holds even within each of the more restricted sectors of the economy (such as the private business and corporate sectors), which have sometimes been advanced as more appropriate for the study of relative shares (Budd 1964).
Solow (1958) has called attention to the possible operation of what might be termed a micro-economic share-stabilizing mechanism. This would exist if there were a tendency, when labor shares are rising, for industries with high labor shares to diminish in relative importance in originating national income and for those with low labor shares to increase in relative importance. However, Solow’s findings concerning the existence of such a mechanism were generally negative.
Changes in the degree of monopoly power represent another type of structural shift that may significantly affect the employee share. The assumption of a significant and growing degree of monopoly was used by Kalecki as the basis for an explanation of relative shares which has been criticized elsewhere (Kaldor 1955-1956). It should be noted, however, that Kalecki’s original formulation referred essentially to wage earners in manufacturing. (For another use of the markup idea, see Weintraub 1959.) In a firm enjoying a sheltered market position, both wage and nonwage incomes may be higher than under competitive conditions, but the nonwage incomes are apt to be more above the competitive level than are the wage incomes, since the firm is presumably hiring labor under market conditions that are more competitive than those under which it is selling its product. Therefore, the share of labor will vary inversely with the degree of monopoly exercised by firms, and if monopoly has had anything to do with the rise in the labor share, monopoly must have become less pervasive. Or, if the degree of monopoly in product markets has remained unchanged or even has increased somewhat, perhaps the rising role of unions has provided an offsetting source of monopoly power that has pushed the wage share up. However, there is no agreement among labor economists that unions have in fact succeeded in raising labor’s share (Reder 1959, pp. 184-185).
Among other structural factors that may affect factor shares, mention may be made of changes in the price level, the size of firms (Goldberg 1964, p. 234), and the quality of labor. For rising prices to bring about a reduction in the property share, their adverse effect upon contractual property incomes (rent and interest) must outweigh their positive effect upon residual property incomes (profits). This differential effect of rising prices upon rent and profit may explain much of the fall in rent and rise in profits mentioned earlier (Brown-lee & Conrad 1961).
Even if structural factors could be found which accounted fof all of the changes observed in the labor share, a theory of factor shares would still be required to explain what mechanism tends to keep the shares constant in the absence of such structural changes. Our data suggest, however, that it is not constancy which requires explanation, but an expansion in the share of income accruing as a reward for current effort and a decline in the share arising as a return on accumulated assets. The shifts are small relative to the over-all growth in real income (more than a fivefold increase from 1900-1909 to 1954-1963) or to the rise in the capital-labor ratio (probably half again as high in 1954-1963 as in 1900-1909). (See Kravis 1959, pp. 936-938.) Nevertheless, the changes are real and significant, considering that limits on shifts in the distribution of income are imposed by the requirements of social stability.
Theories of relative shares
It is possible to formulate a variety of tautological relationships between the wage or the property share, on the one hand, and its various “determinants,” on the other hand. In factor-oriented theories the independent variables are usually the prices and quantities of the factors of production. The marginal productivity theory of distribution, which occupies a commanding position in the literature, may be classified under this heading. For empirical purposes, marginal productivities are usually estimated from an aggregate production function, and shifts in factor shares are seen to depend upon the elasticity of substitution. [SeeProduction.]
In aggregative theories the independent variables usually include Keynesian aggregates, particularly savings and investment. For example, a simple kind of identity often employed is
where R is property income; Y, total income; and K, the capital stock. The property share may easily be related directly to savings and investment propensities, as shown in a formulation used by Kaldor:
where I is investment and sr and sw are the marginal propensities to save out of property and wage incomes, respectively (Kaldor 1955-1956; Kaldor’s theory assumes full employment). If, as Kaldor seems to argue, the savings propensities tend to be constant, then the property share depends on the level of investment.
The line separating the factor-oriented and aggregative theories is not a sharp one. Indeed, if the explanation is pushed far enough, a factor-oriented theory reaches the aggregative variables, and the converse is also true. In addition, some aggregates, such as wages and income, are found in both groups of theories. However, where there is such overlap, the factor-oriented theories are more apt to concern themselves with explanations of the way in which the aggregates are built up from the individual factors or products than are the aggregative theories.
No effort will be made here to review these various approaches to a theory of relative shares, since several such surveys have recently appeared (for example, Reder 1959; Scitovsky 1964). What follows is an attempt at an explanation of the rise in the labor share in empirical terms, using a factor-oriented approach.
The relation of property to wage income can be regarded as the product of capital-labor quantity and price ratios:
where R = total property income, W = aggregate wages (R + W = total income, Y), Q - quantity, P = price, k = capital, and I = labor.
Changes in relative shares thus result from changes in the quantity and/or price ratios. (Once R/W is known, the property share in income, R/Y, can be calculated, since the sum of the wage and property shares must equal 1: w + r=l, where w = W/Y and r = R/Y; thus, (r ÷ R/W) + r = 1. The property share can be found by substituting the numerical value of R/W and solving for r.) Since the ratio of the percentage change in the quantity-ratio to the inverse of the percentage change in the price-ratio is equal to the elasticity of substitution, we are dealing with the familiar proposition that changes in relative shares depend upon the elasticity of substitution. [SeeElasticity.]
Now, if we could assume that the price and quantity ratios would move in opposite directions, the opportunity for factor substitution would clearly serve as a built-in stabilizing mechanism limiting changes in relative shares. Where the opposite percentage changes in the quantity and price ratios are equal—i.e., where the elasticity of substitution is unity—relative shares will of course remain unchanged. Even with fairly large departures from unity, however, factor substitution may confine share shifts to fairly narrow limits. For example, with a 75-25 division of national income between labor and capital, a 20 per cent increase in the ratio of the price of labor to the price of capital would not cause the labor share to stray more than 3 or 4 percentage points from 75 were the elasticity of substitution as low as 0.25 or as high as 2.
In fact, there is reason to believe not only that the quantity and price ratios move in opposite directions, thus tending to limit the extent of the change in relative shares, but also that the elasticity of substitution is below 1. For example, the ratios for the United States at two periods, roughly a half century apart, are as shown in Table 6 (Kravis 1959, p. 940):
These figures yield a “historical” arc elasticity of substitution of 0.64. This compares with an arc elasticity of 0.62 computed by Kendrick for total manufacturing between 1953 and 1957 (1964, p. 141). Kendrick also made separate estimates for 20 two-digit manufacturing industries: 18 were between 0 and 1. Arrow and his colleagues (see Arrow et al. 1961) obtained elasticities ranging from 0.721 to 1.011 for 24 industries based on a cross section of 19 countries; the values fell between 0.800 and 0.899 for 11 of the 24 industries and between 0.900 and 0.999 for 8 industries. The last group of estimates are based on the assumption of an elasticity of substitution that is constant—but not, of course, necessarily unity, as the Cobb-Douglas production function posited.
The magnitude of the elasticity of substitution depends on the techniques of production, on other influences affecting the demand for the factors, and on the supply of the factors.
In the short run with fixed plant, the opportunities for factor substitution may be limited. In the long run, technological progress—especially to the extent that it consists of finding new ways to produce old products—may be viewed partly as a process in which the range of producers’ choice among factor combinations is extended.
Among the other influences on demand are the share-stabilizing influence of responses in commodity markets to an increase in the relative price of a given factor, say labor. Consumers may be expected to respond to an increase in the relative price of labor-intensive commodities by shifting their purchases to other goods, thus bringing about a shift toward a greater utilization of capital in the economy as a whole even though there has been no change in the capital-labor ratio in any industry. Solow’s investigation, reported upon under “Structural explanations,” does not seem to suggest that this kind of mechanism has played a major role in the U.S. economy.
A hypothesis consistent with the facts is (1) that the behavior of the price and quantity ratios cited above is attributable to the differences between the supply conditions under which capital and labor are provided, and (2) that the demand conditions have been permissive rather than determining. This can be brought out by making a series of alternative assumptions about the relative impact of economic growth upon the demands for capital and labor respectively and determining what supply conditions for the two factors could have produced the historical changes in their price and quantity ratios that have been noted.
Let us first assume that the expansion in demand was neutral, in the sense that the relative marginal productivities were unchanged for any given ratio of capital to labor. (Geometrically, the isoquant drawn with capital on the vertical axis and labor on the horizontal axis merely shifts upward and to the right; its slope is unchanged at the point of intersection with any given gradient drawn from the origin indicating the capital-labor ratio.) If both capital and labor were perfectly elastic in supply, there would be proportionate increases in both, and no change in relative prices or shares in income would occur. If one were more elastic in supply than the other, the relative quantity of the more elastic factor would increase, and given imperfect substitutability between the factors, its relative price would fall. In the actual event, capital nearly tripled in quantity, with no secular increase in rate of return (Kravis 1959, p. 938), while the number of man-hours rose by less than 50 per cent despite a better than threefold rise in hourly compensation. Thus, if technical progress was neutral, the facts would fit the hypothesis.
Next consider the case in which economic growth is not neutral but increases the demand for capital relative to labor: For any given capital-labor ratio, the marginal productivity of capital has improved relative to that of labor. In Hicks’s terminology, technical progress is labor-saving (1932, pp. 121-122 in 1935 edition). (The higher isoquant has a smaller slope than the lower one at the points of intersection with any given gradient from the origin.) But we are immediately confronted with the problem of explaining why the return on capital did not rise relative to that of labor. As in the previous case, the answer appears to turn on the supply conditions: additional supplies of capital were readily forthcoming, while the supply of labor was so inelastic that even the smaller increase in the demand for it resulted in large price increases.
Finally, there is the case in which innovations raise the marginal productivity of labor in relation to that of capital (Hicks’s capital-saving category). If the supplies of both factors were perfectly elastic, there would be an increase in the relative quantity of labor. If, at the other extreme, the supplies of both factors were perfectly inelastic, the relative quantities would remain the same and the relative price of labor would rise. The only circumstances that would produce a decrease in the relative quantity of labor as well as an increase in its relative price, such as occurred in the history of the period, are those in which the supply of capital is more readily responsive to increased demand than is the supply of labor.
Whatever the nature of the demand influences, therefore, the increase in the capital-labor ratio and the relative increase in the price of labor are attributable to differences in supply conditions. However, we have explained only the direction of the movements of the quantity and price ratios; to account for the rise in the labor share, we have to explain why labor increased in relative price more than it decreased in relative quantity. The answer to this question depends not only upon the difference in the supply elasticities but also upon the marginal rate of substitution between capital and labor (MRS). If the MRS were constant from one equilibrium position to another, there could be no change in relative prices; only relative quantities would change. The fact that relative prices changed so much indicates not only that there was a great difference in the elasticities of supply but also that the substitutability of capital for labor diminished. Nevertheless, the impetus to the change came from the supply conditions for the factors; otherwise, with neutral innovations there would have been no change in the MRS, and with labor-saving innovations the change in the MRS would have been opposite to the observed direction. Only in the less likely case of capital-saving inventions would the MRS move in the right direction without aid from the supply side, and even in this case we have to invoke the supply conditions to explain the quantity changes.
We have thus far glided over the difficulties encountered in deriving supply and demand curves from historical data. Not the least of these is the familiar problem of distinguishing the supply effects from the demand effects in historical statistics. If we could assume that the supply schedule for labor had remained constant over the entire half century and that the observed prices and quantities reflect the upward shift of the demand for labor, then the arc elasticity of supply of man-hours could be easily calculated as 0.31 for the period covered by the price and quantity ratios given above. If the supply also shifted upward, though not as much as did the demand, the elasticity may well have been less than 0.31; if the number of man-hours offered at each real hourly wage actually tended to diminish, the elasticity would have been greater than 0.31. In any case, the tripling of real earnings per man-hour with an increase in man-hours worked of only 40 per cent is consistent with the hypothesis of inelastic supply or with the related hypothesis that the growth in demand was greater than the growth in supply.
Matters are much less clear-cut with respect to capital. Even if we assume that the actual rate of return represents a good stand-in for the expected rate of return, the rate which presumably governs the supply of capital, it is difficult to draw any generalizations (see Kravis 1959, p. 943). The periods spanning the years of the great depression had lower rates of return and smaller increments in the stock of capital than the more prosperous periods before and after. In the more prosperous periods, however, there was little association between changes in the rate of capital formation and changes in the actual rate of return from one overlapping decade to another. Perhaps the actual rate of return is a poor proxy for the expected rate, particularly since capital gains, which are excluded from the actual rate of return, may at certain times have been a more important motive to capital formation than was income in the sense used in the national accounts. Also, the rate of return that is relevant to new investment is the marginal rate rather than the average rate, which is the only rate available. Finally, and this is an important limitation for labor as well as capital, price might be a relatively minor influence in determining changes in available quantities.
Whatever the reason, then, under conditions of rapid expansion in production, labor was relatively inelastic in supply and rising rapidly in price, and capital was apparently either much more elastic or, at any rate, growing rapidly in supply. Thus entrepreneurs substituted capital for labor, or to put it more precisely, they increased their use of capital at a more rapid rate than they increased their use of labor. It is not clear in what degree the relatively expanded use of capital was possible by virtue of existing techniques—owing either to the adaptability of equipment in use or to the availability of stand-by techniques requiring more capital and less labor—or in what degree it was the result of newly created capital-using techniques whose development was stimulated by the growing relative scarcity and high price of labor. If the common conception of the rate of application of new knowledge to industrial processes has any validity, innovations must have played a major role in the change in the ratio.
A slightly different view of the same phenomena can be obtained by introducing the capital stock into equation (3). This involves decomposing the elements in (3) so as to express the property-labor income shares as the product of (a) output per man-hour, (b) the capital-output ratio, and (c) the ratio of the price of capital to the price of labor:
One of the new terms (Y/QI) is a measure of the average productivity of labor, and the other (Qk/Y), the capital-output ratio, is the reciprocal of the average productivity of capital. The capital-output ratio rose in the depressed 1930s, when capacity was not fully utilized; declined in the booming 1940s, when capacity was used to the hilt; and during the 1950s remained at a level corresponding to about 70 per cent of the 1900-1909 level; in terms of capital productivity, this amounts to an increase of less than 45 per cent between the opening and closing decades of the half century. Labor productivity, on the other hand, doubled within the same time span. (See Kravis 1959.) This relative economizing in the use of labor may seem to imply that innovations during the period must have been labor-saving, but the economizing may flow merely from a shift in factor proportions; the average productivity of labor necessarily rises relative to that of capital whenever the quantity of labor falls relative to that of capital, that is,
whether the change in relative quantities is or is not due to changes in techniques. The presumption in favor of the hypothesis that adoption of labor-saving techniques accompanied the growth in capital relative to labor is supported by the further presumption that a rapidly rising relative wage rate created an inducement for innovations biased in this direction. (Probably the most common view is that inventions have been labor-saving. See Hicks 1932, p. 124 in 1935 edition. For an argument that inventions may have been neutral, see Solow 1957 and Reder 1959.)
Our discussion thus leads to the view that the impetus to the rise in the labor share came from sharp increases in real wages, owing to the lack of responsiveness in the supply of man-hours to the rising demand for labor attendant upon rapid economic growth. The use of relatively more capital was made possible by price-induced substitution and by price-induced capital-using (labor-saving) innovations.
It is possible that important pieces of the share puzzle lie within realms of the social mechanism other than the purely economic. Some of these are obvious and tangible, such as the dependence of changes in the size of the labor force upon the rate of population growth and labor force participation rates. Others, perhaps equally important, are much more difficult to establish. One source of the forces favoring the labor share may conceivably be found in the relative effects upon the supply prices of labor and capital of our society’s acceptance of continuously rising incomes as a normal result of the economic process.
Irving B. Kravis
Arrow, Kennethet al. 1961 Capital-Labor Substitution and Economic Efficiency. Review of Economics and Statistics 43:225-250.
Bach, George L.; and Ando, Albert K. 1957 The Redistributional Effects of Inflation. Review of Economics and Statistics 39:1-13.
Brown, Murray 1963 Depreciation and Corporate Profits. Survey of Current Business 43, no. 10:5-12.
Brownlee, Oswald; and Conrad, Alfred 1961 Effects Upon the Distribution of Income of a Tight Money Policy. American Economic Review 51, no. 2:74-85.
Budd, E. C. 1960 Factor Shares, 1850-1910. Volume 24, pages 365-406 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
Budd, E. C. 1964 Comment on Goldberg’s Paper. Volume 27, pages 276-285 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press. → Comment on Goldberg 1964.
Burkhead, Jesse V. 1953 Changes in the Functional Distribution of Income. Journal of the American Statistical Association 48:192-219.
Business Statistics. → Published since 1931 under various titles. Since 1951 issued by the U.S. Office of Business Economics. See especially the 1957 issue.
Conference on Research in Income and Wealth 1958 A Critique of the United States Income and Product Accounts. Studies in Income and Wealth, Vol. 22. Princeton Univ. Press.
Creamer, Daniel B. 1956 Personal Income During Business Cycles. National Bureau of Economic Research, Studies in Business Cycles, No. 6. Princeton Univ. Press.
Denison, Edward F. 1952 Distribution of National Income: Pattern of Income Shares Since 1929. Survey of Current Business 32, no. 6:16-23.
Douglas, Paul H. 1930 Real Wages in the United States, 1890-1926. Pollack Foundation for Economic Research, Publications, No. 9. Boston: Houghton Mifflin.
Fabricant, Solomon 1952 The Trend of Government Activity in the United States Since 1900. National Bureau of Economic Research, Publication No. 56. New York: The Bureau.
Goldberg, S. A. 1964 Long Run Changes in the Distribution of Income by Factor Shares in Canada. Volume 27, pages 189-237 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
Goldsmith, Raymond W. 1952 The Growth of Reproducible Wealth of the United States of America From 1805 to 1905. Pages 242-328 in International Association for Research in Income and Wealth, Income and Wealth of the United States, Trends and Structure. Income and Wealth, Series 2. Cambridge: Bowes.
Goldsmith, Raymond W. 1955-1956 A Study of Saving in the United States. 3 vols. Princeton Univ. Press. → Volume 1: Introduction; Tables of Annual Estimates of Saving, 1897 to 1949. Volume 2: Nature and Derivation of Annual Estimates of Saving, 1897 to 1949. Volume 3: Special Studies, by R. W. Goldsmith, Dorothy S. Brady, and Horst Mendershausen. See especially Volume 3.
Goldsmith, Raymond W. 1962 The National Wealth of the United States in the Post War Period. National Bureau of Economic Research, Studies in Capital Formation and Financing, Vol. 10. Princeton Univ. Press.
Goldsmith, Raymond W.; and Lipsey, Robert E. 1963 Studies in the National Balance Sheet of the United States. 2 vols. National Bureau of Economic Research, Studies in Capital Formation and Financing, Vol. 11. Princeton Univ. Press. → See especially Volume 1.
Hicks, John R. (1932) 1964 The Theory of Wages. New York: St. Martins.
Johnson, D. gale 1948 Allocation of Agricultural Income. Journal of Farm Economics 30:724-749.
Johnson, D. gale 1954 The Functional Distribution of Income in the United States, 1850-1952. Review of Economics and Statistics 36:175-182. → Published by Harvard University Press. Data in Table 1 reproduced by permission.
Kaldor, Nicholas 1955-1956 Alternative Theories of Distribution. Review of Economic Studies 23:83-100.
Kalecki, Michael 1954 Theory of Economic Dynamics: An Essay on Cyclical and Long-run Changes in Capitalist Economy. New York: Rinehart.
Kendrick, John W. 1961 Productivity Trends in the United States. National Bureau of Economic Research, General Series, No. 71. Princeton Univ. Press.
Kendrick, John W. 1964 Comment on Solow’s Paper. Volume 27, pages 140-142 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
King, Willford I. 1930 The National Income and Its Purchasing Power. National Bureau of Economic Research, Publication No. 15. New York: The Bureau.
Kravis, Irving B. 1957 The Scope of Economic Activity in International Income Comparisons. Volume 20, pages 349-377 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
Kravis, Irving B. 1959 Relative Income Shares in Fact and Theory. American Economic Review 49:917-949.
Kravis, Irving B. 1962 The Structure of Income: Some Quantitative Essays. Philadelphia: Univ. of Pennsylvania Press.
Kuznets, Simon S. 1941 National Income and Its Composition: 1919-1938. 2 vols. National Bureau of Economic Research, Publication No. 40. New York: The Bureau.
Kuznets, Simon S. 1952 Long Term Changes in the National Income of the United States of America Since 1870. Pages 23-241 in International Association for Research in Income and Wealth, Income and Wealth of the United States: Trends and Structure. Income and Wealth, Series 2, Cambridge: Bowes.
Kuznets, Simon S. 1953 Shares of Upper Income Groups in Income and Savings. National Bureau of Economic Research, Publication No. 55. New York: The Bureau.
Kuznets, Simon S. 1959 Quantitative Aspects of the Economic Growth of Nations: IV. Distribution of National Income by Factor Shares. Economic Development and Cultural Change 7, no. 3, part 2.
Kuznets, Simon S. 1961 Capital in the American Economy: Its Formation and Financing. National Bureau of Economic Research, Studies in Capital Formation and Financing, No. 9. Princeton Univ. Press.
Lebergott, Stanley 1964 Factor Shares in the Long Term: Some Theoretical and Statistical Aspects. Volume 27, pages 53-86 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
National Industrial Conference Board 1939 National Income in the United States, 1799-1938, by Robert F. Martin. New York: The Board.
Pesek, Boris P. 1960 A Comparison of the Distributional Effects of Inflation and Taxation. American Economic Review 50:147-153.
Reder, M. W. 1959 Alternative Theories of Labor’s Share. Pages 180-206 in The Allocation of EconomicResources: Essays in Honor of Bernard Francis Haley. Stanford Studies in History, Economics, and Political Science, No. 17. Stanford Univ. Press.
Schuller, G. J. 1953 The Secular Trend in Income Distribution by Type, 1869-1948: A Preliminary Estimate. Review of Economics and Statistics 35:302-324. → Published by Harvard University Press. Data in Table 2 reproduced by permission.
Scitovsky, T. 1964 A Survey of Some Theories of Income Distribution. Volume 27, pages 15-31 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
Solow, Robert M. 1957 Technical Change and the Aggregate Production Function. Review of Economics and Statistics 39:312-320.
Solow, Robert M. 1958 A Skeptical Note on the Constancy of Relative Shares. American Economic Review 48:618-631.
Stigler, George J. 1961 Economic Problems in Measuring Changes in Productivity. Volume 25, pages 47-63 in Conference on Research in Income and Wealth, Studies in Income and Wealth. Princeton Univ. Press.
Survey of Current Business. → Published since 1948. See especially the July issues, 1957-1964.
U.S. bureau of the census 1958 Statistical Abstract of the United States. Washington: Government Printing Office. → Published since 1878.
U.S. bureau of the census 1960 Historical Statistics of the United States; Colonial Times to 1957: A Statistical Abstract Supplement. Washington: Government Printing Office.
U.S. department of agricultureAgricultural Statistics. → Published since 1936. See especially 1953-1962 editions.
U.S. office of business economicsNational Income. → Published since 1934 under various titles. See especially 1951 and 1954 issues.
U.S. office of business economics 1958a U.S. Income and Output: A Supplement to the Survey of Current Business. Washington: The Office.
U.S. office of business economics 1958b New Estimates of National Income, 1946-1957. Survey of Current Business 38, no. 7:3-17.
Weintraub, Sidney 1949 Price Theory. New York: Pitman.
Weintraub, Sidney 1958 An Approach to the Theory of Income Distribution. Philadelphia: Chilton.
Weintraub, Sidney 1959 Forecasting the Price Level, Income Distribution and Economic Growth. Philadelphia: Chilton. → A college edition was published simultaneously as A General Theory of the Price Level, Output, Income Distribution and Economic Growth.
Weintraub, Sidney 1962 A Keynesian Model of the Price Level and the Constant Wage Share. Kyklos 15:701-719.
Wooden, D. C; and Wasson, R. C. 1956 Manufacturing Investment Since 1929 in Relation to Employment, Output, and Income. Survey of Current Business 36, no. 11:8-20.
The distribution of power, prestige, and pelf has been a topic of durable concern to most societies. In distant eras, and in simple cultures, the distribution of economic power and advantage could be fairly closely measured in simple terms—e.g., the number of the flocks in ancient Israel, or the amount of land in the Domesday Book. But recent centuries have witnessed the notable rise of urban industry. They have also seen bewildering gains in geographic and social mobility: “Men become their own fathers,” making their own status. However, the incentives that press the Rastignacs or Jim Bradys of the rising groups toward high consumption make their wealth only the coarsest measure of their economic advantage. Such forces have vitiated the use of data on landed wealth, or even total wealth, as a clear-cut measure of economic differences. Hence, interest in the distribution of wealth has largely given way, in our time, to interest in the distribution of income.
Uses of the data
Income size distributions may be used as measures both of economic productivity and of welfare.
Income as a measure of productivity
For measuring productivity, the relevant income distribution is that for individuals, more particularly those engaged in production for markets. In most economies, the income received by the typical worker, peasant, or businessman reflects chiefly the quantity and quality of the goods and services which he brings to market. Such an indication of the income recipient’s “productivity” measures no inherent, inalienable set of personal talents and charms. Thus, the income that a farmer receives from marketing his crops necessarily reflects, in part, the accumulated knowledge he derives from society: he can raise more rice per acre of land than his father could because better varieties of seed have been developed and because the government provides better weather information. He receives more for each bushel he raises because an improved transportation network and futures market enable him to market his crop at a time, and in a condition, that make it command a better price. Similarly, today’s worker may receive a higher wage per hour for his labor than his grandfather did because of the education that his parents and society have given him and because employment agencies, unions, and newspapers help to create an efficient labor market. To the extent to which the social order and private enterprisers apply new technologies, develop cheaper materials with which the worker can labor, provide capital at lower cost—to that extent the productivity of the worker will advance, and with it the amount of product with which he is compensated.
Two obvious considerations should be noted: All is not roses and fair shares in consequence. Just as inadequacies in the social order may reduce the absolute reward of everyone in it, so government and private restrictions on entry to an industry, a region, or an occupation will tend to affect relative shares. Effective monopolies or public incentives that favor one factor of production will increase the share of those who provide that factor.
The productivity being measured pertains only to the period covered, most commonly a year. Therefore the usual income distribution will reflect differences associated with age and period in life. Thus, it is fairly typical for individuals to have relatively low-value productivity in the years just after they enter the labor force full time and just before they leave it—reflecting a combination of part-time work and low or impaired skills. Perhaps more important is the displacement of income that occurs between years, and within a lifetime, depending on the nature of the work. For example, cyclical variations in the weather and predators that affect rubber or coffee crops will swing incomes in any given year well below or above a longer-term average. If an occupation requires a lengthy training period, with both costs of training and a loss of income during that period—e.g., a machinist’s apprenticeship, a physician’s period in medical school—very low or zero incomes will be recorded for the individual in his younger years, with compensating higher incomes later on. The national size distribution at any time will therefore reflect the proportion of persons in these industries, occupations, and age groups (Mincer 1958; Brady 1965).
We take these as so many givens when we speak of the productivity of the individual income earner. Nevertheless, it is that productivity—however derived—which is relevant in the actual state of the labor market, both in market economies and in state-operated ones.
Income as a measure of welfare
A second common use of income data relates to the measurement of welfare. Moralists have long had difficulty equating “goods” with “the Good.” And economists have become notably wary of interpersonal utility comparisons. Not only do they lack any agreed basis for translating measured income into measurable welfare, but even when a fairly extensive set of axioms is stipulated (including an assumption of equal total output), they fail to agree on whether a more equal pattern of income distribution is preferable to a less equal one (Strotz, Fisher, & Roth-enberg 1961).
For translating income into tests of welfare we must resort to a simpler proposition: In a free consumer market, differentials in income will indicate differentials in the command over goods and services. (Should the state or private sellers engage in rationing—e.g., by limiting the freedom to rent or purchase housing of certain types or in certain areas, to buy imported cars or the services of private clubs—even this premise is denied.)
As an indicator of the command over goods and services, the most informative distribution of income is that for families, not for individuals. The limitation of the latter measure is that in most societies the family acts as the primary agent for redistributing income. Children and housewives earn little or no income, but their command over goods is not equally trivial. Indeed, as the income of family heads has increased in many nations, the earnings of children have dwindled: instead of continuing to work full time in textile mills, children began to spend most of their days in-school. As wives in lower-income families found their husbands’ incomes rising, they left full-time work to earn zero (or at most pin money) levels of income. The facility with which family members can substitute leisure for income will increase as the income of the family head, and the family, increases. Therefore the income distribution of persons tells us too little about their changing command over goods and services, including leisure as a good.
Given the primitive communism that exists within the family structure, the distribution of family income is more serviceable than that of individual income for measuring the distribution of command over goods and services. But even this distribution has important limitations.
(1)If incomes are measured before taxes, the distribution will be substantially more skewed than on an after-tax basis. The precise intent of income taxation in many nations is, of course, to contribute to such leveling. The corvée in eighteenth-century France, road labor in nineteenth-century Africa, conscription in twentieth-century United States (given exemptions that are related to marital status and education)—each is likely to have had a differential impact by income. (Recent empirical studies for several countries appear in International Association …1964.)
(2)Expenditure by the state will differentially benefit families in the different income groups. Whether defense and police protection aid the well-to-do disproportionately has been argued to conflicting conclusions. There is probably more agreement that such explicit payments as family allowances, unemployment insurance, or subsidies to farmers do vary by income level.
(3)Comparisons between more and less industrialized nations (or periods in the life of a nation) are substantially affected by the amount of income received in nonmonetary form. Farm and mining families have frequently received significant amounts of their real income in the form of food and shelter, making no explicit payment for them. Urban residents who receive an identical volume of such goods and services command more of the economy’s real resources: the costs of transport to the city, and of the distribution of goods within it, must be covered. But whether their perceived levels of well-being are greater pari passu is a matter admitting of “a wide answer.”
(4)The more persons who share a given family income, the less the value of goods commanded by each—even assuming economies of scale in the consumption of housing, of works of art, etc. Hence the systematic attempts since Atwater and Ammon to adjust food consumption and total budgets to an “adult male equivalent” or other standardized basis. (For a recent example see Lamale 1965.) Such a scale can rest on a fairly objective basis so far as mere nutrient intake is concerned. But any allow ance for food palatability or for the satisfactions from other budgeted items (clothing, amusements, etc.) tends (a) to embody the investigator’s personal judgments, (b) only to report (somewhat indi rectly) the actual consumption levels or elasticities of a particular society at a given stage in its history, or (c) both.
Possibly more important is the implicit assumption that because welfare will be affected by the number of persons in a family, income must be measured on a per person basis. Any such assumption applies only weakly to those religious groups and entire cultures which regard fecundity per se as a goal or a moral imperative. Since such groups prefer, in principle, more children to more material goods, a per capita income measure will bluntly conflict with one of their primary values.
(5)An equal amount of income does not translate into an equal command over goods and services at all income levels. Lower-income families frequently live in outlying districts, without cheap transportation. They are therefore confronted by few sellers of the goods and services they would buy. Discrimination because of caste (social, cultural, religious) may additionally restrict access to housing. Under such circumstances lower-income families are confronted by higher prices for an identical budget of goods and services than are upper-income f amilies: their real incomes are therefore less than the current distribution of money incomes would indicate.
(6)Many nations seek to assure a per person minimum for particular goods and services (from zoos to well-baby clinics). These are provided without user charges, so that all persons (or all who pass a means, citizenship, and manners test) can have full access to presumably critical items. The list of such items has steadily expanded on every continent. Moreover, public social-welfare payments have increasingly replaced private charities. Thus, a number of the vexing impediments to the use of income distributions to mark the relevant differences in command over goods and services are readily disposed of in the context of actual problems. For given a specific, real world context, it may be possible to bound the impact of particular biases.
Because of the widespread receipt of assistance and income in kind—neither fully included in most income distributions—those concerned with economic welfare have found an analysis of the actual pattern of consumption a helpful supplement. Family budget surveys provide one such body of information. Data in the national accounts (on the constant dollar value of consumption) provide another such body of data. Together they remove any necessity for using the approximate statistics on income distribution to determine the extent of either grinding poverty or wealth beyond the dreams of avarice.
Income distribution data have been tirelessly used as explanatory variables in studies by economists and political scientists. From the first systematic model developed by Tinbergen (1956), economists have tried to utilize distributional data to help explain variations in national saving, shifts in the factor shares of labor and capital, and short run changes in consumption patterns. Because of the lack of continuous estimates of size distribution in most nations until recent years these models have used proxy variables instead, e.g., the separate sums for wage and nonwage income (Klein et al. 1961). One may expect the actual distributions to be exploited more fully in the future.
There is perhaps no need to discuss more general inferences—e.g., that changes in income distribution determine the possibilities of revolutions and riot, land reform, or the development of a middle class (Davis 1941). Such speculations, however perceptive, have used data chiefly for decorative purposes. But the advent of more reliable data and more precise analysis may yet establish what contribution the study of changes in income and wealth size-distributions can make to the study of economic and political history.
Changes in income distribution
Central to much interest in income distribution data is one question: Does the inequality in income distribution increase or decrease through time? In principle, we would answer this question by comparing the income distributions of an identical set of income receivers in different periods. Such comparisons would indicate fairly directly whether the rich were getting richer, the poor getting poorer, etc.
In fact, most analyses simply compare distributions for all income receivers at two dates, whether or not the same recipients are included at both. But between these dates, forces are working to change the underlying population. Hence the reported income distribution will change even if no one receives lower hourly wages, or higher dividends, etc. Such forces include the following:
(1)The consequences of aging and mortality. Younger persons who work part time while in school report an increase in income when they leave school and begin full-time work. Older persons retire between one period and the next, shifting down from wage to pension income levels.
(2)cfcfThe demographic and social consequences of a change in aggregate economic activity. When an economy shifts from underemployment to high employment, incomes will rise. Reported income inequality may rise in consequence. For example, the increase in U.S. incomes from the 1930s to the 1940s led elderly persons to move out of their children’s homes into rooms and apartments of their own (Brady 1958). Presumably both the older persons and the families with growing children found that separate establishments provided a real advance in their welfare. Yet the usual income distribution data will report an increase in inequality: the number of “low-income families”—in the form of newly created “families” of older persons who had previously been included with their children—has increased.
Similarly, the stronger the labor market, the earlier young people find work and establish homes of their own. As a result, instead of one family being reported, with a combined income including the incomes of young persons and older persons, two families will be reported—each with a lower income.
(3)By widening the scope of income taxation, modern legislation has increased the incentives to receive income in forms other than current mone tary receipts. It has thereby helped create a series of remarkable innovations whose consequences ap pear in the distribution of income. For upper-in come groups the most significant of these innova tions has probably been the conversion of ordinary income into the form of capital gains and gains from stock options. But these are typically excluded from the tabulations of income distribution. (It would indeed be difficult to decide how to include them.) Distorted results can therefore be produced by comparing income distributions between nations and between points in time when the incentives to convert income into capital gains differ (and the knowledge of techniques for doing so and the relevant legislative provisions also differ). The distribution only of ordinary income could under such circumstances offer a singularly inadequate indication of trends in income concentration.
Other innovations that affect income distribution include the contract for deferring payment until a future date and the multiplication of nontaxable trusts. The proliferation of business expense accounts since World War II suggests that resources devoted to the feeding and amusement of entrepreneurs, and their coadjutors, have also become increasingly potent substitutes for outright income payment. An executive may find a Picasso on his office wall to be a quite tolerable substitute for the million dollars (pounds, francs, etc.) of income that he would otherwise have to earn in order to enjoy the same painting on his living room wall for a few hours in the evening. The expansion of fringe benefits to workers—in the form of contributions to pension funds, subsidized lunches, etc.—similarly distorts comparisons of reported figures on income.
(4)The expanded role of the state as a taxing agency links to its expanded role as a redistributive mechanism. Public assistance payments and surplus foods add significantly to the resources of lower-income families, but are typically not reported in their incomes. Public guarantees of home loans and bank deposits provide middle-income families with lower interest rates, which may make the difference between owning and not owning their homes. But the saving of interest is never treated as income. The clearing of unsightly slums, the dredging of yacht harbors, and the selection of the best public school teachers for the best residential areas all benefit upper-income groups. The impact of this wandering pattern of taxation and benefit must be evaluated before simple comparisons of changes in income distributions through time can be taken to mean what they appear to mean.
(5)Finally, there are statistical problems of no mean magnitude. The amount of tax evasion is virtually unknown in most nations. Its effect in distorting reported income distributions is even more obscure. In the single publicly available report for the United States, for 1949, something like 23 per cent of taxable farm income was not re ported in tax returns (see Marius Farioletti’s tables in Conference on Research …). Persons reporting $10,000 (or less) in adjusted gross income failed to report 4 per cent of that income, while persons owning businesses understated net profit by from 13 per cent (printing and publishing) to 37 per cent (hotels) and 87 per cent (amusement services). Reported income distribution figures are almost never adjusted for such evasion of taxes or understatement of income. In the very few instances in which they are adjusted (e.g., in the U.S. Department of Commerce figures), the adjustment is not differential by income level, there being no data upon which to base a reasonable differential adjustment. It is clearly captious to be concerned about the validity of data for those few nations which provide both distributions and information giving the user a fair chance to assess them. Nonetheless, intelligent use of income data must take these considerations into account.
Trends in dispersion
A long view of economic development suggests forces that would work toward and against greater inequality of the income distribution. Some theorists have argued that as societies become more developed, the contribution of each individual becomes more specific. This enables him to receive greater rent on his ability, thereby increasing inequality (Lachmann 1951). History does indeed suggest a trend toward concentration, to be surmised from periodic confiscations—the redistribution of the land under Solon, of monastic wealth under Henry vm and the sans-culottes, and of property in land and slaves under Tsar Nicholas and Lincoln. But no less significant has been the long rise in prices generated by the discovery of silver in the Old World and of gold in the New World. This trend has, in Sir Josiah Stamp’s phrase, brought the unseen robbery of generations. By eroding existing accumulations of wealth, it has offered later generations the fair prospect of more equal chances to earn and to accumulate income.
Kuznets’ review of a mass of nineteenth- and twentieth-century data on income distribution in many nations concludes that there has been some long-run tendency toward leveling (1955). The expansion of public education, the opening of occupations to children of lower-class origin, the widening of credit facilities, the cheapening of transport (destroying local monopolies)—all these raised the income levels of the lower-income groups and thereby made for greater equality in the income distribution.
Work initiated by Kneeland and others in the 1930s established a continuous series for U.S. income distribution (U.S. Bureau of the Census; U.S. Office of Business Economics). This work makes possible long-period comparisons for the United States, provided one is prepared to allow for, or ignore, the qualifications noted above on temporal comparisons. These estimates suggest that the distribution of income in the United States became substantially more equal after 1944 than it had been in 1935-1936—whether we measure the distribution of income among families or among consumer units—and even after allowance for capital gains (Goldsmith et al. 1954). Reductions in inequality since 1944, however, prove to be small compared with the change from 1935-1936 to 1944. The lowest fifth of American families received 4-5 per cent of family personal income in 1935-1936, in 1941, and in the years since 1946; the top fifth received 52 per cent in 1935-1936 and has received 45-46 per cent ever since 1946 (Goldsmith et al. 1954, p. 9; Fitzwilliams 1963, p. 18). The proportion of American families with incomes below $3,000 (in 1962 prices)—the rough poverty line suggested by the Council of Economic Advisers—averaged 32 per cent in 1947 and about 20 per cent in 1962 and 1963. Allowing for differential income requirements by family size would significantly cut the proportions below an adjusted poverty line. Doing so would, however, include enough more of the larger families so that poor families would include about the same number of persons (Orshan-sky 1965). Up to this point we have discussed the experience of poverty or riches associated with a single year. What of a more extended period? The data show that approximately three-fourths of the families with incomes below $3,000 in 1962 remained in that status in 1963 as well (U.S. President 1965, p. 165).
Redistributive taxation and expenditure have helped bring about the decline in the proportion of income received by the top fifth since the 1930s and the decline in the proportion of low-income families. However, the massive cut in unemployment appears to have been more directly responsible. One indication of this is that the major shifts between 1935 and 1963 took place from 1935 to 1944, when unemployment fell from one-fifth to one-twentieth of the labor force. Data for Great Britain are similar in this respect—the top 1 per cent got 15.2 per cent of income in 1938 and 10.5 per cent in 1949, with but little further change—e.g., to 9.1 per cent by 1957 (Lydall 1959). Another indication is the striking change in the characteristics of families in the low-income group. These had been fairly representative families in the 1930s, judged by demographic and personal characteristics. By the early 1960s the group had become a mixture of older persons, nonwhites, farm families, families with female heads, and others marginal in characteristics other than income.
The formation of income distributions
The mechanism that creates the distribution of income has been explained in ways that range from historical-sociological theories of great generality to hypotheses of sharply defined stochastic process. One hypothesis, first suggested many decades ago, was that the Gaussian normal distributions (which fit many human characteristics, such as height, weight, IQ) might apply to income as well. But records for many societies, despite their unreliability, agree in suggesting that this is not so. Broadly speaking, two types of explanation developed subsequently. One premises the normal distribution as a starting point, then seeks to explain how that distribution was truncated or otherwise forced so that the usual skewness of income distributions developed. The second category of explanations premises that the underlying distribution is lognormal, or Poisson. Some specialists have sought primarily to find a single function that could describe many existing distributions. Others have been more concerned with understanding what economic processes could reasonably produce the distributions and then have more or less systematically proceeded to fit various functions to data.
Among the analyses concerned with explaining how income distributions arise from the incentives and institutions of typical economies, many have emphasized the arithmetic normal distribution as the starting point. A substantial bias in that distribution may be assumed to result from the impact of property inheritance, from differentials in parental interest and ability to invest in training for their children, and from the consequences of inherited social position. High incomes are then explicable by the greater potential some persons have for earning income (given their advanced training and status) or for acquiring it (i.e., returns from inherited property). The impact of inheritance has been emphasized by Pigou and Dal ton (see Dal ton 1920). Marxist critics have focused also on status and sociological differentiations.
While the inheritance of property was a substantial element in the British experience, the present role of incomes from such inheritance in most Western nations is not such as to make it likely to be a significant factor per se in explaining the skewness of income distributions. On the other hand, the inequality of training and contacts among young persons beginning their work career is surely relevant, particularly given the recent literature that emphasizes private monetary returns to investment in education. To the extent that all this is simply an application of the Biblical stipulation “to him who hath shall be given,” one would expect to see mounting inequality over time. Such a trend is not apparent, either in the West or in underdeveloped nations. (However, such a tendency could be masked by the consequences of concurrent attempts to redistribute income and to widen access to education, which often first take place in a nation during the very periods for which the first data become available, permitting comparison of its income distributions through time.)
It has recently been contended that abilities to earn income in fact form a truncated arithmetic normal distribution—whose apparent skewness in some societies reflects the fact that credit-granting agencies provide capital to persons with high money-making abilities (thus enabling them to compound these to attain very high incomes), whereas these agencies truncate the other end of the income distribution by denying credit to most large-scale speculators, whose skills would otherwise enable them to develop large risky enterprises that would lose large sums of money and generate large negative incomes (Lebergott 1959).
An important group of analysts stipulate that there are really two underlying distributions. Thus Tinbergen (1956) has suggested that persons who possess great ability for certain jobs (e.g., artists, craftsmen) will have a particularly strong desire to engage in them and will therefore lower their wage demands in order to enter them, whereas workers with lesser abilities will choose more widely, taking those jobs which command higher monetary returns. Friedman (1953) has emphasized not two classes of individuals but two classes of actions—more and less venturesome—in which individuals engage. Greater possibilities of very high incomes inhere in the more venturesome (job choices, investment choices, gambles). If a mechanism exists for redistributing the proceeds of quasi lotteries, one can generate some extremely high incomes without generating negative ones—since entry to the lottery requires only a small admission fee. The model is thus consistent with the usual skewed distributions. It will be noted that both models require some rather strong corollary assumptions for them to apply to recent periods or to modern nations—e.g., that highly skilled people are willing to take unusually low wages, that some widespread redis tributive mechanism exists to take from the poor(er) to give to the rich(er). Neither assumption is descriptive of behavior in many labor markets or of the impact of the usual governmental taxing and redistributive mechanisms.
Another group of analysts has emphasized the contribution made to the shape of the over-all income distribution by its component distributions. Since Mill and Cairnes pointed to the presence of “noncompeting groups,” it has been clear that the distribution of incomes for a peasant group, for a wage-earning group, and for the sons of the rich will each have a characteristic shape. If, then, all persons in a given country are taken together, the over-all distribution will reflect the symmetry or, more generally, the actual shape of the underlying distributions (Hayakawa 1951; Miller 1964). Such considerations are, of course, consistent with an over-all distribution ranging from the near-symmetrical to the wildly skewed.
Probably the most widely attempted explanations in recent years involve those which specify the income distribution as lognormal, with the logarithms of income normally distributed even though income itself is not. Originally sparked by Gibrat’s pioneering study (1931), this distribution has received repeated attention in recent decades (see Kalecki 1945; Champernowne 1952; Aitchison & Brown 1957; Bjerke 1961; Mincer 1958). These writers assume that a Markov process is at work in which the incomes received, e.g., in a given year, will change by some percentage from that year to the subsequent year, the size of that percentage being independent of the income in the initial year. Given that the probabilities of such changes are independent, application of the central limit theorem enables us to conclude that as sufficient time passes the original shape of the distribution will no longer be significant. What we will then come to observe is the skewed lognormal distribution. The simpler models of this sort imply vast increases in income inequality, for each of the assumed random changes will add to the variance of the distribution (Kalecki). Such increasing inequality, however, does not appear in most sets of empirical data of reasonable validity. Various additional side conditions have been specified to prevent the model from leading to such a conclusion (Champernowne, Rutherford). One substantial difficulty with these amended models is that they fail to fit recent reliable income distributions. It is also to be noted that by premising random percentage increments, they stipulate a pattern of random reward in the income acquisition process that seems uncharacteristic of many societies. Most economies structure income receipt with respect to economic contribution (e.g., such as marginal productivity of labor), or social status, or some combination of known economic incentives and social restraints.
Modern analysis of income distribution begins with Vilfredo Pareto. Somewhat earlier Quetelet, Leroy Baulieu, and others had given brief consideration to data then flowing from various taxing systems. But it was Pareto, one of the group of economists engaged in transforming a branch of natural philosophy into a rigorous system of analysis, who first observed how similar many income distributions were when evaluated in terms of what is still called the Pareto coefficient (Pareto 1896-1897, vol. 2, p. 305).
The Pareto coefficient
The Pareto coefficient is a in the equation logN = log A —alogx, where N is the number of persons with incomes at least as large as x. Pareto’s review of data for various countries suggested to him that the coefficient was approximately 1.5 in every instance, although in fact he reports data ranging from 1.24 to 1.79 (ibid., p. 312). This putative fact led to the inference that a natural constant had been discovered: “A decrease in the inequality of incomes cannot come about…except when total income increases more rapidly than the population” (ibid., p. 320). Following Pareto, even very modern writers, noting that the parameter ranges from 1.6 to 2.4, infer that such a narrow range, although referring to widely separated countries and occasions, would seem to indicate a common underlying mechanism. Massive differences between economies, centuries, and continents are submerged by this measure into a simple single coefficient, originally offered (and frequently taken) as a kind of ultimate social law.
The theoretical limitations of this measure were canvassed by Macaulay and Mitchell (1922), and others. One difficulty is that the formula will estimate an infinite number of recipients for incomes greater than a near-zero amount: it must therefore be used only to estimate the number above some level arbitrarily chosen to give sensible results. It is, at the very least, a signal difficulty that one function should hold above some income level picked by the analyst on an ad hoc basis, while another presumably explains the distribution below that arbitrary level. Another difficulty is that differences in the coefficient which appear small on casual inspection, and therefore lead to the assumption of its constancy, may not be small so far as any serious economic or political issue is concerned. (Thus the ratio of wives to husbands is fairly close to 1.0 in most Western nations. Yet one can be certain that any community in which the ratio was 1.01 would have an interesting basis for tea-time discussion and police action.) In this respect the position of Harold Davis, while extreme, was more reasonable when he declared that small variations in the coefficient made the difference between revolution and peace in many a historic situation (1941).
In fact, Pareto’s equation does not fit distributions recorded in recent years at all well, and even his original fit was to a mixture in which data for both individuals and corporate bodies were included. It may be a more reasonable inference that the coefficient is simply insensitive to major differences in concentration if our criterion of stability in the coefficient is casual inspection. However, the coefficient is a convenient smoothing device and in recent years has frequently been used for computing income aggregates from distributions.
Pareto’s premise, and that of some later writers, that the constancy of his a demonstrated that redistribution was impossible and that incomes could be improved only by an increase in total product, is an interesting example of a theorist drawing policy conclusions from an empirical observation—with no theory behind his speculation. It was pardonable that half a century of subsequent redistribution through progressive tax systems had not been revealed to him as demonstrating the contrary, but the lack of an analytic model stipulating why no shift was possible was less warranted.
Another measure widely used—in part because it is associated with a simple graphic presentation—is the Lorenz curve (Lorenz 1905). Total income is measured on one axis and total population on the other. For each percentile point the cumulated income and cumulated population are recorded. If all members of the distribution were to receive the same income, a simple diagonal would appear on the graph, running from the origin (southwest) to northeast. As it is, the Lorenz curve always reports that income is not distributed equally. This discovery is hardly one of unusual moment (1) because ocular standards rather than formal tests of significance are involved and (2) because the standard of perfect equality is used, rather than some actual reality, such as, say, the average distribution for several high employment years or that for a nation with an active policy of redistribution, etc. But the curves are most commonly used to demonstrate the degree to which the distribution has shifted toward or away from equality from one period to the next, or differs from equality from one nation to the next. Since the extent of movement may be considered trivial to one temperament and significant to another, the significance of a difference between two curves is best assessed by comparison with the difference between two other curves—e.g., is the change from period 1 to 2 greater than that from 2 to 3? In comparisons between nations it is, of course, essential that comparable populations be contrasted. A contrast between a distribution of income taxpayers in one nation and the total population in another, or between two tax-paying populations with different levels of exemption, may produce fierce findings of difference in the measures despite a total lack of difference in the actual distributions.
The Gini index
For the study of capital formation, class warfare, and related purposes, the index of concentration developed by Corrado Gini has been widely used. It is a straightforward measure based on the area of the triangle under the line of perfect equality: the area between the Lorenz curve and the diagonal of perfect equality is taken as a percentage of the total area in the triangle. It is computed from the equation log N = 8 logY —logc, where N measures the number of individuals with incomes above a given amount “z” and Y measures the aggregate of incomes above z (Δ is commonly termed the Gini coefficient). Gini’s N is a function of S, the total of incomes above z, whereas Pareto’s N is a function of z itself. (Other measures, and computation formulas, appear in Yntema 1933 and Dalton  1949, appendix.)
In addition to such summary measures, considerable use has been made of such straightforward measures as the proportion of income received by the upper 1 per cent or 5 per cent of income recipients (Kuznets 1955; Lampman 1959) or the proportion of families with incomes below some income level. Since many policy proposals are related to a judgment that there are too many poor or too many wealthy families, the use of the full range of data proves to be more relevant than single summary measures such as the Pareto and Gini coefficients. It should be emphasized that all such measures focus on income received—almost always on money income alone. Since an essential aspect of income receipt in most societies (capitalist, communist, primitive) is that money incomes are complemented by nonmonetary factors (ease of work, short hours, income in kind, stability of employment, prestige, etc.), the income data report only the aspects that have been monetized. This limitation is a grave one for nations with substantial rural populations and is becoming a severe one for nations with taxes and regulations that increase incentives toward compensation in nonmonetary form.
Aitchison, john; and brown, J. A. C. 1957 The Log-normal Distribution: With Special Reference to Its Uses in Economics. Cambridge Univ. Press.
Anderson, W. H. L. 1964 Trickling Down: The Relationship Between Economic Growth and the Extent of Poverty Among American Families. Quarterly Journal of Economics 78:511-524.
Bjerke, kjeld 1961 Some Income and Wage Distribution Theories: Summary and Comments. Weltwirt-schaftliches Archiv 86:46-66.
Brady, dorothy S. 1958 Individual Incomes and the Structure of Consumer Units. American Economic Review 48, no. 2:269-278.
Brady, dorothy S. 1965 Age and the Income Distribution. U.S. Department of Health, Education, and Welfare, Social Security Administration, Division of Research and Statistics, Research Report No. 8. Washington: The Department.
Champernowne, david G. 1952 The Graduation of Income Distributions. Econometrica 20:591-615.
Conference on research in income and wealthStudies in Income and Wealth. → See especially Volumes 3, 5, 13, 15, and 23. These volumes contain a sampling of studies by specialists on the meaning and limitations of distribution data. Tables 2 and 5, compiled by Marius Marioletti, in Volume 23 contain data indicating the role of tax evasion in distorting reported income distributions.
Dalton, hugh (1920) 1949 Some Aspects of the Inequality of Incomes in Modern Communities. London: Routledge.
Davis, harold T. 1941 The Analysis of Economic Time Series. Cowles Commission for Research in Economics, Monograph No. 6. Bloomington, Ind.: Principia Press.
Fitzwilliams, J. M. 1963 Size Distribution of Income in 1962. Survey of Current Business 43, no. 4:14-20.
Friedman, milton 1953 Choice, Chance and the Personal Distribution of Income. Journal of Political Economy 61:277-290.
Garvy, george 1954 Functional and Size Distributions of Income and Their Meaning. American Economic Review 44, no. 2:236-253.
Gibrat, robert 1931 Les is inégalites économiques. Paris: Sirey.
Goldsmith, selma F. 1957 Changes in the Size Distribution of Income. American Economic Review 47, no. 2:504-518.
Goldsmith, selma F. et al. 1954 Size Distribution of Income Since the Mid-thirties. Review of Economics and Statistics 36:1-32.
Hayakawa, miyoji 1951 The Application of Pareto’s Law of Income to Japanese Data. Econometrica 19: 174-183.
International association for research in income and wealth 1957 Income and Wealth. Series 6. London: Bowes.
International association for research in income and wealth 1964 Income and Wealth. Series 10. London: Bowes.
Kalecki, michael 1945 On the Gibrat Distribution. Econometrica 13:161-170.
Kingston, J. 1952 A designaldade na distribuiçaūo das rendas (Inequality of Income Distribution). Revista brasileira de economia 6:7-90.
Klein, lawrence R. et al. 1961 An Econometric Model of the United Kingdom. Oxford: Blackwell.
Kuznets, simon S. 1953 Shares of Upper Income Groups in Income and Savings. National Bureau of Economic Research, Publication No. 55. New York: The Bureau.
Kuznets, simon S. 1955 Economic Growth and Income Inequality. American Economic Review 45:1-28.
Lachmann, L. M. 1951 The Science of Human Action. Economica New Series 18:412-427.
Lam ale, helen 1965 Poverty: The Word and the Reality. U.S. Bureau of Labor Statistics, Monthly Labor Review 89:822-835.
Lampman, robert J. 1959 Changes in the Share of Wealth Held by Top Wealth Holders, 1922-1956. Review of Economics and Statistics 41:379-392.
Lebergott, stanley 1959 The Shape of the Income Distribution. American Economic Review 49:328-347.
Lorenz, max O. 1905 Methods of Measuring the Concentration of Wealth. Journal of the American Statistical Association 9:209-219.
Lydall, harold F. 1959 The Long-term Trend in the Size Distribution of Income. Journal of the Royal Statistical Society 122, part 1:1-46.
Macaulay, F.; and mitchell, W. (editors) 1922 The Personal Distribution of Income in the United States. Volume 2 in National Bureau of Economic Research, Income in the United States: Its Amount and Distribution, 1909-1919. New York: Harcourt.
Miller, herman P. 1963 Trends in the Income of Familities and Persons in the United States: 1947-1960. U.S. Bureau of the Census, Technical Papers, No. 8. Washington: Government Printing Office. → Conveniently summarizes U.S. Bureau of the Census P-60 data for 1947-1960.
Miller, herman P. 1964 Rich Man, Poor Man. New York: Crowell.
Mincer, jacob 1958 Investment in Human Capital and Personal Income Distribution. Journal of Political Economy 66:281-302.
Morgan, J. N. et al. 1962 Income and Welfare in the United States. New York: McGraw-Hill.
Morgan, theodore 1953 Distribution of Income in Ceylon, Puerto Rico, the United States and the United Kingdom. Economic Journal 63:821-834.
Musgrave, richard et al. 1956 The Incidence of the Tax Structure and Its Effects on Consumption. Pages 96-113 in U.S. Congress, Joint Committee on Economic Report, Federal Tax Policy for Economic Growth and Stability. Washington: Government Printing Office.
Orshansky, mollie 1965 Counting the Poor: Another Look at the Poverty Profile. Social Security Bulletin 28, no. 1:3-29.
Pareto, vilfredo (1896-(1897) 1927 Cours d’ économie politique professé á Université de Lausanne. 2d ed. 2 vols. Paris: Giard & Briére.
Sargan, john D. 1957 The Distribution of Wealth. Econ-ometrica 25:568-590.
Solow, robert 1960 Income Inequality Since the War. Pages 93-138 in Ralph E. Freeman (editor), Postwar Economic Trends in the United States. New York: Harper.
Strotz, robert; fisher, F.; and rothenberg, J. 1961 How Income Ought to Be Distributed: Paradox Regained. Journal of Political Economy 69:162-180, 271-278.
Survey of Current Business. → Published since 1921. Since 1953 it has presented at intervals current data on income distribution derived by adjusting reports from the Bureau of the Census and the Internal Revenue Service. See U.S. Office of Business Economics entry below.
Tinbergen, jan 1956 On the Theory of Income Distribution. Weltwirtschaftliches Archiv 77, no. 2:155-173.
Tsuru, shigeto 1961 Has Capitalism Changed? An International Symposium on the Nature of Contemporary Capitalism. Tokyo: Iwanami Shoten. → See especially pages 20-21, 86-87.
United nations economic commission for europeEconomic Survey of Europe. → Published annually since 1947. Presents income distribution data at intervals.
U.S. bureau of the censusCurrent Population Reports: Consumer Income. Series-P60. → Issued annually, the Reports provide detailed distribution data for persons and for families, classified in considerable detail.
U.S. office of business economicsIncome Distribution in the United States, by Size, 1944-1950. → Issued in 1953 as a supplement to the Survey of Current Business. The basic Bureau of the Census and Internal Revenue Service data are combined and adjusted for error and incomparabilities by the Office of Business Economics. Estimates for subsequent years appear, at intervals, in the Survey of Current Business (e.g., April 1960; April 1962).
U.S. president 1965 Economic Report of the President. Washington: Government Printing Office. → Published annually since 1947.
Yntema, dwight B. 1933 Measures of the Inequality in the Personal Distribution of Wealth or Income. Journal of the American Statistical Association 28: 423-433.
"Income Distribution." International Encyclopedia of the Social Sciences. . Encyclopedia.com. (October 21, 2016). http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/income-distribution
"Income Distribution." International Encyclopedia of the Social Sciences. . Retrieved October 21, 2016 from Encyclopedia.com: http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/income-distribution
Income distribution captures the proportion of total income accruing to different individuals that accounts for the total income distributed among them during a certain time period. If the unit of analysis is the country, the income distribution for a certain year would show how much of the country’s yearly income went to each person. It may be of interest to capture the country’s distribution of income within and across groups of individuals as well. Groups can be formed according to many criteria, depending on the issue under analysis. Criteria can include geographic (cities or states), gender, social, and ethnic considerations, to name a few. When groups of individuals are considered, it is typically of interest to distinguish between the income distribution within and across groups. For example, how much of a country’s income goes to the urban and to the rural population corresponds to the across-group distribution of income. How much went to each person living in rural areas and how much went to each person living in urban areas is a measure of the distribution of income within groups.
Income distribution can be represented in different ways. It can be represented by an (income) density function, f (y ), where y stands for income; f (y ) dy gives the number of individuals earning income in the [y, y + dy ] interval. Integrating the income-density function to infinity yields the total population, N, while integrating yf (y ) gives total income, Y. Mean income, µ, is given by Y/N.
A plot of the income-density function would be the most comprehensive way of representing income distribution, but this is rarely possible in practice if the unit of analysis is a country. Histograms may provide an approximation, but these representations are not usually used when analyzing the dispersion in the distribution of income. The most widely used graphic representation of income distribution—while by no means the only one possible—is the Lorenz curve. To construct a Lorenz curve, individuals are first ranked by income in ascendant order: yi ≤; yi +1, i = 1, …, N. Then, the cumulative income up to rank j is computed: sj =y 1 + y 2 + yj, j = 1, …, N. The Lorenz curve corresponds to the plot of (j/N, sj/Y ), j = 1, …, N. That is, it shows on the horizontal axis the cumulative population share (from 0 to 1) and on the vertical axis the corresponding income share (also from 0 to 1). It enables the determination of the share of income going to each quartile, quintile, decile, or centile—or any other breakdown of the population.
The Lorenz curve gives a visually compelling idea of the extent of inequality in the distribution of income. The line of perfect equality corresponds to the 45-degree line that goes from the origin to (1,1). That is, the poorest 10 percent of the population have 10 percent of income, then the poorest 20 percent have 20 percent of income, and so forth. The Lorenz curve lies always on or below the line of perfect equality, with “perfect inequality” (all income going to the richest individual) corresponding to the line that makes the lower and right-hand side of the square that encompasses the line of perfect inequality. That is, the shares of income going to all the shares of the population are zero, and 100 percent of income goes to the single individual at the top. Thus, the closer the Lorenz curve is to the line of perfect equality, the more equal the distribution of income; the farther it is, the higher the level of inequality.
Thus, intuitively, the area that lies between the line of perfect equality and the Lorenz curve provides an indication of the extent of inequality. If this area is very small, the Lorenz curve is very close to the area of perfect equality, and inequality is low. If this area is large, then the Lorenz curve is further away from the line of perfect equality, and inequality is high. The ratio of this area to the area of the triangle limited by the lines of perfect equality and perfect inequality is a number that falls always between zero (when the Lorenz curve coincides with the line of perfect equality) and one (when the Lorenz curve coincides with the line of perfect inequality and the area under the Lorenz curve is exactly the same as the area of the triangle). This number is the Gini coefficient, one of the most widely used measures of inequality—and one of the many possible summary measures of income distribution, whereby distribution is summarized by a single number.
While intuitively appealing, the Gini coefficient has a major drawback. As noted, in studies of inequality there is often an interest in grouping individuals and determining the shares of inequality that correspond to asymmetries in the distribution of income across and within groups. It is possible to decompose the Gini coefficient into withingroup and between-group components, but this decomposition is not “perfect,” in the sense that the components do not add up to total inequality—a third term, a residual, is typically required to be added to the other two terms to get to total inequality. The only summary measures of inequality that are perfectly decomposable correspond to a class known as entropy-based measures of inequality, which were pioneered by the Dutch econometrician Henri Theil (1924–2000). He drew inspiration from the entropy-based analysis of information, and thus the name of this class of measures.
The most widely used entropy-based measure of inequality is the Theil index. It is bound between zero and the natural logarithm of the size of the population (and not by one, like the Gini coefficient). The Theil index is the weighted sum of the natural logarithm of the ratio of the income shares to the population shares, where the weights are income shares. When applied to measure inequality across individuals, the “population share” is merely 1/N, so the Theil index is the weighted sum of the natural logarithm of the ratio of each individual’s income, yj/Y, to 1/N, where the weights are yj/Y. When individuals are grouped, the between-group component of the Theil index is the weighted sum of the natural logarithm of the ratio of each group’s income, Yj/Y, to that group’s population share, nj/N, where the weights are Yj/Y (nj and Yj are, respectively, the group’s j population and total income). The within-group component of total inequality is given by the weighted sum of the within-group Theil index for each group, where the weights are the income shares, Yj/Y. Total inequality measured using the Theil index is the sum of the between-group and within-group components.
SEE ALSO Economic Growth; Gini Coefficient; Inequality, Income; Inequality, Political; Justice, Distributive; Kuznets Hypothesis; Theil Index; Wealth
Alison, P. D. 1978. Measures of Inequality. American Sociological Review 43 (December): 865–880.
Bourguignon, François. 1979. Decomposable Income Inequality Measures. Econometrica 47 (4): 901–920.
Cowell, Frank A. 1980. On the Structure of Additive Inequality Measures. Review of Economic Studies 47 (3): 521–531.
Sen, A. 1997. On Economic Inequality. Oxford: Clarendon Press.
Shorrocks, A. F. 1980. The Class of Additively Decomposable Inequality Measures. Econometrica 48 (3): 613–626.
Theil, Henri. 1967. Economics and Information Theory. Chicago: Rand McNally and Company.
Theil, Henri. 1996. Studies in Global Econometrics. Dordrecht, the Netherlands: Kluwer Academic Publishers.
"Income Distribution." International Encyclopedia of the Social Sciences. . Encyclopedia.com. (October 21, 2016). http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/income-distribution-0
"Income Distribution." International Encyclopedia of the Social Sciences. . Retrieved October 21, 2016 from Encyclopedia.com: http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/income-distribution-0
There is no precise agreed definition of personal income, and no unambiguous operational definition setting out which items are to be included or excluded, and in what manner. Definitions tend to rely in practice on whatever information is available within administrative records, regular surveys of income and expenditure, and other sources within official statistics. One of the most common definitions is thus the earnings distribution, because data on the wages and salaries of employees and the earnings and profits of the self-employed are available from many surveys. But the definition of personal income goes wider than this and can include profits of firms in the private sector when distributed as dividends (but not the profits of state enterprises); earnings in kind and fringe benefits (such as free housing, free meals, subsidized loans or the use of a company car); unearned income from investments; income from sub-letting and other imputed income from home ownership; income maintenance payments from the state and any other benefits or insurance receipts. A distinction is drawn between income and wealth, which is the net value of all assets which can be assigned to individuals, but in reality income and capital are not separate entities and can be converted one to the other. This is an important source of practical difficulty in defining income as visible money income.
Earnings and income can be measured as current income (such as income in the last week or previous twelve months), or as usual or normal income, which will differ in cases where the current income is untypical for any reason, such as sickness or unemployment. An important distinction is made between the pre-tax and after-tax income distributions, between original incomes and disposable incomes. The distribution of original income shows the position before any income redistribution policies take effect, and always displays the widest dispersion of income. The distribution of disposable (or net) income shows the position after deducting taxes, social insurance contributions, and any other obligatory deductions from original income, then adding income maintenance and related benefits. Disposable income provides a broad measure of spending power, as distinct from discretionary income, which is disposable income less necessary expenditure on housing, travel-to-work, and similar unavoidable costs.
The distribution of income is studied to assess the redistribution effects of government fiscal and social welfare policies; as a key factor in patterns of consumption; as a measure of economic and hence social inequality, and one that is more accessible to researchers than the distribution of wealth; and to measure poverty. It is sometimes used to study the unanticipated effects of policies overtly concerned with quite different matters, such as divorce or ill-health Economists are interested in the pattern of income distribution as an independent variable in its own right, for example whether greater income inequalities lead to higher savings, or whether industrialization leads to reduced income inequalities.
Most of the (many) methodological problems of investigating income distribution, especially changes therein, are discussed in A. B. Atkinson ( ed.) , Wealth, Income and Inequality (1980)
. The evidence for Britain is usefully summarized in W. D. Rubinstein , Wealth and Inequality in Britain (1986)
. See also GINI COEFFICIENT; LORENZ CURVE.
"income distribution." A Dictionary of Sociology. . Encyclopedia.com. (October 21, 2016). http://www.encyclopedia.com/social-sciences/dictionaries-thesauruses-pictures-and-press-releases/income-distribution
"income distribution." A Dictionary of Sociology. . Retrieved October 21, 2016 from Encyclopedia.com: http://www.encyclopedia.com/social-sciences/dictionaries-thesauruses-pictures-and-press-releases/income-distribution