A. B. Atkinson
2 . 1 I N T RO D U C T I O N
There has been a marked revival of interest in the study of the distribution of top incomes using income tax data. Beginning with the research by Piketty of the long-run distribution of top incomes in France (Piketty 2001, 2003 and Chapter 3 this volume), there has been a succession of studies, as evidenced by the chapters contained in this volume. In using data from the income tax records, these studies use similar sources to the earlier work of Bowley (1914) and Stamp (1914, 1916, 1936) in the UK, and Kuznets (1953) in the US. TheWndings of recent research is, however, of added interest, since the data provide estimates covering nearly all of the twentieth century—a length of time series unusual in economics. The recent research covers a wide variety of countries, and opens the door to the comparative study of top incomes using income tax data.1 Moreover, the techniques are considerably more developed.
This chapter is concerned with methodological issues. Its aim is to review certain aspects of the methodology underlying the new estimates and to make suggestions for its future development. In assessing the methods applied, it is helpful to begin by asking the question—why are we interested in the top of the distribution? Reasons for concern about the bottom of the distribution are more evident. Is interest in the rich just sensationalism? This question is addressed in Section 2.2. Section 2.3 takes up three methodological issues that arise in using the tabulated income tax data, which are all that is currently available for much of the early part of the period. How can we move from the limited information published by the tax authorities to the broad distributional statements in which we are interested? Section 2.4 turns to a subject already addressed in Chapter 1:
the explanation of the observed patterns of diVerence across time and across countries, and the application of econometric modelling. TheWnal section (2.5) summarizes brieXy the issues raised for future research.
1 For an early comparative study of the upper part of the distribution, using income tax data for Germany, France, Great Britain, the Netherlands, and the US, see Statistischen Reichsamt (1930).
2 . 2 W H Y T H E F U S S ?
Enthusiasm for redistributive policies is constantly kindled and fed by the conviction that income and wealth are drastically maldistributed, even if not as much so as in the distant past . . . indeed these extremes are still visible, as between destitute vagrants and millionaire pop-stars or property speculators.
Yet these extremes are obviously exceptions . . . If the great bulk of incomes fell within some quite restricted range—as indeed they do—a reasonable observer might wonder what all the fuss was about (Letwin 1983: 58)
The share of the top income groups has risen signiWcantly in recent decades in the UK, the US, and many other (but not all) countries. In the UK, the share of the top 1% in before tax income rose from 5.7% in 1978 to 8.7% in 1989, and by a further 3 percentage points in the next ten years. The share has eVectively doubled. In the US, the share of the top 1% in before tax income (excluding capital gains) rose from 7.9% in 1976 to 16.9% in 2000. The share of an even wealthier group—the top 0.1%—has trebled in the US over this period.
Why do these increases at the top matter? Several answers can be given. The most general is that diVerent parts of the distribution are interdependent. The outcome for one group is aVected by the outcome for others; people interact in markets and in political decision making. The interdependence was well captured by Tawney when he referred to the fact that ‘what thoughtful rich people call the problem of poverty, thoughtful poor people call the problem of riches’. Here I consider three more speciWc reasons why we should be interested in the top income groups: their command over resources, their command over people, and their global signiWcance.
Income as Command over Resources
The textbook deWnition of income by economists refers to ‘command over resources’. Are, however, the rich suYciently numerous and suYciently in receipt of income that they make an appreciable diVerence to the overall control of resources? If we ask how the richWt into typical income distribution, then they may appear insigniWcant. The most commonly used summary measure of in-equality, the Gini coeYcient, is more sensitive to transfers at the centre of the distribution than at the tails. If we draw a Lorenz curve, the top 1% would be scarcely be distinguishable on the horizontal axis from the vertical endpoint, and the top 0.1% even less so. All of the action in the very top group would be lost in the last millimetre of the graph (on a standard sized book page).
This formulation nonetheless brings out the extent to which the increases in top shares described above are capable of impacting on overall inequality. If we treat the very top group as inWnitesimal in numbers, but with aWnite share S! of total income, then the Gini coeYcient can be approximated byS!þ(1#S!)G,
whereGis the Gini coeYcient for the rest of the population. This means that, if the Gini coeYcient for the rest of the population is 40%, then a rise of 8 percent-age points in the top share causes a rise of 4.8 percentpercent-age points in the overall Gini. Given that the increase in the overall Gini recorded in the US between the 1970s and the 1990s was of the order of 5 percentage points, what is happening at the top is potentially important as an explanation. Figure 2.1 plots the overall Gini coeYcient for the US over the post-war period, derived from the March income supplement of the Current Population Survey (see the foot-notes for the way in which this has been spliced), alongside the share in before tax income estimated by Piketty and Saez (Chapter 5 in this volume). One should not read too much into the similarity of movement, but the picture is suggestive. (The relation between top shares and overall inequality is explored further by Leigh (2006).)
More concretely, we can ask whether increased taxes on the top income group would yield appreciable revenue that could be deployed to fund public goods or redistribution? The standard response by many economists in the past has been that ‘the game is not worth the candle’. In the case of the UK, Prest, questioning the role of steeply progressive tax rates in the 1960s, noted that ‘if the maximum poundage rate for income tax and surtax combined had been reduced to 75%, the loss of tax . . . would have been about £15 million out of a total of £2,929 million in 1963/64’ (Prest 1967: 272). In other words, the share of the top income groups had become quantitatively unimportant.
The notion of ‘taxable capacity’ can be interpreted in diVerent ways. Here I take as a simple measure of the additional taxable capacity of the top 1% in the UK
30 35 40 45 50
1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002
Gini coefficient %
0 5 10 15
Share of top 1% in total income
Share of top 1%
RH axis Gini coefficient
LH axis
Figure 2.1 Share of top 1% and overall Gini coefficient in US, 1947–2002
Note: Different definitions of income and income unit.
Source: Top 1% from this volume, Chapter 5, Table 5.A2. Gini coefficient from US Department of Commerce, Bureau of the Census, Historical Income Tables: the series for families (Table F.4) from 1947 to 1967 is linked at 1967 to the series for households from 1967 to 2002. The latter is shown as a continuous series, but the footnote indicate a number of significant changes in methods of estimation.
the excess over 1% of the net share multiplied by (1—average tax rate). In other words, this measures the income remaining in the hands of the top 1% after income tax that exceeds the mean income, expressed as a proportion of gross income (on which any extra tax would be levied). So that, taking roundedWgures for 1977 in the UK, the total gross income was £100 billion and total net income was £80 billion, giving an average tax rate of 20%. The share of the top 1% in total net income was, in round terms, 4%, so that the ‘excess’ was 3%, or, expressed relative to gross income, (1---0:2)!3¼2:4%. As is clear from Figure 2.2, which plots the ‘excess share’ in the UK from 1937 to 2000, the 1977 value represented a low point. Even with the high rates of tax in force after the Second World War, the excess share was more than 4%. Whereas aWgure of some 2.5% in 1977 could perhaps be dismissed as quantitatively unimportant, subsequently the graph begins to rise sharply, and we are now talking about an excess share of more than 7.5% of total gross personal income. In budgetary terms, this cannot be ignored.
Income as Command over People
Income is important as a source of power. Such a statement is easily made, but less readily translated into a measurable construct. It is not evident for example whether it is absolute or relative income that matters. Is power associated with having more than £X million or with having more than some multiple of mean income? Nor is it clear whether it is the absolute number of people or the relative number. Do 10,000 millionaires have less power in a society of 100 million than in
0 2 4 6 8 10 12
1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997
% Gross income
Figure 2.2 ‘Taxable capacity’ of top 1% in the UK, 1937–2000
Source: Calculated from net income shares and average tax rates given in Tables 4.2 and 4B.1, Chapter 4, this volume.
a society of 1 million? Here I put forward one possible way of approaching the issue. It should be noted that I am concerned here with how far income conveys power, rather than vice versa. The converse role of power in determining the distribution of income is also important: see, for instance, Pen (1978).
The approach to measurement—only one of several that could be adopted—is based on the capacity of those with high incomes to opt out of communal provision. As Barry (2002) has argued, there are two forms of social exclusion, with two associated thresholds. In addition to the social exclusion most commonly studied, there is—at the other end of the scale—elite separation, in which the well oVcan choose to ‘insulate themselves from the common fate and buy their way out of the common institutions’ (Barry 2002: 16). Such voluntary isolation takes the concrete form of private provision of education and health care, and of gated communities. The ability to use ‘exit’ as a strategy is a clear manifestation of power. This in turn suggests that the capacity to opt out should be measured in relation to the cost of private provision, which is heavily inXuenced by the cost of labour. Services such as health and education are labour intensive. The same applies to the costs of policing and servicing a gated community. For this reason, I consider the purchasing power of income expressed in terms of number of people on average gross earnings that could be employed by a given income. Gross earnings may be too low aWgure since it does not include social security taxes and other employment costs; it may be too high aWgure to the extent that the costs of such employment can be set against tax. Whether the numbers should be relative or absolute is less clear. To the extent that those opting out have toWnance public goods, then absolute numbers may be relevant. In terms of the impact on the rest of society, relative numbers may be relevant.
To illustrate this approach for the United Kingdom, suppose that we consider the number of people with gross income in excess of ten times the average earnings of a full-time worker.2Prior to the Second World War, there were some 100,000–
150,000 tax units with an income of this level or higher. The number with an income in excess of ten times average earnings fell steadily after the Second World War and by 1979 was below 20,000. It is interesting to compare the fall with that in the number of indoor private domestic servants. In 1911, there were 1.4 million in Great Britain; by 1952 the number had fallen to 350,000 and by 1971 to 200,000 (Routh 1980: 35). Although the nature of the employment has changed, one suspects that the numbers have increased in the past two decades. Certainly the change in the income distribution has led to a reversal of the previous trend in the number with gross income in excess of ten times average earnings. The number is now broadly back to its 1949 level.
2 Average weekly earnings of male manual workers from Feinstein (1972: table 65). For later years:
1965–68 from Department of Employment (1971: table 42, 1968; 1970–90), covering all workers, from Atkinson and Micklewright (1992: table BE1, 1991–2000), covering all workers, from OYce for National Statistics (2001), New Earnings Survey (2001: table A30). The gross income data are described in Chapter 4.
Top Incomes in a Global Perspective
The analysis so far has considered the role of top incomes in a purely national context, but it is evident that the rich, or at least the super-rich, are global players.
What however is their quantitative signiWcance on a world scale? Does it matter if the share of the top 1% in the US doubles? The top 1% in the US constitutes 1.3 million tax units. How do theyWt into a world of some 6 billion people?
To address this question, I take the estimates of the distribution of income among world citizens constructed by Bourguignon and Morrisson (2002), concentrating on the period since 1910 for which the underlying distributional data are better founded. Their method is to use evidence on the national distribution (or the distribution for a grouping of countries) about the shares of decile groups, and the top 5%. This is then combined with estimates of national GDP per head, expressed in constant purchasing power parity dollars.
(I do not discuss here the issues raised by such a method.) The groups are treated as homogeneous, so that the highest income in each country is the mean income of the top 5%. Their results show that ‘world inequality worsened . . . from 1820 to 1950, pausing only between 1910 and 1929 . . . [and then] continued to worsen . . . improving only between 1950 and 1960’ (2002: 731). Over the twentieth century, the world Gini coeYcient went from 61% in 1910 to 64% in 1950 and then to 65.7% in 1992.
Rightly, most attention has focused on the bottom of the world distribution, but what is happening at the top is also of interest. In particular, the pattern of change reported by Bourguignon and Morrisson for the twentieth century con-trasts with the evidence provided in this volume of sharp falls in top income shares over the Wrst three-quarters of the century in a number of OECD countries.
Chapter 3 shows a fall in the share of the top 1% in before tax incomes in France from 18.3% in 1915 to 9.0% in 1950 and 7.6% in 1980 (Table 3A.1). Estimates for the UK show a fall from 19.2% in 1918, to 11.5% in 1949, and 5.9% in 1979 (Table 4.1). Estimates for the United States show the share falling from 18% in 1913, to 11.4% in 1950, and 8.2% in 1980 (Table 5A.1).
For the world as a whole, Bourguignon and Morrisson (2002: table 1) estimate the share of the top 5% in world income. Starting in 1910, this share was 36.7%.
Over the next 50 years, it fell slightly to 34.1% in 1960, since when it has risen to 36.0% in 1992. There is little sign here of any dramatic eVect at the world level of the sharp falls in top shares at a national level. However, the top 5% in the world distribution comprised in 1992 some 273 million people, with incomes in excess of US$22,000 (the eighth decile group in France was at the margin). The assumptions made in constructing the distribution mean that the richest group, the top 5% in the US, enter as all having incomes of US$88,000. No allowance is made for the inequality within this group. Yet there are large diVerences between, say, the top 1% and the ‘next 4%’. Moreover, their shares have been changing in diVerent ways. As Piketty (2001: 146) has emphasized, the income of the
‘next 4%’ in France is largely derived from salaries rather than from capital income, and diVerent economic forces are likely to have been in operation.
In view of this, I have modiWed the Bourguignon-Morrisson calculations by assuming a continuous Pareto distribution of income for the top 5%—see Box 2.1. The coeYcient of the Pareto distribution is estimated from the share of the top 5% in the total income of the top 10% (see equation (1e) in Box 2.1). For example, for the US in 1992 the Bourguignon-Morrisson data show the share of the top 10% as 30.8% and that of the top 5% as 20.3%, which yields a Pareto coeYcient of 1/(1#log(30.8/20.3)/log2)¼2.509. This coeYcient is changing over time, so that the modiWed procedure adopted here allows both for changes in the share of the top 5% and for changes in the distribution within that group.
Applied to each of the countries (or country groups) it is possible to calculate the number of people with incomes above a speciWed level, reXecting the diVerent degrees of inequality at the top as well as the income required to enter the top 5%
in each country. It should be noted that theseWgures relate to national income, not to household incomes—see Bourguignon and Morrisson (2002: 730). The population also includes everyone, not just adults. For the purposes of deWning the ‘globally rich’ in Figure 2.3, I took those with more than 20 times mean world income, which in 1992 was essentially US$100,000. (In 1910, the Wgure was US$30,000, again in constant purchasing power parity dollars.) In 1992 there were an estimated 7.4 million people with incomes above this level, more than a third of them in the US. They constituted 0.14% of the world population, but received 5.4% of total world income, or rather more than the GDP of Germany.
Clearly, it must be remembered that these estimates are the product of strong assumptions.
Box 2.1 Pareto distribution
The cumulative proportion of people with incomesyiand higher is such that Hi(y)¼(k=yi)Æ
whereÆandkare constants, as in Chapter 1. The cumulative total income in rangeiand above, divided by the mean!, is given by
Gi(y)¼kÆÆ=(Æ#1)yi#(Æ#1)=!
¼Æ=(Æ#1)k=!(Hi)(Æ#1)=Æ
¼Æ=(Æ#1)(yi=!)Hi
The last of these implies that the mean income aboveyiis a constant multipleÆ=(Æ#1) of yi. This multiple is calledbin Chapter 1. The relative share of two groups, with Hiand Hj of the population, are given by
Si=Sj¼(Hi=Hj)(Æ#1)=Æor log (Si=Sj)¼(Æ#1)=Ælog (Hi=Hj) (2:1e)
What is interesting is the pattern of change over time revealed by Figure 2.3. As a proportion of the world population the globally rich fell from 1910 to 1970, mirroring the decline recorded in individual countries. The numbers from the UK fell consistently. Although those for the US were higher in 1929 than in 1910, by 1970 they too had fallen below 0.05% of the world population. But from 1970 we see a reversal, and a rise in the proportion of globally rich above the 1950 level. The number of globally rich doubled in the US between 1970 and 1992.
Moreover, increased inequality at the top has a perceptible eVect. The squares in Figure 2.3 for 1992 show the eVect of a shift in the income distribution in just the US, where each of the nine lower decile groups gives up 0.5% of total income, to the advantage of the top 5%. In other words, the share of the top 5% rises by 4.5 percentage points (the distribution tilts within the top 10%, and indeed within the top 5%). According to the Piketty and Saez estimates in Chapter 5, the share of the top 5% in the US in fact increased by 4.3 percentage points between 1992 and 2000. As may be seen, this makes a perceptible diVerence to the world distribution.
Moreover, increased inequality at the top has a perceptible eVect. The squares in Figure 2.3 for 1992 show the eVect of a shift in the income distribution in just the US, where each of the nine lower decile groups gives up 0.5% of total income, to the advantage of the top 5%. In other words, the share of the top 5% rises by 4.5 percentage points (the distribution tilts within the top 10%, and indeed within the top 5%). According to the Piketty and Saez estimates in Chapter 5, the share of the top 5% in the US in fact increased by 4.3 percentage points between 1992 and 2000. As may be seen, this makes a perceptible diVerence to the world distribution.