"Top Incomes in the Long Run of History" with Tony Atkinson and

10Journal of Economic Literature, Vol. XLIX (March 2011)response by many economists in the past hasbeen that “the game is not worth the candle.”Indeed, net of all federal taxes, in the UnitedStates in 1976 the top percentile receivedonly 5.8 percent of total pretax income, anamount equal to 24 percent of all federal taxes(individual, corporate, estate taxes, and socialsecurity and health contributions) in that year.However, by 2007, net of all federal taxes,the top percentile received 17.3 percent oftotal pretax income, or about 74 percent of allfederal taxes raised in 2007. 4 Therefore, it isclear that the surge in the top percentile sharehas greatly increased the “tax capacity” at thetop of the income distribution. In budgetaryterms, this cannot be ignored. 52.2 Impact on Overall InequalityIt might be thought that top shares havelittle impact on overall inequality. If we drawa Lorenz curve, defined as the share of totalincome accruing to those below percentile p,as p goes from 0 (bottom of the distribution)to 100 (top of the distribution), then the top 1percent would scarcely be distinguishable onthe horizontal axis from the vertical endpoint,and the top 0.1 percent even less so. The mostcommonly used summary measure of overallinequality, the Gini coefficient, is more sensitiveto transfers at the center of the distributionthan at the tails. (The Gini coefficient isdefined as the ratio of the area between theLorenz curve and the line of equality over thetotal area under the line of equality.)4 The 5.8 percent and 17.3 percent figures are based onaverage tax rates by income groups presented in Pikettyand Saez (2006). We exclude the corporate tax and theemployer portion of payroll taxes as the pretax incomeshare series are based on market income after corporatetaxes and employer payroll taxes. We have 5.8 percent= 8.8 percent * (1 − 0.262 − 0.016/2 − .068) and17.3 percent = 23.5 percent * (1 − .225 − 0.03/2 − 0.022).The percentage of all federal taxes is obtained using totalfederal average tax rates that are 24.7 percent and 23.7 percentin 1976 and 2007 from Piketty and Saez (2006).5 We discuss the important issue of the behavioralresponses of top incomes to taxes in section 5.But top shares can materially affect overallinequality, as may be seen from the followingcalculation. If we treat the very top groupas infinitesimal in numbers, but with a finiteshare S * of total income, then, graphically,the Lorenz curve reaches 1 − S * just belowp = 100. As a result, the total Gini coefficientcan be approximated by S * + (1 − S * )G, where G is the Gini coefficient for thepopulation excluding the top group (Atkinson2007b). This means that, if the Gini coefficientfor the rest of the population is 40 percent,then a rise of 14 percentage points in the topshare, as happened with the share of the top1 percent in the United States from 1976 to2006, causes a rise of 8.4 percentage points inthe overall Gini. This is larger than the officialGini increase from 39.8 percent to 47.0 percentover the 1976–2006 period based on U.S.household income in the Current PopulationSurvey (U.S. Census Bureau 2008, table A3). 62.3 Top Incomes in a Global PerspectiveThe analysis so far has considered the roleof top incomes in a purely national context,but it is evident that the rich, or at least thesuper-rich, are global players. What howeveris their quantitative significance on a worldscale? Does it matter if the share of the top1 percent in the United States doubles? Thetop 1 percent in the United States constitutes1.5 million tax units. How do they fit into aworld of some 6 billion people? According tothe estimates of Francois Bourguignon andChristian Morrisson (2002), the world Ginicoefficient went from 61 percent in 1910 to64 percent in 1950 and then to 65.7 percentin 1992, as displayed in figure 4 (full triangleseries, right y-axis). 7 How did the evolution oftop income shares in richer countries, which6 The relation between top shares and overall inequalityis explored further by Leigh (2007).7 As spelled out in Bourguignon and Morrisson (2002),strong assumptions are required to obtain a worldwideGini coefficient based on country level inequality statistics.