A Congressional Budget Office paper by William Randolph estimates that, "domestic labor bears slightly more than 70 percent of the burden of the corporate income tax. The domestic owners of capital (not just taxable financial capital) bear slightly more than 30 percent of the burden." If Randolph is even partly right, that demolishes the central conclusion of Piketty and Saez that "the greater progressivity of federal taxes in 1960, in contrast to 2004, stems largely from the corporate income tax."

Questions about who pays the corporate tax and income distribution estimates based on individual tax returns are both complicated by the ease of shifting business and professional income between the corporate and individual tax forms. Sheltering personal income inside a corporation was commonplace in the 1970s, but also much earlier. In The American Economic Review in 1937, Roy Blakey noted that, "As the surtax rates for individuals were increased, there was more and more of a temptation and opportunity to avoid the surtax by incorporating." He mentioned "incorporation of yachts and country estates" and "personal holding companies (which) were permitted many deductions not allowed to individuals."

Similar ambiguities affect the estate tax. Piketty and Saez assume that wealthy dead people (rather than their no-income grandchildren) pay the death tax in the year in which they die. In a famous 1978 paper in The Journal of Political Economy, however, Joseph Stiglitz reasoned that the estate tax would ultimately be borne by labor, because it reduces capital formation and therefore productivity and real wages.

The most intractable problem with all such estimates, however, is the demonstrably false assumption that people do not change behavior when tax rates change. In discussing what happened after top marginal tax rates came down, a footnote in Piketty and Saez acknowledges that "it is a disputed question whether the surge in reported top incomes has been caused by the reduction in taxation at the top through behavioral responses."

That is, in fact, the essence of the dispute between us. Taxpayers have always reported more income at the top whenever tax rates have been reduced on salaries (1925 and 1988) or on capital gains (1997) or both (2003). Piketty and Saez depict such increased willingness to report income on individual tax returns as an increase in inequality, while I view it as a predictable response to a change in tax incentives.

Simon Kuznets said his 1953 estimates of income distribution were "as if one tried to paint a fine picture with thick brushes and large blobs of somewhat mixed colors." The newer estimates are almost equally crude, but economists seem not quite as candid or humble as they used to be.