Economist N. Gregory Mankiw ponders whether the rich pay their "fair share" of federal taxes.

The C.B.O.'s most recent calculations of federal tax rates show a highly progressive system. (The numbers are based on 2004 data, but the tax code has not changed much since then.) The poorest fifth of the population, with average annual income of $15,400, pays only 4.5 percent of its income in federal taxes. The middle fifth, with income of $56,200, pays 13.9 percent. And the top fifth, with income of $207,200, pays 25.1 percent.

At the very top of the income distribution, the C.B.O. reports even higher tax rates. The richest 1 percent has average income of $1,259,700 and forks over 31.1 percent of its income to the federal government. . . .

When the C.B.O. studies the tax burden, it includes all federal taxes, including individual income taxes, payroll taxes and corporate income taxes. In its analysis, payroll taxes are borne by workers, and corporate taxes by the owners of capital. For the richest 1 percent of the population, 9.3 percentage points of their 31.1 percent tax rate comes from the taxes that corporations have paid on their behalf. . . .

None of these calculations, however, say whether the rich are paying their fair share. Fairness is not an economic concept. If you want to talk fairness, you have to leave the department of economics and head over to philosophy.