## Friday, May 12, 2006

### Furman on Progressivity

My friend and former student Jason Furman has a letter in today's Wall Street Journal, taking on the CEA op-ed from earlier in the week. Here is an excerpt:

Edward P. Lazear and Katherine Baicker of the President's Council of Economic Advisers are correct in stating that a tax-policy change is progressive if it "narrows the difference in take-home earnings" ("America at Work," editorial page, May 8). But they are incorrect in stating that this is what the president's tax cuts have done.

According to the Tax Policy Center, the tax cuts passed since 2001 have raised the after-tax income of the top 1% of Americans by 5%, while raising the after-tax income of the bottom 60% of Americans by just 2%. In other words, the tax cuts have contributed to widening, not narrowing, the difference in take-home earnings.

In a previous post, I noted that there are different ways to frame the progressivity question. Jason says the first of the three frames I described is the "correct" one. Is he right? I report, you decide.

Jason would say that after-tax income is what people care about, so that should be the focus of our discussion. On the other hand, blogger Brandon Berg notes that, by Jason's preferred metric, a tax cut that completely eliminated the tax on the poor, leaving the rich bearing the entire tax burden, could be judged as making the tax code less progressive. Berg views this an odd use of language.

The framing really matters here; it is not mere pedantry. A little algebra is necessary to explain why. The number that Jason reports, which I will call x, is

x=dT/(Y-T),

where Y is before-tax income, T is taxes, and dT is the change in taxes. After slight rearrangement, we can write the percentage change in taxes as:

dT/T = x(Y/T - 1).

The percentage change in the tax burden is a function of Jason's x and the average tax rate T/Y. The average tax rate varies strongly with income.

I don't have the average tax rate for the data that Jason is using, but based on other data I have seen, I would guess that the top 1 percent pays about 31 percent of income in federal taxes, and the bottom 60 percent pays about 12 percent. (This includes all federal taxes, not just income taxes.) Let's use these figures for T/Y. With the above formula and Jason's numbers, we can estimate that taxpayers in the top 1 percent of the income distribution got a 11-percent tax cut while those in the bottom 60 percent got a 15-percent tax cut.

These figures are roughly consistent with figures in the 2005 Economic Report of the President (pages 78-79). Using CBO data, it reported that in 2004 the average tax rate for the lowest quintile was reduced from 6.7 to 5.3 percent (a 21 percent cut), while the average tax rate for the top quintile was reduced from 27.6 to 25.2 precent (a 9 percent cut). Once again, to avoid confusion, I should say that this includes all federal taxes, not just income taxes.

Jason in his letter brings up the intertemporal government budget constraint (not in the above excerpt). Because I addressed that issue in a previous post, I won't comment again.

Finally, I should mention that all of these numbers are based on simplistic assumptions about tax incidence. For example, to the extent that cuts in capital taxes increase capital accumulation, which in turn increases productivity and wages, the true incidence of tax changes could be very different from the incidence assumed in these data. So, even putting the framing issue aside, all of these numbers need to be taken with a grain of salt.