First, I tracked down the percentage of income tax paid by income level in the last decade (because Barro's data appeared a bit dated).
Key income tax policy changes occurred in 2001 (tax cuts in the Economic Growth and Tax Relief Reconciliation Act), 2006 (tax cuts in the Tax Relief and Health Care Act), and 2009 (tax cut in the American Recovery and Reinvestment Tax Act).
Source: National Taxpayers Union
The data is consistent with Barro's argument. After the 2001 tax cuts, the proportion of income taxes paid by the wealthy continued to rise until the dawn of the financial crisis. Empirically we see that tax cuts make sense, but Barro also points to a theoretical foundation. "The much-ridiculed Laffer curve," he wrote, "the idea that lower tax rates could generate more revenue[can] work brilliantly at upper incomes" (120). If the federal government taxes at rate B, surely it could generate more revenue from the equillibrium rate. The graph below depicts this phenomenon.
However, while the rich are paying a greater proportion of taxes than in 2001, there does not appear to be a relationship between government tax revenues per unit of GDP and proportion of taxes paid by the 1%. (X axis is the percent of income taxes paid by the 1% , the y axis is tax receipts/GDPx100). This tends to be the argument against higher taxes on the wealthy - it simply will not substantially increase tax revenues.
Source: Tax Policy Center
Granted, my dataset is limited in a two-day blog post. However, it does not appear automatic that a tax hike on the wealthy will increase total government tax revenues. In that case, what is the motivation for, say, the proponents of the Buffett Rule?
To quote the White House website: "The Buffett Rule would limit the degree to which the best-off can take advantage of loopholes and tax rates that allow them to pay less of their income in taxes than middle-class families."
According to Barro, the reason tax cuts work is because the rich declare more of their income when tax rates are low. He notes, "the first observation...is that the increase in the reported taxable incomes of the rich [after tax cuts] is very great" (120). This assumes the rich are taking advantage of loopholes and manipulate their income structure (between capital gains, income, etc.) in response to tax hikes. So if the Buffett Rule eliminates (or immensely limits) loopholes, the government tax revenues might rise with higher tax rates after all.
So, it seems Barro and Buffett are talking past each other. Barro claims tax revenues from the wealthy will not move with programs like the Buffett Tax, since the rich will just report less taxable income. This is supported by the estimation that the Buffett Tax is estimated to raise only $4.7 billion per year.
Proponents of the Buffett Rule, on the other hand, make an ethical argument. As the clip below shows, they are concerned more with the effective tax rates of individuals. How much of the 1%'s income is paid in taxes each year? They do not care that the economic effects might be negative - that consumption or investment might drop by more than government revenue will rise. It is a matter of fairness. The rich should not pay less of their income in taxes than the poor, they say.
Whether you agree with Buffett or Barro is ultimately political, not economic. It depends on your ethical attitudes about absolute versus relative well-being.
Sources:
http://www.forbes.com/sites/janetnovack/2012/03/22/the-real-reason-the-buffett-rule-would-raise-only-47-billion/
http://www.whitehouse.gov/economy/buffett-rule
http://www.brookings.edu/research/papers/2012/08/01-tax-reform-brown-gale-looney
http://www.ntu.org/tax-basics/who-pays-income-taxes.html
http://www.taxpolicycenter.org/taxfacts/displayafact.cfm?Docid=200
http://www.taxpolicycenter.org/legislation/2000.cfm
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