Arthur Laffer recently observed that

A tax reform to a simple flat-rate tax with no deductions would significantly reduce the current complexity inherent in our progressive tax system, which is full of loopholes, exemptions and special interest carve-outs.

and Matt Yglesias responds as follows:

All the work here is being done by the proviso “with no deductions.” It’s quite true that a flat rate tax with no deductions would significantly reduce complexity. By the same token, a progressive tax with no deductions would reduce complexity. So would a calculus-based system with an infinite number of brackets and no deductions. That’s because eliminating deductions reduces complexity and economic distortions. Moving to a straight proportional tax is just something rich people like because it means they’ll pay less. The one has nothing to do with the other.

By all means, getting rid of deductions is the bigger deal. But is it fair to say that a single-rate tax wouldn’t reduce complexity at all?

In 2005, The Economist surveyed the rise of single-rate taxes in central and eastern Europe:

Fewer brackets are simpler to administer, but one bracket is simplest of all. Under a pure flat tax, the taxman takes the same cut from the last dollar you earn that he took from the first. The appeal to high earners is obvious. But the administrative elegance of such a system is not so immediately apparent. Because every dollar is taxed at the same rate, it does not matter to the tax collector how many dollars are going to whom. Thus, in principle, the taxman could simply withhold 20% of a company’s payroll, without needing to know who was paid what. Add a second rate of tax, however, or a personal exemption, and the tax collector must find out how much money is going into each pay packet before he can be sure of collecting the right amount from the right person. In America, for example, the tax collector needs to tax the wage packets of 130m or more employees, rather than simply taxing the payrolls of 8m or so enterprises.
How much fairness is gained for all this extra complexity? Surprisingly little, suggest Messrs [Jeffrey] Owens and [Stuart] Hamilton [of the OECD]. In New Zealand, for example, only the richest tenth of households pay much more under the country’s progressive income tax than they would under a 25% flat tax (see chart). Most of the redistribution in New Zealand is carried out on the other side of the government’s ledger, by spending more money on poor people.

I imagine that Laffer isn’t advocating a single-rate tax quite like the notional tax code described above.

For a long time, conservative politicians were living in a fantasyland where they’d assert small government bona fides without offering meaningful proposals to reduce the spending burden, which, naturally, made them vulnerable to charges of cowardice and dishonesty. As conservatives grow a bit more explicit about the need to restrain tax expenditures and entitlements, some of our friends are responding in new and creative ways.

P.S. Here’s another interesting part of that 2005 article:

A careful study by two IMF economists, Anna Ivanova and Michael Keen, together with Alexander Klemm, of the Institute of Fiscal Studies in London, tries to unearth the causes of this pleasant fiscal surprise. They find little evidence that Russians, freed from the yoke of progressive taxation, suddenly started working much harder. This is perhaps not surprising, as Russia’s reform actually raised personal income taxes for the many households that previously fell into the 12% bracket.
They did discover a conspicuous increase in compliance with the tax authorities, however. In the year before the flat tax, Russians in the two higher tax brackets reported only 52% of their income to the taxman. In 2001, after falling into the new, all-encompassing 13% bracket, these same households reported 68%.
Many advocates of the flat tax, particularly in America, argue that it sharpens the incentive to work. A progressive income tax, they claim, deters extra effort from society’s best-paid (and therefore most productive) members. Russia’s experience, however, suggests that the principal virtue of the flat tax is its simplicity.

As the author goes on to state, the United States has a much more effective federal government than Russia. Yet there might still be gains from simplicity.