The minimum wage from 1968 was $1.60 an hour which is worth $10.40 today, using the BLS nifty inflation calculator.
http://www.bls.gov/data/inflation_calculator.htm

Raising the federal minimum wage from it's current $7.25 an hour to $10.00 an hour and indexing it to inflation would be a good first step towards reducing income inequality in America without raising taxes.

I think it would be best to start such a discussion by introducing the rubric of economic rent collection.

Inequality is due to the enormous extension of patents and copyright monopolies over the last three decades.

Really? All inequality everywhere? Due only to changes in patents and copyright policies since 1981? That's absurd.
And I know that's not exactly what you meant. However, your reading of Gelman is even more strained than my reading of you. At least I gave a quote from your article that supports my point. There's absolutely zero content in Gelman's article that supports the notion that Gelman wants to restrict the debate about anything. He's commenting on what other people are arguing and bringing his expertise as a statistician to bear on the interpretation of polls.

Since the US and other countries have been highly prosperous at times when income tax rates were much more highly progressive, it should be obvious that high tax rates do not destroy economic incentive. Yet economists, including "liberal" ones, persist in assuming that incentive for constructive economic activity is a linear function of ultimate reward. It is likely that reducing tax rates for capitalist activities leads to get-rich-quick schemes rather than constructive investment. Incentives tend to be more related to comparative rewards or prestige than absolute rewards.

The entire discussion of the economic implications of tax rates takes place in the context of absolutely moronic assumptions about incentives, which are in severe conflict with economic history. Such oversimplifications may make economics theoretically tractable, but economic activity in the real world is governed by actual human psychology, a matter in which economists in general show little interest.

Very painful having to read the article, but Dean's take is exactly correct. It is an attention-span stretcher though.

Everyone knows that Ronald Reagan reduced income taxes (more than one half for the wealthy); what is less commonly understood is that he offset this by raising payroll taxes(more than double for most self-employed). Today, most American families pay more in payroll taxes than they do in income taxes. Prior to 1981, income taxes averaged 12%(+/-1%) of normalized GDP. Reagan reduced income taxes to near 9%. Clinton increased them back to 12%; and Bush/Obama reduced them again to 9 %(and below). However, on budget expenses(which excludes Medicare and Social Security) have remained 12%(+/-1%) of normalized GDP throughout. The deficit in income taxes has been financed by borrowing, largely from the Social Security trust fund. When Clinton raised income taxes back to 12%, this eliminated the on budget deficit. The CBO projected that this, plus the Social Security and Medicare surpluses, was enough to pay off the entire US debt by the time that the Social Security/Medicare trust funds would have to be amortized for beneficiary payments, all without having to raise taxes to pay for the amortization of those trust funds. Like Reagan before him, Bush took those excess payroll tax receipts and gave them “back” as income tax reductions, heavily weighted to the wealthy–who didn’t create those surpluses in the first place. By doing this, Bush guaranteed that income taxes would have to be raised in order to amortize the trust funds. The failure to do so simply permits the 1% to steal the money contributed by workers for their retirement. Everything about not raising taxes or limiting expenses, is about stealing the 99%'s money. The national debt has been caused primarily by income taxes which were reduced far below their historic 12%(+/-1%), not by on budget expenses, which have remained at their historic 12%(+/-1%) throughout. These taxing games have transferred $ trillions from the 99%'s payroll taxes to subsidize the wealthy's income taxes.

I agree with Robert that raising wages would help income inequality, but I do want to nitpick hi argument. An opponent could pick out any year of the minimum wage (say, 1938, the year it all began) and do the calculation, and it could backfire! For example, $0.25 in 1938 has the same purchasing power as $4.01 today.

Picking a year would have to be justified, is all I am saying. It's too weak to be carried out alone.

Use of 1968 as a comparison year is usual, because it is the year in which the minimum wage peaked in real terms. Given that real GDP per capita has doubled since 1968, why should the minimum wage not have continued to increase in real terms, or at least stayed even?