Becker and Posner on the minimum wage

Prof. Gary Becker and Hon. Richard Posner have a recent Wall Street Journal op-ed about the minimum wage, called "How to Make the Poor Poorer."  (Link here, thanks to the Volokh Conspiracy.)  Here is an excerpt:

An increase in the minimum wage raises the costs of fast foods and other goods produced with large inputs of unskilled labor. Producers adjust both by substituting capital inputs and/or high-skilled labor for minimum-wage workers and, because the substitutes are more costly (otherwise the substitutions would have been made already), by raising prices. The higher prices reduce the producers' output and thus their demand for labor. The adjustments to the hike in the minimum wage are inefficient because they are motivated not by a higher real cost of low-skilled labor but by a government-mandated increase in the price of that labor. That increase has the same misallocative effect as monopoly pricing.

Although some workers benefit — those who were paid the old minimum wage but are worth the new, higher one to the employers — others are pushed into unemployment, the underground economy or crime. The losers are therefore likely to lose more than the gainers gain; they are also likely to be poorer people. And poor families are disproportionately hurt by the rise in the price of fast foods and other goods produced with low-skilled labor because these families spend a relatively large fraction of their incomes on such goods. And many, maybe most, of the gainers from a higher minimum wage are not poor. Most minimum-wage workers are part time, and for the majority their minimum-wage income supplements an income derived from other sources.

Now, I realize that there are solid and serious economists who believe that we can increase the minimum wage without harming the poor.  I do not know, for sure, who has the better of the argument.  I would think, though, that we could all agree that it really matters who is right, for purposes of evaluating what seems to be the near-unanimous view among those who care about Catholic Social Thought that the minimum wage should be increased.  Do the bishops, and those who promote this view, know whether or not Becker and Posner are right?  I take it we could agree entirely with Eduardo about the dangers of economic inequality but still think the minimum-wage question depends on answering -- or at least addressing -- some tough empirical questions?