President and Mrs. Obama have said that they would like for Malia and Sasha to have the experience of working at minimum wage jobs.

Alas, I expect that the Obamas view the game as rigged—i.e., Sasha and Malia would take their jobs somewhat in the spirit of the high-profile members of Congress who vow to live briefly on the food stamps ration to learn that the food stamp program is woefully inadequate. I nevertheless applauded the experiment and suggested that the Obama daughters might learn from it.

If they embraced their minimum wage jobs with open minds and hearts, they might see people getting a toehold in the world of work and developing good habits in a minimum wage job. They might also see first-hand how grateful people outside their gilded orbit can be to have the opportunity of an entry-level job. They might even learn that many of those colleagues have no intention of remaining in minimum-wage jobs once they have mastered a skill and shown themselves to be good workers.

Now, a terrific piece in the Wall Street Journal this morning by David Neumark, an economics professor at the Center for Economics and Public Policy at the University of California, Irvine, tells what Sasha and Malia’s father needs to know about the minimum wage.

President Obama, as you know, is working to raise the federal minimum wage to $10.10 from $7.25 an hour. Seattle’s City Council has raised the minimum wage to $15 an hour, and San Francisco is considering the same thing. So, really, we need to know who would benefit by such actions.

Neumark writes that many more low-wage earners will get a raise than will lose their jobs. So why not be gung-ho for a minimum wage hike as a way to alleviate poverty? While a hike would help many low-wage earners, it would not do much for low-income families.

Neumark writes:

One might think that low-wage workers and low-income families are the same. But data from the U.S. Census Bureau show that there is only a weak relationship between being a low-wage worker and being poor, for three reasons.

First, many low-wage workers are in higher-income families—workers who are not the primary breadwinners and often contribute a small share of their family's income. Second, some workers in poor families earn higher wages but don't work enough hours. And third, about half of poor families have no workers, in which case a higher minimum wage does no good. This is simple descriptive evidence and is not disputed by economists.

Neumark quotes evidence showing that in 1939, when the minimum wage was first enacted, eighty-five percent of low-wage workers belonged to poor families. However, since then the public safety net has expanded and family structures have changed. Now only about 17 percent of minimum-wage earners are in poor families.

Neumark writes:

In contrast, as of the early 2000s 34% of low-wage workers were in families that were far from poor, with incomes more than three times the poverty line. In other words, for every poor minimum-wage worker who might directly benefit from the minimum wage, two workers in families with incomes more than three times the poverty line would benefit.

It is hard to design government programs that narrowly target those we are trying to help, so evidence that some of the benefits accrue to those who aren't targeted should not be used as a blanket condemnation. But the extent to which this happens with the minimum wage is staggering.

Using data from Current Population Survey for recent years, a graduate student of Mr. Neumark’s has estimated that, if we hike the minimum wage to $10.10, poor families would get only 18% of the benefits. Families with incomes three times the poverty level or higher would receive 29 percent of the benefits.

Poor families benefit proportionally even less if the minimum wage is raised to $15. Only about 12 percent of the benefits go to poor families, if one uses the same calculations as in the previous example. Hiking the minimum wage could reduce poverty only if it targeted poor families.

Mr. Neumark concludes:

This evidence suggests we should consider alternative policies. The Earned Income Tax Credit directly targets low-income families, rather than low-wage workers. And my research with William Wascher, using Census Bureau data, shows that a higher EITC boosts incomes of poor families, and even—by encouraging work—leads to more low-income families earning their way out of poverty. The EITC could be made more generous, particularly for childless adults who currently get little from it.

Because the EITC operates through the tax code, it also has the virtue, in this era of rising inequality, of being financed disproportionately by those with the highest incomes. Raising the minimum wage is ineffective on that score because it is paid by those who hire low-wage labor. Some employers of low-wage labor may be rich, but many are not.

The desire to help poor and low-income families is understandable. But increasing the minimum wage is a misguided way to do it.

So the minimum wage hike so beloved by President Obama becomes one more government intervention that doesn’t do what it promises. But I guess it makes President Obama feel good, no?