President Obama is pushing hard for an increase in the federal minimum wage to $10.10, from $7.25. State and local governments have jumped on the bandwagon. Massachusetts has passed a minimum of $11, the highest state minimum in the country, and Seattle's City Council has voted to raise the wage floor to $15 an hour over seven years; San Francisco is considering a hike to $15 too. The president and others argue that a higher minimum wage is needed to help poor and low-income families, who have suffered from stagnating wages and rising income inequality. But a higher minimum wage would do little for such families.

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A higher minimum wage raises wages of low-wage workers, and even though most evidence points to job losses from higher minimum wages, the evidence doesn't point to widespread employment declines. Thus, consistent with a recent Congressional Budget Office report, many more low-wage workers will get a raise than will lose their jobs. But that argument is about low-wage workers, not low-income families. Minimum wages are ineffective at helping poor families because such a small share of the benefits flow to them.

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.

A historical perspective is instructive. Assembling Census Bureau data over nearly seven decades, Richard Burkhauser and Joseph Sabia have shown that in 1939, just after the federal minimum wage was established, 85% of low-wage workers (those earning less than one-half the private-sector wage) were in poor families. Such a high percentage implies that, in that year, the new minimum wage targeted poor families well. However, as the public safety net expanded, family structure changed and more people in families began working, this percentage fell sharply over time—to around 17% by the early 2000s.

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.

The effectiveness of minimum-wage targeting may have improved in the past decade because of declines in wages for lower-skill adults, and a lower employment rate among teenagers. But the improvement is only slight. 

Using data from the Current Population Survey for recent years, my graduate student Sam Lundstrom has calculated that if we were to raise the minimum wage to $10.10 nationally, 18% of the benefits of the higher wages (holding employment fixed) would go to poor families. Twenty-nine percent would go to families with incomes three times the poverty level or higher.

What about minimum wages as high as $15 an hour? A higher minimum obviously affects more workers. But because workers at higher wages are even less likely to be in poor families, the targeting only worsens with a higher minimum wage. For example, applying the same calculation as above for a $15 per hour minimum, the share of benefits going to poor families would decline to 12%, and the share to families more than three times the poverty line would increase to 36%. And this does not account for the sizable employment losses that would likely result from such a large minimum-wage increase.

A higher minimum wage can still reduce poverty if the wage gains for workers in poor families outweigh the job losses caused by the increase. Researchers have studied this question, using data from the Census Bureau's Current Population Survey to compare changes in poverty in states that raised their minimum wage vs. states that didn't. Like the longer-running debate on the employment effects of minimum wages, there are some divergent results. However, most studies—this time in contrast to the conclusions that CBO reaches—fail to find any solid evidence that higher minimum wages reduce poverty.

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.

Mr. Neumark is an economics professor and director of the Center for Economics and Public Policy at the University of California, Irvine.