During last night’s State of the Union address, President Obama proposed fighting poverty by raising the minimum wage. It sounds appealing but it will not work.

Labor economists have repeatedly studied the effects of minimum wage increases. They find no correlation between higher minimum wages and lower poverty. Raising the minimum wage to $9 an hour as the President suggests simply would not reduce poverty.

This seems counterintuitive, to put it mildly. Surely low-income families would benefit from higher pay. Why wouldn’t it help? For several reasons.

First, relatively few minimum wage workers are poor. The average minimum wage worker lives in a family making over $50,000 a year. Many minimum wage workers are teenagers or college students working part time—they are not trying to support themselves (or a family) with their income. Only one-ninth of the workers who would potentially benefit live in poverty. Raising the minimum wage will not affect many poor families.

Second, higher minimum wages cost some workers their jobs. The true minimum wage remains $0 an hour. No business pays its employees more than they produce. A higher minimum wage would cause businesses to lay off every worker who does not add at least $9 an hour in value to their enterprise. The President’s proposed 25 percent minimum wage hike would unemploy about 5 percent of low-wage workers. (Some liberal economists disagree, but more recent research undercuts their arguments.)

Now, this may seem like an acceptable trade-off, however, most minimum wage jobs are entry-level positions. As minimum wage workers gain experience they become more productive and can command higher pay. Two-thirds of minimum wage workers earn a raise within a year. The primary value of a minimum wage job is the on-the-job training it provides, not the present low pay.

Raising the minimum wage makes these entry-level jobs harder to find. That makes it harder for less skilled workers to gain the skills necessary to get ahead. In effect it saws off the bottom rung of their career ladder. That is bad enough in normal economic times, let alone during an anemic recovery from a deep recession.

Finally, the welfare state claws back raises that low-income families do receive. Low-income workers qualify for a host of means-tested federal benefits. These include food stamps, housing vouchers, Medicaid, and the Earned Income Tax Credit. As workers’ incomes rise they qualify for less and less aid—effectively an additional tax on their income. The Congressional Budget Office finds these reductions push many low-income workers’ marginal tax rates to nearly 100 percent.

A single parent working full time at the minimum wage makes $15,000 a year. A raise to $9 an hour would increase their pay almost $4,000—almost all of which they would then forfeit through reduced benefits. The structure of the welfare state makes it virtually impossible to fight poverty with a higher minimum wage.

H. L. Mencken once observed that “for every complex problem there is an answer that is clear, simple, and wrong.” He could have been talking about minimum wage increases.