Big ideas can make a big difference. Lyndon Johnson's War on Poverty, declared 50 years ago this week, yielded Medicare and other safety-net programs that matter enormously in the lives of poor Americans. President Obama recently announced his own big idea: Inequality, he says, "challenges the very essence of who we are as a people."

The president's rhetoric thrills progressive Democrats. It folds poverty, lack of opportunity and the supposedly ill-gotten gains of the rich into a unified theory of economic injustice that aligns with the way progressives see the world. They also feel it's good political marketing. Which of these claims is more energizing: The poor stay poor as the rich get richer? Or the poor stay poor because the rich get richer?

Progressives are right that poverty, opportunity and fairness each deserve close attention, and conservatives are wrong in usually preferring to ignore all three. But Democrats are wrong to bundle the issues together.

For one thing, doing so is dubious economics. Much as it appeals to progressive minds, the idea that income inequality is the cause of poverty and social immobility isn't helpful.

Why would the surging incomes of the super rich — the trend that drives income inequality in the United States — suppress incomes at the bottom? If hedge-fund managers and superstar basketball players were paid less, Wal-Mart Stores would pay its shelf-fillers more and the children of poor single mothers would be more likely to go to college? The logic isn't obvious.

I don't deny that there might be subtle connections. Maybe fast-rising incomes at the top shift political power in ways that militate against anti-poverty or pro-opportunity policies. That strikes me as unlikely, but it's possible. Plenty of other channels have been posited — but none proven. What seems to carry the most weight with progressives is the notion that incomes are somehow fixed in the aggregate, implying that the rich cannot thrive except at somebody else's expense — and that's a fallacy.

Progressives lately have been charmed by what's called the Great Gatsby curve, which suggests a statistical relationship between income inequality and a lack of social mobility. Alan Krueger, chairman of the White House Council of Economic Advisers, drew attention in 2012 to findings by Miles Corak of the University of Ottawa: Countries with higher income inequality tend to have lower social mobility. That's interesting, but as progressives have pointed out in other contexts, correlation is not causation. More recently, the correlation has begun to look suspect, in any case.

Here's the point: It doesn't matter. The case for improving social mobility in the United States is compelling in its own right. It needs no support from a unified theory of injustice.

America prides itself on being the land of opportunity, and the promise of reward for effort is the core of the country's social contract. Yet in one respect, the promise is broken. The child of a poor family has a smaller chance of moving up than his or her counterpart in many other advanced economies.

There's plenty of mobility in the middle of the U.S. income distribution, studies show, but if you're born rich or poor, your chances of staying that way are higher in the United States than in many other places.

What's the remedy? Disadvantage at the bottom of the income scale has a cultural component, and there's a limit to what policy can do. However, earlier and better schooling, the traditional ladder to prosperity, would be a good start. Universal prekindergarten education (favored by progressives) is a worthy goal; so is school reform (about which progressives, beholden to teachers' unions, are ambivalent).

Action to relieve poverty, as opposed to improving mobility, also makes sense in its own right. Policy should be smarter and more generous. Raise and widen the earned income tax credit, the subsidy program for low-wage workers. (That's a better way to help the working poor than raising the minimum wage.) And simplify the bewildering tangle of means-tested benefits — 82 at the federal level alone, according to one recent count. A simpler system would improve takeup and cut costs.

Regarding high incomes, the structure of U.S. tax rates is already fairly progressive by international standards. The egalitarian preoccupation with raising the top rate is misguided. A society based on opportunity should be wary of discouraging effort and enterprise by making it harder for people to advance from the middle class to the ranks of the rich. That would reduce upward mobility, after all. Better to attack loopholes that give the rich — especially the very rich — an unfair advantage.

Some of these loopholes are outrageous. The tax code lets heavily lawyered plutocrats shield assets from estate taxes when they die. Moreover, unrealized capital gains are in effect wiped out for tax purposes at death. As a result, enormous flows of income can escape being taxed almost entirely. This needs to be fixed.

Each of these ideas for increasing opportunity, relieving poverty and attacking tax-code injustices makes sense on its own. None require an enfolding disdain for markets, competition or capitalism. On the contrary, the progressive focus on income inequality as the root of all evil distracts the left from pressing for change where it would do the most good.

What about political marketing — firing up the base, winning elections and all that? Maybe inequality is politically potent, the best way to press those other demands. Color me skeptical. It's divisive in its class-war overtones and actually intended to offend and embarrass conservatives. That may be fun to do, but it's also self-defeating. It arouses resistance to change at least as much as it spurs reform.

My policy recommendations are all capable of being supported by liberals and open-minded conservatives alike. In case you're wondering, that's a good thing. When a president names a defining challenge, he's wise to nominate goals — such as waging war on poverty — that are capable of uniting the country rather than dividing it.