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 Barack Obama recently announced his own big idea: Inequality, he says, “challenges the very essence of who we are as a people.”

The president’s rhetorical departure 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. This theory 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 preferring (with rare exceptions) 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 the progressive mind, the idea that income inequality is the underlying 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 U.S., suppress incomes at the bottom? If hedge-fund managers and superstar basketball players were paid less, Wal-Mart Stores Inc. 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 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 have lately been charmed by what’s called the Great Gatsby curve, which suggests a statistical relationship between income inequality and lack of social mobility. Alan Krueger, chairman of the White House Council of Economic Advisors, 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 action to improve social mobility in the U.S. is compelling in its own right. It needs no support from a unified theory of economic 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 in the U.S. 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 U.S. 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 pre-kindergarten education (favored by progressives) is a worthy goal; so is school reform (about which progressives, beholden to teachers’ unions, are ambivalent at best).

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

Some of these loopholes are outrageous. For instance, the tax-code lets heavily lawyered plutocrats shield their assets from estate taxes when they die. Moreover, unrealized capital gains are in effect wiped out for tax purposes at death (acquisition values are reset when the assets are inherited). 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.

The policy recommendations I just made 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 U.S. 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. I wish Obama had stressed opportunity, not inequality.

(Clive Crook is a Bloomberg View columnist.)

To contact the writer of this article: Clive Crook at ccrook5@bloomberg.net.

To contact the editor responsible for this article: James Gibney at jgibney5@bloomberg.net.