REUTERS/Kevin Lamarque

That wasn’t simply an economics speech President Obama gave Wednesday at the Center for American Progress. It was a legacy-building speech--or an attempt at one, at least.

In case anyone wondered where the president’s focus would be over the next few years, Obama’s remarks on income inequality made it clear. “Over the course of the next year and for the rest of my presidency, that’s where you should expect my administration to focus all our efforts,” he said in the speech.

"I believe this is the defining challenge of our time," Obama said. "It drives everything I do in this office." He wrapped the individual policy issues that have dominated his tenure--from health care to the federal budget--into the larger context of "an America where opportunity is real." And he painted the issue in moral terms: "the idea that a child may never be able to escape that poverty because she lacks a decent education or health care or a community that views her future as their own--that should offend all of us. And it should compel us to action. We are a better country than this."

In effect, the president put a stake in the ground: This is my most important issue, and everything I'm working on is designed to address it. By doing so, he gave us a key yardstick by which to measure the success his presidency. Yes, in one sense, we already have yardsticks: Did the economy improve? Did unemployment fall? Did Obamacare work? But the bold goal of improving opportunity and income inequality, he's saying, is his yardstick, how he wants to be measured and remembered.

Whether he can succeed is a much bigger question--but if he wants a chance at creating a true legacy, he needs to try. Back before the 2012 election, I had an interesting conversation with Gautam Mukunda, a Harvard Business School professor who studies leadership. Mukunda's 2012 book "Indispensable" looks at what makes an individual actually matter--in other words, which leaders actually shape history, and which ones are simply shaped by history itself.

In it, he differentiates between what he calls "filtered" leaders (those who have spent years in powerful positions by which we can easily evaluate their performance) and those he calls "unfiltered" (the outsiders or outliers who have not). George H.W. Bush--former vice president, former director of Central Intelligence, former ambassador to the United Nations--was elected as a filtered president. Barack Obama--an Illinois state senator and one-term U.S. senator--was not. Unfiltered leaders, Mukunda posits, are much more likely to ride the extremes. They either become high-impact, indispensable leaders or become spectacular failures.

The advice of the book, Mukunda told me, is that leaders have to know their type, and act in accordance with it. People expect filtered presidents--those elected based on their ability to perform well in past situations--to execute well and manage very well every aspect of the presidency. People expect unfiltered presidents, meanwhile, to be bolder and achieve something for which they are uniquely qualified.

For Obama, Mukunda told me, that something in income inequality. The first African-American president, elected amid the grossest excesses of Wall Street and the greatest financial crisis since the Great Depression, is uniquely qualified to make this issue his legacy. "He shouldn’t just go down the list and say what’s the thing [a president] should do." Rather, he needs to define "the thing that only Barack Obama should do."

Income inequality--which researcher and professor Tim Smeeding has called "a topic that American presidents normally stay away from" and "historic" for a sitting president to address--is that thing for Obama. Whether he can bring notable change on the issue or not, especially given the troubling start to his second term and the utter dysfunction in Washington, is highly debatable. But as Mukunda says, particularly for a leader like Obama with less prior experience, unless he's "doing things that lots of reasonable people say [go] past the edge of what's possible, then he won't leave a legacy."

Jena McGregor is a columnist for On Leadership.

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