Elizabeth Warren has pulled off something remarkable in the Democratic primary: she's managed to set the terms of the challenge to Hillary Clinton without actually entering the race and challenging Clinton herself.

In part, this is because Warren's agenda has been defined down from very specific ideas about financial regulation to a pretty generic form of economic populism. When Hillary Clinton mentioned that "the average CEO makes about 300 times what the average worker makes" and said "the deck is stacked in favor of the powerful," the New York Times wrote that she was "embracing the ideas trumpeted by Ms. Warren."

This is really just standard-issue Democratic populism. As it happens, Clinton used that CEO pay statistic in her 2008 campaign, too. But Warren has become so synonymous with the populist wing of the Democratic Party that Democrats sounding like Democrats gets reported as Democrats sounding like Elizabeth Warren. And that's great news for Hillary Clinton, because it sets up a test she can easily pass.

On economic policy, Clinton is pretty liberal. Her last presidential campaign was full of rhetoric that you could imagine in any Bernie Sanders or Elizabeth Warren speech today:

Over the 12-month period that just ended in July, the slow growth in wages actually accounted for more than two-thirds of the increase in corporate profits. What does that mean? Well, the profits go up, but unlike every other time in our history, the CEOs and the boards of these companies are not sharing the wealth. So companies are actually profiting off of keeping workers' wages stagnant ... In 2005, the last year I could find the numbers for, all income gains went to the top 10 percent of households, while the bottom 90 percent saw their incomes decline. That is not the America that I grew up in.

"Hillary was talking about inequality and wage stagnation before it was in vogue," says Neera Tanden, who served as policy director on Clinton's 2008 campaign and now leads the Center for American Progress. "She was ahead of this debate, not behind it."

If the question of the 2016 Democratic primary is whether Hillary Clinton can sound like a populist, and adopt more populist policies, she's going to answer it with ease. Compared with the status quo, Clinton pretty much agrees with Sanders, with Warren, and with every other liberal: she wants higher taxes on the rich, more social spending, a tighter social safety net, a public option for health insurance, stronger financial regulations than what Congress actually passed, and so on.

There might be individual policies on which Warren or Sanders go further than Clinton — Sanders, for instance, supports single-payer health care — but on most economic issues, Clinton is well to the left of current policy and to the left of the average voter. And on specific issues like financial regulation, she's willing to go further than many expect: she has already named Gary Gensler, a tough financial regulator, to be her campaign's chief financial officer.

There's just not going to be that much room to her left on economic policy. But there is a lot of room to her left on other issues — and these are disagreements that the Warrenization of the Democratic primary is helping to obscure.

How Elizabeth Warren is helping Hillary Clinton

Clinton really is to the right of many liberals on foreign policy and civil liberties issues. She is significantly more hawkish than Sanders, or even Obama. She is more comfortable with — and cast more votes for — the post-9/11 security state than many in the Democratic Party. She has directly criticized the Obama administration's refusal to get more deeply involved in Syria.

This is how Obama beat Hillary in 2008: he made the primary about an issue set where Clinton actually did differ with Democratic primary voters, and where he could draw contrasts she couldn't erase. Here, for instance, is an excerpt from his speech at the 2007 Jefferson-Jackson Dinner — remembered, by many, as the speech in which Obama found the message that won him the election:

When I am this party's nominee, my opponent will not be able to say that I voted for the war in Iraq; or that I gave George Bush the benefit of the doubt on Iran; or that I supported Bush-Cheney policies of not talking to leaders that we don't like. And he will not be able to say that I wavered on something as fundamental as whether or not it is ok for America to torture -- because it is never ok. That's why I am in it.

And this is why the nature of Warren's challenge is actually helpful to Hillary: if the Democratic primary is about economic liberalism, Clinton is going to win it because she is an economic liberal. If it's about whom you trust to keep us out of a war with Iran, Clinton might lose.

This is why Clinton herself has actually been encouraging the perception that Warren is forcing her to the left. She even wrote a short mash note to Warren for Time:

It was always going to take a special kind of leader to pick up Ted Kennedy’s mantle as senior Senator from Massachusetts—champion of working families and scourge of special interests. Elizabeth Warren never lets us forget that the work of taming Wall Street’s irresponsible risk taking and reforming our financial system is far from finished. And she never hesitates to hold powerful people’s feet to the fire: bankers, lobbyists, senior government officials and, yes, even presidential aspirants.

A lot of people read that note as evidence of Clinton's fear of Warren, but the reality is different: Warren's focus on bread-and-butter economics is good for Clinton. It's setting up a test with Democratic primary voters that Clinton can pass, while keeping focus off the issues where Clinton really does disagree with many liberals. Warren's rise in the Democratic Party helps Clinton, and so Clinton is encouraging it.

Why President Clinton would be good for Elizabeth Warren

In his profile of Elizabeth Warren, the New Yorker's Ryan Lizza quoted a Warren adviser who argued that Warren "can get Hillary to do whatever the hell she wants. Now the question is, will Hillary stick to it if she gets in? But at the moment Elizabeth can get her on record and hold her feet to the fire."

On some level, this may not be as difficult as Warren's adviser worries. Political pundits tend to underestimate how frequently presidents follow through on their campaign promises. Getting a candidate on the record during a campaign holds more power than most realize.

But it also speaks to another way in which the Warren-Clinton relationship could become symbiotic: Clinton is exactly the kind of president Warren can push, and Warren is exactly the kind of figure Clinton needs pushing her.

If the country elects a Republicans as president, Warren's influence on that administration will be minimal — President Scott Walker will not much care what Warren thinks, nor will he need her vote.

And if the country elects a president beloved by liberals — like Obama in 2008 — the White House wouldn't need much from Warren. Indeed, that president might usurp Warren's nascent role as the leader of the liberal wing of the Democratic Party.

But Clinton hits the sweet spot for Warren. She's mistrusted by many liberals, so she won't take that role from Warren, and she'll need liberal validators like Warren who can go to the left and say whether a deal is worth making. Clinton, in other words, agrees with Warren enough, and will need Warren enough, that Warren might actually have some power to push her presidency.

And Warren might help Clinton, too. Even if Clinton wins the White House, she'll almost certainly be facing a Republican House — if not a Republican Senate, as well. And just as Speaker Boehner has spent the last four years using the specter of Tea Party defections to force concessions from the Obama administration, Clinton will need a bloc of Senate liberals that she can use as evidence that she's got a left flank willing and able to scuttle a bad deal. Warren has spent the last few years building just that kind of credibility. As Lizza writes:

Warren’s two biggest confrontations have been over Obama nominees whom she saw as too oriented toward Wall Street. While she was setting up the new consumer agency, Warren learned how the decision-making process works for high-profile nominees, and she knew from her own experience that, if Congress creates enough of a problem for a nominee, Obama will abandon him or her.

Warren ended up destroying Larry Summers's chance at becoming Federal Reserve chair and Antonio Weiss's nomination as undersecretary for domestic finance at the Treasury Department. In doing, she's angered the Obama administration — but she also proved that a Democratic president actually needs to win liberal support in the Senate, and Republicans know it.

None of this is to say Warren and Clinton are likely to have an easy relationship. For all the public compliments, there's little warmth between the two pols, and Warren has never forgiven Clinton for voting for the 2003 bankruptcy bill. But Warren and Clinton are bound by something that, in Washington, is more powerful than affection: self-interest.