Who would Hillary Clinton tap to run her economic agenda?

The presidential election isn't until November, and obviously who knows what will happen between now and then. But Hillary Clinton is building up an impressive lead in the polls over Donald Trump. And as the old adage goes, there are few things the D.C. media likes more than wild speculation. So people are already floating names about who Clinton might pick to fill out her team: the cabinet secretaries and other positions that will help her carry out her agenda.

The speculation is even more interesting than usual: First off, Clinton reportedly intends to make history by filling half her Cabinet with women. And second, the left wing of the Democratic Party that flocked to Bernie Sanders will be watching these picks like a hawk, to get a sense of just how far Clinton is willing to take her fledgling alliance with Sanders' movement.

So from an economics perspective, what are the most important positions to be watching, who might Clinton pick, and what would that tell us?

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Here's a quick sketch:

Treasury secretary: The head of the Treasury Department is usually the president's most influential economic advisor, one who plays a key role in formulating and executing things like financial regulation and other big-ticket economic policy. Former Treasury secretaries engineered the bank bailout in 2008, or worked with international bodies to deal with economic crises and enforce austerity around the globe. So this is the 800-pound gorilla in the room.

Probably the most dramatic name being tossed around for this spot is Elizabeth Warren, the Harvard professor and Massachusetts senator who is an influential and fiery critic of the depredations of the financial industry. The Sanders movement and the left would probably find this pick very encouraging, and Wall Street would likely be horrified for exactly the same reason. But so far, Warren herself says she thinks she can keep doing the most good where she is.

Another possibility is Lael Brainard, who currently serves on the Board of Governors of the Federal Reserve. Less is known about her political inclinations than Warren's. She was a deputy in Bill Clinton's White House — an era that is not especially beloved by leftists — but that doesn't necessarily say much about her own views. And she's played a key role in fighting for the Fed to hold off raising interest rates, which aligns her with many left-leaning economists.

Then there's Gary Gensler, a former chairman of the Commodity Futures Trading Commission (CFTC), and a former official at Goldman Sachs. The latter position might not endear him to Sanders' followers, but at CFTC he was instrumental in bringing new regulatory force to bear on things like financial derivatives. Liberal economists sound positive on him.

Other names floating around include Sarah Bloom Raskin, currently second-in-command at Treasury, and even former Facebook COO Sheryl Sandberg.

Director of the National Economic Council (NEC) and the Council of Economic Advisors (CEA): The director of the NEC heads up a group of key economic officials in the executive branch, tasked with helping the president put together and implement economic policy. The CEA is a three-person group that does just what it sounds like: Advise the president on the economy. They release a lot of analysis, too.

"The fact is that progressive economic ideas won't even reach the president if the team is in the traditional economics mode of thinking small, ignoring market failures, bubbles, under-regulating, etc," Jared Bernstein, a senior fellow at the Center on Budget and Policy Priorities and former chief economist to Vice President Joe Biden, told The Week.

Less has been said about Clinton's possible picks here, but Gensler might wind up here if not at Treasury. Another name might be Dani Rodrick, a professor on international economics at Harvard, who's been willing to consider some unorthodox ideas to repair global capitalism.

Labor secretary: The Labor Department is tasked with enforcing the laws that govern unions and all other workplace issues, so this is another key spot. It's currently filled by Thomas Perez, who would probably have been progressives' favorite pick for Clinton's running mate after Warren. Politico reported that there's chatter that former Michigan Gov. Jennifer Granholm (D) could get the nod: "She'd be someone with reliable liberal credentials who could help both in developing policy and as a surrogate and a salve to the left." Granholm is already on Clinton's transition team.

Commerce secretary: The Commerce Department's purpose is to somewhat vaguely liaison with business, universities, and other groups to promote job growth and improved living standards. So it's not as powerful a position, but it still matters. No serious contenders have emerged yet, though Politico did troll progressives by theorizing Virginia Gov. Terry McAuliffe (D) might get it. A long-time Clinton associate, McAuliffe has gotten himself in hot water before, and most recently made headlines by suggesting Clinton's opposition to the Trans-Pacific Partnership isn't serious.

Agriculture secretary: This may seem like an oddball one to include under economic issues. But the Supplemental Nutrition Assistance Program (SNAP) program — commonly known as "food stamps" — is actually housed under its authority. So the head of the Agriculture Department and his or her deputies are deeply involved in running SNAP, and will be called before Congress to testify on it.

Republicans in the House especially are eager to slash SNAP and other programs that aid poorer Americans. So who Clinton picks for this spot could say a lot about how she intends to approach the question of SNAP specifically and the welfare state in general.

Federal Communications Commission, Federal Trade Commission, and the Justice Department: Again, these may not seem like areas that have a lot to do with economics. But these three agencies are the primary enforcers of antitrust law. That enforcement went through a big shift in the 1980s, when officials decided to interpret antitrust law with a lot less breadth or aggressiveness.

Many progressives now see reversing that change as one of the key battles to be fought against rising inequality and the power of big business. So who Clinton puts in the key antitrust spots for those agencies could also be telling.

Finally, some other big economic names to watch, but who the chatter hasn't associated with any post yet, are probably Christina Romer, Alan Krueger, and Austan Goolsbee. They're all former heads of President Obama's CEA; they're particularly interesting because while they're all viewed as liberal-leaning, they've also had dust-ups with the Sanders movement.

Obviously, for all of these spots, it's just too early to know. But when it comes to speculation, there's no time like the present.