Trump’s claim is that were it not for the election and Yellen’s allegiance to President Obama, who appointed her, the Fed would be raising the interest rate they control to slow the economy. If they were to do so, that would hurt Obama and, by proxy, Hillary Clinton, and thus help him.

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In a recent news conference, Yellen directly responded to earlier such claims by Trump:

“Congress very wisely established the Federal Reserve as an independent agency to insulate monetary policy from short-term political pressures. I can say emphatically that partisan politics plays no role in our decisions about the appropriate stance of monetary policy. We do not discuss politics at our meetings and we do not take politics into account in our decisions.”

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I suspect a Trump supporter would argue, “Well, of course that’s what she’d say.” Trump’s accusation is unprovable either way. So how do I know he’s wrong?

First, as I and many others have argued repeatedly, there’s little rationale for a Fed rate hike. They’ve missed their 2 percent inflation target on the downside every month for four years running. Inflationary expectations 10 years out also remain below 2 percent. In fact, Trump consistently argues that economic growth is “pathetic,” meaning his own “analysis” makes the opposite case: The Fed should continue to hold rates where they are.

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Second, economists at Goldman Sachs recently looked at the question of the Fed’s actions around elections by reviewing transcripts of the meetings wherein they make the interest rate call. They found “scant discussion of the effect of election timing on policy decisions, but what discussion does exist suggests that the [Fed] has felt free in previous election years to take the appropriate action but has been somewhat cautious about the public perception of political influence.”

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That last bit is important. In the interest of avoiding any perceptions of politically motivated policy moves, the Fed appears to be careful not to act around elections: “While there is no sign of an election influence on policy decisions in election years overall, the October meetings preceding the election do appear to be slightly less active than other meetings, with rate changes in October occurring in only 2 of 13 election years back to 1964; in both instances these were rate cuts.”

In other words, given his own assessment of the economy, actual conditions on the ground and the Fed’s history around elections, Trump is wrong.

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Still, while some observers probably were aghast that he would bring the Fed into the discussion at all, I disagree. No question: Political independence is absolutely one of the Fed’s most critical attributes. But that’s no reason such an important public institution — one with such a large impact of people’s lives — should be off limits in political debates.

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If that sounds contradictory, let me clarify. The Fed is a political institution, created by our political system, which gives it immense power to set interest rates through controlling the money supply. Top Fed officials are appointed by the president and approved by the Senate.

Moreover, the power our system vests in the Fed gives them the ability to significantly affect the economic lives and living standards of all Americans. If they decide to target inflation rather than full employment, i.e., raise rates to slow the economy, that can increase the overall unemployment rate a bit but the African American unemployment rate much more. To be clear, I’m not saying they should never target inflation. I’m saying that Fed actions have big winners and losers.

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If they fail to adequately regulate financial markets, as was the case when the housing bubble was inflating, that can engender huge costs for those most vulnerable to recession, again, the poor and middle class.

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So it’s at least potentially a plus in my view that presidential aspirants are talking about the Fed, including Bernie Sanders and Clinton herself, as she has argued for replacing the bankers that have long led the powerful 12 regional Fed banks with more diverse, representative stakeholders.