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This controversial theory has got Janet Yellen worried

In a speech on Friday, Federal Reserve chair Janet Yellen stayed her dovish course, maintaining that an increase in the federal funds rate "may well be warranted later this year." She also emphasized the Fed's data dependence, as well as her general tone of "cautious optimism" in the economy.

Yet it was in her discussion of what she termed "special risks and other considerations" where things got interesting. The first of her three special concerns around hiking rates run along the following lines:

"Some recent studies have raised the prospect that the economies of the United States and other countries will grow more slowly in the future as a result of both demographic factors and a slower pace of productivity gains from technological advances," the Fed chief stated.

Read MoreYellen: Rate increase 'may be warranted later this year'

"At an extreme, such developments could even amount to a type of 'secular stagnation,' in which monetary policy would need to keep real interest rates persistently quite low relative to historical norms to promote full employment and price stability, absent a highly expansive fiscal policy," she added.

To take a step back, "secular stagnation" refers to the rather controversial theory that an economy may become stuck in a long-term period of slow growth and low interest rates, due to certain external factors.

A troubling theory makes a comeback

Janet Yellen
Joshua Roberts | Reuters
Janet Yellen

Originally developed in the late 1930s by Alvin Hansen (who earns a footnote in the official transcript of Yellen's speech), it was reanimated by former White House economic adviser Larry Summers, who in 2013 asked whether the U.S. may be mired in secular stagnation.

Interestingly, Hansen's theory was that a lack of technological innovations could be to blame for the stagnation; Summers, however, was more focused on an exogenous shock.

In April 2014, Brown University economists Gauti Eggertsson and Neil Mehrotra published a comprehensive model of secular stagnation, showing how income inequality and a drop in population growth could lead the economy's ideal interest rate to fall.

Essentially, Eggertsson's point is that a surplus of individuals looking to save their money, combined with a paucity of individuals looking to borrow money, can lead the market-clearing interest rate to fall to unusually low levels.

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If the actual interest rate is too high (say, because it is at historically normal levels) then money will not flow from the would-be providers of income to the potential users of income. That would cause an economy to become mired in slow growth for longer than the economic cycle would predict—consequently making the stagnation secular rather than merely cyclical.

That would appear to have implications for Fed policy. For the central bank, the prescription is a familiar one: Keep rates lower for longer, as Yellen noted in her comments on Friday.

While the concept may sound obscure, the prospect is a scary one fraught with pitfalls. The most prominent modern example of a country suffering from secular stagnation is Japan, where a "lost decade" quickly morphed into 20 years of fallow growth.

For her part, Yellen was careful to frame secular stagnation as a risk rather than her base case. Indeed, the theory still remains far outside the mainstream.

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Even uber-dove Narayana Kocherlakota, the non-voting Minneapeapolis Fed president (whose economic work was actually cited in the Eggertsson paper) told reporters in January that prolonged stagnation is a risk that "we should be thinking about as policymakers, but it is in no way my modal outlook."

Still, the critical point Yellen is making is that the mere fact that America risks falling into the economic quicksand "has important monetary policy implications for the near-term." On the margins, however, it may be enough to stay the Fed's hand when it comes to raising rates.

It should be noted that like most economic concepts, secular stagnation is politically polarizing.

Last year, some members of Congress proposed legislation that the Fed should endeavor to follow the "Taylor rule," which mandates the Fed base monetary policy on specific economic measures.

Yet the proposed legislation assumes (implicitly, given the inputs to John Taylor's equation) that the equilibrium real interest rate is 2; Yellen said Friday that she believes it is lower.

If we are in a world marked by secular stagnation, the neutral rate is even lower than Yellen already thinks it is. In such a world, if the Fed begins to act as if the equilibrium interest rate is higher than it actually is, it could result in "appreciable economic costs." That may create or elongate a secularly stagnant environment, she said.

In other words, the economy is a delicate and temperamental beast. That creature—in the view of Yellen and other Fed officials—is best handled by the professionals.

—By CNBC's Alex Rosenberg.

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