A decision by the United Kingdom to leave the European Union could have "significant repercussions" in the U.S. and elsewhere, Federal Reserve Chair Janet Yellen told the Senate banking committe on Tuesday.

Exactly what they might be is unknown, which is a big part of the challenge.

"It's a very important relationship, and it would be significant for the United Kingdom and for Europe as a whole," Yellen said during the first day of her semi-annual testimony to Congress. "It would usher in a period of uncertainty."

Such uncertainty, fueled by unclear data about slowing growth in China and falling oil prices, caused a grim start to 2016 for global financial markets, though the S&P 500 and the Dow Jones Industrial Average have since rallied. Analysts have speculated that a so-called "Brexit" vote might lead to more of the same. 

The United Kingdom, which has close ties to the U.S., is now the second-largest economy in Europe, and many U.S. companies have based regional operations there. Additionally, the U.S. might lose some of the influence it has with Europe through its traditionally close ties with Great Britain.

"There could be a period of market volatility that would affect financial conditions and the U.S. economic outlook," Yellen said.

Last week, the central bank chair cited the U.K. vote, scheduled for Thursday, as one of the reasons the Fed's monetary policy committee opted against raising interest rates in June, despite speculation by several members that it might do so. The Fed is still projecting two increases this year, half its original expectation, which would build on a 25 basis-point hike in December and might take short-term rates to a range of 0.75% to 1%.

That's still slower than many banks might like. Companies from JPMorgan (JPM) - Get Report to Bank of America (BAC) - Get Report , Wells Fargo (WFC) - Get Report and Citigroup (C) - Get Report have seen interest income curbed by years of low rates, which remained at nearly zero for seven years ater the 2008 financial crisis.

Monetary policy committee members now anticipate a pace of three hikes each in 2017 and 2018, which Yellen said would take rates as high as 2.5%.

Short-term rates are "likely to remain, for some time, below the levels that are expected to prevail in the longer run because headwinds -- which include restraint on U.S. economic activity from economic and financial developments abroad, subdued household formation, and meager productivity growth -- mean that the interest rate needed to keep the economy operating near its potential is low by historical standards," Yellen said Tuesday.

Investment bank Morgan Stanley predicted last week that the Fed would raise rates only once this year, in December. "Looming risks and 'Brexit' in particular, have paralyzed the Fed," Ellen Zentner, an economist with the New York bank, said in a note to clients.

The fallout of such a move would likely include a weaker British pound, lower productivity and tougher terms for international trade, the Bank of England's monetary policy committee noted at its June meeting.

"An increasing range of financial asset prices has become more sensitive to market perceptions of the likely outcome of the forthcoming EU referendum," the committee said. " The outcome of the referendum continues to be the largest immediate risk facing UK financial markets, and possibly also global financial markets."

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