By Howard Schneider and Ann Saphir

WASHINGTON (Reuters) - For much of this year, the dollar, oil prices, and economic conditions largely behaved as the U.S. Federal Reserve had expected, allowing policymakers to plot further interest rate increases.

Not anymore. Since Britain's June 23 vote to leave the European Union, every piece of economic, such as Friday's jobs report, data comes with a question mark - how much does it reflect domestic economic developments and how much the short and long-term implications of an economic reordering that may take years to play out.

For Fed policymakers it means balancing the mainly positive flow of U.S. indicators against the risk that major trading partners fall into recession, the dollar surges again, or the terms of Britain's divorce stress the global financial system.

With past overseas events of similar importance, such as the euro zone debt crisis, it has taken the Fed months to get clarity. Brexit may prove just as difficult to decipher, already helping lift the dollar and drive U.S. Treasury yields to historic lows - both trends making it harder for the Fed to move.

"You don't know how long that is going to last and indeed we don't know the magnitude," Federal Reserve Governor Daniel Tarullo said on Wednesday. "I doubt there will be a moment where people say, okay, Brexit is done."

Britain's decision comes at time when the Fed has grown more sensitive to international events, postponing what seemed to be imminent rate increases twice since last summer because of events far from U.S. borders. In minutes of the June meeting, released on Wednesday, policymakers explicitly tied consideration of further rate increases to "additional data on the consequences of the UK vote".

No one expects the United States to slip into a recession because of Brexit. However, recent research by the Fed, the Bank for International Settlements, the International Monetary Fund and some private economists has raised the possibility that the Fed may be fundamentally constrained by outside events, like the UK vote, that have made recovery slow and the Fed's inflation goal elusive.

The dollar appears to have become more sensitive to global economic conditions, and its rapid rise since 2014 has curbed U.S. exports and upended the Fed's inflation outlook. Long-term U.S. bond yields, which remained near record lows on Wednesday, have grown more sensitive to global capital flows and less to Fed policy. Even the Fed's key estimate of a neutral rate of interest may be anchored by such rates in Europe and other, slower-growing, developed economies.

If the past is any indication, uncertainty surrounding Brexit could fog the lens for months to come. In mid-2011, when Italian bond yields spiked amid renewed concerns about the euro zone's future, the Fed added to its statement that "strains in global financial markets" had created "significant downside risks to the economic outlook."

CLOUDY BALL

The Fed kept the language for 16 months, until well after the European Central Bank had intervened with a forceful pledge to keep the currency union intact.

"I would suspect they are really struggling how to decipher short versus long term, and also what is happening in the U.S. domestic economy," said Beth Ann Bovino, chief U.S. economist for S&P Global Ratings. "I would say the Fed's crystal ball is very, very cloudy."

If the U.S. economy keeps growing and creating jobs as expected, the Fed's job will become easier, said San Francisco Fed senior vice president Mary Daly. But any misses will raise questions whether the causes are domestic or can be traced back to events such as Brexit, and if so, whether they will act as a temporary drag or could mark a fundamental shift in the global economy.

The IMF, which is expected to cut its global growth forecast in a mid-July update, is already factoring the Brexit vote into its analysis. In a report on Germany released this week, the IMF noted that the strong trade and financial linkages between Europe's largest economy and the UK had the potential to "derail the growth momentum" in a country whose success is central to lifting eurozone growth, and, in turn, helping the world economy grow faster.

The San Francisco Fed's Daly said any surprises would prompt policymakers to go back to the Fed's models and search for domestic or international causes.

"We are watching this carefully," Daly said in an interview. "If the data don’t evolve as we think and we don’t get consistent job growth as we think, then of course we would say, it looks like another step down."

Investors, who earlier this year had taken the Fed's cue that a rate increase could come in June, have now pushed expectations for a policy move deep into next year.

Ken Matheny, senior economist at Macroeconomic Advisers, said he expected Brexit to nick U.S. growth, but that was all investors and policymakers will be able to say for a while.

"I am not sure that in six months we will know. Maybe we will have some understanding of what the settlement will be between the eurozone and the U.K., but even if we know the settlement do we know the economic impact? I am not sure."

(Reporting by Howard Schneider and Ann Saphir; Editing by Tomasz Janowski)