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The odds of an interest rate hike have begun to shift in a new direction

Just as Washington is gearing up to goose the economy, the Federal Reserve could be teeing up an interest rate increase that could put a damper on things.

The chances that the Fed will hike rates at its March 14-15 meeting have been creeping higher in recent days. By at least one estimate, the probability is now at 50 percent, after being in the teens just last week.

"This is what the Fed wanted," said Peter Boockvar, chief market analyst at The Lindsey Group. "Now, the Fed may not raise, but they wanted at least the flexibility to do it."

Central bank policymakers in the past have been loathe to tighten policy when the market is not anticipating such a move. The Fed last hiked in December, at a time when officials had telegraphed a move and the market had almost completely priced it in.

Hawkish statements in recent days appear to have pushed up the chances.

A summary released last week of the Jan. 31-Feb. 1 meeting revealed that members anticipated a hike "fairly soon," as long as economic data and financial conditions cooperated.

Then, Dallas Fed President Robert Kaplan said Monday that recent comments he has made that a hike should come sooner rather than later should be construed as meaning "in the near future." (Kaplan will be interviewed live by CNBC on Tuesday.)

The combination of events has translated into a coin flip of a chance for a March rate hike, according to Boockvar's calculations.

'Peak easing' could stall growth

Boockvar's math goes like this: The Fed's current short-term rate target is 0.5 to 0.75 percent, which would make the midpoint 0.625 percent. The April funds contract indicates a 0.75 percent funds rate. Given that the contract is exactly half way to another quarter-point move, that would put the chances at 50 percent.

To be sure, Fed watchers use a variety of equations to calculate the funds rate, and the CME's tracking tool, to cite another prediction, gave March only a 31 percent chance Monday afternoon.

Whichever calculation investors wish to buy, it's clear that March is at least on the table for a move, though far from a certainty.

A faster-moving Fed, coupled with curtailed easing from the European Central Bank and Bank of Japan, could have negative implications for global growth, Boockvar said.

"I've been describing this year as an unfolding tug of war between the tail wind of hoped-for tax and regulatory relief against the headwind of a tightening Fed and ECB and BOJ," he said. "Global central banks, in my opinion, have reached peak easing, and this year we are going to see a pullback from that. I think that really matters."

Fed Chair Janet Yellen and Vice Chair Stanley Fischer both are due to speak Friday in the last bits of Fed speak before the meeting. Boockvar said the speeches will be critical to anticipation of whether March in fact features a hike.

Watch: Boockvar on the markets