Investors are closely watching Europe this week, but it's not President Obama's European trip that is getting the most attention. The market is transfixed on what the European Central Bank (ECB) will decide at its policy-making meeting this Thursday, and that could be very dramatic.

The ECB could announce a negative deposit rate for money that banks park with the central bank overnight, or cut its refinancing rate, or both. A negative interest rate would be highly unusual and would essentially mean that the ECB would charge banks a low interest rate, probably around 0.25%, for the money the banks deposit there. The purpose of that or any other new move by the ECB will be to revive economic growth, which has been sluggish.

Related: ECB has room to move in deflation fight: Marc Chandler

A new report released Monday showed that manufacturing activity slowed more than expected in several European Union nations including France, Italy and Austria. Germany's manufacturing index fell to a 7-month low.

Mark Dow, a former economist at the IMF and U.S. Treasury, says no matter what the ECB decides this week, the impact is likely to be limited.

"The transmission mechanism is broken; the banks still have to deleverage," says Dow, who is also the author of the "Behavioral Macro" blog. "Demographics are working against them ... they can signal that they want to do something ... even lowering the value of the Europe doesn't do a lot ... because exports are such a small share of GDP."

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The impact of any ECB policy will not be as effective as the Fed's quantitative easing policy because the European situation is much more complicated, Dow notes. While there is one central European bank, there are multiple sovereign European governments, with their own their individual economic policies, and multiple government bond markets.

And there is lots of European debt. "There's no way for them to grow at the rate necessary to get out from under the debt burden they have built up," says Dow. He expects deflation and negative growth in Europe, and that could disappoint financial markets that have built up expectations in anticipation of the ECB's next move.

As for the U.S. bond market, Dow says it's conceivable that yields, which have been falling to unexpectedly low rates, could continue to decline, but he's not convinced that they will.

"At these levels it doesn't make a lot of sense to be long bonds if you don't have to be," Dow says.

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