Efficient markets?

Does FED statements actually have any informational value? Or should they have?
A comment by Greg Mankiw

Fundamentally, Fed watching is a symptom of ambiguity in monetary policymaking. Fed insiders do not have significantly more data on the economy than everyone else. When financial markets react to Fed statements, therefore, they are not incorporating news about the economy. Instead, they are incorporating news about policymakers' intentions. So if a speech or testimony by a Fed official moves financial markets, it means that the intentions of monetary policymakers were not clear before the speech or testimony.
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Macroeconomic data would move markets; remarks by Fed officials would not.

The ideal would be a completely boring Fed chairman whose speeches are regularly ignored by financial markets. Apparently, we are not there yet.

Further applications... The value of stock analysts etc.