First, does the Fed have an inflation target and are expectations anchored, i.e. are they equal to the target? Yep and yep, see the graph Prof. Delong put up.
Second, what would the impact of a change in the target be? Suppose expectations remain anchored, increasing the target will increase expected inflation, shift the Phillips curve up and we would be right back where we started. More precisely, there would be no change in output and assuming the mechanism behind Okun’s law is invariant to this change in policy, there would be no change in unemployment. (No, I don’t think expectations of inflation are backwards looking, especially now. And even if they are backwards looking, this would increase the chance that changing the target would unanchor expectations. If I did something wrong, my parents were always more pissed if I lied to them about it.)
Third, why might increasing the target unanchor expectations? The Fed could be seen as acting with discretion; that they’ll up the target anytime the public or politicians start whining. Here’s a post explaining why discretion is bad. Its really hard for the Fed to get expectations reanchored.
Fourth, what would be the impact of unanchoring expectations? Inflation would increase and its volatility would be greater. If the public thinks the Fed will do whatever is expedient, they will expect higher inflation. Also, because the Fed’s behavior is less predictable, expectations and actual inflation will be more volatile. High inflation and highly volatile inflation are bad. My bet is that this *permanent* negative effect would be much greater in welfare terms than the cost of the *temporary* high unemployment we’re experiencing now.