Your memory is failing you. Greenspan starting raising rates in 1998 stating it was due to "irrational exuberance" in the markets. He should have been fired that day. His job description is not to destroy the market and create recessions. Greenspan continued to raise rates from late 98-2000. He should have been lowering the rates, we were in a deflationary spiral. He created the nasdaq bubble. Every rate raising was responded with higher prices. People dumped dow stocks which had debt and bought tech stocks which had none.So he's raise them again, and they'd go higher still. The crash catalyst was Clinton's attempted government takeover of MSFT. The day they lost the court case, the crash started. All Greenspan had to do was nothing, or lower rates and the world would have different.
Actually, my memory is quite good, thank you very much. For instance, Mr. Greenspan made his irrational exuberance remarks in 1996, NOT 1998:
http://www.pbs.org/newshour/bb/economy/december96/greenspan_12-6.html
That said, my point was that even though the economy was clearly overheating -- your suggestion that we were deflating during this period is inaccurate -- and the tech bubble was pumping up, Mr. Greenspan chose not to raise rates in December of 1999 due to Y2K fears, and didn't raise them at the January meeting either. Instead, he waited until February of 2000 to continue the tightening that had begun a few years earlier. My belief is that if he had raised rates immediately in January -- maybe by a half a point -- the last 2000 points of the NASDAQ may never have happened.
Regardless, I guess I'm having a hard time understanding your logic. Are you suggesting that the Fed raising rates in the late 90's caused the stock bubble? So, if rates had been lower, people would have been less inclined to buy stocks, and the tech bubble wouldn't have happened in your view?
As for whether the Fed should be concerned with stock valuations, as stocks are a leading economic indicator, certainly this should be a factor under their consideration. However, it probably isn't appropriate for the Fed chairman to be making such statements.