He was juicing the real estate market before the aughts, and he was even warned before the aughts. There are clear indications and evidence that he did that with designs.
I think the general consensus is that Greenspan was an ideologist and effectively a useless Fed chair since he didn’t believe in regulation. The only reason he was probably not ousted was because he had enablers with the added leverage that the economy was doing pretty well during his tenure.