It's a debate the two famed economists have carried out in print since Taylor presented his theory at a 2007 Jackson Hole conference. Greenspan and Taylor met to debate in person for the first time Tuesday night on CNBC's "The Kudlow Report."
In late 2001, Greenspan lowered the federal-funds rate to 1.75 percent from 6.5 percent and lowered the rate again to 1 percent in mid-2003, where it held for a year. The Federal Reserve began raising the fed-funds rate incrementally for the next two years before beginning to lower them again in 2007.
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According to Taylor's eponymous rule, the Fed would have moved rates up earlier and by a larger amount. Greenspan's then-unconventional policy exacerbated the housing bubble that saw home prices "going through the roof," Taylor said. "You can see the bubble started to increase at a more rapid rate around that time."
Taylor also said rising inflation was another sign the funds rate was being held too low: "The funds rate was 1 percent when the inflation rate was already 2 [percent]. In 1997, Alan was also the chair, the funds rate was about 5 percent when the inflation rate was 2 percent. You don't have to have a Taylor Rule to see it was too low by that time."
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Greenspan said it was exactly the right thing to do and if he had to do it over again, he wouldn't change a thing.
"There is no evidence that the actual price levels of homes was significantly affected by the action which we took," Greenspan said. "Human nature being what it is, if you have very successful policy of stabilizing the economy, you are invariably rewarded with a bubble."
The former Fed chairman said that, prior to 2003, there was a high correlation between short-term rates determined by the Fed and the long-term rates that effectively determine home prices. However, he said the correlation since then is zero.
"There's been a complete disconnect between what the Federal Reserve is doing in monetary policy, and the long- and short-term rates," Greenspan said.
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But Taylor said there's really no evidence that suggests there is a disconnect between long-term rates and the Fed's short-term target.
"If there was any disconnect, it was because of the policy of these very low rates, so unusual, so different than the policy that worked well in the '80s and '90s," Taylor said.
On one point, the two economists agree: It's time to unwind the current Fed's policy of bond buying, known as quantitative easing.
"I think they should slow down," Taylor said. "This is a good opportunity. I don't think it's been much good, so it's time to get back as quickly as possible to normal policy."
"I think it's about time," Greenspan agreed. But, he said, the policy's full economic impact will only be known in time: "Overall, it's going to be history's evaluation as to whether this particular, very innovative procedure has worked," Greenspan said.
— By Krista Braun