Three or four mistakes?
As it happens, Bob Barbera and I have written a few papers on just this question. We criticize the standard practice of measuring the gap between the actual rate and the natural rate of interest by comparing the real federal funds rate or the real interest rate on say 10 year treasuries to long-run averages of those quantities. The interest rates that matter for the economy are risky rates such as the yield on Baa corporate bonds. Monetary policy should be measured according to where something like the Baa bond is relative to its long-run average.
The graph below shows how policymakers might be misled by looking at the real fed funds or Treasury rate rather than the Baa bond rate. In the graph, the blue line is the real federal funds rate (fed funds rate minus previous 12 months PCE inflation) relative to its average over 1970-2009; the red line is the analogous figure for the 10-year Treasury rate; and the green line is the analogous figure for the Baa bond yield.
As the economy slipped into recession in 2001, the Fed reduced the federal funds rate dramatically. By early 2003 the real federal funds rate was more than three percentage points below its normal value (which you could take as a very crude estimate of the "natural" fed funds rate). The real Treasury rate was also more than a percentage point below its "natural" rate. By either of these measures policy was very stimulative, so why was growth so sluggish? The answer is that the real Baa rate was still close to its normal (neutral, natural) level; policy was not in fact very stimulative, once you took account of the risk premium on corporate bonds. (The risk premium was high during this period because of the fallout from the Enron and related scandals, 9/11, the wars in Iraq and Afghanistan, and the recession.) The correct policy response was to lower interest rates further, but the Fed's ability to do this was limited by the fact that it was already very close to the zero bound on the nominal federal funds rate.
Recovery began in late 2003 when the real Baa rate fell into expansionary territory. By 2004 it was clear by all measures that policy was very stimulative, and the Fed began to raise the federal funds rate. It's repeated increases in the federal funds rate, however, were not aggressive enough to push the Baa rate up. The overly expansionary monetary policy in this period added fuel to the fire of the housing bubble that was already underway.
By mid-2006 one could argue that the federal funds rate was about at its neutral level, so that monetary policy was appropriate. The real Baa rate, however tells a different story: it was still over a percentage point below its neutral level, fueling excessive growth and speculation.
The Fed would have done better, Bob and I argue, had it paid attention to what was happening with the Baa rate - in particular, the spread between the Baa rate and 10-year Treasuries. This is shown in the graph below. In 2006-07 the Baa-Treasury spread (blue line) was considerably below its long-run average of two percent and even further below the moving average line in red. As Hyman Minsky argued long ago, excessively low risk premia are characteristic of the "ponzi finance" phase of the business cycle that precedes the crash. Bob and I argue that the correct policy strategy is to adjust the nominal federal funds rate one-for-one with the credit spread; had the Fed followed this policy it would have raised the federal funds rate by a further 50 to 100 basis points in 2006. (Note: the graph also suggests that monetary policy should have been tighter in late 2007 and early 2008, which would clearly have been disastrous. This is due largely to the spike in inflation that occured in that period, which reduces the real Baa rate as I've measured it. If you ignore the spike in inflation, monetary policy looks close to neutral in late 2007-early 2008.)

So I think the Fed's mistake occurred in the period 2004-06 when it neglected to raise the federal funds rate sufficiently to offset the shrinking risk premium on corporate bonds. Having said that, however, I have to acknowledge that in 2004 I criticized the Fed for raising interest rates when the economy had not yet recovered from the recession. In fact, I had a brief discussion with Paul Krugman at a conference in September 2004 in which he expressed puzzlement at the Fed's apparently aggressive actions. Smart people (I'm referring to Krugman here, not me) would not necessarily have avoided Greenspan's mistake.





