The most recent salvos in the Fed's culpability for the global financial crisis are centered on a reasonably esoteric debate over the Taylor rule. Ben Bernanke recently defended Fed policy choices by pointing to how monetary policy was in fact not massively inconsistent with a Taylor rule, when inflation forecasts (as opposed to observed inflation levels) are used to determine the inflation gap. John Taylor continues his skewering of the Fed by making clear that measurement issues are insufficient to absolve the Fed from its substantial errors in deviating from the rule, and that in any case using the Fed's inflation forecasts were faulty to begin with.

To better understand the contours of the debate, it is helpful to recall a (very simplified) version of the Taylor rule:

i = A + b*(inflation gap) + c*(output gap),

where i is the policy interest rate, A is a constant term, and b and c are positive parameters. The inflation gap is the difference between the central bank's target inflation and the actual inflation rate, and the output gap is the difference between the economy's current and potential levels of output.

Laid out in this way, the different dimensions of possible disagreement immediately become clear:

- Disagreement over gap measures: Although it is abundantly clear what the inflation and output gaps are in theory, in practice, there is a need to operationalize the gaps with appropriate measures of inflation and output. This is the crux of Bernanke's most recent defense; more precisely, he claimed that inflation forecasts, as opposed to contemporaneous CPI, were a superior measure. However, as David Papell so accurately points out, this is a red herring. The source of Bernanke's different implied Taylor rule rates stem from the use of core PCE inflation, as opposed to headline CPI inflation. Indeed, using the GDP deflator yields yet different Taylor rule recommendations.
- Disagreement over parameter values: This is an empirical question, although it can be seen as a specification issue as well. Glenn Rudebusch has previously argued that using a slightly different specification of the Taylor rule---mainly by allowing some difference to the original Taylor parameters, but also accompanied by tweaks to the functional specification---it is possible to show that the Fed's errors of commission over the pre-crisis period were not that great after all (technical version here).
- Disagreement over specification: This is, implicitly, the second part of Bernanke's defense, where he claims that controlling capital inflows may have been more important for addressing housing bubbles (and since interest rates influence capital inflows into the economy, this implies that the simple version of the Taylor rule may be suffering from an omitted variable).