First, there is the issue of determining the right inflation rate to use in the rule. The best is still the core PCE which is the preferred measure by the Fed. Second and more importantly, there is the issue of measuring the output gap. There is significant disagreement on how to measure this gap and how to form an effective real time measure. The Fed numbers are not available to the public and the CBO estimates may have significant forecast error. You have to know actual and potential GDP to find the gap. Third, there is a disagreement on the weights that should be applied to the rule. This is the measure of the reaction function. Bernanke stated that he thinks the reaction function to output gaps should be higher than what was used by Taylor. Small changes make a big difference on whether monetary policy was wrong in the 2000's. Finally, there is the measure of the equilibrium real rate of interest. Taylor assumes a long-term real rate of 2%. If the natural real rate has fallen, you will get a different policy answer.
Nevertheless, the Taylor Rule framework can be used to help focus any interest rate discussion. When new data comes out, the question is simple. Does it effect inflation, the output gap, or the equilibrium rate of interest.
The graphs above show the original Taylor Rule versus an adjusted Taylor Rule with a different inflation measure and output gap weight. It tells different stories, but it is clear that rates should be higher and the Fed should be taking some action.