Is Taylor Rule relevant at zero-bound?

David Altig does not appear to be convinced and he makes an impressive case.

He points to Glenn Rudebusch's (also here) description of the Taylor Rule

"The resulting empirical policy rule of thumb—a so-called Taylor rule—recommends lowering the funds rate by 1.3 percentage points if core inflation falls by one percentage point and by almost two percentage points if the unemployment rate rises by one percentage point. As shown in Figure 2, this simple rule of thumb captures the broad contours of policy over the past two decades."

As David Altig notes, economists like Brad De Long have pointed to the shaded area in the aforementioned graphic indicating the "difference between the current zero-constrained level of the funds rate and the level recommended by the policy rule" as representing the considerable "monetary policy funds rate shortfall, that is, the desired amount of monetary policy stimulus from a lower funds rate that is unavailable because nominal interest rates can't go below zero".

There have been widely varying estimates of what the federal funds rate should by according to the Taylor Rule - minus 0.955% now (using CBO data on Taylor’s formula of 1.5 times the inflation rate, plus 0.5 times the gap between the economy’s potential growth rate and the current pace, plus 1), minus 4% for 2010 (Macroeconomic Advisers), minus 5% at the end of 2009 (San Francisco Fed), minus 5.8%for 2009 and minus 9% by December 2010 (Jan Hatzius, the chief US economist at Goldman Sachs).

They claim that since nominal funds rate cannot be lowered below zero (though negative interest rates are possible), these large estimates of negative interest rates demands much more aggressive monetary expansion than what the Fed has been doing. Though the Fed has dramatically expanded it balance sheet, more than doubling it to $2 trillion, by pumping in money through purchases of Treasuries, mortgage securities and agency bonds, economists doubt whether they’ve done enough to meet the Taylor formula.

Apart from expanding its balance sheet to lower the cost of capital and credit availability to businesses and households, the Fed has also been buying long-term securities in the open market in an effort to keep the important long-term interest rates at lower levels. As Glenn Rudebusch writes, "The idea is that, even if the funds rate and other short-term interest rates fall to the zero lower bound, there may be considerable scope to lower long-term interest rates."

David Altig feels that the Taylor Rule assumption about the normal chain of transmission from the funds rate to other interest rates and asset price, is doubtful in the present conditions. He thererfore concludes that instead of rigid adherence to the Taylor Rule, the extraordinary circumstances now dictate that Central Banks follow a monetary policy that draws in a much more broader scope of policies and an "array of interest rates". He feels that even if the the Taylor-rule is followed, the "monetary policy funds rate shortfall" should be recast in terms of the real funds rate.

John Taylor though rejects all of them and argues that economists calling for negative interest rates are using "projections to apply the rule in ways he never intended". He clarifies that "the Taylor rule says what the interest rate should be now, given current numbers" and it cannot be applied to forecasts. He points to fed federal funds futures, which project a target rate of 0.5% by February and 1% by a year from now.

Update 1
The data file on teh aforementoned graphic is available here. Paul Krugman (also here and here) uses the Rudebusch Rule to argue that the clamour for raising rates are way too premature.

Update 2
See Brad de Long here on the debate about interpreting the Taylor Rule, which revolves around the value of the coefficient on the output gap. Brad uses an estimate (as estimated by Glenn Rudebush) of the coefficient that is higher than Taylor's orignal estimate. Taylor has rejected this here and here.

John Taylor has claimed that his coefficiencts were derived not from statistically fitting of historical data, as was done by Rudebusch, but from existing monetary theory and models.

What adds to the confusion is the lack of any form of consensus about what constitutes the output gap.