Taylor on what the Taylor rule implies for the present situation

Interesting... from John B. Taylor's blog:

"The Taylor rule says that the federal funds rate should equal 1.5 times the inflation rate plus .5 times the GDP gap plus 1. Currently the inflation rate is about 1.5 percent and the GDP gap is about -5 percent (using the average of the seven estimates of the gap provided in the recent update by Justin Weidner and John Williams).

So a little algebra gives a funds rate of 1.5X1.5 + .5X(-5) + 1 = .75 percent.

This number is nowhere near -6 percent, which is what you sometimes hear people say the Taylor rule implies."

I think I've hear the numbers near -6 percent from Krugman, and possibly Delong... the issue, I guess, is that they are not adopting the specific slope and intercept from Taylor's 1993 paper, but are employing some procedure based on economic data for estimating an appropriate slope and intercept---based on "a period during which the Fed has set interest rates too low for too long".

Update: Actually, the Krugman post I was probably thinking of doesn't use Taylor's 1993 rule (which is indeed the one cited in Taylor's post,  which is also (modulo trivial algebra) equation (1) of his 1993 paper:

f = 1 + 1.5 p + 0.5 y,

where p is the inflation rate over the past four quarters, and y is the deviation of GDP from target ("output gap").  It uses Mankiw's "Taylor rule" (this having become a generic term for prescriptions for setting the federal funds rate as an affine (i.e. straight-line, with slope and intercept) function of inflation and the output gap), i.e.:

f =  c p  + c y  + d

where c and d are coefficients to be chosen on some basis, p and y as before.

Mankiw's uses equal coefficients on inflation and the output gap, whereas Taylor's inflation coefficient is thrice its output coefficient.  Krugman fits c and d  to data for 1998--2008.  Thus he does do what Taylor gives as the explanation for the people who get -6%: "they change the Taylor rule, replacing variables or estimating coefficients with data during which the Fed has set interest rates too low for too long."  Presumably Taylor thinks interests rates were set too low during part of the 2000's at least....I wonder, though, what result one would get by letting output and price coefficients be fitted independently...probably something not too different from Mankiw's rule.

At issue seems to be how the Taylor rule should be determined.  Taylor's 1993 paper shows that his rule fits the behavior of the fed funds rate from 1987--1992 fairly well.  One might reasonably ask that included as part of such a rule be a publicly disclosed formula for updating it, perhaps based on a window of economic data, or some time-profile of weighting of data, so that recent experience influences the rule more than that of decades ago.  Krugman, at least, is quite clear about what he's doing along these lines; Taylor does not derive his rule from an explicit fit, merely showing graphically that it fits the preceding fivish years of data reasonably well.