### 100 Basis Points

Even I won't call for a 100 basis point cut in the federal funds rate target this month. But Greg Mankiw has unwittingly made me realize that a quick adjustment to his rule-of-thumb Taylor equation would argue for just so large a cut.

To start with, Eddy Elfenbein of

Federal funds rate = 8.5 + 1.4(Core inflation-Unemployment)

and gets 5.088. Rounded to the nearest 25 basis points, that's 5.00, exactly what the current consensus expects from the Fed this month.

But in the original

In practice, the consensus estimate for the NAIRU has fallen dramatically over the past 15 years. In the early 1990s, 6% was a sort of canonical magic number (and, as I recall, Greg himself argued in December 1994 that the NAIRU was significantly higher than that). According to the Philadelphia Fed's latest Survey of Professional Forecasters, the median estimate today is 4.7% -- a difference of 1.3 percentage points from the early 90s. (Note on the chart on

So let's make the assumption that Greg's rule applies in the very middle of that transition -- when the consensus NAIRU estimate was half way between 6.0% and 4.7%, or 5.35%. Now write the more general rule:

FFR = C + 1.4(Core inflation-(Unemployment-NAIRU))

plug in 5.35 for the NAIRU, and solve for the constant C:

8.5 + 1.4*(I-U) = C + 1.4*(I-(U-5.35))

Rounding to the nearest tenth, we get

C=1.0

(That value sounds divinely ordained; doesn't it?) Plug in today's 4.7% consensus NAIRU estimate, and you get

FFR=1.0+1.4*(I-(U-4.7))

or

Federal funds rate = 7.6 + 1.4(Core inflation-Unemployment)

Plugging in 4.647 for unemployment and 2.210 for core inflation, as per

Federal funds rate = 4.188

which I'm happy to round up to 4.25

UPDATE: I just checked the Survey of Professional Forecasters, and I now realize my mind was rounding up the median NAIRU estimate from 4.65 to 4.7. Using the accurate median of 4.65, and making the same "middle of the transition" assumption about Greg's rule, would reduce the calculated target federal funds rate by 3.5 bps, to 4.15, so it still rounds to 4.25.

To start with, Eddy Elfenbein of

*Crossing Wall Street*does the calculation (hat tip: Greg Mankiw) using Greg's*original*rule of thumband gets 5.088. Rounded to the nearest 25 basis points, that's 5.00, exactly what the current consensus expects from the Fed this month.

But in the original

*Taylor rule*, it's not the unemployment rate, but the difference between actual and potential output, that shows up in the equation. Okun's law would justify using the unemployment rate instead of output, but the implicit assumption of Greg's equation is that "potential unemployment" -- which is to say, the NAIRU -- is constant over time.In practice, the consensus estimate for the NAIRU has fallen dramatically over the past 15 years. In the early 1990s, 6% was a sort of canonical magic number (and, as I recall, Greg himself argued in December 1994 that the NAIRU was significantly higher than that). According to the Philadelphia Fed's latest Survey of Professional Forecasters, the median estimate today is 4.7% -- a difference of 1.3 percentage points from the early 90s. (Note on the chart on

*Crossing Wall Street*that the Greg's rule tends to come out below the actual funds rate in the early years and above in the later years -- which suggests that the Fed was in fact doing something similar but with changing NAIRU estimates.)So let's make the assumption that Greg's rule applies in the very middle of that transition -- when the consensus NAIRU estimate was half way between 6.0% and 4.7%, or 5.35%. Now write the more general rule:

plug in 5.35 for the NAIRU, and solve for the constant C:

Rounding to the nearest tenth, we get

(That value sounds divinely ordained; doesn't it?) Plug in today's 4.7% consensus NAIRU estimate, and you get

or

Plugging in 4.647 for unemployment and 2.210 for core inflation, as per

*Crossing Wall Street*, giveswhich I'm happy to round up to 4.25

UPDATE: I just checked the Survey of Professional Forecasters, and I now realize my mind was rounding up the median NAIRU estimate from 4.65 to 4.7. Using the accurate median of 4.65, and making the same "middle of the transition" assumption about Greg's rule, would reduce the calculated target federal funds rate by 3.5 bps, to 4.15, so it still rounds to 4.25.

Labels: economics, interest rates, macroeconomics, Mankiw, monetary policy, NAIRU

## 7 Comments:

If you calculate the gdp gap as

((potential-actual)/actual * 100)+5

you get a variable that tracks the unemployment rate very closely.

I like 4.25. It's an excellent number. I vote for 4.25.

Hi all,

if you have any idea of what will the FED do on September, 18th on the light of the recent market turmoil, feel free to leave your vote on my blog's poll at:

http://www.thedailyeconomist.blogspot.com/

best,

Bernardo.

希望大家都會非常非常幸福~

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