Wednesday, September 12, 2007

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 Crossing Wall Street does the calculation (hat tip: Greg Mankiw) using Greg's original rule of thumb

    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 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:

    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


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



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

Plugging in 4.647 for unemployment and 2.210 for core inflation, as per Crossing Wall Street, gives

     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.

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Anonymous Anonymous said...

If you calculate the gdp gap as

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

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

Wed Sep 12, 04:00:00 PM EDT  
Anonymous Anonymous said...

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

Wed Sep 12, 04:22:00 PM EDT  
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