### Has the Fed Gone More Dovish?

**Matthew Martin**12/25/2012 12:00:00 PM

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Just noticed that Greg Mankiw and David Andolfatto are offering different perspectives on the Fed's new explicit unemployment target of 6.5%. Here's Mankiw repeating a point about how the rule is more "dovish" on inflation, and here's Andolfatto on how its actually somewhat "hawkish."

First, a caveat on the language. Isn't being a "dove" on inflation the same as being a "hawk" on unemployment? Why is this discussion so skewed when the Fed's mandate is to minimize both? Anyway...

Mankiw says that this was the pre-recession Taylor rule (which is a formula for finding the target interest rate based on the unemployment and inflation rates):

r = 2.0 - (1.5)(u-5) + (0.5)(pi-2.0)

where r is the nominal interest rate, u is the unemployment rate, and pi is the inflation rate. Here is the forward guidance from the Federal Reserve announcement:"the Committee decided to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that this exceptionally low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6-1/2 percent, inflation between one and two years ahead is projected to be no more than a half percentage point above the Committee’s 2 percent longer-run goal"So, the Fed projects 0<r<0.25 when u<6.5 and pi<2.5. Using the formula above with u=6.5 and pi=2.5 I get r=0. So, the Fed is not more dovish on inflation. According to Mankiw's post "My conclusion about dovishness is robust." I think not. Quite the contrary, Larry Ball's estimate of the Taylor Rule says that the Fed is, if anything, being more hawkish on inflation since if inflation stays less than 2.5%, the Taylor rule predicts negative interest rates, below the 0.25% rate the Fed will target. I think Larry Ball made an arithmetic error, and Mankiw failed to catch it.

At anyrate, I don't know what Larry Ball was thinking. But, I do know that this kind of thinking is misleading anyway: the Fed doesn't actually use a Taylor rule. These are mathematical constructs that macroeconomists used to describe Fed behavior, and it does a reasonably good job, but the fact is that the Taylor Rule is merely an approximations, and it often deviates widely from actual Fed policy as shown below:

This post from Macroblog makes a similar point that the Fed is somehow more dovish before. But again, I think that they are misusing the taylor rule. Their version of the taylor rule is

R = 2.02 - 1.48(U-U*) + 1.17P

where U is the unemployment rate, U* is the "natural rate" of unemployment rate which they assume changes over time and rose during the recession, and P is the inflation rate, while R is the suggested nominal interest rate. Note first that it is different from Larry Ball's estimate, proving that making judgements based on Taylor Rules is pretty stupid--we don't even know what the "true" Taylor rule is, so how can we claim the Fed is deviating from it?! So, with U=7.7, assume that U* as risen to 6, and P=1.5, you get R=1.259, way above the actual 0.25.

The problematic assumption here is that U* has risen during the recession. To be sure, they got this number form the most recent CBO estimates of the "natural rate," but the problem is that the CBO gets this estimate merely by estimating an autoregressive smoothing process. That makes a lot of problematic assumptions even with good data, but it is especially useless when we try to do it in real time, because smoothing processes will always make the "natural rate" converge towards the actual unemployment rate towards the end of the data series overwhich it is estimated. That means, it is currently giving an estimate much too high, and that the CBO estimate is not something that can be used for real-time analysis of the economy. When you redo the calculation with U*=5, you get R=-0.221. So, just like above, this actually says the Fed is more hawkish, not less, than usual.

Finally, there is Andolfatto's point.

Basically, the Fed's forward guidance differs from the previous policy stance only in that it clarified all the ways in which the Fed might increase the interest rate. Lowering the interest rate is nowhere any of the options the fed presented in their release.