Dollars and Jens
Saturday, July 25, 2009
Taylor rules
Calculated risk has some back-and-forth on the Taylor rule, quoting Jan Hatzius:
Taylor argued that his rule implies a fed funds rate of +0.5%. He specifically attacked a reported Fed staff estimate of an “optimal” Taylor rate of -5% as having "... both the sign and the decimal point wrong.”

What’s going on? The answer can be seen in a note published by Glenn Rudebusch of the San Francisco Fed [in May]; it justifies the Fed’s -5% figure and reads like a direct reaction to Taylor’s criticism, even though it does not reference his speech (see “The Fed’s Monetary Policy Response to the Current Crisis,” FRBSF Economic Letter 2009-17, May 22, 2009). The difference is fully explained by two choices. First, Taylor uses his “original” rule with an assumed (but not econometrically estimated) coefficient of 0.5 on both the output gap and the inflation gap, while the Fed uses an estimated rule with a bigger coefficient on the output gap. Second, Taylor uses current values for both gaps, while the Fed’s estimate of a -5% rate refers to a projection for the end of 2009, assuming a further rise in the output gap and a decline in core inflation.
The Taylor rule prescribes (or, in its original formulation, predicts) an interest rate that is a sum of coefficients times the output gap and the rate of inflation. As Hatzius notes, there can be disagreement about the coefficients;* there can also be disagreements about the rate of inflation, and even more about the output gap. The output gap is the fluffier of the two, and Mankiw suggested using the unemployment rate as a proxy; I like this, not only because it gives something that's actually visible, but because, in natural units, he got coefficients of 1.4 on both the unemployment rate and the inflation rate; essentially, the rule is (nearly) that the fed funds rate should be 1.4*(inflation-unemployment+6).

My preferred measure of inflation is the trimmed-mean PCE, which on a smoothed basis is around 1.8% lately.

The current figure, using most recent data, is (1.8-9.5+6)*1.4 = -2.4%.

Even with recent improvements in unemployment claims data, I would expect this target rate to get lower before it gets higher. Since monetary policy doesn't seem to show up in economic data until 8 months later, and doesn't really kick in until after that, I can see the appeal of using predicted values, providing the predictions are decent, but I don't believe the studies I've seen have calibrated their coefficients based on "predicted values" — this 1.4, for example, is based on contemporaneous data. If you want to use predicted values, you need to perform an exercise based on a consistent set of at-the-time predictions.

*A paper by Clarida, Gali, and Gertler — I think — found that fed policy after 1982 was well described by an autoregressive process with a coefficient of about 2 on the inflation rate and 1 on the output gap.

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