## Tuesday, July 16, 2013

### Rewriting the Taylor Rule

r = p + 0.5y + 0.5(p – 2) + 2 is the original Taylor rule, where r = the Federal funds rate, p = the inflation rate, and y = the output gap. Jared Bernstein writes in a comment about the Taylor rule and monetary policy:
I used this version: 2+p+(0.5(p-2)+y where p is year-over-year percent change in the PCE inflation index and y is the output gap: 2*(nairu-unemp) where 2 is the Okun coefficient and the nairu is from CBO.
John Taylor had a couple of issues with what Jared wrote. I did too but my take is a little different than John’s. Let’s start with this:
He then goes on to give this definition the Taylor Rule: The federal funds rate should equal ... 2 + p + 0.5(p – 2) + y ... where p is year-over-year percent change in the PCE inflation index and y is the output gap: 2*(nairu-unemp) where 2 is the Okun coefficient and the nairu is from CBO ... But this is not the policy rule I recommended in a 1993 paper using a formula which has come to be called the Taylor Rule.
Actually, Jared omitted a closing parenthesis so it is not clear if he meant the original Taylor rule or what John Taylor thinks Jared used. To be fair, the original 1993 formula should be simplified to: 1 + 1.5(p) + 0.5(y). Let’s make the algebra as simple as possible. John does admit:
I realize that there are differences of opinion about what is the best rule to guide policy and that some at the Fed (including Janet Yellen) now prefer a rule with a higher coefficient.
But then he adds something where I would differ:
There are other important cross-checks on such calculations. Bernstein’s estimate of the output gap uses an Okun’s law coefficient of 2, but if you use 1.5 (the empirical estimate over the past 50 years) rather than 2, the gap is smaller, which also moves the rate up toward positive territory. Similarly, the average of the San Francisco Fed’s most recent survey of output gaps is smaller than what Bernstein uses.
The original Okun’s law coefficient was actually 3, which would imply a 6.6% gap. I realize there have been other estimates such as an estimate where the coefficient was closer to 2.5 (implying a 5.5% gap). And if one uses the CBO’s measure of the output gap, which is mentioned in the SF Fed’s survey, it indicates an output gap equal to 5.8%. Even if the coefficient for the output gap is 0.5 – as in Taylor’s 1993 paper – an output gap of 5.8% and an inflation rate of 1% implies negative interest rates. But I guess John Taylor’s latest excuse for criticizing any expansionary stance from the FED is his belief that we are not that far from full employment. Go figure!

The original rule John Taylor proposed in 1993 ("Discretion versus Policy Rules in Practice", Carnegie-Rochester Conference Series on Public Policy, Vol. 39, December 1993, pp. 195-214), namely a Taylor Rule that places equal weights on the inflation gap and the output gap.

In 1999 Taylor discussed an alternative version of this rule that placed double the weight on the output gap than on the inflation gap, (“A Historical Analysis of Monetary Policy Rules”, Monetary Policy Rules, Chicago: University of Chicago Press, pp. 319-341).

http://www.nber.org/chapters/c7419.pdf

In a speech delivered in April 2012 Janet Yellen mentioned both versions of the Taylor Rule and referred to them as "Taylor 1993" and "Taylor 1999":

http://www.federalreserve.gov/newsevents/speech/yellen20120411a.htm

In that same speech she used an Okun coefficient of 2.3. In fact both Taylor 1999 and the 2.3 value for the Okun coefficent have cropped up repetedly in speeches by FOMC members. See this one by James Bullard for example:

http://research.stlouisfed.org/econ/bullard/pdf/Bullard_CFAR_StLouis8Nov2012final.pdf

It's interesting that the SF FRB estimate of the CBO's output gap mentions the one calculated from real GDP. If you use the one calculated from nominal GDP it is slightly larger at 6.1%:

http://research.stlouisfed.org/fred2/graph/?graph_id=82210&category_id=0

David Glasner did a very nice post on the Taylor Rule last year:

http://uneasymoney.com/2012/09/13/taylor-rules/

ProGrowthLiberal said...

Mark - thanks. Jared had a follow up post on this little debate where he made a few of the points that you so well document.

WNY-WJ said...

2 questions:

(1) has anyone estimated the current output gap with explicit recognition of hysteresis? It seems plausible that after 5+ years of "under-utilization" of production factors, that these are beginning to deteriorate [http://wnywj.wordpress.com/2013/07/13/the-damage-done-recovery-would-now-require-massive-investment-that-wont-be-soon-forthcoming/ ].

(2) let's assume there is a large output gap... does anyone still believe there is there any real effect via the expectations channel from QE as currently implemented? It seems like Woodford's recommendations for explicit nominal targeting of GDP (real GDP + inflation) is necessary to make irrational market participants - who apparently have a weak understanding of how the economy really works - understand that either real GDP or the price level will rise, thus finally inducing investment in the real economy (i.e., hiring, capital investment, etc.)