The Taylor Rule formulation, which can be viewed as either a description of historical monetary policy or as a prescription of how monetary policy ought to be conducted, is a linear function of an inflation rate and a measure of economic slack.
There are lots of versions out there, as different measures of inflation or slack can be used, and different coefficients can be applied to each variable. One of the simplest, and that results in a pretty good fit to actual historical Fed policy, and therefore the one I've been using, is the Mankiw Rule, which uses core CPI inflation along with the unemployment rate and applies the same coefficient to both.
So, first, a little history. Here is what core CPI and the U3 unemployment rate have looked like since the start of the Greenspan era.
Based on that data, the purple line in the chart below shows what the Taylor Rule would've prescribed, while the red line shows actual Fed policy. (stating-the-obvious note: the former can suggest a negative rate "should" be set, though the latter can't actually go negative, so Fed policy can be "tight" relative to where it ought to be even when the Fed funds rate can't go lower)
Enough history; now how about going forward?
Well, to decide what the Taylor Rule would prescribe for the Fed funds rate, one must have estimates of what the two underlying variables will be. Fortunately, we can use what the Fed itself is predicting. Its central tendency projections are charted below.
Note that the Fed expects unemployment to stay above 7% through 2012, before falling to average just above 5% in the longer-run. Because it doesn't seem likely that unemployment will fall from 7.3% at the start of 2013 to 5% immediately, I applied some assumptions to have it fall steadily over time until it got back to near the 2000 and 2006 lows, falling to 6.3% at the end of 2013, 5.3% at the end of 2014, 4.75% in 2015 and 4.25% in 2016, which averages 5.15% over those 4 years.
And the Fed expects core PCE (rather than core CPI) to not rise to a range of 1.0-1.5% until the end of 2012. So I did similarly for core CPI in the longer term as I did for unemployment, pencilling in a rise from the 2012 projection of 1.25% (the mid-point of the Fed's 1.0-1.5 range) to 1.4% in 2013, 1.55% in 2014, 1.75% in 2015 and 1.9% in 2016.
Based on those projections, the Taylor Rule formulation is shown below (along with where the Fed would be when the Taylor Rule suggests a negative rate is appropriate).
This suggests that even based on the Fed's very own projections for economic slack and inflation, it should keep rates at zero for the next 3 years. The economy would gradually return to normal, and therefore monetary policy could return to normal, gradually thereafter, principally in 2015/2016.
So lets say that's true. What does that suggest for the 10-year Treasury?
Historically, the yield on the 10-year has been less than 150bp above the Fed funds rate. This is very variable over time, depending on the environment. Note that when the Fed funds rate is being lowered, the T10-Fed spread has tended to widen, as the Fed funds rate falls faster than does the 10-year yield. Note also, however, that when Fed policy is roughly static, the T10-Fed spread generally grinds in. That is, once the Fed stops easing, the 10-year typically continues to shift towards the Fed funds rate, narrowing the T10-Fed spread. In recent history, this has been even more noticeable when the Fed has stopped hiking.
So, in any case, while it is a VERY imperfect guide, let's say that the 10-year yield should be about 150bps, not above the current Fed funds rate, but above what the Taylor Rule says the Fed funds rate should be (which allows us to project forward, not just look backwards); if so, you get this:
Obviously the reasonably strong correlation historically can't be as applicable when the Taylor Rule says Fed funds should be negative --- but it does seem to suggest that given the macroeconomic environment, the 10-year yield is actually pretty high, not too low.
Another way of looking at this would be to use the Taylor Rule projection, assume the Fed funds rate will be as prescribed, and calculate what interest rate one would have to earn on a 10-year bond today to match what you would earn by investing at the Fed funds rate as it evolves over time (i.e. a breakeven analysis). I calculate 2.7%. Which is pretty much where the 10-year Treasury is today.
And, if the market starts to view the Fed's projections as too optimistic, there would be room for the Taylor Rule to push interest rate hikes out even further, and thus to lower the yield that a 10-year bond would have to earn to match Fed policy.
In fact, there's very good reason to take the Fed's central tendency projections with a rather large grain of salt: they don't have a good track record. For instance, official projections for unemployment never foresaw a rate anywhere near 10%. In fact, for a laugh, go back to Fed central tendency projections in spring 2008 (after the recession had started) and you can see that the Fed never anticipated core PCE ever getting below 1.7%, nor of unemployment ever getting above 5.7%! Similarly, in January 2009, the Fed thought unemployment would get no higher than 8.8% in 2009, declining in 2010 and falling futher in 2011 to a range of 6.7 to 7.5% (which, needless to say, is in no way consistent with what it is currently pencilling in for either 2010 or 2011).
So, if the Fed is wrong, what if, for instance, one were to expect the disinflationary trend to persist, with core inflation steadily trending down, and if one were to expect unemployment to remain stubbornly high, both of which as I do?
I honestly believe that the unemployment rate could go well into the double-digits; but, for the sake of argument, let's say it simply stays in the 10% neighbourhood (slightly above where it is now) for awhile, not falling until it starts dropping regularly in 2014 and thereafter (this is not really what I expect; I'm pencilling in a more benign view than my own; if the U3 rate doesn't go higher than 10% and if it starts falling regularly in 2014, I would hazard a guess it has as much to do with how the U3 rate is calculated (if you fall off the unemployment rolls, you're no longer unemployed!) as with underlying strong economic growth; I anticipate the broader U6 measure to exceed 20% soon and stay there for quite some time; in any case, for argument's sake...)
So, what if that came to pass? How should monetary policy evolve? A Taylor Rule would suggest the Fed stay at 0 until 2018.
And if the Fed stays at 0 for the next 8 years, then the current spread of 250bp of US 10-years over Fed funds looks very attractive relative to the historical average of 143bp.
And, if you did that same breakeven analysis I did earlier, now using Taylor Rule projections based on MY CPI and U3 forecasts rather than those of the Fed, rather than 2.7 as a breakeven for the 10-year, you'd get 0.3%.
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