The Taylor Rule, part 1

I keep referencing an old blog where I broke out the pieces of the Taylor Rule … poorly.  This will be the new one that I point to, and I think that this is pretty interesting so far.  The media is kind of fetishizing the Taylor Rule because it makes the race more interesting: “Will it be Super Dove Janet Yellen who plays fast and loose with the rules or Super Hawk John Taylor whose decisions are super predictable because they’re all based on a perfect model?”

Here’s a link to the original Taylor Rule research, “Discretion versus policy rules in practice”.  While this introduced the theory as a means for historical analysis of interest rates, if you read his 1999 paper, it actually seems like he was trying to angle for Fed Chair: “A Historical Analysis of Monetary Policy Rules”.

Monetary Policy Rule as a Guideline or Explicit Formula. Finally, equation (1) could represent a guideline, or even a strict formula, for the central bank to follow when making monetary policy decisions. As in the previous paragraph, decisions would be cast in terms of whether the Fed would raise or lower the short-term interest rate. But equation (1) would serve as a normative guide to these decisions, not simply a description of them after the fact.

The original Taylor Rule equation is a little simpler than the rule below, but I’m going to use this one  because it’s easier to break down the component parts.

stir = π+ r* + α1(π – π*) + α2(y – y*)

  • stir = short term interest rate
  • r* = equilibrium real interest rate (2%)
  • π, π* = actual inflation, inflation target (2%)
  • y, y* = real GDP growth, potential GDP growth
  • α1, α2 = in 1993, Taylor recommended a1=a2=0.5.

We’ve already debunked the perfect model fetish.  It’s shocking to me how many of these variables is just how many of them are assumptions or targets.

y*, π*, and r* are all explicitly projections or targets.

y* = (natural rate of employment / actual rate of employment) * (Actual GDP)

Potential GDP is the highest level of GDP growth sustainable over the long term, and it’s created using the Natural Rate of Unemployment projected by the Congressional Budget Office.  I’m not entirely sure how the CBO makes their projections, but it’s telling that the official name for the statistic is “non-accelerating Inflation rate of unemployment” (NAIRU).

π* – long term inflation projection

Just this month, former Fed Governor Tarullo wrote that the Monetary Affairs Division of the Federal Reserve doesn’t approve of FOMC members projecting long term inflation different from 2%.  In the past week, Fed Chair Yellen questioned whether long-term inflation expectations have changed during her tenure.  This ratio (importance of inflation)/(understanding how inflation works) is astronomical.

r* – equilibrium real interest rate projection

Taylor, in 1993, suggested that r* should be 2.  I’m going to let former Fed Governor Tarullo explain to us how the equilibrium real interest rate is “estimated” in practice:

Each participant’s estimate of r* can be calculated by simply subtracting the 2% inflation target from the value given by the participant for the longer-term federal funds rate.

I’m going to stop here for now.  I’ve been cranking out some numbers to look at the FOMC projections vs the Taylor Rule projections, and it’s pretty interesting.  I just haven’t managed to come to any conclusion yet.  I’m pretty sure I’ll get that out tomorrow.

What I’m leaning towards is that using this model will get you any number for Fed Funds that you want … it just depends on the assumptions and projections you make.  Just like the Fed does now.

To be continued …




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