Taylor Rule Advanced: Variants, r*, and Fed Policy

Key Takeaways

• The original 1993 rule weights both the inflation gap and the output gap at 0.5; the 1999 variant doubles the output-gap weight to 1.0 and better fits post-1990s Fed behavior.
• The Taylor principle requires the inflation coefficient to exceed 1, otherwise higher inflation lowers the real rate, eases policy further, and creates a spiral; the original rule satisfies it at 1.5.
• Laubach-Williams estimates of r* have ranged near 0.5–1.0 percent post-2008, far below Taylor's original 2.0 percent assumption, producing systematically tighter prescriptions from the original rule.
• In Q4 2022 the standard Taylor prescription was roughly 6.25 percent while the Fed's midpoint was 4.375 percent, a gap of about 150–200 basis points commonly cited as policy being behind the curve.

What It Is

The original rule is:

r = r* + π + 0.5 * (π - π*) + 0.5 * (y - y*)

Where r is the nominal federal funds rate in percent, r* is the real neutral rate (Taylor assumed 2.0 percent), π is recent inflation, π* is the inflation target (2.0 percent), and (y - y*) is the output gap in percentage points. The weights of 0.5 on the inflation gap and the output gap are the coefficients Taylor estimated.

A closely watched variant is the Taylor (1999) rule, which doubles the output-gap weight to 1.0 and is often a better fit for post-1990s Fed behavior. The Fed's own Monetary Policy Report publishes several rule variants, including inertial and balanced-approach versions.

The Intuition

Discretion lets a central bank react to anything but also lets it drift, overreact, or be surprised. A rule lets markets and households form stable expectations about how policy will respond. Taylor's insight was that a linear rule with modest weights on two observable gaps captures a lot of what disciplined central banks actually do, and that deviations from such a rule line up with well-known policy errors.

The key normative property is the Taylor principle: the coefficient on inflation must exceed 1, which means the real rate rises when inflation rises. Otherwise, higher inflation lowers the real rate, easing policy further, and inflation spirals. In the original rule the coefficient on π is 1.5 (one from the π term plus 0.5 from the gap term), which satisfies the principle.

How It Works

Five inputs determine the prescribed rate at a point in time:

r*  = neutral real rate           (Laubach-Williams estimates put this near 0.5 to 1.0 post-2008, Taylor used 2.0)
π   = recent core inflation       (trailing 4Q core PCE is common)
π*  = inflation target            (2.0 for the Fed)
y   = log real GDP                (or employment gap for employment-augmented variants)
y*  = log potential GDP           (CBO publishes quarterly estimates)

Inertial variants smooth the prescription:

r_t = ρ * r_{t-1} + (1 - ρ) * [r* + π + 0.5 * (π - π*) + 0.5 * (y - y*)]

with ρ often around 0.85 at quarterly frequency. That matches the Fed's observed preference for gradualism. The Cleveland Fed's "Simple Policy Rules" page publishes weekly prescriptions across half a dozen common variants, which makes it easy to see how much of the disagreement is about coefficients versus input gaps.

Worked Example

Take Q4 2022. Core PCE inflation over the preceding four quarters was roughly 4.5 percent. The inflation target is 2.0 percent. CBO's Q4 2022 output gap estimate was close to zero. Assume r* of 0.5 percent, closer to modern Laubach-Williams values than Taylor's original 2.0.

Original Taylor:

r = 0.5 + 4.5 + 0.5 * (4.5 - 2.0) + 0.5 * 0
  = 0.5 + 4.5 + 1.25 + 0
  = 6.25 percent

Taylor (1999) with the higher output-gap weight:

r = 0.5 + 4.5 + 0.5 * 2.5 + 1.0 * 0
  = 6.25 percent (identical here because the gap is near zero)

The midpoint of the Fed's actual target range at the time was 4.375 percent, rising to 5.375 percent by early 2023. A common reading is that the Fed was roughly 100 to 200 basis points below the standard Taylor prescription during 2022, tightening back toward it through 2023. Very different conclusions can be reached by choosing a lower r* or a wider output gap, which is why practitioners publish multiple variants rather than one.

Common Mistakes

1. Treating the rule as a command, not a benchmark. Taylor called his own paper a description, not a prescription. Central bankers use rules as one input into judgment, alongside financial stability, labor market breadth, and shock identification.
2. Using the wrong inflation measure. Core PCE, headline CPI, and trimmed-mean versions give different prescriptions. The Fed explicitly targets PCE, and most staff work uses core PCE for persistence reasons. CPI-based rules can run hot or cold by 50 basis points at cyclical extremes.
3. Ignoring r* uncertainty. The neutral real rate is not observable. Laubach-Williams estimates have ranged from near zero to above 1 percent in the past decade, with wide error bands. Taylor's original 2.0 gives much tighter prescriptions than modern 0.5 to 1.0 inputs.
4. Assuming constant coefficients. Estimates of how strongly the Fed responds to inflation and output gaps shift across regimes. The 1987 to 2000 coefficients differ from 2001 to 2007, which differ again from the post-2008 zero lower bound era.
5. Forgetting the zero lower bound. Rule prescriptions went deeply negative during 2009 to 2014 and 2020 to 2021. The Fed could not follow the rule mechanically and substituted QE and forward guidance, which is why shadow rate estimates became popular as a stand-in.

Frequently Asked Questions

What is the Taylor rule and what does it prescribe? The Taylor rule prescribes a central bank's policy rate as a function of two gaps: how far inflation is above (or below) the 2 percent target, and how far output is above (or below) potential. The original 1993 formula is r = r* + π + 0.5×(π − π*) + 0.5×(y − y*), where r* is the neutral real rate. It was intended as a description of disciplined Fed behavior, not a binding rule.

What is the Taylor principle and why does it matter? The Taylor principle states that the policy rate must rise by more than one-for-one with inflation, that is, the coefficient on inflation must exceed 1. If it does not, higher inflation lowers the real rate, which eases financial conditions and allows inflation to accelerate further. The original rule satisfies the principle: the effective inflation coefficient is 1.5 (one from the π term plus 0.5 from the inflation gap term).

What is r and why does its value change the prescription dramatically?* r* is the neutral real interest rate, the rate consistent with stable inflation and full employment. Taylor's original paper used 2.0 percent, which was reasonable for the 1987–1992 period. Post-2008 Laubach-Williams estimates have put r* near 0.5–1.0 percent, implying that the same inflation and output gaps produce a prescription 100–150 basis points lower than Taylor's original formula would generate.

How do the 1993 and 1999 Taylor rules differ in practice? The 1993 rule weights both the inflation gap and the output gap at 0.5. The 1999 rule doubles the output-gap weight to 1.0. When the output gap is large, either deeply negative in a recession or strongly positive in an overheating economy, the 1999 rule prescribes a more aggressive response. At near-zero output gaps the two rules produce the same result, as they did in the Q4 2022 worked example.

Did the Fed follow the Taylor rule during the 2021–2023 hiking cycle? The Fed was broadly below the standard Taylor prescription through most of 2022. Using a Laubach-Williams r* of 0.5 percent and trailing core PCE near 4.5 percent, the 1993 rule prescribed roughly 6.25 percent in Q4 2022 while the Fed's midpoint was 4.375 percent. The Fed closed most of that gap by early 2023 as the terminal rate reached 5.25–5.50 percent, but critics argued the initial tightening pace was too gradual given the prescription.

Sources

1. Taylor, J.B. (1993). "Discretion versus Policy Rules in Practice." Carnegie-Rochester Conference Series on Public Policy 39. https://web.stanford.edu/~johntayl/Onlinepaperscombinedbyyear/1993/Discretion_versus_Policy_Rules_in_Practice.pdf
2. Federal Reserve Board. "Monetary Policy Report: Policy Rules Section." https://www.federalreserve.gov/monetarypolicy/mpr_default.htm
3. Federal Reserve Bank of Cleveland. "Simple Monetary Policy Rules." https://www.clevelandfed.org/indicators-and-data/simple-monetary-policy-rules
4. Taylor, J.B. and Wieland, V. (2012). "Surprising Comparative Properties of Monetary Models: Results from a New Database." NBER Working Paper 18666. https://www.nber.org/papers/w18666

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.