Taylor Rule

The equation

In November 1992 the Carnegie-Rochester Conference on Public Policy heard a paper by John B. Taylor of Stanford titled "Discretion versus Policy Rules in Practice". It contained a single equation that has shaped central banking for three decades:

i_t = r* + π_t + 0.5 (π_t − π*) + 0.5 (y_t − y_t*)

Each symbol has a clear economic meaning. i_t is the nominal short-term policy interest rate the central bank sets today — for the Federal Reserve that is the target federal funds rate. r* is the equilibrium real interest rate, the rate consistent with the economy operating at potential with stable inflation; Taylor calibrated it to about 2 percent. π_t is the current inflation rate, and π* is the central bank's inflation target, also calibrated to 2 percent. y_t is real output and y_t* is potential output, so (y_t − y_t*) is the output gap — usually expressed as a percentage deviation of GDP from potential. The two coefficients of 0.5 are weights on the inflation gap and the output gap, chosen so that the rule reproduces actual Fed behaviour in the late 1980s and early 1990s.

The structure deserves a moment of attention. The first two terms, r* + π_t, mechanically deliver a real rate of r* at any inflation rate — they are the "neutral" baseline. The third and fourth terms are the active stabilisation: when inflation runs above target the rule prescribes a higher nominal rate, raising the real rate; when output runs above potential the rule again prescribes tightening. The rule is therefore a Taylor-type leaning-against-the-wind reaction function, and the simplicity is part of the point. Anyone with a Bloomberg terminal and an output-gap estimate can compute it.

A worked numerical example

Suppose inflation is running at 4 percent against a target of 2 percent, and the output gap is plus 1 percent — slight overheating. With r* = 2 percent the rule prescribes:

i = 2 + 4 + 0.5 (4 − 2) + 0.5 (1 − 0)
  = 2 + 4 + 1.0 + 0.5
  = 7.5 percent

Compare with a benign baseline of inflation at target and output at potential:

i = 2 + 2 + 0.5 (0) + 0.5 (0) = 4 percent

So a 2-percentage-point increase in inflation alone, with no change in the output gap, raises the prescribed rate by 3 points: 1 point through the +π_t term and a further 0.5 point through the inflation-gap term, for a combined inflation coefficient of 1.5. Add a one-point output-gap shock and you pick up another half point. The rule is linear, it is transparent, and the arithmetic is fourth-grade.

The Taylor principle

The most important property of the rule is hidden in that combined inflation coefficient of 1.5. When inflation rises by one percentage point, the nominal rate rises by 1.5 — which means the real rate, i − π, rises by 0.5. Higher real rates are restrictive: they cool consumption, investment, and demand for credit. Inflation, having risen, is met with monetary tightening.

Suppose instead the central bank's response coefficient on inflation were less than one. Then when inflation rises by one point, the nominal rate rises by less than one point, and the real rate falls. Falling real rates are stimulative — they raise demand and feed further inflation. In a standard New Keynesian model with such a passive response, the rational-expectations equilibrium ceases to be locally determinate: there is a continuum of equilibria, and arbitrary self-fulfilling shifts in inflation expectations can drive inflation anywhere. This is the Taylor principle — first articulated explicitly by Taylor in his 1993 paper and later formalised in models by Clarida, Galí and Gertler (2000): the long-run response coefficient on inflation must exceed one to guarantee a unique stable equilibrium.

Clarida, Galí and Gertler estimate that pre-Volcker Fed reaction functions had an inflation coefficient of about 0.83 — passive, below the threshold — while the post-Volcker Fed under Greenspan operated with coefficients around 2.15, comfortably active. They argue the great inflation of the 1970s was at least partly a violation of the Taylor principle, and the Great Moderation that followed was its restoration.

Empirical fit: 1987 to 2008

The most arresting thing about the Taylor rule is how well it tracks the actual federal funds rate. Over the two decades from Alan Greenspan's appointment in 1987 to roughly the start of the 2008 crisis, the rule's prescription and the realised funds rate move together within about 50 basis points most of the time. Taylor's original 1993 paper showed this remarkable correspondence on data ending in 1992; subsequent updates by Federal Reserve researchers extended it through the 2000s with similar accuracy. For a single equation with two parameters this is an astonishing empirical record — most macroeconomic regressions cannot do as well over a 20-year window.

Why such a clean fit? Three reinforcing factors. First, the late-1980s and 1990s Fed was openly trying to be predictable, and an explicit, transparent reaction function helped achieve that. Second, in normal times the relevant inputs — current inflation and the output gap — really are most of what a central bank cares about, and a parsimonious rule captures the bulk of the variation. Third, Taylor calibrated his coefficients to match observed behaviour, so the fit on the in-sample window is partly mechanical; the surprise is that it persists out of sample.

The deviations and what they meant

Period	Fed actual	Taylor rule	Gap	Interpretation
1987–2001	tracks rule	baseline	±50 bp	Great Moderation, transparent reaction function
2002–2005	~1 %	~3 %	−200 bp	Greenspan kept rates "too easy" — housing-boom debate
2006–2007	~5 %	~5 %	0	Re-converged before crisis
2009–2015	0 % (ZLB)	−5 % to −2 %	+200–500 bp	Rule binds at zero; QE and forward guidance substitute
2016–2019	0.5–2.5 %	2–3 %	−50 to −100 bp	Gradual lift-off; debate over r* decline
2021–2023	0 → 5.5 %	~9 % at peak	−350 bp	Late and below-rule response to post-COVID inflation

The two episodes that command attention are the bookends. From 2002 to 2005 the federal funds rate sat around 1 percent while the rule prescribed roughly 3 percent — a sustained 200-basis-point gap. Taylor himself made this the centrepiece of his 2007 Kansas City Fed Jackson Hole paper "Housing and Monetary Policy", arguing that the deviation seeded the housing boom that collapsed in 2008. Ben Bernanke responded with two defences: that the output gap was hard to measure in real time and the Fed's then-estimate suggested less slack, and that core inflation was unusually low so a softer policy stance was reasonable. The argument has never been fully settled, but it has shaped a generation of monetary-policy research.

At the other end, after Lehman in 2008 the rule began prescribing negative nominal rates — below zero by 2 to 5 percentage points. That is not implementable on currency-issuing reserve balances at meaningful scale, so the Fed hit the zero lower bound and substituted balance-sheet policy: three rounds of quantitative easing, operation twist, and explicit forward guidance about the path of rates. The Wu-Xia "shadow rate", estimated from the term structure of Treasury yields, attempts to extrapolate where the policy stance was in shadow-rate space even when the actual funds rate was stuck at zero; their estimates reach about minus 3 percent at the bottom in 2014, closer to but still above what the unconstrained rule prescribed.

Variants of the rule

• Taylor (1993) original. Coefficients of 0.5 on both gaps. Calibrated, not estimated, to match the 1987–1992 Greenspan Fed. Inflation measured by GDP deflator; output gap by Congressional Budget Office potential GDP. The benchmark in every textbook.
• Taylor (1999). Same form but with a coefficient of 1.0 on the output gap rather than 0.5 — Taylor's own follow-up arguing for more aggressive activity-side response.
• Balanced approach (Yellen). 0.5 inflation, 1.0 output gap. Adopted as the Yellen Fed's reference rule and routinely published by the Federal Reserve Board alongside the original. Calibrated to give a less hawkish response when unemployment is elevated.
• Inertial Taylor rule. Adds a lagged-rate term: i_t = ρ i_{t−1} + (1 − ρ) [Taylor prescription], with ρ around 0.7–0.85. Reflects the fact that real central banks adjust rates gradually rather than stepping discontinuously to the rule's level. Empirical fits improve substantially with inertia.
• First-difference rule. Sets the change in the policy rate as a function of inflation and the output gap, eliminating the need to estimate r* directly. Popular at the Federal Reserve since the secular decline of r* made absolute-level rules unstable.
• Shadow-rate variant (Wu-Xia 2016). Replaces the policy rate with a shadow rate inferred from the term structure of yields, allowing the rule to be evaluated even at the zero lower bound.
• Forecast-based or Clarida-Galí-Gertler rule. Replaces current inflation and output with expected future values. Reflects the forward-looking, expectations-driven nature of New Keynesian models and fits the post-Volcker Fed empirically.

The shifting equilibrium real rate

The single most consequential change in monetary economics since Taylor's paper is the decline in r*. Taylor's 1993 calibration of 2 percent matched the realised average real federal funds rate from 1984 to 1992. Two decades later, careful estimates by Laubach and Williams, by Holston, Laubach and Williams, and by Federal Reserve staff have driven r* down to somewhere between 0.5 and 1 percent for the United States, and close to zero or even negative for the euro area and Japan.

The mechanical implication is dramatic. A 150-basis-point decline in r* shifts every Taylor prescription by 150 basis points, mostly downward. Rules that called for a 4 percent nominal funds rate with inflation and output on target in the early 2000s call for roughly 2.5 percent today, even though every other input is unchanged. Two papers — Williams (2017) and Brand-Bielecki-Penalver (2018) — argue that the lower r* is the principal reason the zero lower bound binds so much more frequently in the 2010s and 2020s, and motivates either higher inflation targets or explicit make-up strategies to compensate. The Fed's 2020 framework review formally moved to an "average inflation targeting" regime in part for this reason.

The zero lower bound and shadow rates

The Taylor rule does not know that nominal rates cannot easily be negative. From 2009 to 2015 it prescribed a federal funds rate of minus 5 to minus 2 percent. Implementing that on positive currency balances is essentially impossible: anyone holding cash effectively earns a zero nominal rate, so charging negative rates on reserves pushes private agents to currency and breaks the policy transmission. A few central banks — the ECB, the Swiss National Bank, the Bank of Japan — have run modestly negative policy rates of around minus 0.5 percent on excess reserves, but no central bank has approached the Taylor rule's deep negative prescriptions.

The shadow-rate approach, formalised by Wu and Xia in 2016, asks: given the term structure of Treasury yields, what single policy-rate path would have generated this yield curve in a world without the zero bound? Their estimate is a "shadow rate" that becomes negative when balance-sheet policy and forward guidance substitute for further conventional easing. Most studies find the shadow rate reached about minus 3 percent at the trough in 2014, indicating that the Fed's combination of QE3 and forward guidance was equivalent to roughly three percentage points of additional rate cuts. That is still less aggressive than the unconstrained Taylor rule prescribed, but it closes most of the gap.

The 2008 crisis debate

Few macroeconomic disputes have been as fierce or as consequential as the question whether the 2002–2005 deviation from the Taylor rule caused the housing bubble. Taylor's side of the argument runs as follows. Real federal funds rates were negative for an extended period. Long rates were anchored by short rates and term premia, so they fell too. Mortgage rates followed. Housing investment surged. Subprime lending exploded. Securitisation distributed the credit risk widely. When rates eventually normalised and house prices rolled over, the system broke. Had the Fed followed the rule and kept rates near 3 percent in 2003–2004, none of that overshoot would have occurred.

Bernanke's reply, in a 2010 speech "Monetary Policy and the Housing Bubble" delivered as Fed Chair, makes three counterclaims. First, real-time output-gap estimates suggested less slack than ex-post revisions later revealed, so the Fed's perceived rule prescription was lower than Taylor's retrospective number. Second, core PCE inflation in 2003 was 1.4 percent, well below the 2 percent target, so a stimulative stance was appropriate. Third, the housing bubble was global: real interest rates were lower than Taylor would prescribe in many countries that did not follow a Greenspan-style policy, including the UK, Spain, and Ireland. So the cross-country pattern of housing booms cannot be explained by Fed deviations alone, implicating credit conditions, lending standards, and global savings imbalances.

The contemporary view is mixed. Most academic surveys conclude monetary policy was a contributing factor but not the sole cause; the consensus weight on the Fed varies. What is undisputed is that the dispute itself has elevated the Taylor rule from an academic curiosity to a permanent feature of the policy-making conversation, and that central-bank communications now routinely include Taylor-rule benchmarks as a way of disciplining narrative deviations from the prescription.

Modern uses

• Federal Reserve Monetary Policy Report. Since 2017 the semi-annual report has included a dedicated section comparing five different policy-rule prescriptions — the 1993 Taylor rule, the balanced-approach rule, an inertial version, a first-difference rule, and a Bauer-Rudebusch alternative — to the FOMC's actual target. The format institutionalises the Taylor rule as a communication device, not a commitment.
• ECB and Bank of England analyses. Staff papers from both central banks regularly publish Taylor-type benchmark calculations to discipline narrative. The Bank of England's MPC has cited rule prescriptions in inflation reports since the late 1990s; the ECB's working-paper series contains dozens of rule-comparison exercises.
• Macro forecasting and DSGE models. Almost every estimated New Keynesian model (Smets-Wouters, the FRB/US model, the New York Fed DSGE model) uses a Taylor-type rule as the monetary-policy block, often inertial with forecast inflation and an estimated output gap.
• Yield-curve modelling. Term-structure researchers use Taylor rules as the short-rate process in affine yield-curve models, exploiting their fit to inflation and output data to anchor long-rate predictions.
• Public commentary and markets. Wall Street strategists routinely publish "Taylor rule scorecards" arguing that the Fed is "behind" or "ahead" of the curve. The rule's transparency makes it ideal as a benchmark for second-guessing FOMC decisions in real time.

Limits and common pitfalls

• Real-time output-gap mismeasurement. Orphanides (2001) showed that real-time output-gap estimates in the 1970s were two to three percentage points away from later revisions, and the same problem recurred in 2002–2005. A Taylor rule applied to badly mismeasured gaps can prescribe systematically wrong rates and yet appear locally rational.
• r* uncertainty. The equilibrium real rate is unobserved; estimates have wide confidence bands and have shifted by over 150 basis points in the past 20 years. Every Taylor prescription is conditional on a chosen r*, and rule users sometimes implicitly impute Taylor's original 2 percent rather than the contemporary estimate.
• Inflation measure ambiguity. Taylor used the GDP deflator; the Fed targets core PCE; markets watch headline CPI. The rule's prescription varies materially across inflation measures, especially during energy-price shocks.
• Silence on financial stability. The rule has no terms for credit growth, asset-price bubbles, leverage, or exchange-rate dynamics. Yet these are first-order concerns for modern central banks. Augmented rules with credit-cycle terms have been proposed (Borio 2014, Curdia-Woodford 2016) but no consensus version exists.
• Silence on the zero lower bound and balance-sheet tools. The unconstrained rule cannot accommodate QE, forward guidance, or yield-curve control. Modern frameworks must layer the rule with explicit ZLB protocols.
• Mistaking the rule for a commitment. The Taylor rule is a benchmark, not a Federal Reserve commitment. The FOMC has repeatedly and publicly emphasised that no rule mechanically substitutes for judgement — the rule is one input among several. Treating it as a binding contract overstates its institutional status.