Taylor Rule Deviations Across Horizons: A Practical Tool for Monetary Policy

Layer 1 — Overview

Research Question

The paper addresses a fundamental limitation of the standard Taylor rule as a monetary policy stance gauge: the rule is defined solely for the overnight federal funds rate (FFR) and cannot assess stance across the maturity spectrum of the yield curve. This limitation becomes acute when the FFR hits its effective lower bound (ELB) and the Federal Reserve resorts to unconventional monetary policy (UMP) instruments—quantitative easing and forward guidance—that are explicitly intended to influence longer maturities. The authors ask: can the Taylor rule idea be extended across the yield curve horizon to produce a maturity-specific monetary policy stance measure that remains informative even during ELB episodes?

Methodology and Data

The paper proposes the “Taylor rule yield curve,” which extends the original Taylor rule to points in time in the future horizon (maturities of 1 through 10 years). The Taylor rule expected rate at maturity h is defined as the average of h annual one-period-ahead Taylor-rule-implied short-term rates, each computed from professional forecasters’ expectations of inflation and the output gap h years ahead. The market counterpart is the Overnight Index Swap (OIS) rate for the corresponding maturity. The “Taylor rule deviation” (TRD) at maturity h is then the difference between the Taylor rule expected rate and the market OIS rate at that maturity—interpretable as the average expected monetary policy stance from the current period through h years ahead.

Data sources: inflation and GDP growth forecasts from Consensus Economics (1–5 years ahead, and 6–10 year average); output gap forecasts constructed using Congressional Budget Office potential output estimates; natural rate of interest estimates from Holston, Laubach, and Williams (2017) available from the Federal Reserve Bank of New York; FFR, core CPI inflation, and GDP growth from FRED; OIS rates from Bloomberg (available from 2002/Q1). Two Taylor rule coefficient sets are examined: the “original” rule (α = 0.5, β = 0.5) and the “balanced” rule (α = 0.5, β = 1.0), with the balanced rule as baseline. An inertia parameter of ρ = 0.85 (quarterly) is assumed, implying annual persistence of approximately 0.52. The sample period runs from 2000/Q1 to 2018/Q4 for the Taylor rule yield curve itself, and from 2002/Q1 to 2017/Q4 for OIS-based TRD analysis.

Main Findings

First, the estimated Taylor rule expected rate curves show that after the onset of the Global Financial Crisis (GFC), the balanced-rule Taylor rate dropped completely below zero for all maturities up to 10 years. During 2008/Q4, the Taylor rule expected rate curve lay approximately 2–3 percentage points below the market rate curve across maturities, reflecting excessively tight market expectations relative to what the Taylor rule framework implied. By 2011/Q4, the market OIS curve fell below the Taylor rule expected rate curve for maturities beyond 4 years—indicating that explicit and forceful forward guidance (the August 2011 FOMC statement committing to “exceptionally low levels for the federal funds rate at least through mid-2013”) had driven market rates below the Taylor-implied accommodative path at the long end.

Second, VAR analysis for the sample period 2002–2017 shows that TRDs at both 2-year and 10-year maturities generate statistically significant impulse responses: positive TRD shocks—indicating a tighter-than-Taylor monetary policy stance—cause both the output gap and inflation to decrease. Importantly, this result holds during the ELB period when the FFR gap and shadow policy rate gap do not yield theoretically consistent impulse responses; in the 2002–2017 subsample, both the FFR gap and the shadow rate gap produce perverse (positive) responses of output and inflation to a tightening shock, presumably because the ELB binds and UMP operates outside the overnight rate. The OIS rates per se (without the Taylor rule expected rate subtracted) show mostly muted and statistically insignificant impulse responses in the same VAR framework. Granger causality tests (62 observations) confirm that TRDs Granger-cause OIS rates for both 2-year (F-statistic = 4.579, p = 0.014) and 10-year (F-statistic = 7.734, p = 0.001) maturities, while the reverse direction is not rejected in either case, highlighting TRDs’ informational superiority over raw OIS rates.

Third, TRDs for 2-, 5-, and 10-year maturities are positively correlated with the VIX in the same quarter (R² values of 0.34, 0.37, and 0.35 respectively), whereas the FFR gap is negatively correlated with the VIX (R² = 0.22). This positive TRD–VIX relationship holds during both ELB (2008/Q1–2015/Q3) and non-ELB subperiods, suggesting TRDs serve as a proxy for risk appetite in financial markets—with a loose-relative-to-Taylor monetary stance associated with lower risk aversion.

Fourth, a stylized New Keynesian model with anticipated future shocks to the Taylor rule (interpreted as “news shocks”) provides theoretical support. When agents learn of a future expansionary Taylor rule shock, they revise upward their expectations of future output and inflation, which—through consumption smoothing (Euler equation) and forward-looking pricing (New Keynesian Phillips curve)—produce contemporaneous expansionary effects. An extended model with habit formation, backward-looking price-setters, and interest rate smoothing generates hump-shaped and persistent IRs consistent with the empirical patterns. Simulations on model-generated data confirm that the TRD measure, but not the future interest rate or contemporaneous rate deviation, recovers statistically significant and correctly signed impulse responses in the VAR.

Scope Conditions

The methodology requires data on professional forecasters’ expectations of output and inflation at multi-year horizons, limiting applicability to countries for which such forecast data exist. Term premium components of OIS rates are excluded from the analysis, which the authors note may make estimates of forward guidance impact conservative. The analysis is confined to the United States for the period 2000/Q1–2018/Q4.

Layer 2 — Q&A

Q1: What is the precise mathematical definition of the Taylor rule deviation (TRD) at horizon h, and how does it differ from the conventional FFR gap?

A: The TRD at maturity h is defined as the difference between the market OIS rate at h-year maturity and the Taylor rule expected rate at that maturity. The Taylor rule expected rate is the average (across years k = 1 to h) of the Taylor-rule-implied short-term interest rates expected k years ahead, where each expected rate uses professional forecasters’ projections of inflation and the output gap at that horizon, together with the current natural rate of interest (assumed unchanged). The conventional FFR gap is the deviation of the overnight FFR from the contemporaneous Taylor rule rate—a scalar at a single point in time. The TRD generalizes this to any maturity: it equals the average expected monetary policy stance (accommodative or tight relative to Taylor) from the current period through h years ahead, capturing the cumulated sum of anticipated and unanticipated disturbances to the Taylor rule.

Q2: Why does the FFR gap fail as a monetary policy stance indicator during the ELB period, and why does the shadow rate gap not resolve this failure?

A: When the FFR hits the ELB, it is pinned near zero regardless of how accommodative the Federal Reserve’s actual policy intentions are; any further intended easing through forward guidance or quantitative easing is not reflected in the overnight rate’s level or its deviation from the Taylor rule. The authors show (Figure 8a, 2002–2017 subsample) that in a three-variable VAR with output gap, inflation, and FFR gap, a positive FFR gap shock generates increases in both output and inflation—the opposite of theoretically expected contractionary effects—because the ELB constrains the FFR while UMP operates through longer maturities. The shadow policy rate (Wu and Xia, 2016) drops below zero during the UMP period and conceptually summarizes the entire yield curve’s accommodation in a single synthetic overnight rate. However, Figure 8b shows that replacing the FFR with the shadow rate leaves the perverse VAR impulse responses qualitatively unchanged in the 2002–2017 subsample, because a single short-term summary rate cannot isolate the maturity-specific information that the TRD captures.

Q3: What does the VAR analysis reveal about TRDs’ ability to capture monetary policy effects at the ELB, and does the maturity of TRD matter?

A: For the 2002–2017 sample period (Figure 9a), VAR impulse responses with the TRD replacing the FFR gap show that a positive TRD shock causes statistically significant decreases in both the output gap and inflation—the theoretically expected contractionary response. This result holds for both 2-year and 10-year TRDs. The fact that the 10-year TRD also produces this correct result indicates that TRDs at long maturities can capture the stance reflected in forward guidance, which explicitly targets expectations about the future course of monetary policy well beyond overnight. The output gap response is quantitatively larger in magnitude than the inflation response across both maturities (figure axis ranges suggest output gap peaks at roughly ±1.0% versus inflation at ±0.2%), consistent with the theoretical model’s prediction that the output gap is more responsive to contemporaneous effects while inflation responds to both current and expected future conditions.

Q4: What is the role of the output gap component versus the inflation component in driving TRD changes?

A: Figures 6 and 7 decompose period-by-period first differences of TRDs into their output gap and inflation contributions for both 2-year and 10-year maturities. The output gap component is the main determinant of changes in TRDs across both maturities, reflecting the substantially volatile outlook on economic growth—especially around the GFC. The inflation component has a considerably smaller contribution, and this difference is even more pronounced for 10-year maturities than for 2-year maturities, reflecting the fact that professional forecasters’ inflation expectations change much less at longer horizons than near-term GDP growth expectations.

Q5: What does the Granger causality analysis reveal about the informational content of TRDs relative to OIS rates?

A: Table 1 reports Granger causality tests using 62 observations. For 2-year maturities, the null that TRD 2Y does not Granger-cause OIS 2Y is rejected at the 5% level (F = 4.579, p = 0.014), while the null that OIS 2Y does not Granger-cause TRD 2Y is not rejected (F = 0.999, p = 0.375). For 10-year maturities, the null that TRD 10Y does not Granger-cause OIS 10Y is rejected at the 1% level (F = 7.734, p = 0.001), while the reverse null is not rejected (F = 0.843, p = 0.436). This unidirectional causality—TRDs leading OIS rates but not vice versa—implies that TRDs contain information about future OIS rate movements not already embedded in current OIS rates, making TRDs informationally superior to raw OIS rates for assessing monetary policy stance.

Q6: How do TRDs relate to VIX, and does this relationship depend on whether the economy is at the ELB?

A: Figures 10 and 11 document that TRDs for 2-, 5-, and 10-year maturities are positively correlated with the VIX in the same quarter (R² values of approximately 0.34, 0.37, and 0.35 for 2Y, 5Y, and 10Y TRDs respectively), meaning that a tighter-than-Taylor monetary policy stance (positive TRD) is associated with higher market risk aversion. By contrast, the FFR gap shows a negative correlation with the VIX (R² = 0.22), the opposite sign. The same positive TRD–VIX correlation is observed when current TRDs are plotted against VIX four quarters later, though the R² values are smaller (ranging from approximately 0.04 to 0.05). Critically, Figure 11 shows that dividing the 2002/Q1–2017/Q4 sample into ELB (2008/Q1–2015/Q3) and non-ELB periods, the positive correlation between the 5-year TRD and VIX holds during both subperiods (R² = 0.37 for ELB current quarter, R² = 0.41 for ELB four quarters ahead), demonstrating that TRDs’ relationship with risk appetite is not an artifact of the ELB environment.

Q7: What does the theoretical New Keynesian model contribute, and what is the mechanism by which anticipated future Taylor rule shocks affect current macroeconomic variables?

A: The paper embeds anticipated future shocks to the Taylor rule (news shocks) in a stylized New Keynesian model with Euler equation, New Keynesian Phillips curve, and Taylor rule. When a one-period-ahead expansionary monetary policy shock (εh,t for h=1) is announced at time t, agents expect expansionary effects in period t+1 (higher output gap and inflation). Through consumption smoothing in the Euler equation, expected higher output in t+1 raises current consumption and thus current output. Through forward-looking pricing in the NKPC, expected higher future inflation raises current inflation. Analytically, the coefficients on the one-period-ahead shock (c_{1,y} and c_{1,π}) satisfy the same signs as the contemporaneous shock coefficients (c_{0,y} and c_{0,π}), confirming the contemporaneous impact. The model shows that for the inflation rate, the future shock has larger impact than the contemporaneous shock (|c_{1,π}| > |c_{0,π}|) because inflation responds to both current and future output gap in the NKPC; for the output gap, the future shock has smaller impact (|c_{1,y}| < |c_{0,y}|) because higher expected inflation raises the nominal interest rate via the Taylor rule’s endogenous feedback, partially offsetting the expansionary effect on current output.

Q8: How do simulations on model-generated data validate the VAR methodology for identifying TRD effects?

A: Figure 17 uses simulated data from the model with inertia (200 periods, corresponding to 50 years) to compare three interest rate measures in a three-variable VAR (output gap, inflation, interest rate measure): (i) the average future interest rate (I), (ii) the contemporaneous interest rate deviation (ε_{0,t}), and (iii) the H-period TRD with H = 8. When the future interest rate I is used, the identified monetary policy shock produces impulse responses with the opposite sign relative to the structural model, because the VAR captures reverse causality between the interest rate and the state of the economy. When the contemporaneous rate deviation ε_{0,t} is used, responses have the intended sign but are not statistically significant, because future anticipated shocks are not materialized in the current period’s rate. When the TRD is used, the identified shock generates statistically significant responses with the correct sign, validating TRD as the appropriate measure for capturing the effects of anticipated future monetary policy shocks in an empirical VAR framework.

Q9: How does the Taylor rule yield curve behave at specific historical episodes, and what do these patterns reveal about monetary policy stance?

A: During 2008/Q4, the Taylor rule expected rate curve (balanced rule) lay approximately 2–3 percentage points below the market OIS curve across all maturities, reflecting that markets expected a much faster policy normalization than the Taylor rule implied given the economic collapse—indicating excessively tight market expectations. By 2011/Q4, after successive rounds of forward guidance, the market OIS curve fell below the Taylor rule expected rate curve for maturities beyond 4 years, with the balanced-rule Taylor expected rates remaining negative for maturities up to 3 years. By 2013/Q4, mid- and long-term market expected rates were roughly aligned with Taylor rule expected rates. In 2015/Q4, when the Fed hiked for the first time post-GFC (while the Taylor rule short-term rate was still negative), the market curve almost perfectly matched the Taylor rule expected curve for maturities beyond one year. In 2017/Q4, the Taylor rule expected rate curve exceeded the market curve by approximately 0.5–1 percentage points, suggesting continued expansionary stance even after policy rate normalization began.

Q10: How robust are the results to the choice between the original and balanced Taylor rule specifications?

A: Robustness checks (Figures 12–14) compare results under the original rule (α = 0.5, β = 0.5) versus the baseline balanced rule (α = 0.5, β = 1.0). The original rule generates smaller fluctuations in Taylor rule expected rates, reflecting its lower coefficient on the more volatile output gap. However, the overall trajectories do not change significantly. The main qualitative difference emerges in 2011/Q4 and 2013/Q4: the balanced rule implies Taylor expected rates are negative for 1–3 year maturities (indicating the ELB was still binding even relative to medium-term Taylor-implied paths), while the original rule produces all-positive Taylor expected rates for these periods. For 2008/Q4, 2009/Q4, 2015/Q4, and 2017/Q4, both specifications yield similar pictures, and the central conclusions about TRDs’ macroeconomic relevance and relationship with risk appetite are robust to the specification choice.

Key Concepts

Taylor Rule Yield Curve: The paper’s proposed extension of the standard Taylor rule from the overnight federal funds rate to all points in the future yield curve horizon (1 through 10 years). For maturity h, it is the average of h annual Taylor-rule-implied expected short-term rates, each calculated using professional forecasters’ h-years-ahead projections of inflation and the output gap plus the current estimate of the natural rate. Not a market instrument but a model-derived benchmark yield curve representing the “neutral” rate at each horizon.

Taylor Rule Deviation (TRD): The gap between the market OIS rate at maturity h and the corresponding Taylor rule expected rate—that is, the deviation of market expectations from what the Taylor rule framework implies should prevail at that horizon. A positive TRD indicates market rates are above the Taylor-implied rate (tighter-than-neutral stance); a negative TRD indicates easier-than-neutral stance. The TRD at maturity h equals the average of expected monetary policy stance residuals from the current period through h years ahead.

Effective Lower Bound (ELB): The floor to which a central bank can reduce the nominal policy rate before further cuts become infeasible or counterproductive. In the paper’s empirical context, the FFR ELB episode for the United States runs from 2008/Q1 to 2015/Q3. During this period, the standard FFR gap and shadow rate gap measures fail to produce theoretically consistent VAR impulse responses.

Taylor Rule Expected Rate: The paper’s specific construct: the average of Taylor-rule-implied future short-term interest rates at each year of maturity, computed from professional forecasters’ consensus projections of inflation and output gap at multi-year horizons. Distinct from any market rate; serves as the “neutral” benchmark at each maturity against which OIS rates are compared.

Balanced vs. Original Taylor Rule: Two coefficient specifications used in the paper. The “original” rule (Taylor, 1993) sets the inflation gap coefficient α = 0.5 and the output gap coefficient β = 0.5. The “balanced” rule (Taylor, 1999) sets α = 0.5 and β = 1.0, placing greater weight on output stabilization; the paper uses the balanced rule as its baseline on the grounds that it better reflects the Federal Reserve’s dual mandate in recent years.

Anticipated Future Taylor Rule Shocks (News Shocks): Shocks to the Taylor rule that are known to agents at time t but materialize in a future period t+h. Following Laséen and Svensson (2011) and Del Negro et al. (2012), the paper embeds these in a New Keynesian model to show that anticipated future expansionary policy has contemporaneous expansionary effects through consumption smoothing and forward-looking pricing—the theoretical mechanism underpinning why TRDs at longer maturities affect current macroeconomic outcomes.

Risk-Taking Channel via TRD: The paper’s finding that TRDs for 2-, 5-, and 10-year maturities are positively correlated with VIX (R² ≈ 0.34–0.37 in the same quarter), holding in both ELB and non-ELB periods. A positive TRD (tighter-than-Taylor stance) corresponds to higher market risk aversion as measured by VIX, enabling TRDs to serve as a maturity-specific measure of risk appetite in financial markets—in contrast to the FFR gap, which shows the opposite (negative) correlation with VIX.