Explicit Neutral Rate (r*) Proxy

Abstract

We construct a daily, market-anchored proxy for the neutral real policy rate. The signal combines long-run real yields and a term-premium-adjusted variant into a composite r* context. The current real policy rate is then evaluated against this proxy to classify the stance as restrictive, near neutral, or accommodative. Directional drift and confidence are derived to support reaction-function analysis.

1. Data (FRED Identifiers)

• FEDFUNDS — Federal Funds Effective Rate
• DFII10 — Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity, Inflation-Indexed
• T10YIE — 10-Year Breakeven Inflation Rate
• THREEFYTP10 — Term Premium on a 10 Year Zero Coupon Bond

All series are sourced from FRED. Market series are daily; the policy rate is forward-filled between updates to reflect known policy settings.

2. Data Handling & Validation

3. Neutral Rate Components

4. Composite Neutral Proxy

We use a simple equal-weighted mean of available components. This is a context proxy and is not intended as a structural estimate of r*.

5. Policy Stance Relative to Neutral

We approximate a real policy rate using expected inflation and compare it to the neutral proxy.

• Restrictive: stance_gap ≥ +0.50
• Near neutral: −0.50 < stance_gap < +0.50
• Accommodative: stance_gap ≤ −0.50

6. Directional Drift of Neutral

We measure the change in the neutral proxy over a three-month (business-day) window to infer drift.

• Rising: drift > +0.10
• Stable: |drift| ≤ 0.10
• Falling: drift < −0.10

7. Confidence

Confidence is driven by cross-proxy dispersion and component availability.

• High: dispersion ≤ 0.20 and ≥2 components available
• Medium: 0.20 < dispersion ≤ 0.35, or only 1 component available
• Low: dispersion > 0.35 or sparse/unstable inputs

8. Output Panel

[
  "rstar_proxy",
  "policy_real_proxy",
  "stance_gap",
  "policy_stance_vs_neutral",
  "neutral_drift",
  "confidence",
  "rstar_market_real",
  "rstar_term_prem_adj_real"
]

9. Implementation Notes (Python)

# Expect df_rstar_inputs indexed by date (business-day), ffilled.
# rstar_market_real = DFII10
# rstar_term_prem_adj_real = DFII10 - THREEFYTP10 (if available)
# rstar_proxy = mean(components)
# policy_real_proxy = FEDFUNDS - T10YIE
# stance_gap = policy_real_proxy - rstar_proxy
# drift_3m = rstar_proxy.diff(63)
# confidence via dispersion std(components) + component count

10. Interpretation & Use

This signal is intended to be interpreted as a policy-stance context indicator: it compares an inflation-adjusted policy-rate proxy to a market-anchored neutral-rate proxy. It does not estimate the structural neutral rate (r*) directly.

10.1 Model Interpretation (how to read the signal)

What the level means

• r*_proxy (neutral context): Higher values imply the market is pricing a higher long-run real rate environment (or lower term premia if using the term-adjusted component). Treat changes as context, not as “true r*”.
• policy_real = FEDFUNDS − T10YIE: A simple real-rate proxy using 10y breakevens as expected inflation. Interpret as an ex-ante real stance approximation; it can diverge from near-term inflation expectations.
• stance_gap = policy_real − r*proxy: The key signal. Positive values indicate policy is above the neutral context (restrictive); negative values indicate below (accommodative).

How to interpret the stance regime (thresholds)

• Restrictive (stance_gap ≥ +0.50): Policy is materially above the neutral context. In macro narratives, this is consistent with ongoing headwinds to growth and tighter financial conditions, even if the central bank is on hold.
• Near neutral (−0.50 < stance_gap < +0.50): Policy is close to the neutral context. Interpretation depends on other signals (inflation momentum, slack, financial stress) and the direction of drift.
• Accommodative (stance_gap ≤ −0.50): Policy is materially below the neutral context. This is consistent with support to growth/risk assets and potentially higher inflation persistence risk, depending on slack and inflation signals.

What the drift means (neutral moving under your feet)

• Rising neutral (drift > +0.10): A higher neutral context can justify “higher for longer” even without rising inflation, and can reduce the apparent restrictiveness of a given policy rate over time.
• Falling neutral (drift < −0.10): A lower neutral context can increase the apparent restrictiveness of an unchanged policy rate, potentially strengthening the case for cuts if other signals deteriorate.
• Stable (|drift| ≤ 0.10): Treat the neutral context as broadly unchanged; focus interpretation on the stance_gap level and changes in expected inflation.

What “confidence” means (signal reliability, not correctness)

Confidence is a measurement quality proxy based on component availability and dispersion across components (where applicable). It should be interpreted as “how stable the proxy is,” not “probability the stance call is correct.”

• High: components broadly agree (low dispersion) and at least two components are present.
• Medium: moderate dispersion, or only one component available.
• Low: high dispersion or sparse/unstable inputs (e.g., term-premium series disruptions).

10.2 How to use it inside a macro model

• Policy restrictiveness framing: Use stance_gap to convert “Fed on hold” into a stance statement (still restrictive vs neutral, near neutral, or accommodative).
• Cross-confirm with inflation momentum and slack: Treat a restrictive stance as more growth-negative when slack indicators worsen; treat it as more inflation-relevant when inflation momentum re-accelerates.
• Prefer sustained moves: Market-implied series are volatile and can be distorted by liquidity and risk premia; use multi-week/month persistence and cross-signal confirmation.
• Scenario narratives: Rising neutral + stable inflation can support “delayed cuts”; falling neutral + weakening growth can support “cuts sooner,” all else equal.

10.3 Key caveats (avoid common misreads)

• Market vs structural r*: Market-implied real yields embed risk and liquidity premia and are not equivalent to structural estimates (e.g., Laubach–Williams / Holston–Laubach–Williams).
• Breakeven inflation distortions: T10YIE can reflect inflation risk premia and liquidity effects in TIPS, not pure expectations. Treat policy_real as an approximation.
• Term premium model uncertainty: THREEFYTP10 is model-based; revisions and regime shifts can affect the term-adjusted component.
• Horizon mismatch: Using 10-year measures to interpret near-term policy can be informative for “neutral context” but can diverge from 1–2 year inflation expectations that often drive near-term policy decisions.

10.4 Academic anchors (why these variables matter)

• Neutral rate (r*) concept: The real interest rate consistent with output at potential and stable inflation; widely used in modern monetary policy analysis and “policy vs neutral” framing.
• Fisher relationship: Nominal rates can be decomposed into real rates plus expected inflation; motivates the real-policy proxy using breakevens as an expectations anchor.
• Rules-based policy and stance gaps: Comparing policy rates to neutral concepts is central to reaction-function analysis (e.g., Taylor-type rules and modern DSGE/New Keynesian policy frameworks).
• Term premium adjustments: Long-maturity yields include term premia that vary over time; adjusting for term premia can better isolate policy-relevant real-rate signals.

10.5 Selected references (starter list)

• Fisher, I. (1930). The Theory of Interest.
• Taylor, J. B. (1993). “Discretion versus policy rules in practice.” Carnegie-Rochester Conference Series on Public Policy.
• Clarida, R., Galí, J., & Gertler, M. (1999/2000). “The Science of Monetary Policy.” Journal of Economic Literature.
• Laubach, T., & Williams, J. C. (2003). “Measuring the Natural Rate of Interest.” Review of Economics and Statistics.
• Holston, K., Laubach, T., & Williams, J. C. (2017). “Measuring the Natural Rate of Interest: International Trends and Determinants.” Journal of International Economics.
• Adrian, T., Crump, R. K., & Moench, E. (2013). “Pricing the Term Structure with Linear Regressions.” Journal of Financial Economics. (term premia framework)
• Kim, D. H., & Wright, J. H. (2005). “An Arbitrage-Free Three-Factor Term Structure Model and the Recent Behavior of Long-Term Yields and Distant-Horizon Forward Rates.” (term premia / expectations decomposition)
• FRED series documentation and technical notes for DFII10, T10YIE, THREEFYTP10, and FEDFUNDS (definitions, revisions, caveats).