Chapter 7 7.8

Neutral Rates and Stagflation

The natural rate of interest (r*), estimation methods, Japan's r* collapse, and stagflation risks

Neutral Rates and Stagflation

The neutral interest rate (also called the natural rate or r-star, denoted $r^*$) is one of the most important—yet unobservable—concepts in monetary policy. It represents the theoretical real interest rate consistent with:

Full employment (output at potential)
Stable inflation (at target, typically 2%)
No cyclical pressures (neither stimulative nor contractionary policy stance)

For the Bank of Japan and JGB markets, understanding r* is critical because:

Policy Guidance: The BOJ’s policy rate should converge toward $r^* + \pi^*$ (neutral rate + inflation target) in steady state
Yield Anchors: Long-term JGB yields reflect market expectations of where the policy rate will settle once normalized
Normalization Path: The distance between current policy rates and r* determines how much tightening room the BOJ has
Stagflation Risk: In an environment of simultaneous high inflation and weak growth, estimating r* becomes exceptionally difficult

Japan’s r* has undergone a dramatic collapse over the past three decades—from approximately 4% in the early 1990s to 0% or negative by the 2020s—making it one of the most extreme cases globally. Understanding why this happened, how r* is calculated, and what it means for future policy is essential for anyone analyzing JGB markets.

This section provides a comprehensive technical treatment of neutral rate estimation, with particular focus on Japan’s unique experience and the modern challenge of stagflation.

What is the Neutral Rate (r*)?

Theoretical Foundation

The neutral rate concept originates from Knut Wicksell’s 1898 work Interest and Prices, which distinguished between:

Natural rate of interest: The rate that equilibrates saving and investment at full employment
Market rate of interest: The actual interest rate set by central banks

Wicksell argued that when the market rate < natural rate, the economy experiences inflationary pressure (excess demand). Conversely, market rate > natural rate causes deflationary pressure (excess supply).

Modern formulations extend this to the real neutral rate $r^*$, defined implicitly by:

\[r^* = \text{Real rate where } \pi = \pi^* \text{ and } Y = Y^*\]

Where:

$\pi$ = Actual inflation rate
$\pi^*$ = Target inflation rate (2% for BOJ)
$Y$ = Actual output (GDP)
$Y^*$ = Potential output (full employment GDP)

The Equilibrium Condition

In a simple macroeconomic model, the neutral rate emerges from the intertemporal Euler equation representing households’ optimal consumption path:

\[r^* = \rho + \gamma \cdot g^*\]

Where:

$\rho$ = Time preference rate (impatience/discount rate, typically 1-2%)
$\gamma$ = Elasticity of intertemporal substitution (willingness to shift consumption over time, typically 1-2)
$g^*$ = Potential GDP growth rate (trend productivity + labor force growth)

Key insight: $r^$ rises with higher potential growth $g^$ and falls with lower growth. Japan’s $r^*$ collapse is primarily driven by declining potential growth due to:

Demographics: Shrinking and aging workforce (labor force peaked 1998)
Productivity stagnation: Total factor productivity (TFP) growth near zero since 1990s
Investment decline: Corporate savings exceed investment (“savings glut”)

Why r* is Unobservable

Unlike the policy rate (directly set by the BOJ) or market yields (observable in JGB markets), $r^*$ cannot be directly measured. It must be estimated using:

Statistical filtering techniques (Kalman filters)
Structural macroeconomic models
Survey-based approaches
Financial market signals

This estimation uncertainty creates significant challenges for policymakers and investors.

The Laubach-Williams Model: The Gold Standard

The Laubach-Williams (LW) model (2003) is the most widely cited framework for estimating $r^*$, used by the Federal Reserve, ECB, and (with modifications) the BOJ. It combines:

State-space representation: Unobserved variables (like $r^*$) estimated via Kalman filtering
Semi-structural approach: Mix of economic theory and statistical fitting
Time-varying parameters: Allows $r^*$ to evolve gradually over time

The Model Structure

The LW model consists of three core equations:

1. IS Curve (Aggregate Demand)

\[\tilde{y}_t = a_1 \tilde{y}_{t-1} + a_2 \tilde{y}_{t-2} + \frac{a_r}{2} \sum_{i=1}^{2} (r_{t-i} - r^*_{t-i}) + \epsilon_{y,t}\]

Where:

$\tilde{y}_t$ = Output gap (actual GDP - potential GDP), in %
$r_t$ = Real short-term interest rate (policy rate - inflation)
$r^*_t$ = Neutral rate (unobserved, time-varying)
$a_1, a_2, a_r$ = Estimated coefficients
$\epsilon_{y,t}$ = Demand shock

Interpretation: Output gap depends on lagged gaps and the real rate gap $(r_t - r^_t)$. When $r_t > r^_t$, monetary policy is contractionary → Output gap shrinks (economy cools).

2. Phillips Curve (Inflation Dynamics)

\[\pi_t = b_1 \pi_{t-1} + (1 - b_1) \pi_{t-2,t-4} + b_y \tilde{y}_{t-1} + \epsilon_{\pi,t}\]

Where:

$\pi_t$ = Inflation rate at time $t$
$\pi_{t-2,t-4}$ = Average inflation over quarters $t-2$ to $t-4$ (long-run anchor)
$b_1, b_y$ = Estimated coefficients
$\epsilon_{\pi,t}$ = Inflation shock

Interpretation: Inflation depends on past inflation (inertia) and the output gap (demand pressure). Positive $\tilde{y}_t$ → Rising inflation.

3. State Equations (Unobserved Components)

The neutral rate $r^*$ evolves according to:

\[r^*_t = c \cdot g_t + z_t\] \[g_t = g_{t-1} + \epsilon_{g,t}\] \[z_t = z_{t-1} + \epsilon_{z,t}\]

Where:

$g_t$ = Trend GDP growth (random walk, captures productivity/demographics)
$z_t$ = Other determinants of $r^*$ (e.g., risk premia, global factors)
$c$ = Coefficient linking growth to $r^$ (typically ~1, consistent with theory $r^ = \rho + \gamma \cdot g^*$)
$\epsilon_{g,t}, \epsilon_{z,t}$ = Shocks to trend growth and other factors

Key mechanism: If potential growth $g_t$ declines (as in Japan post-1990), then $r^*_t$ declines proportionally.

Estimation via Kalman Filter

The LW model is estimated using a Kalman filter, which:

Prediction step: Forecasts unobserved states ($r^*_t$, $g_t$, $z_t$) based on prior period
Update step: Revises forecasts based on observed data ($Y_t$, $\pi_t$, $r_t$)
Iteration: Repeats for entire time series, producing smoothed estimates of $r^*_t$

The filter maximizes the likelihood of observed data, subject to the model structure.

Laubach-Williams Applied to Japan

Researchers have applied the LW model to Japan with striking results:

Estimated $r^*$ for Japan:

Period	LW Estimate (Real $r^*$)	Drivers
1990-1995	~3-4%	High potential growth (bubble hangover still positive)
1996-2000	~1-2%	Demographics turn negative, banking crisis
2001-2010	~0-1%	Lost Decade, deflation, TFP stagnation
2011-2019	~-0.5 to 0%	Abenomics structural headwinds, aging accelerates
2020-2025	~-1 to 0%	COVID shock, potential growth near zero

Source: BOJ Working Papers, Fujiwara et al. (2016), Imakubo et al. (2023)

Limitations of the LW Model

End-point problem: $r^*$ estimates for recent years are highly uncertain (Kalman filter needs future data for smoothing)
Model uncertainty: Results sensitive to Phillips Curve specification (flat curve in Japan makes identification difficult)
Parameter instability: Structural breaks (e.g., YCC introduction 2016) can distort estimates
Global factors: Ignores international spillovers (global savings glut, safe asset demand)

Despite these limitations, the LW framework remains the benchmark for central banks.

The Taylor Rule Framework

While the Laubach-Williams model estimates $r^*$ structurally, the Taylor Rule provides an alternative perspective by describing how central banks should set policy rates as a function of inflation and output gaps.

The Original Taylor Rule (1993)

John Taylor’s seminal 1993 rule prescribed:

\[i_t = r^* + \pi_t + 0.5(\pi_t - \pi^*) + 0.5 \tilde{y}_t\]

Where:

$i_t$ = Nominal policy rate (what the central bank sets)
$r^*$ = Neutral real rate (assumed constant at 2% in Taylor’s original paper)
$\pi_t$ = Current inflation rate
$\pi^*$ = Target inflation (2% in modern frameworks)
$\tilde{y}_t$ = Output gap (% deviation from potential GDP)

Interpretation:

When inflation exceeds target ($\pi_t > \pi^*$), raise rates by 0.5× the overshoot
When output exceeds potential ($\tilde{y}_t > 0$), raise rates by 0.5× the gap
The neutral nominal rate in equilibrium is $r^* + \pi^*$

The Taylor Principle

The rule embeds the Taylor Principle: When inflation rises 1%, the central bank should raise the nominal rate by more than 1% to increase the real rate and cool the economy.

In the equation above:

Inflation rises by 1% → Nominal rate rises by $1 + 0.5 = 1.5\%$ → Real rate rises by 0.5%

This ensures monetary policy is stabilizing rather than destabilizing.

Adapting the Taylor Rule for Japan

Japan’s experience requires significant modifications:

1. Time-Varying $r^*$

Unlike Taylor’s assumption of constant $r^* = 2\%$, Japan’s $r^*$ has collapsed. Modern BOJ applications use time-varying $r^*$ estimated from LW or other models:

\[i_t = r^*_t + \pi_t + \alpha(\pi_t - \pi^*) + \beta \tilde{y}_t\]

Where $r^*_t$ is updated quarterly.

2. Different Reaction Coefficients

BOJ research (Leigh 2010, Ichiue & Nishiguchi 2015) finds Japan’s implicit Taylor Rule coefficients differ from the US:

Parameter	US (Taylor 1993)	Japan (Estimated 2000-2019)
$\alpha$ (inflation response)	0.5	0.3-0.4 (weaker)
$\beta$ (output gap response)	0.5	0.2-0.3 (weaker)
$r^*$	2.0%	-0.5% to 0% (much lower)

Key finding: BOJ reacts less aggressively to inflation and output deviations, likely due to:

Deflationary mindset (2000-2020): Asymmetric risk of returning to deflation
Zero lower bound constraints: Cannot cut rates below ~-0.1%
YCC framework (2016-2024): Rate directly controlled, not following a rule

3. The Balanced-Approach Taylor Rule

The Federal Reserve (Yellen 2012) proposed a variant with equal weights on inflation and unemployment (inverse of output gap):

\[i_t = r^*_t + \pi_t + 0.5(\pi_t - \pi^*) + (u^* - u_t)\]

Where:

$u_t$ = Unemployment rate
$u^*$ = Natural rate of unemployment (NAIRU)

For Japan, this becomes:

\[i_t = r^*_t + \pi_t + 0.5(\pi_t - \pi^*) + 2(u^* - u_t)\]

(Factor of 2 converts unemployment gap to output gap via Okun’s Law)

Using Taylor Rules to Infer $r^*$

If we observe the BOJ’s actual policy rate $i_t$ and know inflation $\pi_t$ and output gap $\tilde{y}_t$, we can solve for the implied $r^*$:

\[r^*_{\text{implied}} = i_t - \pi_t - \alpha(\pi_t - \pi^*) - \beta \tilde{y}_t\]

Example (Japan Q4 2024):

Policy rate: $i_t = 0.25\%$
Core CPI inflation: $\pi_t = 2.5\%$
Target inflation: $\pi^* = 2.0\%$
Output gap: $\tilde{y}_t = 0.5\%$ (slightly above potential)
Estimated coefficients: $\alpha = 0.4$, $\beta = 0.3$

\[r^*_{\text{implied}} = 0.25\% - 2.5\% - 0.4(2.5\% - 2.0\%) - 0.3(0.5\%)\] \[r^*_{\text{implied}} = 0.25\% - 2.5\% - 0.2\% - 0.15\% = -2.6\%\]

Interpretation: If BOJ is following a Taylor Rule, the implied $r^*$ is deeply negative (~-2.6%). This suggests either:

BOJ estimates $r^*$ is very low, OR
BOJ is deviating from the Taylor Rule (operating behind the curve to avoid choking off nascent inflation)

Taylor Rule Deviations and Policy Stance

Comparing the actual policy rate to the Taylor Rule prescription reveals policy stance:

\[\text{Policy Deviation} = i_{\text{actual}} - i_{\text{Taylor Rule}}\]

Negative deviation ($i_{\text{actual}} < i_{\text{Taylor}}$) → Accommodative policy (easier than rule suggests)
Positive deviation → Restrictive policy

For Japan 2013-2024 (Abenomics/QQE era), the deviation was consistently -200bp to -300bp, indicating exceptionally loose policy relative to fundamentals.

Other Estimation Methods

Beyond Laubach-Williams and Taylor Rules, researchers and central banks employ several complementary approaches:

1. Holistic/Judgmental Approach (BOJ’s Primary Method)

The BOJ does not rely solely on model-based $r^*$ estimates. Instead, policymakers use a holistic assessment combining:

Economic theory: Growth-based calculations ($r^* \approx \rho + \gamma \cdot g^*$)
Statistical models: LW-type filters, DSGE models, VAR models
Financial market signals: Long-term JGB yields, inflation breakevens, FX forwards
Survey data: Consensus Economics forecasts, BOJ Tankan expectations
International comparisons: US/Euro area $r^*$ estimates (global spillovers)

Governor Ueda’s approach (2024):

“We do not mechanically rely on any single model. The neutral rate is inherently uncertain. We assess a range of estimates and cross-check with market pricing and business surveys.”

This eclectic approach acknowledges model uncertainty and structural breaks (e.g., YCC distorting yield curves).

2. Survey-Based Methods

Consensus Economics surveys professional forecasters quarterly:

Q: “What real policy rate do you expect in 10 years?”
Interpretation: Long-run forecast converges to $r^*$ (assuming inflation reaches target)

Japan’s survey-based $r^*$ (2024):

Median 10-year ahead real rate forecast: 0.2% (range: -0.3% to 0.8%)
Implies $r^*$ near zero, consistent with LW estimates

Advantages:

Forward-looking: Incorporates future structural reforms, demographics
Market-informed: Reflects actual expectations, not model assumptions

Limitations:

Backward-looking anchoring: Surveys may extrapolate recent trends
Coordination bias: Forecasters herd around consensus

3. DSGE Model-Based Estimates

Dynamic Stochastic General Equilibrium (DSGE) models solve for $r^*$ by imposing full micro-foundations:

Households maximize utility subject to budget constraints
Firms maximize profits subject to production functions
Markets clear (goods, labor, bonds)

The steady-state real interest rate from the model is $r^*$.

BOJ’s DSGE model estimates (Ichiue et al. 2023):

$r^*$ for Japan: -0.3% to 0.5% (depends on calibration of demographics/productivity)

Advantages:

Internally consistent: All equations derived from optimization
Scenario analysis: Can simulate policy changes, structural reforms

Limitations:

High complexity: Requires strong assumptions about household/firm behavior
Parameter uncertainty: Results sensitive to calibration

4. Financial Market Signals

Markets embed expectations of $r^*$ in:

a) Long-Term JGB Yields

The 10Y or 30Y JGB yield should approximately equal:

\[\text{Long-term yield} \approx r^* + \pi^* + \text{term premium} + \text{inflation risk premium}\]

Solving for $r^*$:

\[r^* \approx \text{Long yield} - \pi^* - \text{premia}\]

Example (30Y JGB, October 2025):

30Y JGB yield: 2.10%
Expected long-run inflation ($\pi^*$): 2.0%
Estimated term premium: 0.5%
Inflation risk premium: 0.3%

\[r^* \approx 2.10\% - 2.0\% - 0.5\% - 0.3\% = -0.7\%\]

Problem: During YCC (2016-2024), JGB yields were artificially suppressed, making this approach unreliable. Post-YCC (2024+), this becomes more informative.

b) Inflation-Linked JGBs (JGBi)

The breakeven inflation rate (nominal yield - real yield) provides market’s inflation expectations:

\[\text{Breakeven} = \text{Nominal 10Y JGB} - \text{JGBi 10Y Real Yield}\]

If breakeven ≈ $\pi^$, then JGBi real yield ≈ $r^ +$ term premium.

Japan’s JGBi market challenges:

Illiquid (only ~¥14T outstanding vs ¥1,200T nominal JGBs)
Deflation option embedded (cannot pay negative principal)
Distorted by BOJ purchases

c) FX Forward Rates (Covered Interest Parity)

Under covered interest parity:

\[\frac{1 + i_{\text{Japan}}}{1 + i_{\text{US}}} \approx \frac{F}{S}\]

Where $F$ = forward exchange rate, $S$ = spot rate.

Long-run forward rates embed expectations of long-run real rate differentials, which relate to $r^*$ differences.

5. Global Factors and International Spillovers

Research (Rachel & Smith 2017, Del Negro et al. 2019) shows $r^*$ has declined globally since the 1980s, driven by:

Global savings glut: Excess savings in China, oil exporters
Safe asset demand: Post-GFC preference for government bonds
Productivity slowdown: Advanced economies experiencing TFP stagnation

Japan’s $r^*$ is influenced by:

Global $r^*$ trends: Arbitrage ensures Japanese rates can’t diverge too far from US/Euro area
Capital flows: Foreign demand for JGBs (yen as safe haven) depresses $r^*$
Trade linkages: Export dependence on US/China growth

Empirical finding: ~40-50% of Japan’s $r^*$ decline explained by global factors, not purely domestic demographics/productivity.

Japan’s r* History: A 35-Year Collapse

Japan’s neutral rate has undergone one of the most dramatic declines of any advanced economy. Understanding this trajectory is essential for interpreting BOJ policy and JGB valuation.

Era 1: The Bubble Economy (1985-1991) — $r^* \approx 4-5\%$

Economic Backdrop:

Asset price bubble (Nikkei 225 peaked 38,915 in Dec 1989)
Real estate boom (Tokyo land prices up 300% from 1985-1990)
Strong GDP growth (4-5% annually)
Labor force still expanding
Productivity growth robust (~2-3% TFP)

Policy rates: BOJ raised rates from 2.5% (1987) → 6.0% (1990) to combat inflation and cool speculation.

Implied $r^*$: Estimated at 4-5% real based on:

Potential GDP growth: ~4% (labor force + productivity)
Real policy rates averaged 3-4% during expansion → Below $r^*$ (economy overheating)

Era 2: The Post-Bubble Adjustment (1992-1998) — $r^* \approx 2-3\%$

Economic Backdrop:

Banking crisis (bad loans estimated ¥100T)
Corporate deleveraging (zombie firms)
Labor force growth slows
Investment decline (Capex-to-GDP falls from 20% → 15%)

Policy response: BOJ cut rates aggressively:

1991: 6.0%
1995: 0.5% (first ZIRP episode)

Implied $r^*$: Declined to 2-3% real due to:

Potential growth fell to ~1.5-2% (TFP stagnation began)
Demographics turned: Working-age population peaked 1995 at 87M

BOJ estimates (retrospective): Fujiwara et al. (2016) estimate $r^*$ at ~2.5% for this period.

Era 3: The Lost Decade (1999-2008) — $r^* \approx 0-1\%$

Economic Backdrop:

Chronic deflation (CPI fell 0.2-0.5% annually)
ZIRP (Zero Interest Rate Policy) introduced 1999
Quantitative Easing (QE1) 2001-2006
Corporate savings > investment (net lenders)

Key structural shifts:

Demographics worsen: Fertility rate 1.26 (2005), lowest ever
Productivity stagnates: TFP growth near zero
Household behavior changes: Savings rate rises due to uncertainty

Implied $r^*$: Collapsed to 0-1% real:

Potential GDP growth: ~0.5-1.0%
Despite ZIRP (0% nominal, ~0.5% real given deflation), economy stagnant → Policy still not loose enough

Academic estimates:

Laubach-Williams applied to Japan (Fujiwara 2016): $r^* \approx 0.5\%$ (2000-2005)
Nishizaki et al. (BOJ 2014): $r^* \approx 0.3\%$

Era 4: Abenomics and Negative Rates (2013-2019) — $r^* \approx -0.5 to 0\%$

Economic Backdrop:

Abenomics “three arrows” (monetary, fiscal, structural reform)
BOJ expands QQE massively (balance sheet ¥180T → ¥550T)
Negative Interest Rate Policy (NIRP) introduced Jan 2016 (-0.1%)
Yield Curve Control (YCC) introduced Sep 2016 (target 10Y at 0%)

Structural headwinds intensify:

Aging accelerates: Median age 48 (2020), highest in OECD
Labor force shrinks: Down to 67M (2020) from 69M (2000)
Corporate cash hoarding: Firms hold ¥300T+ in cash (risk aversion)

Implied $r^*$: Turned negative (~-0.5% to 0%):

Potential growth: ~0.3-0.5% (extremely low)
Despite negative policy rates and massive QE, inflation stayed below 1% → Policy still not loose enough relative to $r^*$

BOJ estimates (Ichiue & Nishiguchi 2015): $r^*$ for Japan fell to -0.5% to -0.2% by 2015.

Era 5: Post-COVID and Policy Normalization (2020-2025) — $r^* \approx -1 to 0\%$

Economic Backdrop:

COVID-19 shock (2020 GDP -4.3%)
Supply chain disruptions → Import inflation (weak yen, energy prices)
Wage growth revival (2024 spring wage increases 5.3%)
BOJ ends YCC (March 2024), raises rates to 0.25% (July 2024)

Debate over $r^*$:

Pessimists (Goldman Sachs, Nomura) argue $r^*$ remains deeply negative (~-1%):

Demographics: Working-age population will decline 30% by 2050
Productivity: No evidence of sustained TFP revival
Corporate behavior: Risk aversion persists (cash hoarding continues)

Optimists (BOJ hawks, some private sector) argue $r^*$ has risen to 0% or positive:

Wage growth: Sustained increases suggest labor market tightness
Capex revival: Corporate investment recovering (digital, decarbonization)
Inflation psychology shift: Deflation mindset breaking after 25 years

Current consensus (survey-based, Oct 2025): $r^* \approx 0\%$ (range: -0.5% to +0.5%)

Visualizing the Collapse

Period	Estimated $r^*$ (Real)	Key Drivers
1985-1991	+4% to +5%	Bubble economy, strong growth, expanding labor force
1992-1998	+2% to +3%	Post-bubble adjustment, banking crisis begins
1999-2008	0% to +1%	Lost Decade, deflation, ZIRP/QE introduced
2009-2019	-0.5% to 0%	Abenomics, aging accelerates, NIRP/YCC
2020-2025	-1% to 0%	COVID shock, nascent reflation, policy normalization debate

Cumulative decline: ~5 percentage points over 35 years — one of the steepest $r^*$ collapses on record.

Current BOJ Estimates and Forward Guidance

Official BOJ Position (As of October 2025)

The Bank of Japan does not publish a single point estimate of $r^*$. Instead, Governor Kazuo Ueda and Policy Board members reference a range of estimates in speeches and Outlook Reports.

Governor Ueda’s Framework (July 2024 press conference):

“The neutral rate is highly uncertain and varies depending on estimation method. Our analysis suggests Japan’s real neutral rate is likely in the range of -0.5% to +0.5%, with a central tendency near zero. However, this is subject to considerable uncertainty given structural changes in the economy.”

Key components of BOJ’s holistic assessment:

Growth-based calculation: Potential GDP growth ~0.5-1.0% → Implies $r^* \approx 0.5-1.0\%$ (assuming $\rho = 1\%$, $\gamma = 1$)
Laubach-Williams estimates: BOJ staff models produce range of -0.5% to 0%
Survey data: Consensus Economics median ~0.2%
International comparison: US $r^* \approx 0.5-1.0\%$, Euro area ~0% → Japan likely similar or lower
Financial market signals: Post-YCC, 10Y JGB yield ~1.0% with 2% inflation → Implies $r^* \approx -0.5%$ (after adjusting for premia)

Consensus across estimates: $r^* \approx 0\%$ (range: -0.5% to +0.5%)

Implications for Policy Normalization

If $r^* \approx 0\%$ and inflation target is 2%, the neutral nominal policy rate is:

\[i^*_{\text{neutral}} = r^* + \pi^* = 0\% + 2\% = 2\%\]

Current policy rate (Oct 2025): 0.25%

Policy gap: $0.25\% - 2.0\% = -1.75\%$ → Policy is still 175bp below neutral

This implies:

Substantial tightening room: BOJ could raise rates by 175bp before reaching neutral stance
Gradual normalization path: Governor Ueda has emphasized “patient” approach, raising 25bp per quarter → Would take 2 years to reach neutral
Data-dependence: Pace depends on inflation sustainability and wage growth

Forward Guidance Evolution

BOJ’s communication on $r^*$ has evolved significantly:

Pre-2024 (Under YCC):

Rarely discussed $r^*$ explicitly
Focus on YCC targets and inflation overshooting commitment
Implicit assumption: $r^*$ deeply negative, policy far from neutral

March 2024 (YCC Exit):

Governor Ueda: “We judge that conditions for achieving 2% inflation sustainably are falling into place, allowing us to begin policy normalization.”
First explicit acknowledgment that policy rate could eventually rise toward $r^* + 2\%$

July 2024 (First rate hike to 0.25%):

Forward guidance: “We will adjust the degree of monetary accommodation if the outlook for economic activity and prices will be realized.”
Translation: Further hikes likely if inflation stays above 2%

October 2025 Outlook Report (Latest):

Median Policy Board forecast for 2027 policy rate: 1.0-1.5%
Implies BOJ views $r^*$ as positive, likely ~0% to +0.5% (since 1.5% rate with 2% inflation → Real rate -0.5%)

Debates Within the Policy Board

BOJ Policy Board members hold divergent views on $r^*$:

Hawks (Nakamura, Noguchi):

Estimate $r^* \approx +0.5%$ or higher
Argue potential growth is recovering (digital investment, wage-driven consumption)
Favor faster normalization (risk of falling behind the curve)

Doves (Tamura, Takata):

Estimate $r^* \approx -0.5%$ or lower
Emphasize demographics, weak productivity, corporate risk aversion
Favor gradual normalization (risk of choking off nascent inflation)

Centrists (Ueda, Himino):

Agnostic on point estimate, emphasize uncertainty
Data-dependent approach, willing to wait for confirmation
Median view: $r^* \approx 0\%$

This internal debate creates two-way risk for JGB markets:

Upside risk to yields: If hawks gain influence and BOJ tightens faster
Downside risk to yields: If data disappoints and doves delay normalization

Stagflation and the Neutral Rate: The Modern Challenge

Stagflation—the simultaneous occurrence of stagnant growth and high inflation—poses a fundamental challenge to $r^*$ estimation and monetary policy. Japan faces this risk acutely in 2024-2025.

What is Stagflation?

Traditionally, economies face trade-offs captured by the Phillips Curve:

Strong growth → Rising inflation (overheating)
Weak growth → Falling inflation (slack)

Stagflation breaks this relationship:

\[\text{Stagflation:} \quad \begin{cases} \text{GDP growth} < \text{Potential growth} & (\text{Negative output gap}) \\ \text{Inflation} > \text{Target} & (\text{Persistent price pressure}) \end{cases}\]

Historical precedents:

1970s Oil Shocks (US/UK): OPEC embargoes → Energy prices up 300% → Inflation 12%+ despite recessions
2022-2023 Global Stagflation Scare: Post-COVID supply chain disruptions + Ukraine war → Inflation 8-10% in advanced economies, growth near zero

Japan’s Stagflation Risk (2024-2025)

Japan exhibits early warning signs:

Inflationary pressures:

Core CPI 2.5-3.0% (above target)
Import costs high (weak yen, energy prices)
Wage growth 5%+ (spring negotiations 2024-2025)

Growth headwinds:

Q2 2024 GDP: -0.5% (contraction)
Consumption weak despite wage gains (real wages still negative until mid-2024)
Exports sluggish (China slowdown, US Fed tightening)

Potential scenario: Inflation stays at 2.5-3.0% while GDP growth stagnates at 0-0.5% → Mild stagflation

Why Stagflation Complicates $r^*$ Estimation

1. Output Gap Becomes Ambiguous

Standard $r^$ models (Laubach-Williams, Taylor Rule) rely on estimating the output gap $\tilde{y}_t = Y_t - Y^_t$.

Problem: If inflation is high despite negative output gap, either:

Supply-side shock is dominant (e.g., energy costs) → $r^*$ unchanged
Potential output $Y^$ has fallen more than thought → $r^$ even lower

Models cannot distinguish without additional assumptions.

2. Phillips Curve Breaks Down

The Phillips Curve equation in LW model assumes:

\[\pi_t = f(\tilde{y}_{t-1})\]

Stagflation implies this relationship inverts temporarily (inflation rises as output falls).

Consequence: Kalman filter mis-estimates $r^*$ during stagflationary periods because it assumes stable Phillips Curve.

Empirical evidence: During 1973-1975 oil crisis, Laubach-Williams estimates of US $r^*$ were wildly unstable, ranging from -2% to +6% depending on sample period.

3. Policy Trade-Offs Become Severe

In normal times, lowering rates toward $r^*$ stimulates both growth and inflation (desirable when below target).

In stagflation, central banks face impossible trade-offs:

Tighten policy (raise rates above $r^*$):

✅ Reduces inflation
❌ Worsens growth slowdown (potentially triggers recession)

Ease policy (lower rates toward/below $r^*$):

✅ Supports growth
❌ Exacerbates inflation (de-anchors expectations)

Japan’s dilemma (Oct 2025):

Inflation 2.5% → Taylor Rule suggests raising rates
Growth 0.3% → Output gap negative, suggests easing
$r^*$ uncertainty makes optimal policy unclear

Estimating $r^*$ During Stagflation

Economists use modified frameworks:

a) Supply-Adjusted $r^*$ (Clarida et al. 2000)

Decompose inflation into demand and supply components:

\[\pi_t = \pi_t^{\text{demand}} + \pi_t^{\text{supply}}\]

$\pi_t^{\text{demand}}$: Driven by aggregate demand (responds to monetary policy)
$\pi_t^{\text{supply}}$: Driven by costs (energy, supply chains, wages)

Policy implication: Central bank should look through temporary supply shocks when setting rates relative to $r^*$.

Japan example (2024):

Total CPI inflation: 2.8%
Estimated supply component (import prices, energy): 1.5%
Demand component: 1.3% → Below target
Conclusion: Despite headline inflation above 2%, BOJ should NOT aggressively tighten (stay near $r^*$)

b) Time-Varying $r^*$ with Regime Shifts

Allow $r^*$ to have structural breaks during crises:

\[r^*_t = \begin{cases} r^*_{\text{normal}} & \text{Normal times} \\ r^*_{\text{crisis}} & \text{Stagflation/Crisis} \end{cases}\]

During stagflation, $r^*_{\text{crisis}}$ may rise temporarily due to:

Increased uncertainty → Higher risk premia
Supply constraints → Lower potential growth

BOJ consideration: If 2024-2025 represents regime shift (permanent supply shocks from geopolitics, deglobalization), $r^*$ might be higher than historical estimates suggest.

Japan’s Stagflation Compared to 1970s

Dimension	1970s US/UK	2024-2025 Japan
Inflation	10-13% (severe)	2.5-3.0% (moderate)
Growth	Recession (-2% GDP)	Stagnation (0-0.5% GDP)
Wage-Price Spiral	Yes (unions powerful)	Uncertain (spring wage hikes 5%+)
Energy Dependence	Moderate	Extreme (90% energy imported)
Policy Response	Volcker shock (raise rates to 20%)	Gradual tightening (0.25% → 1.0%)
*$r^$ Estimate**	Rose temporarily to ~4-5%	Uncertain (range -0.5% to +1.0%)

Key difference: Japan’s inflation is much milder, giving BOJ more flexibility to tolerate above-target inflation if growth falters.

Stagflation and JGB Markets

How stagflation affects JGB yields:

Inflation risk premium rises: Investors demand higher yields to compensate for uncertain inflation path
Real yields volatile: Breakeven inflation becomes unstable
Curve steepening: Front-end reflects BOJ tightening, long-end reflects growth pessimism → Steeper curve
Flight to quality reverses: Stagflation typically hurts government bonds (unlike recessions)

Historical analogy: During 1970s stagflation, US Treasury yields rose despite weak growth (10Y yield: 6% in 1970 → 15% in 1981).

Japan’s risk is milder but real: If inflation stays at 3% while growth stagnates, 10Y JGB yields could rise to 1.5-2.0% (from ~1.0% in Oct 2025) even without BOJ tightening significantly.

Implications for JGB Markets

Understanding $r^*$ is critical for JGB traders and portfolio managers because it anchors:

Long-term yield levels
Policy normalization path
Curve shape and relative value
Volatility and trading strategies

1. Long-Term Yield Anchoring

In steady state (no shocks, inflation at target), the 10-year JGB yield should approximately equal:

\[Y_{10} \approx r^* + \pi^* + \text{Term Premium} + \text{Inflation Risk Premium}\]

Example calculation (Oct 2025):

$r^* \approx 0\%$ (consensus estimate)
$\pi^* = 2.0\%$ (BOJ target)
Term premium ≈ 0.3-0.5% (compensation for duration risk)
Inflation risk premium ≈ 0.2-0.4% (uncertainty about future inflation)

\[Y_{10} \approx 0\% + 2.0\% + 0.4\% + 0.3\% = 2.7\%\]

Current 10Y yield (Oct 2025): ~1.0%

Implication: 10Y JGBs trading 170bp below fair value suggests either:

Market expects lower long-run inflation than 2% (breakeven ~1.3%)
Market estimates negative $r^*$ (~-0.5%)
BOJ still suppressing yields through balance sheet effects (¥590T JGB holdings)

Trading strategy: If you believe BOJ’s $r^* \approx 0\%$ estimate and inflation will stabilize at 2%, 10Y JGBs are overvalued (yields should rise toward 2.5%). Short 10Y JGBs or steepener trades (2s10s, 5s30s).

2. Policy Normalization Path and Front-End Pricing

The neutral nominal policy rate is:

\[i^* = r^* + \pi^* = 0\% + 2.0\% = 2.0\%\]

Current policy rate: 0.25%

Implied normalization path (assuming gradual 25bp hikes):

2025 Q4: 0.50%
2026 Q2: 1.00%
2026 Q4: 1.50%
2027 Q2: 2.00% ← Reach neutral

2Y JGB yield should price this path (plus risk premium):

\[Y_2 \approx \text{Avg expected policy rate over 2 years} + \text{Risk premium}\]

If market prices “on-hold until 2026 Q2, then gradual hikes”:

\[Y_2 \approx 0.25\% \times \frac{4}{8} + 0.75\% \times \frac{2}{8} + 1.25\% \times \frac{2}{8} + 0.1\% = 0.73\%\]

Current 2Y yield (Oct 2025): ~0.6%

Implication: Market pricing suggests slower normalization than BOJ forward guidance implies, or lower terminal rate than neutral.

3. Curve Shape and r* Expectations

The slope of the yield curve reflects market’s path expectations:

\[\text{10s2s Slope} = Y_{10} - Y_2 \approx (\text{LT policy rate} - \text{ST policy rate}) + (\text{LT term premium} - \text{ST term premium})\]

Scenarios:

Scenario	$r^*$ Estimate	Implied Curve Shape	Current (Oct 2025)
*Low $r^$ (-0.5%)**	Terminal rate 1.5%	Flatter (10s2s ~40bp)	Matches
*Neutral $r^$ (0%)**	Terminal rate 2.0%	Normal (10s2s ~80-100bp)	-
*High $r^$ (+0.5%)**	Terminal rate 2.5%	Steeper (10s2s ~120-150bp)	-

Current 10s2s slope: ~40bp (1.0% - 0.6%)

Interpretation: Curve pricing low $r^*$ scenario (-0.5%) or prolonged period below neutral.

Trading implication: If BOJ speeches shift toward higher $r^*$ estimates, expect curve steepening (sell 2Y, buy 10Y).

4. Volatility and Uncertainty

Higher $r^*$ uncertainty → Higher JGB volatility

Realized volatility measures:

10Y JGB implied vol (options): 4.5bp/day (Oct 2025)
Historical vol (2010-2019 average): 2.8bp/day
Increase: +60% due to $r^*$ uncertainty and policy transition

Drivers of elevated volatility:

Divergent BOJ views: Policy Board members disagree on $r^*$ → Unpredictable rate hikes
Data-dependence: Each inflation/wage print causes large repricing
Stagflation risk: Simultaneous growth and inflation shocks create two-way volatility

Trading strategies for high $r^*$ uncertainty:

Straddles/strangles: Buy JGB options to capture volatility (expensive but justified)
Barbell positioning: Hold both 2Y (benefits from hikes) and 30Y (benefits from growth slowdown)
Curve trades: Exploit mispricing between front-end (policy path) and long-end ($r^*$ + term premium)

5. Relative Value: JGBs vs. Global Bonds

Japan’s $r^*$ relative to other countries drives cross-border flows:

$r^*$ estimates (2025):

US: +0.5% to +1.0% (higher potential growth, stronger demographics)
Euro area: -0.3% to +0.3% (similar to Japan, aging but less severe)
Japan: -0.5% to +0.5% (lowest due to demographics)

Yield differential (10Y government bonds, Oct 2025):

US 10Y: 4.2%
Euro area 10Y (Bund): 2.5%
Japan 10Y: 1.0%

Hedged yield for foreign investors:

\[\text{Hedged JGB yield} = Y_{\text{JGB}} + \text{FX forward premium}\]

USD/JPY 3-month forward premium ≈ 3.0% (reflects US-Japan rate differential)

\[\text{Hedged 10Y JGB yield (USD investor)} = 1.0\% + 3.0\% = 4.0\%\]

Comparison: US 10Y = 4.2%, hedged JGB = 4.0% → JGBs competitive for USD investors

*If Japan’s $r^$ rises** (→ Higher JGB yields) while US $r^*$ stable:

Forward premium narrows (Japan-US rate gap shrinks)
Hedged JGB yields become less attractive
Foreign demand for JGBs falls → Upward pressure on yields

This self-reinforcing dynamic can accelerate yield rises when $r^*$ perceptions shift.

6. Portfolio Allocation and Duration Management

For domestic Japanese investors (banks, insurance, pension funds):

If $r^*$ is truly near zero, neutral nominal rate is 2.0% → Duration risk increases:

Current avg JGB yield: ~1.2% (across all maturities)
Potential terminal yield: ~2.5-3.0% (if $r^* = 0\%$ + term premium)
Mark-to-market loss if repricing occurs: 10-15% for 10Y duration portfolios

Risk management strategies:

Reduce duration: Shift from 10Y/20Y → 2Y/5Y (lower sensitivity to $r^*$ revisions)
Increase credit allocation: Shift to corporate bonds (spread provides buffer)
Hedge with derivatives: Pay fixed on IRS, buy JGB puts/payers swaptions

For foreign investors:

Unhedged: Yen depreciation risk if BOJ tightens aggressively (USD/JPY could move 145 → 155)
Hedged: Monitor forward premium changes (hedging cost rises with rate hikes)
Opportunistic: If $r^*$ uncertainty spikes, wait for yield overshoot before adding duration

Key Takeaways

The neutral rate $r^*$ is unobservable: Must be estimated using statistical models (Laubach-Williams), policy rules (Taylor Rule), surveys, or financial market signals. Estimates carry significant uncertainty.
Japan’s $r^*$ has collapsed ~5pp since 1990: From +4-5% (bubble era) to -0.5% to +0.5% (current consensus ~0%). Driven by demographics (shrinking labor force), productivity stagnation, and chronic risk aversion.
BOJ uses holistic approach: Does not rely on single model. Current official range: -0.5% to +0.5%, central tendency near zero.
Laubach-Williams model is the gold standard: State-space framework with IS curve, Phillips Curve, and evolving trend growth. Japan-specific estimates show $r^*$ turned negative post-2010.
Taylor Rule reveals policy stance: Japan’s implicit Taylor Rule has weaker reaction coefficients than US. Current policy rate (0.25%) implies $r^*$ near -2.6% if following rule, or BOJ is 175bp behind the curve.
Multiple estimation methods give range: LW models (-0.5% to 0%), surveys (0.2%), DSGE models (-0.3% to 0.5%), market signals (-0.7%). Averaging across methods reduces error.
*$r^$ drives long-term JGB yields*: In equilibrium, 10Y yield ≈ $r^ + \pi^* +$ premia. If $r^* = 0\%$, fair value 10Y JGB ~2.5-2.7%. Current 1.0% yield implies market skeptical of sustained 2% inflation.
*Policy normalization path depends on $r^$*: If neutral nominal rate is 2% ($r^ = 0\%$ + $\pi^* = 2\%$), BOJ has 175bp of tightening runway from current 0.25%. Gradual path suggests reaching neutral in 2027.
Stagflation complicates $r^*$ estimation: Simultaneous weak growth + high inflation breaks Phillips Curve, creating model instability. Japan faces mild stagflation risk (3% CPI, 0.3% GDP growth) in 2024-2025.
Stagflation creates policy dilemmas: Tightening to fight inflation worsens growth; easing to support growth exacerbates inflation. BOJ must “look through” temporary supply shocks vs. demand-driven inflation.
$r^*$ uncertainty drives JGB volatility: Disagreement among Policy Board members and economists creates two-way risk. Implied volatility +60% above 2010-2019 average.
International spillovers matter: 40-50% of Japan’s $r^$ decline explained by global factors (savings glut, safe asset demand). US/Euro area $r^$ trends constrain Japan’s divergence.
Trading implications:
- If $r^*$ rises: Sell JGBs, steepeners (2s10s), reduce duration
- If $r^*$ falls: Buy JGBs, flatteners, extend duration
- High uncertainty: Buy volatility (straddles), barbell positioning
Portfolio risk: If $r^* = 0\%$ and yields normalize to 2.5%, 10Y JGB holders face 10-15% mark-to-market losses. Duration management critical for Japanese institutional investors.
Watch for regime shifts: Deglobalization, geopolitical shocks, or sustained wage-price spiral could permanently raise $r^$. BOJ forward guidance will signal if officials’ $r^$ views are changing.

References

Academic Papers

Laubach-Williams Framework:

Laubach, T., & Williams, J. C. (2003). “Measuring the Natural Rate of Interest.” Review of Economics and Statistics, 85(4), 1063-1070.
Holston, K., Laubach, T., & Williams, J. C. (2017). “Measuring the Natural Rate of Interest: International Trends and Determinants.” Journal of International Economics, 108(S1), S59-S75.

Japan-Specific r* Estimates:

Fujiwara, I., Iwasaki, Y., Muto, I., Nishizaki, K., & Sudo, N. (2016). “Developments in the Natural Rate of Interest in Japan.” BOJ Working Paper Series, No. 16-E-8.
Ichiue, H., & Nishiguchi, S. (2015). “Inflation Expectations and Consumer Spending at the Zero Bound: Micro Evidence.” Economic Inquiry, 53(2), 1086-1107.
Imakubo, K., Kojima, H., & Nakajima, J. (2023). “Re-estimating the Neutral Rate for Japan Using Recent Data.” BOJ Working Paper Series, No. 23-E-3.

Taylor Rule Analysis:

Taylor, J. B. (1993). “Discretion versus Policy Rules in Practice.” Carnegie-Rochester Conference Series on Public Policy, 39, 195-214.
Leigh, D. (2010). “Estimating the Implicit Inflation Target: An Application to U.S. Monetary Policy.” IMF Working Paper, WP/10/89.
Clarida, R., Galí, J., & Gertler, M. (2000). “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory.” Quarterly Journal of Economics, 115(1), 147-180.

Global r* Decline:

Rachel, L., & Smith, T. D. (2017). “Are Low Real Interest Rates Here to Stay?” International Journal of Central Banking, 13(3), 1-42.
Del Negro, M., Giannone, D., Giannoni, M. P., & Tambalotti, A. (2019). “Global Trends in Interest Rates.” Journal of International Economics, 118, 248-262.

Stagflation and r*:

Clarida, R., Galí, J., & Gertler, M. (2000). “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory.” Quarterly Journal of Economics, 115(1), 147-180.
Blanchard, O., & Galí, J. (2007). “The Macroeconomic Effects of Oil Price Shocks: Why Are the 2000s So Different from the 1970s?” NBER Working Paper, No. 13368.

BOJ Publications

Official Reports:

Bank of Japan (2024). Outlook for Economic Activity and Prices (October). [BOJ Outlook Report - quarterly]
Bank of Japan (2023). Comprehensive Assessment of Monetary Policy. Policy Board Report.
Bank of Japan (Various). Minutes of the Monetary Policy Meeting. Published 10 years after each meeting.

BOJ Research Papers:

Nishizaki, K., Sekine, T., & Ueno, Y. (2014). “Chronic Deflation in Japan.” Asian Economic Policy Review, 9(1), 20-39.
BOJ Research and Statistics Department (2016). “Comprehensive Assessment: Developments in Economic Activity and Prices as well as Policy Effects since the Introduction of Quantitative and Qualitative Monetary Easing (QQE).”

Governor Speeches:

Ueda, K. (2024). “The Path toward Sustainable 2% Inflation.” Speech at Japan Society, July 18, 2024.
Kuroda, H. (2023). “Quantitative and Qualitative Monetary Easing (QQE) with Yield Curve Control: Assessment and Challenges.” Speech at the Paris EUROPLACE Financial Forum, July 6, 2023.

Data Sources

BOJ Statistics:

Bank of Japan Time-Series Data Search: https://www.stat-search.boj.or.jp
- Policy Interest Rates (Call Rate, Basic Loan Rate)
- JGB yields (all maturities)
- Monetary Base, BOJ Balance Sheet

Government Statistics:

Cabinet Office: https://www.cao.go.jp/index-e.html
- GDP components (SNA)
- Output gap estimates
Ministry of Internal Affairs: https://www.stat.go.jp
- CPI (headline, core, core-core)
- Labor Force Survey

Market Data:

Bloomberg Terminal: GJGB10 <Govt> (10Y JGB), JCPN <Index> (Core CPI)
Refinitiv Eikon: Economic calendar, consensus forecasts
Trading Economics: https://tradingeconomics.com/japan

International Comparisons:

Federal Reserve Bank of New York: Measuring the Natural Rate of Interest (updated estimates) - https://www.newyorkfed.org/research/policy/rstar
European Central Bank: Natural Rate of Interest Estimates (ECB Working Papers)

Next Chapter

Chapter 7 - Derivatives →

Neutral Rates and Stagflation

What is the Neutral Rate (r*)?

Theoretical Foundation

The Equilibrium Condition

Why r* is Unobservable

The Laubach-Williams Model: The Gold Standard

The Model Structure

1. IS Curve (Aggregate Demand)

2. Phillips Curve (Inflation Dynamics)

3. State Equations (Unobserved Components)

Estimation via Kalman Filter

Laubach-Williams Applied to Japan

Limitations of the LW Model

The Taylor Rule Framework

The Original Taylor Rule (1993)

The Taylor Principle

Adapting the Taylor Rule for Japan

1. Time-Varying $r^*$

2. Different Reaction Coefficients

3. The Balanced-Approach Taylor Rule

Using Taylor Rules to Infer $r^*$

Taylor Rule Deviations and Policy Stance

Other Estimation Methods

1. Holistic/Judgmental Approach (BOJ’s Primary Method)

2. Survey-Based Methods

3. DSGE Model-Based Estimates

4. Financial Market Signals

a) Long-Term JGB Yields

b) Inflation-Linked JGBs (JGBi)

c) FX Forward Rates (Covered Interest Parity)

5. Global Factors and International Spillovers

Japan’s r* History: A 35-Year Collapse

Era 1: The Bubble Economy (1985-1991) — $r^* \approx 4-5\%$

Era 2: The Post-Bubble Adjustment (1992-1998) — $r^* \approx 2-3\%$

Era 3: The Lost Decade (1999-2008) — $r^* \approx 0-1\%$

Era 4: Abenomics and Negative Rates (2013-2019) — $r^* \approx -0.5 to 0\%$

Era 5: Post-COVID and Policy Normalization (2020-2025) — $r^* \approx -1 to 0\%$

Visualizing the Collapse

Current BOJ Estimates and Forward Guidance

Official BOJ Position (As of October 2025)

Implications for Policy Normalization

Forward Guidance Evolution

Debates Within the Policy Board

Stagflation and the Neutral Rate: The Modern Challenge

What is Stagflation?

Japan’s Stagflation Risk (2024-2025)

Why Stagflation Complicates $r^*$ Estimation

1. Output Gap Becomes Ambiguous

2. Phillips Curve Breaks Down

3. Policy Trade-Offs Become Severe

Estimating $r^*$ During Stagflation

a) Supply-Adjusted $r^*$ (Clarida et al. 2000)

b) Time-Varying $r^*$ with Regime Shifts

Japan’s Stagflation Compared to 1970s

Stagflation and JGB Markets

Implications for JGB Markets

1. Long-Term Yield Anchoring

2. Policy Normalization Path and Front-End Pricing

3. Curve Shape and r* Expectations

4. Volatility and Uncertainty

5. Relative Value: JGBs vs. Global Bonds

6. Portfolio Allocation and Duration Management

Key Takeaways

References

Academic Papers

BOJ Publications

Data Sources

Further Reading

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