## _wp03208 - 1. Data Properties

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---

### III. Introduction — summary of aims and main evidence
- Paper analyzes validity of the term-structure model across sample periods using time-series methods.
- Main evidence:
  - A strong relationship between interest rates of different maturities exists when interest rates are relatively high.
  - This relationship weakens as interest rates are lowered, consistent with theory and attributed to less information in yield spreads and BoJ interest rate-smoothing behavior.
  - The term premium becomes a more dominant determinant of long rates during low-rate periods, making long rates more difficult for the BoJ to influence.

### II. History of BoJ monetary policy since 1990 — sub-periods and key actions
- Three broad sub-periods:
  - The transition period:
    - Official discount rate used as main instrument until 1995.
    - Official discount rate dropped from 6.0 to 5.5 percent on July 1, 1991 and continued falling to 0.5 percent on September 8, 1995.
    - On March 31, 1995 the uncollateral call rate designated as an important operating target; July 7, 1995 measures aimed to lead call rate below discount rate.
    - Failures of major financial institutions in late 1997 prompted dual-system asset operations; call rate target publicly announced since 1998 (on September 9, 1998 uncollateral overnight call rate targeted to within ±0.25 percent on average of the discount rate).
  - The zero-interest-rate policy period:
    - Implemented February 12, 1999 to keep uncollateral overnight call rate close to 0 percent; abandoned August 11, 2002 with target raised to around 0.25 percent.
  - The quantitative-easing policy period:
    - Operating target shifted to outstanding balance of the BoJ’s current account.
    - Initial target level of 5 trillion yen increased to 27-30 trillion yen in May 2003.
    - Quantitative-easing intended to continue until CPI records a year-on-year increase of 0 percent or more on a sustainable basis.
    - BoJ purchased government debt securities across maturities: Treasury bills (maturity ≤ one year); medium-term government bonds (2 to 5 years); long-term government bonds (6 to 10 years); super-long-term government bonds (>10 years).
    - Target amount of long-term JGB purchases raised from 400 billion yen per year initially to 1.2 trillion yen per month in October 2002.
- Monetary outcomes summarized:
  - Short-term interest rates declined from 6.0 percent in early 1990 to around 0 percent.
  - Yield on long-term government bonds fell from 7.0 percent to less than 1 percent.
  - Paper uses term “low-interest-rate” policy to refer to both “zero-interest-rate” and “quantitative-easing” periods.

### III. Term-structure theory and implications
- Expectations model and key theoretical implications:
  - Basic rational-expectations relation for non-coupon assets: long-term rate R_{n,t} tied to forward rates f_{j,t} via 1/(n) * sum_{j=0}^{n-1} f_{j,t} = R_{n,t}.
  - Under assumptions (short-term rates r_{t+1,j}, time-invariant forward-term premium φ_j), R_{n,t} decomposes into average expected future short rates plus term-premium components.
  - Policy success definitions:
    - During transition: success reduces both expected short-term rates and long-term rate.
    - During zero-rate regime: success implies expected future short-term rates equal 0, making long-term rate equal to forward-term premium.
  - Zero lower bound implications:
    - Nonlinear relation between long- and short-term rates when short rates ≈ 0 percent.
    - Central bank power to influence long-term rates reduced in low-rate periods.
- Manipulated form (implications from equation (3)):
  - If monetary policy reduces changes in expected future short-term rates, yield spread should decline; with zero change in expected short rates, yield spread approaches term premium and long-short relationship weakens.
  - Statistical implications:
    - If first difference of short-term rate is stationary, so is the yield spread.
    - When long-rate follows unit root, long- and short-term rates are cointegrated (Campbell and Shiller, 1987).
    - Current yield spread should contain information useful for predicting future short-term rates during transition periods; not expected when interest rates are low.
- Time-varying term premium and BoJ reaction:
  - Term premium φ_t modeled as AR(1): φ_t = ρ φ_{t-1} + ε_t with |ρ| < 1.
  - BoJ policy reaction function (equation (5)): r_{t+1} = α r_t + β (R_{n,t} - r_t) + u_t, where β > 0 indicates response to yield spread and α near 1 indicates interest-rate smoothing.
  - Reduced-form estimables (equations (6) and (7)); μ = ρ β. μ = 0 when ρ = 0 and/or β = 0.
  - Prior finding referenced: Kugler (1997) finds persistent term premium and strong BoJ reaction to yield spread between 1982 and 1992.

### IV. Methodology — econometric approach and implementation details
- Estimation approach:
  - Use generalized method of moments (GMM), which nests OLS, 2SLS, IV, and handles weaker assumptions on disturbances.
  - GMM robust to autocorrelation and heterogeneity via covariance adjustment and uses instruments to mitigate endogeneity.
  - Compact model y = X β + u; instruments Z with q > n; orthogonality E[Z'(y - X β)] = 0 yields β̂ via minimization Q(β) = g(β)' W g(β).
  - For non-IID residuals, use heteroscedasticity and autocorrelation consistent (HAC) weighting matrix per Newey and West (1987) with Bartlett kernel and data-driven bandwidth selection.
  - Over-identification tested with Hansen J statistic: J = T g(β̂)' W g(β̂) ∼ χ^2_{q-n}.
  - Instrument choice: in addition to constant term, paper uses three lagged explanatory variables as instruments (parsimonious instrument set recommended).

### V. Data and preliminary empirical results — sample, variables, and descriptive findings
- Data specifics:
  - Weekly data covering 1990/1/5 to 2003/3/30.
  - Full sample divided into three phases: transition period; zero-interest-rate policy period; quantitative-easing policy period.
  - Short-term rates: Gensaki rates with maturities of one, two, and three months.
  - Long-term rates: Japanese swap rates of JGB (discount bonds) with maturities of three and five years.
  - Variables constructed as r×100 and (R - r)×100 where R and r are long- and short-term interest rates expressed as percentages per annum.
- Empirical and descriptive observations:
  - Discrepancy between short- and long-term rates during low-interest-rate period; gap more pronounced during zero-interest-rate policy.
  - JGB ex post returns on average 0 percent (t statistics range from –1.118 to 1.261), but with tendency for expected future interest rates to increase during zero-interest-rate period.
  - Ex post expected short-term rates for first 70 weeks after implementation of zero-interest-rate and quantitative-easing policies:
    - Abrupt decline in ex post interest rates at start of policies reflecting BoJ liquidity provision to offset Y2K uncertainty.
    - Ex post returns less than 0 percent at the beginning, indicating credibility and expectation that policies would last; over time ex post short-term rates tended to increase during low-rate periods except during quantitative-easing where they remained relatively constant.
  - Monetary aggregates under quantitative-easing:
    - Year-on-year increase in M1 of 3.5 percent in 2000, 14 percent in 2001, and more than 20 percent in 2002.
    - M2+CDs (broad money) increased less than 4 percent during these periods.
- Volatility and level comparisons across sub-periods (summary of Table 1):
  - Interest rate changes and spreads are statistically indifferent from zero during the low-interest-rate period and are on average the smallest during quantitative-easing.
  - Standard deviation (volatility) of interest rates and spreads was three to four times higher during the transition period compared with low-rate periods.
  - Volatility during quantitative-easing was smaller than during the zero-interest-rate policy.
  - Both interest rates and yield spreads changed most radically during the transition period.
- Data notes and measurement choices:
  - Ten-year maturity JGB-based yield spread considered but not reported due to non-stationarity.
  - Ex post expected short-term rate calculations exclude observations between zero-interest-rate removal and quantitative-easing start based on survey evidence (Nissei Kiso Kenkyujo); results sensitive to this assumption.
  - Coupon effects and periodic settlement liquidity effects noted as potential influences on term structure estimation.

### Section III — statistical implications and empirical estimation results
- Unit-root and stationarity findings:
  - Unit-root tests (ADF and DF-GLS) assess null hypothesis of a unit root.
  - First difference of Gensaki rates is stationary.
  - Yield spreads:
    - JGB3-based spreads reported to be stationary.
    - JGB5-based spreads follow the unit root process.
  - Interpretation: JGB3 result indicates α in equation (5) is equal to one, supporting BoJ interest-rate smoothing.
- Granger noncausality analysis (VAR(6)):
  - Test setup: two nulls — (1) short-term interest rates do not cause a yield spread; (2) the spread does not cause short-term interest rate dynamics.
  - Unique causality from spreads to short rates requires rejection of (2) and acceptance of (1).
  - Empirical result:
    - Only in the transition period is there sufficient evidence to support that yield spreads cause short-term interest rates.
    - Conclusion not sensitive to Gensaki maturity lengths.
    - No evidence for unique causality during zero-interest-rate and quantitative-easing periods.
- Term-structure model estimation (GMM of equation (7)):
  - Parameter μ:
    - Statistically different from zero before implementation of the zero-interest-rate policy.
    - Becomes insignificant during the low-interest-rate period.
  - Interpretation: yield spreads had explanatory power in the early 1990s but lost usefulness once short-term rates approached 0 percent; result robust to different short-rate maturity lengths.
- Decomposition of μ into ρ and β; estimation issues at zero lower bound:
  - μ = ρ β where ρ is persistence of term premium and β is central bank reaction to the spread.
  - ρ found consistently important (persistence of term premium).
  - Estimation challenges when rates ≈ 0 percent:
    - Probability of rates going lower limited by zero lower bound; OLS may yield biased and inconsistent estimates.
    - Equation (5) estimated using a censored-normal regression model (Tobit) to account for short-term rates censored below 0 percent (equation (14)); threshold (censored point) set at 0 percent and estimated by maximum likelihood.
- Parameter estimates and interpretation:
  - β (BoJ reaction to the spread):
    - Statistically significant only during the transition period.
    - During the low-interest-rate period, β decreases and becomes statistically insignificant.
    - Insensitivity of result to estimation method (OLS vs Tobit).
    - Implies short-term rates largely determined by their own past values when β insignificant.
    - Authors’ β estimates lower than Kugler (1997); interpreted as non-reaction of BoJ to yield spread changes during low-rate period.
  - α:
    - Higher during the quantitative-easing policy than during the zero-interest-rate policy, suggesting stronger smoothing during quantitative easing.
  - ρ:
    - Statistically significant across all sample periods.
    - Close to, but less than, one — indicating persistence of the term premium regardless of sample period.
    - ρ values in line with Kugler (1997).
- Consistency checks:
  - Wald test used to check consistency of μ versus product βρ.
  - Test confirms β and ρ estimators from equations (5) and (6) generally match μ from equation (7), with one exception reported.
  - When μ is statistically insignificant, parameters from (5) and (6) are consistent with those from (7) in all cases.

### Policy-relevant conclusions and recommendations
- Term-structure usefulness:
  - Term structure is useful for analyzing monetary policy during high-rate periods but less so during low-rate periods because short-term rates near 0 percent exhibit limited fluctuation and yield spreads cannot predict short-term-rate dynamics at the zero lower bound.
- Given virtual absence of the interest-rate channel at low rates:
  - Allowing more fluctuation in short-term rates could reactivate the term-structure relationship and help transmit monetary policy effects through interest-rate and expectations channels.
  - The level of long-term rates could be treated as an intermediate target of policy.
- On interest-rate smoothing under quantitative easing:
  - Paper questions strict interest-rate smoothing rationale, arguing that more short-rate variability may better transmit policy.
- Credibility assessments:
  - Both zero-interest-rate and quantitative-easing policies perceived as credible immediately after implementation.
  - An upward trend (although statistically insignificant) in ex post expected short-term rates occurred during the zero-interest-rate policy, indicating declining perceived credibility over time.
  - No such upward trend observed during quantitative easing; QE appears more credible than the zero-rate policy given low and declining long rates.

### Limits and suggestions for further research
- Time-series term-structure techniques have limits:
  - Yield spreads of longer-term assets (e.g., five-year maturity) appear to follow a unit root, while short-rate changes are stationary — complicates standard term-structure application to longer-term rates.
- Model scope:
  - Term-structure model focuses on interest-rate and expectations channels only and does not capture other channels (e.g., exchange rates, credit channels).
- Future research:
  - Seek measures better capturing stance of monetary policy during quantitative easing, recognizing the zero lower bound constraint on nominal short-term rates.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2003/_wp03208.pdf*

### 1. Data Properties......................................................................................................

### 1. Data Properties

### Covered sections
- 1. Data Properties.....................................................................................................................18
- 2. Unit Root Tests ....................................................................................................................19
- 3. Granger Noncausality Tests .................................................................................................19
- 4. The Term-Structure Model (Equation 7) .............................................................................20
- 5. The Term-Structure Model (Equation 5) .............................................................................21
- 6. The Term-Structure Model (Equation 6) .............................................................................22
- 7. Parameter Consistency Test .................................................................................................23

### Figures listed
- 1. Short-Term Interest Rates and JGB Yields..........................................................................24
- 2. Short-Term Rates and Yield-Spread Dynamics...................................................................24
- 3a. A Change in Ex Post Gensaki1M (Average) .....................................................................25
- 3b. A Change in Ex Post Gensaki2M (Average) .....................................................................25
- 3c. A Change in ExPost Gensaki3M (Average) References....................................................26

*Source: _wp03208 - 1. Data Properties......................................................................................................*

### References..............................................................................................................

### _wp03208 - References..............................................................................................................

### I. INTRODUCTION
- Since the Japanese asset bubble burst in early 1990, expansionary fiscal and monetary polices have been implemented to stimulate the Japanese economy; up to early 2003 there had been no strong macroeconomic signal of recovery (e.g., in prices and GDP).  
- The (net) government debt-to-GDP ratio was 13 percent in 1991 and exceeded an estimated 72 percent in 2002 (IMF, 2003), making it the highest among the industrialized countries, and continues to grow.  
- Short-term interest rates have hovered around 0 percent since the mid-1990s.  
- Even with nominal short-term rates near 0 percent (nonnegativity constraint), monetary policy can potentially be further accommodative by injecting liquidity into the market; effects transmit via expectations, credit, exchange rate, and portfolio rebalancing channels.  
- Empirical knowledge on the intermediate-level effectiveness of monetary policy (influencing agents’ expectations, equities, etc., before changes in price or GDP) is limited.  
- This paper analyzes the validity of the term-structure model across sample periods using time-series methods and provides evidence that:
  - A strong relationship between interest rates of different maturities exists when interest rates are relatively high.
  - This relationship weakens as interest rates are lowered, consistent with theory and attributed to less information in yield spreads and BoJ interest rate-smoothing behavior.
  - The term premium becomes a more dominant determinant of long rates during low-rate periods, making long rates more difficult for the BoJ to influence.

### II. A HISTORY OF MONETARY POLICY SINCE 1990
- Three broad sub-periods of BoJ policy since 1990:
  1. The transition period:
     - Official discount rate used as main instrument until 1995.
     - Expansionary policy began July 1, 1991 when official discount rate dropped from 6.0 to 5.5 percent; continued falling to 0.5 percent on September 8, 1995.
     - On March 31, 1995, the uncollateral call rate designated as an important operating target; July 7, 1995 measures aimed to lead call rate below discount rate.
     - Failures of major financial institutions in late 1997 prompted dual-system asset operations and other measures; call rate target announced publicly since 1998 (on September 9, 1998 uncollateral overnight call rate targeted to within ±0.25 percent on average of the discount rate).
  2. The zero-interest-rate policy period:
     - Implemented February 12, 1999 to keep uncollateral overnight call rate close to 0 percent; abandoned August 11, 2002 with target raised to around 0.25 percent.
  3. The quantitative-easing policy period:
     - Operating target shifted to outstanding balance of the BoJ’s current account.
     - Initial target level of 5 trillion yen increased to 27-30 trillion yen in May 2003.
     - Quantitative-easing intended to continue until CPI records a year-on-year increase of 0 percent or more on a sustainable basis (IMF, 2003).
     - BoJ purchased government debt securities (Treasury bills: maturity ≤ one year; medium-term government bonds: 2 to 5 years; long-term government bonds: 6 to 10 years; super-long-term government bonds: >10 years).
     - Target amount of long-term JGB purchases raised from 400 billion yen per year initially to 1.2 trillion yen per month in October 2002.
- Monetary outcomes:
  - Short-term interest rates declined from 6.0 percent in early 1990 to around 0 percent; yield on long-term government bonds fell from 7.0 percent to less than 1 percent.
  - Paper uses term “low-interest-rate” policy to refer to both “zero-interest-rate” and “quantitative-easing” periods.

### III. TERM STRUCTURE OF INTEREST RATES (THEORY AND IMPLICATIONS)
- Basic rational-expectations relationship for non-coupon assets:
  - Long-term rate R_{n,t} relates to forward rates f_{j,t} via equation (1): 1/(n) * sum_{j=0}^{n-1} f_{j,t} = R_{n,t}.  
  - Under assumptions (short-term rates r_{t+1,j}, forward-term premium φ_j time-invariant), equation (2): R_{n,t} = (1/n) * sum_{j=0}^{n-1} E_t[r_{t+1,j}] + φ_0/n-sum representation.  
- Policy success definitions:
  - During transition: success reduces both expected short-term rates and the long-term rate.
  - During zero-rate regime: success implies expected future short-term rates equal 0, making long-term rate equal to forward-term premium.
  - Zero lower bound induces nonlinear relation between long- and short-term rates and reduces central bank power to influence long-term rates in low-rate periods.
- Implications from manipulated form (equation (3)):
  - If monetary policy reduces changes in expected future short-term rates, yield spread should decline; with zero change in expected short rates, yield spread approaches term premium and long-short relationship weakens.
  - Statistical implications: if first difference of short-term rate is stationary, so is the yield spread; when long-rate follows unit root, long- and short-term rates are cointegrated (Campbell and Shiller, 1987).
  - Current yield spread should contain information useful for predicting future short-term rates during transition periods; this unique causality is not expected when interest rates are low.
- Time-varying term premium and central bank reaction:
  - Term premium φ_t modeled as AR(1): φ_t = ρ φ_{t-1} + ε_t with |ρ| < 1.
  - BoJ policy reaction function (equation (5)): r_{t+1} = α r_t + β (R_{n,t} - r_t) + u_t, where β > 0 indicates response to yield spread and α near 1 indicates interest-rate smoothing.
  - McCallum/Kugler framework yields estimable reduced forms (equations (6) and (7)); μ = ρ β. μ = 0 when ρ = 0 and/or β = 0 (no persistence in term premium and/or no reaction to spread).
  - Prior findings: Kugler (1997) finds persistent term premium and strong BoJ reaction to yield spread variance between 1982 and 1992; β larger for Japan versus some other countries.

### IV. METHODOLOGY
- Estimation approach:
  - Use generalized method of moments (GMM), which nests OLS, 2SLS, IV, and handles weaker assumptions on disturbances; robust to autocorrelation and heterogeneity via covariance adjustment and instrumental variables to mitigate endogeneity.
  - Model compact form: y = X β + u; instruments Z with q > n; orthogonality E[Z'(y - X β)] = 0 yields GMM estimator β̂ via minimization Q(β) = g(β)' W g(β).
  - For non-IID residuals, use heteroscedasticity and autocorrelation consistent (HAC) weighting matrix per Newey and West (1987) with Bartlett kernel and data-driven bandwidth selection.
  - Over-identification tested with Hansen J statistic: J = T g(β̂)' W g(β̂) ∼ χ^2_{q-n}.
  - Instrument choice: in addition to constant term, paper uses three lagged explanatory variables as instruments (parsimonious instrument set recommended).

### V. DATA AND PRELIMINARY EMPIRICAL RESULTS
- Data:
  - Weekly data covering 1990/1/5 to 2003/3/30.
  - Full sample divided into three phases: transition period; zero-interest-rate policy period; quantitative-easing policy period.
  - Short-term rates: Gensaki rates with maturities of one, two, and three months (chosen because early call market rate data recorded only to two decimal points and TIBOR available only from 1995).
  - Long-term rates: Japanese swap rates of JGB (discount bonds) with maturities of three and five years.
  - Variables represented as r×100 and (R - r)×100 where R and r are long- and short-term interest rates expressed as percentages per annum.
- Empirical observations and descriptive findings:
  - Discrepancy between short- and long-term rates during low-interest-rate period; gap more pronounced during zero-interest-rate policy, indicating assets are not perfect substitutes.
  - JGB ex post returns on average 0 percent (t statistics range from –1.118 to 1.261), but with tendency for expected future interest rates to increase during zero-interest-rate period.
  - Ex post expected short-term rates for first 70 weeks after implementation of zero-interest-rate and quantitative-easing policies show:
    - Abrupt decline in ex post interest rates at start of policies reflecting BoJ liquidity provision to offset Y2K uncertainty.
    - Ex post returns less than 0 percent at the beginning, indicating credibility and expectation that policies would last; over time ex post short-term rates tended to increase during low-rate periods except during quantitative-easing where they remained relatively constant.
  - Monetary aggregates under quantitative-easing:
    - Year-on-year increase in M1 of 3.5 percent in 2000, 14 percent in 2001, and more than 20 percent in 2002.
    - M2+CDs (broad money) increased less than 4 percent during these periods (IMF, 2003).
  - Volatility and level comparisons across sub-periods (Table 1 summary):
    - Interest rate changes and spreads are statistically indifferent from zero during the low-interest-rate period and are on average the smallest during quantitative-easing.
    - Standard deviation (volatility) of interest rates and spreads was three to four times higher during the transition period compared with low-rate periods.
    - Volatility during quantitative-easing was smaller than during the zero-interest-rate policy.
    - Both interest rates and yield spreads changed most radically during the transition period.
- Data notes and measurement choices:
  - Ten-year maturity JGB-based yield spread considered but not reported due to non-stationarity.
  - Ex post expected short-term rate calculations exclude observations between zero-interest-rate removal and quantitative-easing start based on survey evidence (Nissei Kiso Kenkyujo) about expectations; results sensitive to this assumption.
  - Coupon effects and periodic settlement liquidity effects noted in literature as potential influences on term structure estimation.

*Source: _wp03208 - References..............................................................................................................*

### Section III of this paper discusses some statistical implications related to the

### _wp03208 - Section III: Statistical Implications of the Expectations Model of the Term Structure

### Unit-root and stationarity findings
- Unit-root tests (ADF and DF-GLS) assess null hypothesis of a unit root (order of integration).
- First difference of Gensaki rates is stationary.
- Yield spreads:
  - JGB3-based spreads reported to be stationary.
  - JGB5-based spreads follow the unit root process.
- Interpretation: the JGB3 result indicates α in equation (5) is equal to one, supporting the BoJ’s efforts to smooth short-term interest rates.

### Causality analysis (Granger noncausality, VAR(6))
- Test structure:
  - Based on VAR(6).
  - Two null hypotheses examined: (1) short-term interest rates do not cause a yield spread; (2) the spread does not cause short-term interest rate dynamics.
  - Unique causality from spreads to short rates requires rejection of (2) and acceptance of (1).
- Empirical result:
  - Only in the transition period is there sufficient evidence to support that yield spreads cause short-term interest rates.
  - The conclusion is not sensitive to Gensaki maturity lengths.
  - During periods when short-term interest rates are near 0 percent (zero-interest-rate and quantitative-easing periods), there is no evidence for unique causality.

### Term-structure model estimation (GMM of equation (7), Table 4)
- Results sensitive to sample period.
- Parameter μ:
  - Statistically different from zero before implementation of the zero-interest-rate policy.
  - Becomes insignificant during the low-interest-rate period.
- Interpretation:
  - Yield spreads had explanatory power in the early 1990s but lost usefulness once short-term rates approached 0 percent.
  - Result robust to different short-rate maturity lengths.
  - Statistical insignificance of the term-structure model during the low-interest period concurs with the Granger noncausality finding.

### Decomposition of μ into ρ and β; issues at the zero lower bound
- μ decomposed into ρ (persistence of the term premium) and β (central bank reaction to the yield spread).
- Findings:
  - μ = βρ depends on BoJ’s response parameter β; term premium persistence ρ is consistently important.
- Estimation challenges when rates ≈ 0 percent:
  - Probability of rates going lower is limited by the zero lower bound; OLS may yield biased and inconsistent estimates.
  - Equation (5) is estimated using a censored-normal regression model (Tobit) to account for short-term rates censored below 0 percent (equation (14)).
  - Threshold (censored point) set at 0 percent; estimated by maximum likelihood.

### Parameter estimates and interpretation (Table 5 and Table 6)
- Parameter β (BoJ reaction to the spread):
  - Statistically significant only during the transition period.
  - During the low-interest-rate period, β decreases and becomes statistically insignificant.
  - Result insensitive to estimation method (OLS vs Tobit).
  - Implies short-term rates largely determined by their own past values when β insignificant.
  - Authors’ β estimates lower than Kugler (1997); interpreted as non-reaction of the BoJ to yield spread changes during the low-rate period.
- Parameter α:
  - Higher during the quantitative-easing policy than during the zero-interest-rate policy, suggesting stronger smoothing during quantitative easing.
  - This empirical result contrasts with theoretical expectation that targeting money (QE) yields more volatile interest rates; instead it aligns with BoJ practice.
- Parameter ρ:
  - Statistically significant across all sample periods (Table 6).
  - Close to, but less than, one — indicating persistence of the term premium regardless of sample period.
  - ρ values are in line with those reported by Kugler (1997).

### Consistency checks (Wald test, Table 7)
- Checked consistency of μ versus product βρ using the Wald test.
- Test confirms that β and ρ estimators from equations (5) and (6) generally match μ from equation (7), with one exception reported in Table 7.
- If μ is regarded as zero (statistically insignificant), parameters from (5) and (6) are consistent with those from (7) in all cases.

### Implications for policy transmission and BoJ practice
- During the low-interest-rate period:
  - Long-term rates are largely determined by the forward-term premium.
  - It is very difficult for the BoJ to control (particularly to reduce) long-term rates; interest-rate channel is virtually absent.
  - Relationship between short- and long-rates appears nonlinear in low-rate regimes.
- Interest-rate smoothing:
  - Short-term interest rate smoothing by the BoJ is supported by the evidence (high α and insignificant β in low-rate period).
  - Smoothing appears stronger during the quantitative-easing policy than during the zero-interest-rate policy.
- Credibility (ex post expected short-term rates):
  - Both the zero-interest-rate and quantitative-easing policies were perceived as credible immediately after implementation.
  - An upward trend (although statistically insignificant) in ex post expected short-term rates occurred during the zero-interest-rate policy, indicating declining perceived credibility over time.
  - No such upward trend was observed during quantitative easing; given low and declining long rates, QE appears more credible than the zero-rate policy.

### Policy-relevant conclusions and recommendations (from the paper)
- The term structure is useful for analyzing monetary policy during high-rate periods but less so during low-rate periods because:
  - Short-term rates near 0 percent exhibit limited fluctuation.
  - Yield spreads cannot predict short-term-rate dynamics when rates are at the zero lower bound.
- Given the virtual absence of the interest rate channel at low rates:
  - Allowing more fluctuation in short-term rates could reactivate the term-structure relationship and help transmit monetary policy effects through interest-rate and expectations channels.
  - The level of long-term rates could be treated as an intermediate target of policy.
- The paper questions the rationale of strict interest-rate smoothing under quantitative easing, arguing that more short-rate variability may better transmit policy.

### Limits and suggestions for further research
- Time-series term-structure techniques have limits:
  - Yield spreads of longer-term assets (e.g., five-year maturity) appear to follow a unit root, while short-rate changes are stationary; this complicates application of standard term-structure models to longer-term rates.
- Term-structure model focuses on interest-rate and expectations channels only and does not capture other channels (e.g., exchange rates, credit channels) highlighted in the introduction.
- Future work could seek measures better capturing the stance of monetary policy during quantitative easing, recognizing the zero lower bound constraint on nominal short-term rates.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2003/_wp03208.pdf*

### References

### References

### Monetary policy, deflation, and the zero lower bound
- Baig, Taimur, 2003, “Monetary Policy in a Deflationary Environment,” in Ending the Lost Decade: Policies to Revive Japan’s Stagnant Economy, eds., Tim Callen and Jonathan Ostry (Washington DC: International Monetary Fund) pp. 206-23.
- Blinder, A., 2000, “Monetary policy at the zero lower bound: balancing the risks,” Journal of Money, Credit and Banking, Vol. 32, No. 4, pp. 1093-99.
- Fujiki, Hiroshi, and Shigenori Shiratsuka, 2002, “Policy Duration Effect under the Zero Interest Rate Policy in 1999-2000: Evidence from Japan’s Money Market Data,” Bank of Japan Monetary and Economic Studies, Vol. 20, No. 1, pp. 1-31.
- Goodfriend, Marvin, 2001, “Financial Stability, Deflation, and Monetary Policy,” Bank of Japan Monetary and Economic Studies, Vol. 19 (Special edition, February), pp. 143-76.
- Iwata, Shigeru, and Shu Wu, 2001, “Estimating Monetary Policy Effects When Interest Rates Are Bounded at Zero,” Draft (Lawrence: Economics Department, University of Kansas).
- Jung, Taehun, Yuki Teranishi, and Tsutomu Watanabe, 2001, “Zero Bound on Nominal Interest Rates And Optimal Monetary Policy,” Working Paper, Hitotsubashi University.
- Kato, Ryo, and Shinichi Nishiyama, 2003, “Optimal Monetary Policy When Interest Rates Are Bounded at Zero,” Draft (Tokyo: Bank of Japan).
- Kimura, Takeshi, Hiroshi Kobayashi, Jun Muranaga, and Hiroshi Ugai, 2002, “The Effect of the Increase in Monetary Base on Japan’s Economy at Zero Interest Rates: An Empirical Analysis,” Institute for Monetary and Economic Studies Discussion Paper Series No. 2002-E-22 (Tokyo: Bank of Japan).
- Marumo, Kohei, Takashi Nakayama, Shinichi Nishioka, and Toshihiro Yoshida, 2003, “The Term Structure Model under the Zero Interest Rate Policy (in Japanese), Capital Market Department Working Paper No. 2003-J-1 (Tokyo: Bank of Japan).
- McCallum, Bennett T., 1994, “Monetary Policy and the Term Structure of Interest Rates,” National Bureau of Economic Research Working Paper No. 4938 (Cambridge: NBER).
- Meltzer, Allan H., 1999, “Commentary: What More Can the Bank of Japan Do?” Bank of Japan Monetary and Economic Studies Vol. 17 No. 3, pp. 189-91.
- Nagayasu, Jun, 2003, “The Effectiveness of Monetary Policy on Equity Prices in a Zero Interest Rate Environment,” draft (Washington DC: International Monetary Fund).
- Okina, Kunio, and Shigenori Shiratsuka, 2003, “Policy Commitment and Expectation Formations: Japan’s Experience Under Zero Interest rates,” draft (Tokyo: Bank of Japan).
- Ruge-Murcia, Franciso J., 2002, “Some Implications on the Zero Lower Bound on Interest Rates for the Term Structure and Monetary Policy,” Working Paper 06-2002, University of Montreal.

### Term structure of interest rates and expectations hypotheses
- Campbell, John Y., and Yasushi Hamao, 1992, in Japanese Monetary Policy “The Interest Rate Process and the Term Structure of Interest Rates in Japan,” ed., Kenneth J. Singleton (London: University of Chicago Press) pp. 95-120.
- Campbell, John Y., and Robert J. Shiller, 1987, “Cointegration and Tests of Present Value Models,” Journal of Political Economy, Vol. 95, No. 5, pp. 1062-88.
- Cecchetti, Stephen G., 1998, “The Case of the Negative Nominal Interest Rates: New Estimates of the Term Structure of Interest Rates During the Great Depression,” Journal of Political Economy, Vol. 96, No. 6, pp. 1111-41.
- Kikugawa, Tadashi, and Kenneth J. Singleton, 1994, Modeling the Term Structure of Interest Rates in Japan, Journal of Fixed Income, Vol. 4, No. 2, pp. 6-16.
- Kim, K. A., and P. Limpaphayom, 1997, “The Effect of Economic Regimes on the Relation Between Term Structure And Real Activity in Japan,” Journal of Economics and Business, Vol. 49, No. 4, pp. 379-92.
- Kugler, Peter, 1997, “Central Bank Policy Reaction and the Expectations Hypothesis of the Term Structure, International Journal of Finance and Economics, Vol. 2, No. 3, pp. 217-24.
- Kugler, Peter, 2002, “The Term Premium, Time Varying Interest Rate Volatility and Central Bank Policy Reaction,” Economics Letters, Vol. 76, No. 3, pp. 311-16.
- Nagayasu, Jun, 2002, “On the Term Structure of Interest Rates and Inflation in Japan”, Journal of Economics and Business, Vol. 54, No. 5, pp. 505-523.
- Shikano, Yoshiaki, 1985, “Expectations Theory and Term Structure of Interest Rates,” Bank of Japan Monetary and Economic Studies, Vol. 3, No. 1, pp. 47-70.
- Shiller, Robert, 1979, “The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure,” Journal of Political Economy, Vol. 87, No. 6, pp. 1190-219.
- Shiller, Robert, 1990, “The Term Structure of Interest Rates,” in Handbook of Monetary Economics, B. M. Friedman and F. H. Hahn eds., Vol. 1 pp. 629-722.
- Shirakawa, Hiromichi, 1987, “Fluctuations in Yields on Bonds—A Reassessment of the Expectations Theory Based on Japanese and U.S. Data,” Bank of Japan Monetary and Economic Studies, Vol. 15, No. 2, pp. 71-117.
- Thornton, Daniel L., 2003, “Testing the Expectations Hypothesis: Some New Evidence for Japan,” draft, Institute for Monetary and Economic Studies (Tokyo: Bank of Japan).

### Econometric methods, GMM, and covariance estimation
- Cushing, Matthew J., and Mary G. McGarvey, 1999, “Covariance Matrix Estimation,” in Generalized Methods of Moments Estimation, Laszlo Matyas ed. (Cambridge: Cambridge University Press), pp. 63-95.
- Elliott, Graham, Thomas J. Rothenberg, and James H. Stock, 1996, “Efficient Tests for an Autoregressive Unit Root,” Econometrica, Vol. 64, No. 4 pp. 813-36.
- Hamilton, James, 1994, Time Series Analysis (Princeton: Princeton University Press).
- Hansen, Lars Peter, 1982, “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, Vol. 50, No. 4, pp. 1029-54.
- MacKinnon, James G., 1996, “Critical Values for Cointegration Tests,” in Long-run Economic Relationships, C. W. J. Granger and G. E. Mizon eds., (Oxford: Oxford University Press) pp. 267-276.
- Newey, Whitney K., and Kenneth West, 1987, “A Simple, Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica, Vol. 55, No. 3, pp. 703-09.
- Newey, Whitney K., and Kenneth West, 1994, “Automatic Lag Selection in Covariance Matrix Estimation,” Review of Economic Studies, Vol. 61, No. 4, pp. 631-53.
- Ogaki, Masao, 1999, “GMM Estimation Techniques,” in Generalized Methods of Moments Estimation, Laszlo Matyas ed. (Cambridge: Cambridge University Press) pp. 31-62.

### Japan-focused empirical and policy analyses
- Hosono, Kaoru, Shigeru Sugihara, and Tsuyoshi Mihira, 2001, The Effectiveness and Limits of Monetary Policy (in Japanese) (Tokyo: Toyo Heizai).
- International Monetary Fund, 2003, Japan—Staff Report for the 2003 Article IV Consultation (Washington DC: International Monetary Fund)—forthcoming.
- Kato, Ryo, and Shinichi Nishiyama, 2003, “Optimal Monetary Policy When Interest Rates Are Bounded at Zero,” Draft (Tokyo: Bank of Japan).
- Kimura, Takeshi, Hiroshi Kobayashi, Jun Muranaga, and Hiroshi Ugai, 2002, “The Effect of the Increase in Monetary Base on Japan’s Economy at Zero Interest Rates: An Empirical Analysis,” Institute for Monetary and Economic Studies Discussion Paper Series No. 2002-E-22 (Tokyo: Bank of Japan).
- Marumo, Kohei, Takashi Nakayama, Shinichi Nishioka, and Toshihiro Yoshida, 2003, “The Term Structure Model under the Zero Interest Rate Policy (in Japanese), Capital Market Department Working Paper No. 2003-J-1 (Tokyo: Bank of Japan).
- Ogawa, Kazuo, and Heizo Takenaka, 2001, Policy Crises and Japanese Economy: Causes of Slow Economic Recovery in the 1990s (in Japanese) (Tokyo: Nippon Hyoronsha).
- Saito, Makoto, Shigenori Shiratsuka, Tsutomu Watanabe, and Noriyuki Yanagawa, 2001, “Liquidity Demand and Asset Pricing: Evidence from the Periodic Settlement in Japan,” IMES Discussion Paper Series No. 2001-E-21 (Bank of Japan: Tokyo).
- Thornton, Daniel L., 2003, “Testing the Expectations Hypothesis: Some New Evidence for Japan,” draft, Institute for Monetary and Economic Studies (Tokyo: Bank of Japan).

_References from _wp03208 - References_._

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