## wp1896

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### Introduction and research question
- Main question: Have large-scale asset purchases by major central banks (quantitative easing, QE) affected liquidity conditions of purchased assets?
- Context: Post-GFC QE expanded central bank balance sheets, particularly holdings of domestic government bonds.
- Concern: If balance-sheet expansions impaired market functioning and reduced market liquidity, transaction and hedging costs may increase, partly offsetting intended policy impacts.

### Theoretical channels through which QE can affect market liquidity
- Bank funding channel:
  - QE increases bank reserves and funding liquidity, easing banks’ ability to finance inventories and support market liquidity.
- Risk appetite channel:
  - QE can raise market makers’ risk appetite, increasing willingness to hold inventories and facilitate trades.
- Market functioning channel (opposing mechanisms):
  - Trade-facilitating channel: central bank as solvent, committed, uninformed buyer can reduce search frictions and liquidity risk premia while QE is ongoing or expected.
  - Scarcity effects: large central bank holdings can increase scarcity of securities, raising search costs and lowering market liquidity.

### JGB market as case study and context
- BOJ QQE launched April 2013 with large-scale JGB purchases to expand the monetary base and lower long-term yields.
- Purchase magnitude and holdings:
  - Until September 2016: purchases targeted at ¥80 trillion of JGBs per year (equivalent to almost one-sixth of domestic GDP).
  - After YCC in September 2016: purchases reduced to about ¥40-50 trillion (annualized).
  - By June 2017: BOJ’s JGB holdings rose to over 40 percent of total amount outstanding.
- Comparative central bank holdings (as cited):
  - Bank of England: 25 percent of domestic government debt securities.
  - European Central Bank: 22 percent.
  - Federal Reserve: 17 percent.
- BOJ holdings include both JGBs and Treasury Discount Bills; both exceeded 40 percent of their respective total amount outstanding.
- Importance of JGBs:
  - Japan’s government debt reached almost 200 percent of GDP by June 2017, of which over 90 percent are JGBs or short-term Treasury Discount Bills (TDBs).
  - Nearly 90 percent of such debt is held by residents.
  - JGBs account for more than 10 percent of total bank assets and nearly 40 percent of the assets of insurance companies and pension funds.
  - JGBs accounted for 85 percent of all yen-denominated bond issuance and 99 percent of total trading in yen-denominated bonds during April 2016–March 2017.
  - By December 2016, foreign investors held ¥113 trillion of JGBs and TDBs (nearly 11 percent of total amount outstanding).

### Main empirical findings (high level)
- Primary result: BOJ’s outright purchases have a significantly negative impact on market liquidity when holdings are large — evidence of scarcity effects.
- Conditionality:
  - QQE can improve liquidity when BOJ holdings are relatively small (bank funding, risk appetite, trade-facilitating channels).
  - When BOJ holdings exceed thresholds, purchases reduce market liquidity (flow effects depend on stock of holdings).
- Caveat: Negative liquidity effects are potential side effects; QQE has been effective in lowering JGB yields.

### Measures, data, and empirical strategy
- Liquidity measure:
  - Corwin and Schultz (2012) bid-ask spread estimator (an increase implies a decline in liquidity); uses daily high and low prices and differences between one-day and two-day high–low ratios.
- Sample coverage:
  - Bond-level: fixed rate coupon-bearing JGBs with original maturities 2, 5, 10, 20, 30, 40 years; daily high-low data Jan 31, 2012–Feb 28, 2017; monthly averages.
  - Maturity-level (on-the-run): Dec 29, 2006–Jan 20, 2017.
- Scarcity proxy:
  - Primary proxy: share of each JGB issue held by the BOJ (BOJ holdings / amount outstanding).
- Main empirical models:
  - Model (1): linear interaction fixed-effects panel
    - Dependent variable L_{i,t} (standardized Corwin-Schultz).
    - Key regressors: PURCHASE_{i,t} (purchase intensity normalized by amount outstanding), PURCHASE_{i,t} · S_{i,t-1}, S_{i,t-1}, SLF_{i,t}, controls X_t.
    - Marginal flow effect: ∂E[L_{i,t}]/∂PURCHASE_{i,t} = β1 + β2 · S_{i,t-1}.
  - Model (2): fixed-effects threshold panel regression (threshold S* on S_{i,t-1})
    - Marginal effect = α1 if S_{i,t-1} ≤ S*; = α2 if S_{i,t-1} > S*.
- Controls and robustness:
  - Controls include log Nikkei Stock Average Volatility Index (Nikkei VI), S&P/JPX JGB VIX, dummies for QQE, QQE2 (Oct 2014), NIRP (Jan 2016), YCC (Sep 2016), U.S. election (Nov 2016), GFC (2008–09) for maturity regressions.
  - Standard errors: White robust baseline; Driscoll-Kraay; two-way cluster (maturity and time).
  - SLF (Securities Lending Facility) instrumented by lagged SLF where appropriate.

### Transaction-based indicators and market signals of scarcity
- BOJ SLF use:
  - Minimal until 2016, then increased rapidly to over ¥6 trillion per month by early 2017.
- Fails:
  - Number and amount of fails in JGB transactions trended upward and became more volatile since 2013.
- GC-SC repo spread:
  - Spread increased sharply from end-2016 to early 2017, coinciding with peak SLF use — interpreted as indicating scarcity.
- BOJ transaction-based liquidity indicators:
  - Indicate relative declines in liquidity in both JGB futures and cash markets since QQE.
  - BOJ Bond Market Survey (Nov 2017, 46 respondents): diffusion index (DI) for bond market functioning is negative.

### Maturity-level regression findings (summary)
- Tendencies:
  - Negative impact of BOJ purchases on market liquidity for 2-10 year JGBs, broadly consistent with Hypothesis 1.
- Specifics:
  - In model (1) full sample, β2 estimates statistically insignificant but positive in sign.
  - For 2-10 year subsample, β2 likely significantly positive; β1 significantly negative — consistent with a U-shaped relationship:
    - BOJ purchases tightened spreads when BOJ share small.
    - BOJ purchases widened spreads when BOJ share exceeded threshold.
- Caveats:
  - Limited cross-sectional variation (six maturities) → estimates may be less precise.

### Bond-level regression findings (summary)
- Evidence supports Hypotheses 1 and 2:
  - 훽2 significantly positive across three standard-error methods in full-sample bond-level regressions (implying purchases worsen liquidity as holdings rise).
  - Scarcity effects present for 2-10 year JGBs: 훽2 for subsample significantly positive.
  - U-shaped relationship: 훽1 mostly significantly negative (purchases tighten spreads when holdings low; widen when holdings high).
  - Market liquidity declined significantly after QQE, QQE2, and NIRP announcements.
  - Some (statistically insignificant) evidence YCC announcement improved liquidity; U.S. election reduced liquidity.
- Magnitude examples (reported):
  - One-percentage-point increase in purchase intensity → about 0.3 standard deviations increase in Corwin-Schultz spread (full-sample FE with two-way cluster robust s.e.).
  - Using an example: BOJ purchase increase ≈ 0.3 percent of total amount outstanding for an average JGB issue over a 10-day period.
  - With average BOJ share ≈ 40 percent, sustained increase of 0.3 percent every 10 days for three months → cumulative effect ≈ 1.2 standard deviations (non-threshold) or ≈ 1 standard deviation (threshold) in the Corwin-Schultz spread.
  - Individual-purchase impact: one-percentage-point increase in daily purchase intensity could raise spread by about 0.4 standard deviations (fixed-effects threshold full sample).

### Fixed-effects threshold regression results (selected)
- Estimated thresholds (S*):
  - All JGBs Maturity-Level: 0.05.
  - All JGBs Bond-Level: 0.05.
  - 2–10 year JGBs Maturity-Level: 0.25.
  - 2–10 year JGBs Bond-Level: 0.05.
- Selected coefficient patterns (values preserved as reported):
  - PPPPPP_{i,t}^{BOJ}·1(S_{i,t-1}^{BOJ} ≤ S*):
    - All JGBs Maturity-Level: -19.08*** (5.49).
    - All JGBs Bond-Level: -1.53*** (0.55).
    - 2-10 year JGBs Maturity-Level: -10.89*** (2.50).
    - 2-10 year JGBs Bond-Level: -4.54*** (1.34).
  - PPPPPP_{i,t}^{BOJ}·1(S_{i,t-1}^{BOJ} > S*):
    - All JGBs Bond-Level: 0.35*** (0.13).
    - All JGBs Maturity-Level: 0.36 (0.58).
    - 2-10 year JGBs Bond-Level: 0.42 (0.31).
    - 2-10 year JGBs Maturity-Level: 0.36 (0.59).
  - S_{i,t-1}^{BOJ} coefficients:
    - All JGBs Bond-Level: -0.70*** (0.13).
    - 2-10 year JGBs Bond-Level: -2.50*** (0.20).

### Role of the Securities Lending Facility (SLF)
- SLF usage increased markedly in 2016–17; evidence suggests SLF helped dampen scarcity effects:
  - Bond-level model (1): SLF not significant in full-sample estimation.
  - Separate estimates: interaction coefficient 훽2 mostly significantly positive when SLF not conducted; interaction insignificant when SLF conducted.
  - Pattern suggests SLF operations reduced adverse effects of BOJ purchases on market liquidity; broadly holds for 2-10 year subsample.
- SLF measurement and endogeneity:
  - SLF_{i,t} instrumented by lagged SLF to mitigate endogeneity; some endogeneity concerns remain.

### Robustness, limitations, and caveats
- Robustness:
  - Results hold when replacing Nikkei VI and announcement dummies with time fixed effects.
  - Estimates of 훽1 and 훽2 remain statistically significant with expected signs under two-way clustering and time fixed effects in many specifications.
- Measurement limits:
  - Corwin-Schultz captures cost/tightness dimension only; liquidity has multiple dimensions (cost, quantity, time; tightness, depth, resiliency).
  - Quoted bid-ask spreads not based on actual transactions can be misleading.
- Model sensitivity and endogeneity:
  - Some announcement effects vary across specifications and samples.
  - SLF effects may still be endogenous despite instrumentation.
- Interpretation:
  - Findings should be viewed as potential side effects of QQE and not as evidence that QQE is ineffective; QQE nonetheless lowered JGB yields.

### Key quantitative figures (selected, preserved exactly)
- BOJ purchase targets pre-YCC: ¥80 trillion per year.
- Purchase targets post-YCC: about ¥40-50 trillion (annualized).
- By June 2017: BOJ’s JGB holdings rose to over 40 percent of total amount outstanding.
- Comparative holdings: Bank of England 25 percent; ECB 22 percent; Federal Reserve 17 percent.
- Foreign holdings by Dec 2016: ¥113 trillion (nearly 11 percent of total amount outstanding).
- Example impacts:
  - One-percentage-point increase in purchase intensity → about 0.3 standard deviations increase in Corwin-Schultz spread (full-sample FE with two-way cluster robust s.e.).
  - One-percentage-point increase in daily purchase intensity → about 0.4 standard deviations increase in Corwin-Schultz spread (fixed-effects threshold full sample).
  - Average BOJ share of holdings ≈ 40 percent.
  - Example purchase increase ≈ 0.3 percent of total amount outstanding for an average JGB issue over a 10-day period.
  - Cumulative impact over three months under example scenario ≈ 1.2 standard deviations (non-threshold) or ≈ 1 standard deviation (threshold).

### Policy implications and recommendations
- Central banks with QE programs should monitor liquidity developments of purchased securities and signals of potential scarcity (e.g., increased SLF use, higher repo fails).
- Monitor holdings of each security as a share of total (or tradable) amount outstanding and adjust purchases to avoid creating substantial scarcity.
  - This monitoring is important as QE policies normalize.
- In times of stress, central banks could provide securities lending facilities to temporarily alleviate market liquidity pressure.

### Appendices — measurement and methodology (high level)
- Market liquidity concept: ability to rapidly buy/sell sizable volume at low cost with limited price impact.
- Corwin-Schultz implementation:
  - S = 2( e^α − 1 ) / (1 + e^α ), with α defined per Corwin and Schultz (2012) using two-day high and low prices.
  - Assign zero to estimated high-low spreads < 0; monthly spreads are averages of two-day trading periods within a calendar month.
- Data sources:
  - Daily high and low prices from Bloomberg Finance L.P.
  - Amount outstanding from Japanese Ministry of Finance issuance data; BOJ holdings published at bond level on a 10-day basis since April 30, 2014 and monthly Jan 2012–Mar 2014.
- Panel estimation notes:
  - Maturity-level sample: Dec 29, 2006–Jan 20, 2017.
  - Bond-level sample: Jan 31, 2012–Feb 28, 2017.
  - Driscoll-Kraay used to address heteroskedasticity, autocorrelation, cross-section dependence; two-way clustering by maturity/time; SLF instrumented by lagged SLF in some specifications.

*Source: IMF Working Paper (wp1896), extracted section and tables as provided.*

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

### References

### Introduction and research question
- Main question: Have large-scale asset purchases by major central banks (quantitative easing, QE) affected liquidity conditions of purchased assets?
- Context: Post-GFC QE expanded central bank balance sheets, particularly holdings of domestic government bonds (Figure 1).
- Potential concern: If balance-sheet expansions impaired market functioning and reduced market liquidity, transaction and hedging costs may increase, partly offsetting intended policy impacts.

### Theoretical channels through which QE can affect market liquidity
- Bank funding channel:
  - QE increases bank reserves and funding liquidity, easing banks’ ability to finance inventories and support market liquidity (Brunnermeier and Pederson, 2009).
- Risk appetite channel:
  - QE can raise market makers’ risk appetite, increasing willingness to hold inventories and facilitate trades (Bekaert and others, 2013; Jiménez and others, 2014).
- Market functioning channel (two opposing mechanisms):
  - Trade-facilitating channel: Central bank as solvent, committed, and uninformed buyer can reduce search frictions and liquidity risk premium while QE is ongoing or if investors expect future intervention (Lagos and others, 2011; IMF, 2015; Christensen and Gillan, 2015).
  - Scarcity effects: Large central bank holdings can increase scarcity of securities, raising search costs and lowering market liquidity (IMF, 2015; Schlepper and others, 2017; Pelizzon and others, 2017).

### Survey of empirical findings in the literature
- Mixed evidence overall; no consensus.
- Examples of null or modest effects:
  - Kandrac and Schlusche (2013): No significant liquidity effects from Federal Reserve Treasury purchases; no flow effects on Treasury market liquidity.
  - Kandrac (2013): Negative flow effects from Fed outright MBS purchases on MBS market functioning, magnitude modest.
  - IMF (2015): MBS purchases improved liquidity during first reinvestment program (October 2011–November 2012), had no effect during QE3 (December 2012–October 2014), and reduced liquidity after November 2014 when scarcity effects dominated.
- Examples of positive effects:
  - De Pooter and others (2016): ECB Securities Market Program (May 2010–September 2012) reduced liquidity premia of purchased sovereign bonds.
  - Iwatsubo and Taishi (2016): BOJ’s changes since QQE in April 2013 had a positive impact on JGB liquidity by clarifying purchase schedule and reducing uncertainty.
  - Christensen and Gillan (2017): U.S. QE improved TIPS market liquidity temporarily by increasing sellers’ bargaining power.
- Examples of negative effects:
  - Sakiyama and Yamada (2016): QQE adversely affected liquidity in certain sectors; market depth declined.
  - Schlepper and others (2017): ECB/Eurosystem PSPP (since March 2015) had a statistically and economically significant negative impact on German government bond market liquidity (intraday transaction-level data), highlighting scarcity effects.
  - Pelizzon and others (2017): JGB liquidity showed both “spotlight effect” improvements and deterioration via scarcity effect.

### Japanese Government Bond (JGB) market as a case study
- BOJ’s QQE launched April 2013 with large-scale JGB purchases to expand monetary base and lower long-term yields.
- Purchase magnitude and holdings:
  - Until September 2016: purchases targeted at ¥80 trillion of JGBs per year, equivalent to almost one-sixth of domestic GDP.
  - After YCC in September 2016: purchases reduced to about ¥40-50 trillion (annualized).
  - By June 2017: BOJ’s JGB holdings rose to over 40 percent of total amount outstanding.
- Comparative holdings by other central banks (as of comparable dates in the text):
  - Bank of England: 25 percent of domestic government debt securities.
  - European Central Bank: 22 percent.
  - Federal Reserve: 17 percent.
- BOJ holdings include both JGBs and Treasury Discount Bills; both exceeded 40 percent of their respective total amount outstanding.

### Paper’s main empirical findings on QQE and JGB liquidity
- Primary result: BOJ’s outright purchases have a significantly negative impact on market liquidity, indicating scarcity effects are present when holdings are large.
- Conditional effects:
  - Evidence that QQE improves JGB market liquidity when BOJ’s holdings are relatively small, via bank funding, risk appetite, or trade-facilitating channels.
  - When BOJ’s holdings (as a share of amount outstanding) exceed certain thresholds, QQE reduces market liquidity—flow effects depend on the stock of BOJ holdings.
- Caveat: Negative liquidity effects are characterized as potential side effects; QQE has been effective in lowering JGB yields despite these concerns.

### Role and importance of JGB markets for Japan’s financial system
- JGBs contribute to a stable and low yield curve and provide stable, cheap funding for the Japanese government.
- Government debt context:
  - Japan’s government debt reached almost 200 percent of GDP by June 2017, of which over 90 percent are JGBs or short-term Treasury Discount Bills (TDBs) (Arslanalp and Tsuda, 2014 dataset update).
  - Nearly 90 percent of such debt is held by residents.
- JGBs in financial institution balance sheets (key points):
  - JGBs account for more than 10 percent of total bank assets and nearly 40 percent of the assets of insurance companies and pension funds.
- Market share and usage:
  - JGBs accounted for 85 percent of all yen-denominated bond issuance and 99 percent of total trading in yen-denominated bonds during April 2016–March 2017 (Ministry of Finance, Japan, 2017).
  - JGBs are used as collateral in almost all repurchase agreements (repos) and in the secured call money market, and are the main instrument used by broker-dealers and other market participants to hedge positions.
- Foreign holdings:
  - By December 2016, foreign investors held ¥113 trillion of JGBs and TDBs, nearly 11 percent of total amount outstanding.
- Systemic implication:
  - Disruptions in JGB markets can spread rapidly across the financial system and reduce funding market efficiency; high market liquidity is important to ensure efficient funding transfer.

*Source: wp1896 - References (content extracts).*

### 11.      Despite having substantially increased the monetary base and provided the

### Despite having substantially increased the monetary base and provided the

### Signs of potential scarcity in JGB markets
- BOJ purchases expanded rapidly and substantially across all maturities until the introduction of YCC; concurrent signs of scarcity emerged.
- The BOJ’s Securities Lending Facility (SLF) through repos:
  - Operates since 2004 to provide temporary/secondary supply of Japanese government securities.
  - Use remained minimal until 2016, then increased rapidly to over ¥6 trillion per month by early 2017—despite the adoption of YCC in September 2016.
- Fails in JGB transactions:
  - Both the number and amount of fails have trended upward and become more volatile since 2013.
  - Market participants attribute increased fails partly to higher foreign participation and partly to scarcity of JGBs.
- GC-SC repo spread:
  - The spread between general collateral (GC) and special collateral (SC) repo rates increased sharply from end-2016 to early 2017.
  - A larger GC-SC spread implies a higher lending fee in the SC repo market and typically indicates some degree of scarcity.
  - The elevated GC-SC spread between end-2016 and early 2017 coincides with the period when SLF use peaked.

### Transaction-based indicators and market liquidity trends
- Traditional liquidity indicators (quoted bid-ask spreads; daily price range to transaction volume ratio) suggest JGB market liquidity has not declined.
- BOJ transaction-based liquidity indicators show relative declines in liquidity in both JGB futures and cash markets since QQE:
  - JGB futures market: bid-ask spreads and price impact of individual trades (from transaction data) are somewhat higher; transactions have been on a downward trend (Figure 6).
  - JGB cash market: best-worst quote spreads for short- or super-long-term residual maturities (dealer-to-client market) show a widening trend; transaction volume has declined.
- BOJ Bond Market Survey (since March 2015):
  - Latest survey in November 2017 received 46 respondents.
  - The diffusion index (DI) for bond market functioning is negative, indicating more respondents felt low market functioning than high.
- Market participants commonly attribute the decline in JGB market liquidity at least partly to scarcity of JGBs; scarcity effects may have dominated the positive effects from bank funding, risk appetite, and trade facilitating channels.

### Research questions and hypothesis
- Main empirical questions:
  - What is the impact of the BOJ’s outright purchases on the liquidity in the JGB markets?
  - Is there evidence of scarcity effects?
- Hypothesis 1:
  - The BOJ’s outright purchases have significantly negative (flow) effects on JGB market liquidity.
  - Rationale: If bank funding, risk appetite, and trade-facilitating channels should produce positive effects of QQE on liquidity, an estimated negative impact would imply scarcity effects.

### Measure of market liquidity and data
- Liquidity measure used:
  - Corwin and Schultz (2012) bid-ask spread estimator (a measure of market illiquidity: an increase implies a decline in liquidity).
  - Method relies on daily high and low prices and differences between one-day and two-day high–low ratios to isolate bid-ask spreads.
  - Advantages: uses actual transaction prices; generally outperforms other low-frequency estimators.
- Estimation details:
  - Estimated for each JGB issue and for “on-the-run” JGBs by original maturities 2, 5, 10, 20, 30, and 40 years.
  - Issue-level daily high and low price data used for each day between January 31, 2012 and February 28, 2017.
  - Daily bond-level spreads averaged to monthly measures (summary statistics in Appendix Table 2).
  - On-the-run daily bid-ask spreads available between December 29, 2006 and January 20, 2017.
- Sample scope:
  - Considers fixed rate coupon-bearing JGBs with original maturities 2, 5, 10, 20, 30, and 40 years.
  - Excludes inflation-indexed JGBs, floating rate coupon-bearing JGBs with 15-year original maturity, and JGBs for retail investors typically held to maturity.

### Empirical findings and patterns
- Corwin-Schultz measure dynamics:
  - Gradual increase in the measure after QQE implementation in April 2013 and before YCC introduction in September 2016 (Figure 7).
  - Similar dynamics observed for best-worst quote spreads for short- and super-long-term maturities.
- Liquidity and volatility:
  - Positive correlation between S&P/JPX JGB VIX index (implied volatility) and Corwin-Schultz measure since the GFC.
  - Average correlation about 0.5 during 2008–17.
  - Correlation particularly strong at 0.7 for 10-year JGBs, highlighting importance of 10-year market liquidity for volatility.
- Relationship between BOJ holdings and liquidity:
  - At maturity level, Corwin-Schultz measure appears somewhat correlated with the share of JGBs held by the BOJ for most maturities.
  - Patterns observed:
    - Broadly positive correlation for 2, 5, 30, and 40-year JGBs.
    - U-shaped relationship for 10-year JGBs (benchmark for long-term rates and target of YCC).
  - Cross-country evidence:
    - Using quoted bid-ask spreads for domestic sovereign bonds (2013–15 quarterly average; advanced economies), a U-shaped relationship appears between market liquidity and central bank holdings as share of amount outstanding.
    - Interpretation: QE can initially improve liquidity via bank funding and risk appetite channels, but once central bank holdings exceed a threshold and cause a shortage, scarcity effects can dominate and liquidity declines.
    - This mechanism aligns with prior findings for the U.S. MBS market where QE effects turned negative after QE3 as scarcity increased.

### Implications highlighted
- A deterioration in market liquidity accompanied by higher volatility could threaten stable and cheap funding for the Japanese government and aggravate public debt problems.
- Empirical patterns are consistent with a scarcity channel: large-scale BOJ purchases can reduce market liquidity once the share of BOJ holdings becomes large, offsetting positive QE channels.

*Source: IMF staff analysis (excerpts from the provided chapter).*

### 20.      Based on these observations, we can propose another hypothesis:

### wp1896 - 20.      Based on these observations, we can propose another hypothesis:

### Hypotheses
- Hypothesis 2: The flow effects of the BOJ’s outright purchases on JGB market liquidity become negative when the share of the BOJ’s holdings exceeds a certain threshold.
  - This hypothesis is a sufficient condition for the existence of scarcity effects (Hypothesis 1).
  - It also implies that the flow effects—as defined in D’Amico and King (2013)—of QQE on JGB market liquidity depend on the level of stock.

### Empirical strategy — panel regressions
- Approach:
  - Fixed-effect panel regressions estimated both at the maturity level (on-the-run JGBs) and at the bond level to estimate effects of BOJ outright purchases on the Corwin-Schultz measure of JGB market liquidity.
  - Two possible panel regression models are used to test Hypotheses 1 and 2: a linear interaction fixed-effects model (model (1)) and a fixed-effects threshold panel regression model (model (2)).
- Model (1) specification (interaction, linear in scarcity):
  - Dependent variable: L_{i,t} — Corwin-Schultz measure of JGB market (il)liquidity for bond i or maturity i, normalized by its mean and standard deviation over time.
  - Key regressors:
    - PURCHASE_{i,t} — BOJ’s outright purchases of bond (maturity) i, standardized by amount outstanding (daily purchase intensity).
    - PURCHASE_{i,t} · S_{i,t-1} — interaction with lagged share of BOJ holdings.
    - S_{i,t-1} — lagged share of BOJ’s holdings (proxy for scarcity).
    - SLF_{i,t} — size of BOJ’s SLF operations for bond (maturity) i, standardized by amount outstanding (instrumented where noted).
    - X_t — controls common across bonds/maturities (see controls below).
  - Implication for marginal flow effect:
    - ∂E[L_{i,t}]/∂PURCHASE_{i,t} = β1 + β2 · S_{i,t-1}.
    - Since L is an illiquidity measure, β1 + β2 · S_{i,t-1} > 0 implies BOJ purchases worsen market liquidity (supporting Hypothesis 1).
  - Statistical tests:
    - Evidence of scarcity effects if estimates of β1 and β2 fall into any of: i) β1 > 0 and β2 = 0, ii) β1 = 0 and β2 > 0, or iii) β1 > 0 and β2 > 0.
    - Hypothesis 2 tested by testing β2 > 0.
  - Endogeneity and instrumentation:
    - SLF likely endogenous; mitigate by two-stage least squares instrumenting SLF with lagged SLF (SLF_{i,t-1}) in models with White or two-way cluster robust standard errors.
    - For Driscoll-Kraay standard errors, lagged SLF is used directly (instrumental variables not allowed in Driscoll-Kraay estimation).
- Model (2) specification (fixed-effects threshold panel):
  - Threshold variable: S_{i,t-1} (share of JGBs held by the BOJ).
  - Two regimes depending on threshold S*:
    - If S_{i,t-1} ≤ S*: marginal effect = α1.
    - If S_{i,t-1} > S*: marginal effect = α2.
  - Effects of purchases on market liquidity:
    - ∂E[L_{i,t}]/∂PURCHASE_{i,t} = α1 if S_{i,t-1} < S*; = α2 if S_{i,t-1} ≥ S*.
  - Hypotheses testing:
    - Hypotheses 1 and 2 can be tested by testing α2 > 0 (if BOJ purchases reduce liquidity when share exceeds S*, Hypothesis 2 holds and scarcity effects existed).
  - Estimation method: threshold regression method for non-dynamic panels with fixed effects (Hansen (1999)).

### Data construction and key measurement details
- Scarcity proxy:
  - Primary proxy: share of each JGB issue held by the BOJ (BOJ holdings of each issue divided by amount outstanding of that issue).
  - Justification: holdings by long-term investors are relatively stable; BOJ share is linked to QQE and higher values correspond to higher scarcity.
- BOJ holdings publication and purchase intensity:
  - JGBs held by the BOJ published at bond level on a 10-day basis since April 30, 2014 and on a monthly basis between January 2012 and March 2014.
  - BOJ’s purchases calculated as the amount purchased between two holding dates (net purchases excluding matured bonds).
  - Daily purchase intensity = purchases between holding dates / number of days between them.
  - Purchase intensity normalized by total amount outstanding of the issue.
- Amount outstanding:
  - Computed from issuance data from the Japanese Ministry of Finance (MOF) on face-value basis, including regular auctions and liquidity-enhancing auctions.
  - MOF buybacks from the BOJ during sample period are deducted from amount outstanding.
  - Bond-level amount outstanding only available after 2012 (due to lack of buyback data before 2012); maturity-level amount outstanding from Bloomberg, L.P. used to extend back to December 29, 2006.
- SLF operations:
  - SLF used to control for temporary provision of JGBs to alleviate market liquidity pressure.
  - SLF included in regressions; endogeneity mitigated via lagged SLF instrument or used directly when Driscoll-Kraay standard errors applied.

### Results — maturity-level fixed-effects panel regressions (high-level findings)
- Main tendencies:
  - Results tend to suggest a negative impact of BOJ’s outright purchases on market liquidity of 2-10 year JGBs, broadly consistent with Hypothesis 1.
- Specific findings:
  - In model (1) using full sample (columns 2-4 in Appendix III, Table 1), estimates of β2 are statistically insignificant across White robust, Driscoll-Kraay, and two-way cluster robust standard errors, but signs are positive (consistent with expectation).
  - For the subsample of 2-10 year JGBs (columns 5-7), estimates of β2 are likely to be significantly positive — supporting Hypothesis 2 and providing evidence for scarcity effects (Hypothesis 1).
  - For 2-10 year subsample, β1 estimates in model (1) are significantly negative while β2 is significantly positive — consistent with a U-shaped relationship between JGB market (il)liquidity and the share of BOJ holdings:
    - BOJ purchases tightened Corwin-Schultz bid-ask spreads when BOJ share was small.
    - BOJ purchases widened bid-ask spreads when BOJ share exceeded some threshold.
- Caveats:
  - Maturity-level regressions have limited cross-section variation (six maturities) and hence estimates may be less precise than bond-level regressions.
  - Magnitudes of scarcity effects discussed further in bond-level regressions (bond-level results described in next subsection, not included here).

*Source: wp1896 - 20.      Based on these observations, we can propose another hypothesis:*

### 36.      The maturity-level results also suggest significant deteriorations in JGB market

### wp1896 - 36.      The maturity-level results also suggest significant deteriorations in JGB market

### Maturity-level evidence of liquidity deterioration
- Maturity-level results indicate significant deteriorations in JGB market liquidity across all maturities during the GFC and after the announcement of the NIRP in January 2016.
- BOJ (2017) liquidity indicators constructed from transaction data mostly show a deterioration in JGB market liquidity following the BOJ’s announcement of the NIRP.
- The U.S. election in November 2016 is associated with some declines in market liquidity for both the full sample and the subsample, with a larger impact for the subsample.

### Bond-level fixed-effects panel regression findings
- Results lend support to both Hypotheses 1 and 2.
- Main empirical patterns:
  - A significantly negative flow effect of the BOJ’s purchases on JGB market liquidity: the estimate of 훽2 is significantly positive across three different standard errors in the full-sample bond-level regressions (contrasting with maturity-level regressions with all JGBs).
  - Scarcity effects are found for the 2-10 year JGBs: the estimate of 훽2 for the subsample is also significantly positive.
  - A U-shaped relationship between market liquidity and the BOJ’s share of holdings: estimates of 훽1 are mostly significantly negative for both full sample and subsample.
  - Market liquidity declined significantly after each of the three key BOJ announcements: QQE, QQE2, and NIRP.
  - Some evidence (statistically insignificant) that the announcement of YCC improved market liquidity and that the U.S. election in November 2016 reduced market liquidity.

### Magnitude and cumulative impact examples
- Individual-purchase impact:
  - A one-percentage-point increase in the purchase intensity could raise the Corwin-Schultz bid-ask spread by about 0.3 standard deviations based on the full-sample regression with two-way cluster robust standard error.
  - The average share of the BOJ’s holdings is about 40 percent.
- Cumulative example using QQE expansion (October 2014):
  - BOJ’s purchase increased by about 0.3 percent of total amount outstanding for an average JGB issue over a 10-day period.
  - If such an increase continues for three months when the BOJ’s share is about 40 percent, the cumulative effect on the Corwin-Schultz bid-ask spread is about 1.2 standard deviations by the end of three months.
  - The deterioration in market liquidity could potentially increase the likelihood of “flash-crash”-type scenarios.

### Fixed-effects threshold panel regression results
- Maturity-level threshold regressions produce similar results as non-threshold maturity-level regressions, albeit with less statistical significance.
  - Signs imply a U-shaped relationship between market liquidity and central bank purchases with a positive turning point: 훽1 < 0 and 훽2 > 0 (some estimates not statistically significant).
  - JGB market liquidity likely declined during the GFC, after the announcement of NIRP, and after the U.S. election in November 2016.
- Threshold regressions tend to support a V-shaped relationship between market liquidity and the BOJ’s holdings:
  - Estimates of α1 are all statistically significant for full sample and subsample.
  - α2 estimates are not statistically significant in maturity-level regressions, but the bond-level regression with the full sample shows a significantly positive α2, supporting Hypotheses 1 and 2.
- Magnitude in threshold regressions:
  - A one-percentage-point increase in daily purchase intensity could increase the Corwin-Schultz bid-ask spread by about 0.4 standard deviations based on the full-sample threshold regression.
  - In the scenario where purchases increase by 0.3 percent of total amount outstanding every 10 days for three months and BOJ holdings are about 40 percent, the spread would increase by about one standard deviation by the end of three months.
- Announcement effects in bond-level threshold regressions:
  - QQE, QQE2, and NIRP announcements had significantly adverse impacts on market liquidity, with the largest impact from QQE.
  - The announcement of YCC seems to have improved JGB market liquidity to some extent, consistent with BOJ (2017) liquidity indicators, although improvement is statistically insignificant for 2-10 year JGBs.

### The role of the Special Liquidity Facility (SLF)
- Evidence that the SLF may have helped dampen scarcity effects:
  - The bond-level fixed-effects panel model (1) does not find a significant impact of the SLF on JGB market liquidity in the full-sample estimation (Appendix III, Table 2).
  - Estimating model (1) separately for periods when the SLF did not take place versus when it did:
    - The coefficient of the interaction term, 훽2, is mostly significantly positive when the SLF was not conducted.
    - The interaction coefficient is statistically insignificant when the SLF was conducted.
  - This pattern suggests that when conducted, the SLF seems to have helped reduce the adverse effects of BOJ purchases on market liquidity.
  - The finding broadly holds for the 2-10 year JGB subsample.

### Robustness checks and caveats
- Robustness:
  - Baseline results hold when replacing macro-level announcement dummies and Nikkei VI with time fixed effects.
  - Table 1 (maturity- and bond-level regressions) shows estimates of 훽1 and 훽2 are statistically significant with expected signs under both two-way clustering and time fixed effects.
- Caveats and measurement limits:
  - Market liquidity has multiple dimensions (cost, quantity, time; or tightness, depth, resiliency). The Corwin-Schultz measure captures only the cost/tightness dimension.
  - Some results, particularly announcement effects, vary across model specification and sample choice.
  - SLF effects may still be subject to endogeneity concerns despite using lagged values as instruments.
  - Findings should be interpreted as potential side effects of QQE and not as evidence that QQE is ineffective.
  - Despite liquidity concerns, JGB yields have declined significantly after QQE—indicating QQE has been overall effective in pushing down interest rates, even if lower liquidity may raise liquidity risk premia.

### Key quantitative figures and regression summary (selected)
- Example impacts:
  - One-percentage-point increase in purchase intensity → about 0.3 standard deviations increase in Corwin-Schultz spread (full-sample FE with two-way cluster robust s.e.).
  - One-percentage-point increase in daily purchase intensity → about 0.4 standard deviations increase in Corwin-Schultz spread (fixed-effects threshold full sample).
  - Average BOJ share of holdings ≈ 40 percent.
  - Example purchase increase: ≈ 0.3 percent of total amount outstanding for an average JGB issue over a 10-day period.
  - Cumulative impact over three months under example scenario ≈ 1.2 standard deviations (non-threshold) or ≈ 1 standard deviation (threshold).
- Table 1 (selected entries):
  - Sample periods: maturity-level December 29, 2006–January 20, 2017; bond-level January 31, 2012–February 28, 2017.
  - # obs.: maturity-level 1,086 and 1,110; bond-level 38,893 and 38,895.
  - # groups: maturity-level 6 and 6; bond-level 456 and 458.
  - Overall-푁푁2: maturity-level 0.13 and 0.55; bond-level 0.08 and 0.29.
  - Selected coefficient estimates (FE with two-way clustering by maturity and time / FE with time fixed effects):
    - 푃푃푃푃푃푃_i,t_BoJ (purchase intensity) : -0.58 (1.63) / -2.54*** (0.93) at maturity-level; -0.28 (0.22) / -0.25*** (0.07) at bond-level.
    - 푃푃푃푃푃푃_i,t_BoJ ∙ S_i,t−1_BoJ : 1.48 (3.40) / 5.74*** (2.22) at maturity-level; 0.83** (0.35) / 0.45** (0.20) at bond-level.
    - S_i,t−1_BoJ (lagged BOJ holdings share) : -0.55 (0.47) / -1.03 (1.12) at maturity-level; -1.62** (0.66) / -1.21*** (0.20) at bond-level.
    - SLF_i,t (daily average of SLF for bond i) : 222.68*** (74.49) / 18.05 (147.03) at maturity-level; -0.005 (0.01) / 0.002 (0.003) at bond-level.
    - Announcement dummies (selected): DPD(GS G) 0.87*** (0.19) maturity-level; DPD(NIRP) 0.91*** (0.29) maturity-level; DPD(QQE) 0.14 (0.28) maturity-level / 0.84*** (0.33) bond-level.
  - Note: *, **, and *** denote statistical significance at the 10 percent, 5 percent, and 1 percent levels, respectively.

### Concluding summary
- Using Corwin-Schultz bid-ask spread on bond-level JGB data, the paper finds strong evidence of scarcity (flow) effects of QE on market liquidity: BOJ outright purchases had significantly adverse effects on JGB market liquidity (including 2-10 year subsample).
- Scarcity effects depend on the BOJ’s share of holdings (stock): purchases improved liquidity when holdings were relatively small but reduced liquidity when holdings exceeded thresholds.
- SLF appears to have mitigated scarcity effects when conducted.
- Results are robust to different standard errors and use of time fixed effects, but must be interpreted with caution given measurement limits, model sensitivity, and potential endogeneity.
- The findings should be viewed as potential side effects of QQE and not as evidence that QQE is ineffective.

*Source: IMF Working Paper (wp1896), extracted section and tables as provided.*

### 49.      These findings could have important policy implications. First, central banks that

### wp1896 - 49.      These findings could have important policy implications. First, central banks that

### Policy implications and recommendations
- Central banks that have implemented QE programs should continue to monitor closely the developments in the liquidity of the securities that have been purchased by the central banks, and the signals of potential scarcity for these securities (e.g., an increased use of SLF by private financial institutions or higher fails in repo transactions).
- Central banks should closely monitor its holdings of each security as a share of the total (or tradable) amount outstanding, and adjust its purchases accordingly to avoid creating substantial scarcity of certain securities in the market.
  - This monitoring is particularly important for monetary operations when QE policies have started to or are about to normalize.
- In times of stress, central banks could continue to provide securities lending facilities (SLF) to the market to temporarily alleviate the pressure on market liquidity.

### Appendix I — Market liquidity: concept and measurement
- Market liquidity is defined as the ability to rapidly buy or sell a sizable volume of securities at a low cost and with a limited price impact (IMF, 2015).
- The concept of market liquidity is distinct from:
  - funding liquidity (the ease with which market participants can obtain funding), and
  - monetary liquidity (central bank liquidity, typically referring to monetary aggregates).
- Interconnections:
  - Market makers’ ability to provide market liquidity depends on their availability of funding (Brunnermeier and Pederson, 2009).
  - Market liquidity tends to enhance funding liquidity because traders’ funding depends on the ease with which assets can be sold (Foucault and others, 2013).
  - Higher monetary liquidity from monetary policy easing relaxes funding conditions for banks, which can facilitate market-making activities.
  - The relationship among market, funding, and monetary liquidity is not one-to-one and could be nonlinear (IMF, 2015).
- Measurement dimensions:
  - IMF (2015) classifies measures into three dimensions: cost, quantity, and time.
  - Alternative characterization: tightness, depth, and resiliency (e.g., Kurosaki and others, 2015).
- Examples of measures and the dimensions they capture:
  - Corwin-Schultz bid-ask spreads, effective spreads, imputed “round-trip costs”: cost and tightness dimensions.
  - Quote depth, dealer depth, volume of limit orders at best-ask price: quantity and depth dimensions.
  - Amihud (2002)’s price impact measure: cost and resiliency dimensions.
- Cautionary note (footnote 29):
  - Some commonly used measures can be misleading. For cost dimension, quoted bid-ask spreads that are not based on actual transactions may not reflect actual trade costs.
  - For quantity dimension, market turnover can show high values during market turmoil even though transactions have a large price impact (i.e., market liquidity is low).

### Appendix II — Calculation of the Corwin-Schultz bid-ask spreads
A. Methodology
- The Corwin and Schultz (2012) methodology estimates spreads (S) using two-day high and low prices as a nonlinear function:
  - S = 2( e^α − 1 ) / (1 + e^α)
  - α is defined as [formula as in source]
  - β is defined as ln(H_t / L_t)/2 + ln(H_{t+1}/L_{t+1})/2
  - γ is defined as [ln C(H_{t,t+1}/L_{t,t+1})]^2  (symbols preserved as in source)
  - H is the daily high price of the security; L is the daily low price; t stands for time (in days).
- Implementation specifics:
  - Assign a zero value to estimated high-low spreads that are less than zero (negative values), following Corwin and Schultz (2012).
  - Monthly spreads are calculated by averaging all two-day trading periods within a calendar month.

B. Data
- Daily high (H) and low (L) price data are obtained from Bloomberg Finance L.P. for Japanese government bonds (JGBs) at all available maturity levels.
- Underlying securities are selected using Bloomberg Finance L.P.’s fixed income search (SRCH) function.
- Sample selection criteria include both currently active and inactive JGB securities at all maturities and exclude securities that have already been funged into another security to avoid double counting.
- Appendix II. Table 1. Data Coverage—Number of JGB and JTDB Securities by Issuance Year and Tenor (tabulated counts shown in source):
  - Totals by issuance year columns: 1983-89, 1990-99, 2000-09, 2010-17 and Tenor rows with counts leading to Total = 67288544855 (values preserved exactly as shown).

C. Estimated Corwin-Schultz bid-ask spreads
- Procedure:
  - Estimate bid-ask spreads at bond-level using daily high and low prices.
  - Average estimated bid-ask spreads of each bond within a calendar month to obtain monthly spreads.
- Notes and caveats:
  - On-the-run bonds are defined as the most recently issued JGB securities at each tenor.
  - Footnote 30: Sample starts in December 2006 due to data limitations. Replacement of missing values by zero increases measured spreads for on-the-run bonds for some maturities; without such replacement the measure for on-the-run JGBs would be lower than for all JGBs.
- Appendix II. Table 2. Summary statistics by tenor—Bond-level High-Low Spreads based on Corwin and Schultz (2012) (In percent) — preserved table entries as shown for years 00, 1, 2, 5, 10, 20, 30, 40 and for years 2010, 2016, 2017 (mean, median, high-low, standard deviation values preserved exactly as in source).
- Appendix II. Figures:
  - Appendix II. Figure 1. Average Corwin-Schultz Bid-Ask Spreads (In percent) — time series plotted for tenors: Two-year, Five-year, Ten-year, Twenty-year, Thirty-year, Forty-year JGBs from 2006m12 through 2016m12 (axes and tick labels preserved as in source).
  - Appendix II. Figure 2. Corwin-Schultz Bid-Ask Spreads for On-the-Run JGBs (In percent) — time series plotted for tenors: Two-year, Five-year, Ten-year, Twenty-year, Thirty-year, Forty-year JGBs from 2006m12 through 2016m12 (axes and tick labels preserved as in source).

### Appendix III — Results of panel regressions (summary)
- Sample periods and methods:
  - Appendix III. Table 1: Maturity-Level Fixed-Effects Panel Regressions. Sample period: December 29, 2006–January 20, 2017. Eight lags of the dependent variable and the lagged value of SLS_i,t are used in the FE regressions with Driscoll-Kraay standard error.
  - Appendix III. Table 2: Bond-Level Fixed-Effects Panel Regressions. Sample period: January 31, 2012–February 28, 2017. Eight lags of the dependent variable and the lagged value of SLS_i,t are used in the FE regressions with Driscoll-Kraay standard error.
- Key regression variables (definitions preserved):
  - PPPPPP_{i,t}^{BOJ} denotes the daily average of BoJ’s outright purchases for maturity i (normalized by the total amount outstanding of that maturity).
  - PPPPPP_{i,t}^{BOJ} · S_{i,t−1}^{BOJ} denotes the interaction of BoJ purchases and lagged holdings.
  - S_{i,t−1}^{BOJ} denotes the lagged value of BoJ’s holdings of maturity i as a share of total amount outstanding of that maturity.
  - SLS_{i,t} denotes the daily average of SLF for maturity i (normalized by the total amount outstanding of that maturity), instrumented by its lagged value where indicated.
  - Additional regressors include log VIX_t, dummies for DPDD(GS GG), DPDD(QQQQ), DPDD(QQQQ2), DPDD(NVN P P), DPDD(YYYY), DPDD(US), and a Gil CCCCC coefficient (labels preserved as in source).
- Selected coefficient estimates and statistical significance (values preserved exactly as in source tables):
  - Appendix III. Table 1 (Maturity-level, dependent variable: Corwin-Schultz measure standardized):
    - PPPPPP_{i,t}^{BOJ}: -0.58 (1.56) under FE with robust s.e.; -0.85 (2.30) under FE with Driscoll-Kraay s.e.; -0.58 (1.63) under FE with two-way clustering.
    - For 2-10 year JGBs: PPPPPP_{i,t}^{BOJ} = -3.07** (1.24) under FE with robust s.e.; -3.49 (2.59) under Driscoll-Kraay; -3.07** (1.30) under two-way clustering.
    - PPPPPP_{i,t}^{BOJ} · S_{i,t−1}^{BOJ}: 1.48 (3.07); 2.22 (5.00); 1.48 (3.40). For 2-10 year JGBs: 6.42* (3.48); 7.56 (5.62); 6.42* (3.48).
    - S_{i,t−1}^{BOJ}: -0.55 (0.44); -0.36 (0.67); -0.55 (0.47). For 2-10 year JGBs: -1.11** (0.52); -0.84 (0.63); -1.11** (0.46).
    - SLS_{i,t}: 222.68*** (71.12); 86.99** (35.08); 222.68*** (74.49). For 2-10 year JGBs: 346.52 (362.70); 93.39 (58.18); 346.52 (308.59).
    - log VIX_t: 0.12 (0.15) (all columns); 0.05 (0.20) for 2-10 year JGBs.
    - DPDD(GS GG): 0.87*** (0.09); 0.87*** (0.34); 0.87*** (0.19). For 2-10 year JGBs: 0.94*** (0.10); 0.96** (0.47); 0.94*** (0.20).
    - DPDD(US): 0.87*** (0.24); 0.88*** (0.19); 0.87** (0.36). For 2-10 year JGBs: 1.06*** (0.39); 1.16*** (0.19); 1.06*** (0.36).
    - # obs.: 1,086 (all JGBs); 549 (2-10 year JGBs).
    - # groups: 6 (all JGBs); 3 (2-10 year JGBs).
    - Overall-R^2: 0.13, 0.15, 0.13 (all JGBs); 0.20, 0.20, 0.20 (2-10 year JGBs).
  - Appendix III. Table 2 (Bond-level, dependent variable: Corwin-Schultz measure standardized):
    - PPPPPP_{i,t}^{BOJ}: -0.28*** (0.08); -0.25* (0.15); -0.28 (0.22). For 2-10 year JGBs: -0.58*** (0.10); -0.58*** (0.20); -0.58*** (0.16).
    - PPPPPP_{i,t}^{BOJ} · S_{i,t−1}^{BOJ}: 0.83*** (0.26); 0.67** (0.29); 0.83** (0.35). For 2-10 year JGBs: 1.22*** (0.26); 1.23*** (0.29); 1.22*** (0.23).
    - S_{i,t−1}^{BOJ}: -1.62*** (0.18); -1.62*** (0.48); -1.62** (0.66). For 2-10 year JGBs: -2.53*** (0.20); -2.53*** (0.61); -2.53*** (0.36).
    - SLS_{i,t}: -0.005 (0.01); 0.001 (0.001); -0.005 (0.01). For 2-10 year JGBs: 0.0004 (0.002); -0.0001 (0.001); 0.0004 (0.002).
    - log VIX_t: 0.11*** (0.03); 0.11 (0.22); 0.11 (0.20). For 2-10 year JGBs: 0.17*** (0.04); 0.17 (0.27); 0.17 (0.14).
    - DPDD(QQQQ): 0.84*** (0.05); 0.83*** (0.28); 0.84*** (0.33). For 2-10 year JGBs: 0.83*** (0.08); 0.83*** (0.28); 0.83*** (0.32).
    - DPDD(QQQQ2): 0.21*** (0.03); 0.21** (0.10); 0.21** (0.09). For 2-10 year JGBs: 0.33*** (0.04); 0.33** (0.15); 0.33** (0.17).
    - DPDD(NVN P P): 0.66*** (0.04); 0.66*** (0.17); 0.66*** (0.20). For 2-10 year JGBs: 0.44*** (0.06); 0.44*** (0.14); 0.44*** (0.17).
    - DPDD(YYYY): -0.15*** (0.02); -0.15 (0.10); -0.15 (0.13). For 2-10 year JGBs: -0.08** (0.04); -0.08 (0.18); -0.08 (0.20).
    - DPDD(US): 0.19*** (0.03); 0.19* (0.11); 0.19 (0.18). For 2-10 year JGBs: 0.35*** (0.05); 0.35 (0.22); 0.35 (0.26).
    - # obs.: 38,895 (all JGBs); 16,273 (2-10 year JGBs).
    - # groups: 458 (all JGBs); 256 (2-10 year JGBs).
    - Overall-R^2: 0.04, 0.08, 0.08 (all JGBs); 0.04, 0.12, 0.12 (2-10 year JGBs).
- Instrumentation and estimation notes:
  - SLS_{i,t} is instrumented by its lagged value in FE with robust s.e. and FE with two-way cluster-robust s.e.
  - In maturity-level regressions, SLS_{i,t} was dropped in FE with two-way cluster-robust s.e. for 20-40 year JGBs as its instrument has little variation over time.
- Significance notation:
  - *, **, and *** denote statistical significance at the 10-, 5-, and 1-percent levels, respectively.

*Italicized source: IMF staff summary of wp1896 - content as provided*

### Appendix III. Table 3. Results of Bond-Level Fixed-Effects Threshold Panel Regressions 1/

### Appendix III. Table 3. Results of Bond-Level Fixed-Effects Threshold Panel Regressions 1/

### Dependent variable and estimation method
- Dependent variable: Corwin-Schultz measure (standardized by mean and standard deviation)
- Estimation method: Fixed-Effects Threshold Panel Regression

### Key coefficient estimates (All JGBs — Maturity-Level; Bond-Level; 2–10 year JGBs — Maturity-Level; Bond-Level)
- 푃푃푃푃푃푃
  푖푖,푡푡
  퐵퐵퐵퐵퐵퐵 ∙1(푆푆
  푖푖,푡푡−1
  퐵퐵퐵퐵퐵퐵 ≤ 푆푆∗) 2/ 3/
  - All JGBs Maturity-Level: -19.08*** (5.49)
  - All JGBs Bond-Level: -1.53*** (0.55)
  - 2-10 year JGBs Maturity-Level: -10.89*** (2.50)
  - 2-10 year JGBs Bond-Level: -4.54*** (1.34)
- 푃푃푃푃푃푃
  푖푖,푡푡
  퐵퐵퐵퐵퐵퐵 ∙1(푆푆
  푖푖,푡푡−1
  퐵퐵퐵퐵퐵퐵 > 푆푆∗)
  - All JGBs Maturity-Level: 0.36 (0.58)
  - All JGBs Bond-Level: 0.35*** (0.13)
  - 2-10 year JGBs Maturity-Level: 0.36 (0.59)
  - 2-10 year JGBs Bond-Level: 0.42 (0.31)
- 푆푆
  푖푖,푡푡−1
  퐵퐵퐵퐵퐵퐵
  - All JGBs Maturity-Level: 0.10 (0.29)
  - All JGBs Bond-Level: -0.70*** (0.13)
  - 2-10 year JGBs Maturity-Level: -1.04*** (0.31)
  - 2-10 year JGBs Bond-Level: -2.50*** (0.20)
- 푆푆퐿퐿 푆푆
  푖푖,푡푡−1 4/
  - All JGBs Maturity-Level: 80.22** (36.98)
  - All JGBs Bond-Level: 0.002 (0.01)
  - 2-10 year JGBs Maturity-Level: 90.41 (70.61)
  - 2-10 year JGBs Bond-Level: 0.01 (0.01)
- 푙푙푙푙푙푙
  �
  푉푉푉푉푋푋
  푡푡
  푁푁푖푖푁푁푁푁푁푁푖푖
  �
  - All JGBs Maturity-Level: 0.15 (0.13)
  - All JGBs Bond-Level: -0.01 (0.04)
  - 2-10 year JGBs Maturity-Level: 0.04 (0.17)
  - 2-10 year JGBs Bond-Level: 0.19*** (0.07)

### Control variable coefficients (selected; all reported as in table)
- 퐷퐷푃푃퐷퐷(퐺퐺푆푆 퐺퐺)
  - All JGBs Maturity-Level: 0.98*** (0.11)
  - 2-10 year JGBs Maturity-Level: 0.87*** (0.15)
- 퐷퐷푃푃퐷퐷(푄푄푄푄푄푄)
  - All JGBs Maturity-Level: 0.30* (0.16)
  - All JGBs Bond-Level: 1.21*** (0.03)
  - 2-10 year JGBs Maturity-Level: 0.33 (0.22)
  - 2-10 year JGBs Bond-Level: 1.84*** (0.07)
- 퐷퐷푃푃퐷퐷(푄푄푄푄푄푄2)
  - All JGBs Maturity-Level: 0.04 (0.16)
  - All JGBs Bond-Level: 0.28*** (0.03)
  - 2-10 year JGBs Maturity-Level: 0.42* (0.22)
  - 2-10 year JGBs Bond-Level: 0.35*** (0.06)
- 퐷퐷푃푃퐷퐷(푁푁푉푉푁푁 푃푃)
  - All JGBs Maturity-Level: 0.93*** (0.17)
  - All JGBs Bond-Level: 0.79*** (0.03)
  - 2-10 year JGBs Maturity-Level: 1.11*** (0.23)
  - 2-10 year JGBs Bond-Level: 0.46*** (0.07)
- 퐷퐷푃푃퐷퐷(푌푌퐺퐺퐺퐺)
  - All JGBs Maturity-Level: 0.19 (0.17)
  - All JGBs Bond-Level: -0.23*** (0.03)
  - 2-10 year JGBs Maturity-Level: 0.20 (0.23)
  - 2-10 year JGBs Bond-Level: -0.08 (0.06)
- 퐷퐷푃푃퐷퐷(푈푈푆푆)
  - All JGBs Maturity-Level: 0.85*** (0.18)
  - All JGBs Bond-Level: 0.05 (0.03)
  - 2-10 year JGBs Maturity-Level: 1.15*** (0.25)
  - 2-10 year JGBs Bond-Level: 0.26*** (0.07)
- 퐺퐺푙푙 퐶퐶퐶퐶퐶퐶퐶퐶퐶퐶퐶퐶
  - All JGBs Maturity-Level: -0.76* (0.42)
  - All JGBs Bond-Level: 0.07 (0.11)
  - 2-10 year JGBs Maturity-Level: -0.05 (0.54)
  - 2-10 year JGBs Bond-Level: -0.21 (0.22)

### Estimated threshold, sample sizes, groups, and fit
- Estimated threshold (푆푆∗): 0.05 (All JGBs Maturity-Level), 0.05 (All JGBs Bond-Level), 0.25 (2–10 year JGBs Maturity-Level), 0.05 (2–10 year JGBs Bond-Level)
- # obs.: 1026 (All JGBs Maturity-Level); 22,446 (All JGBs Bond-Level); 549 (2–10 year JGBs Maturity-Level); 4644 (2–10 year JGBs Bond-Level)
- # groups: 6; 174; 3; 36
- Overall-푁푁2: 0.18; 0.09; 0.23; 0.20

### Notes and definitions (as reported)
- Sample periods for the maturity- and bond-level FE panel regressions are December 29, 2006–January 20, 2017 and January 31, 2012–February 28, 2017, respectively. 1/
- 푃푃푃푃푃푃
  푖푖,푡푡
  퐵퐵퐵퐵퐵퐵 denotes the daily average of BoJ’s outright purchases of maturity i (normalized by the total amount outstanding of that maturity). 2/
- 1(∙) denotes the indicator function, which equals 1 if the argument is true and 0 otherwise. 푆푆
  푖푖,푡푡−1
  퐵퐵퐵퐵퐵퐵 denotes the lagged value of BoJ’s holdings of maturity i as a share of the total amount outstanding of that maturity. 3/
- The lagged value of 푆푆퐿퐿푆푆
  푖푖,푡푡 is used to mitigate the endogeneity issue. 4/
- Note: *, **, and *** denote statistical significance at the 10 percent, 5 percent, and 1 percent levels, respectively.

*Source: Appendix III. Table 3, wp1896 (PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1896.pdf_