## Testing the Liquidity Support Effects of the U.S. Treasury Buyback Program — Working Paper No. WP/2025/088

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### Background of the Buyback Program
- Design and operational mechanics:
  - Program launched in May 2024: “aim to support liquidity in off-the-runs by providing a regular, predictable opportunity to sell them back to the Treasury.”
  - Objective: improve dealers’ confidence in making markets in off-the-run securities and provide opportunities for dealers to free up balance sheet allocated to less-liquid positions at a fair price.
  - Frequency and envelopes:
    - Conducted generally once per week.
    - Initially: up to $2 billion for nominal coupon securities and up to $500 million for TIPS per operation.
    - Since August 2024: nominal coupon maximum envelope increased to $4 billion per operation.
  - Three-stage procedure (per quarter and per operation):
    - Stage 1 (quarterly refunding announcement): Treasury announces buyback schedules for the incoming quarter, operation dates, targeted bucket of the yield curve, and total buyback envelope.
    - Stage 2 (day before operation): Treasury announces a preliminary list of CUSIPs eligible for buybacks.
    - Stage 3 (operation day and settlement): final list of eligible CUSIPs announced in the morning (so far identical to preliminary list), primary dealers submit bids in the afternoon, Treasury announces accepted bids (usually at 2pm), settlement next day.

- Selection process and potential bias:
  - Stage 1 selection is predetermined and rotated; Treasury does not select securities at that stage.
  - Treasury does not disclose criteria/methodology for which securities become eligible in Stage 2.
  - For Stage 3, Treasury states “offers are evaluated based on their proximity to prevailing market prices at the close of the operation, as well as measures of relative value.”
  - Selection processes introduce potential selection bias; empirical methodology to address this is detailed in section 3.

- Empirical outcomes and distributional patterns:
  - Operation outcomes vary: many operations maxed envelopes; some accepted significantly fewer bids; on July 24th, no bids were accepted.
  - Coverage and acceptance patterns:
    - Treasury typically includes approximately 80% of CUSIPs within the targeted category in eligible lists (assessed by number of CUSIPs and outstanding amounts).
    - On average, bids from around half of the eligible CUSIPs were accepted, constituting approximately one-quarter of the total bid amount received.
    - About 10 to 20 percent of all securities have been listed in buybacks one to six times.
    - Buyback purchases are concentrated: more than half of securities have not been bought back.
  - Quantitative magnitudes relative to market and dealer activity:
    - Total buyback envelope (capped at $4 billion) represents about 0.1 percent of the targeted category of the off-the-run market.
    - Buyback amount accounts for approximately 10 percent of the average total daily off-the-run transactions (FINRA) for the same category five days prior to buyback.
    - From primary dealers’ perspective, buyback amount is about 8 and 4 percent of their daily transaction and holdings position on the nearest Wednesday prior to buyback.
  - Table 1 figures (as presented):
    - buyback listed: 81.2% (No. of CUSIPs) / 83.8% (AmountTotal off-the-runPrimary dealer outstandingtransactiontransaction position)
    - buyback accepted: 35.9% / 0.1% / 10.2% / 7.5% / 4.1%
    - acceptance rate: 44.1% / 22.5%
    - Note: Table reports eligible and accepted CUSIPs as share (number of CUSIPs and amount outstanding) of all CUSIPs in the targeted bucket. Accepted rate in amount outstanding = ratio between bids accepted and total bids submitted.

- Historical context and comparisons:
  - Prior Treasury buybacks (2000–2002): Treasury repurchased $67.5 billion across 45 operations ($1.5 billion per operation, on average).
  - Federal Reserve purchase programs (2010–2021): Fed purchased $5.34 trillion of Treasury securities over ~1200 operations (~$4.5 billion per operation, on average).

### Strategies to Address Selection Bias in Buybacks
- Instrumental-variable (IV) strategy for listing-selection bias:
  - Purpose: correct selection bias in first DID comparing listed vs not listed within same targeted bucket (“listing effect”).
  - Two-stage specification:
    - First-stage (Equation 3): 1_{i∈I_j} = Γ × X_{ij} + α_j + ε_{ij}, with X_{ij} = average across previous fifteen days of pre-announcement conditions for each security.
    - Second-stage (Equation 4): y_{isjt} = β_1 1_{i∈I_j} × 1_{t≥t_j} + β_2 1_{i∈I_j} + β_3 1_{t≥t_j} + δ r_{it} + α_i + α_j + α_{st} + ε_{isjt}, with 1_{i∈I_j} instrumented by predicted b 1_{i∈I_j}.
  - IV construction uses pre-buyback characteristics:
    - amount outstanding
    - SOMA share of outstanding (Treasury avoids buybacks that would raise SOMA ownership above 70%)
    - remaining maturity and remaining maturity squared
    - coupon rate
  - Rationale: characteristics align with Treasury decision rules and argued plausibly orthogonal to contemporaneous liquidity conditions.
  - First-stage performance: 1st stage F-stat: 30.31 (columns reporting IV).

- Use of cash management buybacks as exogenous laboratory:
  - Cash management buybacks primarily aim to reduce Treasury cash-balance volatility (often timed before April 15, June 15, September 15, December 15); liquidity support not primary objective.
  - Treasury excludes CUSIPs maturing in months with substantial positive net fiscal revenue from cash management eligible lists.
  - Identification: use maturity month and same pre-buyback characteristics to build IV for inclusion; IV pertinent to selection but plausibly exogenous to liquidity conditions.

- Second DID (purchasing effect) and other selection concerns:
  - Second DID compares securities with bids accepted versus eligible but not accepted.
  - Acceptance selection may correlate with liquidity (e.g., “relative value” and proximity to prevailing market prices); same IV approach used to address acceptance-selection bias.
  - Confidentiality of Treasury decision rules introduces unpredictability, which may partially mitigate selection bias.

- Strategies to evaluate buyback impact on primary-dealer balance sheets:
  - Inventory-adjustment model (Equation 5):
    - ∆y_t = α + η y_{t−1} + β_1 · buyback_t + β_2 · issuance_t + β_3 · redemption_t + ε_t
    - ∆y_t = change in net position of Treasury bills, coupons, or total Treasuries from week t−1 to t.
    - β_1 captures buyback effects on net Treasury positions; controls include Federal Reserve and Foreign central bank holdings.
  - IV for aggregate buyback amount:
    - Instrument: announced maximum envelope of buybacks (pre-announced at quarterly refinancing), argued exogenous to dealers’ existing positions.
    - Sources of variation: buckets of the yield curve and changes in Treasury operational capacity around August 2024.

- Empirical first-stage and listing predictors (Logit, Table 3):
  - For coupons with maturities < 2 years:
    - amount outstanding, billion USD: -0.0255** (s.e. 0.011)
    - remaining maturity, years: 9.8101*** (s.e. 2.835)
    - remaining maturity square, years: -3.1002** (s.e. 1.450)
    - coupon, pps: -0.3081*** (s.e. 0.033)
    - SOMA share of outstanding if buyback, percent: -0.0481*** (s.e. 0.009)
    - buyback eligible, predicted: 1.0083*** (s.e. 0.023) — regression of actual listed on predicted listed
  - Observations: 1,620 (col 1), 1,596 (col 2)
  - R-squared: 0.6080 (col 1), 0.657 (col 2)
  - Operation FE: yes
  - Interpretation: Treasury tends to include securities with smaller SOMA holdings and lower coupons; higher likelihood for securities with longer remaining maturities.

- Listing effect estimates (Table 4) — baseline and IV:
  - post buyback list release: 0.1496** (0.060) (col 1); 0.2732*** (0.086) (col 3 IV)
  - buyback listed: 0.0527 (0.142) (col 1); -0.9666* (0.518) (col 3 IV)
  - post buyback list release × buyback listed (treatment):
    - -0.1871** (0.080) (col 1 baseline; bid-ask spread)
    - -0.3617*** (0.113) (col 3 IV; bid-ask spread)
  - ∆on-the-run yield, bps: -0.0359*** (0.007) (col 1); -0.0360*** (0.007) (col 3)
  - Off-the-run spread effect (interaction): -1.9203** (0.814) (col 6 IV)
  - Magnitudes summarized:
    - Baseline: being listed reduces bid-ask spreads by about 0.2 basis points.
    - IV: listing reduces bid-ask spreads by about 0.4 basis point.
    - Off-the-run spreads fall by about 1.9 basis point for listed securities after listing announcement.
  - Robustness: “near neighbors” controls yield estimates almost identical to baseline.
  - Bid/ask decomposition: changes driven mainly by ask component (ask decreases); bid component barely changes.

- Dynamics of listing effect:
  - Largest effect on day of eligible-list release: bid-ask spread declines by 0.5 basis points relative to day before.
  - Effect halves to 0.2 basis points the following day when buyback auction operates.
  - Interpretation: listing effect is transitory and reverts as dealers rebalance.

- Cash-management buybacks — selection rules and IV fit (Table 5):
  - Logit average estimates:
    - amount outstanding, billion USD: 0.002*** (0.000) (col 1); 0.003 (0.003) (col 2)
    - remaining maturity, years: -9.570*** (0.057) (col 1); -29.11*** (7.177) (col 2)
    - remaining maturity square, years: 2.761*** (0.020) (col 1); 8.774*** (2.497) (col 2)
    - coupon, pps: -0.0825*** (0.016) (col 1); -0.2992*** (0.084) (col 2)
    - SOMA share if buyback, percent: -0.0092*** (0.001) (col 1); -0.0628*** (0.010) (col 2)
    - buyback listed, predicted: 0.9854*** (0.094) (col 3); 0.9932*** (0.012) (col 4)
  - Observations: 1,370 (col 1), 987 (col 2)
  - R-squared: 0.2990 (col 1), 0.7000 (col 2)
  - Month dummies improve fit (R-squared increases to 0.7); predicted eligibility fit reaches 0.8 when month dummies included.

- Listing effect for cash-management buybacks (Table 6):
  - post buyback list release: 0.1315*** (0.031) (col 1); 0.1483*** (0.036) (col 2 IV)
  - buyback listed: -0.0530 (0.079) (col 1); -0.4350*** (0.165) (col 2 IV)
  - post buyback list release × buyback listed (listing effect):
    - -0.3142*** (0.062) (col 1 baseline)
    - -0.3534*** (0.071) (col 2 IV)
  - Off-the-run spread interaction:
    - -2.3687*** (0.314) (col 3 baseline)
    - -2.8583*** (0.372) (col 4 IV)
  - ∆on-the-run yield, bps: -0.0157*** (0.005) (col 1); -0.2778*** (0.014) (col 3)
  - First-stage F-stat: 82.758 (col 2) and 82.49 (col 4)
  - Interpretation:
    - Being listed in cash-management buybacks reduces bid-ask spread by about 0.3 basis point after announcement.
    - Inclusion reduces off-the-run spread by approximately 2.5 basis points post-announcement.

### Accepted vs. Non-accepted: The Purchasing Effect of Buybacks
- Method and predictive power:
  - Logit regression predicting purchased in buybacks conditional on being included in eligible list; coefficients vary across targeted buckets.
  - Pre-buyback characteristics have substantially lower predictive power for purchase decisions than for listing (R-squared ≈ 0.2).
  - IV approach problematic:
    - Actual bid prices submitted by primary dealers correlated with liquidity and violate IV exclusion.
    - Treasury discloses bid prices only for CUSIPs purchased, not for non-accepted bids.
    - IV fails weak instrument test in almost all regressions.

- Buyback acceptance regression highlights (Table 7):
  - amount outstanding, billion USD: 0.0249 (s.e. 0.018)
  - remaining maturity, years: -4.5267** (s.e. 2.288)
  - remaining maturity square, years: 1.0146 (s.e. 1.219)
  - coupon, pps: 0.0043 (s.e. 0.051)
  - SOMA share if buyback, percent: 0.0179 (s.e. 0.013)
  - buyback accept, predicted: 0.7682*** (s.e. 0.098)
  - Observations: 975 (col 1) and 1,237 (col 2)
  - R-squared: 0.235 and 0.204
  - Operation FE: yes; Sample: full

- Purchasing effect findings (Table 8):
  - Bid-ask spread:
    - baseline post buyback = -0.0304 (s.e. 0.030)
    - IV post buyback = -0.1794*** (s.e. 0.059)
  - buyback accept:
    - baseline = -0.0174 (s.e. 0.067)
    - IV = -0.4615 (s.e. 0.573)
  - post buyback × buyback accept:
    - baseline = 0.1941*** (s.e. 0.061)
    - IV = 0.7773*** (s.e. 0.213)
  - ∆on-the-run yield, bps: -0.0408*** (s.e. 0.012) baseline; -0.0400*** (s.e. 0.012) IV
  - Observations: 56,511 (all columns)
  - R-squared: 0.943 (col 1), -0.005 (col 2), 0.956 (col 3), 0.021 (col 4)
  - 1st stage F-stat: 6.97 (Kleibergen-Paap Wald F)
  - Key summary:
    - Baseline indicates modest increase in bid-ask spread for securities purchased relative to listed-but-not-repurchased.
    - IV estimates not corroborative because IV fails weak instrument test.
    - Off-the-run spread results insignificant in both baseline and IV regressions.

- Interpretation of null/weak purchasing effects:
  - Market reversion: after buyback, no additional buyback demand until next operation; demand and spread curves may revert.
  - Liquidity measurement nuance: price-based liquidity measures may not capture trading-volume improvements; purchased CUSIPs might exhibit volume gains even if spreads do not narrow.
  - Data limitations: limited transparency and sparse pricing for off-the-run Treasuries; buybacks may supply transaction data reducing price dispersion without narrowing spreads.

- When is impact more pronounced? (section 4.4 summary):
  - Drivers: prevailing liquidity stress and buyback capacity to address imbalances.
  - Demand proxied by bid-to-cover ratio; supply capacity proxied by buyback envelope as proportion of primary dealers’ net positions or daily transaction volume.
  - Front-end diagnostics (nominal coupons 1 month–2 years):
    - Bid-to-cover ratio up to 8 (versus 1.5–4 for other buckets).
    - Buyback envelope ≈ 3 percent of daily transactions of primary dealers prior to buyback.
    - Primary dealers have large net positions and transaction volume at front end.
  - Empirical evidence (Table 9 and Figure 6):
    - Listing impact most pronounced at front end (< 3 years):
      - 1m–3yr baseline: post buyback list release = 0.5686** (s.e. 0.279); post buyback list release × buyback listed = -0.2404** (s.e. 0.115) → reduction of 0.2404 basis point.
      - 1m–3yr IV: post buyback list release × buyback listed = -0.7606*** (s.e. 0.181) → 0.8 basis point.
    - 3–30yr results insignificant: post buyback list release × buyback listed = -0.1897 (s.e. 0.120) (baseline) and -0.1531 (s.e. 0.152) (IV).
    - Observations: 29,620 (1m–3yr) and 49,820 (3–30yr)
    - 1st stage F-stat: 11.12 and 15.91
    - Dynamics: for 1m–3yr, listing reduces bid-ask spread by 0.5 bps on listing day and effect lasts three days; for 3–30yr, effect marginal and dissipates.

  - Operation-level variation and excess positions:
    - Relative primary dealer holdings as percent of total recent issuance and as percent of total assets amplify listing effect.
    - One percentage point increase in excess position (share of total recent issuance) amplifies listing effect by 2 basis points.
    - One percentage point increase as share of total assets amplifies listing effect by 0.2 basis points.

### Listing and Purchasing Effects on Relative Prices
- Measurement:
  - Relative prices = deviations of actual prices from model-implied counterparts (present discounted value following Selgrad (2023)); discount function based on Fed Yield Curve Models and Data.
- Listing effect on relative prices:
  - Inclusion in eligible list raises relative bid and ask prices by ≈ 9 cents (baseline) and ≈ 19 cents (IV).
  - Table 10 listing coefficients:
    - post buyback list release: -0.0756*** (bid price baseline; s.e. 0.014) and -0.1444*** (bid price IV; s.e. 0.020)
    - post buyback list release × buyback listed: 0.0937*** (bid baseline; s.e. 0.017) and 0.1892*** (bid IV; s.e. 0.023)
    - Equivalent ask price interactions: 0.0918*** (baseline; s.e. 0.017) and 0.1854*** (IV; s.e. 0.023)
- Purchasing effect on relative prices:
  - Baseline: bid and ask prices for securities bought back increase by 4 cents relative to not bought back.
    - post buyback × buyback accept (baseline bid): 0.0397** (s.e. 0.016)
    - ask equivalent: 0.0412** (s.e. 0.016)
  - IV: purchase raises bid and ask prices by ≈ 28 cents.
    - post buyback × buyback accept (IV bid): 0.2761*** (s.e. 0.037)
    - ask equivalent: 0.2820*** (s.e. 0.037)
  - Large negative buyback accept (IV) in some specs: -0.8819*** (bid IV; s.e. 0.229) and -0.8830*** (ask IV; s.e. 0.229)
  - Observations for price regressions: 78,969 (cols 1–4) and 56,057 (cols 5–8)
  - 1st stage F-stat: 30.26 (cols 2 and 4) and 18.70 (cols 6 and 8)
  - Interpretation:
    - Listing raises dealer valuations (~9 cents baseline; 19 cents IV).
    - Purchasing elevates relative prices (4 cents baseline; ~28 cents IV).
    - Relative price impacts are persistent, maintaining elevated levels weeks after transaction; price impacts more durable than spread impacts.

### Have Buybacks Alleviated Primary Dealers Treasury Security Positions?
- Aggregate balance-sheet estimation and baseline findings:
  - Inventory-adjustment model (Equation 5) estimates align with literature (Table 11 Panel A).
  - Mean reversion in Treasury positions:
    - beginning position, billion USD coefficients: -0.2225*** (∆Bill), -0.0143*** (∆Coupon), -0.0236*** (∆Total).
    - Mean reversion stronger for bill positions.
  - Issuance and redemption effects:
    - Issuance, billion USD: 0.1085*** (∆Bill), 0.1049*** (∆Coupon), 0.1134*** (∆Total).
    - Redemption, billion USD: -0.0742*** (∆Bill), -0.0485*** (∆Coupon), -0.1000*** (∆Total).
  - Interpretation: issuance of $1 billion increases primary dealer positions by ≈ $100 million; redemption of $1 billion reduces positions by $50–$100 million.

- Direct buyback effects on dealer positions (security- and bucket-level):
  - Including buybacks yields no significant response in aggregate Treasury positions during buyback week (Panel A cols 4–6).
  - Restricting sample to post-May 2024: redemptions become insignificant even without buyback regressors.
  - Targeted coupon-bucket effects:
    - One billion dollar buyback reduces position in targeted coupon bucket by $180 million (col 7).
    - IV results (Panel B) confirm reduction in buyback-targeted bucket and no significant impacts on other Treasury holdings.
  - Context: Primary dealers Treasury coupon positions averaged ≈ $230 billion since first buyback (standard deviation $45 billion).

- Dynamic impacts (local projections, Figure 9):
  - Targeted coupon bucket: $1 billion buyback shrinks positions in targeted bucket by ≈ $200 million; decrease persists for buyback week and following week.
  - Treasury bills: bill holdings begin to decline a couple weeks after program starts—falling by as much as $2 billion over six weeks in response to a $1 billion buyback.
  - Mechanisms for bill reductions despite coupons targeted:
    - Dealers receive proceeds as reserves from coupon buybacks and may use proceeds to shrink overall exposure including bill holdings.
    - Reserve injections reduce need to hold bills as short-term liquidity vehicles.
    - Unwinding coupon positions funded with repos collateralized by bills can lead to selling bills.

- Comparison with redemptions:
  - Magnitude: buybacks impact dealer positions by order of magnitude larger than redemptions.
    - $1 billion buyback induces bill-holding changes ≈ $2 billion.
    - Redemption impacts typically < $100 million.
  - Persistence: redemption effects short-lived (max two weeks); buyback effects on bill positions can endure up to six weeks.
  - Example: $1 billion redemption may reduce bill positions by ≈ $75 million during redemption week.

- Theoretical rationale (model summary and parameterization):
  - Framework: dealer capacity and pricing model (Duffie (2023)) with convex inventory costs and stochastic investor flows; buybacks act as predictable demand injections truncating illiquidity tail states.
  - Key numerical parameterization:
    - A(a) = ce^{-αa}, B(b) = κe^{βb} with c = e40, k = e^{-20}, α = β = 3.
    - Dividend: d(x) = x.
    - Inventory cost: g(x) = 0.01x^2.
    - Inventory upper limit: ̄x = 50.
    - Buyback activation threshold: e x = 25.
    - Buyback demand K(a) assumed = 0.05A(a) (motivated by buyback size ≈ 10% of dealer transaction volume and conditional purchase probability ≈ 50%).
  - Mechanisms:
    - Listing effect: inclusion shifts pricing curve, raises bid and ask, narrows spreads, especially when dealers hold large inventories.
    - Purchasing effect: purchases move dealers to lower-inventory point, increasing prices; spread response depends on where along U-shaped spread curve the drawdown occurs.

- Magnitude, interpretation, net assessment:
  - Effects measurable but moderate:
    - Example: $2 billion reduction in bill holdings < one-twentieth of average dealer holdings.
  - Buybacks small relative to off-the-run market but provide sustained and directionally meaningful liquidity support.
  - Inclusion in eligibility list narrows bid-ask spreads relative to unlisted securities (stronger for short maturities and when dealers hold sizable inventories).
  - Both listing and purchasing increase prices of affected securities.
  - Buybacks alleviate holdings of targeted coupon bucket for a couple weeks and bill holdings for over one month.
  - Outcomes consistent with convex dealer inventory cost model where predictable buyback demand truncates extreme illiquidity states.

- Policy implications and potential design improvements:
  - Timing and scaling:
    - Consider scheduling buybacks shortly after new on-the-run issuances when dealers hold larger unwanted inventories.
    - Scale up buybacks during periods of emerging stress to strengthen liquidity support.
  - Alternative formats:
    - If Treasury General Account limits scaling, swap-format operations (exchanging off-the-runs for on-the-runs) could increase program impact.

### Appendix and Additional Findings (Targeting Effect, Trading Volume, and Sourcing)
- Targeted vs Non-targeted (Appendix A.1):
  - DID comparing targeted securities with non-targeted within bucket; treatment assignment exogenous via pre-announced schedule.
  - Main finding: “The targeting effect of buybacks appears to be insignificant.”
    - Baseline (Table A1 col 1): post buyback list release = -0.0005 (s.e. 0.001); buyback targeted = -0.0077* (0.004); post buyback list release × buyback target = 0.0037 (0.006); ∆on-the-run yield, bps = -0.0536*** (0.009); Observations = 495,715; R-squared = 0.966.
    - 1m–3yr (col 2): buyback targeted = -0.0268** (0.012); post buyback list release × buyback target = 0.0170 (0.018); Observations = 178,628; R-squared = 0.964.
    - 3–30yr (col 3): post buyback list release × buyback target = -0.0015 (0.004); Observations = 317,087; R-squared = 0.967.
    - Off-the-run spread (col 4): post buyback list release × buyback target = -0.2907 (0.182); Observations = 495,715; R-squared = 0.359.
  - Interpretation: buyback effects measured by spreads are localized to listed/accepted securities and small at aggregate bucket level.

- Trading volume dynamics (Table A1 col 5, Figure A.1):
  - Baseline first-difference regression: post buyback list release × buyback target = 0.0423 (0.050); ∆trading volume of on-the-runs, same maturity = 0.1344** (0.043); Observations = 49,572; R-squared = 0.267.
  - Dynamic evidence (Figure A.1):
    - Trading volume increases on buyback operation day by nearly $3 billion and drops the next day, almost offsetting the prior-day increase.
    - No significant changes in interdealer trades for targeted bucket.
  - Interpretation:
    - Buybacks produce a near-term dealer-to-customer volume spike (~$3 billion on operation day) that largely reverses.
    - Sourcing likely from dealers’ inventories or dealer-to-customer trades rather than interdealer trades.

- Overall implication from appendix: liquidity and spread effects concentrated on securities directly listed or accepted; aggregate bucket-level improvements are insignificant.

*Source: wpiea2025088-print-pdf*

### 2.1  Background of the Buyback Program

### 2.1  Background of the Buyback Program

### Design and operational mechanics
- In May 2024, the Treasury launched the liquidity support buyback program “aim to support liquidity in off-the-runs by providing a regular, predictable opportunity to sell them back to the Treasury.”
- Objective: improve dealers’ confidence in making markets in off-the-run securities and provide opportunities for dealers to free up balance sheet allocated to less-liquid positions at a fair price.
- Frequency and envelopes:
  - The liquidity support buybacks are generally conducted once per week.
  - Initially, each operation had a total envelope of up to $2 billion for nominal coupon securities and up to $500 million for TIPS.
  - Since August 2024, the maximum envelope for nominal coupons has increased to $4 billion per operation, as Treasury expands its technical capacity.
- Three-stage procedure (per quarter and per operation):
  - Stage 1 (quarterly refunding announcement): Treasury announces buyback schedules for the incoming quarter, including operation dates, targeted bucket of the yield curve (Treasury usually rotates the targeted bucket and anticipates purchasing within each maturity bucket at least one time per quarter), and total buyback envelope.
  - Stage 2 (day before operation): Treasury announces a preliminary list of CUSIPs eligible for buybacks.
  - Stage 3 (operation day and settlement): Treasury announces the final list of eligible CUSIPs in the morning (so far, identical to the preliminary list), primary dealers submit bids in the afternoon, Treasury announces accepted bids (usually at 2pm), and settlement happens the next day.

### Selection process and potential bias
- The announcement of the buyback schedule (Stage 1) does not involve selection from the Treasury because timing and targeted buckets are predetermined and rotated.
- Subsequent stages involve selection:
  - Treasury does not disclose the criteria or methodology used to determine which securities become eligible for buybacks in Stage 2.
  - For Stage 3, Treasury states that “offers are evaluated based on their proximity to prevailing market prices at the close of the operation, as well as measures of relative value.”
- The selection processes introduce potential selection bias; the empirical methodology to address this issue is detailed in section 3.

### Empirical outcomes and distributional patterns
- Outcomes vary across operations:
  - Many operations maxed out the total envelope of buyback amount; some operations accepted significantly fewer bids.
  - Notably, on July 24th, no bids were accepted during the buyback operation.
- Coverage and acceptance patterns (summary from text and Table 1):
  - Typically, the Treasury includes approximately 80% of CUSIPs within the targeted category in the eligible list for buybacks (assessed by number of CUSIPs and outstanding amounts).
  - On average, bids from around half of the eligible CUSIPs were accepted by the Treasury, which constituted approximately one-quarter of the total bid amount received.
  - About 10 to 20 percent of all the securities have been listed in buybacks for one to six times.
  - Buyback purchases are concentrated: more than half of the securities have not been bought back.
- Quantitative magnitudes relative to market and dealer activity:
  - The total buyback envelope, capped at $4 billion so far, is relatively small compared to the overall size of the off-the-run market; the resultant buyback sizes represent about 0.1 percent of the targeted category of the off-the-run market.
  - The buyback amount accounts for approximately 10 percent of the average total daily off-the-run transactions (as reported by FINRA) for the same category five days prior to buyback.
  - From the primary dealers perspective, the buyback amount is about 8 and 4 percent of their daily transaction and holdings position on the nearest Wednesday prior to buyback.
- Table 1 figures (as presented):
  - No. of CUSIPs / AmountTotal off-the-runPrimary dealer outstandingtransactiontransaction position
  - buyback listed81.2%83.8%
  - buyback accepted35.9%0.1%10.2%7.5%4.1%
  - acceptance rate44.1%22.5%
  - Note: Table reports eligible and accepted CUSIPs as share (in terms of number of CUSIPs and amount outstanding) of all the CUSIPs in the bucket targeted by buyback. The accepted rate in terms of amount outstanding is calculated as the ratio between bids accepted and total bids submitted. It also reports the accepted amount as share of daily off-the-run transactions for the buyback targeted buckets reported in FINRA or conducted by primary dealers, and as share of primary dealers’ position for the targeted bucket.

### Historical context and comparisons
- Prior Treasury buybacks:
  - The last Treasury buybacks occurred between 2000 and 2002, during which the Treasury repurchased $67.5 billion of its securities across 45 operations ($1.5 billion per operation, on average).
  - Context then was different: fiscal surplus and declining refinancing needs, raising average maturity as short- and intermediate-term obligations retired at maturity. Objectives included smoothing cash balance increases, maintaining issue sizes of new securities, and conceivably reducing cost of borrowing.
- Federal Reserve purchase programs (comparison):
  - Between 2010 and 2021, the Federal Reserve purchased $5.34 trillion of Treasury securities over approximately 1200 operations (around $4.5 billion per operation, on average).
  - Primary aim of those purchases: lower long-term interest rates and stimulate borrowing and investment.

*Source: wpiea2025088-print-pdf - 2.1  Background of the Buyback Program*

### 3.2  Strategies to Address Selection Bias in Buybacks

### 3.2  Strategies to Address Selection Bias in Buybacks

### Instrumental-variable (IV) strategy to address listing-selection bias
- Purpose: Correct for selection bias in the first DID that compares Treasury securities listed for buybacks with those not listed within the same targeted bucket (the “listing effect”).
- Specification:
  - First-stage (Equation 3): 1_{i∈I_j} = Γ × X_{ij} + α_j + ε_{ij}, with X_{ij} = average across previous fifteen days of pre-announcement conditions for each security.
  - Second-stage (Equation 4): y_{isjt} = β_1 1_{i∈I_j} × 1_{t≥t_j} + β_2 1_{i∈I_j} + β_3 1_{t≥t_j} + δ r_{it} + α_i + α_j + α_{st} + ε_{isjt}, with 1_{i∈I_j} instrumented by predicted b 1_{i∈I_j}.
- IV construction — pre-buyback characteristics used:
  - amount outstanding
  - SOMA share of outstanding (Treasury avoids buybacks that would raise SOMA ownership above 70%)
  - remaining maturity and remaining maturity squared
  - coupon rate
- Rationale: These characteristics are relevant to Treasury decision rules and are argued to be plausibly orthogonal to contemporaneous liquidity conditions.

### Use of cash management buybacks as an exogenous laboratory
- Rationale: Cash management buybacks primarily aim to reduce Treasury cash-balance volatility (often timed immediately before major tax payment dates: April 15, June 15, September 15, December 15), and liquidity support is not their operational priority.
- Operational pattern: Treasury excludes CUSIPs maturing in months with substantial positive net fiscal revenue (April, June, September, December) from cash management eligible lists.
- Identification strategy: Use maturity month and the same pre-buyback characteristics to build an IV for inclusion in buybacks; this IV is pertinent to selection but plausibly exogenous to a security’s liquidity condition.

### Strategies for the second DID (purchasing effect) and other selection concerns
- Second DID compares securities with bids accepted versus those eligible but not accepted.
- Selection on acceptance could be correlated with liquidity (e.g., “relative value” and proximity to prevailing market prices), so the same IV approach is applied to help account for acceptance-selection bias.
- Confidentiality of Treasury decision rules introduces a degree of unpredictability from market participants’ perspective, which may partially mitigate selection bias.

### Strategies to evaluate buyback impact on primary-dealer balance sheets
- Inventory-adjustment model (Equation 5):
  - ∆y_t = α + η y_{t−1} + β_1 · buyback_t + β_2 · issuance_t + β_3 · redemption_t + ε_t
  - ∆y_t = change in net position of Treasury bills, coupons, or total Treasuries from week t−1 to t.
  - β_1 captures buyback effects on net Treasury positions; controls include Federal Reserve and Foreign central bank holdings.
- IV for aggregate buyback amount:
  - Instrument: announced maximum envelope of buybacks (pre-announced at each quarterly refinancing), argued exogenous to dealers’ existing positions.
  - Variation sources: buckets of the yield curve and changes in Treasury operational capacity around August 2024.

### Empirical findings — selection rule and IV first-stage (Logit estimates, Table 3)
- Logit predictors for being listed in buyback eligible list (buybacks targeting coupons with maturities < 2 years):
  - amount outstanding, billion USD: -0.0255** (standard error 0.011)
  - remaining maturity, years: 9.8101*** (standard error 2.835)
  - remaining maturity square, years: -3.1002** (standard error 1.450)
  - coupon, pps: -0.3081*** (standard error 0.033)
  - SOMA share of outstanding if buyback, percent: -0.0481*** (standard error 0.009)
  - buyback eligible, predicted: 1.0083*** (standard error 0.023) — column 2 regression of actual listed on predicted listed
- Sample and fit:
  - Observations: 1,620 (column 1), 1,596 (column 2)
  - R-squared: 0.6080 (column 1), 0.657 (column 2)
  - Operation FE: yes
- Interpretation:
  - Treasury tends to include securities with smaller SOMA holdings and lower coupons; higher likelihood for securities with longer remaining maturities.

### Listing effect results (Table 4) — baseline and IV estimates
- Key coefficients (reported with standard errors in table):
  - post buyback list release: 0.1496** (0.060) in column 1; 0.2732*** (0.086) in column 3 (IV)
  - buyback listed: 0.0527 (0.142) in column 1; -0.9666* (0.518) in column 3 (IV)
  - post buyback list release × buyback listed (treatment effect):
    - -0.1871** (0.080) in column 1 (baseline listing effect on bid-ask spread)
    - -0.3617*** (0.113) in column 3 (IV listing effect on bid-ask spread)
  - ∆on-the-run yield, bps: -0.0359*** (0.007) in column 1; -0.0360*** (0.007) in column 3
  - Off-the-run spread effect (interaction): -1.9203** (0.814) in column 6 (IV)
- First-stage performance:
  - 1st stage F-stat: 30.31 (columns reporting IV)
- Magnitudes summarized in text:
  - Baseline: being listed reduces bid-ask spreads by about 0.2 basis points.
  - IV: listing reduces bid-ask spreads by about 0.4 basis point (doubling baseline).
  - Off-the-run spreads fall by about 1.9 basis point for listed securities after listing announcement.
- Robustness:
  - Using “near neighbors” (similar remaining maturities) as control yields estimates almost identical to baseline (column 2).
- Bid / ask decomposition:
  - Changes driven mainly by the ask component (ask part decreases), with bid component barely changing — consistent with dealers lowering selling prices when they expect Treasury to be an eventual buyer.

### Dynamics of listing effect
- Timing:
  - Largest effect on the day of eligible-list release: bid-ask spread declines by 0.5 basis points relative to the day before.
  - Effect halves to 0.2 basis points the following day when the buyback auction operates.
- Interpretation: Listing effect is transitory and reverts as dealers rebalance across securities.

### Cash-management buybacks — selection rules and IV fit (Table 5)
- Cash-management Logit average estimates across operations:
  - amount outstanding, billion USD: 0.002*** (0.000) in column 1; 0.003 (0.003) in column 2
  - remaining maturity, years: -9.570*** (0.057) in column 1; -29.11*** (7.177) in column 2
  - remaining maturity square, years: 2.761*** (0.020) in column 1; 8.774*** (2.497) in column 2
  - coupon, pps: -0.0825*** (0.016) in column 1; -0.2992*** (0.084) in column 2
  - SOMA share of outstanding if buyback, percent: -0.0092*** (0.001) in column 1; -0.0628*** (0.010) in column 2
  - buyback listed, predicted: 0.9854*** (0.094) in column 3; 0.9932*** (0.012) in column 4
- Sample and fit:
  - Observations: 1,370 (column 1), 987 (column 2)
  - R-squared: 0.2990 (column 1), 0.7000 (column 2)
  - Month dummies materially improve fit (R-squared increases from 0.3 to 0.7); predicted eligibility fit reaches 0.8 when month dummies are included.

### Listing effect for cash-management buybacks (Table 6)
- Baseline and IV results:
  - post buyback list release: 0.1315*** (0.031) in column 1; 0.1483*** (0.036) in column 2 (IV)
  - buyback listed: -0.0530 (0.079) in column 1; -0.4350*** (0.165) in column 2 (IV)
  - post buyback list release × buyback listed (listing effect):
    - -0.3142*** (0.062) in column 1 (bid-ask spread baseline)
    - -0.3534*** (0.071) in column 2 (bid-ask spread IV)
  - Off-the-run spread interaction:
    - -2.3687*** (0.314) in column 3 (baseline)
    - -2.8583*** (0.372) in column 4 (IV)
  - ∆on-the-run yield, bps: -0.0157*** (0.005) in column 1; -0.2778*** (0.014) in column 3
- First-stage performance for cash-management IV:
  - 1st stage F-stat: 82.758 (column 2) and 82.49 (column 4)
- Interpretation:
  - Being listed in cash-management buybacks reduces bid-ask spread by about 0.3 basis point after the announcement.
  - Inclusion in cash-management buyback listings reduces off-the-run spread by approximately 2.5 basis points post-announcement; this effect is larger than the bid-ask impact.

*Source: wpiea2025088-print-pdf - 3.2  Strategies to Address Selection Bias in Buybacks*

### 4.3  Accepted vs. Non-accepted: The Purchasing Effect of Buybacks

### 4.3  Accepted vs. Non-accepted: The Purchasing Effect of Buybacks

### Method and Predictive Power
- Estimation approach:
  - Logit regression specification akin to that in Table 3, dependent variable: purchased in buybacks, conditional on being included in the eligible list.
  - Coefficients allowed to vary across buybacks that target different buckets.
- Predictive performance and diagnostics:
  - Pre-buyback characteristics exhibit substantially lower predictive power for purchase decisions than for listing decisions.
  - R-squared of about 0.2 (low fit).
  - IV approach deemed problematic because:
    - Actual bid prices submitted by primary dealers (likely important for acceptance) are correlated with liquidity and violate IV exclusion.
    - Treasury discloses bid prices only for CUSIPs ultimately purchased, not for non-accepted bids.
  - IV fails weak instrument test in almost all regressions.

### Buyback acceptance regression highlights (Table 7)
- Selected coefficient estimates (column indicators preserved in context):
  - amount outstanding, billion USD: 0.0249 (standard error 0.018)
  - remaining maturity, years: -4.5267** (standard error 2.288)
  - remaining maturity square, years: 1.0146 (standard error 1.219)
  - coupon, pps: 0.0043 (standard error 0.051)
  - SOMA share of outstanding if buyback, percent: 0.0179 (standard error 0.013)
  - buyback accept, predicted: 0.7682*** (standard error 0.098)
- Observations: 975 (column 1) and 1,237 (column 2)
- R-squared: 0.235 and 0.204
- Operation FE: yes; Sample: full
- Significance notation: ***, **, * denote 1%, 5%, 10% respectively. Standard errors clustered at operation level.

### Purchasing Effect Findings (Table 8)
- Baseline and IV results for spreads (treatment = accepted in buybacks; control = listed but not repurchased):
  - Bid-ask spread (baseline): post buyback = -0.0304 (std. err. 0.030)
  - Bid-ask spread (IV): post buyback = -0.1794*** (std. err. 0.059)
  - buyback accept (baseline): -0.0174 (std. err. 0.067)
  - buyback accept (IV): -0.4615 (std. err. 0.573)
  - post buyback × buyback accept (baseline): 0.1941*** (std. err. 0.061)
  - post buyback × buyback accept (IV): 0.7773*** (std. err. 0.213)
  - ∆on-the-run yield, bps: -0.0408*** (std. err. 0.012) in baseline; -0.0400*** (std. err. 0.012) in IV
- Observations: 56,511 (all columns)
- R-squared: 0.943 (col 1), -0.005 (col 2), 0.956 (col 3), 0.021 (col 4)
- 1st stage F-stat: 6.97 (reported; Kleibergen-Paap Wald F)
- Key summary statements:
  - Baseline indicates a modest increase in bid-ask spread for securities purchased in buybacks relative to listed-but-not-repurchased (column 1, Table 8).
  - IV estimates are not corroborative because the IV fails the weak instrument test (column 2).
  - Off-the-run spread results insignificant in both baseline and IV regressions (columns 3 and 4).

### Interpretation of Null/Weak Purchasing Effects
- Possible explanations for lack of robust purchasing effect on spreads:
  - Market reversion: after a buyback, primary dealers face no additional buyback demand until next operation, so demand and spread curves may revert to pre-buyback state. (To be explored in model section 5.)
  - Liquidity measurement nuance: price-based liquidity indicators (bid-ask spread, off-the-run spread) may not capture liquidity improvements that manifest via trading volume — trading-volume improvements could still occur for purchased CUSIPs (see targeting effect in subsection A.1).
  - Data limitations: limited transparency of transaction data in the off-the-run market (Neal (2024)); off-the-run Treasuries traded less frequently, providing sparser pricing data. Buybacks may supply transaction data that reduces price dispersion even if bid-ask spreads do not narrow.

---

### When Is the Impact of Buybacks More Pronounced? (Summary of section 4.4)
- Conceptual drivers:
  - Impact depends on prevailing liquidity stress and buyback capacity to address market imbalances.
  - Demand proxied by bid-to-cover ratio of buyback auctions.
  - Supply capacity proxied by buyback envelope as proportion of primary dealers' net positions or daily transaction volume within the targeted buyback category.
  - Greater demand and supply increase likelihood of substantial liquidity-supporting effects.
- Front-end (nominal coupons with remaining maturity between one month and two years) diagnostics:
  - Bid-to-cover ratio for front-end bucket reaches as high as 8, versus a range of 1.5 to 4 for other buckets.
  - Buyback envelope constitutes approximately 3 percent of the daily transactions of primary dealers prior to the buyback (about half the average size observed in other buckets).
  - Primary dealers have large net positions and transaction volume at the front end (short-term Treasuries more liquid, lower interest rate risks, used in high-volume transactions such as repo).
- Empirical evidence (Table 9 and Figure 6):
  - Listing impact most pronounced at front end (maturities < 3 years):
    - Column 1 (1m-3yr baseline): post buyback list release = 0.5686** (std. err. 0.279)
    - post buyback list release × buyback listed = -0.2404** (std. err. 0.115) → reduction in bid-ask spread by 0.2404 basis point (i.e., a quarter basis point) for listed vs. not listed.
    - Column 2 (1m-3yr IV): post buyback list release × buyback listed = -0.7606*** (std. err. 0.181) → IV impact reaches 0.8 basis point.
  - For maturities longer than three years (3-30yr), impact falls to insignificant:
    - Column 3 (3-30yr baseline): post buyback list release × buyback listed = -0.1897 (std. err. 0.120)
    - Column 4 (3-30yr IV): post buyback list release × buyback listed = -0.1531 (std. err. 0.152)
  - Observations: 29,620 (1m-3yr) and 49,820 (3-30yr)
  - R-squared: 0.958 (col 1), -0.106 (col 2), 0.955 (col 3), 0.001 (col 4)
  - 1st stage F-stat: 11.12 and 15.91 (reported)
  - Dynamic persistence:
    - For 1 month to 3 years maturities, being listed reduces bid-ask spread by half basis point relative to not listed; effect lasts throughout three days after listing.
    - For 3 to 30 years maturities, listing effect is only marginally negative on listing day and dissipates thereafter.
- Operation-level variation and primary dealers’ excess positions:
  - Two measures of excess position:
    - Relative primary dealer holdings as percent of total recent issuance (share of front-end Treasuries held by primary dealers divided by outstanding Treasuries of same maturity recently issued, less than 12 weeks ago).
    - Relative primary dealer holdings as percent of total assets (share of front-end Treasuries held by primary dealers divided by their total assets).
  - Strong correlation (Figure 7):
    - A one percentage point increase in primary dealers’ excess position on front-end nominal coupons as share of total recent issuance would amplify the listing effect of buybacks by 2 basis points.
    - A one percentage point increase in primary dealers’ excess position as share of total assets would amplify the listing effect by 0.2 basis points.

---

### Listing and Purchasing Effects on Relative Prices (Section 4.5 and Table 10)
- Measurement:
  - Relative prices constructed as deviations of actual prices from model-implied counterparts (present discounted value of future cash flows following Selgrad (2023)); discount function based on Fed Yield Curve Models and Data from the Federal Reserve.
- Listing effect on relative prices:
  - Inclusion in buyback eligible list significantly raises relative bid and ask prices by approximately 9 cents (baseline).
  - IV estimates imply an even larger listing effect of about 19 cents.
  - Table 10 listing coefficients (columns 1–4):
    - post buyback list release: -0.0756*** (bid price, baseline; std. err. 0.014) and -0.1444*** (bid price, IV; std. err. 0.020)
    - post buyback list release × buyback listed: 0.0937*** (bid price, baseline; std. err. 0.017) and 0.1892*** (bid price, IV; std. err. 0.023)
    - Equivalent ask price interactions: 0.0918*** (baseline; std. err. 0.017) and 0.1854*** (IV; std. err. 0.023)
- Purchasing effect on relative prices:
  - Baseline estimates: bid and ask prices for securities bought back increase by 4 cents relative to those not bought back.
    - post buyback × buyback accept (baseline bid price): 0.0397** (std. err. 0.016)
    - Equivalent ask price: 0.0412** (std. err. 0.016)
  - IV estimates: buyback purchase raises bid and ask prices by approximately 28 cents.
    - post buyback × buyback accept (IV bid price): 0.2761*** (std. err. 0.037)
    - Equivalent ask price: 0.2820*** (std. err. 0.037)
  - buyback accept coefficient (IV) large and negative in some specifications: -0.8819*** (bid price IV; std. err. 0.229) and -0.8830*** (ask price IV; std. err. 0.229)
- Additional diagnostics:
  - Observations for price regressions: 78,969 (columns 1–4) and 56,057 (columns 5–8)
  - R-squared reported: 0.928 (col 1), -0.927 (col 2), 0.952 (col 3), -0.952 (col 4) — table formatting preserved as in source.
  - 1st stage F-stat: 30.26 (columns 2 and 4) and 18.70 (columns 6 and 8)
  - Standard errors clustered at CUSIP level.
- Interpretation:
  - Listing raises dealer valuations (approx. 9 cents baseline; 19 cents IV), consistent with perceived increased demand and reduced perceived holding risk.
  - Purchasing further elevates relative prices (4 cents baseline; ~28 cents IV), suggesting Treasury transactions alleviate pressures on dealer balance sheets and prompt repricing.
  - Dynamic patterns (Figure 8): relative prices jump at listing announcement and are reinforced modestly after the buyback operation; price impacts from both listing and purchasing are persistent, maintaining elevated levels weeks after transaction — implying more durable effects on absolute prices than on spreads.

*Source: 4.3 Accepted vs. Non-accepted: The Purchasing Effect of Buybacks — wpiea2025088-print-pdf*

### 4.6  Have Buybacks Alleviated Primary Dealers Treasury Security Positions?

### 4.6  Have Buybacks Alleviated Primary Dealers Treasury Security Positions?

### Aggregate balance-sheet estimation and baseline findings
- Baseline balance sheet management model estimated as specified in Equation 5; estimates in Table 11 (Panel A, columns 1–3) align with magnitudes in the literature.
- Primary dealers exhibit mean reversion in Treasury positions:
  - Beginning position coefficients (Panel A): beginning position, billion USD: -0.2225*** (∆Bill), -0.0143*** (∆Coupon), -0.0236*** (∆Total).
  - Mean reversion stronger for bill positions than coupon positions.
- Issuance and redemption effects (Panel A):
  - Issuance, billion USD: 0.1085*** (∆Bill), 0.1049*** (∆Coupon), 0.1134*** (∆Total).
  - Redemption, billion USD: -0.0742*** (∆Bill), -0.0485*** (∆Coupon), -0.1000*** (∆Total).
- Interpretation:
  - An issuance of one billion dollar is estimated to augment primary dealer positions by approximately $100 million.
  - A redemption of one billion dollar would reduce positions by between $50 million and $100 million.

### Direct buyback effects on primary dealer positions (security- and bucket-level)
- Including buybacks in regressions (Panel A, columns 4–6) yields no significant response in aggregate Treasury positions during the buyback week.
  - When restricting the sample to buyback periods (post May 2024), redemptions become insignificant even without buyback regressors.
- Targeted coupon-bucket effects (Panel A, column 7 and Panel B IV results):
  - In response to a one billion dollar buyback, the position in the targeted coupon bucket declines by $180 million (column 7).
  - IV results (Panel B) confirm that buybacks reduce primary dealers holdings of the buyback-targeted bucket but show no significant impacts on the rest of Treasury holdings.
- Context on scale:
  - Primary dealers Treasury coupon positions have averaged around $230 billion since the first buyback in May 2024, with a standard deviation of $45 billion (Table 2).

### Dynamic impacts over subsequent weeks (local projections and Figure 9)
- Targeted coupon bucket:
  - A one billion buyback shrinks primary dealers’ position in the buyback targeted coupon bucket by about $200 million; the decrease persists for the buyback week and the following week.
- Treasury bills:
  - Primary dealers’ holdings of Treasury bills begin to decline a couple of weeks after the buyback program starts—falling by as much as $2 billion over six weeks in response to a one billion buyback.
- Mechanisms for bill reductions despite coupons being targeted:
  - Dealers receive proceeds as reserves from coupon buybacks and may use proceeds to shrink overall exposure, including bill holdings.
  - Reserve injections reduce the need to hold bills as short-term liquidity vehicles (e.g., margin calls or repo collateral).
  - Unwinding coupon positions (often funded with repos collateralized by bills) can lead to exiting associated repos and selling bills.

### Comparison with redemptions
- Magnitude difference:
  - Buybacks impact primary dealers’ positions by an order of magnitude larger than redemptions.
  - A one billion dollar buyback typically induces bill-holding changes around $2 billion.
  - Redemption impacts are typically less than $100 million.
- Persistence difference:
  - Redemption effects are short-lived (impact on Treasury positions lasts a maximum of two weeks).
  - Buyback effects on bill positions can endure for as long as six weeks.
- Example redemption magnitude:
  - A one billion dollar redemption may reduce bill positions by approximately $75 million during the redemption week (using the longer sample; local projection based on column 1 Table 11, not shown in the chart).

### Theoretical rationale (model summary and parameterization)
- Model framework: dealer capacity and pricing framework of Duffie (2023) with convex inventory costs and stochastic investor flows; buybacks act as predictable demand injections that truncate illiquidity tail states.
- Key numerical parameterization used for simulations:
  - Demand and supply functional forms: A(a) = ce^{-αa}, B(b) = κe^{βb} with c = e40, k = e^{-20}, α = β =  3.
  - Dividend: d(x) = x.
  - Inventory cost: g(x) = 0.01x^2.
  - Inventory upper limit: ̄x = 50.
  - Buyback activation threshold: e x = 25.
  - Buyback demand K(a) assumed equal to 0.05A(a) (motivated by buyback size ≈ 10% of dealer transaction volume and conditional purchase probability ≈ 50%).
- Mechanisms in the model:
  - Listing effect: inclusion on the buyback eligible list shifts the entire pricing curve (raises both bid and ask prices) and narrows bid-ask spreads, especially when dealers hold large inventories (the buyback provides an “insurance policy”).
  - Purchasing effect: realized buyback purchases move dealers along the price curve to a lower-inventory point, increasing prices but not necessarily narrowing spreads; purchasing can either narrow or widen spreads depending on where along the U-shaped spread curve the inventory drawdown moves the dealer.

### Magnitude, interpretation, and net assessment
- Effects are measurable but moderate in scale:
  - Example: the $2 billion reduction in Treasury bill holdings represents less than one-twentieth of the average dealer holdings.
  - Buybacks are small relative to the broader off-the-run Treasury market, yet they provide sustained and directionally meaningful liquidity support to dealers.
- Overall assessment:
  - Inclusion in the buyback eligibility list narrows bid-ask spreads relative to unlisted securities (stronger for short-maturity securities and when dealers hold sizable inventories).
  - Both listing and purchasing increase prices of affected securities.
  - Buybacks alleviate holdings of the buyback-targeted Treasury coupon bucket for a couple of weeks and holdings of Treasury bills over a period exceeding one month.
  - These outcomes are consistent with a model of convex dealer inventory costs where predictable buyback demand truncates extreme illiquidity states and reduces dealers’ required compensation for holding inventory.

### Policy implications and potential design improvements
- Timing and scaling:
  - Since liquidity effects are more pronounced when dealers hold larger unwanted inventories, Treasury might consider scheduling buybacks shortly after new on-the-run issuances, when dealers often roll older securities into new ones.
  - Buybacks could be scaled up during periods of emerging stress to strengthen liquidity support.
- Alternative formats:
  - If Treasury General Account balances constrain scaling, swap-format operations—exchanging off-the-runs for on-the-runs—could offer a flexible alternative to increase program impact.

*Source: Chapter 4.6, "Have Buybacks Alleviated Primary Dealers Treasury Security Positions?" (wpiea2025088-print-pdf).*

### References

### wpiea2025088-print-pdf - References

### Key empirical approach (Appendix A.1: Targeted vs. Non-Targeted — The Targeting Effect of Buybacks)
- Methodology:
  - Difference-in-differences (DID) comparing Treasury securities targeted by buybacks (treatment) with those not targeted (control).
  - Treatment assignment exogenous because buyback schedule is pre-announced in quarterly refunding announcements (one week to three months before operations).
  - Controls: bucket-specific time fixed effects (noted as α_st) and on-the-run yield r_it to control for demand and supply conditions affecting CUSIP_i.
  - Trading volume analysis uses FINRA dealer-to-customer trading volume (excluding buyback trades) in first differences to address non-stationarity.
  - Baseline regression follows Equation 1; dynamic impacts estimated based on Equation 2 for plotting trading volume deviations.

### Main findings on spreads and liquidity
- Targeting effect on spreads:
  - "The targeting effect of buybacks appears to be insignificant."
  - Baseline estimates (Table A1, column 1) show bid-ask spreads for CUSIPs within the targeted bucket do not differ statistically from other securities following release of the buyback list.
  - This insignificance holds when splitting into less liquid buckets (column 2) and more liquid buckets (column 3).
  - When measured by off-the-run spreads, liquidity condition for the targeted bucket does improve, but the magnitude is not significant (column 4).
  - Interpretation: Effects of buybacks, if measured by spreads, are localized and concentrated among securities listed or accepted in buybacks, resulting in a relatively small aggregate impact on the entire bucket.

- Exact coefficients and statistics from Table A1 (selected):
  - Column 1 (Bid-ask spread, full sample):
    - post buyback list release: -0.0005 (standard error 0.001)
    - buyback targeted: -0.0077* (0.004)
    - post buyback list release × buyback target: 0.0037 (0.006)
    - ∆on-the-run yield, bps: -0.0536*** (0.009)
    - Observations: 495,715
    - R-squared: 0.966
  - Column 2 (Bid-ask spread, coupons 1m-3yr):
    - post buyback list release: -0.0034 (0.004)
    - buyback targeted: -0.0268** (0.012)
    - post buyback list release × buyback target: 0.0170 (0.018)
    - ∆on-the-run yield, bps: -0.0579*** (0.010)
    - Observations: 178,628
    - R-squared: 0.964
  - Column 3 (Bid-ask spread, coupons 3-30yr):
    - post buyback list release: 0.0002 (0.000)
    - buyback targeted: 0.0016 (0.003)
    - post buyback list release × buyback target: -0.0015 (0.004)
    - ∆on-the-run yield, bps: -0.0506*** (0.008)
    - Observations: 317,087
    - R-squared: 0.967
  - Column 4 (Off-the-run spread, full sample):
    - post buyback list release: 0.0432 (0.026)
    - buyback targeted: -0.3345* (0.170)
    - post buyback list release × buyback target: -0.2907 (0.182)
    - ∆on-the-run yield, bps: -0.6265** (0.272)
    - Observations: 495,715
    - R-squared: 0.359
  - Column 5 (∆Trading volume, full sample, first differences):
    - post buyback list release: -0.0049 (0.005)
    - buyback targeted: -0.0215 (0.025)
    - post buyback list release × buyback target: 0.0423 (0.050)
    - ∆trading volume of on-the-runs, same maturity: 0.1344** (0.043)
    - Observations: 49,572
    - R-squared: 0.267
  - Table notes:
    - ***, **, * represent significance of 1%, 5% and 10%, respectively.
    - Standard errors clustered at CUSIP level.
    - Fixed effects included: CUSIP FE, Bucket-specific time FE, Operation FE, Maturity FE (in some columns), Time FE (in some columns).
    - Samples: full; coupons 1m-3yr; coupons 3-30yr; full (off-the-run); full (trading volume).

### Main findings on trading volume dynamics
- Aggregate and instantaneous volume effects:
  - Buybacks boost trading volumes of the targeted bucket primarily on the operation day.
  - Column 5 of Table A1 indicates trading volume does not change significantly following buybacks in the baseline regression (first differences).
  - Dynamic plot evidence (left panel of Figure A.1):
    - Trading volume increases on the buyback operation day by nearly $3 billion.
    - Trading volume drops the next day, almost offsetting the prior-day increase.
  - Possible mechanisms for the volume spike:
    - Buyback trades may send a price signal to the market and help clear potential trades in infrequently traded off-the-run securities.
    - FINRA’s dealer-to-customer reporting records both sell and buy sides; the increase could reflect customers selling off-the-run securities to dealers who then sell them back to Treasury on customers’ behalf.
    - Data limitations prevent precisely disentangling these channels.

- Interdealer trading:
  - No significant changes in interdealer trades for the buyback-targeted bucket (right panel of Figure A.1).
  - Interpretation: Securities bought back by Treasury are likely sourced from primary dealers’ own balance sheets or from customers (via dealer-to-customer trades), and less likely sourced from other dealers via interdealer trades.

### Interpretation and implications
- Localization of buyback effects:
  - The liquidity and spread effects of buybacks are concentrated on the securities directly listed or accepted in buybacks; aggregate bucket-level spread improvements are insignificant.
- Operational signaling and temporary volume effects:
  - Buyback operations produce a near-term increase in dealer-to-customer trading volume (nearly $3 billion on operation day), but this effect is short-lived and largely reverses within days.
- Sourcing of buybacked securities:
  - Evidence points to Treasury buybacks being sourced from dealers’ own inventories or from dealer-to-customer trades, rather than interdealer trades.

*Testing the Liquidity Support Effects of the U.S. Treasury Buyback Program — Working Paper No. WP/2025/088*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025088-print-pdf.pdf_