## wpiea2023096-print-pdf

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---

### Introduction — overview and objectives
- Central bank swap and repo lines:
  - Provide foreign currency liquidity across jurisdictions via two legs: (i) agreement between a source central bank and a recipient central bank; (ii) liquidity injections into the domestic market via repo lines with domestic financial institutions.
  - When a swap line is active, recipient central bank accesses source currency in exchange for domestic currency at the spot exchange rate, up to a maximum amount, and at a fixed interest rate below market rate; at maturity the same amount is exchanged at the same fixed spot exchange rate.
  - In repo lines, recipient central bank must pledge assets denominated in the source-country currency as collateral.
  - These arrangements are collateralized loans of the source central bank’s currency and do not involve exchange rate risk for the counterparties because the forward exchange rate is fixed.
- Objective: analyze the effect of ECB euro liquidity lines (swap and repo) and their signalling effect in reducing liquidity tensions and generating positive spillbacks to euro area (EA) countries.
- Rationale for using announcement dates:
  - Announcement is publicly available and any signalling effect will appear on that date.
  - If lines serve as a prevention tool, the announcement alone should provide sufficient confidence to improve FX swap market functioning.
- Empirical strategy summary:
  - Measure euro borrowing costs in FX markets using daily deviations of the covered interest parity (CIP) before and after announcement on targeted versus control currencies.
  - Identification uses a difference-in-differences (DID) strategy following Cetorelli et al. (2020) and Bahaj and Reis (2022a).
  - Euro basis defined as B_t = ln(F_t) − ln(S_t) − (r_t − r*_t).

### Key descriptive facts on ECB liquidity lines
- Between October 2008 and August 2022 the ECB established fourteen new swap and repo lines; many were renewed and expanded, especially during the COVID-19 crisis.
- Counterparts mostly EU countries outside the EA: Bulgaria, Croatia, Czech Republic, Denmark, Hungary, Latvia, Poland, Romania, Sweden; since 20 March 2020 also non-EU: Serbia, San Marino, Albania, Republic of North Macedonia.
- On 25 June 2020 the ECB announced establishment of the EUREP, a temporary Eurosystem repo facility for a broader set of non-European central banks.
- Facility characteristics:
  - Except for swap lines within the G10 network, most facilities are temporary, with a maximum amount at a fixed rate defined as a spread over the OIS reference date with a minimum floor.
  - Repo facilities require adequate euro-denominated collateral and feature a higher lending rate compared to swap lines.
- Activation information scarce; based on recipient-country sources, at least lines with Magyar Nemzeti Bank, Sveriges Riksbank and Bank of England have been used in small amounts.

### Sample and data
- Sample period: 6 October 2008 through 18 August 2022 per ECB press releases.
- Targeted countries in baseline sample: Bulgaria, Denmark, Croatia, Hungary, Poland, Serbia, Sweden.
- Exclusions: euro-using counterparts (e.g., San Marino), G10 network (reciprocal), National Bank of the Republic of North Macedonia, National Bank of Romania, Bank of Albania (data limitations), Bank of Latvia (not in ECB press releases).
- Listed announcement events (selected dates and counterparties):
  - October 16, 2008: Repo agreement with the Magyar Nemzeti Bank (HU).
  - October 27, 2008: Swap agreement with the Danmarks Nationalbank (DK).
  - November 21, 2008: Repo agreement with the National Bank of Poland (PL).
  - June 10, 2009: Activation of swap agreement with the Sveriges Riksbank (SE) signed on 20 December 2007.
  - March 20, 2020: Reactivation of swap line with Danmarks Nationalbank (DK).
  - April 15, 2020: Precautionary swap agreement with the Central Bank of Croatia (HR).
  - April 22, 2020: Precautionary swap agreement with the Bulgarian National Bank (BG).
  - July 17, 2020: Repo agreement with the National Bank of Serbia (RS).
  - July 23, 2020: Repo agreement with the Magyar Nemzeti Bank (HU).
  - August 28, 2020: Extension of repo facility with the Central Bank of Croatia (HR).
  - February 04, 2021: Extension of temporary swap and repo lines with non-euro area central banks (HR, RS, HU).
  - March 28, 2021: Swap agreement with Narodowy Bank Polski (PL) and extension of temporary repo lines with central banks of Hungary (HU).
- Robustness controls include Norway and Iceland as never-targeted countries.
- Data sources: Refinitiv for market rates and equity indices; BIS Consolidated Banking Statistics for bank claims; IMF International Financial Statistics for banking aggregates.

### Paper structure
- Section 1: overview of ECB repo and swap lines network.
- Section 2: data description.
- Section 3: empirical analysis of direct effect on euro funding costs in FX markets.
- Section 4.1 and 4: theoretical mechanism and empirical spillback tests.
- Section 5: conclusions and policy implications.

---

### 3.1 Mechanism — intuition and model summary
- Intuition:
  - Liquidity lines provide recipient-country banks a cheaper outside option to the FX market, improving bargaining terms with traders and capping forward prices in FX swaps.
  - Announcement lowers expected future short-dated swap prices (e.g., 1-week) because of activation probability, which reduces longer-dated swap prices (e.g., 3-month) via the term structure.
- Stylized model (two-country three-period):
  - EA bank assets and liabilities: A0, 1, D0, E0 with balance A0 + 1 = D0 + E0 (Eq. (5)).
  - Local bank borrows 1 unit euro at gross rate 1 + rC, invests in loan returning rL > rC, holds local deposits D* earning r*, short-term investment I* yielding rI and pays X = (rI − r*) D* at t = 1.
  - Exchange rate S at t = 1: low with probability q (SL (X + D*) < 1 + rC), high with probability 1 − q (SH (X + D*) > 1 + rC).
  - Refinancing via FX swaps costly: Cs(b) = (1 + b)[1 + rC − λS] (Eq. (6)); define b̄ such that Cs(b̄) = 1 + rL (Eq. (7)).
  - If unable to refinance, EA bank may liquidate and receive λL,1.
- Regimes and propositions:
  - Swap price distributions with and without a liquidity line satisfy Fl_b(x) ≥ Fnl_b(x) with strict inequality on (b(0), bnl(1)] (Eq. (20)).
  - Three regimes for b̄ relative to distribution determine whether announcement affects default probability.
  - Proposition 1: Announcement increases euro area stock prices except in cases where local banks never default, always default, or have full bargaining power.
  - Proposition 2: In Case 1 (EA bank safe), the stock-price increase is decreasing in local bank liquidation value λL1 (Eq. (28)).

---

### 3.2 Empirical strategy — identification and estimation
- Identification:
  - High-frequency DID: short window around announcement (two days before and one day after; main post defined as day of announcement t and day after t+1).
  - Comparison between treated currencies (targeted at t) and control currencies that are targeted at other events or never targeted (robustness includes Norway and Iceland).
- Main regression (collapsed panel, residual dependent variable):
  - resi,t,e = β1 Ti,e × Postt + β2 Ti,e + Σe β3e Postt,e + β4 mpt + φ′ Zt + μi,e + ui,t,e
    - Ti,e: treated indicator (absorbed by μi,e).
    - Postt: 1 on day t and t+1, 0 on t−1 and t−2.
    - mpt: ECB monetary policy meeting dummy.
    - Zt: global controls including Global Citi Economic Surprise Index and EU high-yield spread.
    - Currency-event fixed effects μi,e included; standard errors clustered at currency-event level.
- Dependent variables and residualization:
  - Direct effect dependent variable: residuals of FX basis after purging country-specific factors via basis_jt = α_j + βΩ_jt + res_jt.
  - Controls Ω_jt include forty-day equity volatility, long-term sovereign yields, quarterly change in gross public debt as percent of GDP, annual moving average of current account balance as percent of GDP, short-term external debt as percent of international reserves, inflation rate, Central Bank’s International Reserves in billions of USD, sovereign credit rating transformed linearly.
- Graphical diagnostics:
  - Frequency distributions and average evolution plots (Figure 4 and Figure 5) show leftward shift and divergence of residual FX basis for treated currencies at t = 0.

---

### 3.3 Results — direct effect on FX basis
- Main finding:
  - Announcement of ECB euro swap and repo lines reduces euro funding cost in FX swap markets by 51 basis points in the short window around the announcement in the baseline sample of small EU countries.
  - Note: residuals are in percent; table effects are in pp and should be multiplied by 100 to interpret in basis points.
- Magnitude and statistical details (Table 1 / Table 4 summaries):
  - Baseline estimated Treated × Post: -0.512 ∗∗ (column 1), -0.511 ∗∗ (column 2).
  - MP meetings: -0.209 ∗ (column 2).
  - EU high yield: -0.956 ∗∗ (column 2).
  - Surprise index: -0.00132 (column 2).
  - Observations: 324 (both columns).
  - R2: 0.115 (column 1), 0.167 (column 2).
  - Currency × Event FE and PostMat included; standard errors clustered at currency-event level.
  - Effect corresponds to about 40% of one standard deviation of the residuals (reference to Table 8).
- Robustness checks:
  - Extended sample adding Norway and Iceland: magnitude reduces to 37 basis points (Extended Sample TreatedPost: -0.373 ∗ (p = 0.051) / -0.373 ∗ (0.052); Observations: 428).
  - Placebo/anticipation test (announcement moved three days earlier): TreatedPost coefficients far from statistically significant (Appendix Table 6).
  - Re-estimation with basis (not residuals) and daily country-specific covariates: TreatedPost = -0.410 ∗∗ (0.026) (Table 5).
  - Event-by-event estimators (TWFE DID, SDID, Synthetic Control) average effects: −0.679 (0.606) DID, −0.259 (0.471) SDID, −0.484 (0.473) SC (standard errors in parentheses).
  - Time-series event study regressions produce statistically significant estimates slightly higher than DID estimates (Table 15; post coefficients range from -0.447 to -0.484 with various significance levels).
- Interpretation:
  - Announcement of ECB euro liquidity lines exerts a measurable signalling effect that reduces the euro funding cost in FX markets for targeted currencies in the immediate announcement window; results robust across specifications and placebo checks.

---

### 4.1 Mechanism (formal model) — summary of setup and implications
- Model features:
  - Two-country, three-period setup with EA bank (source) and local bank (recipient).
  - Cross-border lending with currency and maturity mismatches creates refinancing risk after an exchange rate shock at t = 1; repayment at t = 2.
  - Traders’ expectations over swap prices affected by announcement probability of activation α, lowering expected swap prices when a line is announced.
- Key model equations and implications:
  - Equity value dynamics: V2 = max{(1 + r) A1 − (1 + r) D1, 0} (Eq. (9)); initial stock price V0(x) = β^2 E0 V2 (Eq. (11)).
  - Refinancing cost Cs(b) and threshold b̄ determine whether local bank can refinance via FX swaps (Eqs. (6)–(7)).
  - Announcement changes swap price distribution: Fl_b(x) ≥ Fnl_b(x) with strict inequality on (b(0), bnl(1)] (Eq. (20)), which reduces local bank default probability in certain regimes.
  - Proposition 1: Announcement increases EA stock prices except in the degenerate cases listed.
  - Proposition 2: In Case 1 (EA bank safe), announcement effect decreases with higher liquidation value λL,1 (Eq. (28)).

---

### 4.2 Empirical strategy for spillback — identification via banking exposure
- Hypothesis: After an ECB liquidity line announcement, EA bank equity prices increase relatively more in EA countries whose banking sectors are more exposed to the targeted non-EA recipient countries.
- Exposure measure:
  - EXPj,e = 1 if average exposure of EA country j to non-EA targeted countries at event e is higher than the 75th percentile of cross-country exposure distribution; robustness uses 65th percentile and continuous exposure.
  - Exposure calculated from BIS Consolidated Banking Statistics as share of claims on country i over total cross-border claims of domestic banks of country j, averaged over targeted countries.
- Estimation equation (collapsed four-day window):
  - ∆PriceResj,t,e = β1 Postt × EXPj,e + Xe β2e Postt,e + β3 EXPj,e + β4 mp t + φ′ Zt + μj,e + uj,t,e  (Eq. (21))
  - Dependent variable: changes of purged average log stock price residuals for banks in EA country j.
  - Controls: VIX, EU high yield, MP meetings, country-event fixed effects μj,e; standard errors clustered at country-event level.
- Sample: EA countries AT, BE, DE, ES, FI, FR, IR, PT, IT.

---

### 4.3 Empirical spillback results — banking exposure and equity responses
- Main estimates (Table 3):
  - Column 1 (Exposure p75): Post × Exp = 0.0175 ** (p < 0.05).
  - Column 2 (Exposure p65): Post × Exp = 0.0148 * (p < 0.10).
  - Column 3 (Continuous): Post × Exp = 0.0299 ** (p < 0.05).
  - Observations: 284; R^2 = 0.275 / 0.272 / 0.303 across columns.
  - Controls included and currency × event fixed effects present.
- Interpretation:
  - Announcement of an ECB euro liquidity line increases EA stock prices by 1.75% for EA countries with banking sectors more exposed to targeted currencies (column 1).
  - Effect robust to alternative exposure thresholds and continuous exposure measure.
  - The estimated 1.75% effect corresponds to approximately half a standard deviation of stock price variations.
- Additional diagnostics:
  - Figure 9 (Appendix A.4) shows similar evolution of stock price changes for highly exposed and less exposed countries in a ten-day window; Tables 11–12 document country-level exposure classifications (e.g., Italy and Austria more exposed on average).

---

### 5 Conclusion — implications and open questions
- Central bank liquidity lines act as backstop facilities in distress, preventing local liquidity shortages from becoming global financial stability problems.
- Empirical findings for the ECB:
  - Announcements of ECB euro liquidity lines are associated with decreases in the premium paid by foreign agents to borrow euros in FX markets in a narrow announcement window (baseline effect: 51 basis points).
  - Positive spillbacks to the euro area: relatively higher bank equity prices for EA countries highly exposed via banking links to targeted currencies (about 1.75% increase).
- Theoretical and empirical consistency:
  - Announcements reduce local bank default probabilities in certain regimes, increasing expected profits of EA banks holding claims and raising EA bank stock prices.
- Descriptive evidence on usage and scope:
  - ECB mainly provided FX insurance to nearby central banks (mainly non-EA EU countries); role appears more regional than global compared to the Fed.
- Policy-relevant open question:
  - Whether making such arrangements more permanent or predictable could boost usage of the euro as an international currency and reduce CIP deviations in crises, against a backdrop of uncertainty from the war in Ukraine and risk of Euro Area fragmentation.

*Source: wpiea2023096-print-pdf*

### Introduction

### Introduction

### Overview of central bank liquidity lines
- Central bank swap and repo lines provide foreign currency liquidity across jurisdictions and consist of two legs: (i) an agreement between a source central bank and a recipient central bank; (ii) liquidity injections into the domestic market via repo lines with domestic financial institutions.
- When a swap line is active, the recipient central bank can access the source central bank’s currency in exchange for its domestic currency at the spot exchange rate, up to a maximum amount, and at a fixed interest rate below market rate; at maturity the same amount is exchanged at the same fixed spot exchange rate.
- In central bank repo lines, the recipient central bank must pledge assets denominated in the source-country currency as collateral.
- These arrangements are collateralized loans of the source central bank’s currency and do not involve exchange rate risk for the counterparties because the forward exchange rate is fixed.

### Objective and methodological approach
- Objective: analyze the effect of ECB euro liquidity lines (swap and repo) and their signalling effect in reducing liquidity tensions and generating positive spillbacks to euro area (EA) countries.
- Rationale for using announcement dates:
  - Announcement is publicly available and any signalling effect will appear on that date.
  - If lines serve as a prevention tool, the announcement alone should provide sufficient confidence to improve FX swap market functioning.
- Empirical strategy:
  - Measure euro borrowing costs in FX markets using daily deviations of the covered interest parity (CIP) before and after the announcement of a euro liquidity line on targeted currencies versus a control, non-targeted group.
  - Identification relies on a difference-in-differences (DID) strategy following Cetorelli et al. (2020) and Bahaj and Reis (2022a).
  - The euro basis is defined as B_t = ln(F_t) − ln(S_t) − (r_t − r*_t).

### Main empirical findings (direct effect)
- Considering ECB lines established with small European countries, the mere announcement of euro swap and repo lines reduces the euro funding cost in foreign exchange swap markets by 51 basis points.
- The euro was emphasized as the second most important currency in the international monetary system: the ECB reports the euro represents around 36% of the share of global payments at the end of 2022 and around 20% of the share in global holdings of foreign reserves.

### Spillback mechanism and empirical findings
- Theoretical mechanism (stylized model):
  - Announcement of a central bank liquidity line decreases the bankruptcy probability of recipient-country financial intermediaries by reducing their refinancing cost.
  - This raises the expected payoff of the source-country credit to the recipient bank, increasing the source-country bank’s value and its stock market price.
- Empirical test:
  - Leverage heterogeneity across EA countries via the share of cross-border claims of EA banks towards recipient countries as a proxy for exposure.
  - In a DID framework introducing banking-sector exposure, EA countries with the most exposed banking sectors experience a relative increase in their equity prices of about 1.75% in a four-day window around the announcement.
  - Interpretation: more exposed banks see market valuation increases and improved profitability expectations after announcements.

### ECB liquidity lines: timeline, scope, and characteristics
- Between October 2008 and August 2022 the ECB established fourteen new swap and repo lines to provide euro liquidity; many were renewed and expanded, especially during the COVID-19 crisis.
- Counterparts were mostly EU countries outside the EA: Bulgaria, Croatia, Czech Republic, Denmark, Hungary, Latvia, Poland, Romania, and Sweden; since 20 March 2020 agreements were also signed with non-EU countries: Serbia, San Marino, Albania and Republic of North Macedonia.
- On 25 June 2020 the ECB announced the establishment of the EUREP, a new and temporary Eurosystem repo facility to provide euro liquidity to a broader set of non-European central banks.
- Euro liquidity lines are mainly clustered around crisis episodes, suggesting a role as a liquidity backstop; some lines were used in the context of ERM II (peg to the euro), e.g., Bulgaria on 22nd April 2020.
- Facility characteristics:
  - Except for swap lines within the G10 network, most facilities are temporary, with a maximum amount of allotment at a fixed rate defined as a spread over the OIS reference date with a minimum floor.
  - Repo facilities require adequate collateral in euro-denominated assets and feature a higher lending rate compared to swap lines.
- Activation information is scarce; based on recipient-country sources, at least lines with the Magyar Nemzeti Bank, the Sveriges Riksbank and the Bank of England have been used, although in small amounts.

### Sample and data used in the analysis
- Time window for analysis: 6 October 2008 through 18 August 2022 as reported in the ECB press releases.
- Sample comprises seven targeted countries: Bulgaria, Denmark, Croatia, Hungary, Poland, Serbia, and Sweden.
- Exclusions and reasons:
  - Exclude countries targeted by the lines but that use the euro as the main currency (e.g., San Marino).
  - Exclude the G10 network due to reciprocal nature of swap lines to avoid confounding with USD or other currency provisions.
  - Exclude agreements with National Bank of the Republic of North Macedonia, National Bank of Romania and Bank of Albania due to data limitations.
  - Exclude Bank of Latvia since it was not included in ECB press releases.
- Listed included announcement events (dates and counterparties):
  - October 16, 2008: Repo agreement with the Magyar Nemzeti Bank (HU).
  - October 27, 2008: Swap agreement with the Danmarks Nationalbank (DK).
  - November 21, 2008: Repo agreement with the National Bank of Poland (PL).
  - June 10, 2009: Activation of swap agreement with the Sveriges Riksbank (SE) signed on 20 December 2007.
  - March 20, 2020: Reactivation of swap line with Danmarks Nationalbank (DK).
  - April 15, 2020: Precautionary swap agreement with the Central Bank of Croatia (HR).
  - April 22, 2020: Precautionary swap agreement with the Bulgarian National Bank (BG).
  - July 17, 2020: Repo agreement with the National Bank of Serbia (RS).
  - July 23, 2020: Repo agreement with the Magyar Nemzeti Bank (HU).
  - August 28, 2020: Extension of the repo facility with the Central Bank of Croatia (HR).
  - February 04, 2021: Extension of its temporary swap and repo lines with non-euro area central banks (HR, RS, HU).
  - March 28, 2021: Swap agreement with Narodowy Bank Polski (PL) and extension of temporary repo lines with central banks of Hungary (HU) in the context of heightened geopolitical tensions triggered by the Russian invasion of Ukraine.
- Robustness check: two non-targeted countries included — Norway and Iceland.
- Dependent variables and construction:
  - Direct effect: change in euro funding cost in FX markets measured by CIP deviations and the euro basis B_t = ln(F_t) − ln(S_t) − (r_t − r*_t); one-week euro currency deposits used when possible; OIS preferred but Euribor used where necessary.
  - Residualization: basis is purged of country-specific factors via country-by-country regressions basis_jt = α_j + βΩ_jt + res_jt; controls Ω_jt include a mix of high-frequency and lower-frequency macro/financial variables (forty-day equity volatility, long-term sovereign yields, quarterly change in gross public debt as percent of GDP, annual moving average of current account balance as percent of GDP, short-term external debt as percent of international reserves, inflation rate, Central Bank’s International Reserves in billions of USD, sovereign credit rating transformed linearly).
  - EA spillback effect: EA banks’ stock prices (Datastream aggregate bank equity indices) purged from country-specific banking health factors (short-term interest rate — 3-month T-Bill or closest maturity, nominal effective exchange rate deviation, net foreign assets of domestic banks over GDP, loan-to-deposit ratio).
  - Exposure measure: BIS Consolidated Banking Statistics (quarterly) used to compute each EA country j exposure to non-EA country i as share of claims on country i over total cross-border claims of domestic banks of country j; exposure averaged over targeted countries and used to classify EA countries as highly exposed if above the 75th percentile (robustness uses 65th percentile and continuous measure).
- Data sources: Refinitiv databases for market rates and equity indices; BIS Consolidated Banking Statistics for bank claims; IMF International Financial Statistics for banking aggregates where noted.

### Paper structure
- Section 1: overview of the ECB repo and swap lines network across time.
- Section 2: data used in the analysis.
- Section 3: empirical analysis of the direct effect of ECB liquidity line on euro funding costs in FX markets.
- Section 4.1: mechanism behind the signalling effect and theoretical framework illustrating the spillback channel; Section 4: stylized model and empirical tests of spillback effects.
- Section 5: conclusions on desirability of a more stable and permanent central bank liquidity network and proposed lines of future research.

*Source: wpiea2023096-print-pdf - Introduction*

### 3.1    Mechanism

### 3.1 Mechanism

### Mechanism summary
- Central bank liquidity lines provide recipient-country banks with a cheaper outside option to the FX market, improving their bargaining terms with traders and capping the forward price in FX swaps.
- The announcement of a liquidity line, through the term structure, lowers the expected price of future short-dated swaps (e.g., 1-week) because of the probability of activation, which in turn decreases longer-dated swap prices (e.g., 3-month) at time t.
- Intuitive example in text: a trader with access to 1-week swap agreements and 3-month swap agreements at timet faces lower expected future 1-week swap prices after an announcement, implying lower 3-month swap prices att.

### Key references within mechanism
- Bahaj and Reis (2022a) as the underlying theoretical foundation for the cap on forward prices via active liquidity lines.
- Proof referenced in Appendix for formal derivation.

---

### 3.2 Empirical strategy

### Identification approach
- High-frequency difference-in-differences (DID) approach following Bahaj and Reis (2022a).
- High-frequency dimension: analyze changes in financial variables in a short window around announcement (window spans two days before and one day after the announcement).
- DID dimension: compare treated currencies (targeted by the ECB euro liquidity line at timet) with an adequate control group to avoid bias from confounding global factors and staggered treatment timing.

### Treatment and control definition
- Treated currency: currency targeted by the ECB line at timet; the same currency can be non-treated in other periods t̃ ≠ t.
- Control group: currencies that are targeted at previous or future dates (i.e., currencies targeted at least once are used as controls in other events), with robustness checks adding two currencies never targeted by ECB lines.
- Rationale: countries targeted at least once share eligibility characteristics; short window prevents contamination from subsequent announcements.

### Estimation design and timing assumptions
- Collapsed panel around announcements; two-way fixed effects DID estimator (Bertrand et al., 2004 guidance).
- Identification relies on randomness of announcement date within short-term window; placebo and anticipation tests performed (robustness subsection reports no evidence of anticipation).
- Standard errors clustered at currency-event level; include currency-event fixed effects μi,e to absorb time-invariant currency event factors.

### Regression framework (notation and variables)
- Mean outcomes: yTt (targeted countries at timet), yNTt (non-targeted countries).
- DID estimator for treatment effect βt: βt = (yTt − yNTt) − (yTt−1 − yNTt−1).
- Main estimating equation (collapsed panel, residual dependent variable):
  resi,t,e = β1 Ti,e × Postt + β2 Ti,e + Σe β3e Postt,e + β4 mpt + φ′ Zt + μi,e + ui,t,e
  - Ti,e: indicator equal to 1 if currency i is treated in event e (absorbed by μi,e).
  - Postt: equals 1 on day of announcement (t) and day after (t+1), zero on two days prior (t−1 and t−2).
  - Postt,e: event-specific post dummies to allow heterogeneous effects across events.
  - mpt: dummy for ECB monetary policy meeting dates.
  - Zt: global controls vector including Global Citi Economic Surprise Index and EU high-yield spread.
  - Dependent variable in baseline: residuals of FX basis after purging country-specific factors (stock market volatility, change in public debt, current account balance, sovereign rating, sovereign yield, short-term debt, reserves and inflation).

### Graphical diagnostics presented
- Figure 4: Frequency distribution of FX basis in 4-day window around announcements for treated versus non-treated currencies shows leftward shift for treated currencies.
  - Country sample listed: Bulgaria, Denmark, Croatia, Hungary, Poland, Serbia, Sweden.
  - Pre-treatment defined as two days prior; post-treatment defined as day of treatment and day after.
- Figure 5: Average evolution of residual FX basis in the 4-day window shows marked divergence at t = 0 between treated and untreated groups.

---

### 3.3 Results

### Main finding
- ECB euro liquidity line announcements are associated with a decline in euro funding cost in the FX market.
- Baseline estimated effect on FX basis residuals: average decrease of 51 basis points in the short window around the announcement in a sample of small EU countries.
  - Note from text: since residuals are in percent, table effects are in pp and should be multiplied by 100 to interpret in basis points.

### Magnitude and statistical details
- Effect corresponds to about 40% of one standard deviation of the residuals (reference to Table 8 in Appendix).
- Table 1 coefficients (Baseline Sample, Dependent Variable: FX Basis Residuals):
  - Treated × Post: -0.512 ∗∗ (column 1), -0.511 ∗∗ (column 2)
    - p-value indicators: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
  - MP meetings: -0.209 ∗ (column 2)
  - EU high yield: -0.956 ∗∗ (column 2)
  - Surprise index: -0.00132 (column 2)
  - Observations: 324 (both columns)
  - R2: 0.115 (column 1), 0.167 (column 2)
  - Currency × Event FE: yes (both)
  - PostMat: yes (both)
- Standard error notes: clustered at currency-event level.

### Robustness checks and additional evidence
- Adding Norway and Iceland (never targeted by ECB lines) to sample: divergence remains; magnitude reduces to 37 basis points (reported in Appendix Table 4).
- Placebo/anticipation test: moving announcement date three days earlier yields effects far from statistically significant and sometimes positive, indicating no anticipation and supporting parallel pre-trends (results in Appendix Table 6 A.2).
- Re-estimating with basis (not residuals) as dependent variable and including daily country-specific covariates (stock market volatility and sovereign yield): results confirmed (Appendix Table 5 A.2).
- Event-by-event estimation using three estimators (TWFE DID, Arkhangelsky et al. (2021) SDID, Abadie et al. (2015) Synthetic Control):
  - Kept 15 days prior to each announcement; dropped any country treated during this window from controls.
  - Average treatment effects and standard errors (in parentheses): −0.679 (0.606) for DID, −0.259 (0.471) for SDID, −0.484 (0.473) for SC.
  - While standard errors relatively high, the overall negative effect is confirmed.
- Time-series event study regressions of FX basis residuals on post-treatment dummy and controls (Appendix B) produce statistically significant estimates slightly higher but similar in magnitude to DID results.
- Notes on inference with one treated unit: bootstrap used; caveats on bootstrap reliability with just one treated unit discussed.

### Interpretation
- The announcement of ECB euro liquidity swap lines has a measurable signalling effect that reduces the euro funding cost in FX markets for targeted currencies in the immediate announcement window.
- The effect is regionally important and robust to multiple specifications and placebo checks.

---

*Source: IMF working paper section 3.1–3.3 (wpiea2023096-print-pdf).*

### 4.1    Mechanism

### 4.1 Mechanism

### Model setup and timeline
- Stylized two-country three-period model with a representative euro area (EA) bank in the source-country and a local bank in the recipient-country.
- Cross-border lending with currency and maturity mismatches generates refinancing risk following an exogenous exchange rate shock.
- Timeline (Figure 6 / Figure 7): t=0 endowments and announcement; t=1 exchange rate shock and refinancing/liquidation; t=2 repayment.

### Balance sheets at t = 0
- Euro area bank:
  - Assets: A0 (€) and 1 (€) (one-period euro-denominated debt of the local bank)
  - Liabilities: D0 (€) (insured deposits)
  - Equity: E0 (€)
  - Balance sheet constraint: A0 + 1 = D0 + E0 (Eq. (5))
  - Assumption: D1 = (1 + r) D0 (deposits paid at t = 2).
- Local bank:
  - Borrows 1 unit (euro-denominated) from EA bank at gross rate 1 + rC.
  - Invests in a euro-denominated loan maturing at t = 2 with net return rL > rC.
  - Holds insured local currency deposits D* remunerated at net rate r*, invests short-term I* yielding rI and paying X = (rI − r*) D* in local currency at t = 1.

### Exchange rate shock and refinancing via FX swaps
- At t = 1, exchange rate S (Euro per unit of local currency) is:
  - Low with probability q such that SL (X + D*) < 1 + rC
  - High with probability 1 − q such that SH (X + D*) > 1 + rC
- If low realization, local bank cannot repay using internal funds. Market rollover assumed impossible; local bank seeks to refinance via FX swaps.
- Cost of refinancing via FX swaps, Cs(b), where b ∼ Fh b, h ∈ {nl, l}:
  - Cs(b) = (1 + b)[1 + rC − λS]  (Eq. (6))
  - Define b̄ such that Cs(b̄) = 1 + rL  (Eq. (7))
- If unable to refinance, EA bank can liquidate and receives λL,1 (liquidation value of long-term loan at t = 1).
- Assumption: λL,1 + λS < 1 + rC (EA banks face loan default risk).

### Effect on euro area bank stock prices without liquidity lines
- Equity owners are risk-neutral with discount factor β. Stock price equals expected value of equity at t = 2.
- A1 realizations (Eq. (8)):
  - If loan liquidated at t = 1: A1 = λS + λL,1 + (1 + r) A0
  - If loan repays at t = 1: A1 = (1 + rC) + (1 + r) A0
- Value of equity at t = 2: V2 = max{(1 + r) A1 − (1 + r) D1, 0}  (Eq. (9))
- t = 0 stock price V0(x) = β^2 E0 V2  (Eq. (11))
- Two cases:
  - Case 1 (EA bank perfectly safe):
    - Condition: (1 + r)(λS + λL,1) − (1 + r)^2 + (1 + r)^2 E0 ≥ 0  (Eq. (15))
    - t = 1 default probability of local bank: p1 = q(1 − Fh b(b̄))  (Eq. (16))
    - Stock price V0 given by Eq. (17).
  - Case 2 (EA bank defaults if local bank defaults at t = 1):
    - Condition: (1 + r)(λS + λL,1) − (1 + r)^2 + (1 + r)^2 E0 < 0  (Eq. (18))
    - Stock price V0 given by Eq. (19).

### Liquidity line announcement mechanism
- FX swap effective cost b = r* + f − s (equivalent to FX swap basis, net of foreign deposit rate).
- An active liquidity line caps forward prices in FX swaps; provides a cheaper outside option for local banks, improving their bargaining terms with traders and reducing b(δa) for δa > 0.
- Swap price distribution relation with announcement:
  - Fl b(x) ≥ Fnl b(x) with strict inequality for x ∈ (b(0), bnl(1)]  (Eq. (20))
- Three regimes depending on b̄ and distribution:
  - Regime 1: b̄ < b(0) → local bank default probability pl1 = pnl1 = q (always default when low exchange rate)
  - Regime 2: b̄ ∈ [b(0), bnl(1)) → pl1, pnl1 ∈ (0, q) with pl1 ≤ pnl1; liquidity line announcement decreases p1 unless local bank has all bargaining power
  - Regime 3: b̄ ≥ bnl(1) → pl1 = pnl1 = 0 (never default)
- Propositions:
  - Proposition 1: A liquidity line announcement in times of a freeze of the international inter-bank lending market leads to an increase in euro area stock prices unless local banks exposed to a low exchange rate realization (a) never default, (b) always default, (c) have all bargaining power in negotiating FX swap prices.
  - Proposition 2: In Case 1 (safe euro area bank), the effect is decreasing in the liquidation value λL1 of the local bank.

### 4.2 Empirical strategy

### Identification approach
- Differences-in-Differences strategy exploiting heterogeneous banking exposure of EA countries to recipient countries targeted by ECB lines.
- Main hypothesis: Following an ECB liquidity line announcement, equity prices of EA banks more exposed to targeted currencies increase relatively more than less exposed banks.
- Exposure measure:
  - EXPj,e = 1 if average exposure of EA country j to non-EA countries targeted by the line at event e is higher than the 75th percentile of the cross-country exposure distribution; 0 otherwise.
  - Robustness: threshold reduced to the 65th percentile and a continuous exposure variable considered.
- Dependent variable: changes (not levels) of purged average log stock price residuals for banks in EA country j at time t in event e, denoted ∆PriceResj,t,e. Purging follows Section 2.
- Estimation equation (collapsed panel around four-day window per announcement):
  - ∆PriceResj,t,e = β1 Postt × EXPj,e + Xe β2e Postt,e + β3 EXPj,e + β4 mp t + φ′ Zt + μj,e + uj,t,e  (Eq. (21))
- Controls: country-event fixed effects, Post dummy per event, global controls Zt. Standard errors clustered at country-event level.
- Sample focuses on ECB euro liquidity line events to reduce contamination from USD or other currency lines.

### 4.3 Results

### Main empirical findings
- Table 3 (two-way fixed effects DID on four-day window around ECB euro liquidity line announcements, EA sample: AT, BE, DE, ES, FI, FR, IR, PT, IT):
  - Column 1 (Exposure p75): Post × Exp coefficient = 0.0175 ** (p < 0.05)
  - Column 2 (Exposure p65): Post × Exp coefficient = 0.0148 * (p < 0.10)
  - Column 3 (Continuous): Post × Exp coefficient = 0.0299 ** (p < 0.05)
  - Controls: VIX, EU high yield, MP meetings; Observations = 284; R^2 = 0.275 / 0.272 / 0.303 across columns; full controls and currency × event fixed effects included.
- Interpretation:
  - Announcement of an ECB euro liquidity line increases EA stock prices by 1.75% for EA countries with banking sectors more exposed to targeted currencies (column 1).
  - Robust to alternative exposure definitions (65th percentile) and continuous exposure specification.
  - Figure 9 (Appendix A.4) shows similar evolution of stock price changes for highly exposed and less exposed countries in a ten-day window; Table 11 (Appendix A.4) documents country exposure classifications (Italy and Austria on average more exposed).

### Additional notes
- Stock price series contain a unit root; hence use of changes for stationarity.
- The estimated 1.75% effect corresponds to approximately half a standard deviation of stock price variations.

### 5 Conclusion

- Central bank liquidity lines act as backstop facilities in distress, preventing liquidity shortages from becoming global financial stability problems.
- ECB expanded its network of swap lines during episodes of global stress (global financial crisis and COVID-19).
- This paper documents for the ECB:
  - ECB euro liquidity line announcements are associated with decreases in the premium paid by foreign agents to borrow euros in FX markets in a narrow announcement window.
  - Positive spillbacks to the euro area in the form of relatively higher bank equity prices for EA countries highly exposed via banking links to targeted currencies.
- Theoretical mechanism and empirical evidence are consistent: liquidity line announcements reduce local bank default probabilities in certain regimes, increasing expected profits of EA banks holding claims and raising EA bank stock prices.
- Descriptive evidence: ECB has mainly provided FX insurance to nearby central banks (mainly non-EA EU countries); role more regional than global, in contrast with the Fed.
- Policy-relevant open question: whether these arrangements can boost usage of the euro as an international currency if made permanent or predictable, potentially reducing CIP deviations in crises. Current context: uncertainty from the war in Ukraine and high risk of Euro Area fragmentation.

*Source: wpiea2023096-print-pdf - 4.1 Mechanism (IMF Working Paper content provided).*

### References

### wpiea2023096-print-pdf - References

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### Appendix A.1 — Data Sources
- Stock Prices: sourced from Datastream (Refinitiv); country aggregates from listed banks.
- Germany banks: Deutsche Bank, Commerzbank, Aareal, Deutsche Pfandbriefbank, Procredit, Umweltbank.
- France banks: BNP, Crédit Agricole, Société Generale, Natixis, Nord CCI, Ille de France, Brie Picardie, Crédit Foncier.
- Italy banks: Intesa, Unicredit, Generali, BPM, BPER, Finecobank, Monte dei Paschi, Credito Emiliano, Illimity, Sondrio, Profilo, Sistema, Piccolo credito.
- Spain banks: Santander, BBVA, Caixabank, Bankinter, Sabadell, Liberbank, Unicaja.
- Belgium banks: KBC, Banque Nationale de Belgique, KBC Ancora.
- Austria banks: Erste, Raiffeisen, BAWAG Group, Oberbank, BKS, Addiko Bank, Bank für Tirol und Vorarlberg.
- Finland banks: Nordea, Aktia.
- Ireland banks: Bank of Ireland, Permanent THB.
- Portugal bank: Banco Comercial Portugues.

### Appendix A.2 — Regression Tables (key coefficients and statistics)
- Table 4: Effect of ECB liquidity swap line announcement (Dependent Variable: FX Basis Residuals)
  - TreatedPost coefficients:
    - Baseline Sample (columns (1) and (2)): -0.512 ∗∗ (p-values in parentheses (0.030)), -0.511 ∗∗ (0.031)
    - Extended Sample (columns (3) and (4)): -0.373 ∗ (0.051), -0.373 ∗ (0.052)
  - MP meetings: -0.209 ∗ (0.052) and -0.0405 (0.760)
  - EU high yield: -0.956 ∗∗ (0.022) and -0.544 (0.268)
  - Surprise index: -0.00132 (0.203) and -0.00196 ∗∗ (0.022)
  - Observations: 324, 324, 428, 428
  - R^2: 0.1150, 0.1670, 0.0590, 0.076
  - Currency x Event FE: yes; PostMat: yes
  - Significance notation: ∗ p <0.10, ∗∗ p <0.05, ∗∗∗ p <0.01

- Table 5: Effect of ECB liquidity line announcement (Baseline Sample) (Dependent Variable: FX Basis)
  - TreatedPost: -0.410 ∗∗ (0.026)
  - EU high yield: -1.087 ∗∗ (0.024)
  - MP meetings: -0.233 ∗∗ (0.027)
  - Surprise index: -0.00117 (0.324)
  - Stock exchange volatility: 2.365 (0.385)
  - Sovereign yield: -0.824 (0.176)
  - Observations: 332
  - R^2: 0.197
  - Currency x Event FE: yes; PostMat: yes

- Table 6: Effect of ECB liquidity line announcement (Placebo) (Dependent Variable: FX Basis Residuals)
  - TreatedPost: 0.0984 (0.744), -0.0987 (0.745), -0.0124 (0.969), -0.0127 (0.969)
  - MP meetings: 0.0639 (0.841), 0.266 (0.447)
  - EU high yield: -0.349 (0.462), -0.130 (0.753)
  - Surprise index: 0.00824 (0.276), 0.0104 (0.197)
  - Observations: 324, 324, 428, 428
  - R^2: 0.0430, 0.0560, 0.0360, 0.043
  - Note: placebo window anticipated by 3 days; extended sample adds Iceland and Norway to control group.

### Appendix A.3 — Timeline and main features of ECB lines (announcements)
- Notes on timeline:
  - Timeline based on ECB press releases; omits some information due to space constraints.
  - Does not include the Term Auction Facility nor the EUREP.
  - Swap time extensions refer to central bank swap lines and domestic CB repo operations against ECB-eligible collateral with domestic financial institutions.
  - Does not include discontinuations of lines or maturities.
  - “Reciprocal” column: indicates at least one counterpart’s press release explicitly refers to agreement being reciprocal.
  - “Euro provision” column: indicates whether press release shows clear intention of providing euro liquidity.
  - Publicly announced: “p” indicates same-day press release; “np” indicates ex-post announcement.
  - Federal Reserve(*) and Federal Reserve(**) indicate contexts of multilateral agreements and additional currency provisions as described.
  - Sveriges Riksbank (§) indicates arrangement not publicly announced in 2007; activation announced in 2009.
  - ( §§ ) sourced from other ECB documents; such announcements not included in analysis assuming press releases are main signalling channel.
  - LEG 1: maximum length of drawing between two central banks.
  - LEG 2: maturities of operations with domestic counterparts (repo facilities).
- Selected timeline entries (date, country, counterpart, euro provision, reciprocal, instrument, expiration/leg info, maximum amount):
  - 13-Sep-2001, USA, Federal Reserve, No, No, swap, 13-Oct-2001, —, —, USD 50 bn
  - 12-Dec-2007, USA, Federal Reserve (*), No, Yes, swap, —, —, 28 and 35 days, USD 20 bn
  - 20-Dec-2007, SWE, Sveriges Riksbank (§), Yes, Yes, swap, —, 3 months, —, EUR 10 bn
  - 10-Jan-2008, USA, Federal Reserve (*), No, Yes, swap time extension, —, —, 28 days, USD 20 bn
  - 18-Sep-2008, USA, Federal Reserve (*), No, Yes, swap volume expansion, —, —, 1, 28 and 84 days, USD 40 bn
  - 29-Sep-2008, USA, Federal Reserve (*), No, Yes, swap volume expansion, 30-Apr-2009, —, —, USD 120 to 240 bn
  - 16-Oct-2008, HUN, Magyar Nemzeti Bank, Yes, Yes, repo, —, —, —, EUR 5 bn
  - 27-Oct-2008, DNK, Danmarks Nationalbank, Yes, Yes, swap, —, —, —, EUR 12 bn
  - 15-Oct-2008, USA, Federal Reserve (*), No, Yes, foreign exchange swaps expansion of collateral pool, 31-Jan-2009, —, —, —
  - 6-Apr-2009, USA, Federal Reserve (*), Yes, Yes, swap volume expansion, 30-Oct-2009, —, —, EUR 80 bn
  - 10-Jun-2009, SWE, Sveriges Riksbank, Yes, Yes, swap activation of 2007 line, —, 3 months, —, EUR 3 bn (EUR 10 bn max)
  - 10-Oct-2013, CHN, People’s Bank of China, No, Yes, swap, 8-Oct-2016, —, —, CNY 350bn / EUR 45bn
  - 15-Mar-2020, USA, Federal Reserve (*), No, Yes, swap rate change, —, —, 7 days and 84 days, —
  - 20-Mar-2020, DNK, Danmarks Nationalbank, Yes, Yes, swap reactivation / swap volume expansion, As long as needed, —, —, EUR 24 bn
  - 15-Apr-2020 to 28-Aug-2020: multiple repo and swap lines for HRV, BGR, ROU, SRB, ALB, HUN, MKD, SMR with expirations mostly 31-Dec-2020 or 30-Jun-2021 and maximum amounts listed (e.g., EUR 2 bn, EUR 4.5 bn, EUR 1 bn, EUR 0.4 bn, EUR 4 bn, EUR 0.1 bn).
  - 28-Mar-2022, POL, Narodowy Bank Polski, Yes, No, swap, 15-Jan-2023, 3 months, —, EUR 10 bn
  - 27-Apr-2022, ROU, Banca Nationala a României, Yes, No, repo time extension, 15-Jan-2023, 3 months, —, EUR 1 bn
  - Numerous time extensions with specific expiration dates and maximum amounts for ALB, HUN, MKD, SMR, SRB, and others with dates 15-Jan-2023.

### Appendix A.4 — Additional Tables and Figures (selected statistics and summaries)
- Table 8: Summary Statistics (Country, Mean, SD, N for Basis Residuals and Basis)
  - BG: Mean -0.006, SD -0.005, N .748 .698 3638 3587 (as formatted in source)
  - DK: Mean .11, SD .003, N 3.443 .436 3638 3522
  - HR: Mean - .19501, SD 1.521, N 1.194 3638 3284
  - HU: Mean .658, SD .0181, N 1.292 1.195 3638 3458
  - IS: Mean .267, SD - .0863, N 3.601 2.571 3638 3522
  - NO: Mean - .173, SD .009, N .755 .7636 3638 3522
  - PL: Mean - .013, SD .034, N 1.346 1.332 3638 3587
  - RS: Mean - .02202, SD .059, N 1.767 2915 27135
  - SE: Mean - .11, SD - .003, N 1.379 1.398 3638 3522
  - ALL: Mean - .044, SD - .003, N 1.51 .2186476 161784
  - Note: Unbalanced panel from 1st October 2008 to 10th September 2022.

- Table 9: Summary Statistics (selected variables)
  - MP meetings: mean .038, sd .191, N 0132019
  - ∆ Public debt ratio: mean .162, sd .48, min -10.5218, max .663, N 1608
  - CAB: 1.54 mean, sd 15.85, min -22.09, max 23.38, N 2019
  - External debt ratio: 247.53 mean, sd 32.81, min 1.083, N 183931235 (as formatted)
  - Rating: A-4BB-AAA3 2019 (as formatted)
  - Int. reserves: 43.59 mean, sd 32.45, min 2.947, N 15631749
  - Inflation: 2.599 mean, sd 2.844, min -2.614, max 18.583, N 1933
  - VIX: 19.999 mean, sd 9.519, min 9.148, max 2.693, N 2019
  - EU high yield: 5.023 mean, sd 3.433, min 2.341, max 23.613, N 2019
  - Surprise index: 3.68565 mean, sd 5.59, min -304.621, max 2.432, N 2019
  - Sovereign yield: 3.129 mean, sd 2.018, min -0.792, max 15.013, N 1716
  - Stock exchange volatility: 1.04 mean, sd 2.73, min 2.243, max 11.373, N 2019
  - Note: Unbalanced panel from 1st October 2008 to 10th September 2022. CAB is the current account balance. International reserves in billions of USD. External debt ratio measured as a percentage of international reserves.

- Table 10: Stock price summary (selected country rows; columns expressed in percent where noted)
  - AT: log Stock Price 5.849, Δ(%) - .01, Resid. log Stock Price 9.224, Δ(%) 2.143, Δ(%) Resid. 2.436, N values listed (e.g., 4136 4132 96)
  - BE: log Stock Price 5.813, Δ(%) - .013, Resid. log Stock Price 15.407, Δ(%) 2.624, Δ(%) Resid. 3.455, N values listed
  - DE: log Stock Price 4.779, Δ(%) - .043, Resid. log Stock Price 3.01533, etc. (as formatted in source)
  - ALL: log Stock Price 5.176, Δ(%) - .033, Resid. log Stock Price .021.144, Δ(%) 2.569, Resid. 3.377, N 325103250927555
  - Note: Unbalanced panel from 1st October 2008 to 15th September 2022. Columns 3, 4, 6 and 7 are expressed in percent.

- Tables 11–12: Banking exposure dummy by EA country and announcement at 75th and 65th percentile thresholds
  - Example entries for Announcement 16oct2008: AT 1, BE 1, DE 1, ES 1, FI 1, FR 0, IT 0, PT 1 (as formatted)
  - Exposure defined as percentage of banking sector claims of EA country j on non-EA country i over total claims of domestic banks of EA country j globally. Dummy = 1 if exposure ≥ percentile threshold.

- Figures and event-study plots:
  - Figure 8: Basis in Levels: Averaged over Events 2008-2020 (panels for Baseline Sample and Extended Sample showing Mean FX Basis for Treated vs Untreated over a four-day window around announcements).
  - Figure 9: Stock Price Changes (left panel: average evolution of residuals of average bank stock prices in 10-day window; right panel: cumulative residuals since announcement). Residuals from regressions on short term rate, net foreign assets, loan-to-deposit ratio, and NEER deviations.
  - Figures 10–13: Time series of CIP Deviations and Basis Residuals by country across publication dates (visual evolution across 2007–2022 sample).
  - Figures 14–15: Pretrends SDID (Arkhangelsky et al. (2021) SDID estimator) for all events, dependent variable FX Basis residuals; treated currencies and treatment dates indicated per panel.

- Table 13: Summary Statistics (selected country-level macro variables)
  - BG: ∆ Public debt ratio .2; Int. reserves 21.94; External debt ratio 59.52; Rating BBB-; SD and N columns follow as formatted.
  - DK: ∆ Public debt ratio .12; Int. reserves 72.98; External debt ratio 303.196; Rating AAA; SD and N columns follow.
  - HR: ∆ Public debt ratio .68; Int. reserves 17.61; External debt ratio 33.081; Rating BB+; SD and N columns follow.
  - HU: ∆ Public debt ratio .27; Int. reserves 37.32; External debt ratio 58.542; Rating BBB-; SD and N columns follow.
  - Note: Table continues with IS and other countries as in source.

*Source: wpiea2023096-print-pdf - References*

### 616.201    BBB+

### 616.201    BBB+

### Summary Statistics (Table 14)
- Panel: Unbalanced panel from 1st October 2008 to 10th September 2022.
- Definition notes:
  - International reserves is the level of Central Bank’s international reserves inbillions of USD.
  - The external debt ratio is measured as a percentage of international reserves.
  - CAB is the current account balance.
- Selected country-level means, standard deviations (SD), and sample sizes (N):
  - BG: Mean CAB -1.08; Inflation 2.57; Sovereign yield 2.37; Stock exchange volatility .86. SD CAB 5.324; Inflation 3.55; Sovereign yield 1.42; Stock exchange volatility .56. N = 3638, 3631, 3638, 3638.
  - DK: Mean CAB 7.26; Inflation 1.52; Sovereign yield 1.24; Stock exchange volatility .89. SD CAB 1.726; Inflation 1.53; Sovereign yield 1.27; Stock exchange volatility .46. N = 3638, 3631, 3638, 3638.
  - HR: Mean CAB -.23; Inflation 1.6; Sovereign yield 3.98; Stock exchange volatility .78. SD CAB 3.429; Inflation 2.3; Sovereign yield 1.74; Stock exchange volatility .69. N = 3638, 3608, 3335, 3638.
  - HU: Mean CAB .32; Inflation 3.29; Sovereign yield 4.4; Stock exchange volatility 1.33. SD CAB 2.613; Inflation 2.65; Sovereign yield 1.48; Stock exchange volatility .73. N = 3638, 3631, 3638, 3638.
  - IS: Mean CAB .2; Inflation 4.33; Sovereign yield 5.84; Stock exchange volatility 1.02. SD CAB 6.747; Inflation 3.44; Sovereign yield 1.64; Stock exchange volatility 1.16. N = 3638, 3631, 3638, 3638.
  - NO: Mean CAB 9.22; Inflation 2.34; Sovereign yield 2.2; Stock exchange volatility 1.27. SD CAB 4.568; Inflation 1.2; Sovereign yield .95; Stock exchange volatility .8. N = 3638, 3631, 3638, 3638.
  - PL: Mean CAB -2.16; Inflation 2.76; Sovereign yield 2.9; Stock exchange volatility 1.09. SD CAB 2.503; Inflation 3.02; Sovereign yield 1.16; Stock exchange volatility .54. N = 3638, 3631, 3638, 3638.
  - RS: Mean CAB -5.85; Inflation 3.93; Sovereign yield 4.15; Stock exchange volatility 1. SD CAB 2.374; Inflation 3.53; Sovereign yield 1.58; Stock exchange volatility .57. N = 2915, 2908, 2915, 2915.
  - SE: Mean CAB 4.72; Inflation 1.33; Sovereign yield 1.35; Stock exchange volatility 1.13. SD CAB 1.344; Inflation 1.69; Sovereign yield 1.12; Stock exchange volatility .61. N = 3638, 3631, 3638, 3638.
  - ALL (aggregate): Mean CAB 1.8; Inflation 2.12; Sovereign yield 2.61; Stock exchange volatility 1.01. SD CAB 6.45; Inflation 2.4; Sovereign yield 1.81; Stock exchange volatility .68. N = 64761, 64455, 64458, 64761.

### Time Series Regression — Event Study (Table 15)
- Regression specification:
  - Res_jt = α_j + β1 post_jt + β X_jt + γ W + u_jt, where post_jt = 1 on announcement day and the following day for the treated country, zero otherwise; W are monthly dummies; X_jt is a vector of controls. Fixed effects estimation with heterogeneous robust s.e.; results robust to Driscoll-Kraay standard errors.
  - The extended sample adds Iceland and Norway to the control group.
- Key coefficients and statistics (columns labeled Baseline Sample and Extended Sample; dependent variable: Residuals):
  - post coefficient:
    - Column (1): post = -0.447, p-value indicated by ∗ (p <0.10). Standard error (0.064).
    - Column (2): post = -0.432, p-value indicated by ∗ (p <0.10). Standard error (0.066).
    - Column (3): post = -0.484, p-value indicated by ∗∗ (p <0.05). Standard error (0.023).
    - Column (4): post = -0.458, p-value indicated by ∗∗ (p <0.05). Standard error (0.020).
  - MP meetings:
    - Column (1): -0.0373, standard error (0.437).
    - Column (2): -0.0387, standard error (0.425).
    - Column (3): 0.008420, standard error (0.871).
    - Column (4): 0.00538, standard error (0.916).
  - EU high yield (included in some specifications):
    - Column (3): -0.0279, standard error (0.507).
    - Column (4): -0.0358, standard error (0.297).
  - Surprise index (included in some specifications):
    - Column (3): 0.00000882, standard error (0.987).
    - Column (4): -0.000350, standard error (0.470).
- Sample sizes and fit:
  - Observations: Column (1) 13720; Column (2) 13720; Column (3) 17961; Column (4) 17961.
  - R-squared: Column (1) 0.0450; Column (2) 0.0460; Column (3) 0.0740; Column (4) 0.074.
  - Month FE: yes in all columns.
  - Currency FE: yes in all columns.
- Interpretation notes from text:
  - Event study estimates are slightly higher than DID estimates; results robust to using week×year dummies instead of monthly fixed effects.
  - Post takes the value of 1 on the day of the announcement and the day after for the currency targeted by the line in t, and zero otherwise.

### Proof — Announcement Effect (Section C) and Propositions
- Main formal result:
  - Denote S_l(n,n+1) and S_nl(n,n+1) as swap prices maturing at time n+1 with and without a liquidity line, respectively. As shown in Bahaj and Reis (2022a), S_l(n,n+1) < S_nl(n,n+1).
  - If a trader faces probability α_h (h ∈ {a,na}) that a liquidity line will be activated between 0 and N, with α_a > α_na when a line was announced, then no-arbitrage implies:
    - S_nl,na(0,N) = E_0 Σ_{n=1}^N [(1−α_na) S_nl(n−1,n) + α_na S_l(n−1,n)]
    - S_nl,a(0,N) = E_0 Σ_{n=1}^N [(1−α_a) S_nl(n−1,n) + α_a S_l(n−1,n)]
  - Hence S_nl,a(0,N) < S_nl,na(0,N): the announcement reduces euro funding cost on the FX market via the term structure.
- Proposition 1 (stock-price effect of announcement):
  - Denote Euro Area bank stock prices by V_nl_0 if no liquidity line is announced, and V_l_0 if a line is announced.
  - Case 1:
    - V_l_0 − V_nl_0 = β_2 (1 + r) q_h [F^l_b( b̄ ) − F^nl_b( b̄ )] [1 + r_c − λ_S − λ_L,1] ≥ 0. (Eq. (25))
  - Case 2:
    - V_l_0 − V_nl_0 = β_2 (1 + r) q_h [F^l_b( b̄ ) − F^nl_b( b̄ )] [1 + r_c] ≥ 0. (Eq. (26))
  - From Eq. (20): (F^l_b( b̄ ) − F^nl_b( b̄ )) ≥ 0 and therefore F^l_b( b̄ ) > F^nl_b( b̄ ) ⇒ V_l_0 − V_nl_0 > 0.
  - CDF properties summarized:
    - F^l_b( b̄ ) − F^nl_b( b̄ ) = 0 if b̄ ≤ b(0)
    - F^l_b( b̄ ) − F^nl_b( b̄ ) > 0 if b̄ ∈ (b(0), b^nl(1))
    - F^l_b( b̄ ) − F^nl_b( b̄ ) = 0 if b̄ ≥ b^nl(1)  (Eq. (27))
- Proposition 2 (sensitivity to λ_L,1 in Case 1):
  - ∂(V_l_0 − V_nl_0)/∂λ_L,1 = −β_2 (1 + r) q_h [F^l_b( b̄ ) − F^nl_b( b̄ )] ≤ 0. (Eq. (28))
  - The inequality is strict under the conditions stated in Proposition 1.

*ECB Euro Liquidity Lines Working Paper No. WP/2023/096*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023096-print-pdf.pdf_