## wp17116

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### Introduction and motivation
- The global financial crisis is characterized as "a liquidity crisis, not just a solvency crisis."
- Liquidity risk manifests as:
  - a liquidity crunch: firms’ access to funding markets is impaired, or
  - a pricing crunch: lenders demand much higher spreads.
- Funding liquidity risk is extracted by observing the costs that banks pay to secure market liquidity.
- A sudden increase in bank funding costs can deplete banks’ capital buffers and threaten financial stability.
- Two motivations for assessing banks’ vulnerability to funding cost changes:
  - Funding costs reflect counterparty credit risk and help determine appropriate capital buffers.
  - Funding costs affect future capital positions and can generate adverse dynamics through reduced internal capital generation and limited pass-through to lending rates.

### Research questions and empirical approach
- Primary questions:
  - What is the magnitude of the interaction between funding costs and solvency?
  - How can the estimated effects be used for stress testing purposes?
- Dataset and sample:
  - Supervisory reporting data of 54 large banks over 2004–2013.
  - Shared across supervisory agencies from six countries under strict confidentiality arrangements.
- Empirical strategy:
  - Focus on the endogenous (two-way) interaction between solvency and funding costs.
  - Use a simultaneous equation approach with exogenous instrumental variables.
  - Rationale: OLS likely yields biased coefficients due to endogeneity between capital and funding costs; the direction of bias is theoretically ambiguous.
  - Authors note that OLS underestimates the impact of capital on funding costs in their findings.

### Main empirical findings
- Evidence supports joint determination of funding costs and bank solvency.
- Evidence of non-linear interactions between funding costs and solvency risk.
- The solvency–funding relationship has "not changed significantly during the crisis."
- Size of effects found:
  - "A 100 bps increase in regulatory capital is associated with a 105 bps decrease in funding costs."
  - This is large relative to the existing literature, where the effect "tends to be smaller, at an average of 50 basis points."
- Illustrative application: empirical results used to inform stress testing projections using the 2014 EU-wide stress test exercise.

### Construction of the dataset
- Panel characteristics:
  - Unbalanced panel of 54 large banks from six countries.
  - Sample period: 2004Q4 to 2013Q4.
  - United States contribution: 33 banks.
  - Other contributors: six Austrian, six Canadian, six Dutch, and three Nordic banks.
- Data provenance:
  - Bank data shared among regulatory agencies under strict confidentiality and subject to filtering and quality checks.
  - Supervisory data based on reported regulatory balance sheets and include confidential supervisory information.

### Measurement choices and proxies
- Funding-cost proxy:
  - Marginal cost of long-term unsecured wholesale funding proxied by the five-year senior single name CDS spread for each bank.
  - Preference for five-year fair value CDS spreads over short-term funding measures because short-term quotes often reflect quoted prices rather than transaction prices and UMP limited variation in short-term market rates.
  - Caveats: CDS market liquidity may be limited for some banks; addressed with bank-specific fixed effects; CDS signal marginal shadow cost of funding even if a bank is shut out of markets.
- Solvency proxy:
  - Core tier 1 ratio (CT1) chosen; CET1 not used because it was introduced only recently and not available for the sample period.
  - Alternative robustness check: expected default frequency (EDF) over five years estimated by Moody’s Credit Edge.
- Additional bank-specific variables:
  - Loan loss provisions in percent of total assets (LLP).
  - Net income in percent of total assets (NI).
  - Liquidity risk (LiRisk) = short-term wholesale debt (remaining maturity < three months) over stock of liquid assets (cash and central bank excess reserves, sovereign debt with risk-weights of 0 and 20 percent).
- Market and macro controls:
  - LIBOR-OIS spread, OIS, VIX index.
  - Crisis dummy (Crisis_d): 0 from 2004Q4 to 2008Q3; 1 from 2008Q4 to 2013Q4.
  - Country-level credit growth (loan_growth).
  - Regulatory capital swing dummy (ΔCT1_d): increase of CT1 by more than 20 percent quarter-on-quarter in nominal terms.

### Identification and instrumental variables
- Instrument selection principle: directly related to one endogenous variable and only indirectly related to the other via the first.
- Specification 1 instruments:
  - LLP as instrument in the CT1 equation; NI used as exogenous variable in the solvency equation.
  - S&P (lag 1), sovereign CDS spread (CDS_gov), and LIBOR-OIS used for identification of the FVCDS equation.
- Specification 2:
  - Adds ΔCT1_d (deliberate management action dummy) in the CT1 equation.

### Data features, summary statistics, and robustness checks
- Frequency harmonisation: analysis focuses on quarterly data.
- Stationarity: meta unit root tests by Choi (2001) reject unit roots in most variables.
- Reported summary statistics and data points (preserved verbatim):
  - Median CDS spread across all banks and the entire period: 131 bps.
  - EDF quartiles: 0.08 percent (first), 0.3 percent (second), 0.94 percent (third).
  - Correlation observations:
    - Regulatory and market-based measures of bank solvency have correlation coefficient below 10 percent.
    - Correlation between NI and LLP: 40 percent.
  - CT1 distribution over sample period:
    - First quartile (CT1): 7.89 percent.
    - Third quartile (CT1): 11.55 percent.
    - Mean (CT1): 10.5 percent.
  - Number of observations for the ΔCT1_d dummy across banks and quarters: 70 observations.
- Robustness approaches:
  - Separate estimations for pre- and post-Lehman sub-samples.
  - Alternative solvency measure (EDF) used to assess robustness.
- Miscellaneous:
  - Potential impact of emergency liquidity assistance (ELA) discussed; authors report confidence that no bank in sample received ELA.
  - High correlation between VIX and LIBOR-OIS around Lehman noted as an artifact of simultaneous spikes.

### Estimation methods and diagnostics
- Structural model: YΓ = XB + U; reduced form Y = XΠ + V with Y = [solvency, funding costs]'.
- Estimation:
  - Two-stage least squares (2SLS).
  - Three-stage least squares (3SLS) combining 2SLS with SUR.
- Diagnostic tests:
  - Instrument relevance via F-statistic and p-value.
  - Instrument exogeneity via J-test and Lagrange multiplier test (LMF).
  - Endogeneity tested via Durbin-Wu-Hausman test.
  - Hausman overidentification test to choose between 3SLS and 2SLS.
- Comparison with OLS highlights substantial biases: OLS can produce counterintuitive positive correlations where simultaneous estimation yields negative relationships.

### Estimation results (regulatory solvency CT1 and CDS funding costs)
- Baseline specification (Specification 1): 782 observations from 38 banks.
  - A 100 bps increase in a bank’s CDS spread is associated with a reduction of a bank’s CT1 ratio by 32 bps.
  - The McElroy R² for the system is 90 percent.
- Funding-cost equation (baseline):
  - A 100 bps higher CT1 ratio is associated with a decrease in bank funding costs by 105 bps (robust across specifications).
  - Net income (NI) → lower funding costs.
  - Sovereign CDS significant (sovereign–bank nexus).
  - LIBOR-OIS increases bank funding costs.
  - VIX significant but with a negative sign attributed to correlation between LIBOR-OIS and VIX.
  - McElroy R² of 81 percent and adjusted R² of 82 percent for the funding-cost equation.
- Specification 2 (adds deliberate management capital increases and funding structure):
  - Sharp capital increases variable not statistically significant.
  - CT1 coefficient in funding-cost equation slightly higher at -113 bps.
  - Interaction of FVCDS with share of short-term debt:
    - FVCDS coefficient in solvency equation increases to -1.1 from -0.32.
    - Interaction term is +0.06.
    - Example: An increase of FVCDS of 105 bps decreases CT1 by 100 bps if no short-term debt; with short-term debt at 10 percent of total assets (sample average), effect reduced by 60 bps to about 50 bps.
  - In funding equation CT1 coefficient changes to -0.87 from -1.13; VIX becomes insignificant; LIBOR_OIS coefficient decreases from 1.71 to 1.03; crisis dummy coefficient decreases from 2.97 to 1.97.
- Specification 3 (adds squared values of endogenous variables):
  - CT1 remains significant in funding-cost equation; CDS spreads remain significant in solvency equation.
  - No supporting evidence of non-linear effects between funding costs and regulatory capital.
  - Loan loss provisions coefficient becomes significantly higher.
- OLS vs. simultaneous system:
  - OLS yields coefficients of 0.17 and 0.14 for CT1 and CDS spreads respectively in Specification 1, suggesting a positive relationship that contradicts simultaneous estimates.
  - For Specification 1 OLS coefficient of CDS in solvency equation: +0.14 (vs. -0.32 under simultaneous approach), indicating OLS underestimates the negative relationship.

### Robustness checks using EDF and liquidity risk
- EDF specification: 946 observations for 38 banks from 2004Q4 to 2013Q4.
  - Specification 1 (EDF): A 100 bps increase of CDS spreads is associated with an average increase in the EDF of 66 bps.
  - LIBOR-OIS and VIX significant in solvency equations; VIX now has expected sign.
  - Crisis dummy statistically significant but has a negative sign (consistent with CT1 and EDF having different signs).
  - R² is 78 percent for solvency equation; funding-cost equation R² is 77 percent.
  - McElroy R nearly 100 percent for market-based measures.
- Specification 2 (management action variable): not statistically significant.
- Specification 3 (adds squared changes of endogenous variables):
  - Funding costs have a significant non-linear impact on the solvency equation: as funding costs increase, banks’ distance to default decreases, raising solvency risk.
- Diagnostics:
  - Weak instruments rejected in all equations.
  - J-Test and LMF generally fail to reject exogeneity (except FVCDS equation in Specification 3).
  - Durbin-Hausman-Wu test indicates endogeneity is less of an issue for EDF than for CT1.
  - System overidentification tests favor 3SLS across EDF specifications.
- OLS comparison with EDF:
  - OLS coefficients underestimate the impact of solvency risk on funding costs across specifications but to a smaller extent than CT1-based results.
  - For Specification 1 the OLS coefficient of CDS in the solvency equation is 0.59 (below the simultaneous estimate in robustness checks).

### Liquidity risk measure (LiRisk) and related estimates
- Purpose: control for banks’ liquidity risk bearing capacity and how funding composition affects default risk.
- Baseline (regulatory capital measure):
  - Coefficient on regulatory capital without liquidity measure: 1.048.
  - Coefficient on regulatory capital with liquidity measure: 1.028.
  - Statistical significance: remains significant at the 1 percent confidence level.
- Market-based solvency measure (EDF):
  - Coefficient on EDF before liquidity measure: 1.40.
  - Coefficient on EDF after liquidity measure: 1.37.
  - Statistical significance: remains significant at the 1 percent confidence level.
- Liquidity indicator: not statistically significant across specifications.
- Caveat: a bank’s exposure to other risks may affect its liquidity; exposures can erode liquidity positions or affect funding costs, thereby increasing liquidity risk.

### Application to stress testing (2014 EU-wide stress test illustration)
- Stress test context:
  - Adverse macroeconomic scenario: ECB’s 2014 EU-wide stress test conducted by the EBA.
  - EU-wide stress test sample size: 124 EU banks.
  - Static balance sheet assumption; stress horizon: three years (2014–2016).
- Sample used for illustration:
  - Of the 15 EU banks in authors’ sample, 11 banks were included in the EU stress test; analysis focuses on this 11-bank subset.
  - Aggregate CET1 ratio for the 11-bank subset at cut-off date: 14.5.
  - Aggregate CET1 ratio for the entire sample: 11.1 percent.
  - Impact of stress on capital ratios:
    - Subset of banks: 283 bps.
    - Entire population covered in the exercise: 270 bps.
- Assumptions and parameterisation:
  - Use coefficients from Specification 1 (Table 4) to endogenize banks’ funding costs.
  - Econometric results in terms of CT1 rather than CET1; undisclosed CT1 for sub-sample expected to be close to CET1 because the weighted-sized gap between Tier 1 and CET1 stood at only 100 bps in 2013.
  - Assume average funding structure of the 11 banks similar to the average bank in the 15-bank sample.
- Iteration and persistence:
  - Interaction expression (compact) presented in source as equation (3); iteration forward shown in equation (4) demonstrates hysteresis: the interaction effect at time t carries forward to t+1 via impacts on CT1 and FVCDS, producing persistence of solvency shocks.

### Quantified stress-test illustration results (11 EU banks)
- 2014 adverse scenario movements for the sample:
  - Weighted-average CET1 ratio decreases by 130 bps: from 14.5 percent in 2013 to 13.2 percent in 2014.
  - Average net income ratio (NI) falls by 40 bps: to -0.2 percent from 0.2 percent in 2013.
- Given estimated elasticities, solvency shock triggers an increase in banks’ marginal wholesale funding cost of 160 bps in 2014. This shock generates a further reduction of banks’ capital ratios by 51 bps.
- Aggregate impacts over 2014–2016:
  - Macroeconomic stress alone reduces aggregate capital ratio by 283 bps.
  - Overall impact including solvency–funding adverse dynamics reduces average capital ratio by 414 bps over 2014–2016.
- Interaction (feedback) effect on CET1 for the average bank:
  - 51 bps in 2014
  - 43 bps in 2015
  - 37 bps in 2016
- Relative impact of interaction vis-a-vis macro effect rises from 40 percent in 2014 to over 50 percent in 2016.
- Interaction effect in monetary units for the sample triggers reductions in aggregate capital of:
  - €3.8 billion in 2014
  - €3.3 billion in 2014
  - €2.8 billion in 2014
  (reported as such in source text.)

### Bank-level heterogeneity and drivers
- Banks with shorter funding tenors, greater reliance on CDS-sensitive funding instruments, and/or lower RWA to total assets ratios are more affected by the solvency → funding-cost feedback.
- Weaker banks tend to post higher RWAs, magnifying capital losses in monetary terms.
- In a crisis, wholesale funding tends to shift to shorter-dated tenors, increasing rollover needs at higher funding rates and worsening the interaction.

### Methodological robustness and caveats
- Empirical strategy: 3SLS simultaneous equation approach (and 2SLS reported), using supervisory quarterly data from 2004Q4 to 2013Q4.
- Results indicate a larger impact of solvency on funding costs than previous OLS-based studies; OLS estimates tend to underestimate the solvency–liquidity interaction nexus.
- Stability of coefficients confirmed across alternative measures of solvency risk and banks’ capacity to bear liquidity risk.
- Specification and instrument quality tests reported (F statistics, J tests, LMF tests, Hausman tests).
- Authors caution interpretation given instrument selection and remaining endogeneity concerns; recommend further research using larger high-quality samples and broader instruments.

### Policy implications and recommendations
- Stress-test models that ignore dynamics between solvency and funding costs are likely to underestimate the impact of stress on bank solvency and financial stability.
- Two mechanisms highlighted:
  - Short-term back-book effect: higher funding costs erode capital buffers quickly.
  - Longer-term adverse dynamics: risk-sensitive investors demand higher compensation, lengthening persistence of funding shocks and further depleting capital.
- Incorporating solvency–liquidity interactions in supervisory stress-test models is quantitatively relevant and can substantially alter estimated capital shortfalls.
- The cumulated interaction effect has implications for cost–benefit assessments of capital regulation: higher capital requirements’ costs are partly offset by lower debt servicing costs through a mitigated solvency–funding feedback.
- Recommendation: incorporate solvency and liquidity interactions in the design of prudential regulation and in stress-testing frameworks to better capture amplification channels evident during systemic stress.

*Source — Content excerpt from wp17116 (pdf: wp17116).*

### References ________________________________________________________________40

### wp17116 - References ________________________________________________________________40

### Introduction and motivation
- The global financial crisis is characterized as "a liquidity crisis, not just a solvency crisis."
- Liquidity risk manifests as:
  - a liquidity crunch: firms’ access to funding markets is impaired, or
  - a pricing crunch: lenders demand much higher spreads.
- Funding liquidity risk is extracted by observing the costs that banks pay to secure market liquidity.
- A sudden increase in bank funding costs can deplete banks’ capital buffers and threaten financial stability.
- Two motivations for assessing banks’ vulnerability to funding cost changes:
  - Funding costs reflect counterparty credit risk and help determine appropriate capital buffers.
  - Funding costs affect future capital positions and can generate adverse dynamics through reduced internal capital generation and limited pass-through to lending rates.

### Research questions and empirical approach
- Two primary questions:
  - What is the magnitude of the interaction between funding costs and solvency?
  - How can the estimated effects be used for stress testing purposes?
- Dataset and sample:
  - Supervisory reporting data of 54 large banks over 2004–2013.
  - Shared across supervisory agencies from six countries.
  - Strict confidentiality arrangements were in place.
- Empirical strategy:
  - Focus on the endogenous (two-way) interaction between solvency and funding costs.
  - Use a simultaneous equation approach with exogenous instrumental variables.
  - Rationale: OLS likely yields biased coefficients due to endogeneity between capital and funding costs; the direction of bias is theoretically ambiguous.
  - The authors note that OLS underestimates the impact of capital on funding costs in their findings.

### Main empirical findings
- Evidence supports joint determination of funding costs and bank solvency.
- Evidence of non-linear interactions between funding costs and solvency risk.
- The solvency–funding relationship has "not changed significantly during the crisis."
- Size of effects found:
  - "A 100 bps increase in regulatory capital is associated with a 105 bps decrease in funding costs."
  - This is large relative to the existing literature, where the effect "tends to be smaller, at an average of 50 basis points."
- The paper illustrates application of empirical results to inform stress testing projections using the 2014 EU-wide stress test exercise.

### Comparative literature summary (selected points preserved verbatim)
- Annaert et al. (2010): sample of 31 large euro area banks over 2004 through October 2008 — a one percentage point drop in weekly bank stock returns is associated with a 64 basis points rise in a bank’s CDS spread.
- Hasan et al. (2016): sample of 161 global banks from 23 countries over 2001–2011 — an increase of one percentage point in market-based leverage raises CDS spreads by an average of 101 basis points; rises to 103 basis points after 2007.
- Aymanns et al. (2016): solvency shock of 500 bps leads to an average increase in interbank funding cost of about 20 bps, with a peak impact of 40 bps in 2007.
- Babihuga and Spaltro (2014): panel of 52 banks in 14 advanced economies over 2001–2012 — in the long-run, a one percentage point increase in bank regulatory capital reduces funding costs by 26 basis points; in the short-term an increase in bank capital is associated with rising bank funding costs two quarters ahead.
- Gray et al. (2012): contingent claims analysis (CCA) approach — find non-linear relationship between market-based solvency and funding costs; under adverse scenarios FVCDS rises disproportionately relative to EDF.
- Pierret (2014): fixed-effect panel VAR on 49 U.S. banks over 2000–2013 — asymmetric relationship: higher solvency risk (SRISK) limits access to short-term funding; firms with more liquidity risk exposure have higher insolvency risk in a crisis.

### Implications for stress testing and policy
- Stress test models that ignore the dynamics between solvency and funding costs are likely to underestimate the impact of stress on bank solvency and financial stability.
- Two mechanisms highlighted:
  - Short-term back-book effect: higher funding costs erode capital buffers quickly.
  - Longer-term adverse dynamics: risk-sensitive investors demand higher compensation, lengthening persistence of funding shocks and further depleting capital.
- Application: use estimated solvency–funding interaction to adjust stress testing projections of bank capital ratios under stressed conditions (illustrated using the 2014 EU-wide stress test).

_Italic: Source — Content excerpt from wp17116 - References ________________________________________________________________40 (pdf: wp17116 - References ________________________________________________________________40)_

### 1.1 percentage points, suggesting that riskier banks find their access to wholesale markets

### wp17116 - 1.1 percentage points, suggesting that riskier banks find their access to wholesale markets limited.

### The relation between solvency risk and funding costs
- A sharp rise in bank funding costs can erode net interest income and adversely affect bank capital.
- The transmission channels are complex:
  - Banks may absorb higher funding costs, reducing profitability.
  - Banks may pass on costs to customers through higher lending rates, which can compress income if liabilities reprice faster than assets and demand for new lending falls.
- The effect of bank capital on funding costs is non-linear due to the short-put option embedded in bank assets and depends on scarcity effects, investors’ funding liquidity, and systematic risk factors.
- The section uses a reduced-form simultaneous equation approach with broad controls to calibrate solvency–funding cost interaction for supervisory stress tests.

### Construction of the new dataset
- Panel characteristics:
  - Unbalanced panel of 54 large banks from six countries.
  - Sample period: 2004Q4 to 2013Q4.
  - United States contribution: 33 banks.
  - Other contributors: six Austrian, six Canadian, six Dutch, and three Nordic banks.
- Data provenance:
  - Bank data shared among regulatory agencies under strict confidentiality and subject to filtering and quality checks.
  - Supervisory data based on reported regulatory balance sheets and include confidential supervisory information.

### Measurement choices and proxies
- Funding-cost proxy:
  - Marginal cost of long-term unsecured wholesale funding proxied by the five-year senior single name CDS spread for each bank.
  - Rationale: CDS liquidity higher for large international banks; CDS spreads are market-implied risk-neutral probabilities and not affected by changes in bond maturity structures.
  - Preference for five-year fair value CDS spreads over short-term funding measures because:
    - Short-term funding quotes often reflect quoted prices rather than transaction prices.
    - Counterparty risk perceptions often trigger volume reactions (shortening tenors or reducing lines) rather than higher rates.
    - Unconventional monetary policy (UMP) limited variation in short-term market rates; expected impact of UMP on analysis is limited.
  - Caveats acknowledged for CDS usage:
    - Market liquidity for CDS may be limited for some banks; addressed with bank-specific fixed effects.
    - CDS may not represent funding costs if a bank is shut out of markets, but they signal marginal shadow cost of funding.
    - CDS may reflect counterparty concerns over the issuer of protection; not expected to systematically bias spreads over the sample.
- Solvency proxy:
  - Core tier 1 ratio (CT1) chosen to reflect high-quality regulatory capital relative to risk-weighted assets.
  - CET1 not used because it was introduced only recently and not available for the sample period.
  - Alternative robustness check: expected default frequency (EDF) over five years estimated by Moody’s Credit Edge.
- Additional bank-specific variables included:
  - Loan loss provisions in percent of total assets (LLP) as asset quality proxy.
  - Net income in percent of total assets (NI) as proxy for return on assets and recapitalisation capacity.
  - Liquidity risk (LiRisk) defined as short-term wholesale debt (remaining maturity < three months) over stock of liquid assets (cash and central bank excess reserves, sovereign debt with risk-weights of 0 and 20 percent).
- Market and macro controls:
  - LIBOR-OIS spread as proxy for interbank market tensions.
  - Overnight index swap (OIS) to proxy monetary policy stance and UMP.
  - VIX index to proxy global risk aversion.
  - Crisis dummy (Crisis_d): 0 from 2004Q4 to 2008Q3; 1 from 2008Q4 to 2013Q4.
  - Country-level credit growth (loan_growth) to capture loan demand.
  - Regulatory capital swing dummy (ΔCT1_d): increase of CT1 by more than 20 percent quarter-on-quarter in nominal terms used to proxy deliberate management action (share issuance, asset sales, or public support).

### Identification and instrumental variables
- Instrument selection aims to satisfy exclusion restrictions: directly related to one endogenous variable and only indirectly related to the other via the first.
- Specification 1 instruments:
  - LLP used as instrumental variable in the CT1 equation (LLP directly affects CT1; affects FVCDS only indirectly via CT1).
  - NI used as exogenous variable in the solvency equation.
  - S&P (lag 1), sovereign CDS spread (CDS_gov), and LIBOR-OIS used for identification of the FVCDS equation (lagged S&P rating, CDS_gov, and LIBOR-OIS directly affect bank CDS spreads but not CT1).
- Specification 2:
  - Adds ΔCT1_d (deliberate management action dummy) in the CT1 equation; ΔCT1_d affects FVCDS only via CT1.

### Data features, summary statistics, and robustness checks
- Frequency harmonisation: empirical analysis focuses on quarterly data despite higher-frequency regulatory data for funding costs.
- Stationarity: meta unit root tests by Choi (2001) reject unit roots in most variables.
- Reported summary statistics and data points:
  - Most variables are denoted in percentage points, including CDS spreads.
  - Median CDS spread across all banks and the entire period: 131 bps.
  - EDF quartiles: 0.08 percent (first), 0.3 percent (second), 0.94 percent (third).
  - Correlation observations:
    - Regulatory and market-based measures of bank solvency have correlation coefficient below 10 percent.
    - EDF measures are more closely linked to other market-based measures including government CDS and S&P ratings.
    - Correlation between NI and LLP: 40 percent.
  - CT1 distribution over sample period (quartiles and central tendency):
    - First quartile (CT1): 7.89 percent.
    - Third quartile (CT1): 11.55 percent.
    - Mean (CT1): 10.5 percent.
    - Median (CT1): [value truncated in source text].
- Robustness approaches:
  - Separate estimations for pre- and post-Lehman sub-samples to check for regime shifts and stronger post-Lehman sensitivity of wholesale investors to solvency risk.
  - Alternative solvency measure (EDF) used to assess robustness to different bank resilience metrics.
- Miscellaneous data notes:
  - Potential impact of emergency liquidity assistance (ELA) on CDS spreads discussed; authors report confidence that no bank in sample received ELA.
  - Number of observations for the ΔCT1_d dummy across banks and quarters: 70 observations.
  - High correlation between VIX and LIBOR-OIS around Lehman is noted as an artifact of simultaneous spikes; otherwise they measure different phenomena.

*Source: wp17116 - 1.1 percentage points, suggesting that riskier banks find their access to wholesale markets limited.*

### 9.42 percent. The chart reveals banks’ efforts to build their capital buffers in the wake of the

### wp17116 - 9.42 percent. The chart reveals banks’ efforts to build their capital buffers in the wake of the

### Key empirical findings on solvency and funding costs
- Average CT1 ratios increased from 7.4 percent in 2007 to 13.7 percent in 2013.
- The CDS first quartile is located at 45 bps, the second quartile is located at 131 bps and the third quartile is located at 249 bps.
- Market-based measures for solvency and funding costs track each other closely; in periods of stress, CDS spreads react more strongly than EDF measures.
- Funding costs remained elevated after the financial crisis despite banks’ efforts to rebuild regulatory capital ratios, suggesting market-based hurdle rates may have increased post-crisis.
- The distribution of market-based measures has become wider relative to regulatory capital measures, indicating higher discrimination by investors across banks’ creditworthiness.
- Geographic evolution:
  - North American banks’ funding stress subsided following stronger regulatory capital ratios built after the crisis.
  - European banks experienced higher funding costs despite strong capital ratios, particularly during the sovereign debt crisis in 2012, pointing at adverse bank–sovereign dynamics.
- Post-crisis CT1 ratios are, on average, about 323 bps higher now than before the crisis.

### Methodological approach (simultaneous equation panel)
- Model estimated: YΓ = XB + U (structural form), rewritten in reduced form Y = XΠ + V.
- Y is a vector of two endogenous variables: solvency and funding costs.
- X includes bank-specific variables, country-specific variables, and global variables.
- Identification requires at least two exogenous sources of variation in bank solvency and funding costs.
- Estimation methods:
  - Two-stage least squares (2SLS): regress each dependent variable on all exogenous variables to obtain fitted values; then regress the other dependent variable on the fitted values plus exogenous variables.
  - Three-stage least squares (3SLS): combines 2SLS with seemingly unrelated regressions (SUR) to account for correlated errors.
- Diagnostic tests applied:
  - Relevance of instruments tested via F-statistic and p-value (weak instrument problem).
  - Instrument exogeneity tested via J-test and Lagrange multiplier test (LMF).
  - Endogeneity of RHS solvency and liquidity variables tested via regression-based Durbin-Wu-Hausman test.
  - Hausman overidentification test applied to choose between 3SLS and 2SLS.
- Comparison with OLS highlights substantial biases in OLS estimates for endogenous variables; OLS can produce counterintuitive positive correlations where simultaneous estimation yields negative relationships.

### Estimation results (regulatory solvency CT1 and CDS funding costs)
- Baseline specification (Specification 1): 782 observations from 38 banks.
  - A 100 bps increase in a bank’s CDS spread is associated with a reduction of a bank’s CT1 ratio by 32 bps.
  - The McElroy R² for the system is high at 90 percent.
- Funding cost equation:
  - A 100 bps higher CT1 ratio is associated with a decrease in bank funding costs by 105 bps (robust across specifications).
  - Net income (NI) has a statistically and economically significant impact on funding costs (higher NI → lower funding costs).
  - Sovereign risk (sovereign CDS) is significant, indicating a sovereign–bank nexus.
  - Bank rating is statistically significant with expected sign.
  - Tensions in interbank markets (LIBOR-OIS) increase bank funding costs.
  - Global risk aversion (VIX) is significant but with a negative sign attributed to correlation between LIBOR-OIS and VIX.
  - McElroy R² of 81 percent and adjusted R² of 82 percent for the funding-cost equation.
- Specification 2 (includes deliberate management capital increases and funding structure):
  - Sharp capital increases variable is not statistically significant.
  - Results for endogenous and other exogenous variables largely unchanged; CT1 coefficient in funding-cost equation slightly higher at -113 bps.
  - Interaction of FVCDS with share of short-term debt:
    - FVCDS coefficient in solvency equation increases to -1.1 from -0.32.
    - Interaction term is +0.06.
    - Example: An increase of FVCDS of 105 bps decreases CT1 by 100 bps if no short-term debt; with short-term debt at 10 percent of total assets (sample average), effect reduced by 60 bps to about 50 bps.
  - In funding equation CT1 coefficient changes to -0.87 from -1.13; VIX becomes insignificant; LIBOR_OIS coefficient decreases from 1.71 to 1.03; crisis dummy coefficient decreases from 2.97 to 1.97.
- Specification 3 (adds squared values of endogenous variables to capture non-linear effects, sign-preserving):
  - CT1 remains significant in funding-cost equation; CDS spreads remain significant in solvency equation.
  - No supporting evidence of non-linear effects between funding costs and regulatory capital.
  - Loan loss provisions coefficient becomes significantly higher.
- OLS vs. simultaneous system:
  - OLS yields statistically significant coefficients of 0.17 and 0.14 for CT1 and CDS spreads respectively in Specification 1, suggesting a positive relationship between funding costs and CT1 that contradicts simultaneous estimates.
  - For Specification 1 OLS coefficient of CDS in solvency equation: +0.14 (vs. -0.32 under simultaneous approach), indicating OLS underestimates the negative relationship.

### Robustness checks (market-based solvency measure EDF and liquidity risk)
- Use of EDF as solvency proxy (Table 6): 946 observations for 38 banks in six countries from 2004Q4 to 2013Q4.
- Specification 1 (EDF):
  - A 100 bps increase of CDS spreads is associated with an average increase in the EDF of 66 bps.
  - Provisioning ratio and loan growth are not statistically significant.
  - LIBOR-OIS and VIX included in solvency equations; both significant. VIX now has expected sign; LIBOR-OIS influences solvency negatively through funding costs.
  - Crisis dummy is statistically significant but has a negative sign (consistent with CT1 and EDF having different signs); after controlling for funding costs and market conditions, EDF is somewhat lower post-Lehman, reflecting high capitalization efforts.
  - R² is 78 percent for solvency equation; funding-cost equation R² is 77 percent.
  - McElroy R nearly 100 percent, suggesting specifications with market-based measures of solvency and liquidity may be less relevant than those with regulatory CT1.
- Specification 2 (management action variable included): This variable not statistically significant; coefficients and standard errors of LIBOR_OIS and VIX largely unaffected; crisis dummy not significant.
- Specification 3 (adds squared changes of endogenous variables):
  - Funding costs have a significant non-linear impact on the solvency equation: as funding costs increase, banks’ distance to default decreases, raising solvency risk.
  - Other coefficients remain similar.
- Diagnostics for EDF specifications:
  - Quality-of-instruments tests reject weak instruments in all equations.
  - J-Test and LMF tests generally fail to reject exogeneity of instruments (except FVCDS equation in Specification 3).
  - Durbin-Hausman-Wu test indicates endogeneity is less of an issue for EDF than for CT1 (significant only at 7 percent in one specification).
  - System overidentification tests favor 3SLS across EDF specifications.
- OLS comparison with EDF:
  - OLS coefficients underestimate the impact of solvency risk on funding costs across specifications, though to a smaller extent than in CT1-based results.
  - For Specification 1 the OLS coefficient of CDS in the solvency equation is 0.59 (below the simultaneous estimate reported in the robustness checks).

### Analytical implications and interpretation
- Solvency and funding costs are endogenously determined and contemporaneously interact; failing to account for this endogeneity leads to systematic and significant underestimation of the effects on solvency of funding shocks in stress tests.
- Market investors appear to price banks with greater discrimination post-crisis (wider distribution of market-based measures).
- The sovereign–bank nexus can produce episodes where strong regulatory capital does not insulate banks from higher funding costs (example: European banks in 2012).
- Management actions to raise capital show limited direct statistical significance in explaining endogenous dynamics once CT1 and funding costs are accounted for, but funding structure (share of short-term debt) materially moderates the transmission from funding-cost shocks to CT1.
- Non-linear effects are more evident when using market-based solvency (EDF) than regulatory solvency (CT1), implying market measures may be more sensitive to extreme funding-cost moves.

*Italic: Source — wp17116 (excerpt provided).*

### 0.66 estimate under the simultaneous panel approach.

### wp17116 - 0.66 estimate under the simultaneous panel approach.

### B. Introducing a Measure of Liquidity Risk
- Purpose:
  - Introduce a measure of liquidity risk (LiRisk) to control for banks’ liquidity risk bearing capacity and address how changes in maturity or composition of funding affect measures of default risk.
- Baseline specification (regulatory capital measure):
  - Coefficient on regulatory capital without liquidity measure: 1.048.
  - Coefficient on regulatory capital with liquidity measure: 1.028.
  - Statistical significance: remains significant at the 1 percent confidence level.
- Market-based solvency measure (EDF):
  - Coefficient on EDF before liquidity measure: 1.40.
  - Coefficient on EDF after liquidity measure: 1.37.
  - Statistical significance: remains significant at the 1 percent confidence level.
- Liquidity indicator:
  - Not statistically significant across specifications.
- Caveat:
  - A bank’s exposure to other risks may affect its liquidity; exposures can erode liquidity positions or affect funding costs, thereby increasing liquidity risk.

### VI. Application to Stress Testing
- Objective:
  - Apply the estimated relationship between solvency and funding costs to project banks’ capital ratios under stress and estimate the additional impact of endogenizing the solvency–funding cost channel.
- Stress test context:
  - Adverse macroeconomic scenario: ECB’s 2014 EU-wide stress test conducted by the European Banking Authority (EBA).
  - EU-wide stress test sample size: 124 EU banks.
  - Assumption: static balance sheet (no new growth; constant business mix and model).
  - Stress horizon: three years—i.e., 2014–2016.
- Sample used for illustration:
  - Of the 15 EU banks covered in the authors’ sample, 11 banks were also included in the EU stress test exercise; analysis focuses on this subset of 11 banks.
  - Aggregate CET1 ratio for the 11-bank subset at cut-off date: 14.5.
  - Aggregate CET1 ratio for the entire sample: 11.1 percent.
  - Impact of stress on capital ratios:
    - Subset of banks: 283 bps.
    - Entire population covered in the exercise: 270 bps.
- Assumptions and proxies:
  - Use coefficients from Specification 1 (Table 4) to endogenize banks’ funding costs.
  - Econometric results are in terms of CT1 rather than CET1; undisclosed CT1 for sub-sample expected to be close to CET1 because the weighted-sized gap between Tier 1 and CET1 stood at only 100 bps in 2013.
  - Assume average funding structure of the 11 banks is similar to the average bank in the 15-bank sample; note potential overestimation for retail-funded banks and underestimation for wholesale-funded banks.
- Estimated interaction framework (equations from the source):
  - Interaction expression (compact): ti fc ti titi FVCDSCT NICTFVCDS , , * , , 1 1     (presented in source as equation (3)).
  - Definitions:
    - * ,1 ti CT denotes bank i’s change in regulatory capital at time t excluding the interaction effect.
    - fc ti CT ,1 denotes the interaction effect.
    - α denotes the marginal effect of capital (net income) in the funding equation.
    - β denotes the marginal effect of net income (NI) in the funding equation.
    - δ denotes the marginal effect of funding cost in the capital equation.
  - Iteration forward (equation (4) in source) demonstrates that the interaction effect at time t carries forward to t+1 via its impact on *1,1   ti CT and therefore on 1,  ti FVCDS, producing a hysteresis effect in capital ratios.
  - Equation (4) (as presented in source) shows the multi-period cumulative terms and the compound interaction of β, δ, α across horizons, implying persistence of solvency shocks.
- Quantification for the 11 EU banks:
  - Starting inputs: individual bank projections of CET1 and net income ratio (NI) as projected by EBA in 2014.
  - Use estimated coefficients for NI and CT1 in the funding cost equation (FVCDS) to parameterize adverse dynamics and compute impact on capital ratios at end of stress horizon.
  - 2014 movements under the adverse scenario for the sample:
    - Weighted-average CET1 ratio decreases by 130 bps: from 14.5 percent in 2013 to 13.2 percent in 2014.
    - Average net income ratio (NI) falls by 40 bps: to -0.2 percent from 0.2 percent in 2013.
  - Given the estimated elasticities of funding costs to CT1 and NI:
    - The solvency shock triggers an increase in banks’ marginal wholesale funding cost of 160 bps in

*Source: wp17116 - 0.66 estimate under the simultaneous panel approach.*

### 2014. This shock generates a further reduction of banks’ capital ratios by 51 bps. The

### wp17116 - 2014. This shock generates a further reduction of banks’ capital ratios by 51 bps.

### Findings on solvency–funding cost interaction
- The interaction between solvency shocks and bank-specific funding costs materially amplifies capital depletion beyond macroeconomic stress alone.
- Macroeconomic stress reduces the aggregate capital ratio by 283 bps over 2014–2016.
- The overall impact, including the macro shock and the adverse dynamics of the solvency–funding cost nexus, reduces banks’ average capital ratio by 414 bps over 2014–2016.
- For the average bank in the sample, the interaction (feedback) effect on CET1 is:
  - 51 bps in 2014
  - 43 bps in 2015
  - 37 bps in 2016
- The relative impact of the interaction effect vis-a-vis the macro effect rises from 40 percent in 2014 to over 50 percent in 2016.
- The interaction effect in monetary units for the sample of banks triggers reductions in aggregate capital of:
  - €3.8 billion in 2014
  - €3.3 billion in 2014
  - €2.8 billion in 2014
  (reported as such in source text.)

### Bank-level heterogeneity and drivers
- Banks with shorter funding tenors, greater reliance on CDS-sensitive funding instruments (i.e., unsecured wholesale funding), and/or lower RWA to total assets ratios are more affected by the solvency → funding-cost feedback.
- Weaker banks tend to post higher RWAs, magnifying capital losses in monetary terms.
- In a crisis, wholesale funding tends to shift to shorter-dated tenors, increasing rollover needs at higher funding rates and potentially worsening the interaction.

### Stress-test application (2014 EBA exercise)
- Incorporating the dynamic solvency–funding cost interaction into the 2014 EU-wide stress test indicates stressed capital ratios could be depleted by a further half of the capital shortfall estimated in the original EBA analysis.
- Figure 3 decomposition (basis points) shows by year:
  - 2014: Solvency–funding nexus: -51; Macro effect: -131; Overall effect: -182
  - 2015: Solvency–funding nexus: -43; Macro effect: -85; Overall effect: -128
  - 2016: Solvency–funding nexus: -37; Macro effect: -67; Overall effect: -104
- Table 14 reports bank-level estimated impacts (basis points) of funding-cost ↔ CET1 interactions and corresponding Δ Funding Costs and Δ CET1 for individual banks under the adverse scenario (table entries preserved as reported).

### Methodology and robustness
- Empirical strategy: 3SLS simultaneous equation approach (and 2SLS specifications reported), exploiting a newly constructed dataset based on high-quality supervisory data (quarterly data from 2004Q4 to 2013Q4).
- Results indicate a larger impact of solvency on funding costs than previous OLS-based studies; OLS estimates tend to underestimate the solvency–liquidity interaction nexus.
- Stability of coefficients confirmed across alternative measures of solvency risk and banks’ capacity to bear liquidity risk.
- Specification and instrument quality tests reported (F statistics, J tests, LMF tests, Hausman tests); robustness checks reported across multiple tables and specifications, including controls for liquidity risk (LiRisk) and OLS comparisons.
- Authors caution results should be interpreted with care given instrument selection and remaining endogeneity concerns; they recommend further research using larger high-quality samples and broader instruments.

### Policy implications and recommendations
- Incorporating solvency–liquidity interactions in supervisory stress-test models is quantitatively relevant and can substantially alter estimated capital shortfalls.
- The cumulated interaction effect has implications for cost–benefit assessments of capital regulation: higher capital requirements’ costs are partly offset by lower debt servicing costs through a mitigated solvency–funding feedback.
- The analysis supports calibrating the solvency–funding nexus effect in quantitative cost–benefit analyses of bank regulation.
- Recommendation: incorporate solvency and liquidity interactions in the design of prudential regulation and in stress-testing frameworks to better capture amplification channels evident during systemic stress.

*Source: Author's calculations using EBA's stress test results and estimation results (excerpt from wp17116).*

### REFERENCES

### REFERENCES

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### Econometrics, panel data, and GMM methodology
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- _________________ and O. Bover (1995), “Another look at the instrumental variable estimation of error-components models” Journal of Econometrics, 68 (1), 29–51.
- Bhargava, A. (1991), Identification and panel data models with endogenous regressors. Review of Economic Studies, 58 (1), 129–140.
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- McElroy, M. B (1977), Goodness of Fit for Seemingly Unrelated Regressions. Journal of Econometrics, 6, 381–387.
- Nickell, S. (1981), “Biases in dynamic models with fixed effects,” Econometrica, 49(6), 1417–1426.
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- Staiger, D., J. H. Stock (1997), “Instrumental Variables Regression with Weak Instruments,” Econometrica, 65 (3), 557–586.

### Banking, liquidity, solvency, stress testing, and CDS research
- Aymanns, C., Caceres, C., Daniel, C., and Schumacher, L., (2016), “Bank Solvency and Funding Costs”. IMF Working Paper WP/16/64, Washington D.C.
- Babihuga, Rita and Marco Spaltro (2014), “Bank Funding Costs for International Banks,” IMF Working Paper, April 2014.
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- ___________ (2013b), “Literature review of factors relating to liquidity stress—extended version,” Working Paper 25.
- ___________ (2015), “The interplay of accounting and regulation and its impact on bank behavior: Literature review,” Working Paper 28.
- Cetina, J. (2015), “Incorporating Liquidity Shocks and Feedbacks in Bank Stress Tests,” OFR Brief Series, July.
- European Banking Authority (2014a), “Methodological Note EU-Wide Stress Test 2014”.
- _____________ (2014b), “2014 EU-Wide Stress Test Results” at http://www.eba.europa.eu/risk-analysis-and-data/eu-wide-stress-testing/2014/results
- Gray, D., Wehrhahn, R., and Savage, L. (2012), Israel: Technical Note on Stress Test of the Banking, Insurance, and Pension Sectors, IMF Country Report No. 12/88.
- Pierret, D. (2014), “Systemic risk and the solvency-liquidity nexus of banks,” International Journal of Central Banking, 11 (3), 193–227.
- Puhr, C. and S. W. Schmitz (2014), “A view from the top – the interaction between solvency and liquidity stress,” Journal of Risk Management in Financial Institutions, 7 (1), 38–51.
- Schmitz, S. W. (2013), The Impact of the Liquidity Coverage Ratio (LCR) on the Implementation of Monetary Policy. Economic Notes 42 (2), 135–170.
- Valderrama, L., (2017), “An Agent-Based Model for Stress Testing,” IMF WP forthcoming.
- Cetina, J. (2015), “Incorporating Liquidity Shocks and Feedbacks in Bank Stress Tests,” OFR Brief Series, July.
- Distinguin, I., Roulet, C. and A. Tarazi, (2013), “Bank Regulatory Capital and Liquidity: Evidence from US and European Publicly Traded Banks,” Journal of Banking and Finance 37 (9), 3295–3317.
- Annaert, J., M. De Ceuster, P. Van Roy and C. Vespro (2013), “What determines euro area bank CDS spread?” Journal of International Money and Finance 32, 444–461
- Hasan, I., Liu, L. and G. Zhang (2016), “The Determinants of Global Bank Credit-Default-Swap Spreads,” Journal of Financial Services Research (forthcoming).
- Ericsson, J., Jacobs, K., and Oviedo, R., (2009), “The determinants of credit default swap premia,” Journal of Financial and Quantitative Analysis, 44 (2), 109–132.
- Hull, J. A. White (2000), Valuing Credit Default Swaps I: No Counterparty Default Risk, Journal of Derivatives, 8 (1), 29–40

### Technical reports, working papers, and methodologies
- Aymanns, C., Caceres, C., Daniel, C., and Schumacher, L., (2016), “Bank Solvency and Funding Costs”. IMF Working Paper WP/16/64, Washington D.C.
- Babihuga, Rita and Marco Spaltro (2014), “Bank Funding Costs for International Banks,” IMF Working Paper, April 2014.
- European Banking Authority (2014a), “Methodological Note EU-Wide Stress Test 2014”.
- _____________ (2014b), “2014 EU-Wide Stress Test Results” at http://www.eba.europa.eu/risk-analysis-and-data/eu-wide-stress-testing/2014/results
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- Valderrama, L., (2017), “An Agent-Based Model for Stress Testing,” IMF WP forthcoming.

*Source: wp17116 - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17116.pdf_