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---

### Measure and methodology
- Introduces the information-production ratio (푖푖푖푖푖푖_t) constructed as the cross-sectional standard deviation of credit default swap (CDS) spreads of financial companies relative to nonfinancial companies.
- The 푖푖푖푖푖푖_t is distinct from average CDS spreads—the two are uncorrelated.
- Investors modeled as using a basket of reference securities as a proxy for banks’ solvency when direct information is scarce; a shrinkage regression (LASSO) is applied to select reference securities that explain most variation in banks’ CDS returns.
- Theoretical framework (based on Dang et al. (2017) modified): private-information incentive 훹훹 = 푘푘 − 푒푒 + 휔휔 − 훾훾/푑푑 and investors infer bad-state probability 푑푑 = 푤푤푑푑_a + (1−푤푤)푑푑_r, with 푑푑_r ≥ 푑푑_a. Equation 3: 훹훹 = 푘푘 − 푒푒 + 휔휔 − 훾훾/(푤푤푑푑_a + (1−푤푤)푑푑_r).
- Definition and calculation:
  - 휎휎_{t,FIN} = cross-sectional standard deviation of CDS spreads across financial firms on day t (equation 4).
  - Analogous nonfinancial measure 휎휎_{t,NONFIN}.
  - Information-production ratio: 푖푖푖푖푖푖_t = 휎휎_{t,FIN} / 휎휎_{t,NONFIN} (equation 5).
  - Innovations estimated from AR(1) over daily data 2006–2014 and converted to growth rates (equations 6–7).
- Data:
  - Euro-denominated five-year CDS contracts for senior, unsecured debt with MM/MM14 clauses; U.S. sample uses dollar-denominated contracts with MR/MR14 and Markit rating requirement.
  - Source datasets: Markit and Bloomberg.
  - Sample size: roughly 3.4 million day-firm observations, of which 1.2 million are financial companies.
  - Senior secured debt not used due to sparsity: only 25,000 observations for financials, with only 13 data points available before 2007.

### Reference-security modelling and selection
- Hypothesis: when bank-specific information is scarce, investors infer bank solvency from a portfolio of reference-security returns; bank-CDS portfolio returns modeled as linear combination of N reference-security returns (equation 10).
- LASSO implementation:
  - Reasons: OLS impractical with many candidate securities relative to time dimension.
  - Model selection: extended Bayesian information criterion.
  - Separate LASSO runs on three samples: pre-crisis (before June 1, 2007), global financial crisis (June 1, 2007 to July 1, 2009), European debt crisis (July 1, 2009 to April 1, 2014).
- Candidate reference securities (27) include:
  - Equity indices: S&P 350 Europe, Euro Stoxx 50, FTSE 100, CAC 40, DAX, IBEX 35, FTSE MIB, PSI All-Share, ISEQ Overall, ASE General.
  - Real estate: S&P Europe Property, S&P Europe REIT.
  - Sovereign bonds: Bloomberg-Barclays TR indices for Portugal, Ireland, Italy, Greece, Spain, Germany.
  - FX: EURUSD, GBPUSD.
  - Fixed income: iBoxx Euro Collateral Overall, iBoxx Euro Overall, iBoxx Corporate BBB, iBoxx Corporate AAA.
  - CDS: iTraxx Europe five-year TR.
  - Monoline insurers: Syncora, MBIA.
- Findings on selected betas:
  - Pre-crisis: iTraxx beta = 0.16 (dominant).
  - Global financial crisis: iTraxx 0.52, iBoxx BBB 0.28, Greek sovereigns 0.09, iBoxx AAA 0.08, German bunds −0.36.
  - European debt crisis: Spanish sovereigns 0.04, Irish sovereigns 0.03, iBoxx beta shifts to −0.19, bund beta −0.07; periphery equity indices and S&P Europe Property enter with smaller betas.
- Model-evaluation steps:
  - Growing window-rolling regression to estimate predicted bank-CDS returns and residuals.
  - Average daily residual ε̅_t = (1/N) Σ_{F=1}^{N} (i_{F,t}^{CDS} − î_{F,t}^{CDS}) (equation 12).
  - Two-variable VAR over June 2007–April 2014 with variables (푖푖푖푖푖푖_t_Δ, ε̅_t) and 15-trading-day lags (equation 13).

### Key empirical findings and evolution of information production
- Levels and spikes:
  - Pre-crisis average in 2006: about 0.6.
  - Jump to 5.6 on October 7, 2008.
  - Local maximum of 2.9 in February 2011.
  - Information production in the financial sector grew 22 times its 2006 average immediately after Lehman and settled around 7 times at end-2008, while nonfinancial sector production only doubled.
- Regional patterns:
  - United Kingdom: spikes in late 2008 and 2009; stabilizes at triple the pre-crisis average.
  - Periphery: low in initial GFC stages; spikes in early 2011.
  - Core Europe: dramatic spike in October 2008; otherwise low except late 2011 blip.
  - United States: spike in 2008 and another in 2010 before slow recovery.
- Properties of 푖푖푖푖푖푖_t:
  - Discriminates financial-crisis information production from adverse real shocks.
  - Cross-sectional variation in CDS spreads increases in bad states as average CDS spread rises; regressions show a strong positive relationship in every region.
  - 푖푖푖푖푖푖_t is novel and uncorrelated with average CDS spreads, market returns, and several common cyclical measures (European VIX, 10-year Spanish-Bund spread, Bloomberg European Financial Conditions index, various Libor spreads). No relationship at the 5-percent level with major equity indices; European bank index correlated at the 10-percent level.

### Event-study results: abnormal information production and interventions
- Framework: event studies measure abnormal information production (푖푖푖푖푖푖_t_Δ) in the five trading days after policy events using 푖푖푖푖푖푖_t_Δ = 훼 + 훽·핀핀(Event_t) + year fixed-effects + ε_t (equation 8); 핀핀(Event)=1 in the five days following the event.
- Stress tests:
  - U.S. 2009 stress test: announcement associated with −5.7 percent average abnormal information production; results associated with −12.1 percent average abnormal information production.
  - An average daily 푖푖푖푖푖푖_t_Δ of −12.1 percent corresponds to an approximately 60 percent cumulative reduction in information production.
  - European stress tests: Europe-wide effects −2.3 percent (2010) and −2.1 percent (2012).
    - Heterogeneity: periphery reductions −3.9 percent and −3.7 percent; core increases 1.9 and 9.8; United Kingdom flat; U.S. fall only after 2012 test.
- Other intervention types:
  - Capital injections: average reduction −4.7 percent across all countries; −9.5 percent in Europe; −0.9 percent in the United Kingdom.
  - Open-market/asset-purchase: ECB August 2011 bond purchase program −14.6 percent; TALF and QE had smaller but significant reductions.
  - BNP suspension of redemptions and initial August 2007 liquidity provision led to an increase of 12.6 percent in information production.
  - Periphery interventions (Greece May 2010 and July 2011, Ireland November 2010, Portugal May 2011) generally reduced information production; significance mainly for 2010 interventions.
- Aggregate interpretation:
  - Capital injections and periphery-targeted policy responses reduced abnormal information production on average; other intervention types show mixed or region-specific effectiveness.
  - "The devil is ultimately in the details": similar intervention types can yield widely different effects depending on credibility, institutional context, and design features.

### VAR, model residuals, and investor behavior
- Impulse-response findings:
  - An impulse to the model residual when the model is pessimistic relative to realized returns leads to a reduction in information production.
  - The model residual is persistent in sign.
  - Authors interpret persistence and post-surprise declines in 푖푖푖푖푖푖_t as evidence that investors prioritize tail risk (downside risk) over model accuracy per se.

### Information production, bank outcomes, and fiscal costs
- Country-level regressions:
  - Cost/GDP_{F,t} = 훼 + 훽1 푖푖푖푖푖푖_{F,t−1} + 훽2 푖푖푖푖푖푖_{F,t−1}^2 + ε_{F,t} (equation 14).
  - Sample: 14 countries each with eight years of observations (Austria, Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, United Kingdom).
  - Including the squared centered term shows the effect is exponential.
  - With country fixed-effects the squared effect remains significant and positive.
- Magnitude example:
  - The standard deviation of 푖푖푖푖푖푖_{t−1} is 0.95, so an 푖푖푖푖푖푖_{t−1} one standard deviation above average predicts a cost of financial intervention in the next year of 0.68 percent of GDP.
- Bank-level effects (Table 8 summaries):
  - When Europe-wide 푖푖푖푖푖푖_{t−1} is one unit higher:
    - funding falls the next semiannual period by 1.0 percent,
    - gross loans fall by 0.8 percent,
    - total assets fall by 1.1 percent,
    - total equity falls by 0.9 percent.
  - Interpretation: higher 푖푖푖푖푖푖 implies deleveraging—assets fall faster than equity—leading to credit contraction to the real economy.

### COVID-19 findings (through August 2020)
- Method: 푖푖푖푖푖푖_t calculated for Europe and the United States requiring firms to report CDS spreads each day of 2019 and 2020 through August 2020.
- Observations:
  - COVID-19 did not begin as a financial crisis: cross-sectional variance across nonfinancial companies increased dramatically in March 2020 and remains elevated.
  - 푖푖푖푖푖푖_t fell in the United States and Europe (including the United Kingdom).
  - As of August 2020, the cross-sectional standard deviation of nonfinancial companies is roughly 10 times its level at the beginning of the year, whereas financials are only 13 percent higher.
- Conclusion: decline in 푖푖푖푖푖푖_t reflects the fundamentally nonfinancial origin of the shock.

### Policy implications and transmission channels
- Policymakers’ information management is "first-order important" during financial crises; maintaining information insensitivity of safe assets supports trust and financial lubrication.
- Interventions can affect information production via four transmission channels (motivated by Equation 3):
  - Increase monitoring cost (훾훾↑), e.g., short-sale bans that raise monitoring costs.
  - Reduce reliance on reference-security signals by making bank exposures more transparent (increase 푤푤 toward actuarial-based 푑푑_a), e.g., credible stress tests.
  - Reduce the reference security’s implied bad-state probability (푑푑_r↓) by interventions that lower liquidity premia (e.g., asset liquidity facilities).
  - Reduce actuarial bad-state probability (푑푑_a↓)—harder to target directly and dependent on broader economic context.
- Empirical policy takeaways:
  - Stress tests can be effective but heterogeneous: country-level stress tests (2009 U.S.; 2010 and 2012 Europe) reduced information production in targeted jurisdictions; aggregate effects can differ.
  - Capital injections and periphery-targeted public interventions reduced abnormal information production in empirical tests.
  - Asset-purchase programs can set a floor on information-sensitive asset prices, implicitly managing information by affecting market prices.
  - Credibility, institutional context, and design detail determine effectiveness.

### Conceptual insights and puzzles
- Investors use observable reference securities to infer bank solvency when direct balance-sheet information is infrequent or coarse; this can cause overestimation of losses because market prices embed both credit fundamentals and liquidity premia.
- Persistent model error in reference-security regressions and the observed decline in information production following positive model surprises suggest investors weight tail risks more heavily than model accuracy.

### Conclusion and practical use
- Information production (푖푖푖푖푖푖_t) is a useful tool:
  - As a quantitative ex-post policy evaluation metric.
  - As an ex ante indicator of crisis.
  - As a predictor of adverse real outcomes for the banking system and fiscal costs.
- Monitoring 푖푖푖푖푖푖_t can give early signals of credit contraction and potential fiscal costs; policymakers should design interventions that address investors’ tail-risk perceptions to reduce information production on average.

*Source: wpiea2021005-print-pdf (canonical URL: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021005-print-pdf.pdf)*

### References _____________________________________________________________ 23

### wpiea2021005-print-pdf - References _____________________________________________________________ 23

### Measure and methodology
- Introduces the information-production ratio (푖푖푖푖푖푖_t) constructed as the cross-sectional standard deviation of credit default swap (CDS) spreads of financial companies relative to nonfinancial companies.
- The 푖푖푖푖푖푖_t is distinct from average CDS spreads—the two are uncorrelated.
- Investors are modeled as using a basket of reference securities as a proxy for banks’ solvency when direct information is scarce; a shrinkage regression is applied to select reference securities that explain most variation in banks’ CDS returns.
- Theoretical framework (based on Dang et al. (2017) modified): private-information incentive 훹훹 = 푘푘 − 푒푒 + 휔휔 − 훾훾/푑푑 and investors infer bad-state probability 푑푑 = 푤푤푑푑_a + (1−푤푤)푑푑_r, with 푑푑_r ≥ 푑푑_a. Equation 3: 훹훹 = 푘푘 − 푒푒 + 휔휔 − 훾훾/(푤푤푑푑_a + (1−푤푤)푑푑_r).

### Key empirical findings
- Relative information production for the banking sector spiked 22 times after the Lehman Brothers’ bankruptcy in 2008, fell in intervening years, and surged again during the European debt crisis.
- The 2010 and 2012 European stress tests were associated with a large reduction in information production in periphery countries; this large reduction did not hold at the aggregate Europe-wide level.
- The 2009 U.S. stress tests are linked to a substantial decline in abnormal information production.
- Capital injections and interventions in European periphery countries reduced abnormal information production; other intervention types did not have a statistically significant effect.
- Reference securities selected differ by crisis:
  - Global financial crisis selections include: iTraxx 5y, iBoxx BBB Europe, Greek government bonds, and German Bunds.
  - European debt crisis selections include: Irish and Spanish sovereign bonds, and periphery equity indices.
- In a vector autoregression, information production falls when realized returns exceed the reference-security model’s expectation; the model error is persistent in sign.
- COVID-19 effects as of August 2020:
  - The cross-sectional standard deviation of nonfinancial companies is roughly 10 times its level at the beginning of the year.
  - Financials are only 13 percent higher as of August 2020.
- Link to government intervention costs and bank outcomes:
  - A unit higher level of the polynomial 푖푖푖푖푖푖_{t−1}^2 within a country predicts a 1.3 percentage point increase in financial intervention costs the following year as a share of that country’s GDP.
  - For European banks, a one-unit higher level of information production in the preceding year is associated with subsequent-year changes of:
    - bank lending: contraction of 0.8 percent,
    - total assets: contraction of 1.1 percent,
    - total equity: contraction of 0.9 percent.

### Policy implications and channels
- Policymakers’ information management is "first-order important" during financial crises; maintaining information insensitivity of safe assets supports trust and financial lubrication.
- Interventions can affect information production via four transmission channels (discussion begins in the text and is motivated by Equation 3); examples include:
  - Increasing the cost of monitoring banks (훾훾↑), e.g., short-sale bans that raise monitoring costs.
  - Reducing reliance on reference-security signals by making bank exposures more transparent (increasing 푤푤 toward actuarial-based 푑푑_a), e.g., credible stress tests.
  - Asset purchase programs can set a floor on information-sensitive asset prices, implicitly managing information by affecting market prices.
  - Capital injections and public interventions in periphery countries reduced abnormal information production in empirical tests.
- The effectiveness of stress tests is heterogeneous: country-level stress tests (e.g., 2010 and 2012 Europe; 2009 U.S.) reduced information production in targeted jurisdictions, but aggregate effects can differ.

### Conceptual insights and puzzles
- Investors use observable reference securities to infer bank solvency when direct balance-sheet information is infrequent or coarse; this creates potential overestimation of losses because market prices embed credit fundamentals and liquidity premia.
- Persistent model error in reference-security regressions and the observed decline in information production following positive model surprises suggests investors focus more on tail risk than on model accuracy per se.

_Original content: wpiea2021005-print-pdf (canonical URL: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021005-print-pdf.pdf)_

### 2008. Second, officials can reduce investor’s beliefs about the reference security’s efficacy

### wpiea2021005-print-pdf - 2008. Second, officials can reduce investor’s beliefs about the reference security’s efficacy

### Channels to reduce reliance on a reference security
- (1−푤푤 ↓): examples include policies such as widespread use of funding guarantees (the FDIC’s “Debt Guarantee Program”) or capital backstops (the U.S. Treasury’s “Capital Assistance Program”).
- Reduce the probability of the bad state implied by the reference security (푑푑
푟푟
↓) via interventions that reduce fire-sales and information production by lowering the liquidity premium, which investors may erroneously infer to be equivalent to solvency—so long as the bank remains a going concern.
  - Example: Ashcraft, Malz, and Pozsar (2012) show that the Federal Reserve’s Term Asset-Backed Securities Loan Facility improved ABS liquidity.
- Reduce the actuarial probability of the bad state (푑푑
푎푎
↓). The fourth channel is harder to target with any specific policy and depends on the broader economic context.

### III. METHODOLOGY AND DATA — A. Measuring Information Production
- Daily information production measured using the cross-sectional standard deviation of credit default swap (CDS) spreads for senior unsecured debt of financial companies relative to nonfinancial companies.
- New measure: the “information-production ratio” (푖푖푖푖푖푖
푡푡
).
- Rationale:
  - CDS spreads reflect market expectations of default probabilities.
  - Senior debt is more information-insensitive than equity; in low payoff states senior debtholders have limited incentives to acquire information (Dang et al. (2015)).
  - Equity is information-sensitive and facilitates price discovery (Holmström (2015)).
- Data:
  - Euro-denominated five-year CDS contracts for senior, unsecured debt on nongovernment entities with modified-modified restructuring (MM and MM14) clauses.
  - All data sourced from Markit and Bloomberg.
  - Sample includes roughly 3.4 million day-firm observations, of which 1.2 million are financial companies.
  - Senior secured debt not used due to sparsity: only 25,000 observations for financials, with only 13 data points available before 2007.
  - Firm inclusion requirement: full year of CDS spreads reported in 2006.
  - U.S. sample uses dollar-denominated contracts with modified-restructuring clauses (MR and MR14) and requires that the contract has a Markit rating.
  - Additional data: price and return data from Bloomberg and bank-specific balance sheet information from Fitch.
- Calculation steps:
  - Cross-sectional standard deviation of CDS spreads across financial companies on a given day, denoted 휎휎
푡푡,퐹퐹퐹퐹퐹퐹푎푎  퐹퐹퐹퐹퐹퐹 푎푎퐹퐹퐹퐹:
    - 휎휎
푡푡,퐹퐹퐹퐹퐹퐹푎푎  퐹퐹퐹퐹퐹퐹푎푎퐹퐹퐹퐹 = �1
푛푛 �(퐹퐹
퐶퐶퐶퐶푆푆
퐹퐹,푡푡
−휇휇
퐹퐹,푡푡
)2  (4)
    - where CD푆푆
퐹퐹,푡푡 is the CDS spread for financial company 푖푖, 푛푛 is the number of financial companies, and 휇휇
퐹퐹,푡푡 is the average CDS spread across financial companies on day 푖푖.
  - Equivalent nonfinancial measure: 휎휎
푡푡,푁푁푁푁 퐹퐹−푓푓퐹퐹퐹퐹푎푎퐹퐹퐹퐹퐹퐹푎푎퐹퐹퐹퐹.
  - Information-production ratio defined as:
    - 푖푖푖푖푖푖
푡푡
=
휎휎
푡푡,퐹퐹퐹퐹퐹퐹푎푎  퐹퐹퐹퐹퐹퐹 푎푎퐹퐹퐹퐹
휎휎
푡푡,푁푁푁푁 퐹퐹−푓푓퐹퐹퐹퐹푎푎퐹퐹퐹퐹퐹퐹푎푎퐹퐹퐹퐹  (5)
- Linking incentives to observed information production:
  - Cannot directly measure 훹훹 (incentive to acquire private information); assume 훹훹
푡푡 is affine in 푖푖푖푖푖푖
푡푡:
    - 훹훹
푡푡
=푎푎+푏푏(푖푖푖푖푖푖
푡푡) (6)
  - Estimate innovations to 푖푖푖푖푖푖
푡푡 based on residual from AR(1) estimated from daily data 2006–2014:
    - 푖푖푖푖푖푖
푡푡
=휌휌
0
+휌휌푖푖푖푖 푖푖
푡푡−1
+푢푢
푡푡
  - Convert innovations to growth rate as:
    - 푖푖푖푖푖푖
푡푡
훥훥
=
푢푢
푡푡
푖푖푖푖푖푖
푡푡−1
 (7)
- Empirical observations:
  - Information production controls for relative change vs. nonfinancial sector; high relative growth signals elevated risks of bank-runs and safe asset destruction.
  - Information production in the financial sector (휎휎
푡푡,퐹퐹퐹퐹퐹퐹푎푎  퐹퐹퐹퐹퐹퐹 푎푎퐹퐹퐹퐹
) grew 22 times its 2006 average immediately after Lehman and settled around 7 times at end-2008, while nonfinancial sector production only doubled.

### Three properties of the information-production ratio (푖푖푖푖푖푖
푡푡
)
- First: permits discriminating information production during financial crises from that during episodes of adverse real shocks; consistent with Muir (2015) and Krishnamurthy and Muir (2015).
- Second: cross-sectional variation in CDS spreads increases in bad states as average CDS spread rises; empirical support:
  - Table 3: regressions of changes in 휎휎
푡푡,퐹퐹퐹퐹퐹퐹푎푎  퐹퐹퐹퐹퐹퐹 푎푎퐹퐹퐹퐹 on changes in average financial CDS spreads show a strong positive relationship in every region.
  - Last five columns: regressions with dependent variable 푖푖푖푖푖푖
푡푡
훥훥 show positive significant relationships between changes in average bank CDS spreads and innovations to the information-production ratio in all regions except the United Kingdom.
- Third: 푖푖푖푖푖푖
푡푡 is novel and not a restatement of average CDS spreads, market return, or other common cyclical measures.
  - Regressing 푖푖푖푖푖푖
푡푡 on CDS spreads shows no statistically significant relationship.
  - Table 4: no statistically significant relationship between 푖푖푖푖푖푖
푡푡
훥훥 and changes in:
    - European VIX
    - 10-year Spanish-Bund spread
    - Bloomberg European Financial Conditions index
    - slope of overnight to three-month Libor curve
    - Libor-OIS three-month spread
  - No relationship between 푖푖푖푖푖푖
푡푡
훥훥 and the S&P 350 Europe, the FTSE100, the S&P 500, or bank equity indices for Europe, the United Kingdom, and the United States at the 5-percent level; only the European bank index is correlated at the 10-percent level.

### III. METHODOLOGY AND DATA — B. Abnormal Information Production and Policy Responses
- Approach: event studies to measure abnormal information production (푖푖푖푖푖푖
푡푡
훥훥) in the five trading days after policy events.
- Policy event types tested:
  - stress tests
  - capital injections
  - institution-specific interventions
  - open market operations and asset purchase programs
  - important country-specific events
- Estimation of abnormal information production by intervention type and averaged across countries and interventions.
- Event-study regression specification:
  - 푖푖푖푖푖푖
푡푡
훥훥
=훼훼+훽훽핀핀(Event푡푡)+휃휃
푡푡
+휀휀
푡푡  (8)
    - 핀핀(Event) = 1 if date 푖푖 is in the five days following the event, 0 otherwise.
    - 휃휃
푡푡 are year fixed-effects.
  - Null hypothesis: the event creates no cumulative incentive for information production over the following five days, so ∑
푖푖푖푖푖푖
푡푡
훥훥5
푡푡=1
=0.
  - Interpretation: 훽훽>0 implies increased average information production; 훽훽<0 implies a decrease.
- Tests run separately for regions: Europe, core Europe, periphery Europe, the United Kingdom, and the United States.
- Empirical note: because 푖푖푖푖푖푖
푡푡
훥훥 is estimated as the residual from an AR(1), 피피[푖푖푖푖푖푖
푡푡
훥훥] =0 over the full sample. The average Europe-wide 푖푖푖푖푖푖
푡푡
훥훥 is nearly zero at −0.006 over the full sample, but averages vary by year.

*Italic: Content summarized from wpiea2021005-print-pdf - 2008. Second, officials can reduce investor’s beliefs about the reference security’s efficacy*

### 0.027 in 2011 and −0.039 in 2014. Since we are specifically interested in the effect a single

### wpiea2021005-print-pdf - 0.027 in 2011 and −0.039 in 2014. Since we are specifically interested in the effect a single

### Methodology: event studies and identification
- Event-study framework compares 푖푖푖푖푖푖푡푡훥훥 in the time-series because no cross-section is available.
- Implicit assumption: markets digest news about interventions within five days; alternative horizons do not qualitatively change results.
- Year fixed-effects are included to isolate the effect of a single intervention on information production from broader trends.
- Measurement error is higher for periods with many successive interventions (notably September and October 2008) because policies occurring within the same five-day window cannot be separately identified.

### Testing the reference-security view of crises
- Hypothesis: when investors lack bank-specific information, they infer bank solvency from a basket of reference securities that should explain most variation in banks’ CDS returns.
- Analytical set-up:
  - Investors infer probability of a bad state dr in equation 3 from a linear transformation of a portfolio return on bank CDS: 푖푖푑푑푡푡푟푟 = 훾0 + 훾1 푖푖푡푡CDS (equation 9).
  - Bank-CDS portfolio returns are modeled as a linear combination of N reference-security returns (equation 10): 푖푖푡푡CDS = 훼 + Σ_{j=1}^{N} 훽_j 푖푖_{j,tt}ref + 휀t.
- Rationale: functional form motivated by affine multifactor models (Fama French (1993), Adrian et al. (2014), He et al. (2017)).

### Reference-security selection: LASSO implementation and samples
- OLS impractical when the number of candidate securities is large relative to the time dimension; therefore the least absolute shrinkage and selection operator (LASSO) is used to identify a parsimonious subset of descriptive securities.
- Extended Bayesian information criterion used to select the optimal LASSO model.
- Separate LASSO runs on three samples:
  - Pre-crisis: before June 1, 2007.
  - Global financial crisis: June 1, 2007 to July 1, 2009.
  - European debt crisis: July 1, 2009 to April 1, 2014.
- Dependent variable: panel of short CDS returns for financial companies, where CDS spreads are translated to returns using equation (11):
  - 푖푖_{F,t}^{CDS} = −1 × [ (CDS_{F,t} − CDS_{F,t−1})/250 + CDS_{F,t} × RPV01_{t−1} ] (as specified in source).
  - RPV01 is the risky present value of one basis point using a linearly interpolated Euribor swap curve.

### Candidate reference securities (27)
- Equity: S&P 350 Europe, Euro Stoxx 50, FTSE 100 (United Kingdom), CAC 40 (France), DAX (Germany), IBEX 35 (Spain), FTSE MIB (Italy), PSI All-Share (Portugal), ISEQ Overall (Ireland), ASE General (Greece).
- Real Estate: S&P Europe Property, S&P Europe REIT.
- Sovereign Bonds: Bloomberg-Barclays All Bonds Total Return indices for Portugal, Ireland, Italy, Greece, Spain, and Germany.
- Exchange Rates: EURUSD, GBPUSD.
- Fixed Income: iBoxx Euro Collateral Overall, iBoxx Euro Overall, iBoxx Corporate BBB, iBoxx Corporate AAA.
- CDS: iTraxx Europe five-year total return.
- Monoline Insurers: Syncora, MBIA.
- Data notes: all indices are total return indices and converted to euro-denominated terms if not originally in euros; American equity returns and monolines are lagged by one day.

### Evaluating model accuracy and dynamics
- After LASSO selection, a growing window-rolling regression is used to estimate predicted bank-CDS returns 푖̂_{F,t}^{CDS} and model residuals.
- Average daily residual across N firms:
  - ε̅t = (1/N) Σ_{F=1}^{N} (푖_{F,t}^{CDS} − 푖̂_{F,t}^{CDS}) (equation 12).
  - ε̅t > 0 indicates realized returns outperform the basket-implied expectation; ε̅t < 0 indicates underperformance.
- A time-series of residuals is formed by splicing global financial crisis and European debt crisis model residuals.
- Vector autoregression (VAR) over June 2007 to April 2014:
  - Two-variable VAR using (푖푖푖푖푖푖t훥훥, ε̅t) with 15 trading-day lags selected using Akaike’s information criterion (equation 13).

### Evolution of information production (푖푖푖푖푖푖t)
- Pre-crisis average in 2006: about 0.6.
- Jump to 5.6 on October 7, 2008 (shortly before the U.K. capital injection plan).
- Local maximum of 2.9 in February 2011 (shortly after Fitch downgraded Greek sovereign debt to junk).
- Regional patterns (Figure 2 summary):
  - United Kingdom: spikes in late 2008 and 2009; stabilizes at triple the pre-crisis average.
  - Periphery: low in initial GFC stages; spikes in early 2011.
  - Core Europe: dramatic spike in October 2008; otherwise low except late 2011 blip.
  - United States: spike in 2008 and another in 2010 before slow recovery.
- Table summaries:
  - Average information-production ratio broadly similar across countries: ranging from 0.5 to 0.9.
  - Periphery has the largest volatility in 푖푖푖푖푖푖t; United States has the largest volatility of 푖푖푖푖푖푖t훥훥.
  - Europe-wide 푖푖푖푖푖푖t훥훥 is correlated at the 5 percent level with all other regions’ 푖푖푖푖푖푖t훥훥.

### Abnormal information production: event-study findings
- U.S. 2009 stress test:
  - Announcement associated with −5.7 percent average abnormal information production.
  - Results associated with −12.1 percent average abnormal information production.
  - An average daily 푖푖푖푖푖푖t훥훥 of −12.1 percent corresponds to an approximately 60 percent cumulative reduction in information production.
  - This is the largest U.S. reduction and the third-largest across regions (after U.S. bank capital injection on European core: −17.7 percent; ECB August 2011 bond purchase program: −14.6 percent).
- European stress tests (2009–2012):
  - Europe-wide effects: −2.3 percent (2010) and −2.1 percent (2012).
  - Heterogeneity: periphery experienced reductions (−3.9 percent and −3.7 percent), core experienced increases (1.9 and 9.8), United Kingdom flat; U.S. 푖푖푖푖푖푖t훥훥 fell after the 2012 test only.
  - 2010 European stress test included 91 banks: seven below 6 percent Tier 1 ratio, 24 below 7 percent, 39 below 8 percent.
- Other intervention findings (Table 6 and aggregated Table 7):
  - Capital injections, institution-specific interventions, open-market operations, and asset-purchase programs compressed abnormal information production in Europe (core and periphery) but not in the U.K. and U.S. uniformly.
  - Capital injections: average reduction of −4.7 percent across all countries; −9.5 percent in Europe; −0.9 percent in the United Kingdom.
  - Open-market/asset-purchase: ECB August 2011 bond purchase program had −14.6 percent; TALF and QE had smaller but significant reductions.
  - BNP suspension of redemptions and initial August 2007 liquidity provision led to a large increase of 12.6 percent in information production.
  - Periphery interventions (Greece May 2010 and July 2011, Ireland November 2010, Portugal May 2011) generally reduced information production; significance mainly for 2010 interventions.
- Key interpretation:
  - Similar intervention types can yield widely different effects; credibility, institutional context, market expectations, and idiosyncratic design features matter—“the devil is ultimately in the details.”
  - Aggregated event study (five-day windows across events of a type) finds capital injections and periphery-targeted policy responses reduced abnormal information production, while other types did not show statistically significant pooled effects.

### LASSO and reference-securities results (summary)
- LASSO-selected baskets show banks’ returns covaried strongly with traded securities during both the global financial crisis and the European debt crisis.
- Table 6 (source reference) indicates the model-selected basket’s R^2 nearly quadrupled from pre-crisis to the global financial crisis (from 1.1 percent to [value truncated in provided content]).

### Information production, bank outcomes, and real outcomes: regression frameworks
- Country-level regressions relate lagged, demeaned country-specific information production 푖푖푖푖푖푖_{F,t−1} to net cost of government interventions (Cost/GDP_{F,t}):
  - Cost/GDP_{F,t} = 훼 + 훽1 푖푖푖푖푖푖_{F,t−1} + 훽2 푖푖푖푖푖푖_{F,t−1}^2 + ε_{F,t} (equation 14).
  - Cost/GDP is net cost to government interventions as share of 2008 nominal GDP; negative net cost = net revenues.
  - Country dummy 핀핀(푅푅푒푒푖푖푖푖푖푖 ℎ푒푒푖푖 푒푒) = 1 if Greece, Ireland, Italy, Portugal, or Spain; 0 otherwise.
  - Sample: 14 countries each with eight years of observations. The 14 countries are: Austria, Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, and the United Kingdom.
- Bank-level analysis (Fitch data):
  - Sample: largest 500 banks by asset rank in H1 2007, consolidated, euro-area, semiannual IFRS reporting; excludes central banks, state/government banks, supranational banks.
  - Required variables: total assets, total equity, common equity, operating return on average assets, operating return on average equity, net income, pre-provision profits, provisions, gross loans.
  - Dependent variables: log differences in total funding, gross loans, total assets, total equity.
  - Independent variables (lagged one semiannual period): 푖푖푖푖푖푖, total assets, total equity to assets, return on average equity, provisions to pre-provision profit, income to assets.
  - Data treatment: variables winsorized at 5 percent and 95 percent; country and bank fixed-effects included; variables multiplied by 100 for coefficient interpretation.

### Main empirical conclusions (as reported)
- 푖푖푖푖푖푖t peaked after Lehman Brothers and again at the onset of the European debt crisis; average pre-crisis level ~0.6; spikes to 5.6 (October 7, 2008) and 2.9 (February 2011).
- The 2009 U.S. stress test was associated with large declines in information production (−5.7 percent announcement; −12.1 percent results), while European stress tests had heterogeneous effects across periphery and core.
- Capital injections and targeted periphery policy responses reduced abnormal information production on average; other interventions show mixed or region-specific effectiveness.
- The LASSO-selected reference-security baskets explain substantially more of banks’ return variation during crises than in pre-crisis periods.
- High levels of 푖푖푖푖푖푖t predict bank balance-sheet contraction and higher subsequent government costs of financial interventions.
- 푖푖푖푖푖푖t fell through the worse phases of the COVID-19 crisis, reflecting the fundamentally different nature of that shock.

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021005-print-pdf.pdf*

### 3.9 percent) and grew eight-fold during the European debt crisis (from 1.1 percent to

### wpiea2021005-print-pdf - 3.9 percent) and grew eight-fold during the European debt crisis (from 1.1 percent to

### Reference securities and model behavior
- Pre-crisis, only one variable, the iTraxx, had a large beta (0.16).
- In the global financial crisis the LASSO-selected betas include:
  - iTraxx: 0.52
  - iBoxx BBB: 0.28
  - Greek sovereign bonds: 0.09
  - iBoxx AAA: 0.08
  - German bunds: −0.36
- During the European debt crisis the selected reference securities change:
  - Greek sovereign bonds dropped; Spanish and Irish sovereign bonds added with betas 0.04 and 0.03, respectively.
  - iBoxx beta shifts from 0.08 to −0.19.
  - Bund beta attenuates to −0.07.
  - Periphery equity indices (PSI, IBEX, ISEQ, ASE) and the S&P Europe Property index are selected with smaller betas.
- Interpretation:
  - Pre-crisis senior bank debt was information-insensitive; during crises bank debt became information-sensitive and baskets of reference securities became better proxies of banks’ soundness, including solvency.
  - Reference securities selected are economically distinct across pre-crisis, global financial crisis, and European debt crisis samples.

### Model fit, impulse responses, and investor behavior
- 푅푅2 coefficients increase with crises, matching the intuition that bank CDS returns covary more with traded securities once senior bank debt becomes information-sensitive.
- Figure 6 (cumulative orthogonalized impulse response functions) findings:
  - An impulse to the model residual when the model is pessimistic relative to realized returns leads to a reduction in information production.
  - The model residual is persistent in sign; the subsequent decline in 푖푖푖푖푖푖
푡푡
훥훥 is surprising under a strict accuracy-focused investor model.
  - Authors resolve this by arguing investors prioritize tail risk (downside risk) over outright model accuracy.

### Information production and real outcomes
- Key empirical links:
  - The level of information production in a country predicts the government’s subsequent cost of interventions in financial institutions (Table 7).
  - Column one of Table 7: positive correlation between centered 푖푖푖푖푖푖
푡푡−1 and intervention cost, though effect not significantly different from zero.
  - Including a squared centered term, 푖푖푖푖푖푖
푡푡−1
2, shows the effect is exponential.
  - With country fixed-effects (fourth column) the effect is still significant and positive.
- Magnitude example:
  - The standard deviation of 푖푖푖푖푖푖
푡푡−1 is 0.95, so an 푖푖푖푖푖푖
푡푡−1 one standard deviation above average predicts a cost of financial intervention in the next year of 0.68 percent of GDP.
- Bank balance-sheet consequences (Table 8):
  - When Europe-wide 푖푖푖푖푖푖
푡푡−1 is one unit higher (roughly one standard deviation):
    - funding falls the next semiannual period by 1.0 percent,
    - gross loans fall by 0.8 percent,
    - total assets fall by 1.1 percent,
    - total equity falls by 0.9 percent.
  - Interpretation: higher 푖푖푖푖푖푖
푡푡−1 implies banks delever as assets fall faster than equity, producing a form of capital adequacy that contracts credit to the real economy.

### Event studies and interventions
- No specific type of intervention uniformly reduces information production.
- On average, capital injections and periphery country agreements reduced information production.
- Stress tests and other event-type analyses are reported in Tables 5 and 6 and summarized in Table 7 (event-window regressions of 푖푖푖푖푖푖
푡푡
훥훥 on event indicators).

### Impact of COVID-19
- Method: 푖푖푖푖푖푖
푡푡 calculated for Europe and the United States requiring companies to have reported CDS spreads each day of 2019 and 2020 through August 2020.
- Findings (Figure 8):
  - COVID-19 did not begin as a financial crisis. In March 2020 cross-sectional variance across nonfinancial companies increased dramatically and levels remain elevated amid continued COVID-19 crisis.
  - 푖푖푖푖푖푖
푡푡 fell in the United States and Europe (including the United Kingdom).
  - As of August 2020, the cross-sectional standard deviation of nonfinancial companies is roughly 10 times its level at the beginning of the year, whereas financials are only 13 percent higher.
  - Conclusion: decline in 푖푖푖푖푖푖
푡푡 reflects the fundamentally nonfinancial origin of the shock.

### Measurement and definition of information production
- 푖푖푖푖푖푖
푡푡 is defined as the daily cross-sectional standard deviation of five-year euro-denominated senior secured debt CDS spreads within financial companies divided by the same measure within nonfinancials, excluding government reference entities.
- Country-level and region-level measures use analogous methodologies; the United States measure uses a few different cleaning steps described in section III.

### Conclusion (implications for policy)
- Information production is first-order important for crisis-time policymakers.
- Uses of information production:
  - Tool for quantitative ex-post policy evaluation.
  - Ex ante indicator of crisis.
  - Predictor of adverse real outcomes for the banking system and cost of crisis to the taxpayer.
- Practical implications:
  - Monitoring 푖푖푖푖푖푖
푡푡 can give early signals of credit contraction and potential fiscal costs.
  - Policymakers should recognize that investors focus on downside/tail risks; interventions that address tail-risk perceptions (e.g., capital injections, credible periphery agreements) can reduce information production on average.

*Italicized source: wpiea2021005-print-pdf - 3.9 percent) and grew eight-fold during the European debt crisis (from 1.1 percent to*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021005-print-pdf.pdf_