## 2.1 The Crisis and the Irish Case

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---

### Overview of the crisis
- Ireland experienced one of the worst banking crises after the Global Financial Crisis, originating from a boom-bust cycle in the domestic property market financed by bank loans.
- Surge in output in 2003-2007 was a construction boom; banks became highly exposed to the housing market via rapid credit expansion to home owners and property developers.
- As international funding conditions shifted in 2007/2008 and domestic investors withdrew, property prices declined sharply, construction collapsed, and banks faced an unprecedented increase in NPLs, requiring public recapitalisation of major credit institutions.
- Public bailouts resulted in fast recapitalisation but left banks with threatening levels of NPLs.

### Key indicators and stress-test findings
- Tier 1 Capital Ratio:
  - Regulatory requirement: 8%
  - European average reported: 14.1%
  - After public bailouts, Irish banks’ Tier 1 Capital Ratio levelled off well above the 8% requirement and the European average.
- Texas Ratio (definition preserved):
  - Texas Ratio = Impaired Loans + Loans 90 days past due but not impaired / Tangible Equity + Loan Loss Provisions.
  - A value above 100% is widely considered critical.
  - The Irish banking sector only recovered to below this threshold in 2014.
  - Development of the Texas Ratio is driven by the NPL ratio.
- NPLs and relative magnitudes:
  - Ireland’s NPL ratios rose to approximately four times the European average, driving the Texas Ratio to critical levels throughout the observation period.
- Stress tests:
  - EBA (2016a) and IMF (2016) stress tests indicate that, while Irish banks seem well capitalised in normal conditions, regulatory requirements may not be reached under the adverse scenario.
  - The difference of Tier 1 capital levels between the baseline and adverse scenario is largest for Ireland.
  - Credit risk is the main contributor, accounting for a 6 percentage point difference in the Tier 1 capital ratio between baseline and adverse scenarios.

### Public ownership detail
- Through the public bank bailouts, 99.9% of Allied Irish Banks and 15% of Bank of Ireland became state-owned.

### Data (section 2.1.1)
- Sample coverage and structure:
  - Data source: commercial loan level data from the Central Bank of Ireland provided by Irish banks in biannual frequency.
  - Time coverage: from 2011 Q4 up to 2016 Q2.
  - Observations and borrowers:
    - 1,686,325 observations (loan×time).
    - 244,908 borrowers.
  - Geographic and categorical coverage:
    - 26 Irish counties.
    - 8 sectors.
    - 3 segments: Corporate, SME and Micro SME.
    - 4 product types: leasing/hire purchase, overdraft, term loan and other.
- Variable detail and limitations:
  - Loan-specific characteristics: product type, maturity, interest rate, repayment schedule, securitisation indicator, and a mapped rating of the risk of the loan (from banks’ internal PD models homogenised by the Central Bank of Ireland).
  - Borrower-specific characteristics: firm sector and segment.
  - Caveats due to confidentiality:
    - Firms’ names are not available: cannot enrich data with balance sheet information or control for firm characteristics.
    - Cannot identify the same firm across different banks; borrower identification across products is only within a bank.
    - Once a loan defaults, the borrower and all related loans are excluded from the sample.

---

### 2.2 Forbearance

### Types and operational definitions (constructed from loan-level data)
- Amortisation stop:
  - Banks temporarily suspend instalments and allow borrowers to only make interest payments; outstanding loan amount remains constant until further agreement or maturity.
  - Detectable via banks’ reported changes in the amortisation status of each loan.
- Limit extension:
  - Increase in the total limit that can be drawn by the borrower (common for overdrafts); defined as a positive change in the total limit.
- Term (maturity) extension:
  - Pushing back the due date of the loan; non-amortising loans become due later, and for loans with constant repayments this can reduce instalments.
- Rollover:
  - Considered when a significant loan disappears from the sample (expired or concordantly ended) but the borrower limit does not decrease by more than half of the discontinued loan’s amount, implying limits on other products were increased or new products were issued.
- Interest rate change (subsidised lending):
  - An advantageous change in the interest rate is defined as a decrease in a borrower’s interest rate that is greater than the decrease for the safest borrowers within the same sector, segment, and product type; this accounts for the general environment of decreasing interest rates.

### Heterogeneity and borrower risk classification
- Borrower risk categories: safe, average, risky (ratings from banks’ internal models homogenised by the Central Bank).
- Observed pattern:
  - Share of treated loans is highest for the riskiest borrowers for every forbearance measure.
  - Most commonly applied measures for risky borrowers:
    - 1st: limit extension
    - 2nd: interest rate change
    - Least common: rollover and amortisation stop
  - Concentration of forbearance on risky borrowers indicates banks’ incentives to prevent default despite risk aversion.

### Banks’ incentives and constraints (2.2.2)
- Incentives to adopt forbearance:
  - Banks have an incentive to prevent default to avoid negative impacts on capital ratios.
  - Under the F-IRB approach, a provisioning shortfall is deducted from Tier 1 capital in case of default.
  - Banks may “underprovision” and only realise the loss at default due to discretionary provisioning.
  - A default leads to higher future provisions since these are based on historical observed default rates.
  - IFRS 9 (effective January 2018) will lead to earlier recognition of expected losses and mitigate underprovisioning.
- Forbearance effects on regulatory capital and risk weighted assets:
  - Maturity extension: mechanically increases the risk weight as maturity is part of the risk weight formula (see Capital Requirements Regulation Article 153 (1) for the F-IRB approach).
  - Limit increase: increases exposure at default and thereby risk weighted assets.
  - Interest rate reduction: leads to lower capital because of lower future interest earnings (risk weights unaffected).
  - Amortisation stop: effect on capital depends on whether missed payments are repaid in full once amortisation resumes.
  - Rollover: akin to maturity extension for risk-weight purposes because exposure stays on the bank’s book.
- Resource allocation trade-offs and the role of uncertainty:
  - New lending increases risk weighted assets; after the Global Financial Crisis commercial lending had very high risk weights.
  - Capital ratios alone may not capture pressure to optimise risk weighted assets due to credit risk uncertainty.
  - Deterioration in the economic environment can lead to average downgrades, increasing risk weighted assets and decreasing capital.
  - The Texas Ratio is argued to be a more informative measure of pressure because it incorporates uncertainty surrounding capital levels and credit risk.

---

### 3 Forbearance Patterns and Results

### 3.1 Portfolio composition and forbearance prevalence
- Rating-weighted shares (by outstanding balance):
  - Defaulted loans: 32.3%
  - Riskiest category (not defaulted): 26.1%
  - Safe category: 6.4%
- Segment and product structure:
  - Corporate lending: 18.9% of outstanding balance but only 0.3% of loans.
  - SME segment: largest amount outstanding; majority of loans go to micro SMEs.
  - Product types: term loans represent the largest share by volume and number of loans.
  - Average loan sizes:
    - Term loans: 120,000e on average.
    - “Other” category: 265,000e average (driven by large corporate loans, such as syndicated loans).
- Borrowers receiving forbearance:
  - 89,255 borrowers receive any kind of measure (more than a third of all borrowers in the sample).
  - Most frequent measures by borrower counts:
    - 1st: limit extension
    - 2nd: interest rate change
    - 3rd: term extension
    - 4th: amortisation stop
    - 5th: rollover
  - Rollover was applied to 11,353 borrowers in the sample.

### 3.2 Empirical approach (logit model)
- Objective: estimate the probability that any one of the five forbearance measures i will be applied to borrower j in the next six months.
- Model specification (exact functional form preserved):
  - Pr(forb_{i,j,t+1}) = α + β1 X_{l,t} + β2 T_{k,t} + β3 Rating_{l,t} * T_{k,t} + forb. before_{j,t} + fixed effects + ε
- Variables and fixed effects:
  - X_{l,t}: time-varying loan characteristics (rating and ln(Outstanding Balance)).
  - T_{k,t}: time-varying Texas Ratio of bank k.
  - Rating_{l,t} * T_{k,t}: interaction to capture differential impact of Texas Ratio by borrower riskiness.
  - forb. before_{j,t}: dummy if borrower j received any forbearance measure before.
  - Fixed effects include: loan age, sector×time, bank×segment×product type, county, bank×time (when included, Texas Ratio drops out and analysis focuses on interaction with rating).
- Identification note:
  - Non-performing loans are excluded once default occurs, avoiding endogeneity from including NPLs on the left-hand side and the Texas Ratio (which includes NPLs) on the right-hand side.
- Estimation strategy:
  - First, estimate probability of receiving any of the five forbearance measures.
  - Second, estimate specification for each measure individually.

### 3.3 Results — Overall Forbearance (3.3.1)
- Main empirical findings (logit regressions; standard errors clustered at bank×time level):
  - For the average Texas Ratio of 105%, the probability of a risky loan receiving forbearance is 5 percentage points higher than for a safe loan and at an absolute value of about 52%.
  - For a risky loan, the difference in predicted probability is around 60 percentage points between a bank with a Texas Ratio at the 95th percentile (134%) and a bank at the 5th percentile (70%).
  - Given the higher Texas Ratio, a representative borrower of a risky loan has a 70% probability of receiving any forbearance measure within the next six months.
  - At an average Texas Ratio of 105%, the odds of a risky loan receiving forbearance are 28.5% higher than for a safe loan, ceteris paribus.
  - At the 95th percentile Texas Ratio (134%) versus the 5th percentile (70%), the odds of receiving forbearance for a risky loan are 67% higher, ceteris paribus.
  - If the borrower already received forbearance, the odds are 224% higher to receive forbearance again.
- Interpretation:
  - Increasing probability of forbearance with decreasing borrower rating driven by borrower demand (only borrowers in need ask) and informational advantage/strategic demand.
  - Increasing probability with increasing bank stress (Texas Ratio) consistent with constrained banks preserving capital by forbearing loans.
- Robustness and alternative bank stress measures:
  - Interaction of risky borrower rating and bank Texas Ratio remains significantly positive when including bank×time fixed effects and further controls.
  - ln(Outstanding Balance) : Texas Ratio interaction shows no significant additional effect of loan size at high Texas Ratios.
  - Alternative bank-level variables tested: loan to deposits ratio, total gross loans, operating profit to average assets, Tier 1, NPL ratio.
  - NPL Ratio identified as the most important driver of forbearance after adding loan age and sector×time fixed effects; Tier 1 ratio interaction with rating is insignificant when both included.
- Other determinants:
  - Larger loans are more likely to receive a forbearance measure.

### 3.3 Results — Different Measures (3.3.2)
- Dependent variables: indicator if a specific measure was granted within the following 6 months.
- Term extensions and Limit extensions:
  - Interaction of borrower’s rating and bank’s Texas Ratio significantly positive (safe rating as base).
  - Baseline probability of receiving a limit extension is significantly lower for a risky borrower than for a safe borrower, but interaction dominates for Texas Ratio > 120%.
  - Limit extension defined as forbearance only for borrowers in distress (risky); for safe borrowers limit extension often corresponds to growth financing.
- Amortisation stop, Interest rate change, Rollover:
  - No significant influence of bank’s or borrower’s risk on probability of these measures (interaction terms positive but insignificant given conservative clustering).
  - Loan size is the only variable with a significant coefficient: amortisation stop and interest rate change more likely for larger loans; rollover less likely for larger loans.
- Repeated treatment:
  - For all individual measures, probability of receiving the measure is higher if the borrower received prior forbearance.

### 3.3 Results — Sequencing (3.3.3)
- Counts and sequences:
  - Total borrowers in sample: 244,908.
  - Borrowers receiving two or more forbearance measures: 52,255.
  - Borrowers receiving three or more forbearance measures: 33,342.
- Observed sequencing patterns:
  - Limit extensions most common as a first measure, followed by interest change; rollover least common.
  - As second measure, limit extensions are less often applied relative to being first; other measures used more frequently as second measures.
  - As third measure, limit extensions much less likely; amortisation stop and interest rate changes more likely.
- Interpretation:
  - Limit extension tends to be applied earlier (often first).
  - Interest rate changes and amortisation stops become more important as second and third measures — amortisation stop may function as a “measure of last resort.”

---

### 4 Effectiveness of Forbearance (selected results referenced by 3.3)

### Empirical approach (brief)
- Logit hazard model for Pr(Def_{j,t}) with regressors including borrower-level forbearance dummy F_{j,t}, Rating_{l,t} * F_{j,t}, forb. before_{j,t}, loan characteristics, and fixed effects (loan age, bank×time, bank×segment×product type, county, sector×time). Standard errors clustered at bank×time level.
- Focus on β3 for Rating = Risky to assess effectiveness for risky borrowers.

### Main effectiveness findings
- Conditional on rating, interaction of any forbearance with rating is positive: risky borrowers who received forbearance are more likely to default than risky borrowers who did not receive forbearance (robust across fixed effects).
- Using column (6) with all fixed effects, the odds of default for a borrower having received any forbearance measure in the last six months are 20% higher than if the borrower was not treated.
- For risky borrowers (all other variables at mean or mode):
  - Probability of default if no measure in last six months: around 8.7%.
  - Probability of default if received forbearance in last six months: around 9.25%.
- For average borrower (appendix), predicted default probabilities range from 1.4% to 1.8%.
- Interpretation of higher default after forbearance:
  - Two possible mechanisms (cannot be disentangled):
    - Selection bias: banks give forbearance to the “worst” risky borrowers (closest to default).
    - Strategic borrower behavior: borrowers demand forbearance knowing they will default even with forbearance.
  - These mechanisms appear to outweigh any positive impact of forbearance in preventing default.
- Individual measure effectiveness:
  - Term extensions, interest rate changes, and amortisation stops: associated with higher probability of default for risky borrowers.
  - Limit extensions and rollovers: coefficients negative but insignificant in long-run specifications — no evidence they lower default rates for stressed borrowers.
  - Timing results:
    - Limit Extension is significantly negatively related with defaults in the short term (up to two periods after the measure) but uncorrelated thereafter — suggests short-term concealment of distress rather than long-term prevention.
    - Amortisation Stops are associated with higher probabilities of default at any future point — consistent with selection of the riskiest borrowers and its use as a later-stage measure.

---

### 5 Credit Supply, Forbearance, and New Lending (section 5.1 Empirical Approach)

### Background and data treatment
- Literature shows stressed banks keeping relationships with risky borrowers issue significantly lower volumes of new lending; presence of zombie firms depresses job creation, deter entry of healthy firms, and decrease employment and investment.
- For Ireland, seasonally adjusted quarterly new lending to Irish SMEs analyzed alongside SME survey data on credit applications and rejections.
  - Seasonality adjusted using X13-ARIMA-SEATS.
  - Application and rejection rate data for Irish SMEs from RED-C Reports on SME lending (Department of Finance of Ireland).
- Observed pattern: high application rate for new products in 2012 that continuously dropped; low new lending volumes coincided with high credit demand and high rejection rates.

### Regression specification
- Buckets b by bank, segment, time, and county.
- OLS regression:
  - Share(New Lending)_{b,t} = α + Share(Forbearance)_{b,t−1} + fixed effects + ε
- Definitions:
  - Share(New Lending)_{b,t} = sum of lending to new borrowers / total lending in bucket b in time t.
  - Share(Forbearance)_{b,t−1} = sum of loans to forborne borrowers / total lending in t−1 in bucket b.
- Fixed effects control for macro environment (county×time), variation between banks (bank), and variation between banks over time (bank×time).
- Time unit for analysis: six months (explicitly noted in robustness discussion).

### Main empirical results
- Negative correlation between forbearance and new lending in the same bucket across all specifications.
- Interpretation: higher share of forbearance within a certain segment and county by a specific bank is associated with a lower share of new loans.
- Robustness to fixed effects saturation (columns 1–4).
- Magnitude (most conservative specification, column (4)):
  - A 1% higher share of forborne loans is correlated with a 0.076% lower share of new lending.
- Robustness checks:
  - Contemporaneous new lending (column (5)) because time unit is six months.
  - Natural logarithm of new lending and forbearance (column (6)).
  - Both robustness checks remain highly significant in the most conservative specification.

### Interpretation and mechanism
- Forbearance—occurring mostly for risky borrowers—appears to be a trade-off for new loans, which are potentially safer.
- Coincidence of high credit demand with low new lending and high rejection rates supports a supply-side constraint narrative linked to forbearance patterns.

---

### Conclusions and policy implications (linked to broader section 6 summary)
- Forbearance measures defined in the paper: extension in credit limit or maturity, pause in amortisation, comparably lower interest rate change, and rollover of a loan product.
- Risky borrowers are more likely to receive a limit or maturity extension when banks face high levels of NPLs relative to capitalisation and provisions.
- Limit extension reduces probability of default up to one year; for longer horizons and other forbearance measures a higher probability of default is found.
- Policy-relevant points:
  - Banks with a high share of forborne loans issue lower volumes of new credit, potentially tightening financial conditions for new (and potentially more productive) firms.
  - Health of banks’ loan books matters: high NPLs can pressure banks to forbear and avoid categorising loans as non-performing—an incentive influenced by the regulatory framework.
  - Widespread uncertainty about the real quality of loan books can lead to systemic risk and undermine trust in banking sector solvency.
  - While broad-based forbearance was justified during the initial high-uncertainty months of the Covid-19 pandemic, as liquidity versus solvency is clarified, findings can help policymakers design a more targeted approach in later recovery phases.

*Source: wpiea2020140-print-pdf*

### 2.1  The Crisis and the Irish Case

### 2.1  The Crisis and the Irish Case

### Overview of the crisis
- Ireland experienced one of the worst banking crises after the Global Financial Crisis, originating from a boom-bust cycle in the domestic property market financed by bank loans.
- The surge in output in 2003-2007 was a construction boom; banks became highly exposed to the housing market via rapid credit expansion to home owners and property developers.
- As international funding conditions shifted in 2007/2008 and domestic investors withdrew, property prices declined sharply, construction collapsed, and banks faced an unprecedented increase in NPLs, requiring public recapitalisation of major credit institutions.
- Public bailouts resulted in fast recapitalisation but left banks with threatening levels of NPLs.

### Key indicators and stress-test findings
- Tier 1 Capital Ratio:
  - Regulatory requirement: 8%
  - European average reported: 14.1%
  - After public bailouts, Irish banks’ Tier 1 Capital Ratio levelled off well above the 8% requirement and the European average.
- Texas Ratio (defined exactly as in source):
  - Texas Ratio = Impaired Loans + Loans 90 days past due but not impaired / Tangible Equity + Loan Loss Provisions.
  - A value above 100% is widely considered critical.
  - The Irish banking sector only recovered to below this threshold in 2014.
  - The development of the Texas Ratio is driven by the NPL ratio.
- NPLs and relative magnitudes:
  - Ireland’s NPL ratios rose to approximately four times the European average, driving the Texas Ratio to critical levels throughout the observation period.
- Stress tests:
  - EBA (2016a) and IMF (2016) stress tests indicate that, while Irish banks seem well capitalised in normal conditions, regulatory requirements may not be reached under the adverse scenario.
  - The difference of Tier 1 capital levels between the baseline and adverse scenario is largest for Ireland.
  - A breakdown shows credit risk as the main contributor, accounting for a 6 percentage point difference in the Tier 1 capital ratio between baseline and adverse scenarios.

### Public ownership detail
- Through the public bank bailouts, 99.9% of Allied Irish Banks and 15% of Bank of Ireland became state-owned.

---

### 2.1.1  Data

### Sample coverage and structure
- Data source: commercial loan level data from the Central Bank of Ireland provided by Irish banks in biannual frequency.
- Time coverage: from 2011 Q4 up to 2016 Q2.
- Observations and borrowers:
  - 1,686,325 observations (loan×time).
  - 244,908 borrowers.
- Geographic and categorical coverage:
  - 26 Irish counties.
  - 8 sectors.
  - 3 segments: Corporate, SME and Micro SME.
  - 4 product types: leasing/hire purchase, overdraft, term loan and other.

### Variable detail and limitations
- Loan-specific characteristics include: product type, maturity, interest rate, repayment schedule, securitisation indicator, and a mapped rating of the risk of the loan (from banks’ internal PD models homogenised by the Central Bank of Ireland).
- Borrower-specific characteristics include: firm sector and segment.
- Caveats due to confidentiality:
  - Firms’ names are not available: cannot enrich data with balance sheet information or control for firm characteristics.
  - Cannot identify the same firm across different banks; borrower identification across products is only within a bank.
  - Once a loan defaults, the borrower and all related loans are excluded from the sample.

---

### 2.2  Forbearance

### Types and operational definitions of forbearance (constructed from loan-level data)
- Amortisation stop:
  - Banks temporarily suspend instalments and allow borrowers to only make interest payments; outstanding loan amount remains constant until further agreement or maturity.
  - Detectable via banks’ reported changes in the amortisation status of each loan.
- Limit extension:
  - Increase in the total limit that can be drawn by the borrower (common for overdrafts); defined as a positive change in the total limit.
- Term (maturity) extension:
  - Pushing back the due date of the loan; non-amortising loans become due later, and for loans with constant repayments this can reduce instalments.
- Rollover:
  - Considered when a significant loan disappears from the sample (expired or concordantly ended) but the borrower limit does not decrease by more than half of the discontinued loan’s amount, implying limits on other products were increased or new products were issued.
- Interest rate change (subsidised lending):
  - An advantageous change in the interest rate is defined as a decrease in a borrower’s interest rate that is greater than the decrease for the safest borrowers within the same sector, segment, and product type; this accounts for the general environment of decreasing interest rates.

### Heterogeneity and borrower risk classification
- Forbearance measures are heterogeneous in purpose and borrower need; safe borrowers may request credit for positive projects, while stressed borrowers may request credit to cover due payments.
- Borrower risk categories: safe, average, risky (ratings from banks’ internal models homogenised by the Central Bank).
- Observed pattern:
  - Share of treated loans is highest for the riskiest borrowers for every forbearance measure.
  - Most commonly applied measures for risky borrowers:
    - 1st: limit extension
    - 2nd: interest rate change
    - Least common: rollover and amortisation stop
  - This concentration of forbearance on risky borrowers indicates banks’ incentives to prevent default despite risk aversion.

---

### 2.2.2  The Banks’ Incentives and Constraints

### Incentives to adopt forbearance
- Banks have an incentive to prevent default to avoid negative impacts on capital ratios:
  - Under the F-IRB approach, a provisioning shortfall is deducted from Tier 1 capital in case of default.
  - Banks may “underprovision” and only realise the loss at default due to discretionary provisioning.
  - A default leads to higher future provisions since these are based on historical observed default rates.
  - IFRS 9 (effective January 2018) will lead to earlier recognition of expected losses and mitigate underprovisioning.

### Forbearance effects on regulatory capital and risk weighted assets
- Maturity extension: mechanically increases the risk weight as maturity is part of the risk weight formula (see Capital Requirements Regulation Article 153 (1) for the F-IRB approach).
- Limit increase: increases exposure at default and thereby risk weighted assets.
- Interest rate reduction: leads to lower capital because of lower future interest earnings (risk weights unaffected).
- Amortisation stop: effect on capital depends on whether missed payments are repaid in full once amortisation resumes.
- Rollover: akin to maturity extension for risk-weight purposes because exposure stays on the bank’s book.

### Resource allocation trade-offs and the role of uncertainty
- New lending increases risk weighted assets; after the Global Financial Crisis commercial lending had very high risk weights.
- Capital ratios alone may not capture pressure to optimise risk weighted assets due to credit risk uncertainty.
- Deterioration in the economic environment can lead to average downgrades, increasing risk weighted assets and decreasing capital.
- The Texas Ratio (see definition above) is argued to be a more informative measure of pressure because it incorporates uncertainty surrounding capital levels and credit risk.

---

### 3  Forbearance Patterns

### 3.1  Descriptive analysis: portfolio composition and forbearance prevalence
- Rating-weighted shares (by outstanding balance):
  - Defaulted loans: 32.3%
  - Riskiest category (not defaulted): 26.1%
  - Safe category: 6.4%
- Segment and product structure:
  - Corporate lending: 18.9% of outstanding balance but only 0.3% of loans.
  - SME segment: largest amount outstanding; majority of loans go to micro SMEs.
  - Product types: term loans represent the largest share by volume and number of loans.
  - Average loan sizes:
    - Term loans: 120,000e on average.
    - “Other” category: 265,000e average (driven by large corporate loans, such as syndicated loans).
- Borrowers receiving forbearance:
  - 89,255 borrowers receive any kind of measure (more than a third of all borrowers in the sample).
  - Most frequent measures by borrower counts:
    - 1st: limit extension
    - 2nd: interest rate change
    - 3rd: term extension
    - 4th: amortisation stop
    - 5th: rollover
  - Rollover was applied to 11,353 borrowers in the sample.

### 3.2  Empirical approach (logit model)
- Objective: estimate the probability that any one of the five forbearance measures i will be applied to borrower j in the next six months.
- Model specification (exact functional form preserved):
  - Pr(forb_{i,j,t+1}) = α + β1 X_{l,t} + β2 T_{k,t} + β3 Rating_{l,t} * T_{k,t} + forb. before_{j,t} + fixed effects + ε
- Variables:
  - X_{l,t}: time-varying loan characteristics (rating and ln(Outstanding Balance)).
  - T_{k,t}: time-varying Texas Ratio of bank k.
  - Rating_{l,t} * T_{k,t}: interaction to capture differential impact of Texas Ratio by borrower riskiness.
  - forb. before_{j,t}: dummy if borrower j received any forbearance measure before.
- Fixed effects included:
  - loan age fixed effects
  - sector×time fixed effects
  - bank×segment×product type fixed effects
  - county fixed effects
  - bank×time fixed effects (when included, the Texas Ratio drops out and the analysis focuses on the differential impact via the interaction with rating)
- Identification notes:
  - Non-performing loans are excluded from the sample once default occurs, so the specification avoids endogeneity that would arise from including NPLs on the left-hand side and the Texas Ratio (which includes NPLs) on the right-hand side.
- Estimation strategy:
  - First, estimate probability of receiving any of the five forbearance measures.
  - Second, estimate the specification for each measure individually to identify patterns driving results.

*Source: wpiea2020140-print-pdf - 2.1  The Crisis and the Irish Case*

### 3.3  Results

### 3.3 Results

### 3.3.1 Overall Forbearance
- Model and fixed effects
  - Logit regressions shown in Table 3; fixed effects added in sequence across columns (1)–(7): loan age, sector×time, bank×time, bank×segment×product type, and county.
  - Standard errors clustered at bank×time level.
- Main empirical findings
  - For the average Texas Ratio of 105%, the probability of a risky loan receiving forbearance is 5 percentage points higher than for a safe loan and at an absolute value of about 52%.
  - For a risky loan, the difference in predicted probability is around 60 percentage points between a bank with a Texas Ratio at the 95th percentile (134%) and a bank at the 5th percentile (70%).
  - Given the higher Texas Ratio, a representative borrower of a risky loan has a 70% probability of receiving any forbearance measure within the next six months.
  - At an average Texas Ratio of 105%, the odds of a risky loan receiving forbearance are 28.5% higher than for a safe loan, ceteris paribus.
  - At the 95th percentile Texas Ratio (134%) versus the 5th percentile (70%), the odds of receiving forbearance for a risky loan are 67% higher, ceteris paribus.
  - If the borrower already received forbearance, the odds are 224% higher to receive forbearance again.
- Interpretation and mechanisms
  - Increasing probability of forbearance with decreasing borrower rating driven by:
    - Only borrowers in need ask for forbearance.
    - Borrowers possess informational advantage and may strategically demand forbearance when default is unavoidable.
  - Increasing probability of forbearance with increasing bank stress (Texas Ratio) consistent with constrained banks preserving capital by forbearing loans.
- Robustness and alternative bank stress measures
  - Interaction of risky borrower rating and bank Texas Ratio remains significantly positive when including bank×time fixed effects and further controls.
  - Robustness test adding ln(Outstanding Balance) : Texas Ratio interaction shows no significant additional effect of loan size at high Texas Ratios.
  - Alternative bank-level variables tested (loan to deposits ratio, total gross loans, operating profit to average assets, Tier 1, NPL ratio).
  - NPL Ratio identified as the most important driver of forbearance after adding loan age and sector×time fixed effects; Tier 1 ratio interaction with rating is insignificant. When including both, only the NPL Ratio interaction remains significant — indicating level of NPLs drives results when using Texas Ratio as bank stress proxy.
- Other determinants
  - Larger loans are more likely to receive a forbearance measure.

### 3.3.2 Different Measures of Forbearance
- Dependent variables and approach
  - Table 4 analyzes individual forbearance measures where dependent variable equals one if a specific measure was granted within the following 6 months.
- Measures with results consistent with main findings
  - Term extensions and Limit extensions:
    - Interaction term of borrower’s rating and bank’s Texas Ratio significantly positive (safe rating as base).
    - Baseline probability of receiving a limit extension is significantly lower for a risky borrower than for a safe borrower, but this is outweighed by the interaction for values of the Texas Ratio greater than 120%.
    - Limit extension defined as forbearance only for borrowers in distress (risky); for safe borrowers limit extension often corresponds to growth financing.
- Measures with no significant risk or bank stress effect
  - Amortisation stop (column (2)), Interest rate change (column (4)), Rollover (column (5)):
    - No significant influence of bank’s or borrower’s risk on probability of these measures (interaction terms positive but insignificant given conservative clustering).
    - Loan size is the only variable with a significant coefficient: amortisation stop and interest rate change more likely for larger loans; rollover less likely for larger loans.
- Repeated treatment
  - For all individual measures, probability of receiving the measure is higher if the borrower received prior forbearance.

### 3.3.3 Sequencing of forbearance measures
- Sample counts and sequencing overview
  - Total borrowers in sample: 244,908.
  - Borrowers receiving two or more forbearance measures: 52,255.
  - Borrowers receiving three or more forbearance measures: 33,342.
- Observed sequencing patterns (descriptive, Table 5)
  - Distribution of measures taken first resembles overall distribution in Figure 4 and Table 2.
  - Limit extensions most common as a first measure, followed by interest change; rollover least common.
  - As a second measure (among cases with at least two measures), limit extensions are less often applied relative to being first; other measures used more frequently as second measures.
  - As a third measure, limit extensions are much less likely; amortisation stop and interest rate changes more likely.
- Interpretation
  - Limit extension tends to be a measure applied earlier (often first).
  - Interest rate changes and amortisation stops become more important as second and third measures — amortisation stop may function as a “measure of last resort.”

### 4 Effectiveness of Forbearance (selected results from section 4 referenced by 3.3)
- Empirical approach (brief)
  - Logit hazard model for Pr(Def_{j,t}) with regressors including borrower-level forbearance dummy F_{j,t}, Rating_{l,t} * F_{j,t}, forb. before_{j,t}, loan characteristics, and fixed effects (loan age, bank×time, bank×segment×product type, county, sector×time). Standard errors clustered at bank×time level.
  - Focus on β3 for Rating = Risky to assess effectiveness for risky borrowers.
- Main effectiveness findings (Table 6 and related figures)
  - Conditional on rating, interaction of any forbearance with rating is positive: risky borrowers who received forbearance are more likely to default than risky borrowers who did not receive forbearance (robust across fixed effects).
  - Using column (6) with all fixed effects, the odds of default for a borrower having received any forbearance measure in the last six months are 20% higher than if the borrower was not treated.
  - For risky borrowers (all other variables at mean or mode):
    - Probability of default if no measure in last six months: around 8.7%.
    - Probability of default if received forbearance in last six months: around 9.25%.
  - For average borrower (appendix), predicted default probabilities range from 1.4% to 1.8% (Figure 8).
- Interpretation of higher default after forbearance
  - Two possible mechanisms (cannot be disentangled):
    - Selection bias: banks give forbearance to the “worst” risky borrowers (closest to default).
    - Strategic borrower behavior: borrowers demand forbearance knowing they will default even with forbearance.
  - These mechanisms appear to outweigh any positive impact of forbearance in preventing default.
- Individual measure effectiveness (Tables 7, 8, 9, 12)
  - Term extensions, interest rate changes, and amortisation stops: associated with higher probability of default for risky borrowers.
  - Limit extensions and rollovers: coefficients negative but insignificant in long-run specifications — no evidence they lower default rates for stressed borrowers.
  - Timing results:
    - Limit Extension is significantly negatively related with defaults in the short term (up to two periods after the measure) but uncorrelated thereafter — suggests short-term concealment of distress rather than long-term prevention.
    - Amortisation Stops are associated with higher probabilities of default at any future point — consistent with selection of the riskiest borrowers and its use as a later-stage measure.

*Source: IMF working paper — section 3.3 Results (extracted content).*

### 5.1  Empirical Approach

### 5.1  Empirical Approach

### Background and motivation
- Literature documents that stressed banks keeping relationships with risky borrowers issue significantly lower volumes of new lending (examples cited: Acharya et al. (2019); Caballero et al. (2008)).
- Presence of zombie firms found to depress job creation, deter entry of healthy firms, and decrease employment and investment in healthy firms (Giannetti and Simonov, 2013).
- Prior empirical evidence suggests a relationship between credit supply and lower volumes of new credit.
- For Ireland, seasonally adjusted quarterly new lending to Irish SMEs is analyzed alongside SME survey data on credit applications and rejections.
  - New lending exhibits significant seasonality, treated using the X13-ARIMA-SEATS procedure.
  - Application and rejection rate data for Irish SMEs obtained from RED-C Reports on SME lending provided by the Department of Finance of Ireland.
- Observed pattern: high application rate for new products in 2012 that continuously dropped; low new lending volumes coincided with high credit demand and high rejection rates, suggesting supply-side constraints.

### Regression specification
- Borrowers are grouped into buckets b by bank, segment, time, and county under the assumption that lending decisions are made separately for these groups.
- Estimated OLS regression:
  - Share(New Lending)_{b,t} = α + Share(Forbearance)_{b,t−1} + fixed effects + ε
- Definitions:
  - Share(New Lending)_{b,t} is the sum of lending to new borrowers over the total lending in bucket b in time t.
  - Share(Forbearance)_{b,t−1} is the sum of loans to forborne borrowers over the total lending in t−1 in bucket b.
- Fixed effects included to control for:
  - Macroeconomic environment (county×time)
  - Variation between banks (bank)
  - Variation between banks over time (bank×time)

### Main empirical results
- Negative correlation between forbearance and new lending in the same bucket across all specifications (see Table 10 referenced).
- Interpretation: higher share of forbearance within a certain segment and county by a specific bank is associated with a lower share of new loans.
- Result robust to saturating the regression with fixed effects (columns 1–4).
- Magnitude (most conservative specification, column (4)):
  - A 1% higher share of forborne loans is correlated with a 0.076% lower share of new lending.

### Robustness checks
- Two robustness approaches:
  - Use contemporaneous new lending (column (5)) because unit of time is relatively large (six months) and substitution between new lending and forbearance could occur within the same period.
  - Use natural logarithm of new lending and forbearance instead of shares (column (6)).
- Findings: both robustness checks yield results that remain highly significant even in the most conservative specification.

### Interpretation and mechanism
- Forbearance—occurring mostly for risky borrowers—appears to be a trade-off for new loans, which are potentially safer.
- Coincidence of high credit demand with low new lending and high rejection rates supports a supply-side constraint narrative linked to forbearance patterns.

### Key statistics and technical notes
- Seasonality adjustment method: X13-ARIMA-SEATS.
- Data sources explicitly mentioned:
  - New lending data: CBI (used in author’s calculations; figure axis described as seasonally adjusted in m EUR).
  - Application/Rejection rates: RED-C SME Market Report.
- Time unit for analysis: six months (explicitly noted in robustness discussion).

### Conclusions and policy implications (link to broader section 6 summary)
- Forbearance measures:
  - Defined in the paper as: extension in credit limit or maturity, pause in amortisation, comparably lower interest rate change, and rollover of a loan product.
  - Risky borrowers are more likely to receive a limit or maturity extension when banks face high levels of NPLs relative to capitalisation and provisions.
  - Limit extension reduces probability of default up to one year; for longer horizons and other forbearance measures a higher probability of default is found.
- Policy-relevant points:
  - Banks with a high share of forborne loans issue lower volumes of new credit, potentially tightening financial conditions for new (and potentially more productive) firms.
  - Health of banks’ loan books matters: high NPLs can pressure banks to forbear and avoid categorising loans as non-performing—an incentive influenced by the regulatory framework.
  - Widespread uncertainty about the real quality of loan books can lead to systemic risk and undermine trust in banking sector solvency.
  - While broad-based forbearance was justified during the initial high-uncertainty months of the Covid-19 pandemic, as liquidity versus solvency is clarified, findings can help policymakers design a more targeted approach in later recovery phases.

*Source: wpiea2020140-print-pdf, section 5.1.*

### References

### References (wpiea2020140 - References)

### Key literature cited
- Accornero, M., P. Alessandri, L. Carpinelli, and A. M. Sorrentino (2017): “Non-performing loans and the supply of bank credit: evidence from Italy,” Bank of Italy Working Paper.
- Acharya, V., T. Eisert, C. Eufinger, and C. Hirsch (2018): “Same story, different place?: Post-crisis recapitalization of banks in Japan and Europe,” Finance and Investment: The European Case, 137–147.
- Acharya, V. V., T. Eisert, C. Eufinger, and C. Hirsch (2019): “Whatever It Takes: The Real Effects of Unconventional Monetary Policy,” The Review of Financial Studies, 32, 3366–3411.
- Aiyar, S., A. Banerji, B. Barkbu, W. B. W., P. Berkmen, J. Bluedorn, J. Garrido, A. Jobst, J. John, K. Kang, T. Kinda, H. L. H., Y. Liu, D. Monaghan, M. M. M., S. Saksonovs, H. Schoelermann, and T. Wu (2015): “Euro Area Policies: Selected Issues,” International Monetary Fund.
- Albertazzi, U. and D. J. Marchetti (2010): “Credit supply, flight to quality and evergreening: an analysis of bank-firm relationships after Lehman,” Bank of Italy Working Paper, 756.
- Bonaccorsi di Patti, E. and A. Kashyap (2017): “Which Banks recover from large adverse Shocks?” NBER Working Paper.
- Caballero, R. J., T. Hoshi, and A. K. Kashyap (2008): “Zombie lending and depressed restructuring in Japan,” American Economic Review, 98, 1943–77.
- Diamond, D. W. and R. G. Rajan (2011): “Fear of Fire Sales, Illiquidity Seeking, and Credit Freezes,” The Quarterly Journal of Economics, 126, 557–591.
- Eisfeldt, A. L. and A. A. Rampini (2008): “Managerial incentives, capital reallocation, and the business cycle,” Journal of Financial Economics, 87, 177–199.
- Giannetti, M. and A. Simonov (2013): “On the Real Effects of Bank Bailouts: Micro Evidence from Japan,” American Economic Journal: Macroeconomics, 5, 135–67.
- Homar, T., H. Kick, and C. Salleo (2015): “What drives forbearance – Evidence from the ECB Comprehensive Assessment,” ECB Working Paper.
- Honohan, P. (2010): “The Irish Banking Crisis: Regulatory and Financial Stability Policy 2003-2008,” Report of the Commission of Investigation into the Banking Sector in Ireland.
- Huizinga, H. and L. Laeven (2012): “Bank valuation and accounting discretion during a financial crisis,” Journal of Financial Economics, 106, 614–634.
- Kang, K. and N. Jassaud (2015): “A Strategy for Developing a Market for Nonperforming Loans in Italy,” IMF Working Paper, 15/24.
- Keuschnigg, C. and M. Kogler (2017): “Schumpeterian Banks: Credit Reallocation and Capital Requirements,” CEPR Working Paper, 12443.
- Lane, P. R. (2011): “The Irish Crisis,” The Euro Area and The Financial Crisis, 59–80.
- Peek, J. and E. S. Rosengren (2005): “Unnatural Selection: Perverse Incentives and the Misallocation of Credit in Japan,” American Economic Review, 95, 1144–1166.
- Schivardi, F., E. Sette, and G. Tabellini (2017): “Credit Misallocation During the European Financial Crisis,” SEP Working Papers.
- Sekine, T., K. Kobayashi, and Y. Saita (2003): “Forebearance lending: The case of Japanese firms,” Monetary and Economic Studies, 21, 69–92.
- Watanabe, W. (2010): “Does a large loss of bank capital cause Evergreening? Evidence from Japan,” Journal of the Japanese and International Economies, 24, 116–136.
- Zhang, D., J. Cai, D. G. Dickinson, and A. Kutan (2016): “Non-performing loans, moral hazard and regulation of the Chinese commercial banking system,” Journal of Banking and Finance, 63, 48–60.
- EBA (2016a): “EBA Risk Dashboard Q3 2016,” 07/2016.
- EBA (2016b): “EBA Stress Test 2016,” 07/2016.
- IMF (2016): “IMF Country Report No. 16/258,” 07/2016.

### Overview of tables and empirical content
- Sample and summary statistics:
  - Averages over 1,686,325 observations (loan×time) held by 244,908 borrowers.
  - Ratings split by ex-ante probability of default: Safe, Average, Risky, Default.
- Table 1: Summary statistics by segment, rating, and product type (sample shares by outstanding balance and by number of loans):
  - Ratings: Safe 6.4% / 8.7%; Average 35.2% / 40.0%; Risky 26.1% / 32.5%; Default 32.3% / 18.9%.
  - Segment: Corporate 18.9% / 0.3%; SME 61.6% / 30.7%; Micro SME 19.4% / 69.0%.
  - Product Type: Term Loan 81.8% / 49.6%; Overdraft 6.9% / 34.3%; Leasing/Hire Purchase 4.6% / 14.3%; Other 6.7% / 1.7%.
- Table 2: Number of borrowers who received a forbearance measure (across time; borrowers may receive more than one measure):
  - Rollover 11,353
  - Amortisation Stop 14,087
  - Term Extension 17,377
  - Interest Rate Change 27,837
  - Limit Extension 69,209
  - Any measure 89,255
  - All borrowers 244,908

### Main empirical results (selected, by table)
- Table 3 (Logit regression: Probability of application of any forbearance measure - Texas Ratio):
  - ln(Outstanding Balance) coefficients across specifications: 0.218, 0.213, 0.207, 0.212, 0.132, 0.130, 0.096 (all marked with significance where shown).
  - Texas Ratio interactions: Rating - Average :Texas Ratio 0.009, 0.009, 0.012∗∗∗, 0.001, 0.003∗∗, 0.003∗∗, 0.002.
  - Rating - Risky :Texas Ratio 0.014, 0.014, 0.017∗∗∗, 0.006∗, 0.008∗∗∗, 0.008∗∗∗, 0.008∗∗.
  - Forbearance Before coefficient: 1.178∗∗∗ (0.098).
  - Observations: 1,393,284 (columns) and 1,324,317 (column 7).
- Table 4 (Logit regression: Probabilities of different measures being applied, taking into account prior forbearance):
  - Forbearance Before coefficients across measures: 1.178∗∗∗; 1.184∗∗∗; 0.676∗∗∗; 1.667∗∗∗; 0.728∗∗∗; 0.291∗∗∗.
  - ln(Outstanding Balance) shows positive association with several measures: e.g., 0.096∗∗∗ for Any measure.
  - Observations vary by measure: 1,324,317; 1,321,654; 972,779; 1,304,003; 1,181,047; 1,285,117.
- Table 5 (Sequences of measures among borrowers with multiple measures):
  - First Measure (of 2 or more): Term Extension 5,370 (8.6%); Limit Extension 34,201 (55.1%); Interest Rate Change 14,271 (23.0%); Amortisation Stop 5,102 (8.2%); Rollover 3,179 (5.1%).
  - Second Measure (of 2 or more): Term Extension 6,506 (10.4%); Limit Extension 32,109 (51.1%); Interest Rate Change 15,119 (24.1%); Amortisation Stop 5,687 (9.0%); Rollover 3,438 (5.5%).
  - Third Measure (of 3 or more): Term Extension 3,598 (8.8%); Limit Extension 19,860 (48.6%); Interest Rate Change 11,186 (27.4%); Amortisation Stop 4,341 (10.6%); Rollover 1,840 (4.5%).
  - Total number of borrowers in these sequences: 52,255 (first/second) and 33,342 (third).
- Table 6–9 (Logit and Logit Hazard regressions: Influence of forbearance on Probability of Default):
  - Rating Average and Rating Risky have substantial positive coefficients for probability of default across specifications (e.g., Table 6 Rating Average 1.199∗∗∗; Rating Risky 2.895∗∗∗).
  - Interactions of Rating categories with Any Measure or specific measures often show nonzero coefficients (examples: Table 6 Rating Average :Any Measure −0.274…0.217∗∗∗; Rating Risky :Any Measure −0.234…0.184∗∗∗).
  - Table 8 (Probability of Default t+1): Rating Average coefficients 0.926∗∗∗ … 1.033∗∗∗ across columns; Rating Risky coefficients 3.268∗∗∗ … 3.322∗∗∗.
  - Table 12 (1 to 6 periods ahead): Rating - Risky :Any measure coefficients across t+1 to t+6: 0.281∗∗∗; 0.246∗∗∗; 0.269∗∗∗; 0.273∗∗∗; 0.274∗∗∗; 0.284∗∗∗.
- Table 10 (OLS: Relationship between forbearance and new lending by buckets):
  - Share(Forbearance)t−1 coefficients: −0.034∗∗∗; −0.053∗∗∗; −0.066∗∗∗; −0.076∗∗∗ across columns (1)-(4).
  - Share(Forbearance)t coefficient: −0.045∗∗∗ (column 5).
  - ln(Forbearance)t coefficient: −0.160∗∗∗ (column 6).
  - Observations: 754, 754, 754, 754, 873, 872. R2 reported per column: 0.033; 0.136; 0.383; 0.419; 0.290; 0.597.

### Robustness and additional analyses
- Table 11: Robustness with double interaction term Texas Ratio×Outstanding Balance:
  - ln(Out. Bal.) coefficients: 0.271∗∗; 0.264∗∗; 0.261∗∗; 0.244∗∗; 0.180∗∗; 0.178∗∗; 0.185∗∗.
  - ln(Out. Bal.):Texas Ratio coefficients small and statistically indistinct in reported columns.
  - Forbearance Before: 1.179∗∗∗ (0.098).
  - Observations: 1,393,284 (most columns) and 1,324,317 (column 7).
- Table 12: Time-dynamic effects by measure and horizon (t+1 to t+6) with detailed coefficients and observations for each horizon and measure.
- Table 13: Logit regression including NPL Ratio and Tier 1 Ratio:
  - NPL Ratio and its interactions with Rating categories reported; example: NPL Ratio k −0.029; Rating Risky l :NPL Ratio k 0.030∗∗.
  - Tier 1 Ratio interactions: Rating Risky l :Tier 1 Ratio k 0.067∗ (columns shown).
  - Forbearance Before: 1.175∗∗∗; 1.177∗∗∗; 1.175∗∗∗ across early columns.
  - Observations: 1,393,284 (columns 1–6) and 1,324,317 (columns 7–9).

### Appendix: Additional graphs and tables
- Figure 8: Predicted probability of default for a loan depending on any measure being taken and any measure having been taken before. Annotations include percentages on y-axis from 1.4% to 1.8% and labels FALSE/TRUE for Any measure.
- Table 11–13: Additional robustness checks and dynamic horizon regressions (see entries above for key coefficients and observations).
- Table 1–13 cover variable definitions, regression specifications, fixed effects, clustering details (standard errors clustered at Bank x Time level), and significance conventions:
  - Significance levels: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

### Description of variables and exact measure definitions
- Forbearance measures are dummy variables equal to 1 if measure i has been applied in period t.
- Rollover:
  - A loan is considered rolled over if a significant loan disappears from the sample (expired or concordantly ended) but the borrower limit does not decrease by more than half of the expired loan’s amount.
  - A loan is considered significant if it makes up for at least half of the total borrower limit.
- Change in interest rate:
  - Compute percentage change in interest rate per loan across time, ∆r_l.
  - Compute bucket mean change ∆r_b by Sector, Segment, Product Type, and Rating.
  - Deviation ∆r_l,b = ∆r_l − ∆r_b.
  - Define an advantageous change if ∆r_l,b < ∆r_l,b ‖lowest decile of best rating categories.
- Amortisation stop:
  - Dummy = 1 if a loan switches from amortising to non amortising.
- Limit extension:
  - Dummy = 1 if there is an increase in the borrower’s total limit (sum of all loans).
- Term extension:
  - Defined by a positive change of the maturity of a loan product.
- Overall forbearance dummy:
  - Switches to 1 if any loan of a borrower received any of the forbearance measures in a given period.

### Abbreviations (as provided)
- EBA  European Banking Authority
- F-IRB  Foundation-Internal Ratings Based
- IFRS   International Financial Reporting Standards
- IMF    International Monetary Fund
- NPL    Non-performing Loans
- OMT    Outright Monetary Transactions
- REA    Risk Exposure Amount
- SME    Small Medium Enterprise

*Italicized source: wpiea2020140-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020140-print-pdf.pdf_
