## 11. Summary: Conditional Profitability (ROE) Distributions

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### Introduction and motivation
- European banks’ profitability has been low for over a decade in aggregate and particularly for a “tail” of weak performers.
- Two headline measures—return on assets (ROA) and return on equity (ROE)—edged up in 2018 but low profitability remains a concern for numerous banks.
- Low profitability is a systemic financial stability concern because banks need profits to (re-)build buffers, and weak profits can foster risk-taking (“gambling for resurrection”) and raise the cost of raising capital.
- The paper emphasizes bank heterogeneity and focuses on conditional profitability distributions rather than average effects to better capture outcomes for weaker banks.

### Main results and findings
- The most robust determinants of bank profitability across large euro area banks appear to be:
  - Real GDP growth.
  - The nonperforming loan (NPL) ratio.
- Growth effects:
  - An increase in the growth rate of 1 percentage point is associated with a 15–35 basis point rise in ROA.
  - Example baseline OLS: A 1 percentage point increase in growth raises ROA by 27 basis points.
  - Average ROA across banks over 2007–2016 was 34 basis points.
  - Some evidence suggests growth boosts bank profits mainly by reducing loan loss provisions and enhancing noninterest income.
- NPL effects:
  - A 1 percentage point decline in the NPL ratio can lift ROA by about 4–9 basis points.
  - Example baseline OLS: A 1 percentage point lower NPL ratio raises ROA by 5 basis points.
  - Higher stocks of NPLs are associated with higher servicing costs tied to impaired loans, which drag on profitability.
- Conditional distributional results (109 SIs, 2007–2016):
  - Under the baseline, the likelihood of a representative bank’s ROE falling below 8 percent remains elevated at 83 percent, ceteris paribus.
  - Raising growth by 1 standard deviation (that is, 3.3 percentage points) reduces this likelihood by 21 percentage points.
  - Under a scenario with higher growth and a lower NPL ratio, the probability of a representative bank having ROE less than 8 percent declines to 49 percent — a difference of 33 percentage points relative to the baseline.
  - The joint materialization of higher growth and lower NPLs reduces the probability of ROE falling below 8 percent more than these shocks considered individually (reflecting nonlinear interactions).
- Other determinants:
  - Lower cost-to-income ratios are associated with higher profitability for banks outside the weakest end of the profitability spectrum.
  - Results on business models and market concentration are mixed.
  - It is difficult to identify whether higher short-term interest rates and a steeper yield curve would generally raise ROA or ROE; counterbalancing effects differ across banks depending on business models.

### Methodology and analytical approach
- Two-step empirical strategy:
  - Panel regression analysis to establish reliable determinants of bank profitability (focus on SSM-significant institutions, SIs).
  - Quantile regressions to generate profitability distributions conditional on bank-specific, cyclical, and structural determinants; selected determinants are shocked to assess changes in the shape of the distribution.
- Quantile-regression based conditional distributions:
  - Quantile regressions estimate conditional quantile functions for q = {0.05; 0.25; 0.50; 0.75; 0.95}.
  - A flexible parametric ‘skewed’ t-distribution is fitted to the estimated quantiles to recover a smoothed conditional probability density function.
  - The skewed-t density f(y; μ, s, v, ξ) with parameters {μ, s, v, ξ} is chosen for flexibility in skewness and tail behavior; parameters are pinned down by minimizing squared distance between estimated quantiles and theoretical quantiles.

### Data, sample, and stylized facts
- Data sources and sample:
  - Balance sheet and income statement information from the FitchConnect database for 2007–2016, complemented with country-level macro data and structural indicators.
  - Sample includes 109 SSM-supervised significant institutions (SIs), amounting to about €23 trillion in total assets in 2015.
  - A balanced sample of 45 SSM SIs (accounting for 56 percent of sample assets in 2016) is used for some stylized facts.
- Key stylized facts:
  - Average profitability has been on a downtrend since 2007, with wide variation across banks.
  - ROA outturn for 2016 was 0.34 percent, equal to the sample average (2007–2016).
  - Average ROE stood at only 4.1 percent in 2016.
  - Many banks’ ROE levels are expected by market analysts to most likely remain below 8 percent in coming years.
  - Over the sample period, European growth rate and the NPL ratio averaged 0.8 percent and 7.4 percent, respectively.
  - Bank business models are diverse: “traditional” banks (above-median loans-to-assets and deposits-to-assets) comprise €4 trillion in assets; “nontraditional” banks (large share of trading assets, more wholesale funding, include some G-SIBs) account for €14 trillion in assets.
  - NPL and cost-to-income ratios display significant dispersion across banks; NPLs remain elevated in 2016 and progress in reduction is uneven.

### Key empirical findings on bank profitability
- ROE distribution characteristics (2016):
  - Highly skewed distribution.
  - Banks below the 25th percentile (<Q1) have an average ROE of –16 percent, 20 percentage points worse than the next quartile.
  - ROE in the top quartile (>Q3) is about 5 percentage points higher than in the second highest quartile.
  - Banks in the left tail (lowest ROE) have on average:
    - ROA of –1 percent
    - NPL ratio of 22 percent
    - cost-to-income ratio of 81 percent
- Baseline OLS determinants of ROA (selected exact coefficients):
  - Size (log assets): -0.532** (0.2590)
  - GDP growth: 0.272*** (0.0681)
  - NPL ratio: -0.0457** (0.0217)
  - Observations: 794; R-squared: 0.482
- Over the sample period, growth and the NPL ratio had averages of 0.8 percent and 7.4 percent, respectively.

### Robustness and supplementary results
- Additional variables and estimation approaches considered:
  - Bank-specific loan growth and change in the NPL ratio, country slope of the yield curve (5-year minus 3-month government bond yields), FCIs, and the area-wide short-term interest rate.
  - Re-estimation using a balanced sample and the GMM estimator (Arellano and Bond, 1991) yield broadly similar findings to the baseline OLS.
- Specific robustness findings:
  - The change in the NPL ratio is statistically significant but strongly correlated with GDP growth; both stock and flow of NPLs drag on profitability.
  - A steeper yield curve or higher short-term interest rates do not significantly improve profitability on average in this sample.
  - Tighter financial conditions (higher FCI) tend to adversely affect bank earnings through valuation losses and rising funding costs.
  - A lagged dependent variable is statistically insignificant and negative in some specifications.
- Risk-adjusted profitability:
  - The z-score and volatility-scaled ROA/ROE regressions show the NPL ratio remains highly statistically significant; the growth–risk-adjusted profit link is less precisely estimated in cross-section.
- Winsorization:
  - 2.5 percent winsorization was also considered.

### Quantile regressions and heterogeneity
- Growth and the NPL ratio remain robust determinants of profitability across quantiles (25th, 50th, 75th) for ROA and ROE.
  - Coefficients on growth and NPLs decrease monotonically from the 25th to the 75th quantiles.
  - Example: ROA growth coefficient is 0.2 in the 25th quantile and 0.09 in the 75th quantile.
- Implications:
  - Banks with greater profitability challenges benefit most from higher GDP growth and from lower NPL ratios.
  - Contrary to OLS, quantile regressions indicate operational efficiency matters: lower cost-to-income ratios are associated with higher ROA outside the weakest profitability tail.
  - A greater deposit-to-asset ratio is positively correlated with ROA in the quantile regressions.

### Conditional profitability distributions and shocks
- Baseline conditional ROE distribution (from quantile regressions evaluated at sample means):
  - Mean of 5 percent
  - Mode of 9 percent
  - Standard deviation of 20 percent
  - Distribution has a long left tail of chronically low-profitability banks.
- Effects of shocks to growth and NPLs (one standard deviation shocks relative to sample averages):
  - Over the 2007–2017 sample, the standard deviations are:
    - growth: 3.3 percent
    - NPL ratio: 8.9 percent
  - A positive one standard deviation shock to growth shifts the ROE distribution rightward, reduces variance, and thins the left tail while increasing mass around approximately 12 percent ROE.
  - A negative one standard deviation shock to the NPL ratio produces a broadly similar rightward shift and thinning of the left tail.
  - In both shocked cases the distribution remains skewed with a persistent left tail, though the area under that tail is reduced.
- Illustrative simulations and probability shifts (selected exact figures from Table 10 and text):
  - ROE Threshold: <8 percent / >8 percent
    - Baseline: 82.5 / 17.5
    - Higher Growth: 61.4 / 38.6
    - Lower NPLs: 71.9 / 28.1
    - Higher groth and Lower NPLs: 49.1 / 50.9
  - Under the baseline distribution, the probability of a “representative” bank in the sample having ROE less than 8 percent is 83 percent (text); Table 10 reports 82.5 percent as baseline.
  - An increase in growth of one standard deviation:
    - Reduces the likelihood of ROE being below 8 percent to 61 percent (text).
    - Raises the probability of ROE greater than 8 percent by 21 percentage points (to 39 percent) (text).
  - A 1 standard deviation decrease in the NPL ratio:
    - The likelihood of ROE below 8 percent declines to 72 percent (text).
    - Table 10 reports the “Lower NPLs” scenario probability of ROE < 8 as 71.9 percent and > 8 as 28.1 percent.
  - Joint shock (growth + lower NPLs):
    - The probability of ROE less than 8 percent declines to 49 percent (text).
    - Table 10 reports for “Higher groth and Lower NPLs” ROE < 8 at 49.1 percent and ROE > 8 at 50.9 percent.
- Interaction and nonlinearity:
  - The joint materialization of the two shocks reduces the probability of ROE falling below 8 percent by more than if these shocks are considered individually (reflecting underlying nonlinear interactions).
  - The interaction term, when introduced into the baseline (quantile) regression specifications, is not robustly statistically significant (text).

### Policy implications and recommendations
- Macro and asset-quality priorities:
  - Policies that support higher GDP growth can materially improve bank profitability (notably for weaker banks).
  - Reducing NPL stocks and flows lowers provisioning and other related costs, thereby improving ROA and pre-provision profitability.
- Bank-level operational reforms:
  - Improving operational efficiency (reducing cost-to-income ratios) is important for profitability, especially outside the weakest tail of banks.
  - Adjustments to business models (for example, increasing deposit-to-asset ratios) show promise in improving ROA.
- Monitoring and macroprudential outlook:
  - Persistent skewness and a long left tail in profitability distributions imply concentrated vulnerability among a subset of banks and warrant targeted supervisory attention.
  - Shocks to growth and NPLs alter not only mean profitability but the entire distribution, suggesting stress testing and policy design should incorporate distributional impacts, not only average effects.
- Specific policy recommendations (as stated):
  - Some banks, particularly those in the weakest tail of the profitability distribution, should resolutely address their NPL stocks.
  - Policies to achieve greater cost efficiency (e.g., digitalization) could enhance profitability for many banks.
  - Revamping business models should be pursued with custom-tailored approaches given heterogeneous results across banks.
  - The combination of a decisive reduction of NPLs amid a strong recovery could significantly increase banks’ profitability prospects—joint shocks produce larger gains than individual shocks due to nonlinear interactions.

### Appendix: Quantile Regressions — Return on Equity (selected coefficient panels)
- Sample and quantiles:
  - Quantiles reported: 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th
  - Observations: 798
- Selected coefficient estimates (coefficient (standard error)):
  - logA_l:
    - 10th: -7.726 (4.49)
    - 20th: -8.229 (3.21)
    - 30th: -6.564 (2.39)
    - 40th: -4.563 (1.47)
    - 50th: -4.409 (2.62)
    - 60th: -3.668 (1.36)
    - 70th: -3.470 (1.02)
    - 80th: -4.166 (1.18)
    - 90th: -6.617 (1.81)
  - equitytotalassets_l:
    - 10th: -0.146 (0.40)
    - 20th: 0.122 (0.28)
    - 30th: 0.190 (0.21)
    - 40th: -0.034 (0.13)
    - 50th: -0.186 (0.23)
    - 60th: -0.274 (0.12)
    - 70th: -0.453 (0.09)
    - 80th: -0.627 (0.10)
    - 90th: -1.061 (0.16)
  - gdpgrowth:
    - 10th: 2.678 (0.37)
    - 20th: 2.488 (0.26)
    - 30th: 2.277 (0.20)
    - 40th: 1.916 (0.12)
    - 50th: 1.681 (0.21)
    - 60th: 1.378 (0.11)
    - 70th: 1.064 (0.08)
    - 80th: 1.001 (0.10)
    - 90th: 0.965 (0.15)
  - nplratio_l:
    - 10th: -0.542 (0.16)
    - 20th: -0.414 (0.12)
    - 30th: -0.451 (0.09)
    - 40th: -0.472 (0.05)
    - 50th: -0.464 (0.09)
    - 60th: -0.215 (0.05)
    - 70th: -0.160 (0.04)
    - 80th: -0.137 (0.04)
    - 90th: -0.180 (0.06)
  - costtoincome_l:
    - 10th: -0.006 (0.03)
    - 20th: -0.026 (0.02)
    - 30th: -0.031 (0.01)
    - 40th: -0.013 (0.01)
    - 50th: -0.009 (0.02)
    - 60th: 0.002 (0.01)
    - 70th: 0.013 (0.01)
    - 80th: 0.020 (0.01)
    - 90th: 0.035 (0.01)
  - loanstoassets_l:
    - 10th: -0.131 (0.14)
    - 20th: -0.156 (0.10)
    - 30th: -0.102 (0.07)
    - 40th: -0.103 (0.04)
    - 50th: -0.130 (0.08)
    - 60th: -0.110 (0.04)
    - 70th: -0.123 (0.03)
    - 80th: -0.092 (0.04)
    - 90th: -0.101 (0.05)
  - depositstoassets_l:
    - 10th: 0.089 (0.14)
    - 20th: 0.064 (0.10)
    - 30th: 0.022 (0.07)
    - 40th: 0.021 (0.05)
    - 50th: 0.022 (0.08)
    - 60th: 0.094 (0.04)
    - 70th: 0.130 (0.03)
    - 80th: 0.083 (0.04)
    - 90th: 0.084 (0.06)
  - noninterestincomegrossrevenues_l:
    - 10th: -0.021 (0.02)
    - 20th: -0.033 (0.02)
    - 30th: -0.021 (0.01)
    - 40th: -0.010 (0.01)
    - 50th: -0.008 (0.01)
    - 60th: 0.000 (0.01)
    - 70th: 0.007 (0.00)
    - 80th: 0.012 (0.01)
    - 90th: 0.024 (0.01)
  - largest5:
    - 10th: -0.199 (0.19)
    - 20th: -0.292 (0.14)
    - 30th: -0.258 (0.10)
    - 40th: -0.196 (0.06)
    - 50th: -0.222 (0.11)
    - 60th: -0.179 (0.06)
    - 70th: -0.155 (0.04)
    - 80th: -0.140 (0.05)
    - 90th: -0.146 (0.08)
- Notes:
  - Bank and year fixed effects not shown.
  - Standard errors in parentheses.
  - *** p<0.01, ** p<0.05, * p<0.1

*Source: IMF Working Paper—“11. Summary: Conditional Profitability (ROE) Distributions” (excerpt provided).*

### References ________________________________________________________________34

### References ________________________________________________________________34

### Figures
- 1. Euro Area Banks (Significant Institutions): Key Trends and Stylized Facts ___________31
- 2.Illustrative Conditional Profitability (ROE) Distributions _________________________32

### Tables
- 1. Euro Area Bank Sample ___________________________________________________22
- 2. Descriptive Statistics of Main Variables_______________________________________23
- 3. Stylized Facts: Key Bank-Specific Determinants ________________________________23
- 4. Baseline Profitability Regressions: Return on Assets and Components _______________24
- 5. Robustness Analysis: Return on Assets _______________________________________25
- 6. Return on Equity Regressions _______________________________________________26
- 7. Robustness Analysis: Risk-Adjusted Profitability Measures _______________________27
- 8. Quantile Regressions: Return on Assets _______________________________________28
- 9. Quantile Regressions: Return on Equity _______________________________________29

*Source: wpiea2019254-print-pdf - References ________________________________________________________________34*

### 11. Summary: Conditional Profitability (ROE) Distributions ________________________30

### 11. Summary: Conditional Profitability (ROE) Distributions

### Introduction and motivation
- European banks’ profitability has been low for over a decade in aggregate and particularly for a “tail” of weak performers.
- Two headline measures—return on assets (ROA) and return on equity (ROE)—edged up in 2018 but low profitability remains a concern for numerous banks.
- Low profitability is a systemic financial stability concern because banks need profits to (re-)build buffers, and weak profits can foster risk-taking (“gambling for resurrection”) and raise the cost of raising capital.
- The paper emphasizes bank heterogeneity and focuses on conditional profitability distributions rather than average effects to better capture outcomes for weaker banks.

### Main results and findings
- The most robust determinants of bank profitability across large euro area banks appear to be:
  - Real GDP growth.
  - The nonperforming loan (NPL) ratio.
- Growth effects:
  - An increase in the growth rate of 1 percentage point is associated with a 15–35 basis point rise in ROA.
  - This effect is considerable given that average ROA across banks over 2007–2016 was 34 basis points.
  - Some evidence suggests growth boosts bank profits mainly by reducing loan loss provisions and enhancing noninterest income.
- NPL effects:
  - A 1 percentage point decline in the NPL ratio can lift ROA by about 4–9 basis points.
  - Higher stocks of NPLs are associated with higher servicing costs tied to impaired loans, which drag on profitability.
- Conditional distributional results (109 SIs, 2007–2016):
  - Under the baseline, the likelihood of a representative bank’s ROE falling below 8 percent remains elevated at 83 percent, ceteris paribus.
  - Raising growth by 1 standard deviation (that is, 3.3 percentage points) reduces this likelihood by 21 percentage points.
  - Under a scenario with higher growth and a lower NPL ratio, the probability of a representative bank having ROE less than 8 percent declines to 49 percent — a difference of 33 percentage points relative to the baseline.
  - The joint materialization of higher growth and lower NPLs reduces the probability of ROE falling below 8 percent more than these shocks considered individually (reflecting nonlinear interactions).
- Other determinants:
  - Lower cost-to-income ratios are associated with higher profitability for banks outside the weakest end of the profitability spectrum.
  - Results on business models and market concentration are mixed.
  - It is difficult to identify whether higher short-term interest rates and a steeper yield curve would generally raise ROA or ROE; counterbalancing effects differ across banks depending on business models.

### Methodology and analytical approach
- Two-step empirical strategy:
  - Panel regression analysis to establish reliable determinants of bank profitability (focus on SSM-significant institutions, SIs).
  - Quantile regressions to generate profitability distributions conditional on bank-specific, cyclical, and structural determinants; selected determinants are shocked to assess changes in the shape of the distribution.
- Quantile-regression based conditional distributions:
  - Quantile regressions estimate conditional quantile functions for q = {0.05; 0.25; 0.50; 0.75; 0.95}.
  - A flexible parametric ‘skewed’ t-distribution is fitted to the estimated quantiles to recover a smoothed conditional probability density function.
  - The skewed-t density f(y; μ, s, v, ξ) with parameters {μ, s, v, ξ} is chosen for flexibility in skewness and tail behavior; parameters are pinned down by minimizing squared distance between estimated quantiles and theoretical quantiles.

### Data, sample, and stylized facts
- Data sources and sample:
  - Balance sheet and income statement information from the FitchConnect database for 2007–2016, complemented with country-level macro data and structural indicators.
  - Sample includes 109 SSM-supervised significant institutions (SIs), amounting to about €23 trillion in total assets in 2015.
  - A balanced sample of 45 SSM SIs (accounting for 56 percent of sample assets in 2016) is used for some stylized facts.
- Key stylized facts:
  - Average profitability has been on a downtrend since 2007, with wide variation across banks.
  - ROA outturn for 2016 was 0.34 percent, equal to the sample average (2007–2016).
  - Average ROE stood at only 4.1 percent in 2016.
  - Many banks’ ROE levels are expected by market analysts to most likely remain below 8 percent in coming years.
  - Over the sample period, European growth rate and the NPL ratio averaged 0.8 percent and 7.4 percent, respectively.
  - Bank business models are diverse: “traditional” banks (above-median loans-to-assets and deposits-to-assets) comprise €4 trillion in assets; “nontraditional” banks (large share of trading assets, more wholesale funding, include some G-SIBs) account for €14 trillion in assets.
  - NPL and cost-to-income ratios display significant dispersion across banks; NPLs remain elevated in 2016 and progress in reduction is uneven.

### Policy implications and takeaways
- An economic recovery alone will likely be insufficient to resolve many banks’ enduring profitability challenges.
- For many banks, particularly weaker ones, a determined reduction in NPLs combined with improvements in cost efficiency holds the most promise for durably raising profitability.
- Benefits of aggressive NPL reduction are amplified in the context of a robust economic upswing; joint policies that support growth and NPL resolution can materially reduce the probability of banks’ ROE falling below threshold levels important to investors.
- Customized approaches to revising individual bank business models, and measures to improve cost-to-income ratios, are important complements to macroeconomic recovery.

*Source: IMF Working Paper—“11. Summary: Conditional Profitability (ROE) Distributions” (excerpt provided).*

### 3.3 percent as shown in Table 2). In 2016, growth rate rose to 1.2 percent and its standard

### wpiea2019254-print-pdf - 3.3 percent as shown in Table 2). In 2016, growth rate rose to 1.2 percent and its standard

### Key empirical findings on bank profitability
- The ROE distribution in 2016 is highly skewed:
  - Banks below the 25th percentile (<Q1) have an average ROE of –16 percent, 20 percentage points worse than the next quartile.
  - ROE in the top quartile (>Q3) is about 5 percentage points higher than in the second highest quartile.
  - Banks in the left tail (lowest ROE) have on average:
    - ROA of –1 percent
    - NPL ratio of 22 percent
    - cost-to-income ratio of 81 percent
- Baseline OLS results identify real GDP growth and the NPL ratio, besides total assets, as the most reliable determinants of ROA:
  - A 1 percentage point increase in growth raises ROA by 27 basis points.
  - Average ROA across banks over 2007–2016 was 34 basis points.
  - A 1 percentage point lower NPL ratio raises ROA by 5 basis points.
  - Over the sample period, growth and the NPL ratio had averages of 0.8 percent and 7.4 percent, respectively.
- Channels driving the procyclicality of ROA:
  - Higher growth increases noninterest revenue streams and reduces loan-loss provisioning.
  - 60 percent of the effect of lagged NPLs on ROA stems from provisioning needs.
  - Elevated NPL stocks are associated with higher operational and legal costs and with lower pre-provision ROA.

### Robustness and supplementary results
- Additional variables and estimation approaches:
  - Bank-specific loan growth and change in the NPL ratio, country slope of the yield curve (5-year minus 3-month government bond yields), FCIs, and the area-wide short-term interest rate were considered.
  - Re-estimation using a balanced sample and the GMM estimator (Arellano and Bond, 1991) yield broadly similar findings to the baseline OLS.
- Specific robustness findings:
  - The change in the NPL ratio is statistically significant but strongly correlated with GDP growth; both stock and flow of NPLs drag on profitability.
  - A steeper yield curve or higher short-term interest rates do not significantly improve profitability on average in this sample.
  - Tighter financial conditions (higher FCI) tend to adversely affect bank earnings through valuation losses and rising funding costs.
  - A lagged dependent variable is statistically insignificant and negative in some specifications.
- Risk-adjusted profitability:
  - The z-score and volatility-scaled ROA/ROE regressions show the NPL ratio remains highly statistically significant; the growth–risk-adjusted profit link is less precisely estimated in cross-section.

### Quantile regressions and heterogeneity
- Growth and the NPL ratio remain robust determinants of profitability across quantiles (25th, 50th, 75th) for ROA and ROE.
  - Coefficients on growth and NPLs decrease monotonically from the 25th to the 75th quantiles.
  - Example: ROA growth coefficient is 0.2 in the 25th quantile and 0.09 in the 75th quantile.
- Implications of quantile results:
  - Banks with greater profitability challenges benefit most from higher GDP growth and from lower NPL ratios.
  - Contrary to OLS, quantile regressions indicate operational efficiency matters: lower cost-to-income ratios are associated with higher ROA outside the weakest profitability tail.
  - A greater deposit-to-asset ratio is positively correlated with ROA in the quantile regressions.

### Conditional profitability distributions and shocks
- Baseline conditional ROE distribution (from quantile regressions evaluated at sample means):
  - Mean of 5 percent
  - Mode of 9 percent
  - Standard deviation of 20 percent
  - Distribution has a long left tail of chronically low-profitability banks.
- Effects of shocks to growth and NPLs (one standard deviation shocks relative to sample averages):
  - Over the 2007–2017 sample, the standard deviations are:
    - growth: 3.3 percent
    - NPL ratio: 8.9 percent
  - A positive one standard deviation shock to growth shifts the ROE distribution rightward, reduces variance, and thins the left tail while increasing mass around approximately 12 percent ROE.
  - A negative one standard deviation shock to the NPL ratio produces a broadly similar rightward shift and thinning of the left tail.
  - In both shocked cases the distribution remains skewed with a persistent left tail, though the area under that tail is reduced.
- Quantitative assessments:
  - Probabilities of ROE being above and below an 8 percent threshold were computed under the baseline and under shocked distributions (presented in the original Table 10).

### Policy-relevant implications and recommendations
- Macro and asset-quality priorities:
  - Policies that support higher GDP growth can materially improve bank profitability (notably for weaker banks).
  - Reducing NPL stocks and flows lowers provisioning and other related costs, thereby improving ROA and pre-provision profitability.
- Bank-level operational reforms:
  - Improving operational efficiency (reducing cost-to-income ratios) is important for profitability, especially outside the weakest tail of banks.
  - Adjustments to business models (for example, increasing deposit-to-asset ratios) show promise in improving ROA.
- Monitoring and macroprudential outlook:
  - Persistent skewness and a long left tail in profitability distributions imply concentrated vulnerability among a subset of banks and warrant targeted supervisory attention.
  - Shocks to growth and NPLs alter not only mean profitability but the entire distribution, suggesting stress testing and policy design should incorporate distributional impacts, not only average effects.

*Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019254-print-pdf.pdf*

### 2.5 percent winsorization was also considered.

### wpiea2019254-print-pdf - 2.5 percent winsorization was also considered.

### Illustrative simulations and probability shifts
- Under the baseline distribution, the probability of a “representative” bank in the sample having ROE less than 8 percent is 83 percent; i.e., 83 percent of the distribution is below 8 percent.
- An increase in growth of one standard deviation:
  - Reduces the likelihood of ROE being below 8 percent to 61 percent (text).
  - Raises the probability of ROE greater than 8 percent by 21 percentage points (to 39 percent) (text).
  - Note: the text also reports a closely related baseline probability of ROE < 8 percent as 82.5 percent in Table 10.
- A 1 standard deviation decrease in the NPL ratio:
  - The likelihood of ROE below 8 percent declines to 72 percent (text).
  - Table 10 reports the “Lower NPLs” scenario probability of ROE < 8 as 71.9 percent and > 8 as 28.1 percent.
- Joint shock: growth increases by one standard deviation and the NPL ratio decreases by one standard deviation:
  - The probability of ROE less than 8 percent declines to 49 percent (text).
  - Table 10 reports for “Higher groth and Lower NPLs” (sic) ROE < 8 at 49.1 percent and ROE > 8 at 50.9 percent.
- Interaction and nonlinearity:
  - The joint materialization of the two shocks reduces the probability of ROE falling below 8 percent by more than if these shocks are considered individually (reflecting underlying nonlinear interactions).
  - The interaction, when introduced into the baseline (quantile) regression specifications, is not robustly statistically significant (text).

### Key empirical findings on determinants of profitability
- The empirical analysis reveals that real GDP growth and the NPL ratio are the most reliable medium-term determinants of euro area bank profitability (conclusions).
- Higher growth raises profits on average, but a significant share of banks in the weakest tail of the profitability distribution would most likely continue to struggle even with a cyclical upswing (conclusions).
- Greater cost efficiency (through digitalization, for example) could enhance profitability of many banks (conclusions).
- Business model results are mixed; revamping business models could improve profitability for some banks, suggesting the need for custom-tailored approaches (conclusions).

### Regression and robustness highlights (selected exact coefficients and results)
- Baseline ROA regressions (Table 4) — selected coefficients (standard errors in parentheses):
  - Size (log assets): -0.532** (0.2590)
  - GDP growth: 0.272*** (0.0681)
  - NPL ratio: -0.0457** (0.0217)
  - Observations: 794; R-squared: 0.482
- Robustness analysis (Table 5) — GDP growth consistently positive and significant:
  - GDP growth coefficients reported across columns: 0.272***; 0.187***; 0.269***; 0.225**; 0.306**; 0.177***; 0.353***; 0.159*** (standard errors as tabulated).
  - NPL ratio coefficients often negative and significant (e.g., -0.0457**, -0.0711***, -0.0557***, -0.0568**, -0.0622**, -0.0426*, -0.0695***, -0.0847***).
- Return on Equity regressions (Table 6) — selected coefficients:
  - GDP growth: coefficients include 4.329**; 2.502; 3.842**; 3.452; 4.596; 2.915***; 5.671*; 1.551* (standard errors as tabulated).
  - NPL ratio: examples include -0.416; -0.961**; -0.728**; -0.890*; -1.180*; -0.378; -0.836**; -1.682**.
  - Observations: 794 in many specifications; R-squared values reported (e.g., 0.220, 0.246, 0.217).
- Quantile regressions indicate profitability in the lower ends of the distribution are more sensitive to changes in growth and the NPL ratio (text and Table 8, Table 9).

### Conditional ROE distribution summary (selected exact figures from Table 10)
- ROE Threshold: <8 percent / >8 percent
  - Baseline: 82.5 / 17.5
  - Higher Growth: 61.4 / 38.6
  - Lower NPLs: 71.9 / 28.1
  - Higher groth and Lower NPLs: 49.1 / 50.9
- Descriptive statistics (Table 10):
  - Growth — Mean: 0.8; Standard deviation: 3.3
  - NPL — Mean: 7.4; Standard deviation: 8.9

### Policy implications and recommendations (as stated)
- Some banks, particularly those in the weakest tail of the profitability distribution, should resolutely address their NPL stocks (conclusions).
- Policies to achieve greater cost efficiency (e.g., digitalization) could enhance profitability for many banks (conclusions).
- Revamping business models should be pursued with custom-tailored approaches given heterogeneous results across banks (conclusions).
- The combination of a decisive reduction of NPLs amid a strong recovery could significantly increase banks’ profitability prospects—joint shocks produce larger gains than individual shocks due to nonlinear interactions (discussion and illustrative simulations).

*Source: wpiea2019254-print-pdf - 2.5 percent winsorization was also considered.*

### Appendix Table 1. Quantile Regressions: Return on Equity

### Appendix Table 1. Quantile Regressions: Return on Equity

### Notes
- Bank and year fixed effects not shown.
- Standard errors in parentheses.
- *** p<0.01, ** p<0.05, * p<0.1
- Quantile regressions

### Sample and quantiles
- Quantiles reported: 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th
- Observations: 798

### Coefficient estimates (by variable and quantile)
- logA_l
  - 10th: -7.726 (4.49)
  - 20th: -8.229 (3.21)
  - 30th: -6.564 (2.39)
  - 40th: -4.563 (1.47)
  - 50th: -4.409 (2.62)
  - 60th: -3.668 (1.36)
  - 70th: -3.470 (1.02)
  - 80th: -4.166 (1.18)
  - 90th: -6.617 (1.81)

- equitytotalassets_l
  - 10th: -0.146 (0.40)
  - 20th: 0.122 (0.28)
  - 30th: 0.190 (0.21)
  - 40th: -0.034 (0.13)
  - 50th: -0.186 (0.23)
  - 60th: -0.274 (0.12)
  - 70th: -0.453 (0.09)
  - 80th: -0.627 (0.10)
  - 90th: -1.061 (0.16)

- gdpgrowth
  - 10th: 2.678 (0.37)
  - 20th: 2.488 (0.26)
  - 30th: 2.277 (0.20)
  - 40th: 1.916 (0.12)
  - 50th: 1.681 (0.21)
  - 60th: 1.378 (0.11)
  - 70th: 1.064 (0.08)
  - 80th: 1.001 (0.10)
  - 90th: 0.965 (0.15)

- nplratio_l
  - 10th: -0.542 (0.16)
  - 20th: -0.414 (0.12)
  - 30th: -0.451 (0.09)
  - 40th: -0.472 (0.05)
  - 50th: -0.464 (0.09)
  - 60th: -0.215 (0.05)
  - 70th: -0.160 (0.04)
  - 80th: -0.137 (0.04)
  - 90th: -0.180 (0.06)

- costtoincome_l
  - 10th: -0.006 (0.03)
  - 20th: -0.026 (0.02)
  - 30th: -0.031 (0.01)
  - 40th: -0.013 (0.01)
  - 50th: -0.009 (0.02)
  - 60th: 0.002 (0.01)
  - 70th: 0.013 (0.01)
  - 80th: 0.020 (0.01)
  - 90th: 0.035 (0.01)

- loanstoassets_l
  - 10th: -0.131 (0.14)
  - 20th: -0.156 (0.10)
  - 30th: -0.102 (0.07)
  - 40th: -0.103 (0.04)
  - 50th: -0.130 (0.08)
  - 60th: -0.110 (0.04)
  - 70th: -0.123 (0.03)
  - 80th: -0.092 (0.04)
  - 90th: -0.101 (0.05)

- depositstoassets_l
  - 10th: 0.089 (0.14)
  - 20th: 0.064 (0.10)
  - 30th: 0.022 (0.07)
  - 40th: 0.021 (0.05)
  - 50th: 0.022 (0.08)
  - 60th: 0.094 (0.04)
  - 70th: 0.130 (0.03)
  - 80th: 0.083 (0.04)
  - 90th: 0.084 (0.06)

- noninterestincomegrossrevenues_l
  - 10th: -0.021 (0.02)
  - 20th: -0.033 (0.02)
  - 30th: -0.021 (0.01)
  - 40th: -0.010 (0.01)
  - 50th: -0.008 (0.01)
  - 60th: 0.000 (0.01)
  - 70th: 0.007 (0.00)
  - 80th: 0.012 (0.01)
  - 90th: 0.024 (0.01)

- largest5
  - 10th: -0.199 (0.19)
  - 20th: -0.292 (0.14)
  - 30th: -0.258 (0.10)
  - 40th: -0.196 (0.06)
  - 50th: -0.222 (0.11)
  - 60th: -0.179 (0.06)
  - 70th: -0.155 (0.04)
  - 80th: -0.140 (0.05)
  - 90th: -0.146 (0.08)

*Source: Appendix Table 1, "Quantile Regressions: Return on Equity."*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019254-print-pdf.pdf_