## 4. Profitability

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### Model specification and variables
- Estimated equation (panel data, i = 1,...,96; t = 1998,...,2005):
  - profit_{i,t} = α1 + β1 capital_{i,t} + β2 npl_{i,t} + β3 bcycle_{i,t} + β4 inflation_{i,t} + β5 reer_{i,t-1} + β6 int_r_{i,t} + β7 ovr_head_{i,t} + β8 conc_{i,t} + ε_{i,t}  (Equation (4))

- Variable definitions and expected effects:
  - capital: ratio of equity capital to assets. Expected effect: +. Explanation: Banks with higher capital face lower funding costs and higher net interest margins and profits.
  - npl: non performing loans to total loans (proxy for credit risk). Expected effect: -. Explanation: Higher exposure to risk is associated with lower profitability.
  - bcycle: cycle component (HP-filtered) of real GDP growth. Expected effect: -. Explanation: Economic booms are associated with higher bank profitability.
  - inflation: annual change in the inflation rate. Expected effect: ambiguous. Explanation: Inflation may raise realized interest margins and profitability if pass-through to income exceeds pass-through to costs.
  - reer: annual change in the real effective exchange rate. Expected effect: ambiguous. Explanation: Depends on the financial system’s share of assets held abroad.
  - int_r: average change in short term interest rates over the previous two years. Expected effect: +. Explanation: Depends on pass-through to lending vs deposit rates.
  - ovr_head: overhead cost (accounting value of a bank’s overhead costs as a share of total assets). Expected effect: -. Explanation: Higher costs reduce profits.
  - conc: concentration measured by assets of the 4 largest banks to total assets. Expected effect: -. Explanation: Increased competition lowers banks’ profits.
  - Interaction dummies: conc*bcycle (conc1*bcycle, conc2*bcycle) test whether the business cycle impact on profitability differs by market concentration (Low, Medium, High; conc1 and conc2 are dummy categories with one omitted group).

### Empirical estimation approach
- Reported specifications: pooled OLS; within groups (fixed effects); random effects.
- Hausman test generated an insignificant p-value; discussion focuses on the random effects results.
- Dependent variable: Return on assets (ROA).

### Main empirical results (Table 4, dependent variable: Return on assets (ROA) to total assets ratio)
- Coefficient estimates (standard errors in parentheses; significance: * 10%; ** 5%; *** 1%):
  - Constant:
    - Pooled OLS: -1.31 (0.33)***
    - Within Groups: -1.03 (0.92)
    - Random Effects: -1.36 (0.54)**
    - Random Effects alternate: -2.00 (0.69)***
  - capital:
    - 0.18 (0.02)***; 0.38 (0.04)***; 0.27 (0.03)***; 0.28 (0.03)***
  - npl:
    - -0.06 (0.02)***; -0.05 (0.02)***; -0.05 (0.02)***; -0.05 (0.02)***
  - bcycle:
    - 0.06 (0.03)*; 0.22 (0.06)***; 0.11 (0.04)***; 0.09 (0.05)*
  - inflation:
    - -0.02 (0.00)***; -0.01 (0.00); -0.01 (0.00)***; -0.01 (0.00)***
  - reer:
    - -0.02 (0.01)**; -0.02 (0.01)***; -0.02 (0.01)***; -0.02 (0.01)***
  - int_r:
    - 0.01 (0.01); 0.03 (0.01)***; 0.02 (0.01)***; 0.02 (0.01)**
  - overhead:
    - -0.30 (0.08)**; -0.65 (0.36)*; -0.27 (0.15)*; -0.21 (0.11)*
  - concentration:
    - 0.73 (0.40)*; -3.66 (1.13)***; -0.67 (0.25)**; -2.11 (0.83)**
  - conc1*bcycle:
    - 0.18 (0.10)*
  - conc2*bcycle:
    - 0.03 (0.07)

- Robust findings highlighted:
  - bcycle has a positive, significant, and robust relationship with profitability (ROA) across specifications: economic booms are associated with higher bank profitability.
  - Interaction conc1*bcycle = 0.18 (0.10)* is positive and significant, implying a larger business cycle impact on profitability in the conc1 concentration category (less concentrated financial systems).
  - capital is positively associated with ROA (coefficients around 0.18 to 0.38, significant at the 1% level).
  - npl is negatively associated with ROA (about -0.05 to -0.06, significant at the 1% level).
  - inflation and int_r show mixed evidence: inflation coefficients are negative and significant in several specifications (e.g., -0.02 (0.00)*** in pooled OLS); int_r is positive and significant in several specifications (e.g., 0.03 (0.01)*** within groups).
  - overhead costs are negatively associated with profitability (coefficients range from -0.30 to -0.21, statistically significant).
  - reer changes are negatively associated with ROA in reported specifications.

### Interpretation and substantive findings
- Stylized facts and econometric evidence:
  - Profitability (ROA) is procyclical: stronger during economic upturns and weaker in downturns.
  - The procyclicality of profitability varies across country and industry structures: market concentration modifies the magnitude of the cycle–profitability link (positive conc1*bcycle).
  - Risk and efficiency matter: higher capital ratios are associated with higher profitability; higher NPLs and higher overhead reduce profitability.
  - Interest rate environment matters: higher short-term interest rates are associated with higher profitability in several specifications, consistent with greater pass-through to lending rates than deposit rates for the average banking system in the sample.
  - Exchange rate movements and inflation show significant associations with profitability in the sample, with negative reer coefficients and mixed inflation coefficients across specifications.

### Implications highlighted by the chapter
- The business cycle is an important determinant of bank profitability; procyclicality suggests comparisons of profitability across countries or over time should account for the phase of the business cycle.
- Market structure and bank-specific characteristics (capital, NPLs, overheads) influence how profitability responds to macroeconomic conditions.
- Given cyclicality, the study recommends that use of FSIs (including profitability measures) in financial system surveillance could be enhanced by cyclically adjusting indicators—filtering out the effects of the business cycle—to avoid misleading cross-country or time comparisons.

### Appendix I: Contemporaneous correlations (FSIs and real GDP growth, 1998–2005)
- Contemporaneous correlations between selected FSIs and Real GDP growth (1998–2005) are presented by GDP per capita classes (via bank deposits to GDP):
  - Class size definitions (by ratio of bank deposits to GDP):
    - Class size 1 = ratio of bank deposits to GDP < 0.28.
    - Class size 2 = ratio of bank deposits to GDP between 0.28 and 0.61.
    - Class size 3 = ratio of bank deposits to GDP > 0.61.
- FSIs plotted:
  - Regulatory capital to risk weighted assets
  - Capital to assets
  - Non performing loans to total loans
  - Return on equity
  - Return on assets
- Real GDP growth lags analyzed:
  - Real GDP growth (t)
  - Real GDP growth (t-1)
  - Real GDP growth (t-2)
- Correlation axis scale in figure: -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 (percent).

### Appendix II: Data description — FSIs and macro/industry variables
- Financial Soundness Indicators (definitions):
  - Capital to assets: capital and reserves / total assets.
  - Regulatory capital to risk-weighted assets: aggregated regulatory capital / aggregated risk-weighted assets.
  - Non performing loans to total loans (NPL): value of NPLs / total value of loan portfolio (including NPLs, before deduction of specific loan-loss provisions).
  - Return on assets (ROA): net income (before taxes) / average value of total assets over the same period.
  - Return on equity (ROE): net income (gross income less gross expenses) / average value of capital (capital and reserves) over the same period.
- Macroeconomic variables listed:
  - Real per capita GDP (constant 2000, in US dollars)
  - Real interest rate
  - Real GDP growth
  - Consumer price index
  - Real lending rate
  - Real effective interest rate
  - Unemployment rate
  - Banking system claims on the private sector to GDP
  - Terms of trade (of goods and services)
- Industry variables listed:
  - BCP index (quality of regulatory supervision)
  - Bank deposits to GDP (size of the financial sector)
  - Deposit money bank assets to GDP (Claims on domestic real nonfinancial sector by deposit money banks as a share of GDP)
  - Concentration (Assets of three largest banks as a share of assets of all commercial banks)
  - Overhead (Accounting value of a bank's overhead costs as a share of its total assets)
- Data sources:
  - Article IV reports (IMF)
  - FSAP reports (IMF)
  - WDI (World Bank)
  - IFS (IMF)
  - WEO
  - Fitch's Bankscope database

### Appendix III: Econometric models (methods described)
- Pooled OLS:
  - OLS on pooled sample across countries and time; treats observations as separate; assumes common coefficients; discards country specific effects into error term.
- Within Groups (fixed effects):
  - Eliminates country-specific unobservable fixed effects; requires strict exogeneity; inconsistent with lagged dependent variables and other endogenous regressors.
- 2SLS (Anderson-Hsiao):
  - First-differenced 2SLS with instruments in second lags of levels; consistent as N → ∞ with T fixed.
- GMM (Differenced and System):
  - Differenced-GMM uses first differences as instruments; System-GMM uses both levels and differences as instruments to improve precision.

### Appendix IV: Model for capital adequacy (partial adjustment framework)
- Conceptual setup:
  - Banks aim at a target capital ratio CAR*.
  - Observed change in bank capital ratio comprises discretionary adjustment toward target and exogenous shocks.
- Key equations (from source):
  - ΔCARj,t = ΔdCARj,t + εj,t  (equation (1))
  - ΔdCARj,t = α (CAR*j,t - CARj,t-1) + ε,t;j  (equation (2); α is speed of adjustment)
  - ΔCARj,t = α (CAR*j,t - CARj,t-1) + εj,t  (equation (3))
- Interpretation:
  - α denotes speed of adjustment of CAR to optimal CAR*.
  - CAR*j,t is unobservable and assumed to depend on bank characteristics, regulatory factors, and macroeconomic factors.
  - εj,t represents exogenous random shocks (e.g., unanticipated economic shocks or unanticipated change in earnings).

*Source: IMF staff calculations, chapter "4. Profitability" and accompanying appendices (from provided content).*

### References..............................................................................................................

### References................................................................................................................................28

### Figures
- 1 Studies of Macro-Financial Sector Linkages ....................................................................5
- 2.      FSIs and the Business Cycle, 1998-2005..........................................................................8
- 3. Variation Across Regions: Cyclicality of FSIs, 1998-2005..............................................9

### Tables
- 1.      Capital Adequacy............................................................................................................17
- 2.      Capital Adequacy............................................................................................................18
- 3.      Asset Quality ..................................................................................................................19

*Source: _wp07115 - References..........................................................................................................*

### 4.      Profitability ..................................................................................................

### 4.      Profitability

### Model specification and variables
- Estimated equation (panel data, i = 1,...,96; t = 1998,...,2005):
  profit_{i,t} = α1 + β1 capital_{i,t} + β2 npl_{i,t} + β3 bcycle_{i,t} + β4 inflation_{i,t} + β5 reer_{i,t-1} + β6 int_r_{i,t} + β7 ovr_head_{i,t} + β8 conc_{i,t} + ε_{i,t}  (Equation (4))

- Variable definitions and expected effects:
  - capital: ratio of equity capital to assets. Expected effect: +. Explanation: Banks with higher capital face lower funding costs and higher net interest margins and profits.
  - npl: non performing loans to total loans (proxy for credit risk). Expected effect: -. Explanation: Higher exposure to risk is associated with lower profitability.
  - bcycle: cycle component (HP-filtered) of real GDP growth. Expected effect: -. Explanation: Economic booms are associated with higher bank profitability.
  - inflation: annual change in the inflation rate. Expected effect: ambiguous. Explanation: Inflation may raise realized interest margins and profitability if pass-through to income exceeds pass-through to costs.
  - reer: annual change in the real effective exchange rate. Expected effect: ambiguous. Explanation: Depends on the financial system’s share of assets held abroad.
  - int_r: average change in short term interest rates over the previous two years. Expected effect: +. Explanation: Depends on pass-through to lending vs deposit rates.
  - ovr_head: overhead cost (accounting value of a bank’s overhead costs as a share of total assets). Expected effect: -. Explanation: Higher costs reduce profits.
  - conc: concentration measured by assets of the 4 largest banks to total assets. Expected effect: -. Explanation: Increased competition lowers banks’ profits.
  - Interaction dummies: conc*bcycle (conc1*bcycle, conc2*bcycle) test whether the business cycle impact on profitability differs by market concentration (Low, Medium, High; conc1 and conc2 are dummy categories with one omitted group).

### Empirical estimation approach
- Reported specifications: pooled OLS; within groups (fixed effects); random effects. Hausman test generated an insignificant p-value, so discussion focuses on the random effects results.
- Dependent variable used: Return on assets (ROA).

### Main empirical results (Table 4, dependent variable: Return on assets (ROA) to total assets ratio)
- Coefficient estimates (standard errors in parentheses; significance: * 10%; ** 5%; *** 1%):
  - Constant: -1.31 (0.33)*** [Pooled OLS]; -1.03 (0.92) [Within Groups]; -1.36 (0.54)** [Random Effects]; -2.00 (0.69)*** [Random Effects alternate]
  - capital: 0.18 (0.02)***; 0.38 (0.04)***; 0.27 (0.03)***; 0.28 (0.03)***  
  - npl: -0.06 (0.02)***; -0.05 (0.02)***; -0.05 (0.02)***; -0.05 (0.02)***  
  - bcycle: 0.06 (0.03)*; 0.22 (0.06)***; 0.11 (0.04)***; 0.09 (0.05)*  
  - inflation: -0.02 (0.00)***; -0.01 (0.00); -0.01 (0.00)***; -0.01 (0.00)***  
  - reer: -0.02 (0.01)**; -0.02 (0.01)***; -0.02 (0.01)***; -0.02 (0.01)***  
  - int_r: 0.01 (0.01); 0.03 (0.01)***; 0.02 (0.01)***; 0.02 (0.01)**  
  - overhead: -0.30 (0.08)**; -0.65 (0.36)*; -0.27 (0.15)*; -0.21 (0.11)*  
  - concentration: 0.73 (0.40)*; -3.66 (1.13)***; -0.67 (0.25)**; -2.11 (0.83)**  
  - conc1*bcycle: 0.18 (0.10)*  
  - conc2*bcycle: 0.03 (0.07)

- Robust findings highlighted in the study:
  - The business cycle (bcycle) has a positive, significant, and robust relationship with profitability (ROA) across specifications: economic booms are associated with higher bank profitability.
  - Interaction term conc*bcycle: conc1*bcycle = 0.18 (0.10)* is positive and significant, implying that the positive impact of the business cycle on profitability is larger in less concentrated financial systems (conc1 corresponds to a concentration category).
  - Capital (equity to assets) is positively associated with ROA: coefficients around 0.18 to 0.38 and significant at the 1% level across specifications.
  - Non-performing loans (npl) are negatively associated with ROA: coefficient about -0.05 to -0.06 and significant at the 1% level.
  - Inflation and real interest rates: mixed evidence—table reports inflation coefficients negative and significant in several specifications (e.g., -0.02 (0.00)*** in pooled OLS), while int_r is positive and significant in several specifications (e.g., 0.03 (0.01)*** within groups), indicating that on average the banking system in the sample can benefit from higher interest rates (pass-through to lending rates exceeding pass-through to deposit rates).
  - Overhead costs are negatively associated with profitability: coefficients range from -0.30 to -0.21 and are statistically significant.
  - Real effective exchange rate changes (reer) are negatively associated with ROA in reported specifications.

### Interpretation and substantive findings
- Aggregate stylized facts and econometric evidence:
  - Profitability (ROA) is procyclical: stronger during economic upturns and weaker in downturns.
  - The procyclicality of profitability varies across country and industry structures: market concentration modifies the magnitude of the cycle–profitability link (conc1*bcycle positive and significant).
  - Risk and efficiency matter: higher capital ratios are associated with higher profitability, while higher NPLs and higher overhead reduce profitability.
  - Interest rate environment matters: higher short-term interest rates are associated with higher profitability in several specifications, consistent with greater pass-through to lending rates than deposit rates for the average banking system in the sample.
  - Exchange rate movements and inflation show significant associations with profitability in the sample, with negative reer coefficients and mixed inflation coefficients across specifications.

### Implications highlighted by the chapter
- The business cycle is an important determinant of bank profitability; this procyclicality suggests that comparisons of profitability across countries or over time should account for the phase of the business cycle.
- Market structure and bank-specific characteristics (capital, NPLs, overheads) influence how profitability responds to macroeconomic conditions.
- Given cyclicality, the study recommends that use of FSIs (including profitability measures) in financial system surveillance could be enhanced by cyclically adjusting indicators—filtering out the effects of the business cycle—to avoid misleading cross-country or time comparisons.

*Source: IMF staff calculations, chapter "4. Profitability" (from the provided content).*

### APPENDIX I: CONTEMPORANEOUS CORRELATIONS (FSIS AND REAL GDP GROWTH)

### APPENDIX I: CONTEMPORANEOUS CORRELATIONS (FSIS AND REAL GDP GROWTH)

### Contemporaneous correlations between selected FSIs and real GDP growth (1998–2005)
- Figure 1c presents contemporaneous correlations (Percent) between selected Financial Soundness Indicators (FSIs) and Real GDP growth for 1998–2005, grouped by GDP per capita (classification via bank deposits to GDP).
- Class size definitions (by ratio of bank deposits to GDP):
  - Class size 1 = for countries where the ratio of bank deposits to GDP is < 0.28.
  - Class size 2 = for countries where the ratio of bank deposits to GDP is between 0.28 and 0.61.
  - Class size 3 = for countries where the ratio of bank deposits to GDP is > 0.61.
- FSIs plotted in Figure 1c:
  - Regulatory capital to risk weighted assets
  - Capital to assets
  - Non performing loans to total loans
  - Return on equity
  - Return on assets
- Real GDP growth lags analyzed:
  - Real GDP growth (t)
  - Real GDP growth (t-1)
  - Real GDP growth (t-2)
- Correlation axis scale in figure: -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 (percent).

### Appendix II: Data description — Financial Soundness Indicators and macro/industry variables
- Financial Soundness Indicators (definitions as provided):
  - Capital to assets: capital and reserves / total assets.
  - Regulatory capital to risk-weighted assets: aggregated regulatory capital / aggregated risk-weighted assets (based on national practice; some industrial countries report ratios consistent with Basel Committee definitions).
  - Non performing loans to total loans (NPL): value of NPLs / total value of loan portfolio (including NPLs, before deduction of specific loan-loss provisions).
  - Return on assets (ROA): net income (before taxes) / average value of total assets over the same period.
  - Return on equity (ROE): net income (gross income less gross expenses) / average value of capital (capital and reserves) over the same period.
- Macroeconomic variables listed:
  - Real per capita GDP (constant 2000, in US dollars)
  - Real interest rate
  - Real GDP growth
  - Consumer price index
  - Real lending rate
  - Real effective interest rate
  - Unemployment rate
  - Banking system claims on the private sector to GDP
  - Terms of trade (of goods and services)
- Industry variables listed:
  - BCP index (measuring the quality of regulatory supervision)
  - Bank deposits to GDP (measuring size of the financial sector)
  - Deposit money bank assets to GDP (Claims on domestic real nonfinancial sector by deposit money banks as a share of GDP) -- measuring size of the financial sector.
  - Concentration (Assets of three largest banks as a share of assets of all commercial banks)
  - Overhead (Accounting value of a bank's overhead costs as a share of its total assets)
- Data sources referenced (as listed):
  - Article IV reports (IMF)
  - FSAP reports (IMF)
  - WDI (World Bank)
  - IFS (IMF)
  - WEO
  - Fitch's Bankscope database
- Note: FSAP... Financial System Assessment Program (IMF/World Bank), IFS...International Finance Statistics (IMF), WDI...World Development Indicators (World Bank), WEO...World Economic Outlook (IMF).

### Countries in sample (regional breakdown)
- Asia / Middle East and North Africa / Latin America (selected enumerated entries shown in source):
  - Asia sample includes: 1 Bangladesh, 2 China, 3 Hong Kong SAR, 4 India, 5 Indonesia, 6 Korea, 7 Malaysia, 8 Philippines, 9 Singapore, 10 Thailand, 11 Armenia, 12 Belarus, 13 Bosnia & Herzegovina, 14 Bulgaria, 15 Croatia, 16 Czech Republic, 17 Estonia, 18 Hungary, 19 Israel, 20 Kyrgyz Republic, 21 Latvia, 22 Lithuania, 23 Moldova, 24 Poland, 25 Romania, 26 Russia, 27 Serbia & Montenegro, 28 Slovak Republic, 29 Slovenia, 30 Turkey, 31 Ukraine.
  - Middle East and North Africa / Latin America sample includes: 32 Argentina, 33 Bolivia, 34 Brazil, 35 Chile, 36 Colombia, 37 Costa Rica, 38 Dominican Republic, 39 Ecuador, 40 El Salvador, 41 Honduras, 42 Jamaica, 43 Mexico, 44 Nicaragua, 45 Panama, 46 Paraguay, 47 Peru, 48 Uruguay, 49 Venezuela.
  - Middle East and North Africa entries also listed among numbers: 50 Azerbaijan, 51 Egypt, 52 Jordan, 53 Kazakhstan, 54 Kuwait, 55 Lebanon, 56 Morocco, 57 Pakistan, 58 Saudi Arabia, 59 Tunisia, 60 United Arab Emirates.
- Emerging Europe / Sub-Saharan Africa / Western Europe / Other Industrial (selected enumerated entries shown in source):
  - Emerging Europe includes entries overlapping with Asia list (e.g., 11 Armenia through 31 Ukraine; 45 Panama appears in list structure).
  - Sub-Saharan Africa includes: 65 Angola, 66 Botswana, 67 Gabon, 68 Ghana, 69 Kenya, 70 Madagascar, 71 Mauritius, 72 Mozambique, 73 Nigeria, 74 Senegal, 75 Sierra Leone, 76 South Africa, 77 Uganda, 78 Zambia, 79 Zimbabwe.
  - Western Europe includes: 80 Austria, 81 Belgium, 82 Finland, 83 France, 84 Germany, 85 Greece, 86 Iceland, 87 Ireland, 88 Italy, 89 Luxembourg, 90 Netherlands.
  - Other Industrial includes: 61 Australia, 62 Canada, 63 Japan, 64 United States, 91 Norway, 92 Portugal, 93 Spain, 94 Sweden, 95 Switzerland, 96 United Kingdom.

### Appendix III: Econometric models (methods described)
- Pooled OLS (OLS on levels):
  - Estimates OLS on pooled sample across countries and time periods; treats individual data points as separate observations.
  - Does not explore within-country information; assumes coefficients common to all countries and periods; discards country specific effects into error term (omitted variable bias).
  - Does not address endogeneity in presence of lagged dependent variables.
- Within Groups (fixed effects):
  - Transforms model (theta differenced) to eliminate country-specific unobservable fixed effects; produces unbiased and consistent estimators under strict exogeneity.
  - Requires strict exogeneity; inconsistent in presence of lagged dependent variables and other endogenous explanatory variables.
  - Associated with loss of identification because observed fixed effects are eliminated with unobserved ones.
- 2SLS (Anderson-Hsiao Two Stage Least Squares):
  - Transform model to eliminate individual effects, then apply instrumental variables; consistent as N → ∞ with T fixed.
  - Anderson and Hsiao (1981, 1982) proposed first-differenced 2SLS with instruments specified in second lags of levels.
  - First differencing does not eliminate all country specific observable effects; no loss in identification; estimator is consistent as N → ∞ for fixed T panels, but generally not efficient.
- GMM (Differenced and System):
  - Addresses dynamic panel-data problems (moving average form of serial correlation and heteroskedasticity) via Generalized Method of Moments (Hansen; Holtz-Eakin, Newey and Rosen; Arellano and Bond).
  - Differenced-GMM specified in levels with first differences as instruments.
  - Arellano and Bover (1995) argue differences may be weak instruments; System-GMM uses both levels (for equations in first differences) and differences (for equations in levels) as instruments to improve precision.

### Appendix IV: Model for capital adequacy (partial adjustment framework)
- Conceptual setup:
  - Banks aim at a target capital ratio CAR*.
  - Observed change in bank capital ratio comprises discretionary adjustment toward target and exogenous shocks.
- Equations from source:
  - Observed decomposition: ΔCARj,t = ΔdCARj,t + εj,t (equation (1) in source).
  - Partial adjustment for discretionary change:
    - ΔdCARj,t = α (CAR*j,t - CARj,t-1) + ε,t;j  (equation (2) in source; α is speed of adjustment).
  - Substituted observed change:
    - ΔCARj,t = α (CAR*j,t - CARj,t-1) + εj,t  (equation (3) in source).
- Interpretation:
  - α denotes speed of adjustment (in the long run of CAR to optimal CAR*).
  - Target capital ratio CAR*j,t is unobservable and assumed to depend on individual bank characteristics, regulatory factors, and macroeconomic factors.
- Institutional considerations:
  - Institutional inertia, high costs of rapid change, or lack of information may prevent instantaneous adjustment to CAR*.
  - εj,t represents exogenous random shocks (e.g., unanticipated economic shocks or unanticipated change in earnings).

### Key methodological references cited (selected)
- Anderson, T.W. and C. Hsiao, 1981; 1982.
- Arellano, M., and S.R. Bond, 1991.
- Arellano, M., and O. Bover, 1995.
- Hansen, L.P., 1982.
- Holtz-Eakin, D., W. Newey and H.S. Rosen, 1988.
- Shrieves and Dahl (1992) and other partial adjustment literature references noted in source.

*Source: _wp07115 - APPENDIX I: CONTEMPORANEOUS CORRELATIONS (FSIS AND REAL GDP GROWTH)*

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