## 1. Panel Regression Results

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### I. Introduction — context and headline quantitative findings
- Economic crises cause a surge in nonperforming loans (NPL); empirical literature reports a negative relationship between economic activity and asset quality for advanced and developing economies.
- Heterogeneity across banks and cross-sectional dependence (CSD) from common shocks can bias estimates if homogeneity is assumed; framework accounts for dynamics, heterogeneity, and CSD.
- Headline quantitative rules of thumb for Ecuador (authors’ estimates under July 2016 oil projections):
  - Short-run: NPL increases by 0.15 pp for every 1 pp fall in real GDP growth.
  - Long-run: NPL increases by 0.55 pp for every 1 pp fall in real GDP growth.
- Baseline NPL projections (two-year horizon, weighted by banks’ credit stocks):
  - Weighted average NPL: 3.8 percent in March 2015 → 6.4 percent at end-2016 → 9.3 percent at end-2017; peak 9.7 percent in 2017Q2.
- Considerable heterogeneity across banks: under baseline some banks reach nearly 15 percent NPL while others remain below 2 percent.

### II. Stylized facts for Ecuador (data patterns motivating the approach)
- Recent large shocks: (i) oil price fall; (ii) real appreciation of the US dollar (dollarization context).
- Real GDP growth highly correlated with real oil price with some delay; real GDP growth fell to about zero percent at end-2015.
- NPL dynamics:
  - Average NPL fell from about 10 percent in 2004 to less than 4 percent before the global financial crisis; rebounded above 5 percent during the crisis and later declined.
  - NPL started rising again with the end of the commodity supercycle; 2016Q1 NPL reached 3.9 percent.
  - Median NPL in 2016Q1: 5.8 percent.
- Banking system features:
  - High concentration; banks of varying size and asset quality.
  - From early 2015, steady deposit withdrawals reduced liquidity buffers; real credit growth follows deposit growth with delay, indicating possible credit rationing.
  - Substantial heterogeneity: more than 10 percent of banks had real credit growth above 10 percent despite deposit falls.

### III. Three-stage econometric stress-testing framework
- Stage 1 — Aggregate macro-financial VAR(푝):
  - Reduced-form specification: z_t = b + Σ_{j=1}^p D_j z_{t−j} + Σ_{j=1}^p F_j x_{t−j} + e_t
  - z_t: real GDP, real credit by private banks, real deposits of private banks (logs); x_t: exogenous real oil price (log).
  - Structural identification via Cholesky ordering: real GDP → real credit → real deposits.
  - Forecasts conditional on IMF-WEO oil price projections (July 2016) for a two-year horizon.
- Stage 2 — Bank-level panel ARDL on logistic-transformed NPL:
  - y_{i,t} = α + Σ_{k=1}^n β_k x_{t−k} + Σ_{k=1}^n δ_k z_{i,t−k} + u_{i,t}, where x_t = real GDP growth; z_{i,t} = bank-specific real deposit growth and real credit growth.
  - Estimators applied: POLS; FEOLS; SGMM (Windmeijer correction); Mean Group (MG); Augmented Mean Group variants (AMG-I and AMG).
  - Target-adjustment specification: y_{i,t} = α + γ y_{i,t−1} + Σ β_k x_{t−k} + Σ δ_k z_{i,t−k} + u_{i,t}.
  - Preferred estimator: AMG that controls for an unobserved common dynamic factor μ̂_t• and averages bank-specific coefficients.
- Stage 3 — Projection:
  - Combine VAR conditional forecasts with bank-specific AMG coefficients to simulate bank-specific NPLs two years out of sample.
  - Common dynamic factor μ̂_t• held at its last observed value.
  - Bank projections aggregated using credit-stock weights to produce weighted average NPL.

### IV. VAR estimation, diagnostics, and dynamics
- Samples and preprocessing:
  - VAR sample: 2002q3 to 2015q4; variables seasonally adjusted (Census X-13).
- Stationarity and cointegration:
  - Levels: series are I(1); first differences are stationary (ADF first-difference statistics: Real GDP -5.799***; Real deposits -6.179***; Real credit -8.206***; Real price of oil -6.711***).
  - Johansen cointegration test: Trace statistic for "None" = 41.003; Max-Eigen statistic for "None" = 26.189* (no cointegration deemed).
- Lag selection and stability:
  - Information criteria and LR tests favor two lags (authors choose two lags).
  - VAR stable: companion matrix roots’ moduli all < 1 (reported largest modulus 0.959518 reported as 0.959).
- Residual diagnostics:
  - Lagrange Multiplier Test: Lag 1 LM Statistic 9.340381; Prob. 0.4065 (no autocorrelation).
  - Portmanteau Test for lag 3: Q-Stat 10.8677; Prob. 0.2849.
- Impulse response highlights (three-year horizon):
  - Real GDP: contemporaneous reaction to its shocks; persistent effect; real credit does not significantly affect real GDP.
  - Real deposits: a one-standard deviation real GDP shock raises deposits for about two years; deposits display strongly significant self-impact lasting more than three years.
  - Real credit: responds significantly to a one-standard deviation real GDP shock after three quarters lasting about three years; credit responds positively and immediately to deposit shocks.

### V. VAR conditional forecasts (IMF-WEO oil price projections, July 2016)
- Forecast patterns under July 2016 oil projections:
  - Real GDP growth projected to remain negative through end-2017, recovering above current levels from its trough in the last quarter of 2016 due to higher projected oil prices.
  - Real deposit growth projected to continue falling until mid-2016 and recover thereafter.
  - Real credit growth shows a delayed fall relative to deposits, reaching its bottom at end-2016.

### VI. Panel estimation results and aggregation to NPL impacts
- Data and sample for panel:
  - Bank-level panel: 22 banks over 2005-15; three banks dropped for short series; AMG estimations drop a fourth bank; observations vary between 704 and 718 depending on estimator.
- Estimation regularities:
  - Lagged dependent variable always significant → persistence in NPL dynamics.
  - First lag of real GDP growth consistently negative and significant across estimators.
  - AMG preferred specification reports a common dynamic factor coefficient 0.307***.
- Short-run and long-run aggregated effects (ARDL aggregation, authors’ averages):
  - Short-run average effect: 0.15 pp increase in NPL per 1 pp fall in real GDP growth.
  - Long-run average effect: 0.55 pp increase in NPL per 1 pp fall in real GDP growth.
- Bank heterogeneity:
  - Bank-specific short-run and long-run coefficients vary; some banks show small counterintuitive positive effects in short- or long-run, but the cross-bank average provides the central rule of thumb.

### VII. NPL projections and scenario dispersion
- Baseline (July 2016 oil price projections) weighted-average NPL path:
  - 3.8 percent (March 2015) → 6.4 percent (end-2016) → 9.3 percent (end-2017), peak 9.7 percent (2017Q2).
- Scenario construction:
  - Optimistic and pessimistic scenarios derived from VAR forecast confidence bands.
- Cross-sectional dispersion:
  - Under baseline projections some banks approach nearly 15 percent NPL while others remain below 2 percent.
  - Distributional percentiles (10th, 25th, 75th, 90th) were used to summarize heterogeneity across scenarios.

### VIII. Conclusions and policy implications
- Stress testing that accounts for bank heterogeneity and CSD produces more accurate assessments of systemic risk and recapitalization needs than aggregate approaches.
- Quantitative rules of thumb for Ecuador (average bank):
  - Short-run: 0.15 pp increase in NPL per 1 pp fall in real GDP growth.
  - Long-run: 0.55 pp increase in NPL per 1 pp fall in real GDP growth.
- Under July 2016 oil projections the macro-financial forecasts imply a negative effect on NPL ratios, with weighted average NPL likely more than doubling over the next two years in the baseline, but with substantial cross-bank heterogeneity (approximately 2 to 15 percent NPL across banks).
- Policy uses of the framework:
  - Enhance surveillance granularity to target supervisory actions on institutions more sensitive to cyclical fluctuations and with lower buffers.
  - Inform preparatory measures: additional provisions, new capital requirements, improved risk management, selective lending constraints.
  - Enable targeted regulatory or macroprudential measures where needed.
  - Adaptable to sub-segments (sector, business line, region) if data are available, enabling targeted policy responses and avoiding over- or underestimation of systemic risk.

### IX. Appendix I — VAR specification tests (key numerical outputs)
- Augmented Dickey-Fuller unit-root test (levels; selected reported statistics):
  - Real GDP (levels): 3.546; -1.103; -2.510
  - Real deposits (levels): 2.006; -2.569; -0.157
  - Real credit (levels): 0.761; -1.989; -1.421
  - Real price of oil (levels): -1.205; -1.951; -1.651
- Augmented Dickey-Fuller (first differences):
  - Real GDP: -5.799***; -5.905***; -5.953***
  - Real deposits: -6.179***; -6.075***; -7.991***
  - Real credit: -8.206***; -8.093***; -7.991***
  - Real price of oil: -6.711***; -6.635***; -6.563***
- Johansen cointegration test (selected statistics):
  - None: Trace Statistic 41.003; Max-Eigen Statistic 26.189*
  - At most 1: Trace Statistic 14.814; Max-Eigen Statistic 8.443
- VAR lag-selection (selected rows as reported):
  - Lag 1: Final prediction Error -17.294; Akaike Information Criterion -16.459*; Schwartz Information Criterion -16.981
  - Lag 2: Modified LR Statistic 20.258*; Final prediction Error 5.33e-12*; Akaike Information Criterion -17.465*; Hannan-Quinn Information Criterion -17.019*
- VAR stability (companion matrix root moduli):
  - Root 1: Modulus 0.959518 (reported as 0.959)
  - Root 2: Modulus 0.818237 (reported as 0.818)
  - Root 3/4: Modulus 0.667
  - Root 5/6: Modulus 0.118
- VAR residual autocorrelation tests:
  - Lagrange Multiplier Test lag 1: LM Statistic 9.340381; Prob. 0.4065
  - Portmanteau Test lag 3: Q-Stat 10.8677; Prob. 0.2849; Adj Q-Stat 11.36909; Prob. 0.2513; df 9

*Source: _wp16236 — authors’ calculations and analysis contained in the source document.*

### 1. Panel Regression Results ............................................................................................

### 1. Panel Regression Results

### Figures referenced in this section
- 1. Variables’ Correlation and Dispersion — page 9
- 2. Stationarity of VAR Series — page 13
- 3. Macro-Financial Linkages — page 15
- 4. SVAR Conditional Forecasts — page 16
- 5. Relationship between NPL and Real GDP Growth — page 18
- 6. Estimated Parameters — page 21
- 7. Weighted Average of NPL Projections — page 22
- 8. Heterogeneity in NPL Projections — page 22

*Source: _wp16236 - 1. Panel Regression Results*

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

### _wp16236 - References .............................................................................................................

### I. INTRODUCTION
- Economic crises lead to a surge in nonperforming loans (NPL); empirical literature reports a negative relationship between economic activity and asset quality for advanced and developing economies.
- Even with macro-prudential regulation, deteriorating economic cycles almost unavoidably increase NPLs, threatening financial stability by jeopardizing solvency and slowing credit growth or affecting credit quality.
- Stress testing loan portfolios for resilience to economic deterioration is critical to anticipate recapitalization needs, guide financial regulation, and develop crisis preparedness tools.
- Heterogeneity across banks and cross-sectional dependence (CSD) from common shocks can bias estimates if homogeneity is assumed.
- The paper proposes a three-stage stress testing framework accounting for dynamics, heterogeneity, and CSD, applied to Ecuador.
  - Under July 2016 oil projections:
    - Short-run increase in NPL associated with one percentage point (pp) fall in real GDP growth: 0.15 pp.
    - Long-run effect: 0.55 pp.
  - Weighted average NPL for the financial system projected to more than double over the next two years, but banks exhibit heterogeneity with NPLs ranging between 2 and 15 percent over the next two years.

### II. LITERATURE REVIEW (Top-down stress testing and modeling approaches)
- Top-down credit stress testing typically comprises four components: macro-financial scenario design; impacts on banks’ performance; solvency calculation; contagion and feedback analysis. This paper focuses on the first two.
- Macro-financial scenario modeling approaches:
  - Structural models: advantages/disadvantages; assumptions and restrictions (Jones et al., 2004).
  - VAR (and VECM) and global VAR (GVAR): flexible, smaller requirements; GVAR requires large data and stronger assumptions.
  - Pure statistical simulation approaches: allow distributional flexibility but limited for policy analysis.
- Mapping macro-financial scenarios to bank-level stress:
  - Borrower-level models demand extensive micro data.
  - Loan-performance models rely on NPL, loan loss provisions, default rates; can be run at multiple aggregation levels.
- Econometric methods for loan performance:
  - OLS, fixed effects, dynamic specifications, IV/cointegration, GMM-based (Arellano and Bond, 1991; Blundell and Bond, 1998).
  - Existing literature often uses fixed effects but generally neglects CSD.
  - GVAR and other common-factor approaches can address CSD but require large cross-sections.
- For Ecuador: relatively small cross-section, longer time series, size heterogeneity, likely high CSD → need methods that address heterogeneity and CSD with modest cross-section size.

### III. STYLIZED FACTS (Ecuador)
- Two significant shocks affecting Ecuador recently: (i) oil price fall, and (ii) real appreciation of the US dollar (dollarization context).
- Real GDP growth highly correlated with real oil price with some delay; as of end-2015, real GDP growth fell to about zero percent.
- NPL dynamics:
  - Since 2004 average NPL fell from about 10 percent to less than 4 percent before the global financial crisis; rebounded above 5 percent during the crisis and later declined.
  - With the end of the commodity supercycle, NPL started rising again; in the first quarter of 2016, NPL reached 3.9 percent.
  - NPL ratio and real GDP growth show a negative correlation; correlation stronger with non-oil real GDP growth but real GDP growth used for forecasts.
- Banking system characteristics:
  - Highly concentrated, composed of small, medium, and large banks with considerable variation in asset quality.
  - Median NPL in 2016Q1: 5.8 percent.
  - From early 2015, steady deposit withdrawals reduced liquidity buffers; real credit growth follows deposit growth with delay, suggesting credit rationing in response to falling deposits.
  - Heterogeneity across banks in deposit and credit growth is substantial; for more than 10 percent of banks real credit growth remained above 10 percent despite deposit falls.

### IV. ECONOMETRIC APPROACH (Three-stage framework)
- Stage 1: Estimate a VAR(푝) of macro-financial linkages for the aggregate financial system to generate forecasts accounting for feedback between real and financial variables.
  - VAR specification (reduced form):
    - z_t = b + Σ_{j=1}^p D_j z_{t−j} + Σ_{j=1}^p F_j x_{t−j} + e_t
    - z_t includes real GDP, real credit by private banks, real deposits of private banks (all in logs); x_t is exogenous real oil price (log).
  - Structural VAR recovered via Cholesky decomposition with contemporaneous ordering: real GDP → real credit → real deposits (퐴_0^{-1} matrix structure given).
  - Forecasts conditional on IMF-WEO oil price projections (July 2016) for a two-year horizon.
- Stage 2: Bank-level panel estimation of NPL response using ARDL specification on the growth rate of the logistic transformation of NPL:
  - y_{i,t} = α + Σ_{k=1}^n β_k x_{t−k} + Σ_{k=1}^n δ_k z_{i,t−k} + u_{i,t}
  - x_t: real GDP growth; z_{i,t}: bank-specific real deposit growth and real credit growth.
  - Estimation approaches used:
    - Pooled OLS (POLS), OLS with fixed effects (FEOLS), System GMM (SGMM) with Windmeijer (2005) correction, Mean Group (MG), Augmented Mean Group (AMG-I and AMG) to capture parameter heterogeneity and CSD.
  - Target adjustment dynamics introduced: y_{i,t} = α + γ y_{i,t−1} + Σ β_k x_{t−k} + Σ δ_k z_{i,t−k} + u_{i,t} (in various estimator forms).
  - AMG estimator used in preferred specification to control for unobserved common dynamic factor μ̂_t• in each bank equation, then averaging bank-specific estimates.
- Stage 3: Combine VAR forecasts and bank-specific AMG coefficients to simulate bank-specific NPL responses for two years out of sample; common dynamic factor μ̂_t• held at last observed period value; projections averaged using stocks of credit as weights.

### VI. CONCLUSIONS AND POLICY IMPLICATIONS
- High NPLs commonly arise during downturns and can threaten financial stability via solvency and credit-growth/channels.
- Granular stress testing that accounts for bank heterogeneity and CSD provides more accurate assessments of systemic risk and recapitalization needs than aggregate approaches.
- Key quantitative rule of thumb for Ecuador (average bank):
  - Short-run: 0.15 pp increase in NPL per 1 pp fall in real GDP growth.
  - Long-run: 0.55 pp increase in NPL per 1 pp fall in real GDP growth.
- Under July 2016 oil projections, macro-financial forecasts imply a negative effect on NPL ratios, likely more than doubling the weighted average NPL over the next two years in baseline projections, but with substantial cross-bank heterogeneity (approximately 2 to 15 percent NPL across banks).
- Policy uses of the framework:
  - Enhance surveillance granularity to focus supervisory actions on institutions more sensitive to cyclical fluctuations and with lower balance sheet buffers.
  - Inform preparatory measures: additional provisions, new capital requirements, improved risk management, selective lending constraints.
  - Enable targeted regulatory or macroprudential measures (e.g., imposing generic provisions or tightening measures where needed).
  - Adaptable to sub-segments (sector, business line, region) if data are available, aiding targeted policy responses and avoiding over- or underestimation of systemic risk.

*Source: Authors’ calculations and analysis contained in _wp16236 - References .............................................................................................................*

### Appendix I. VAR Specification Tests

### Appendix I. VAR Specification Tests

### Augmented Dickey-Fuller Unit Root Test for VAR Series
- Notes: The null hypothesis is that the series has a unit root. The lagged differences are included in the specifications to obtain white noise residuals. The Schwartz Information Criterion is used to select the optimal lag length. ***, **, * next to a number indicate statistical significance at 1, 5 and 10 percent, respectively.
- Series — Levels (No intercept, no trend; Intercept, no trend; Intercept, trend):
  - Real GDP: 3.546; -1.103; -2.510
  - Real deposits: 2.006; -2.569; -0.157
  - Real credit: 0.761; -1.989; -1.421
  - Real price of oil: -1.205; -1.951; -1.651
- Series — First differences (No intercept, no trend; Intercept, no trend; Intercept, trend):
  - Real GDP: -5.799***; -5.905***; -5.953***
  - Real deposits: -6.179***; -6.075***; -7.991***
  - Real credit: -8.206***; -8.093***; -7.991***
  - Real price of oil: -6.711***; -6.635***; -6.563***

### Johansen Cointegration Test
- Notes: The null hypothesis is that the series do not have a cointegration relationship. The Schwartz Information Criterion is used to select the optimal lag length. The critical values are from MacKinnon (1991). ***, **, * next to a number indicate statistical significance at 1, 5 and 10 percent, respectively.
- Number of cointegrating equations — Trace Statistic; Max-Eigen Statistic:
  - None: 41.003; 26.189*
  - At most 1: 14.814; 8.443
  - At most 2: 6.370; 5.154
  - At most 3: 1.216; 1.216

### VAR Lag Selection
- Notes: * next to a number indicate the preferred lag lenght. Source: Authors' calculations.
- Reported criteria and statistics (as presented in source):
  - Lag 0: Modified LR Statistic 4.63E-08; Final prediction Error -8.376; Akaike Information Criterion -7.898; Schwartz Information Criterion -8.197
  - Lag 1: Modified LR Statistic 363.0826.24E-12; Final prediction Error -17.294; Akaike Information Criterion -16.459*; Schwartz Information Criterion -16.981
  - Lag 2: Modified LR Statistic 20.258*; Final prediction Error 5.33e-12*; Akaike Information Criterion -17.465*; Schwartz Information Criterion -16.273; Hannan-Quinn Information Criterion -17.019*
  - Additional reported rows (as in source):
    - 38.2346.30E-12; -17.324; -15.773; -16.743
    - 47.0187.71E-12; -17.166; -15.258; -16.451
    - 58.8238.78E-12; -17.102; -14.835; -16.253
    - 67.0551.07E-11; -17.004; -14.381; -16.022
    - 74.8571.44E-11; -16.844; -13.863; -15.727
    - 810.4951.44E-11; -17.036; -13.697; -15.785

### VAR Stability
- Roots and moduli of companion matrix:
  - Root 1: Modulus 0.959518 (reported as 0.959)
  - Root 2: Modulus 0.818237 (reported as 0.818)
  - Root 3: 0.653693 - 0.131739i; Modulus 0.667
  - Root 4: 0.653693 + 0.131739i; Modulus 0.667
  - Root 5: 0.106625 - 0.050209i; Modulus 0.118
  - Root 6: 0.106625 + 0.050209i; Modulus 0.118

### VAR Residual Autocorrelation
- Notes: The null hypotheses of the Lagrange multiplier (LM) and Portmanteau Test is that there is no autocorrelation at the indicated lag. ***, **, * next to a number indicate statistical significance at 1, 5 and 10 percent, respectively. Source: Authors' calculations.
- Lagrange Multiplier Test (LM Statistic; Prob.):
  - Lag 1: LM Statistic 9.340381; Prob. 0.4065
  - Lag 2: LM Statistic 4.528068; Prob. 0.8734
  - Lag 3: LM Statistic 4.610048; Prob. 0.8669
  - Lag 4: LM Statistic 8.060404; Prob. 0.5281
- Portmanteau Test (Q-Stat; Prob.; Adj Q-Stat; Prob.; df):
  - For lag 3: Q-Stat 10.8677; Prob. 0.2849; Adj Q-Stat 11.36909; Prob. 0.2513; df 9
  - For lag 4: Q-Stat 19.34311; Prob. 0.371; Adj Q-Stat 20.55078; Prob. 0.3027; df 18

*Source: Authors' calculations.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16236.pdf_