## cr18161

## Source details

**Canonical URL:** [cr18161](https://www.imf.org/-/media/files/publications/cr/2018/cr18161.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/cr/2018/cr18161.pdf.md)
- [Structured JSON version](/-/media/files/publications/cr/2018/cr18161.pdf.json)

---

### EXECUTIVE SUMMARY — Key findings on household credit dynamics
- Household credit growth in Romania picked up starting in 2015, with a rapid rise from 2016 onward.
- Detailed loan-level data from the Central Credit Register cover more than 220,000 mortgages and 170,000 consumer loans and are used to analyze determinants of default.
- The probability of default (PD) of a borrower is highly sensitive to changes in DSTI around the 50 percent mark, particularly for mortgage loans.

### Main recommendation
- Set an explicit stressed DSTI limit of 50 percent for household loans to ensure borrowers’ DSTI remains below the identified sensitivity threshold after shocks to interest rate, income, and exchange rate are applied.

### Rationale for DSTI-focused macroprudential policy
- DSTI caps directly target household vulnerabilities by limiting debt-service burdens and thereby reducing likelihood of default.
- DSTI caps complement other tools (e.g., LTV limits, sectoral capital tools) and become more binding when mortgage and house-price growth outpace household disposable income.
- Romania’s comprehensive credit register enables granular calibration of macroprudential instruments across full macroeconomic cycles.

### Policy proposal (design features)
- Impose an explicit stressed DSTI limit applicable to all household borrowing (mortgages, including Prima Casa loans, and consumer loans) rather than relying on banks’ internal limits.
- Apply the limit to the stressed DSTI level calculated at origination after imposing shocks to interest rate, FX, and income; the stressed DSTI must be below the DSTI limit.
- Recalibrate shocks for consumer lending and introduce comparable shocks for mortgage lending:
  - FX shocks (consumer loans) remain: 35.5 percent for EUR, 40.9 percent for U.S. dollars, and 52.6 percent for other FX.
  - Interest rate shock (consumer loans) recalibrated to 2 percentage points (up from 0.6 percentage points).
  - Income shock (consumer loans) increased to 10 percent (up from 6 percent).
  - For mortgage loans, FX and interest rate shocks identical to consumer loans; proposed shock to income is 6 percent.
- Calculate DSTI using the borrower’s total debt-service obligations (all outstanding loans), not only the service associated with the new loan.

### Exemptions to reduce efficiency costs
- Exempt the interest rate shock for loans granted with fixed rate for an initial period of at least five years.
- Allow a blanket exemption from the DSTI cap and from stressing DSTI for 15 percent of the quarterly flow of new loans granted by each bank; the value of an exempted loan cannot exceed the RON equivalent amount of EUR 250,000.

### Data (coverage and construction)
- Central Credit Register coverage: loans to borrowers with credit or commitments whose cumulated value is equal to or higher than the reporting threshold above RON 20,000 (Equivalent of approximately EUR 4,400), observed at June 2016 and again in June 2017 to register performing status 1-year ahead.
- Interest rates for debt-service computation: extracted from the Monetary Balance Sheet (average interest rate reported by each bank by loan class, maturity and currency). Monthly installment computed using a constant annuity assumption.
- Monthly income: wages reported for the fiscal year of 2016 from the Ministry of Public Finance, used to compute DSTI.
- Debt-service computed using information from both Central Credit Register and Credit Bureau.
- Data consolidated by debtor using national personal identification number. DSTI = total monthly debt service / monthly income.
- DSTI values above 300 percent and below 5 percent are winsorized at those respective values.
- Initial loan selection: around 356,000 mortgage loans and 634,000 unsecured consumer loans.
  - After exclusions (restructured/refinanced; converted FX to RON; flagged “unlikely to pay”; overdue >90 days; residual maturity <12 months): 334,000 mortgage loans and 480,000 unsecured consumer loans.
  - After merging June 2016 and June 2017 observations and flagging nonperforming (>90 days past due): 228,000 mortgage loans and 174,000 unsecured consumer loans.
  - 27,000 debtors are common to both databases.
- Note on matching interest rates: loans of same type, granted by same bank, in same currency and same maturity class share the same “average” interest rate as reported by the respective banks.

### Loan and Debtor Characteristics (summary and medians)
- Average amounts (remaining on-balance sheet at June 2016):
  - Mortgage: EUR 30,559
  - Unsecured consumer: EUR 6,000
- Median monthly installment:
  - Mortgage: EUR 172
  - Unsecured consumer: EUR 151
- Median interest rate:
  - Mortgage: 3.6 percent
  - Unsecured consumer: 9.4 percent
- Median residual maturity:
  - Mortgage: 23.9 years
  - Unsecured consumer: 4.1 years
- Typical debtor median values:
  - Median age: Mortgage 36; Unsecured consumer 43
  - Median income (EUR): Mortgage 569; Unsecured consumer 557
  - NPL rate (median): Mortgage 0.2%; Unsecured consumer 2.3%
- Currency split (in percent):
  - Mortgage loans: Euro 50; CHF 2; RON 48
  - Unsecured consumer loans: Euro 2; CHF 0; RON 98
- Additional descriptive points:
  - Monthly installments for unsecured consumer loans are quite close to mortgage installments despite lower outstanding amounts, reflecting higher interest rates and shorter maturities.
  - Approximately 56 percent of mortgage loans are Prima Casa loans.
  - 16 percent of debtors with unsecured consumer loans also have a mortgage loan.
  - Median DSTI:
    - Mortgage borrower: 33 percent
    - Unsecured consumer borrower: 39 percent (for those with only unsecured consumer loans median is 38 percent)
  - Overlap: roughly 15 percent of borrowers with a consumer loan have a mortgage also and 5 percent have a secured consumer loan.

### Methodology (two-step PD modeling)
- Step 1: Bottom-up micro PD model (logistic regression) for June 2016–June 2017 predicting one-year ahead PDs using debtor-level characteristics observed in June 2016 and default outcomes in June 2017.
  - Dependent variable: default = loan 90 days or more overdue (1 = default, 0 = non-default).
  - Logit specification includes age, residual maturity, FX dummy, DSTI, other loan variables, bank fixed effects, year of origination fixed effects, development region fixed effects.
  - Separate PD models for mortgage and unsecured consumer loans.
- Step 2: Macroeconomic model: one-factor Merton model linking macro variables to average sectoral PD, estimated on quarterly data Q1 2004 through Q3 2017. Key macro variables: annual GDP growth and annualized quarterly change in REER.
  - One-year-ahead projection (Q3 2018) based on NBR macro projections yields estimated PDs: Consumer loans: 2.7 percent; Mortgage loans: 0.56 percent.
- Adjustment: intercept of micro-level PD model adjusted so mean of estimated PDs π(x) converges to πd from macro model following King and Zeng (2002).

### Results (marginal effects and interpretations)
- DSTI, residual maturity, and income bracket are significant in both mortgage and unsecured consumer PD models.
- Marginal effects (percentage point changes in PD resulting from a 1-unit change; for DSTI the marginal effect calculated for 10 percentage points change):
  - Mortgage loans (marginal effects):
    - Age: 0.000%
    - Residual maturity: 0.03%***
    - DSTI (10 percentage points): 0.04%***
    - Below average wage (dummy): 0.28%***
    - Greater 2x average wage (dummy): -0.22%***
    - FX (dummy): 0.090%
    - First Home dummy: -0.88%***
    - Adjusted R squared: 0,21
    - Number of observations: 228 123
  - Unsecured Consumer loans (marginal effects):
    - Age: -0.11%***
    - Residual maturity: 0.58%***
    - DSTI (10 percentage points): 0.09%***
    - Below average wage (dummy): 2.06%***
    - Greater 2x average wage (dummy): -1.39%***
    - Other mortgage credit (dummy): -2.28%***
    - Adjusted R squared: 0,13
    - Number of observations: 174 475
  - Significance notation: * p < 0.10, ** p < 0.05, *** p < 0.01
- Textual interpretations based on marginal effects:
  - A 10 percentage point increase in DSTI raises the PD by 6 percent for mortgage loans and by 3 percent for unsecured consumer loans (statement in text based on marginal effects).
  - Debtors with income below the average wage are 50 percent more likely to default on a housing loan and 100 percent more likely to default on an unsecured consumer loan compared to those with income between average and double average wage.
  - Debtors with income more than twice the average wage have PDs 30 percent lower for mortgage loans and 45 percent lower for unsecured consumer loans.
  - Prima Casa mortgage loans have PD lower by 80 percent compared to standard housing loans.
  - For unsecured consumer loans, debtors who also have a mortgage have PD 75 percent lower than debtors with a consumer loan only.
  - Increasing residual maturity by one year leads to a 20 percent increase in PD for unsecured consumer loans and 4 percent increase for mortgage loans.
- Model performance:
  - Bottom-up regression predictions closely match observed PDs across income categories.
  - Macro model indicates slight uptick for mortgage PDs in Q3 2018 relative to Q3 2017; consumer PDs expected to remain more or less constant.
- Distributional effects:
  - PD distribution for borrowers with income greater than double the average wage is significantly more left skewed compared to those with wages below average wage.

### Stressed DSTI calculation and PD implications
- Policy proposal shocks for stressed DSTI:
  - FX shocks: 35.5 percent for EUR, 40.9 percent for U.S. dollars, and 52.6 percent for other FX for unsecured consumer and mortgage loans.
  - Interest rate shock: 2 percentage points for both loan types.
  - Income shock: 10 percent for consumer loans and 6 percent for mortgages.
- Implementation note: exercise applies a 35 percent depreciation for all currencies (simplification); FX loans are predominantly denominated in euros (95 percent).
- Stressed DSTI computed at debtor-level using preserved formulae:
  - DSTI_shocked = f_d_shock * (1 + shock_FX) / (1 − shock_income) * S / V
  - f_d_shock = (r + IR_shock) * (1 − (1 + r + IR_shock)^(−n))
  - Definitions: n = residual maturity, r = initial interest rate, S = credit amount, V = monthly income, shock_FX and shock_income as above.
- Recalculated stressed DSTI levels are input into the PD model to obtain changes in average PDs.

### Key quantitative impacts of the calibrated shocks (Q3 2018 base)
- Unsecured consumer loans:
  - A 2-percentage point interest rate increase, a 35 percent exchange rate shock, and a 10 percent income decrease lead to:
    - Median DSTI increased by 8 percentage points.
    - Average PD increases by 4 percent.
- Mortgage loans:
  - Same interest rate and FX shocks and a 6 percent income decrease lead to:
    - Median DSTI increased by 15 percentage points.
    - Average PD increases by 25 percent.
  - Explanation: higher sensitivity due to longer maturities and larger exposures.

### Setting a DSTI limit: empirical approach and findings
- Regression approach: logistic regression with interactions between DSTI and DSTI-interval dummies. Baseline group: DSTI < 20 percent. DSTI intervals used: up to 30, 40, 50, 60, 70, 100, 200, and >200 percent.
- Empirical non-linearity:
  - Interaction coefficients are statistically significant for both loan types.
  - For consumer loans coefficients increase significantly above the 30 percent threshold.
  - For mortgage loans coefficients increase significantly above the 50 percent threshold.
- Recommendation:
  - The highest positive impact of DSTI on PDs is around the 50 percent threshold.
  - Recommendation to set DSTI limit at 50 percent (particularly strong for mortgage loans).
  - For consumer loans the limit could be set between 30 percent and 50 percent.

### Impact analysis: DSTI limit counterfactuals (average PDs, NPLs, and loan volumes)
- Impact on average PDs — Average PD (%) by DSTI limit:
  - Mortgage Loans:
    - W/O DSTI limit: 0.72
    - W/ DSTI limit: 0.46 (40%), 0.47 (45%), 0.48 (50%), 0.48 (55%), 0.49 (60%)
  - Unsecured Consumer Loans:
    - W/O DSTI limit: 3.14
    - W/ DSTI limit: 2.82 (40%), 2.85 (45%), 2.87 (50%), 2.89 (55%), 2.91 (60%)
- Counterfactual NPL ratios as of Sept. 2017 if a maximum DSTI limit had applied since origination:
  - Mortgage Loans:
    - NPL ratio: Sept. 2017 (%) = 2.92
    - Counterfactual NPL ratio (40%/45%/50%/55%/60%): 1.01, 1.05, 1.44, 1.50, 1.37
  - Unsecured Consumer Loans:
    - NPL ratio: Sept. 2017 (%) = 7.76
    - Counterfactual NPL ratio (40%/45%/50%/55%/60%): 2.64, 2.86, 3.13, 3.38, 3.41
  - Coverage ratio for income-available debtors is 76 percent for mortgages and 69 percent for unsecured consumer loans.
- Forward-looking 3-year NPL impact — scenario where only new flow of credit is affected:
  - Mortgage Loans:
    - NPL ratio in 3 years, No change in policy: 4.44
    - NPL ratio in 3 years, Limit on DSTI (40%/45%/50%/55%/60%): 4.13, 4.14, 4.15, 4.16, 4.16
  - Unsecured Consumer Loans:
    - NPL ratio in 3 years, No change in policy: 12.57
    - NPL ratio in 3 years, Limit on DSTI (40%/45%/50%/55%/60%): 12.04, 12.09, 12.13, 12.16, 12.19
  - Interpretation: for a 50 percent DSTI limit, the NPL ratio would be smaller by 0.3 percentage points (mortgages) and by 0.4 percentage points (unsecured consumer loans) in three years versus today.
- Impact on loan volumes — Decline in annual flow of new loans (In percent):
  - Adjustment of New Total Loans:
    - w/o 15 percent exemption: 17 (40%), 13 (45%), 11 (50%), 9 (55%), 7 (60%)
    - w/ 15 percent exemption: 12 (40%), 9 (45%), 7 (50%), 5 (55%), 4 (60%)
  - Adjustment of New Mortgage Loans:
    - w/o 15 percent exemption: 18, 15, 12, 9, 8
    - w/ 15 percent exemption: 14, 11, 8, 6, 4
  - Adjustment of New Unsecured Consumer Loans:
    - w/o 15 percent exemption: 15, 12, 10, 9, 7
    - w/ 15 percent exemption: 10, 8, 6, 4, 3
  - Specific point: for a 50 percent DSTI limit the annual flow of new loans will drop by 11 percent without the exemption and by 7 percent with the 15 percent exemption.

### Equations and projection mechanics (preserved)
- NPL ratio at time t:
  - NPL ratio_t = NPL_t / total loans_t
- Total loans projection for k = 1 to 3:
  - total loans_t,t+k = total loans_t * [ (1 − rr)^k + (1 + rnl)^(k−1) ]
- NPL projection for k = 1 to 3:
  - NPL_t,t+k = NPL_t + ( total loans_t * (1 − rr)^k − NPL_t ) * (1 − (1 − PD_old)^k ) + total loans_t * ( (1 + rnl)^k − 1 ) * (1 − (1 − PD_new)^k )
- Definitions preserved: rr = reimbursement rate, rnl = rate of new lending, PD_old = 1-year PD without DSTI change, PD_new = 1-year PD after imposing DSTI limit, t = current time, k = years (results shown for k=3).

### Conclusions and policy implications
- DSTI is an important determinant of household loan PDs: observed default frequencies and model-estimated sensitivities confirm DSTI’s significance.
- Calibration principle: DSTI limit should incorporate plausible income shocks so borrowers can service debt after a reasonably calibrated negative income shock; same principle applies for FX and interest rate shocks.
- Expected benefits:
  - A macroprudential DSTI limit can substantially reduce household NPLs in the long run.
  - Counterfactuals indicate household NPL ratios would be roughly half current levels if the proposed DSTI limit had applied to existing loans.
- Cost in terms of credit provision:
  - Applying the DSTI limit to new credit, with an exemption allowing banks to grant up to 15 percent of previous year’s new loans outside the limit, limits credit reduction to a modest 7–11 percent.
- Policy recommendation reiterated:
  - Set DSTI limit at 50 percent (particularly for mortgage lending); consumer loan limit could be set between 30 percent and 50 percent.

### Appendix I — PD Model: choice of explanatory variables and estimation
- Variable selection:
  - Univariate analysis, Kolmogorov-Smirnov tests, monotonicity assessment, univariate logistic regressions (variables with ROC < 50 percent excluded).
  - Multicollinearity screening: covariates with correlation of less than 75 percent kept.
- Estimation procedure:
  - Multivariate backward selection logistic regression.
  - Bootstrapping with 100 iterations to assess model stability; each iteration sampled 20 percent defaulting debtors and 80 percent non-defaulting debtors (all nonperforming used due to low defaults).
- Macroeconomic one-factor Merton-type model summarized with preserved equations and assumptions (homogeneous portfolio, standard normal F_t and U_it, asset return correlation parameter ρ).
- PD Model: Full coefficient tables preserved for mortgage and consumer loan specifications (selected coefficients and t-stats reported in source).

*cr18161 - EXECUTIVE SUMMARY*

### EXECUTIVE SUMMARY __________________________________________________________________________ 5

### EXECUTIVE SUMMARY

### Key findings on household credit dynamics
- Household credit growth in Romania picked up starting in 2015, with a rapid rise from 2016 onward.
- Detailed loan-level data from the Central Credit Register cover more than 220,000 mortgages and 170,000 consumer loans and are used to analyze determinants of default.
- The probability of default (PD) of a borrower is highly sensitive to changes in DSTI around the 50 percent mark, particularly for mortgage loans.

### Main recommendation
- Set an explicit stressed DSTI limit of 50 percent for household loans to ensure borrowers’ DSTI remains below the identified sensitivity threshold after shocks to interest rate, income, and exchange rate are applied.

### Rationale for DSTI-focused macroprudential policy
- DSTI caps directly target household vulnerabilities by limiting debt-service burdens and thereby reducing likelihood of default.
- DSTI caps complement other tools (e.g., LTV limits, sectoral capital tools) and become more binding when mortgage and house-price growth outpace household disposable income.
- Romania’s comprehensive credit register enables granular calibration of macroprudential instruments across full macroeconomic cycles.

### Policy proposal (design features)
- Impose an explicit stressed DSTI limit applicable to all household borrowing (mortgages, including Prima Casa loans, and consumer loans) rather than relying on banks’ internal limits.
- Apply the limit to the stressed DSTI level calculated at origination after imposing shocks to interest rate, FX, and income; the stressed DSTI must be below the DSTI limit.
- Recalibrate shocks for consumer lending and introduce comparable shocks for mortgage lending:
  - FX shocks (consumer loans) remain: 35.5 percent for EUR, 40.9 percent for U.S. dollars, and 52.6 percent for other FX.
  - Interest rate shock (consumer loans) recalibrated to 2 percentage points (up from 0.6 percentage points).
  - Income shock (consumer loans) increased to 10 percent (up from 6 percent).
  - For mortgage loans, FX and interest rate shocks identical to consumer loans; proposed shock to income is 6 percent.
- Calculate DSTI using the borrower’s total debt-service obligations (all outstanding loans), not only the service associated with the new loan.

### Exemptions to reduce efficiency costs
- Exempt the interest rate shock for loans granted with fixed rate for an initial period of at least five years.
- Allow a blanket exemption from the DSTI cap and from stressing DSTI for 15 percent of the quarterly flow of new loans granted by each bank; the value of an exempted loan cannot exceed the RON equivalent amount of EUR 250,000.

### Empirical and impact analysis (select results)
- PD rises markedly when DSTI reaches around 50 percent; this threshold motivates the 50 percent DSTI cap.
- Imposing a 50 percent stressed DSTI limit is estimated to:
  - Reduce three-year-ahead NPL ratios by 0.3 to 0.4 percentage points for mortgages and consumer loans, respectively.
  - Lower aggregate loan levels by 7–11 percent, depending on the share of loans exempted from the DSTI limit.

### Implementation considerations
- The proposed DSTI limit replaces reliance on banks’ internal DSTI limits and standardizes shocks across loan types.
- The exemption framework aligns with practices in other jurisdictions (e.g., New Zealand, U.K., Portugal) and aims to preserve lending flexibility where justified by borrower circumstances or product features.

*cr18161 - EXECUTIVE SUMMARY*

### 14.      This paper uses debtor-level data to inform the calibration of the new DSTI limit. It

### 14.      This paper uses debtor-level data to inform the calibration of the new DSTI limit. It

### Key finding and proposal
- Borrowers with DSTI levels close to 50 percent are highly sensitive to changes in their DSTI levels, particularly for mortgage loans. Even small shocks to the DSTI level are associated with large increases in the PD.
- Proposal: set the debtor’s DSTI limit at 50 percent for all new borrowing (mortgage or consumer loans).

### A. Data
- Central Credit Register coverage: loans to borrowers with credit or commitments whose cumulated value is equal to or higher than the reporting threshold above RON 20,000 (Equivalent of approximately EUR 4,400), observed at June 2016 and again in June 2017 to register performing status 1-year ahead.
- Interest rates for debt-service computation: extracted from the Monetary Balance Sheet (average interest rate reported by each bank by loan class, maturity and currency). Monthly installment computed using a constant annuity assumption.
- Monthly income: wages reported for the fiscal year of 2016 from the Ministry of Public Finance, used to compute DSTI.
- Debt-service computed using information from both Central Credit Register and Credit Bureau (which also covers some loans below RON 20,000).
- Data consolidated by debtor using national personal identification number. Total monthly debt service = sum of monthly annuities per debtor. DSTI = total monthly debt service / monthly income.
- DSTI values above 300 percent and below 5 percent are winsorized at those respective values.
- Initial loan selection: around 356,000 mortgage loans and 634,000 unsecured consumer loans.
  - Exclusions: (i) restructured and refinanced; (ii) converted from FX to RON; (iii) flagged “unlikely to pay” under the EBA definition of nonperformance; (iv) overdue payments more than 90 days; (v) residual maturity less than 12 months.
  - After exclusions: 334,000 mortgage loans and 480,000 unsecured consumer loans.
  - After merging June 2016 and June 2017 observations and flagging nonperforming (more than 90 days past due): 228,000 mortgage loans and 174,000 unsecured consumer loans.
  - 27,000 debtors are common to both databases.
- Note on matching interest rates: loans of same type, granted by same bank, in same currency and same maturity class share the same “average” interest rate as reported by the respective banks.

### B. Loan and Debtor Characteristics (summary and medians)
- Average amounts (remaining on-balance sheet at June 2016):
  - Mortgage: EUR 30,559
  - Unsecured consumer: EUR 6,000
- Median monthly installment:
  - Mortgage: EUR 172
  - Unsecured consumer: EUR 151
- Median interest rate:
  - Mortgage: 3.6 percent
  - Unsecured consumer: 9.4 percent
- Median residual maturity:
  - Mortgage: 23.9 years
  - Unsecured consumer: 4.1 years
- Typical debtor median values:
  - Median age: Mortgage 36; Unsecured consumer 43
  - Median income (EUR): Mortgage 569; Unsecured consumer 557
  - NPL rate (median): Mortgage 0.2%; Unsecured consumer 2.3%
- Currency split (in percent):
  - Mortgage loans: Euro 50; CHF 2; RON 48
  - Unsecured consumer loans: Euro 2; CHF 0; RON 98
- Additional descriptive points:
  - Monthly installments for unsecured consumer loans are quite close to mortgage installments despite lower outstanding amounts, reflecting higher interest rates and shorter maturities.
  - Share of unsecured consumer loans in foreign currency is close to zero; foreign currency mortgage loans are mostly vintages issued before 2011 regulation.
  - Approximately 56 percent of mortgage loans are Prima Casa loans.
  - 16 percent of debtors with unsecured consumer loans also have a mortgage loan.
  - Debtors with mortgage loans are on average younger; income levels are comparable across loan types.
  - Median DSTI:
    - Mortgage borrower: 33 percent
    - Unsecured consumer borrower: 39 percent (for those with only unsecured consumer loans median is 38 percent)
  - Overlap: roughly 15 percent of borrowers with a consumer loan have a mortgage also and 5 percent have a secured consumer loan.

### C. Methodology
- Two-step approach (following Costeiu and Neagu (2013)):
  1. Bottom-up micro PD model (logistic regression) estimated for June 2016–June 2017: predicts one-year ahead PDs using debtor-level characteristics observed in June 2016 and default outcomes in June 2017.
     - Dependent variable: default = loan 90 days or more overdue (1 = default, 0 = non-default).
     - Logit specification: f(x) = ln[π(x)/(1−π(x))] = β0 + β1*age + β2*residual maturity + β3*FX dummy + β4*DSTI + β5*other loan specific variables + β6*bank fixed effects + β7*year of origination fixed effects + β8*development region fixed effects.
     - Separate PD models for mortgage and unsecured consumer loans.
     - Univariate analysis selected significant regressors: age, loan residual maturity, DSTI, FX dummy; plus Prima Casa dummy (mortgage) and a dummy for debtors with both consumer loan and mortgage (consumer loans). Income group dummies, years of origination, and bank fixed effects included.
  2. Macroeconomic model: one-factor Merton model linking macro variables to average sectoral PD, estimated on quarterly data Q1 2004 through Q3 2017. Key macro variables with greatest explanatory power: annual GDP growth and annualized quarterly change in REER. Separate macro models for mortgage and unsecured consumer loans.
     - One-year-ahead projection (Q3 2018) based on NBR macro projections yields estimated PDs:
       - Consumer loans: 2.7 percent (for Q3 2018)
       - Mortgage loans: 0.56 percent (for Q3 2018)
- Adjustment procedure: intercept of micro-level PD model is adjusted so mean of estimated PDs π(x) converges to πd from macro model, following King and Zeng (2002): ln(π(x)/(1−π(x))) = α + Xβ + ln( (πd/(1−πd)) * ((1−p)/p) ) + ε, where p is sample share of defaulted borrowers.

### D. Results (marginal effects and observations)
- DSTI, residual maturity, and income bracket are significant in both mortgage and unsecured consumer PD models.
- Marginal effects (Table 4) — values represent percentage point changes in PD resulting from a 1-unit change in explanatory variable; for DSTI the marginal effect calculated for 10 percentage points change:
  - Mortgage loans (marginal effects):
    - Age: 0.000%
    - Residual maturity: 0.03%***
    - DSTI (10 percentage points): 0.04%***
    - Below average wage (dummy): 0.28%***
    - Greater 2x average wage (dummy): -0.22%***
    - FX (dummy): 0.090%
    - First Home dummy: -0.88%***
    - Adjusted R squared: 0,21
    - Number of observations: 228 123
  - Unsecured Consumer loans (marginal effects):
    - Age: -0.11%***
    - Residual maturity: 0.58%***
    - DSTI (10 percentage points): 0.09%***
    - Below average wage (dummy): 2.06%***
    - Greater 2x average wage (dummy): -1.39%***
    - Other mortgage credit (dummy): -2.28%***
    - Adjusted R squared: 0,13
    - Number of observations: 174 475
  - Significance notation: * p < 0.10, ** p < 0.05, *** p < 0.01
  - Bank, year of origination and regional fixed effects estimated but not reported.
- Interpretations and notable observations:
  - A 10 percentage point increase in DSTI raises the PD by 6 percent for mortgage loans and by 3 percent for unsecured consumer loans (statement in text based on marginal effects).
  - Debtors with income below the average wage are 50 percent more likely to default on a housing loan and 100 percent more likely to default on an unsecured consumer loan compared to those with income between average and double average wage.
  - Debtors with income more than twice the average wage have PDs 30 percent lower for mortgage loans and 45 percent lower for unsecured consumer loans.
  - Prima Casa mortgage loans have PD lower by 80 percent compared to standard housing loans.
  - For unsecured consumer loans, debtors who also have a mortgage have PD 75 percent lower than debtors with a consumer loan only.
  - Increasing residual maturity by one year leads to a 20 percent increase in PD for unsecured consumer loans and 4 percent increase for mortgage loans.
  - Lending standards have tightened over time: loans originated before 2007 have significantly higher PDs compared to those originated in 2015, all else equal. Similar results apply to consumer loans.
- Model performance:
  - The bottom-up regression predictions closely match observed PDs across income categories (Figure 3).
  - The macro model indicates a slight uptick for mortgage PDs in Q3 2018 relative to Q3 2017; consumer PDs expected to remain more or less constant.
- Distributional effects:
  - Income distribution importantly affects predicted PDs: PD distribution for borrowers with income greater than double the average wage is significantly more left skewed compared to those with wages below average wage (Figure 5).

### E. Stressed DSTI and Probability of Default
- The analysis translates proposed shocks to stressed DSTI and the implications for stressed PDs (methodology described in prior sections and results summarized above).
- Emphasis: borrowers with DSTI near 50 percent exhibit high sensitivity of PD to DSTI shocks, especially for mortgage loans — motivating the 50 percent DSTI limit proposal.

*Sources: NBR, Credit Bureau, and the Ministry of Public Finance (as presented in this chapter).*

### 33.      We evaluate the impact of shocks to interest rate, exchange rate and income on PDs

### 33.      We evaluate the impact of shocks to interest rate, exchange rate and income on PDs

### Methodology: shocks, DSTI recalculation, and PD model
- Policy proposal shocks envisaged for calculating stressed DSTI:
  - FX shocks: 35.5 percent for EUR, 40.9 percent for U.S. dollars, and 52.6 percent for other FX for unsecured consumer and mortgage loans.
  - Interest rate shock: 2 percentage points for both loan types.
  - Income shock: 10 percent for consumer loans and 6 percent for mortgages.
- Implementation note: for the FX shock the exercise applies a 35 percent depreciation for all currencies (simplification), while FX loans are predominantly denominated in euros (95 percent).
- Stressed DSTI is calculated at debtor-level using:
  - DSTI_shocked = f_d_shock * (1 + shock_FX) / (1 − shock_income) * S / V
  - f_d_shock = (r + IR_shock) * (1 − (1 + r + IR_shock)^(−n))
  - Definitions preserved from source: n = residual maturity, r = initial interest rate, S = credit amount, V = monthly income, shock_FX and shock_income as above.
- The recalculated stressed DSTI levels are input into the PD model to obtain changes in average PDs.

### Key quantitative impacts of the calibrated shocks (Q3 2018 base)
- Unsecured consumer loans:
  - A 2-percentage point interest rate increase, a 35 percent exchange rate shock, and a 10 percent income decrease lead to:
    - Median DSTI increased by 8 percentage points.
    - Average PD increases by 4 percent.
- Mortgage loans:
  - Same interest rate and FX shocks and a 6 percent income decrease lead to:
    - Median DSTI increased by 15 percentage points.
    - Average PD increases by 25 percent.
  - Explanation: higher sensitivity due to longer maturities and larger exposures.

### Setting a DSTI limit: approach and empirical findings
- Objective: identify DSTI limit that meaningfully reduces default likelihood without imposing unnecessarily strict constraints.
- Regression approach: logistic regression with interactions between DSTI and DSTI-interval dummies. Baseline group: DSTI < 20 percent. DSTI intervals used: up to 30, 40, 50, 60, 70, 100, 200, and >200 percent.
- Empirical non-linearity:
  - Interaction coefficients are statistically significant for both loan types.
  - For consumer loans coefficients increase significantly above the 30 percent threshold.
  - For mortgage loans coefficients increase significantly above the 50 percent threshold.
- Recommendation:
  - The highest positive impact of DSTI on PDs is around the 50 percent threshold.
  - Recommendation to set DSTI limit at 50 percent (particularly strong for mortgage loans).
  - For consumer loans the limit could be set between 30 percent and 50 percent.

### Model fit and coefficient highlights (selected results)
- Table 5 (selected coefficient signs and statistical significance preserved as in source):
  - Mortgage Loans: Age −0.016***; Residual maturity 0.002***; DTI −0.095***; DTI interaction [50, 60) 0.093***; First Home (dummy) −1.614***; Adjusted R squared 0.216; Number of observations 221,957.
  - Unsecured Consumer Loans: Age −0.046***; Residual maturity 0.009***; DTI −0.027***; DTI interaction [30, 40) 0.031***; Below average wage (dummy) 0.675***; Greater 2x average wage (dummy) −0.559***; Adjusted R squared 0.145; Number of observations 171,161.
- Observed PD patterns by DSTI buckets (June 2017):
  - Mortgages: PD increases significantly with DSTI above 50 percent.
  - Consumer loans: PD increases closer to 30 percent DSTI.
  - Model projections for PDs by DSTI group (Q2 2017) align closely with observed default frequencies.

### Impact analysis: DSTI limit counterfactuals (average PDs, NPLs, and loan volumes)
- Impact on average PDs (Table 6) — Average PD (%) by DSTI limit:
  - Mortgage Loans:
    - W/O DSTI limit: 0.72
    - W/ DSTI limit: 0.46 (40%), 0.47 (45%), 0.48 (50%), 0.48 (55%), 0.49 (60%)
  - Unsecured Consumer Loans:
    - W/O DSTI limit: 3.14
    - W/ DSTI limit: 2.82 (40%), 2.85 (45%), 2.87 (50%), 2.89 (55%), 2.91 (60%)
- Counterfactual NPL ratios as of Sept. 2017 if a maximum DSTI limit had applied since origination (Table 7):
  - Mortgage Loans:
    - NPL ratio: Sept. 2017 (%) = 2.92
    - Counterfactual NPL ratio (40%/45%/50%/55%/60%): 1.01, 1.05, 1.44, 1.50, 1.37
  - Unsecured Consumer Loans:
    - NPL ratio: Sept. 2017 (%) = 7.76
    - Counterfactual NPL ratio (40%/45%/50%/55%/60%): 2.64, 2.86, 3.13, 3.38, 3.41
  - Note: coverage ratio for income-available debtors is 76 percent for mortgages and 69 percent for unsecured consumer loans.
- Forward-looking 3-year NPL impact (Table 8) — scenario where only new flow of credit is affected:
  - Mortgage Loans:
    - NPL ratio in 3 years, No change in policy: 4.44
    - NPL ratio in 3 years, Limit on DSTI (40%/45%/50%/55%/60%): 4.13, 4.14, 4.15, 4.16, 4.16
  - Unsecured Consumer Loans:
    - NPL ratio in 3 years, No change in policy: 12.57
    - NPL ratio in 3 years, Limit on DSTI (40%/45%/50%/55%/60%): 12.04, 12.09, 12.13, 12.16, 12.19
  - Interpretation: for a 50 percent DSTI limit, the NPL ratio would be smaller by 0.3 percentage points (mortgages) and by 0.4 percentage points (unsecured consumer loans) in three years versus today.
- Impact on loan volumes (Table 9) — Decline in annual flow of new loans (In percent):
  - Adjustment of New Total Loans:
    - w/o 15 percent exemption: 17 (40%), 13 (45%), 11 (50%), 9 (55%), 7 (60%)
    - w/ 15 percent exemption: 12 (40%), 9 (45%), 7 (50%), 5 (55%), 4 (60%)
  - Adjustment of New Mortgage Loans:
    - w/o 15 percent exemption: 18, 15, 12, 9, 8
    - w/ 15 percent exemption: 14, 11, 8, 6, 4
  - Adjustment of New Unsecured Consumer Loans:
    - w/o 15 percent exemption: 15, 12, 10, 9, 7
    - w/ 15 percent exemption: 10, 8, 6, 4, 3
  - Specific point: for a 50 percent DSTI limit the annual flow of new loans will drop by 11 percent without the exemption and by 7 percent with the 15 percent exemption.

### Equations and projection mechanics (as presented)
- NPL ratio at time t:
  - NPL ratio_t = NPL_t / total loans_t
- Total loans projection for k = 1 to 3:
  - total loans_t,t+k = total loans_t * [ (1 − rr)^k + (1 + rnl)^(k−1) ]
- NPL projection for k = 1 to 3:
  - NPL_t,t+k = NPL_t + ( total loans_t * (1 − rr)^k − NPL_t ) * (1 − (1 − PD_old)^k ) + total loans_t * ( (1 + rnl)^k − 1 ) * (1 − (1 − PD_new)^k )
- Definitions preserved: rr = reimbursement rate, rnl = rate of new lending, PD_old = 1-year PD without DSTI change, PD_new = 1-year PD after imposing DSTI limit, t = current time, k = years (results shown for k=3).

### Conclusions and policy implications
- DSTI is an important determinant of household loan PDs:
  - Observed default frequencies and model-estimated sensitivities confirm DSTI’s significance.
- Calibration principle:
  - DSTI limit should incorporate plausible income shocks so borrowers can service debt after a reasonably calibrated negative income shock; same principle applies for FX and interest rate shocks.
- Expected benefits:
  - A macroprudential DSTI limit can substantially reduce household NPLs in the long run.
  - Counterfactuals indicate household NPL ratios would be roughly half current levels if the proposed DSTI limit had applied to existing loans.
- Cost in terms of credit provision:
  - Applying the DSTI limit to new credit, with an exemption allowing banks to grant up to 15 percent of previous year’s new loans outside the limit, limits credit reduction to a modest 7–11 percent.
- Policy recommendation reiterated:
  - Set DSTI limit at 50 percent (particularly for mortgage lending); consumer loan limit could be set between 30 percent and 50 percent.

*Source: IMF staff analysis as presented in the supplied chapter.*

### Appendix I. PD Model: Choice of Explanatory Variables

### Appendix I. PD Model: Choice of Explanatory Variables

### Variable selection methodology
- Univariate analysis used to evaluate each variable's ability to discriminate between good and bad debtors.
- Tests performed:
  - Kolmogorov-Smirnov test to evaluate if characteristics of defaulters and non-defaulters are drawn from significantly different continuous distributions.
  - Assessment of whether the log odds of the default flag are monotonically and linearly related to a covariate.
  - Univariate logistic regressions to measure discriminatory power; variables with a ROC of less than 50 percent were excluded.
- Multicollinearity screening:
  - Covariates with correlation of less than 75 percent were kept in final model specifications.

### Estimation procedure
- Multivariate backward selection logistic regression estimated.
- Bootstrapping exercise with 100 iterations used to assess model stability.
- For each bootstrap iteration:
  - Sampled 20 percent defaulting debtors and 80 percent non-defaulting debtors from the dataset.
  - Because of a low number of defaults, all nonperforming debtors were used and performing debtors were sampled proportionally.

### Macroeconomic one-factor Merton-type model (Appendix II)
- Portfolio assumption: homogeneous portfolio of agents; standardized logarithmic return on assets assumed standard normal.
- Asset return process for each firm (Equation 5):
  - 푅_it = √휌 퐹_t + √(1−휌) 푈_it
  - Where:
    - 푅_it denotes the logarithmic asset return for economic agent i at time t.
    - 퐹_t stands for the logarithmic asset return of the economy at time t, assumed standard normal.
    - 푈_it represents agent-specific asset return, assumed standard normal.
    - 휌 expresses the correlation between returns on assets of any two debtors.
    - 퐹_t and 푈_it are assumed to be uncorrelated.
- Default threshold T modeled as linear combination of macroeconomic variables 푥_jt:
  - 푝_it = 푃(푅_it < T) = 푃(√휌 퐹_t + √(1−휌) 푈_it < 훽_0 + ∑_{j=1}^N 훽_j x_jt) = 휑(훽_0 + ∑_{j=1}^N 훽_j x_jt)
  - 휑 denotes the cumulative distribution function of the standard normal distribution.
  - 훽_0 is a constant; 훽_j are coefficients of macroeconomic variables x_jt.
- Sectoral default rate under law of large numbers:
  - 푝_t = 휑(훽_0 + ∑_{j=1}^N 훽_j x_jt)

### PD Model: Full table of results (Appendix III)

- Mortgage Loans — Coefficient | t stat
  - Intercept: -2.545 | -8.46
  - Age: 0.004 | 0.72
  - Residual maturity: 0.004 | 7.00
  - DSTI: 0.006 | 10.20
  - Below average wage (dummy): 0.434 | 5.09
  - Greater 2x average wage (dummy): -0.369 | -4.24
  - FX (dummy): 0.151 | 1.41
  - First Home dummy: -1.588 | -17.51
  - Originated before 2007: 1.248 | 7.01
  - Originated 2007: 0.910 | 5.45
  - Originated 2008: 1.348 | 8.78
  - Originated 2009: 0.643 | 3.57
  - Originated 2010: 0.674 | 3.68
  - Originated 2011: 0.446 | 2.76
  - Originated 2012: 0.126 | 0.87
  - Originated 2013: 0.321 | 2.24
  - Originated 2014: 0.103 | 0.78
  - Bank dummy 2: -0.530 | -5.33
  - Bank dummy 3: -1.258 | -8.32
  - Bank dummy 4: -1.057 | -6.86
  - Bank dummy 5: -0.324 | -2.52
  - Bank dummy 6: -0.909 | -6.06
  - Bank dummy 7: -0.626 | -4.25
  - Bank dummy 8: -1.136 | -6.89
  - Bank dummy 9: -0.168 | -0.81
  - Bank dummy 10: 0.418 | 1.98
  - Bank dummy 0: -0.237 | -1.59
  - Regional dummy 2: -0.305 | -2.52
  - Regional dummy 3: -0.300 | -2.40
  - Regional dummy 4: -0.237 | -2.29
  - Regional dummy 5: 0.106 | 0.93
  - Regional dummy 6: 0.096 | 0.79
  - Regional dummy 7: 0.178 | 1.28
  - Regional dummy 8: 0.240 | 1.90
  - Source: NBR and IMF staff calculations.

- Consumer Loans — Coefficient | t stat
  - Intercept: -0.726 | -8.55
  - Age: -0.041 | -50.44
  - Residual maturity: 0.017 | 12.71
  - DSTI: 0.003 | 14.57
  - Below average wage (dummy): 0.769 | 33.59
  - Greater 2x average wage (dummy): -0.651 | -23.52
  - Other mortgage credit: -1.431 | -42.20
  - Originated before 2011: 0.045 | 0.74
  - Originated 2011: -0.527 | -8.32
  - Originated 2012: 0.544 | 4.91
  - Originated 2013: 0.353 | 5.20
  - Originated 2014: 0.059 | 1.49
  - Bank dummy 2: 0.165 | 6.00
  - Bank dummy 3: -0.188 | -5.70
  - Bank dummy 4: 0.736 | 21.93
  - Bank dummy 5: -0.782 | -22.76
  - Bank dummy 6: 0.538 | 8.89
  - Bank dummy 7: -0.324 | -5.64
  - Bank dummy 8: -1.269 | -13.97
  - Bank dummy 9: 0.375 | 5.04
  - Bank dummy 10: 0.715 | 10.57
  - Bank dummy 0: 0.044 | 0.95
  - Regional dummy 2: -0.335 | -10.86
  - Regional dummy 3: -0.614 | -16.84
  - Regional dummy 4: -0.302 | -10.63
  - Regional dummy 5: -0.249 | -8.59
  - Regional dummy 6: -0.320 | -9.74
  - Regional dummy 7: -0.507 | -11.98
  - Regional dummy 8: -0.165 | -4.04
  - Source: NBR and IMF staff calculations.

*IMF staff calculations and NBR data as presented in the source.*

---


_Source: https://www.imf.org/-/media/files/publications/cr/2018/cr18161.pdf_