## wpiea2022065-print-pdf

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---

### Introduction — scope, purpose, and model extensions
- Purpose: examine the relationship between household mortgage probabilities of default (PDs) and loss given default (LGD) and their macroeconomic drivers in a structural micro-macro simulation model for policy counterfactual analyses.
- Coverage: model set up for 21 EU countries and the U.S.
- Uses: obtain scenario-conditional forecasts of PDs and LGDs to assess household sector resilience and quantify impact on banks’ retail loan books; can incorporate policy counterfactuals (fiscal policy, macroprudential policy, COVID-19 measures such as debt moratoria and guarantees).
- Key model extensions beyond Gross and Población (2017):
  - nonlinear debt repayment mechanism;
  - distinction between variable and fixed rate loans;
  - inclusion of debt-holding pensioners;
  - extended interest income module;
  - further refined LGD module.
- Method: ex-post nonlinear regressions (bridge equations) translate macro-financial scenarios into PDs and LGDs without rerunning the microsimulation while replicating microsimulation outcomes.
- Highlighted empirical finding: payment moratoria deployed during the COVID-19 pandemic notably contained household credit risk and shielded banks’ retail loan portfolios from substantial losses under baseline and counterfactual scenarios informed by the IMF’s World Economic Outlook (WEO) combined with country-specific moratoria design.

### Model structure and major components
- Architecture: enhanced Integrated Dynamic Household Balance Sheet (IDHBS) microsimulation with modules for employment (Module B), household balance-sheet simulation (Module C), asset revaluation, consumption, and PD/LGD computation.
- Required macro-financial scenario inputs (five variables):
  - unemployment rates;
  - short-term interest rates;
  - house prices;
  - income growth (conditional on being employed);
  - stock price growth.
- Employment simulation:
  - country-level logistic models relate household members’ employment status to structural characteristics (age, education, gender, marital status, nationality);
  - stochastic draws: D repetitions for all individuals while shifting the intercept and setting a persistence parameter to match population-level unemployment rate paths and persistence in unemployment (simulations run for H periods into the future).
  - retirees: included in household population for PD/LGD estimation but excluded from employment status models and stochastic employment simulations.
- Household balance-sheet simulator:
  - produces household-level PD and LGD estimates by simulating flows and stocks conditional on macro-financial scenarios;
  - PDs computed as mortgage exposure-weighted averages (consumer-debt-only households receive zero weight for PD aggregation in this paper);
  - LGDs computed only for households with mortgage debt, and mortgage debt-weighted country aggregates are reported.
- Financial asset revaluation:
  - stock holdings revalued using country-aggregate log stock price return RET_{c,t}: S_{i,t} = exp(ln(S_{i,t-1}) + RET_{c,t});
  - bond holdings revalued with a modified duration approach assuming average bond duration D = 2-year.
- Consumption: three model options considered; Mode 3 used as base case.

### Default and strategic default criteria; repayment mechanics
- Default definition: default occurs when a household cannot service its combined annuity for at least one quarter (default if household’s financial assets FA_{i,t} ≤ 0).
- Optional negative-equity criterion for limited-recourse jurisdictions:
  - augmented default rule: default if FA_{i,t} ≤ 0 OR V_{i,t} ≤ P_{i,t};
  - house value evolution: V_{i,t} = exp(ln(V_{i,t-1}) + HPG_{c,t}).
- Principal repayment dynamics: P_{i,t} = P_{i,t-1} − A_{i,t}^{principal} (quarterly principal repayment subtracted each quarter).
- Interest fixation types:
  - distinguishes fixed and variable rate debt based on microdata reporting (if unknown, assigned per predominant country share in 2017).
- Nonlinear repayment schedule:
  - initial residual duration M (months) approximated from reported loan-specific annual interest rate i_{0,i}, outstanding principal P_{0,i}, and current quarterly annuity A_{0,i} as of survey date; M rounded up to nearest integer.
- Variable-rate loans:
  - monthly interest payment A_{i,t}^{interest,variable} evolves with variable interest rate path i_{i,t}^{var} that evolves endogenously with scenario short-term rate r_{c,t} via i_{i,t}^{var} = max(0, i_{i,t}^{var,0} + Δr_{c,t});
  - total monthly annuity and principal repayment recomputed monthly for variable-rate loans.

### LGD module and calibration details (Annex 2)
- LGD projection:
  - projects each household’s predicted housing collateral sales value V_{0,i,t+H} at resolution time H quarters using quarter-on-quarter log house price growth (HPG).
  - Nominal expected recovery value (ERV_i): ERV_i = min( exp( ln(V0,i) + sum(HPG_s s=1..H) ), (1 + C + 0.25·i0,i) · P0,i ), where:
    - C captures administrative and legal costs measured as a percentage of outstanding principal;
    - 0.25·i0,i reflects capitalization of three months’ interest missed;
    - min operator reflects bankruptcy law crediting any excess recovery back to borrower.
- Discounting modes:
  - Accounting mode: use household reported effective mortgage interest rate i0,i for discounting.
  - Economic mode: use country-level expected return R_{c,m}, time-varying and moving parallel to short-term rate r_{c,m}: R_{c,m+t} = R_{c,m} + r_{c,m+t} − r_{c,m}. Country-level expected return at outset computed via eq. (12) subtracting an expected loss (credit spread) component.
- Discount factor DF_i:
  - Accounting LGD mode: DF_i = (1 + i0,i/12)^{-s}.
  - Economic LGD mode: DF_i uses average expected return path R_{c,m} over horizon up to resolution time.
- Final LGD formula with cure probability CP_c: LGD_i = (1 − CP_c) · [1 − (ERV_i / P0,i)].
- Fixed calibration choices:
  - Cost percentage C set to 5 percent for all countries.
  - Collateral sales period H set to eight quarters.
  - Initial cure probability (CP) set per country on a grid from 5 to 40 percent (in 5 p.p. increments), chosen so baseline simulation-based LGD matched external benchmark.
- Note: LGD module does not explicitly model recourse to defaulted borrowers’ future income.

### Data, anchors, anchoring procedure, and simulation grid
- Microdata sources: EU HFCS and U.S. PSID; both survey waves correspond to the year 2017.
- External anchors:
  - Default rate starting points for 2017 sourced from the EBA Risk Dashboard.
  - LGD starting points informed by banks’ reported coverage ratios in the EBA/ECB/SSM stress test 2018 and rounded to nearest 5 p.p. increment.
- Anchoring: compute “raw” PDs and LGDs under baseline (2017 realized macro paths) and shift them in absolute terms to match external anchor values.
- Grid-based simulation setup:
  - 20 equally spaced points for each variable’s range.
  - Grids and ranges:
    - Unemployment rate: from 3 to 15 percent (Greece: 10 to 25 percent).
    - Interest rates: from 0 to 10 percent.
    - Stock price growth: from -50 to 25 annual log percent.
    - Compensation per employee growth: from -10 to 20 annual log percent.
    - Residential house price growth: from -50 to 25 annual log percent.
    - Cure rate parameter: from 5 to 40 percent.
- PD simulations used grids for unemployment, interest rates, stock price growth, and compensation growth. For no-recourse countries, HPG grid also considered with strategic default incentive overlay.
- LGD simulations used house price growth, cure rate grid, and interest rate grid under economic LGD mode; under accounting LGD mode, interest-rate dependence disappears by design.
- Monthly payment-flow calculations aggregated to quarterly by summing non-overlapping three-month steps.

### Determinants and sensitivities of mortgage PDs
- Primary PD drivers: unemployment rates and interest rates have notable positive influence on PDs (ceteris paribus).
- Cross-country PD sensitivity highlights:
  - High PD sensitivity to unemployment: Poland, Slovakia, U.S.
  - Low PD sensitivity to unemployment: France, Germany, Italy, Netherlands.
  - Large countries and U.S. show low sensitivity of mortgage PDs to short-term interest rate changes.
  - Stock price growth matters where households hold more financial assets in stocks.
- Structural explanations:
  - PD dependence on unemployment correlates with population-level wage replacement rates.
  - PD dependence on interest rates correlates with variable-rate contract shares.
  - Counterfactual “no unemployment benefit” simulation shows sizable increases in PD–unemployment dependence in countries with high replacement rates (Netherlands, Portugal, France, Ireland); less effect in countries with low replacement rates (US, Hungary, Greece).

### Drivers and sensitivities of mortgage LGDs
- LGD dependence:
  - LGDs sensitive to house price growth and (in economic mode) to interest rates.
  - Accounting LGD mode removes interest-rate dependence.
- Homogeneity: Average LGD sensitivities are more homogeneous across countries than PD sensitivities.
- Key driver: LGD sensitivity to future house price drops driven notably by current LTVs (distance-to-negative-equity metric).
  - Countries with high current LTVs (US, Netherlands) show larger LGD–house-price-growth dependency.

### Bridge equations, benchmarking, and back-testing
- Bridge equations:
  - Second-order polynomials fitted to simulation outcomes (logit-transformed PDs and LGDs regressed on grids) capture nonlinear relationships and allow scenario-conditional forecasting without rerunning the microsimulation.
  - PD–house-price-growth dependence can be switched on where strategic default incentives matter (e.g., US); for most European countries this relationship is treated as hypothetical.
- Benchmarking and back-testing:
  - Microsimulation outputs compared to EBA/ECB/SSM Stress Test 2018 scenario-conditional locational mortgage default rates and LGDs; LGD module run in accounting mode to match banks’ accounting LGD computations—broad correspondence observed.
  - U.S. back-testing: microsimulation run for 32-year sample (1988Q1–2019Q4, 188 quarters) using realized macro-financial history.
    - Strategic default incentive set to 50 percent (when negative equity triggers default criterion, strategic default occurs with probability 50 percent).
    - Full-sample R-square equals 74 percent for structural model.
    - Estimating regression of logit PDs on macro variables yields R-square of 67 percent (reported for comparison).

### Scenario-conditional forecasting and COVID-19 fiscal policy analysis
- Scenarios (three):
  1. No-pandemic baseline counterfactual = December 2019 IMF WEO.
  2. Adverse scenario = October 2020 WEO (proxy for pandemic without policy support).
  3. Pandemic baseline scenario = October 2020 WEO including policy responses; split into:
     - Translating macro scenarios via microsimulation.
     - Translating macro scenarios plus reflecting COVID-19 policies in microsimulation.
- Simulation horizon: three years (2020–22).
- LGD mode for scenario analysis: accounting mode.
- Household debt moratoria:
  - Micro-level simulation reflects country-specific durations of moratoria.
  - In France and the US, no explicit supervisor/government moratoria were announced; a duration of six months has been assumed for both to reflect bank-level moratoria practices.
- Scenario impact excerpts (changes in capital ratio ∆ Capital Ratio reported for Pandemic, Adverse and Pandemic, Policies Reflected scenarios versus No Pandemic counterfactual; median/25th percentile over 22 countries):
  - Example row entries: q=0.25 / q=0.5: -0.58 pp, -0.25 pp, -0.12 pp, -0.05 pp.
  - Another example row: -0.54 pp, -0.25 pp, -0.10 pp, -0.04 pp.
  - Another example row: -1.21 pp, -0.46 pp, -0.19 pp, -0.14 pp.
  - Table entries labeled "Loan Loss Contr. to ∆CAPR" and "∆RWA Contr. to ∆CAPR" provide decomposition of capital ratio changes.
- Main scenario finding: household-sector-oriented policies (moratoria, interest support, guarantees) can have notable mitigating effects on PDs, LGDs, and bank loss rates; most uncertainty surrounds the adverse-no-policy proxy calibration.

### Discussion: debt moratoria, guarantees, and policy instruments
- Rationale: moratoria treat temporary illiquidity, avoid costly collateral seizure, and reduce house-price declines that would raise LGDs and amplify losses.
- Advantages of state/supervisory-led moratoria: ease bank decision processes, reduce borrower renegotiation burden, provide accounting guidance.
- IFRS 9 guidance: banks decide stage-migration criteria; IASB, EBA, ECB recommended “look through” pandemic shocks and avoid rigid application of prior criteria.
- Observed bank behavior: many banks placed more loans under moratoria into Stage 2, implying higher provisioning (EBA 2020b).
- Policy instruments and conditionalities:
  - Interest income support: partial coverage of accruing interest so borrowers do not face accrued interest obligations at moratorium end (Italy cited as example).
  - Conditionality examples: eligibility criteria such as job loss, material income loss, cash-equivalent savings thresholds (Belgium used EUR 25,000 threshold).
  - Guarantees: lower LGDs by covering losses on default; can reduce PDs indirectly via lower interest rates on new lending and variable-rate contracts; should avoid overstimulating housing demand and house-price overvaluation.
- Interaction with firm support: wage subsidies and firm support reduce household PDs by lowering job loss risk.

### Conclusions and practical utility
- Model usage: extended IDHBS structural micro–macro simulation model used for 21 EU countries and the US to uncover PD and LGD drivers.
- Key dependencies:
  - Mortgage PDs: primarily driven by unemployment and interest rates.
  - Mortgage LGDs: primarily driven by house price dynamics and initial LTVs.
- Cross-country heterogeneity explained by labor market and loan contract structures:
  - PD–employment tighter in countries with low unemployment benefits (e.g., US).
  - PD–interest-rate dependence stronger where variable-rate shares are higher (e.g., Netherlands).
  - LGD sensitivity to house prices higher where initial LTVs are high (US, Netherlands, several CEE countries).
- Predictive performance and recommendations:
  - Model outputs benchmarked against EBA 2018 stress-test-informed forecasts and back-tested for the US; found reasonable consistency (R-square 74 percent) and predictive performance.
  - Nonlinear regressions (bridge equations) allow scenario-conditional forecasting without rerunning microsimulation.
  - For policy counterfactuals (fiscal, monetary, macroprudential, borrower support), running the microsimulation is recommended.
  - Model can inform sizing of wage subsidies or cash grants to achieve target PD levels.

### Key numeric parameters and statistics (exact values from source)
- Bond duration used for revaluation: D = 2-year.
- Collateral sales period H = eight quarters.
- Cost percentage C = 5 percent.
- Cure probability grid: from 5 to 40 percent (in 5 p.p. increments).
- Grid points: 20 equally spaced points per variable.
- Unemployment grid: from 3 to 15 percent (Greece: 10 to 25 percent).
- Interest-rate grid: from 0 to 10 percent.
- Stock price growth grid: from -50 to 25 annual log percent.
- Compensation growth grid: from -10 to 20 annual log percent.
- Residential house price growth grid: from -50 to 25 annual log percent.
- Simulation horizon for COVID scenarios: three years (2020–22).
- Assumed moratorium duration for France and the US in simulation: six months.
- U.S. back-test sample: 32-year sample (1988Q1–2019Q4, 188 quarters).
- Strategic default incentive in U.S. back-test: 50 percent.
- Full-sample R-square (structural model, U.S. back-test): 74 percent.
- R-square for regression of logit PDs on macro variables (comparison): 67 percent.
- Example ∆ Capital Ratio table entries (q=0.25 / q=0.5 rows): -0.58 pp, -0.25 pp, -0.12 pp, -0.05 pp; -0.54 pp, -0.25 pp, -0.10 pp, -0.04 pp; -1.21 pp, -0.46 pp, -0.19 pp, -0.14 pp.

*Source: wpiea2022065-print-pdf - References and Annexes (IMF Working Paper content provided).*

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

### wpiea2022065-print-pdf - References ............................................................................................................................... 30

### Introduction — scope, purpose, and model extensions
- Purpose: examine the relationship between household mortgage probabilities of default (PDs) and loss given default (LGD) and their macroeconomic drivers in a structural micro-macro simulation model for policy counterfactual analyses.
- Coverage: model set up for 21 EU countries and the U.S.
- Uses: obtain scenario-conditional forecasts of PDs and LGDs to assess household sector resilience and quantify impact on banks’ retail loan books; can incorporate policy counterfactuals (fiscal policy, macroprudential policy, COVID-19 measures such as debt moratoria and guarantees).
- Key model extensions beyond Gross and Población (2017) (GP 2017):
  - nonlinear debt repayment mechanism;
  - distinction between variable and fixed rate loans;
  - inclusion of debt-holding pensioners;
  - extended interest income module;
  - further refined LGD module.
- Method: devise ex-post nonlinear regressions for PDs/LGDs from the microsimulation to translate macro-financial scenarios into risk metrics without rerunning the microsimulation while replicating its outcomes.
- Main empirical finding highlighted: payment moratoria deployed during the COVID-19 pandemic notably contained household credit risk and shielded banks’ retail loan portfolios from substantial losses under baseline and counterfactual scenarios informed by the IMF’s World Economic Outlook (WEO) combined with country-specific moratoria design.

### Literature context and gaps addressed
- Macro importance: household debt dynamics documented in literature on pre-2007–09 U.S. run-up and cross-country evidence linking credit/housing booms to recessions.
- Microdata-based household analyses: long-standing tradition since early 2000s; many country-specific studies summarized (Table 1).
- Gaps in previous literature:
  - Most prior microdata analyses focus on vulnerability metrics (financial margins, DSTI ratios, debt-to-asset ratios) and one-period or descriptive scenarios.
  - Virtually none provide explicit multi-period scenario simulations that produce PDs and LGDs suitable for linking to bank stress tests.
- Contribution: present model produces multi-period PDs and LGDs that can be linked to bank credit risk metrics (e.g., using a 90-day past due criterion for PD computation).

### Model structure and major components
- Overall architecture: enhanced Integrated Dynamic Household Balance Sheet (IDHBS) model used for scenario-conditional forecasting (schematic in Figure 1; drivers summarized in Figure 2).
- Macro-financial scenario inputs (five required variables):
  - unemployment rates;
  - short-term interest rates;
  - house prices;
  - income growth (conditional on being employed);
  - stock price growth.
- Employment simulation (Module B):
  - country-level logistic models relate household members’ employment status to structural characteristics (age, education, gender, marital status, nationality; see Annex 3);
  - stochastic draws: D repetitions for all individuals while shifting the intercept and setting a persistence parameter to match population-level unemployment rate paths and persistence in unemployment (simulations run for H periods into the future).
  - retirees: included in the household population for PD/LGD estimation but excluded from employment status models and stochastic employment simulations.
- Household balance-sheet simulator (Module C):
  - produces household-level PD and LGD estimates by simulating flows and stocks conditional on macro-financial scenarios (house prices, wage growth, stock prices, interest rates);
  - PDs computed as mortgage exposure-weighted averages (consumer-debt-only households receive zero weight for PD aggregation in this paper);
  - LGDs computed only for households with mortgage debt, and mortgage debt-weighted country aggregates are reported.
- Financial asset revaluation:
  - stock holdings revalued using country-aggregate log stock price return RET
ୡ,୲: S
୦୦,୲ = exp(ln(S
୦୦,୲ିଵ) + RET
ୡ,୲);
  - bond holdings revalued with a modified duration approach assuming average bond duration D = 2-year.
- Consumption process: three model options considered; Mode 3 is used as the base case mode.

### Default and strategic default criteria
- Default definition: occurs when a household cannot service its combined annuity for at least one quarter (default if household’s financial assets FA
୦୦,୲ା୦ ≤ 0).
- Optional negative-equity criterion for limited-recourse jurisdictions:
  - augmented default rule: default if FA
୦୦,୲ା୦ ≤ 0 OR V
୦୦,୲ା୦ ≤ P
୦୦,୲ା୦ (house value aligned with scenario path vs principal debt balance).
  - house value evolution: V
୦୦,୲ = exp(ln(V
୦୦,୲ିଵ) + HPG
ୡ,୲).
- Principal repayment dynamics: P
୦୦,୲ା୦ = P
୦୦,୲ା୦ିଵ − A
୦୦,୲ା୦୔ (quarterly principal repayment subtracted each quarter).

### Treatment of loan contracts and repayment mechanics
- Interest fixation types:
  - model distinguishes fixed and variable rate debt based on microdata reporting of outstanding mortgage contracts (if unknown, assigned per predominant country share in 2017).
- Nonlinear repayment schedule:
  - initial residual duration M (months) approximated from reported loan-specific annual interest rate i
୦୦,୲బ, outstanding principal P
୦୦,୲బ, and current quarterly annuity A
୦୦
୘୭୲,୕ as of the survey date; M rounded up to nearest integer.
- Fixed-rate loans:
  - monthly interest payment flow A
୦୦,୲ାୱ్, fixed = i
୦୦,୲బ / 12 × P
୦୦,୲ାୱିଵ;
  - principal repayment flows derived from annuity decomposition.
- Variable-rate loans:
  - monthly interest payment A
୦୦,୲ାୱ్, variable is a function of a variable interest rate path i
୦୦,୲ାୱିଵ that evolves endogenously with the scenario short-term rate r
୲ାୱ
ୱ୧୫ via i
୦୦,୲ାୱ = max(0, i
୦୦,୲ାୱିଵ + ∆r
୲ାୱ
ୱ୧୫);
  - total monthly annuity and principal repayment recomputed monthly for variable-rate loans.

### Calibration, microdata, and back-testing
- Microdata sources:
  - Household Finance and Consumption Survey (HFCS) for EU countries in the sample;
  - Panel Survey of Income Dynamics (PSID) for the U.S.
- Model maps microdata variables into simulation modules (Annex 2) and reports microdata characteristics (Annex 1).
- Back-testing: results corroborate the model’s ability to capture relevant channels through which macroeconomic conditions influence household PDs and LGDs.
- Practical outputs: scenario-conditional PDs and LGDs and their translation into bank-level retail portfolio credit risk assessments; ex-post nonlinear regressions enable fast mapping from macro scenarios to PD/LGD outcomes without rerunning microsimulations.

*Source: wpiea2022065-print-pdf - References (IMF working paper content provided).*

### Annex 2.

### Annex 2 — wpiea2022065-print-pdf

### Model extensions and LGD module
- Primary model extension relative to GP (2017): fixed-variable rate distinction and a nonlinear repayment feature to align with contract design.
- Nonlinear repayment schedules implemented for fixed and variable rate loans.
- LGD module projects each household’s predicted housing collateral sales value, V0,i,t+H, at resolution time (H quarters) using quarter-on-quarter log house price growth (HPG).
- Nominal expected recovery value: ERV_i = min( exp( ln(V0,i) + sum(HPG_s s=1..H) ), (1 + C + 0.25·i0,i) · P0,i ), where:
  - C captures administrative and legal costs measured as a percentage of outstanding principal.
  - The inclusion of 0.25·i0,i reflects capitalization of three months’ interest missed.
  - The min operator reflects bankruptcy law crediting any excess recovery back to borrower.
- Discounting modes for LGD:
  - Accounting mode: use household reported effective mortgage interest rate i0,i for discounting.
  - Economic mode: use country-level expected return Rc,m, time-varying and moving parallel to short-term rate r_c,m: R_c,m+t = R_c,m + r_c,m+t − r_c,m. Country-level expected return at outset computed via eq. (12) subtracting an expected loss (credit spread) component.
- Discount factor DF_i:
  - In accounting LGD mode: DF_i = (1 + i0,i/12)^{-s} (expression given in eq. (13) of source).
  - In economic LGD mode: DF_i uses average expected return path R_c,m over horizon up to resolution time.
- Final LGD formula incorporates cure probability CP_c: LGD_i = (1 − CP_c) · [1 − (ERV_i / P0,i)] (see eq. (14)).
- LGD module does not explicitly model recourse to defaulted borrowers’ future income.
- Fixed parameter choices used in calibration:
  - Cost percentage C set to 5 percent for all countries.
  - Collateral sales period H set to eight quarters.
  - Initial cure probability (CP) set per country on a grid from 5 to 40 percent (in 5 p.p. increments), chosen so baseline simulation-based LGD matched external benchmark.

### Data, anchors, and calibration
- Microdata sources: EU HFCS and U.S. PSID; both survey waves correspond to the year 2017.
- External anchor values:
  - Default rate starting points for 2017 sourced from the EBA Risk Dashboard.
  - LGD starting points informed by banks’ reported coverage ratios in the EBA/ECB/SSM stress test 2018 and rounded to nearest 5 p.p. increment.
- Anchoring procedure: compute “raw” PDs and LGDs under baseline (2017 realized macro paths) and shift them in absolute terms to match external anchor values.
- LGD cost percentage C = 5 percent; stated that changing C to 2.5 or 7.5 percent implies no notable changes after re-anchoring.

### Simulation design and grids
- Grid-based simulation setup: 20 equally spaced points for each variable’s range.
- Grids and ranges:
  - Unemployment rate: from 3 to 15 percent (Greece: 10 to 25 percent).
  - Interest rates: from 0 to 10 percent.
  - Stock price growth: from -50 to 25 annual log percent.
  - Compensation per employee growth: from -10 to 20 annual log percent.
  - Residential house price growth: from -50 to 25 annual log percent.
  - Cure rate parameter: from 5 to 40 percent.
- PD simulations used grids for unemployment, interest rates, stock price growth, and compensation growth. For no-recourse countries, HPG grid also considered with strategic default incentive overlay.
- LGD simulations used house price growth, cure rate grid, and interest rate grid under economic LGD mode. Under accounting LGD mode, interest-rate dependence disappears by design.
- Monthly payment-flow calculations aggregated to quarterly by summing non-overlapping three-month steps.

### Determinants and sensitivities of mortgage PDs
- Primary drivers: unemployment rates and interest rates have notable positive influence on PDs (ceteris paribus).
- Average PD sensitivities computed by regressing logit-transformed PDs from microsimulation on drivers’ grids.
- Cross-country patterns:
  - High PD sensitivity to unemployment: Poland, Slovakia, U.S.
  - Low PD sensitivity to unemployment: France, Germany, Italy, Netherlands.
  - Large countries and U.S. show low sensitivity of mortgage PDs to short-term interest rate changes.
  - Stock price growth matters where households hold more financial assets in stocks.
- Structural explanations:
  - PD dependence on unemployment correlates with population-level wage replacement rates.
  - PD dependence on interest rates correlates with variable-rate contract shares.
  - Cash stocks and other features also affect sensitivities.
- Counterfactual “no unemployment benefit” simulation shows sizable increases in PD-unemployment dependence in countries with high replacement rates (Netherlands, Portugal, France, Ireland). Less effect in countries with low replacement rates (US, Hungary, Greece).

### Drivers and sensitivities of mortgage LGDs
- LGD dependence:
  - LGDs sensitive to house price growth and (in economic mode) to interest rates.
  - Accounting LGD mode removes interest-rate dependence.
- Average LGD sensitivities are more homogeneous across countries than PD sensitivities.
- LGD sensitivity to future house price drops driven notably by current LTVs (distance-to-negative-equity metric).
  - Countries with high current LTVs (US, Netherlands) show larger LGD–house-price-growth dependency.

### Bridge equations and polynomials
- Second-order polynomials fitted to simulation outcomes (logit-transformed PDs and LGDs regressed on grids).
- Bridge equations capture nonlinear relationships between PDs/LGDs and structural drivers for scenario-conditional forecasting without re-running microsimulation.
- PD–house-price-growth dependence can be switched on where strategic default incentives matter (e.g., US); for most European countries this relationship is treated as hypothetical.

### Benchmarking, back-testing, and predictive performance
- Benchmark: compared microsimulation outputs to EBA/ECB/SSM Stress Test 2018 scenario-conditional locational mortgage default rates and LGDs; LGD module run in accounting mode to match banks’ accounting LGD computations.
- Broad correspondence observed between microsimulation results and banks’ model-based forecasts.
- U.S. back-testing:
  - Microsimulation run for 32-year sample (1988Q1–2019Q4, 188 quarters) using realized macro-financial history.
  - Strategic default incentive set to 50 percent (when negative equity triggers default criterion, strategic default occurs with probability 50 percent).
  - Full-sample R-square equals 74 percent for structural model.
  - Estimating regression of logit PDs on macro variables yields R-square of 67 percent (reported for comparison).

### Scenario-conditional forecasting and COVID-19 fiscal policy analysis
- Three scenarios considered (Table 6):
  1. No-pandemic baseline counterfactual = December 2019 IMF WEO.
  2. Adverse scenario = October 2020 WEO (proxy for pandemic without policy support).
  3. Pandemic baseline scenario = October 2020 WEO including policy responses; split into:
     - Translating macro scenarios via microsimulation.
     - Translating macro scenarios plus reflecting COVID-19 policies in microsimulation.
- Scenario simulation horizon: three years (2020–22).
- LGDs computed under accounting mode for scenario analysis.
- Household debt moratoria:
  - Micro-level simulation reflects country-specific durations of moratoria (Figure 14).
  - In France and the US, no explicit supervisor/government moratoria were announced; a duration of six months has been assumed for both to reflect bank-level moratoria practices.
- Scenario impacts (selected aggregated metrics reported):
  - Change in capital ratio (∆ Capital Ratio) reported for Pandemic, Adverse and Pandemic, Policies Reflected scenarios versus No Pandemic counterfactual (median/25th percentile over 22 countries). Examples from table rows:
    - q=0.25 / q=0.5: -0.58 pp, -0.25 pp, -0.12 pp, -0.05 pp (rows in table snippet).
    - Another row: -0.54 pp, -0.25 pp, -0.10 pp, -0.04 pp.
    - Another row: -1.21 pp, -0.46 pp, -0.19 pp, -0.14 pp.
  - Note: table entries labeled "Loan Loss Contr. to ∆CAPR" and "∆RWA Contr. to ∆CAPR" provide decomposition of capital ratio changes.
- Main finding: household-sector-oriented policies (moratoria, interest support, guarantees) can have notable mitigating effects on PDs, LGDs, and bank loss rates; most uncertainty surrounds the adverse-no-policy proxy calibration.

### Discussion: debt moratoria and guarantees
- Rationale for moratoria: treat temporary illiquidity and avoid costly collateral seizure and large house-price declines that would raise LGDs and amplify losses.
- Advantages of state/supervisory-led moratoria: ease bank decision processes, reduce borrower renegotiation burden, provide accounting guidance.
- IFRS 9 guidance: banks decide stage-migration criteria; additional guidance by IASB, EBA, ECB recommends “look through” pandemic shocks and avoid rigid application of prior criteria.
- Observed behavior: many banks placed more loans under moratoria into Stage 2, implying higher provisioning (EBA 2020b).
- Policy instruments:
  - Interest income support: governments can consider partial coverage of accruing interest so borrowers do not face accrued interest obligations at moratorium end (Italy cited as example where interest was partially covered).
  - Conditionality: eligibility criteria (job loss, material income loss, cash-equivalent savings thresholds) can limit moral hazard—example Belgium set savings threshold EUR 25,000.
  - Guarantees lower LGDs by covering losses on default; can also reduce PDs indirectly via lower interest rates on new lending and variable-rate contracts. Guarantee schemes should avoid overstimulating new housing demand and house-price overvaluation.
- Interaction with firm support: wage subsidies and firm support reduce household PDs by lowering job loss risk.

### Conclusions
- The extended IDHBS structural micro–macro simulation model was used for 21 EU countries and the US to uncover PD and LGD drivers.
- Key dependencies:
  - Mortgage PDs: primarily driven by unemployment and interest rates.
  - Mortgage LGDs: primarily driven by house price dynamics and initial LTVs.
- Cross-country heterogeneity explained by labor market and loan contract structures:
  - PD–employment tighter in countries with low unemployment benefits (e.g., US).
  - PD–interest-rate dependence stronger where variable-rate shares are higher (e.g., Netherlands).
  - LGD sensitivity to house prices higher where initial LTVs are high (US, Netherlands, several CEE countries).
- Model outputs were benchmarked against EBA 2018 stress-test-informed forecasts and back-tested for the US; found reasonable consistency and predictive performance (R-square 74 percent).
- Practical utility:
  - Nonlinear regressions (bridge equations) allow scenario-conditional forecasting without rerunning microsimulation.
  - For policy counterfactuals (fiscal, monetary, macroprudential, borrower support), running the microsimulation is recommended.
  - Model can inform sizing of wage subsidies or cash grants to achieve target PD levels.

*Source: Annex 2 of wpiea2022065-print-pdf (IMF working paper content provided).*

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### Annex 1. Microdata characteristics (figures summary)
- Figures A1–A6 summarize basic characteristics of the microdata for the EU (HFCS data) and the U.S. (PSID data).
- Figure A1. Shares of Bond and Stock Holdings in Households’ Total Financial Assets
  - Note: For the U.S., bond holdings of households are not separately reported but contained in the aggregate, which here is called “Deposits & Other.” The chart shows the shares for 21 EU countries and the U.S.
- Figure A2. Shares of Variable and Fixed Rate Mortgages (Volume-Weighted)
  - Note: The chart shows the variable rate mortgage shares for 20 EU countries and the U.S. (Finland is excluded because the HFCS microdata do not report the contract type for Finish households).
- Figure A3. Consumption Expenditure (Annual)
  - Note: The underlying microdata are as of 2017 for all countries. Microdata for the U.S. converted from USD to EUR (at av. 2017 USD-EUR exchange rate).
- Figure A4. Consumption Expenditure (Monthly)
  - Note: The underlying microdata are as of 2017 for all countries. Micro data for the U.S. were converted from USD to EUR (at av. 2017 USD-EUR exchange rate).
- Figure A5. Consumption Expenditure to Income, Rent to Income, LTVs, and DSTIs
  - Note: The box plots are based on the underlying household level data for the respective 22 countries. Red lines are medians. The whiskers extend to minima and maxima (after exclusion of outliers).
- Figure A6. Retirees’ Holdings of Mortgage Debt and Consumer Debt
  - Note: The shares of retirees’ debt holdings are based on the 2017 survey waves of the HFCS and the PSID.

### Annex 2. Mapping HFCS and PSID data into the model (Table A1 summary)
- Table A1 summarizes how the data from the HFCS and PSID databases were mapped into the IDHBS micro-macro simulation model. Selected mappings include:
  - H Current value of house: HFCS DA1110 / PSID ER66031
  - TFATotal financial assets (incl. cash, stocks, bonds, pensions, life insurance): HFCS DA2100 - DA2104 (value of business) - DA2107 (money owed to others) / PSID ER71435 + ER67847 + ER67819 + ER71445
  - B Current market value of bonds: HFCS DA2103 / PSID Incl. in TFA, cannot be separated
  - S Current market value of stocks: HFCS DA2105 / PSID ER71445
  - D M Outstanding balance of mortgage debt: HFCS DL1100 / PSID ER66051 + ER66072
  - D NM Outstanding balance of non-mortgage debt: HFCS DL1200 / PSID ER71459 + ER71463 + ER71467 + ER71471 + ER71475 + ER71480
  - I Household income total, quarterly, gross of tax: HFCS DI2000 / 4 / PSID ER71426 / 4, if not available then from ER71330 / 4
  - R Rental income, quarterly: HFCS HG0310 / 4 / PSID (ER71294 + ER71322) / 4
  - OI Other regular income, quarterly: HFCS (HG0110 + HG0210) / 4 / PSID (ER71351 + ER71353 + ER71381 + ER71383) / 4
  - Annuity for mortgage debt, quarterly: HFCS DL2100 * 3 / PSID (ER66053 + ER66074) * 3
  - Annuity for non-mortgage debt, quarterly: HFCS DL2200 * 3 / PSID ER71504 / 4 (for car debt only)
  - OER Rental expense, quarterly: HFCS HB2300 * 3 / PSID ER71494 / 4
  - E Living expense, excl. annuities and rent, quarterly: HFCS DOCOGOOD / 4 / PSID (ER71487 + ER71491 - ER71494 - ER71492 + ER71503 - ER71504 + ER71515 + ER71516 + ER71517 + ER71522 + ER71525 + ER71526) / 4
  - HH_ID Household ID: HFCS SA0010 (made unique across countries) / PSID ER66002
  - HW Household weight: HFCS HW0010 / PSID ER71571
  - HH_RESCountry of residence: HFCS SA0100 / PSID Set to "US" for all HHs
  - Myear Year of 1st mortgage origination; for MPRU exp. only: HFCS HB1301 / PSID ER66060
  - MiniDur Duration of 1st mortgage at origination in years; for MPRU exp. only: HFCS HB1601 Generated as 2017 - ER66060 + ER66061
  - DType Rate type of total debt (variable vs. fixed): HFCS DL1110 {a,b,c}i / PSID ER66057 (from 1st mortgage)
  - i M Current interest rate on mortgage debt: HFCS W.A. from mortages outstanding (HB170x) and their interest rates (HB190x) / PSID ER66058 (whole number) & ER66059 (after comma)
  - i D Current interest rate on total debt: HFCS Total absolute annual interest flow (DI1412) over total current debt (DL1000) / PSID Mortgage interest rate (above), multiplied by factor that reflects ratio of non-mortgage debt interest rate to mortgage rates
  - M RES Synthetic residual duration of total debt in months (needed for variable rate loans only)
  - EtoI Living expenses (excl. Annuities and rent) as share of gross income
  - Labor income (gross of tax) mappings, unemployment benefit mappings, HM-level identifiers, and demographic variables mapped as specified in the table.

- The table also shows transformations such as:
  - Model Variable A = A M + A NM
  - Other computed variables and transformations including ceiling and log expressions as shown in the Table A1 layout.

### Annex 2. Tables A2–A4: Recoding mappings (labor, marital, education)
- The labor status mapping compresses HFCS and PSID categories to a binary indicator for employment status. Categories indicated with (*) are excluded from the employment status model (Annex 3) but included in the household member sample for the microsimulation model.
- Table A2. LABOR STATUS RECODING (selected mappings)
  - Mapped to HFCS: Work -> 1 Employed
  - Sick leave, but work -> 1 Employed
  - Unemployed -> 2 Unemployed
  - Student -> NaN (varies)
  - Retiree (*) -> 5 Retiree(*)
  - Disabled -> NaN / 5 Disabled
  - Domestic tasks (*) -> 8 Other / NaN
  - Other -> NaN
- Table A3. MARITAL STATUS RECODING (selected mappings)
  - PSID Original -> Modified mapped to HFCS
  - 1 Single -> 1 Single
  - 2 Married -> 2 Married
  - 3 Cons. union -> 2 Married
  - 4 Widowed -> 2 Married
  - 5 Divorced -> 1 Single
  - 5 Separated -> 1 Single
  - 8 DK (0 cases) -> 11 Single
  - 9 NA (1 case) -> 11 Single
- TABLE A4. EDUCATION STATUS RECODING (selected mappings)
  - HFCS Original: 1 Primary (ISCED1) -> Modified: 1 No university degree
  - 2 Secondary (ISCED2) -> 1 No university degree
  - 3 Upper secondary (ISCED3+4) -> 1 No university degree
  - 5 University (ISCED5+6+7+8) -> 2 University degree
  - PSID Original mappings similarly recoded into No university degree / University degree categories.

### Annex 3. Logistic models for household member employment status
- Table A5 presents the logit model estimates for the employment status of individual household members contained in the HFCS (21 EU countries) and the PSID (US).
  - Note: The left-hand side variable is coded as 0 = unemployed, 1 = employed. Marital status: 0 = married, 1 = single. Education: 0 = university degree, 1 = no university degree. Gender: 0 = female, 1 = male. Domestic/foreign indicator: 0 = foreign, 1 = domestic national.
- Figure A6 visualizes estimated unemployment probabilities alongside country aggregate unemployment rates from the survey databases as of 2017.
  - Note: Country blocks are collected side by side. At each point where the horizontal line moves to a different level, a new country block starts.
- Coefficients (by country code AT BE CY DE EE FI FR GR HR HU IE IT LT LU LV MT NL PL PT SK SI UK US) — selected coefficient rows:
  - Intercept: 4.40 2.30 2.49 3.82 2.20 2.51 1.26 1.22 0.92 4.06 3.49 0.85 4.05 2.28 3.37 5.40 4.35 2.84 2.73 3.52 2.50 3.19
  - Marital status‐: -1.13 -1.21 -1.30 -1.11 -0.25 -0.87 -0.87 -0.73 -0.58 -0.72 -1.03 -0.70 -0.68 -0.31 -0.70 -0.76 -0.22 -0.83 -0.77 -0.96 -0.69 -1.17
  - Education‐: -1.14 -0.85 -0.93 -1.15 -0.79 -0.68 -0.85 -0.65 -0.92 -1.13 -0.90 -0.94 -0.81 -0.84 -1.05 -2.32 -1.00 -1.30 -0.95 -0.98 -1.69 -0.83
  - Gender‐: -0.17 -0.03 0.49 -0.12 -0.20 0.00 0.16 0.59 0.57 0.04 -0.12 -0.02 -0.37 0.06 -0.52 0.54 0.52 0.63 0.16 0.51 0.08 -0.25
  - Dom/Foreign: 0.82 0.71 0.37 1.08 0.76 1.10 0.81 0.46 0.42 -0.61 0.09 -0.24 0.07 0.95 0.08 -0.28 0.47 0.39 0.03 0.12 0.65 -0.09
  - Age: -0.02 0.01 -0.01 -0.01 0.01 -0.01 0.03 0.00 0.01 0.01 0.00 0.04 -0.02 0.03 0.01 0.00 -0.03 0.00 0.00 -0.02 0.01 0.02
- P-Values (selected rows by country):
  - Intercept: 0.0% across listed countries (see table for full row)
  - Marital status: p-values range from 0.0% to 21.2% across countries as listed.
  - Education: 0.0% across most countries with a few 0.1% entries.
  - Gender: p-values vary widely (e.g., 21.8%, 81.0%, 0.0%, 35.1%, 18.5%, 99.2%, etc.) as shown in the table.
  - Dom/Foreign and Age: p-values vary across countries; see table for full details.
- Stats (by country):
  - Obs. (observations): 3,325 2,194 2,101 5,300 3,497 11,984 15,308 3,333 1,645 6,380 5,728 6,750 1,869 2,104 2,343 6,878 7,319 2,568 2,403 10,583 (as presented in the table)
  - AUROC: 0.67 0.69 0.67 0.71 0.64 0.66 0.70 0.61 0.60 0.67 0.67 0.68 0.64 0.70 0.70 0.70 0.68 0.67 0.62 0.65 0.66 0.69

*What Drives Mortgage Default Risk in Europe and the U.S.? Working Paper No. WP/2022/065*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022065-print-pdf.pdf_