## wpiea2020134-print-pdf

## Source details

**Canonical URL:** [wpiea2020134-print-pdf](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020134-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020134-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020134-print-pdf.pdf.json)

---

### I. Evolution, purpose, and analytical framework
- Borrower-based measures in Slovakia: activated since late 2014 and progressively tightened to address strong credit growth and household indebtedness.
- Original NBS recommendation became legally binding and was twice amended to extend scope and increase effectiveness.
- Need: quantify the impact of combined borrower-based measures on household and bank resilience.
- Analytical framework:
  - Modular semi-structural micro-macro approach adapted from Gross and Población (2017).
  - Components:
    - Micro modules for employment and new lending.
    - Structural error correction model (ECM)-based macro module.
    - Dynamic household balance sheet simulator integrating micro and macro modules.
  - Default detection rule based on households’ capacity to service mortgage debt payments to compute PDs and LGDs for household and bank mortgage portfolios.

### Policy exercise, scenario design, and calibration (Slovakia, beginning of 2018)
- Policy exercise approximates fully phased-in tightening of borrower-based measures and estimates risk profile of new lending during exuberant credit growth.
- Policy scenario (start of exuberant period, beginning of 2018):
  - LTV tightened to 80 percent (with a 20 percent exemption up to maximum allowed LTV of 90 percent).
  - DSTI limited to 80 percent.
  - DTI limited to eight times annual income.
- Bindingness (share of loans issued above the limit; sample):
  - LTV most binding, followed by DTI and DSTI.
  - Total share of mortgage lending constrained by all measures: 55 percent (44 percent + 5 percent + 3 percent + 3 percent).
- Implementation of exemption:
  - Share of loans with LTV above 80 percent within HFCS sample: about 50 percent.
  - Assumption for 20 percent exemption: 60 percent of loans with LTV above 80 percent are reduced to LTV of 80 percent; remaining mortgages unchanged unless exceeding 90 percent, then reduced to 90 percent.
- New lending simulated with two pre-adverse “exuberant” years + three-year adverse period.

### Data sources and core methodological inputs
- Microdata: third wave of HFCS (household- and household-member-level variables).
- Macroeconomic inputs: NBS macro time series and structural macro model (Reľovský and Široká 2009) to generate a three-year central adverse scenario consistent with NBS stress test with end-2017 data.
- Simulation architecture:
  - Macro module focal variable: unemployment rate; ten thousand random macro paths around central adverse scenario.
  - Micro employment logit (explanatory variables include education, marital status, gender, age, nationality); retirees, parental leave, students excluded.
  - Counterfactual new mortgage lending generator: simulates distributions of new mortgage lending (LTV, DTI, DSTI) for five years, scaled to match aggregate mortgage lending forecasts.
  - Household balance sheet simulator: simulates mortgage debt servicing, detects defaults, computes PDs and LGDs over three-year adverse period.
- Key assumptions (selected):
  - Unemployed: income reduced to unemployment benefit for first two quarters, then to zero through end of adverse period.
  - Default if income/unemployment benefit, liquid asset depletion, and temporary maturity extension cannot cover debt service over 18 months.
  - Collateral recovery net of haircut equal to decline in house prices between origination and end of adverse period; house prices assumed to gradually decline by up to 30 percent through adverse period.
  - Banks incur administrative costs related to recovery.

### Main simulation results — median scenario (new loans 2018–22; cumulative over three-year adverse horizon)
- Aggregate table (cumulative results for new loans provided during 2018–22; median scenario):
  - Exp. loss (€ mil) 6238-39%
  - Loss rate 0.30% 0.20% -0.1 pp
  - LGD 19% 13% -6 pp
  - PD 1.68% 1.61% -0.07 pp
  - NPL ratio 1.56 % 1.52 % -0.04 pp
  - New loans (€ bln.) 20.70 18.70 -10%
- Key quantitative impacts:
  - Expected portfolio losses on new mortgage loans decline by almost 40 percent by end of adverse horizon, yielding a reduction of 10 basis points in mortgage portfolio loss rate.
  - Losses from loans granted during 2018–19 (exuberant period) represent 67 percent of total cumulative losses over the three-year adverse horizon; loans granted in 2020 represent an additional 24 percent of losses.
  - Joint measures act mainly through LGD reductions rather than PDs:
    - LTV cap: impacts primarily via LGD channel.
    - DSTI: impacts primarily via PD channel.
  - DTI contributes more to slowing household indebtedness (lower new mortgage lending volumes) than to portfolio riskiness.
  - Impact on new mortgage lending: 10 percent decline in new mortgage lending → slowdown in outstanding mortgage credit growth of 1 to 2 p.p. per year; effect is frontloaded (occurs before adverse period).
- Temporal dynamics:
  - LGD reductions more pronounced at beginning of adverse horizon.
  - PD reductions become more important toward end of horizon as unemployment and incomes deteriorate.
- Robustness / sensitivity checks (change in loss rate relative to baseline):
  - Help from other HHMs (adding income of HHMs who are not mortgage borrowers): No -0.10 pp
  - Ability to shrink living costs to ½ of subsistence minimum: No -0.09 pp
  - Inability to use HHs financial assets to cover drop in income: Yes 0.06 pp
  - Inability to reduce debt service by maturity extension: Yes 0.04 pp
- Symmetric uncertainty:
  - 95 percent confidence interval: +/- 1 b.p. around median 7 b.p. decrease in aggregate PD, and 1.6 p.p. around median 6 p.p. decrease in aggregate LGD.

### Interaction with capital-based measures and bank resilience
- Illustrative translation into capital adequacy (using NBS macro stress testing and end-2018 stress test results):
  - Estimated cumulative three-year credit losses from housing loans under adverse scenario (no-policy) = 0.5 percent of RWA.
  - Applying loss reduction under policies (39 percent) to 0.5 percent of RWA → equivalent increase in capital adequacy by 0.2 percent of RWA through decreased credit losses.
  - Policies improve capital adequacy by 0.5 percent of RWA due to lower risk weights: LGDs fall by about one quarter → one-quarter decrease in risk weights on housing loans for IRB portfolios.
  - Negative effect from foregone interest revenues: 0.2 percent of RWA cumulative over adverse scenario (computed as absolute change in lending volumes × average interest rate in housing loan portfolio).
  - Net illustrative effect: improvements via lower losses and lower risk weights partially offset by foregone interest revenues (quantitative contributions summarized above).

### Model mechanics: allocation, default rule, outputs, and common adverse assumptions
- Allocation of new loans:
  - HFCS household weight Wh,t increased each quarter by increments wh,i proportional to simulated change in total new lending and household incomes.
  - New mortgage amount Lh,orig(t) scaled from HFCS 2015–17 amounts by income changes; collateral rescaled to keep same LTV.
- Default detection and PD/LGD computations:
  - Four employment combinations with joint probabilities determine household income outcomes; unemployed HHM income factor bt = 0.75 during first six months, 0 later.
  - Illiquidity gap Gaph,t(sj) = Incomeh,t(sj) − Total paymentsh,t − Subsistence minimumh.
  - Default if Σt=1..18 Gaph,t(sj) > FAh.
  - PDh,(t−1,t) = Σj Prob(sj) × Dh(sj).
  - LGDh,t = max(Lh,t − REh,T , 0) + 0.1 × Lh,t (fixed foreclosure cost = 10% of Lh,t).
- Key output aggregates:
  - PD_T = ΣΣ PDh,(t−1,t) × Wh,t.
  - NPL_T = ΣΣ PDh,(t−1,t) × Lh,t × Wh,t.
  - EL_T = ΣΣ PDh,(t−1,t) × LGDh,t × Lh,t × Wh,t.
  - LGD_T = EL_T / NPL_T.
  - LR_T = EL_T / Volume_T.
  - Calculations repeated over 10,000 macro (unemployment) adverse scenarios.
- Common adverse scenario assumptions (Table A6):
  - Adverse period (stress horizon): 3 years
  - New loan simulation period: 5 years
  - Aggregate unemployment ratio: 5% gradual (cumulative) increase over adverse period
  - Aggregate mortgage credit growth: 2.3% gradual (annual) decrease over adverse period
  - Change in property prices (collateral value): 30% gradual (cumulative) decrease over adverse period
  - Change in income if unemployed: 25% decrease (cumulative) during the first 2 quarters; no income thereafter
  - Change in income if employed: 20% decrease (cumulative) during first 5 quarters if in sensitive sector; 10% if less sensitive; 5% if non-sensitive
  - Max borrower age: 70 years
  - Fixed cost of foreclosure: 10% of outstanding amount of defaulted mortgage loan

### Data descriptors and model inputs (selected)
- Descriptive HFCS statistics (Table A2 — Panel B exact values):
  - No. of HHs in whole population: 1,852,059
  - No. of borrowing HHs in HFCS sample of 2015-2017: 92
  - No. of HHMs in borrowing HFCS sample of 2015-2017: 155
  - No. of total borrowing HHs represented by the HFCS sample of 2015-2017: 11,291
  - Borrowing HHM/HH ratio: 1.7
  - Average LTV (weighted): 77%
  - Share of new loans with LTV>80%: 55%
  - Average DSTI (weighted): 43%
  - Share of new loans with DSTI>80%: 14%
  - Average DTI (weighted): 4.9
  - Share of new loans with DTI>8: 15%
- Employment logit (Table A4 exact coefficients):
  - Intercept: -0.323
  - Education (higher = 2, secondary = 1, primary = 0): 2.039***
  - Marital status (single = 1): -0.638***
  - Gender (male = 1, female = 0): 0.034
  - Age (years): 0.008
  - Nationality (foreign = 1): -0.797
  - Total number of observations: 2 322
  - AUROC: 0.75
- Annex 3: reported versus imputed house price values:
  - Median deviation between reported and imputed values: about 2 percent
  - 25th percentile: −22 percent
  - 75th percentile: +32 percent

### Conclusions, policy implications, and open questions
- Main conclusions:
  - Combinations of borrower-based measures (LTV, DSTI, DTI) enhance household and bank resilience to macroeconomic shocks and tend to be complementary because they operate via different channels (LGD vs PD).
  - Benefits are larger when measures limit accumulation of high-risk lending before downturns → early, preemptive implementation is warranted.
  - Borrower-based policies can influence endogenous business cycle dynamics by reducing likelihood of imbalance buildup and subsequent recessionary scenarios.
- Policy takeaway applied: framework and results informed tightening DSTI on new retail lending from 80 percent to 60 percent in Slovakia.
- Open / forward-looking considerations:
  - Microdata are important for distributional analysis by age, income, employment — left for future research.
  - More elaborate cost-benefit analysis, including cyclical dampening effects and alternative sequencing/phase-in timing, is warranted but beyond present paper.

*Source: wpiea2020134-print-pdf*

### References ............................................................................................... 21

### I. INTRODUCTION

### Evolution and purpose of borrower-based measures in Slovakia
- Borrower-based measures have been activated and gradually tightened in Slovakia since late 2014 to address the buildup of systemic risk related to strong credit growth and household indebtedness (Figure 1).
- The original National Bank of Slovakia (NBS) recommendation—to establish a comprehensive framework for prudential lending practices—subsequently became legally binding and was twice amended to extend the scope and increase effectiveness in addressing financial stability risks.
- The data and quantitative toolkit used to analyze the impact of the measures have been progressively enhanced as the risks and policy mix evolved over time.
- As borrower-based measures have become increasingly focused on addressing financial stability risks stemming from the excessive dynamic of household debt, there has been a growing need to quantify the impact of the combination of borrower-based measures on household and bank resilience.

### Analytical framework and methodology
- A modular framework is employed to quantify the change in the resilience of households and banks, resulting from the tightening of borrower-based measures, under an adverse macroeconomic scenario.
- The semi-structural micro-macro approach of Gross and Población (2017) is adapted to the Slovak context.
- Components of the framework:
  - Micro modules for employment and new lending.
  - A structural error correction model (ECM)-based macro module.
  - A dynamic household balance sheet simulator that integrates micro and macro modules.
- A rule for default detection, based on the households’ capacity to service their mortgage debt payments, enables the calculation of resilience parameters: probabilities of default [PDs] and losses given default [LGDs] for household and bank mortgage portfolios.

### Policy exercise and forward-looking risk estimation
- A policy exercise is implemented to closely approximate the fully phased-in tightening of the borrower-based measures in Slovakia.
- The framework also entails the estimation of the risk profile of new lending during periods of exuberant credit growth to serve as forward-looking indicators of banks’ lending practices.
- Rationale: As losses materialize only with a lag when an economic downturn occurs, it is important to be able to estimate risk parameters (PDs, LGDs, expected losses) for new lending.

*Source: wpiea2020134-print-pdf - References ............................................................................................... 21*

### 2018. A comparison with a counterfactual no-policy scenario quantifies the potential (ex-

### 2018. A comparison with a counterfactual no-policy scenario quantifies the potential (ex-ante) impact of macroprudential measures on resilience parameters under an adverse macroeconomic scenario

### Key findings and policy takeaways
- Borrower-based measures can noticeably improve household and bank resilience to macroeconomic shocks, in particular when multiple measures are applied.
- Borrower-based measures tend to complement each other, as the impact of individual instruments is largely transmitted via different channels (PD versus LGD).
- The resilience benefits of borrower-based measures are more sizeable if the measures effectively limit the accumulation of risks before an economic downturn occurs, suggesting that an early implementation of borrower-based measures is warranted.
- The model framework and results contributed to informing the most recent macroprudential policy decision in Slovakia related to borrower-based measures, that is, to tighten the debt service-to-income ratio on new retail lending from 80 percent to 60 percent.

### Literature and positioning
- The paper builds on and methodologically enhances the initial cross-country framework of Gross and Población (2017), adapting it to Slovakia and extending it to consider endogenous loan granting.
- It emphasizes the importance of microdata and micro-founded models for:
  - informing timing and calibration of borrower-based instruments (LTV, DSTI, DTI);
  - reviewing distributional implications of such measures.
- Multi-period stochastic simulation frameworks (since 2016) and microdata-based approaches in FSAPs are referenced as methodological lineage and contrast.

### Data sources and core methodological framework
- Microdata: third wave of the Household Finance and Consumption Survey (HFCS) for household- and household-member-level variables (mortgage loans, property values, other consumer debt, liquid financial assets, employment status, income, sociodemographic characteristics).
- Macroeconomic inputs: macroeconomic time series from the NBS database; structural macro model used by NBS for official medium-term forecasts (Reľovský and Široká 2009) to generate a three-year central adverse scenario consistent with NBS stress test exercise with end-2017 data.
- Simulation architecture (modular):
  - Macro module: generates adverse macroeconomic scenarios (focal variable: unemployment rate); ten thousand random macro paths simulated around the central adverse scenario to reflect uncertainty in exogenous foreign variables.
  - Micro modules:
    - Logit model for probability of household members (HHMs) staying employed (explanatory variables include education, marital status, gender, age, nationality); retirees, parental leave, students excluded.
    - Counterfactual new mortgage lending generator: simulates distributions of new mortgage lending (LTV, DTI, DSTI) for five years (two exuberant years + three-year adverse period), scaled to match aggregate mortgage lending forecasts from a satellite of the macro module.
  - Household balance sheet simulator: combines micro and macro inputs to simulate mortgage debt servicing, detect defaults, and compute PDs and LGDs over the three-year adverse period.
- Key behavioral and mechanical assumptions:
  - If mortgage debtors become unemployed, income reduced to unemployment benefit for first two quarters, then to zero through end of adverse period.
  - Borrowers who remain employed experience income declines depending on sector cyclicality.
  - Default occurs if income/unemployment benefit, liquid asset depletion, and temporary maturity extension cannot cover debt service over 18 months.
  - Collateral recovery net of a haircut equal to decline in house prices between origination and end of adverse period; house prices assumed to gradually decline by up to 30 percent through the adverse period.
  - Banks incur administrative costs related to recovery of claim.

### Policy scenario simulated (Slovakia, beginning of 2018) — calibration and borrower behavior
- Policy scenario approximations at the beginning of 2018 (start of exuberant period):
  - LTV tightened to 80 percent (with a 20 percent exemption up to maximum allowed LTV of 90 percent).
  - DSTI limited to 80 percent.
  - DTI limited to eight times annual income.
- Bindingness in sample (by instrument, in terms of loans issued above the limit):
  - LTV is most binding, followed by DTI and DSTI.
  - Total share of mortgage lending constrained by all the measures is 55 percent (44 percent + 5 percent + 3 percent + 3 percent).
- Implementation of exemption and borrower response:
  - Share of loans with LTV above 80 percent within HFCS sample was about 50 percent.
  - To implement regulatory exemption (20 percent of new loans allowed with LTV above 80 percent), assumption: 60 percent of loans with LTV above 80 percent are reduced to LTV of 80 percent; remaining mortgages unchanged unless exceeding 90 percent, in which case reduced to 90 percent.
- New lending simulations include two pre-adverse “exuberant” years to capture riskier loan issuance just before downturn.

### Main simulation results — resilience and lending effects (median scenario, 2018–22 adverse horizon)
- Table 1 (cumulative results over the three-year adverse scenario for new loans provided during 2018–22; median scenario):
  - Exp. loss (€ mil)6238-39%
  - Loss rate0.30% 0.20% -0.1 pp
  - LGD19% 13% -6 pp
  - PD1.68% 1.61% -0.07 pp
  - NPL ratio1.56 % 1.52 % -0.04 pp
  - New loans (€ bln.)20.70 18.70 -10%
- Key quantitative impacts:
  - Expected portfolio losses on new mortgage loans decline by almost 40 percent by the end of the adverse horizon, resulting in a reduction of 10 basis points in terms of the mortgage portfolio loss rate.
  - Losses from loans granted during 2018–19 (exuberant period) represent 67 percent of total cumulative losses over the three-year adverse horizon; loans granted in 2020 represent an additional 24 percent of losses.
  - The joint measures exert their impact primarily through changes in LGDs rather than PDs; LTV cap exerts impact primarily via LGD channel, DSTI via PD channel.
  - DTI contributes relatively more to slowing household indebtedness (via lower new mortgage lending volumes) than to portfolio riskiness.
  - Impact on new mortgage lending: a 10 percent decline in new mortgage lending translates into a slowdown in outstanding mortgage credit growth of 1 to 2 p.p. per year; impact on new lending is frontloaded (occurs before adverse period).
- Temporal dynamics:
  - Reduction in LGDs is more pronounced at the beginning of the adverse horizon; reduction in PDs becomes more important toward the end of the simulation horizon as unemployment and income deteriorate progressively.
- Robustness / sensitivity:
  - Sensitivity checks on borrower behavior (help from other HHMs; ability to shrink living costs to ½ of subsistence minimum; exclusion of financial asset drawdown; exclusion of forbearance) do not materially change the effectiveness of policies in the simulation.
  - Specific sensitivity table (change in loss rate relative to baseline):
    - Help from other HHMs (adding income of HHMs who are not mortgage borrowers) No -0.10 pp
    - Ability to shrink living costs to ½ of subsistence minimum No -0.09 pp
    - Inability to use of HHs financial assets to cover drop in income Yes 0.06 pp
    - Inability to reduce debt service by maturity extension Yes 0.04 pp
  - Symmetric uncertainty around central adverse macro scenario yields a 95 percent confidence interval of +/- 1 b.p. around the median 7 b.p. decrease in aggregate PD, and 1.6 p.p. around the median 6 p.p. decrease in aggregate LGD.

### Interaction with capital-based measures and bank resilience
- Illustrative translation of borrower-based impact into capital adequacy implications (using NBS macro stress testing framework and end-2018 stress test results):
  - Estimated cumulative three-year credit losses from housing loans under adverse scenario (no-policy) = 0.5 percent of RWA (taken from macro stress testing results).
  - Applying loss reduction under policies (39 percent; see Table 1) to the 0.5 percent of RWA translates into an equivalent increase in capital adequacy by 0.2 percent of RWA through decreasing credit losses over the three-year adverse horizon.
  - Policies contribute to improving capital adequacy ratios by 0.5 percent of RWA due to lower risk weights: LGDs fall by about one quarter, leading to a one-quarter decrease in risk weights on housing loans for banks’ IRB portfolios.
  - Negative effect from foregone interest revenues: 0.2 percent of RWA cumulative over the adverse scenario period (computed as absolute change in lending volumes multiplied by average interest rate in housing loan portfolio, including moderation in lending starting in exuberant period).
  - Net illustrative effect: improvements in capital adequacy via lower losses and lower risk weights partially offset by foregone interest revenues; quantitative contributions summarized above.

### Conclusions and policy implications
- Integrated micro-/macro-data and methodologies are instrumental for assessing effectiveness of macroprudential policies addressing household-sector risks:
  - Microdata convey distributions and evolution of borrower risks and inform determinants of employment and income—key for PDs.
  - Microdata are crucial to understand how combinations of borrower-based measures relate to distributions of lending standards, individually and jointly.
  - An integrated macro module anchors household balance sheets in the broader economy and provides forward paths for macro aggregates.
- Policy-relevant conclusions:
  - Combinations of borrower-based measures (LTV, DSTI, DTI) enhance household and bank resilience to macroeconomic shocks and tend to be complementary because they operate via different channels.
  - Policy benefits are larger when measures limit accumulation of high-risk lending before downturns; therefore, early, preemptive implementation of borrower-based measures is warranted.
  - Borrower-based policies may influence endogenous business cycle dynamics by reducing likelihood of imbalance buildup and subsequent recessionary scenarios.
- Open/forward-looking considerations:
  - Microdata are important for distributional analysis of macroprudential policies (age, income, employment) — left for future research.
  - More elaborate cost-benefit analysis, including cyclical dampening effects and alternative sequencing/phase-in timing, is warranted but beyond the scope of the present paper.

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

### REFERENCES

### REFERENCES (wpiea2020134-print-pdf)

### Literature coverage
- Extensive bibliography on household financial vulnerability, macroprudential policy, stress testing, and micro-macro modeling, including working papers, central bank reports, journal articles, and IMF Country Reports.
- Key topics represented: macroprudential policies and housing finance; household-level stress testing and microsimulation; borrower-based macroprudential tools (LTV, DSTI, DTI); household survey/microdata analyses; links between household balance sheets and bank stress tests.
- Representative references (names and years preserved as in source): Ahuja & Nabar (2011); Alam et al. (2019); Albacete & Fessler (2010, 2013); Igan & Kang (2011); Leika & Marchettini (2017); Nier et al. (2019); Gross & Población (2017); IMF Country Reports (2011, 2012, 2013, 2015, 2017a, 2017b, 2019), and many others listed.

### HFCS household and household-member level data (Annex 2 / Table A1)
- Identification variables:
  - IDssa0010: Household identification number
  - ra0010 / ra0010: Personal ID / Personal identification number
  - im0100: Imputation sample ID
- Income and employment status (HHM level) variables (exact variable codes preserved):
  - pe0400 Main employment - NACE
  - pe0100 Labour status
  - pg0110 gross cash employee income
  - pg0210 gross self-employment income (profit/losses of unincorporated enterprises)
  - pg0310 gross income from public pensions
  - pg0510 gross income from unemployment benefits
  - hg0510 gross income from private business other than self-employment
  - hg0410 gross income from financial investments
  - hg0310 gross rental income from real estate property
  - hg0610 gross income from other income sources
  - hg0110 gross income from regular social transfers
  - pne0200 Gross income from employment
  - pne0800 Gross income from Other job
  - pne0300 Gross income from business activities
  - pxg0600 Net income (including all incomes)
- Socio-demographic characteristics (HHM level) variables:
  - era0300 age
  - ra0200 gender
  - ra0100 relationship to reference person
  - ra0400 country of birth
  - pa0100 marital status
  - pa0200 highest level of education completed
- Assets - housing collateral (HH level) variables:
  - hb0900 / hb2801 current value of the collateral
  - hb0800 property value at the time of its acquisition
  - hb2501 other property type
  - hb2801 other property current value
  - hb2701 % of the property belonging to household
- Assets - liquid financial assets (HH level) variables:
  - hd1110 value of sight accounts
  - hd1210 value of saving accounts
  - hd1330 market value of mutual funds - all funds together
  - hd1420 market value of bonds
  - hd1510 value of publicly traded shares
  - hd1620 value of additional assets in managed accounts
- Liabilities - mortgage debt (HH level) variables:
  - hb1010 / hb3011 Number of mortgages
  - hb1301 / hb3301 Year when mortgage was taken or refinanced
  - hb1401 / hb3401 initial amount borrowed
  - hb1601 / hb3601 length of the loan at the time of borrowing/refinancing
  - hb1901 / hb3901 current interest rate of the loan
  - hb2001 / hb4001 monthly amount of payment made on loan
- Consumer loans and other debt (HH level) variables:
  - hc0200 household has credit line or overdraft
  - hc0300 household has a credit card
  - hc0220 amount of outstanding credit line/overdraft balance
  - hc0320 amount of outstanding credit cards balance
  - hc0110 monthly leasing payments
  - hc0601 amount initially borrowed
  - hc0701 intitial length of the loan
  - hc0801 outstanding balance of loan
  - hc0901 current interest rate of loan
  - hc1001 monthly payment on loan
  - hc1100 total amount owed for additional non-collateralised loans
  - hc1200 monthly payment on additional non-collateralised loans
  - hc0361 private loan outstanding amount
- Source: HFCS and authors' calculations.

### Descriptive statistics and lending standards (Table A2 — Panel B exact values)
- No. of HHs in whole population: 1,852,059
- No. of borrowing HHs in HFCS sample of 2015-2017: 92
- No. of HHMs in borrowing HFCS sample of 2015-2017: 155
- No. of total borrowing HHs represented by the HFCS sample of 2015-2017: 11,291
- Borrowing HHM/HH ratio: 1.7
- Average LTV (weighted by volume of the loan and HH weight): 77%
- Share of new loans with LTV>80%: 55%
- Average DSTI (weighted by volume of the loan and HH weight): 43%
- Share of new loans with DSTI>80%: 14%
- Average DTI (weighted by volume of the loan and HH weight): 4.9
- Share of new loans with DTI>8: 15%
- Note: LTV, DSTI and DTI per national regulatory definitions. Source: HFCS and authors' calculations.

### Definitions and formulas for lending metrics (Table A2 Panel A — formulas preserved)
- LTV (퐿푇푉푖): formula preserved in source using variable names:
  - First mortgage amount 퐹푖푟푠푡 푚표푟푡푔푎푔푒 푎푚표푢푛푡 / Value of HMR_i (plus adjustments for same collateral and FV of second mortgage as specified)
  - First mortgage amount_i = hb1401
  - Value of HMR_i = hb0800
  - FV of second mortgage_i = hb1402 * (1 + hb1902) * (hb1301 + hb1302) + hb2002 * (1 + hb1902) * ((1 + hb1902) * (hb1301 + hb1302) * 1) hb1902 (formula text preserved)
- DSTI (퐷푆푇퐼푖):
  - DSTI_i = Debt payments_i / Income_i + Subsistence min
  - Debt payments_i formula preserved involving hb1401, hb1901, hb1601, and multipliers
  - Income_i = upxg0600_1 + upxg0600_2
  - Subsistence minimum values:
    - 198.09 + 90.42 * #children if #debtors = 1
    - 336.28 + 90.42 * #children if #debtors = 2
- DTI (퐷푇퐼푖):
  - DTI_i = Total debt_i / (Income_i * 12)
  - Total debt_i = hb1401 + FV of second mortgage + hc0220 + hc0320 + hc0801

### Macro data variables (Table A3 — categories and exact variable IDs)
- Supply side variables (examples, IDs preserved):
  - delta: Depreciation rate of capital
  - F_L: Total employment in EA12
  - F_Y: Gross domestic product in EA12
  - K: Capital stock, whole economy
  - L: Employment, total
  - NAIRU_IL0: NAIRU, ILO concept
  - TFPTotal: Total factor productivity
  - U_GAP: Unemployment gap
  - Y_GAP: Output gap
- Demand side variables (examples):
  - AWealth
  - CONS Private consumption
  - DISP_Y Households disposable income
  - I_residInvestment private residential (dwellings)
  - D Government consolidated gross debt
  - NFANet foreign assets
- Prices and rates (examples):
  - CI_CE_PH Compensation per employee
  - CMD Competitors prices on the import side in €
  - HICPHICP
  - i_HH Composite interest rate (for consumption)
  - i_HHP_LT Households long term interest rates
  - i_nom_3m 3M EURIBOR
  - PX Export deflator
  - RER_M = PY/(PM_exE)
- Source: NBS macro database and authors' calculations.

### Macro model structure and satellite models (Box A1)
- Core macro model:
  - Structural error correction model (ECM) used for the central three-year adverse scenario; standard medium-size econometric model of a small open economy with backward-looking expectations.
  - Three main blocks: supply side, demand side, price block.
  - Steady state output determined by the supply side; short-term fluctuations derived from the demand side.
  - Model introduced by Reľovský and Široká (2009) and repeatedly re-estimated, updated, and enlarged.
- Satellite model for retail loan growth:
  - Annual absolute changes of outstanding volume of total retail loans estimated using a set of 9 VEC models.
  - Each VEC uses three explanatory variables chosen from: (1) nominal or real GDP; (2) level and growth in HICP; (3) unemployment ratio; (4) 3M EURIBOR; (4) property or flat prices; (5) five or ten-year spread between Slovak and German government bond yields.
  - Models use log-differences: ∆ln(RL_t) formulation preserved as in source.
  - Average of the nine models' estimates used; retail loans transformed to retail housing loans by assuming unchanged share of housing loans in total retail loans.
- Satellite model for nonperforming housing loans:
  - Bayesian Model Averaging (BMA) model used.
  - Equations estimated via least squares: ∆NPL_t depends on lags of ∆NPL and a set X of explanatory variables.
  - Maximum number of lags: 4; optimal lag length chosen using Bayesian information criterion.
  - Typical explanatory variables: real and nominal GDP (levels and growth rates), inflation (index or annual change), unemployment rate, property and flat prices.
  - Final equations weighted using the Bayesian information criterion.

### Micro modules: employment probability logit and counterfactual mortgage lending (Box A2)
- Logit equation for the probability of staying employed of household members preserved in mathematical form in source.
- Table A4: Estimated coefficients of the logit model (exact values):
  - Intercept: -0.323
  - Education (higher = 2, secondary = 1, primary = 0): 2.039***
  - Marital status (single = 1): -0.638***
  - Gender (male = 1, female = 0): 0.034
  - Age (years): 0.008
  - Nationality (foreign = 1): -0.797
  - Total number of observations: 2 322
  - AUROC: 0.75
- Notes on application:
  - Model estimated on HFCS data from 2016; data covers the full HFCS sample, not only clients with mortgage debt.
  - Each HHM assigned the HFCS weight of the HH, normalized across members.
  - Initial employment rate obtained by multiplying employment status by normalized weight and summing across members.
  - Employment rate is decreased each period of the adverse scenario by the positive change in the unemployment rate from the macro module.
  - Parallel implied employment ratio computed using HHM probabilities of staying employed from logit parameters; squared difference between the two implied ratios minimized to solve for period-by-period value of the logit intercept parameter ensuring consistency.
  - Adjusted logit intercept parameters used to calculate joint probability of staying employed for household members, then used to compute household default probability.
  - Example interpretation preserved: when a HHM with HFCS weight of 1,624 has probability drop from 0.99 to 0.97 between Q2 and Q3, then about 30 HHMs ((0.99-0.97) × 1,624) with similar characteristics become unemployed in the population.
- Counterfactual new mortgage lending: the new lending in each quarter t = 1,...,20 of the five-year simulation horizon is simulated based on two conditions that determine lending (text preserved up to provided cutoff).

*Source: wpiea2020134-print-pdf - REFERENCES (HFCS, NBS and authors' calculations as presented in the PDF).*

### 1. Allocation of new loans: by increasing the HFCS weight of each household in order

### 1. Allocation of new loans: by increasing the HFCS weight of each household in order

### Allocation methodology
- New loans are allocated by increasing the HFCS weight of each household h ∈ H over quarters to match the period-by-period simulated amount of new lending from the credit satellite of the macro module.
- The HFCS weight Wh,t of household h in quarter t is increased by increments wh,i in each quarter i:
  - 푊௛,௧ = Σ wh,i (i = 1,...,t).
- The increment wh,t is based on the original HFCS weight wh (2015–17) proportionately rescaled to the change in overall new mortgage lending:
  - 푤௛,௧ = 푤௛ × (total new lendingt / total new lendingHFCS) × (income1,h,2015–17 + income2,h,2015–17) / (income1,h,t + income2,h,t).
- The weight adjustment is interpreted as equivalent to new households (with similar sociodemographic characteristics as existing HFCS sample households) entering the mortgage market and being allocated new loans.
- During the exuberant period the new lending adjustment is applied as above; during the adverse scenario the recalculation of weights also accounts for the diminishing effect of declining incomes on the value of individual new loans.
- These calculations refer to the no-policy scenario. When policy measures (limits on LTV, DTI, DSTI) are introduced, the amount of new lending granted to individual households may be further decreased to reflect those limits; loans affected are assumed still granted but with a lower volume.

### New loan amount and collateral rescaling
- The amount of a simulated new mortgage granted to household h in quarter t is calculated so that DTI/DSTI and LTV of that household remain the same as in the original sample, adjusting for changes in incomes of HHMs and in house prices.
- The amount of the new mortgage Lh,orig(t) granted to household h in quarter t = 1,...,20 is based on the amount of mortgage granted during 2015–17 in the HFCS sample (Lh,orig(2015–17)), adjusted for decline of income of the HHMs if relevant:
  - 퐿௛,଴௧ = 퐿௛,଴ுி஼ௌ × (income1,h,t + income2,h,t) / (income1,h,2015–17 + income2,h,2015–17).
- The value of the real estate collateral is analogously rescaled to keep the same LTV.

### Business-cycle sensitivity of incomes (Table A5)
- Income decline of employed HHMs depends on business cycle sensitivity of the economic sector where the HHM is employed (NACE-based).
- Sectors listed under sensitivity categories:
  - Most sensitive: Transport, Electronics industry, Real estate activities, Trade, Agriculture, Food manufacturing, Recreation, Construction, Machine industry, Textile industry, Chemical industry, Services, Telecommunications, Utilities, Forestry and logging, Materials, Mining and quarrying, General government
  - (Table A5 notes: "Most sensitive", "Less sensitive", "Non-sensitive" as headings; Source: NBS, Annexes to the Analysis of the Slovak Financial Sector, 2018)

### Rule for default detection and simulation of PD and LGD (Box A3)
- For each representative household, the new loan is assigned a maximum of persons (algorithm favoring the younger and higher earners out of the income-earning HHMs).
- PUh,i,t denotes the probability that HHM i (i = 1,2) in household h becomes unemployed between t−1 and t, where t = 1,...,20:
  - PUh,i,t = PEh,i,t − PEh,i,t−1, where PEh,i,t is the probability of staying employed (from a logit model).
- There are four possible employment combinations s1...s4 with joint probabilities and resulting household incomes:
  - Prob(s1): (1 − PUh,1,t) × (1 − PUh,2,t); Income = income1 + income2
  - Prob(s2): PUh,1,t × (1 − PUh,2,t); Income = bt × income1 + income2
  - Prob(s3): (1 − PUh,1,t) × PUh,2,t; Income = income1 + bt × income2
  - Prob(s4): PUh,1,t × PUh,2,t; Income = bt × (income1 + income2)
- Unemployed HHM income assumption:
  - bt = 0.75 during the first six months (unemployment benefit), 0 later.
- For each situation sj (j = 1,2,3,4), the illiquidity gap of household h is:
  - Gaph,t(sj) = (Incomeh,t(sj) − Total paymentsh,t − Subsistence minimumh).
- Default assumption:
  - Default occurs if the drawdown of household financial assets (FAh) is not sufficient to cover illiquidity gaps during at least 18 months.
  - Default indicator Dh(sj) = 1 if Σt=1..18 Gaph,t(sj) > FAh; 0 otherwise.
- Probability of default for household h over period (t−1,t):
  - PDh,(t−1,t) = Σj Prob(sj) × Dh(sj).
- Loss given default LGDh,t of household h at time of default t:
  - LGDh,t = max(Lh,t − REh,T , 0) + 0.1 × Lh,t, where 0.1 × Lh,t is the fixed cost of foreclosure.
- Real estate value at time T:
  - REh,T = REh,orig × (PT / PO) = Lh,orig / LT Vh × (PT / PO).

### Key output variables and portfolio metrics (Box A4)
- Portfolio aggregated probability of default at time T (end of adverse horizon):
  - PD_T = ΣΣ PDh,(t−1,t) × Wh,t (summing over households and t = 1..T), where Wh,t is the HFCS weight at time t.
  - PD is net of already defaulted loans and driven only by the adverse scenario.
- Total cumulative amount of defaulted (nonperforming) loans at time T:
  - NPL_T = ΣΣ PDh,(t−1,t) × Lh,t × Wh,t (summing over households and t).
- Total cumulative expected loss at time T:
  - EL_T = ΣΣ PDh,(t−1,t) × LGDh,t × Lh,t × Wh,t.
- Cumulative portfolio aggregated NPL ratio:
  - NPL ratio_T = NPL_T / Volume_T.
- Portfolio aggregated loss given default at time T:
  - LGD_T = EL_T / NPL_T.
- Portfolio aggregated loss rate at time T:
  - LR_T = EL_T / Volume_T.
- Total volume of outstanding loans at time T granted since the beginning of the simulation horizon:
  - L_T = ΣΣ Lh,t × Wh,t.
- All computations are repeated over 10,000 macro (unemployment) adverse scenarios.

### Common assumptions across adverse scenarios (Table A6)
- Adverse period (stress horizon): 3 years
- New loan simulation period: 5 years
- Aggregate unemployment ratio: 5% gradual (cumulative) increase over adverse period
- Aggregate mortgage credit growth: 2.3% gradual (annual) decrease over adverse period
- Change in property prices (collateral value): 30% gradual (cumulative) decrease over adverse period
- Change in income if unemployed: 25% decrease (cumulative) during the first 2 quarters; no income thereafter
- Change in income if employed:
  - 20% decrease (cumulative) during the first 5 quarters if employed in sensitive sector
  - 10% decrease (cumulative) during the first 5 quarters if employed in less sensitive sector
  - 5% decrease (cumulative) during the first 5 quarters if employed in non-sensitive sector
- Max borrower age: 70 years (maximum borrower age until the loan maturity can be extended)
- Fixed cost of foreclosure: 10% of the outstanding amount of the defaulted mortgage loan

### Annex 3: Reported versus imputed current house price values
- The model uses households’ self-assessed value of their real estate property as of the survey date as an input.
- Benchmark imputation: index households’ real estate value from time of acquisition to the present using aggregate house price developments.
- Distribution comparison results:
  - The median deviation between reported and imputed house price values equals about 2 percent.
  - The 25th percentile equals −22 percent.
  - The 75th percentile equals +32 percent.
- Caveats of imputation:
  - Imputation was conducted based on an aggregate house price index for Slovakia without regional differentiation.
- Robustness check conclusion:
  - Model results are overall robust to misestimation of households’ house values, but accounting for this uncertainty in future applications deserves more dedicated analysis.

*Source: IMF working paper content (wpiea2020134-print-pdf, selected sections).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020134-print-pdf.pdf_