## wp17228 — Operationalizing the Concept of Household Financial Vulnerability

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### I. Background, objectives, and applicability
- Core observation:
  - The global financial crisis showed household-sector strains can crucially determine intensity, duration and macroeconomic impact of crises.
- Identified gaps:
  - Lack of a uniform conceptual framework and consensus on operative definitions of household vulnerability.
  - Estimation methods often overlook endogeneity from unobserved heterogeneity and measurement errors.
  - Rare review/validation of estimates; limited solutions for persistent data gaps, especially in emerging markets and developing countries.
- Paper objectives:
  - Provide an integrated perspective and comprehensive framework as a blueprint for empirical research on household financial vulnerability.
  - Operationalize household vulnerability with modelling and estimation options depending on purpose and data availability.
  - Illustrate integration of micro- and macro-data, merging of microdata sources, and estimation enhancements to reduce bias and allow implementation with data limitations.
- Applicability:
  - Framework designed to be widely applicable across countries at different development levels and can deliver meaningful assessments with relatively incomplete and fragmented information sets.

### II. Framework overview — three-step procedure
- Step 1: Database Preparation (Section III.A)
  - Working definition of household financial vulnerability (liquidity and solvency dimensions).
  - Core variable set (critical): Income; Living Costs; Debt Service Payments; Liquid Assets; Debt Level; Status of Financial Obligations (paid in full / overdue).
  - Complementary variable set (enhancing precision or informing macro‑financial impact): Other Assets; Demographic and Social Characteristics; Liability Characteristics; Guarantees; Insurance; Legal Features of Loans; etc.
  - Measurement guidance: identify most precise indicator for each core variable and propose proxies when data limited.
  - Data operations: update microdata using extrapolation techniques; aggregate and map information across microdata sources using matching keys.
- Step 2: Definition of Household Distress and Validation (Section III.B)
  - Select vulnerability measures and define distress criteria.
  - Use statistical methods to select measures by estimating capacity to predict actual household distress; use macro‑correlations and institutional information.
  - Approach choice: non‑parametric binary if individual status-of-obligations data available; otherwise consider parametric approaches.
  - Correct for endogeneity where needed (Section III.B.2 and Appendix III).
  - Validate initial-state vulnerability estimates against actual vulnerability information (e.g., NPLs); iterate if inconsistent.
- Step 3: Stress Testing (Section III.C)
  - Build baseline and adverse scenarios (single- or multi-period) and create forward paths for variables in vulnerability measures.
  - Recompute household vulnerability under baseline and adverse scenarios.
  - Obtain distributions of distressed households under baseline and adverse scenarios using validated distress criteria.

### III. Measurement: core indicators and operational formulas
- Liquidity (extended financial margins)
  - Absolute Financial Margin (i.1): FM = LA - LC - DP (notation preserved from source: h,tLA, h,tLC, h,tDP)
  - Relative Financial Margin (i.2): RFM = (LA - LC - DP) / Y
  - Use forward projections of (i.1) or (i.2) to assess probability of liquidity distress along projection horizon: τh,PD = f(FM, X) with X ∈ {R, S} and τh,PD interpreted as probability of liquidity distress.
- Solvency (truncated intertemporal budget constraint)
  - Practical operationalization: truncated projection horizons (empirically inferior to 5 years often used).
  - Solvency probability h,T PD based on initial net debt and discounted stream of income-expenditure balances over projection horizon T.
- Role of debt level:
  - Primarily informs solvency and can provide insight on liquidity capacity in certain loan structures (e.g., interest-only, balloon payments).
  - Key for assessing banking-sector impact (loss-given-default) and can be used to estimate debt payments when unavailable.

### IV. Deriving core variables when microdata incomplete (Section 2.D)
- Key principle:
  - Methodology can be applied if a measure of income exists in a microdata source; remaining information can be derived from macro-data sources.
- Income (h,tY)
  - Ideal: disposable income (gross income adjusted for net current transfers — taxes, social security contributions, receipts of social benefits).
  - Practical proxy when transfers missing: gross income.
  - Basic requirement: availability of microdata including (disposable or gross) income.
- Debt payments (h,tDP)
  - h,tDP = h,tMP + h,tPP + h,tCCP where MP = mortgage payments, PP = personal loan payments, CCP = credit card payments.
  - Measurement choices:
    - First choice: actual scheduled payments.
    - Second choice: estimates via micro- and/or macro-data (central bank average DTI, residual maturity, lending rates, indebtedness by income group).
  - Credit‑Foncier rule: constant payment assumption using amount outstanding, per‑period interest rate, and remaining repayments; using scheduled number of payments when borrowers accelerated payoffs leads to underestimation of debt service for those households.
  - Credit card payment proxy: reported outstanding balance.
  - If individual debt levels unavailable: use national average household DTI ratio and indebtedness by income groups to compute payments via repayment formula.
- Living costs (h,tLC)
  - Best indicator: expenses for necessary items (basic consumption for essential items).
  - Proxies: national poverty line; household survey; authorities’ estimates; national accounts.
- Liquid assets (h,tLA)
  - Best: assets readily converted into cash with minimal loss (deposits).
  - Sources/proxies: household income and wealth survey; monetary survey with deposit distribution across income groups (authorities, Findex).
  - Note: financial assets other than deposits frequently negligible in developing economies and can be ignored there.
- Debt levels
  - Best: individual outstanding debt levels by category (mortgage, personal loans, credit cards).
  - Proxies: debt at origination; average household DTI ratios (possibly by debt category).
  - Sources: household survey; central bank information on average DTI, indebtedness by income groups.
- Status of debt obligations
  - Best: individual information on status (days of arrears or categorical performing/forborne/in arrears/in default).
  - Proxy: nation-wide exposures in arrears, forbearance, or NPLs.
  - Sources: microdata (household indebtedness survey, banks’ loan books) or central bank aggregate NPLs or arrears.
  - For debt-free households: use status of other financial obligations or share below poverty line to calibrate distress thresholds (may underestimate fragility).
  - Multiple indicators can be consolidated via dimensionality reduction (e.g., Nonlinear Principal Components Analysis).

### V. Extrapolation and merging microdata sources (Section 3)
- Consolidation steps: extrapolate microdata to a common reference period; merge sources into unified time-consistent database.
- Extrapolation methods:
  - Uprating: update monetary variables in line with aggregate counterparts; non-monetary characteristics unchanged. Note: maintains household-specific variation but applies identical temporal adjustment factor to all households (can widen decile gaps).
  - Static aging: uprating plus adjusting household weights to reflect changes in group sizes.
  - Dynamic aging: model fertility, household formation/dissolution, labor market transitions (uses transition probabilities).
  - Recommendation: limit updates at this stage; perform full update in Step 3 after validation unless status of financial obligations dictates otherwise.
- Merging without common identifiers:
  - Parametric matching: regressions using common characteristics (region, age, employment, education).
  - Non‑parametric matching: use common variables or monotonic relations as matching keys; map by empirical distributions along matching keys.
- Appendix I contains further parametric and non‑parametric merging details (listed in source).

### VI. Choice of vulnerability measures and distress definitions
- Non‑parametric binary approaches (threshold rules)
  - Household considered distressed when vulnerability indicators cross specified thresholds.
  - Combining multiple indicators:
    - Indicators considered separately with individual thresholds; interpretations via formulations (iv.1) (conservative) and (iv.2).
    - Synthetic index f(·) compared to threshold τ as in (v.) — can be regression-fitted or non‑parametric weighting algorithms that maximize correct prediction.
  - Directionality: for indicators where higher values imply higher vulnerability (e.g., DSTI), inequality signs reversed.
  - Other non‑parametric methods: classification trees, machine learning (limited use to date).
- Parametric approaches
  - Model relation between vulnerability measures and status of financial obligations; yield continuous probabilities in [0,1].
  - Methods: binary regressions, artificial neural networks.
  - Trade-offs:
    - Binary methods: simple, limited data/computation, easy thresholds, but dichotomous classification and potential misinterpretation of severity.
    - Synthetic-index binary: more compute/data intensive.
    - Parametric: more granular, multi-category distress modeling, sensitive to distributional assumptions in small samples.
  - Semi-parametric: parametric methods can derive synthetic indicators used within non‑parametric frameworks.

### VII. Addressing endogeneity and measurement error
- Sources: selection bias, measurement errors (e.g., income under-reporting), omitted variables, unobserved heterogeneity.
- Example bias: using gross income instead of disposable income can understate poor households’ income and overstate wealthy households’ income, biasing financial margins and thresholds (illustrated in source notation).
- Calibration strategy when endogeneity non‑negligible:
  - Partition observations into subsets where estimation bias sources are expected uniform (e.g., by gross income when transfers unobserved).
  - Estimate specific distress thresholds per subset.
- Threshold estimation methods:
  - With individual status-of-obligations data:
    - Simple: set threshold equal to average/median index among defaulted households in subset.
    - Preferable: signaling detection (non‑parametric) to balance detection and false alarms; computationally demanding in multivariate settings.
    - For high-dimensional indicators: build synthetic index and derive thresholds for it.
  - Without individual status-of-obligations data:
    - Calibrate thresholds to reproduce average NPLs or arrears at subset level.
    - For debt-free households, use share below poverty line.
  - Practical constraints: finer partitions reduce within-subset bias but reduce sample sizes; parametric partitioning can face small-sample inference issues.
- Alternative estimation corrections for parametric/binary regressions: linear probability models, maximum likelihood, control function, special regressor methods.
- Extension: methods applicable to solvency-related distress (Appendix III reference).

### VIII. Validation diagnostics and corrective actions (Section 3)
- In‑sample validation:
  - Fitting deviation: deviation between simulated share of distressed households and actual share by subset.
  - ROC curve and AUC: assess discrimination capacity.
  - If individual status unavailable: compare average simulated NPLs with national-average NPLs.
- Out‑of‑sample validation:
  - Cross‑validation (training/testing splits, multiple rounds, average results).
- Diagnostics outcomes:
  - Significant mismatches imply omitted variables and/or measurement errors; remedies include re‑estimation with additional indices or endogeneity correction techniques.

### IX. Stress testing: framework, scenarios, and uncertainty treatment
- Pre‑simulation: extrapolate unified database to simulation period if microdata reference differs; one‑period analyses are liquidity‑focused; multi‑period analyses capture solvency and feedback loops.
- Baseline projections: derive forward paths for vulnerability measures from macroeconomic projections or models (e.g., DSGE); multi‑period analyses can include feedback loops.
- Adverse scenarios:
  - Shocks applied to income, interest rates, exchange rates, asset prices; uniform or subset‑selective shocks.
  - Unemployment shocks addressed via Monte Carlo simulations.
- Uncertainty:
  - Include lower and upper confidence-interval values around baseline distress projections for each household group and time point; compute joint distribution of indicators to derive shares associated with bounds.
  - Distribution of vulnerability measures can come from stochastic simulations (e.g., VAR residuals).

### X. Namibia application — database, calibration, and key results
- Context and key metrics:
  - Household debt estimated by Bank of Namibia (BON) at about 90 percent of disposable income at end-2015.
  - Debt service burden estimated at 16.1 percent of disposable income.
  - Interest payments correspond to roughly 10 percent of disposable income.
  - Residential mortgage exposure: 38 percent of total loans and advances at end-2016.
  - Impairment figures in household loan books: about 1.5 percent of total loans and advances (broadly stable).
- Data sources and harmonization:
  - NHIES (2009-2010): 9,600 households; gross income, expenditures, outstanding debt levels, region, employment status.
  - Mortgage database (end-2014): 22,000 mortgage loans (≈ one fourth of outstanding mortgage loans) with loan origination value, outstanding balance, amortization, interest payment, days overdue, property value, guarantees, region.
  - NHIES updated to end-2014 by uniformly increasing incomes by national yearly growth rate (Financial Stability Report of BON) and expenditures by average annual CPI (NSA). Update performed to mortgage database observation period.
  - Mapping: non‑parametric matching on region and monotonic relation between household income and amortization payment; partition into 130 cells (region × income/amortization deciles).
  - Mapping rules differ for performing vs non‑performing loans; non‑performing loans paired with weighted averages of the minimum and average cell income/expenditures with weights optimized to maximize predictive performance.
  - Flow variables annualized; living costs defined as sum of “basic” expenditure items (food, transport, health, education); loan non‑performing if monthly payment overdue > 30 days.
- Construction of household indicators (end‑2014)
  - Household relative financial margin 2014,hFM computed per household in cell (i,j) with cell-specific weights ji,α and ji,β (calibrated).
  - Additional measures: 2014,hLTV (outstanding loan-to-value) and 2014,hOTO (outstanding loan-to-loan-at-origination).
  - Assets only available via property value proxy for gross wealth (limitations noted).
- Indicator selection and regression results (binary logistic regression of arrears on FM, LTV, OTO)
  - FM: Coefficient = -0.041; SE = 0.019; p-value = 0.0296
  - LTV: Coefficient = -0.681; SE = 0.167; p-value = 0.000
  - OTO: Coefficient = 0.0000; SE = 0.003; p-value = 0.958
  - Constant: Coefficient = -3.726; SE = 0.087; p-value = 0.000
  - Interpretation: FM significant and negative (higher margins → lower arrears probability); LTV coefficient sign likely reflects reverse causality; OTO not significant.
  - Outcome: use financial margins (FM) to derive household vulnerability via non‑parametric signal detection approach; ji,α and ji,β initially set to zero in preliminary analysis.
- Signal detection calibration and distress thresholds (cell/decile results)
  - Thresholds calibrated per cell to balance type I and type II errors, maximizing AUC; in 74 cells with overdue data algorithm applied; in remaining 56 cells lowest FM in cell used as threshold.
  - Calibrated average distress thresholds by income decile (first row, bold — FM units):
    - Decile 1: -4.02
    - Decile 2: -1.18
    - Decile 3: -0.40
    - Decile 4: -0.01
    - Decile 5: 0.14
    - Decile 6: 0.39
    - Decile 7: 0.54
    - Decile 8: 0.59
    - Decile 9: 0.63
    - Decile 10: 0.66
  - Alternative calibration using average share of distressed households by decile (second row, italic — FM units):
    - Decile 1: -5.11
    - Decile 2: -1.34
    - Decile 3: -0.51
    - Decile 4: -0.13
    - Decile 5: 0.07
    - Decile 6: 0.37
    - Decile 7: 0.50
    - Decile 8: 0.57
    - Decile 9: 0.60
    - Decile 10: 0.63
- Model comparison (signal detection vs alternative calibrations vs fixed threshold)
  - Signal detection approach outperforms alternatives; goodness of fit very high in all deciles except decile 2.
    - Excluding decile 2, mean absolute percentage error = 3 percent.
  - Calibration using average share of distressed households: average mean absolute percentage error = 20 percent; performs well when distress uniformly distributed.
  - Fixed threshold = 0: extremely poor performance, especially in lowest deciles (fails to correct for endogeneity/measurement issues).
- Stress testing setup (update to end-2016; one‑period ahead)
  - Baseline assumptions:
    - Individual household income growth = non‑mining GDP per capita growth (April 2017 IMF WEO database).
    - Population growth = linear projection of WB development indicators.
    - Household debt grows in line with non‑mining GDP per capita (average household DTI ratio constant).
    - Household expenditures grow in line with inflation projections (April 2017 IMF WEO).
    - Lending rate increases proxied by Jibar forward rates.
  - Adverse scenarios:
    - Interest rate shocks: 200bp and 300bp.
    - Alternative nominal gross income growth assumptions (uniform across deciles).
    - Household indebtedness grows with income; inflation projections as baseline.
  - Financial margins recomputed under baseline and adverse scenarios and compared with calibrated distress thresholds.
- Namibia stress‑test results (key statistics)
  - Under 300bp adverse shocks, share of distressed households ranges between 19.5 and 23 percent depending on income growth assumptions.
  - Extract from Table 4 (Namibia: Share of Distressed Households)
    - Nominal Gross Income Growth Rate (Percent) columns include Baseline and alternative scenarios proxied by non‑mining GDP per capita growth:
      - Interest Rate Increase (bps): None | 2.8 (Baseline entry)
      - 200bps scenario distress shares: 13.0 | 14.1 | 15.2 | 16.3 (depending on growth assumptions)
      - 300bps scenario distress shares: 19.5 | 20.6 | 21.8 | 23.0 (depending on growth assumptions)
    - Note: *Nominal Gross Income Growth Rate is proxied by the growth rate in non‑mining GDP per capita.
  - Distributional findings:
    - Most vulnerable households located in middle- and middle/upper-income deciles.
    - Lowest deciles less impacted because they rely on social transfers and subsidies not included in income definition.
    - Highest decile less vulnerable due to larger buffers despite higher indebtedness.
    - Decile 2 may understate vulnerability because thresholds set relatively high to limit false alarms.
  - Banking-sector implication:
    - Based on mortgage distribution across deciles, banks’ mortgage arrears projected to increase up to 19.6 percent of total mortgage loans in the most adverse scenario.
  - Caveat:
    - Accuracy depends on assumption that relation between FM and household distress unchanged between 2014 and 2017 (e.g., no structural changes in social benefits or tax rates). Distress thresholds validated with 2014 data assumed valid for 2017.

### XI. Conclusions and policy uses
- Methodological contributions:
  - Integrated best practices into a coherent framework and proposed estimation extensions to improve estimate quality and allow implementation with data limitations.
  - Framework captures non‑linear responses to shocks by accounting for distributional heterogeneity and default correlations.
- Uses for stress testing and financial stability:
  - Can provide inputs for banks’ stress testing as an alternative to macroeconomic credit risk models for household average probability of default.
  - By accounting for distributional heterogeneity, reveals non‑linearities and default correlations missed by aggregate frameworks.
- Uses for macroprudential policy calibration:
  - Household vulnerability estimates useful to calibrate instruments such as LTV and DSTI limits.
  - Micro-based calibration reduces risk of imposing unneeded credit restrictions (type II error) or missing systemic risk buildup (type I error).
- Uses for macroeconomic policy and welfare analysis:
  - Framework can assess impacts of policy changes and shocks on household welfare, poverty, and income distribution — especially relevant in developing countries.
- Practical applicability:
  - Suitable for advanced economies (banking stress tests, macroprudential calibration) and developing economies (welfare and poverty impacts) where data limitations can be addressed with the proposed extensions.

*Source: wp17228 — IMF Working Paper content provided.*

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

### wp17228 - References ......................................................................................................................

### Glossary
- AUC Area Under the Curve
- BIS Bank for International Settlements
- BON Bank of Namibia
- DTI Debt-to-Income
- DSTI Debt-Service-to-Income
- DSGE Dynamic Stochastic General Equilibrium
- ECB European Central Bank
- GDP Gross Domestic Product
- HFCS Housing Finance and Consumption Survey
- LTV Loan to Value
- NHIES National Household Income and Expenditure Survey
- NLPCA Nonlinear Principal Components Analysis
- NPLs Nonperforming Loans (used interchangeably with distressed assets)
- NSA Namibia Statistics Agency
- OECD Organization of Economic Cooperation and Development
- ROC Receiver Operating Characteristic
- WEO IMF World Economic Outlook

### I. Background — problem statement and objectives
- Core observation: The global financial crisis demonstrated that household-sector strains can crucially determine the intensity, duration and macroeconomic impact of crises.
- Identified gaps in the literature:
  - Lack of a uniform conceptual framework and consensus on operative definitions of household vulnerability.
  - Prevailing estimation methods tend to overlook endogeneity caused by unobserved heterogeneity and measurement errors in household microdata.
  - Rare review and validation of estimates in empirical applications.
  - Limited solutions addressing persistent data gaps, restricting applications in emerging markets and developing countries.
- Paper objectives:
  - Provide an integrated perspective and comprehensive framework as a blueprint for empirical research on household financial vulnerability.
  - Operationalize the concept of household vulnerability with modeling and estimation options depending on purpose and data availability.
  - Illustrate integration of micro- and macro-data, merging of microdata sources, and estimation enhancements to reduce bias and allow implementation with data limitations.
- Applicability emphasis:
  - Framework is designed to be widely applicable across countries at different development levels.
  - Can deliver meaningful assessments even with relatively incomplete and fragmented information sets.

### II. Assessment of household financial vulnerability: state of the literature
- Common empirical practice:
  - Increasing use of household microdata (surveys and other sources) to conduct sensitivity analysis and capture distributional impacts of macro or policy changes.
  - Typical methodological structure: a three-step procedure (select indicators, define distress criteria, simulate scenarios).
- Limitations of aggregate indicators:
  - Aggregate measures (e.g., average household DTI and DSTI ratios) are useful for time- and cross-country detection of vulnerability build-up, but can mask heterogeneity across households.
- Competing paradigms for indebted households:
  - Solvency-based indicators: debt-to-asset ratio, debt-to-income ratio (references: Albacete and Linder, 2013; Bańbuła et al., 2016).
  - Liquidity-based indicators: DSTI ratios, financial margins (income minus minimum expenses and debt payments).
- Limitations of single-dimension indicators:
  - High indebtedness does not necessarily imply short-term default risk; some highly indebted households maintain current payments.
  - Liquidity measures may ignore asset liquidation or collateral borrowing, while debt-level metrics may miss sensitivity to prolonged shocks.
- Bridging approaches (examples mentioned in literature):
  - Incorporate assets into financial margins (Herrala and Kauko, 2007; Karasulu, 2008; Gross and Población, 2017).
  - Integrate liquid-asset usage conditions with financial margins (Ampudia et al., 2014; Meriküll and Rõõm, 2017).
  - Project long-term impacts using pseudo-panel techniques or macro-variable projections (Djoudad, 2010, 2012; Gross and Población, 2017).
- Endogeneity and measurement-error challenges:
  - Non-parametric binary classifiers that label households as distressed when a vulnerability measure breaches a fixed threshold are vulnerable to inconsistency in presence of unobserved heterogeneity and measurement errors.
  - Specific risks:
    - Ignoring asset usage induces unobserved heterogeneity and may overestimate vulnerability among wealthy households.
    - Under-reporting of income in survey data (Deaton, 1997; Meyer et al., 2009; Hurst et al., 2014) and under-reporting of asset-related income (Moore et al., 2000) can bias vulnerability upward.
- Validation and precision:
  - Most studies do not adequately assess the precision of estimates; few provide statistical quality assessment (Hallo and Papp, 2007; Herrala and Kauko, 2007; Arins et al., 2014; Michelangeli and Pietruti, 2014) or calibrate vulnerability measures to reduce fitting errors (Ampudia et al., 2016; Meriküll and Rõõm, 2017).
  - Importance: inaccurate estimates can lead to either undetected systemic risk or undue credit restrictions if used for macroprudential calibration.
- Data availability, quality, and timeliness:
  - Detailed household financial microdata are scarce, subject to non-response bias, measurement errors, and low frequency.
  - Advanced-economy developments:
    - OECD guidelines for micro statistics on household wealth (OECD, 2013).
    - Euro area Household Finance and Consumption Survey (HFCS), carried out every three years starting with 2011.
    - Extrapolation of microdata via aggregate country-level developments used by several studies (Ampudia et al., 2014; ECB, 2014; Hlaváč et al., 2014; IMF, 2012; Michelangeli and Pietrunti, 2014).
  - Emerging markets: slower progress in data collection and fewer household-level studies (examples: Fuenzalida and Ruiz-Tagle, 2011; Tiongson et al., 2010).

### Assessment of household financial vulnerability: the proposed framework (overview)
- Framework structure: three-step procedure intended as an organizing device for empirical research (illustrated in Figure 1).
- Step 1: Database Preparation (Section III.A)
  - Provide a working definition of household financial vulnerability.
  - Define variables classified into:
    - Core set (critical): Income, Living Costs, Debt Service Payments, Liquid Assets, Debt Level, Status of Financial Obligations.
    - Complementary set (enhancing precision or informing macro-financial impact): Other Assets, Demographic and Social Characteristics, Liability Characteristics, Guarantees, Insurance, Legal Features of Loans, etc.
  - Measurement guidance:
    - Identify the most precise indicator for each core variable and propose proxies when data are limited.
  - Data operations:
    - Update microdata using extrapolation techniques.
    - Aggregate and map information across microdata sources using matching keys (see Section III.A.3 and Appendix I).
- Step 2: Definition of Household Distress and Validation of Estimates (Section III.B)
  - Select vulnerability measures and define distress criteria.
  - Methods:
    - Use statistical methods to select vulnerability measure(s) by estimating their capacity to predict actual household distress.
    - Use macro-correlations and institutional information to guide measure selection.
  - Approach selection:
    - If individual information on status of financial obligations is available, consider non-parametric binary approaches; otherwise consider parametric approaches.
  - Endogeneity correction:
    - Evaluate whether endogeneity issues are negligible. If not negligible, apply estimation techniques to correct sources of endogeneity (Section III.B.2 and Appendix III).
  - Validation:
    - Derive initial-state vulnerability estimates and validate against actual vulnerability information (e.g., NPLs). If inconsistent, iterate with additional measures or estimation methods.
- Step 3: Stress Testing (Section III.C)
  - Build baseline and adverse scenarios (single- or multi-period) and create forward paths for variables in vulnerability measures.
  - Recompute household vulnerability measures under baseline projections and adverse scenarios.
  - Obtain distributions of distressed households under baseline and adverse scenarios using validated distress criteria.

### Key references to figures, tables, and appendices in the content unit (as listed)
- Tables: Table 1; Table 2 (Namibia thresholds by income deciles); Table 3 (Namibia: share of distressed households).
- Figures: Figure 1 (Outline of the Framework); Figure 2 (Relevant Information to Conduct Household Sensitivity Analysis); Figure 3 (Update of the CDF of Income Using Country-Level Growth Rates); Figures 4–9 (Namibia-specific diagnostics and scenario results).
- Appendices: Appendix I (Aggregation Methods for Household Micro-Data Sources); Appendix II (Algorithm to Determine Weights and Optimal Thresholds); Appendix III (How to Address Endogeneity Issues in the Context of Solvency); Appendix IV (Applications of the Framework).

*Source: wp17228 - References (IMF working paper content provided).*

### 1. O

### 1. O
OPERATIONALIZING THE CONCEPT OF HOUSEHOLD FINANCIAL VULNERABILITY

### Definition and conceptual framework
- Household financial vulnerability: a situation where a household is exposed to the risk of failure to meet its financial obligations timely and completely, thus incurring financial distress.
- Two dimensions:
  - Liquidity: short-term ability to cover obligations when due.
  - Solvency: long-term fulfillment of the intertemporal budget constraint; may be operationalized using truncated projection horizons rather than the infinite-horizon no-Ponzi condition.
- Distinction: vulnerability applies to both debt-free and indebted households; the chapter focuses on indebted households.

### Core variables for operational measurement
- Core variables (deemed germane to household financial vulnerability assessment):
  - Income
  - Living costs
  - Debt payments
  - Liquid assets
  - Debt levels
  - Status of financial obligations (paid in full / overdue) — used for calibration and validation of vulnerability estimates

- Household liquidity (main vulnerability index, extended financial margins):
  - Equation as presented:
    h,th,th,th,t
    A
    h,t
    DPLCLAYFM
                     Absolute Financial Margin  (i.1)
  - Interpretation: flow variables h,tLCY , and h,tDP correspond to household h’s (monthly, quarterly, or yearly) income, living costs, and debt payments, while h,tLA is the available stock of liquid assets at time t.
  - Relative version (normalized by income):
    h,t
    h,th,th,th,tR
    h,t
    Y
    DPLCLAY
    FM
    
    
                      Relative Financial Margin  (i.2)
  - Use: forward projections of (i.1) or (i.2) assess whether households will incur liquidity problems along the simulation horizon:
    
    X
    h,h,
    FMfPD
    
    
    , (with X	∈
    ሼ
    ܴ,ܣ
    ሽ
    and	ݐ൅1 ൑  ߬൑ ݐ൅ܶ)
    where ߬ is a generic point along the (monthly, quarterly, or yearly) projection period [ሿܶ൅ݐ൅1,ݐ, and h,PD is the probability of incurring distress associated with liquidity problems at that time.

- Household solvency (practical operationalization):
  - Use a truncated intertemporal budget constraint over a shorter projection horizon (empirically used horizons inferior to 5 years in the literature).
  - Solvency probability associated with initial net debt and the (discounted) stream of income-expenditure balances over the projection period:
    
    X
    Th,t
    X
    h,t
    X
    h,t
    X
    Th,t
    X
    h,t
    X
    h,t
    X
    h,t
    X
    h,th,T
    LCLCLCYYYADfPD
    
    ,... , , ,,... , , , ,
    2121
    , (with X	∈
    ሼ
    ܴ,ܣ
    ሽ
    )
    where ܶ is the projection horizon (in months, quarters, or years), h,T PD is the probability household h will incur distress associated with solvency, and X h,t D and X h,t A are, respectively, household h’s initial debt and asset levels (which may be expressed in nominal terms or as ratios of household h’s income).

- Role of debt level:
  - Primarily informs solvency (vulnerability to persistent shocks such as permanent lower income or prolonged higher interest rates).
  - In some jurisdictions, debt levels also provide insight on liquidity capacity (e.g., interest-only loans requiring balloon payments).
  - Debt levels are key for assessing banking-sector impact (loss-given-default) and can be used to estimate debt payments if unavailable.

### Complementary variables (optional, depending on data availability and modelling needs)
- Purpose: i) construct additional vulnerability indexes; ii) build projections of core variables; iii) assess macro-financial stability impact.
- Examples provided:
  i. Information on physical and less-liquid financial assets:
     - Useful to assess capacity to withstand prolonged stress and inform solvency over long horizons.
     - Not included in core because prices/liquidity can decline in crises; even low debt-to-asset ratios may not prevent vulnerability if assets are illiquid or fire-sold at discounts.
  ii. Demographic and social characteristics:
     - Help determine future earning potential and financial fragility for specific groups, contributing to projections of core variables (especially income).
  iii. Information to assess macro-financial impact:
     - Value of collateral, presence of government or other guarantees, mortgage typology (fixed rates, ARM, interest-only, denominated in foreign currency, etc.), use of mortgage (primary or secondary residence), legal features of loans (full recourse or not), holding of an insurance policy, etc.

### Empirical practice and projection horizons
- Empirical works referenced use projection periods inferior to 5 years:
  - Djoudad (2010, 2012): simulated DSTI variable paths over a 3-year period using pseudo-panel techniques.
  - Gross and Población (2017): used a GVAR and a logistic model to derive forward paths of household balance sheets up to 16 quarters ahead.

*Source: IMF working paper, "1. O — OPERATIONALIZING THE CONCEPT OF HOUSEHOLD FINANCIAL VULNERABILITY" (wp17228).*

### 2. D

### 2. D

### Overview
- Purpose: Guidance on deriving estimates of core household vulnerability variables when ideal microdata are incomplete or unavailable.
- Key principle: The methodology can be applied if a measure of income is available in a microdata source (household survey, credit registry, etc.), even if imperfect; remaining information can be derived from macro-data sources.
- Estimation biases from imperfect data can be reduced/corrected in Step 2 through approaches addressing endogeneity (Section III.B.2).

### Income variable
- Ideal measure:
  - h,t Y should measure disposable income (maximum amount a household h can spend without reducing or pledging wealth).
  - Disposable income = gross income adjusted for net current transfers (taxes on income and wealth, social security contributions, receipts of social benefits from government).
- Practical proxy when net current transfers are missing or incomplete:
  - Use gross income (income that accrues to households because of involvement in production or ownership of assets).
- Requirement:
  - Availability of a microdata source including (disposable or gross) income is the basic requirement to proceed.

### Debt payments
- Definition:
  - h,t DP refer to the sum of household h’s (monthly, quarterly, or annual) payments for different forms of debt.
- Component decomposition (symbolic):
  - h,t DP = h,t MP + h,t PP + h,t CCP
  - where h,t MP = mortgage payments; h,t PP = personal loan payments; h,t CCP = credit card payments of household h at time t.
- Nature of mortgage and personal loan payments:
  - h,t MP and h,t PP refer to households’ scheduled payments.
- Measurement choices:
  - First choice: (monthly, quarterly or annual) actual debt payment.
  - Second choice: estimates based on available micro- and/or macro-data sources.
- Sources when microdata on scheduled/actual payments are unavailable:
  - Central bank information on average household DTI ratios, residual maturity and lending rates, complemented with information on indebtedness of different income groups (authorities’ data or Findex database).
- Notes on actual vs. scheduled payments:
  - Actual payments may overestimate or underestimate future debt service burden if households repaid more principal than required, or if mortgages have atypical structures (e.g., interest-only).
- Estimating scheduled payments via a credit-Foncier rule:
  - The credit-Foncier rule assumes constant payments over loan life. Under this rule the scheduled mortgage (or personal loan) payment h,t MP (or h,t PP) is a function of the initial amount borrowed 0h,t M, the per-period interest rate 0h,t i and the total number of repayments T to be made over the life of a loan (see equation (ii.) in source).
  - If the amount at origination is not available, outstanding mortgage h,t MP and interest rate h,t i at time t can be used while T is replaced by the actual number of remaining payments.
  - Using scheduled number of payments rather than actual when borrowers have accelerated payoffs leads to underestimation of mortgage payments and the debt service burden for households that repaid more principal than scheduled.
- Credit card payments:
  - h,t CCP at time t can be estimated as the reported outstanding balance.
- When individual debt levels are unavailable:
  - Use national average household DTI ratio, complemented with information on indebtedness of different income groups, and plug into the repayment formula to compute payments.

### Living costs, liquid assets, debt levels, and status of debt obligations (Table 1 summary)
- Living Costs (h,t LC)
  - Purpose: To assess liquidity and solvency (monthly, quarterly, or annual).
  - Best indicator: expenses for necessary items (basic consumption for essential items).
  - Possible proxies:
    - National poverty line;
    - Household survey (if available);
    - Alternatively, authorities’ estimates and/or national accounts.
- Liquid Assets (h,t LA)
  - Purpose: To assess liquidity and solvency.
  - Best indicator: Assets readily converted into cash with minimal loss in value (information on deposits held by households).
  - Possible sources/proxies:
    - Household income and wealth survey;
    - Monetary survey complemented with information on distribution of deposits across income groups (authorities’ data or Findex).
  - Note: Holdings of financial assets different from deposits are frequently negligible in developing economies and can be ignored there.
- Debt Levels
  - Purpose: To assess solvency and macro-financial impact; to compute debt payments if not available in microdata.
  - Best indicator: Individual outstanding debt levels by debt category (home mortgages, personal loans, credit cards).
  - Possible proxies:
    - Individual debt levels at origination;
    - Average household DTI ratios (possibly by debt category).
  - Data sources:
    - Household survey or another microdata source; central bank information on average household DTI ratios, complemented with indebtedness by income groups (authorities’ data or Findex).
- Status of Debt Obligations
  - Purpose: To calibrate and validate vulnerability estimates.
  - Best indicator: Individual information on status of debt payments (numeric days of arrears or categorical performing/forborne/in arrears/in default).
  - Possible proxy: Nation-wide exposures in arrears, forbearance, or non-performing loans (NPLs).
  - Sources:
    - Microdata (household indebtedness survey, banks’ loan books) if available;
    - Alternatively, central bank information on aggregate NPLs or arrears.
  - Additional guidance:
    - For debt-free households, replace status of debt obligations with status of other financial obligations (overdue or not on non-debt payments) or other indicators of economic/financial difficulty.
    - If individual data are not available, the share of households below the national poverty line can help calibrate distress thresholds, though it may underestimate fragile households.
    - If multiple indicators of distress are available, they can be consolidated via dimensionality reduction (e.g., Nonlinear Principal Components Analysis) to obtain a synthetic index.

- Numerical example on using DTI shares by income deciles:
  - If shares of households with a mortgage in lowest four income deciles and upper six income deciles are 20 percent and 40 percent, respectively, and national average DTI = 50 percent, then:
    - indebted households in lowest 4 deciles have a DTI of 250 percent (=0.5/0.2*100);
    - indebted households in highest 6 deciles have a DTI of 125 percent (=0.5/0.4*100).
  - Procedure to derive outstanding debt levels for groups:
    - Randomly select indebted households corresponding to the group shares;
    - Multiply household income level by the group DTI ratio;
    - Estimate periodic payments using formula (iii.) assuming constant amortization and average remaining maturity at national level.

### Extrapolating and merging microdata sources (Section 3)
- Consolidation steps when information is fragmented across microdata with different reference periods:
  1. Extrapolate data in microdata sources to a common reference period.
  2. Merge different microdata sources into a unified, time-consistent database.
- Extrapolation methods:
  - Uprating: update monetary variables in line with aggregate counterparts; non-monetary characteristics unchanged.
    - Commonly used in applications (Ampudia et al., 2014; ECB, 2014; Hlaváč et al., 2014; IMF, 2012; Michelangeli and Pietrunti, 2014).
    - Maintains household-specific variation but applies identical temporal adjustment factor to all households, which can distort distributions by widening decile gaps.
    - Example note from Figure 3: portrays a proportional increase of 15 percent across the income distribution.
  - Static aging: uprating of monetary variables plus adjusting household weights to reflect changes in group sizes.
  - Dynamic aging: models fertility, household formation/dissolution, labor market transitions (uses transition probabilities).
  - Recommendation: limit updates at this stage to what is needed for a time-consistent database; avoid updating variables to the analysis period if different from microdata reference period (perform full update in Step 3 after validation).
  - Exception: if uprating is used and status of financial obligations is available in one source, monetary variables in other sources should be extrapolated to the observation period of the database with status of financial obligations to allow initial vulnerability estimates without updating status of obligations.
- Considerations to reduce bias:
  - Prefer projecting variables to the reference period of the most recent database unless status of financial obligations dictates otherwise.
  - Dynamic aging is preferable when modeling status of household financial obligations endogenously via transition probabilities.
- Merging microdata sources:
  - If household identifiers are absent, use statistical matching:
    - Parametric matching: regressions using common household characteristics (region, age group, employment status, education level) to transfer information.
    - Non-parametric matching: use any variable available in both databases or monotonic relations as matching keys; map by empirical distributions along matching keys.
  - Appendix I contains further details on parametric and non-parametric merging methods.

*Source: wp17228 - 2. D (IMF PDF chapter content).*

### 1. CHOICE OF THE VULNERABILITY MEASURES AND DEFINITION OF DISTRESS

### 1. CHOICE OF THE VULNERABILITY MEASURES AND DEFINITION OF DISTRESS

### Selection of vulnerability measures
- Core variables (e.g., extended financial margins in (i.1) and (i.2)) can be complemented with additional measures (net wealth, leverage) to enhance discrimination of distressed households.
- Selection can be guided by macro correlations and/or the institutional setting (example: jurisdictions with personal bankruptcy may require net wealth or leverage measures to capture strategic/default behavior of “underwater borrowers”).
- Complementary variables can be used to build additional vulnerability indexes (Section III.A.1. reference).

### Non-parametric binary approaches
- Most studies adopt a non-parametric binary approach: household is at risk of financial distress when its vulnerability measures cross specified thresholds.
- Two ways to combine multiple vulnerability measures:
  - Indicators considered separately, each with its own reference threshold. Household considered distressed when some or all indicators fall below their reference threshold. Representations noted as (iv.1) and (iv.2). th_PD,t is a binary variable taking value 1 when indicators fall below identified thresholds at time t and zero otherwise; tn,I and nτ are the vulnerability indicator n at time t and its reference threshold; N is total number of vulnerability indices. Formulation in (iv.1) is more conservative than (iv.2).
  - Indicators combined in a synthetic index: composite index f(·) compared to threshold τ as in (v.). Synthetic index can be constructed via regression fitted values or non-parametric weighting algorithms that maximize correct prediction (example: Namibia application). Synthetic index reflects relative importance of composing indicators but may be harder to interpret for policy use.

- Note: For indicators where higher values imply higher vulnerability (e.g., DSTI ratios), the inequality sign direction (< vs. >) should be reversed.

- Other non-parametric methods include classification trees and machine learning, though these have not yet been widely used for household financial vulnerability assessment (to the authors' knowledge).

### Parametric approaches
- Parametric methods model the relation between vulnerability measures (explanatory variables) and status of financial obligations (dependent variable).
- These yield continuous probabilities of distress in [0,1]. Methods used include binary regressions and artificial neural networks (citations: Holló and Papp, 2007; Herrala and Kauko, 2007; Arins et al., 2014).
- Trade-offs:
  - Binary methods (iv.1, iv.2): simple, parsimonious, limited data/computation, do not require individual info on status of obligations (if thresholds not calibrated), can identify non-linearities, provide easy indicative thresholds for policy. Limitation: dichotomous classification (non-distressed/distressed) that may interpret “distressed” as “defaulted” and ignore severity gradations.
  - Binary method with synthetic index (v.): more compute and data intensive due to building index and calibrating threshold.
  - Parametric methods: more data and compute intensive but allow granular modeling, multi-category distress modeling (arrears, non-performing, forbearance), and continuous household-level distress probabilities. Limitation: sensitivity of test statistics to distributional assumptions, especially in small samples.
- Non-parametric and parametric methods are not mutually exclusive: parametric methods can derive synthetic indicators used within non-parametric binary frameworks (semi-parametric approaches).

### Interpretation and extensions
- Binary approaches can be extended to multi-category classification by calibrating different thresholds for categories (arrears, non-performing, forborne).
- Parametric methods can model relations with arrears or forbearances rather than defaults depending on available information and purpose.
- The assessment framework can address liquidity-related distress and can be adapted for solvency-related distress (e.g., present value of income-expenditure balances vs. thresholds).

### Noted equation/notation references retained from source
- References to specifications: (i.1), (i.2), (iv.1), (iv.2), (v.), and the composite index f(·) with threshold τ.
- Mention that th_PD,t is a binary variable interpretable as household’s probability of distress at time t.

---

### 2. ADDRESSING ENDOGENEITY ISSUES IN VULNERABILITY ESTIMATES

### Sources and implications of endogeneity
- Endogeneity in household microdata arises from selection bias, measurement errors, and omitted variables and may lead to inconsistent vulnerability estimates.
- Particularly relevant for binary approaches where precision relies on selection of reference thresholds.
- Common practice has been to use ad hoc thresholds based on economic considerations or historical arrears/default evidence (examples: financial margins threshold universally set at zero; DSTI ratios set within a range of 20 and 40). These can be biased when indicators are proxies or measured with error.

### Example of bias from proxying income
- Using gross income instead of disposable income (missing net current transfers and taxes) can understate income of poorer households and overstate income of wealthier households, producing estimated financial margins:
  - p_th_FM, < p_th_FM, (estimated vs. actual for a generic poor household h)
  - w_tk_FM, > w_tk_FM, (estimated vs. actual for a generic wealthy household k)
- Setting a universal distress threshold at zero in such cases can overestimate distress among the poor and underestimate distress among the wealthy.

### Calibration strategy to correct endogeneity
- When unobserved heterogeneity and/or measurement errors are non-negligible, calibrate distress thresholds separately for household groups where bias sources and magnitudes are expected to be uniform.
- Calibration steps:
  i) Partition observations into subsets where estimation bias sources are expected to be uniform.
     - Use observable variables correlated with endogeneity sources to perform partitioning (example: partition by gross income when transfers are unobserved).
     - More granular partitions reduce within-subset endogeneity but reduce sample sizes per subset (trade-off).
  ii) Estimate specific distress thresholds for each subset.

### Methods to estimate thresholds per subset (depend on data availability)
- If individual information on status of financial obligations is available:
  - Simple approach: set distress threshold equal to average (or median) value of the index among defaulted households in the subset.
  - Preferable approach: signaling detection approach (non-parametric) to find thresholds that best balance detection and false alarms. Caveat: computationally demanding for multivariate analyses with many indicators.
  - For high-dimensional indicator sets, combine indicators into a synthetic index and derive thresholds for that index.
  - Alternative: fix thresholds for indexes expected to be free of unobserved heterogeneity/measurement error and calibrate only biased measures.

- If individual information on status of obligations is not available and analysis uses one vulnerability index:
  - Calibrate using average data on level of non-performing loans (NPL) or loan arrears.
  - Set distress threshold for each subset equal to the index value that reproduces the average NPL (or arrears) in that subset.
  - This assumes the subset-level NPL equals national average if no better information exists.
  - For debt-free households, thresholds can be calibrated using the share of population below the poverty line.
- If multiple vulnerability indexes and no status information:
  - Option: fix thresholds for indexes believed free from bias and calibrate only the threshold for the indicator expected to be biased using average NPL or arrears.

### Practical notes on calibration and multivariate testing
- Signaling detection approach applied univariately is computationally tractable; multivariate extension would require high-dimensional grid search and testing many indicator combinations (limited literature: Borio and Lowe, 2002; Alessi and Detken, 2011; Ferrari et al., 2015).
- Calibration can also produce multi-category classifications by deriving multiple thresholds corresponding to different distress categories (arrears, defaults, etc.).
- Parametric methods can, in theory, be corrected similarly by partitioning and estimating model parameters per subset, but in practice this may lead to small-sample inference problems and unreliable parametric inference.
- Alternative methods for addressing endogeneity in parametric/binary regressions include linear probability model estimators, maximum likelihood estimation, control function based estimation, and special regressor methods.

### Extension to solvency-related distress
- The discussion focused on liquidity-related distress but methods can be extended to solvency-related distress (see Appendix III reference).

*Source: IMF Working Paper — wp17228, Section 1. CHOICE OF THE VULNERABILITY MEASURES AND DEFINITION OF DISTRESS*

### 3. VALIDATION OF VULNERABILITY ESTIMATES

### 3. VALIDATION OF VULNERABILITY ESTIMATES

### Validation approaches and diagnostics
- Purpose: assess how accurately the model can replicate household distress.
- In-sample validation:
  - Simple fitting deviation (estimation error): compute, for each household subset, the deviation between the simulated share of distressed households and the actual share of households in distress.
  - ROC curve: calculate area under the Receiver Operating Characteristic (ROC) curve for each subset to assess discrimination capacity for the event of interest (distressed households).
  - If individual information on the status of financial obligations is not available: compare average simulated non-performing loans with actual national-average non-performing loans.
- Out-of-sample validation:
  - Cross-validation: split data into complementary subsets (training set and validation/testing set); perform analysis on training set and validate on testing set; perform multiple rounds with different partitions and average validation results.
- Model diagnostics and corrective actions:
  - Significant differences between simulated and actual shares of distressed households signal omitted relevant variables and/or measurement errors.
  - Remedies include re-estimation using additional or alternative vulnerability indices and/or techniques to correct for sources of endogeneity.

### STEP 3: STRESS TESTING (framework and scenario design)
- Pre-simulation:
  - Extrapolate unified database variables to the simulation period using methods in Section III.A.3 when reference period of microdata differs from analysis period.
  - Framework supports one-period (liquidity-focused, less computation) and multi-period (solvency-focused, more computation) analyses.
- Baseline projections:
  - Derive forward paths of vulnerability measures from simulations obtained from macroeconomic data or theoretical models (e.g., DSGE).
  - In multiperiod analyses, include possible feedback loops between household sector and rest of economy.
- Adverse scenarios:
  - Shocks typically applied to income, interest rates, exchange rates, and asset prices.
  - Shocks may be uniform across households or selective for subsets.
  - Changes in unemployment rates affecting household income often addressed using Monte Carlo simulations.
- Uncertainty treatment:
  - Reflect baseline projection uncertainty by including, for each household group and each point in time, lower and upper values of a confidence interval centered on baseline distress projections.
  - Procedure: compute the joint distribution of vulnerability indicators and derive the share of distressed households associated with lower and upper confidence interval values.
  - Note: The distribution of vulnerability measures could be obtained through stochastic simulations of forward paths of macroeconomic data from VAR residuals.

### Namibia application: context and key metrics
- Purpose: assess household vulnerability in Namibia in context of 2016 Article IV consultation; focus restricted to indebted households.
- Household indebtedness context:
  - Household debt estimated by Bank of Namibia (BON) at about 90 percent of disposable income at end-2015.
  - Debt service burden estimated at 16.1 percent of disposable income.
  - Interest payments correspond to roughly 10 percent of disposable income.
  - Residential mortgage exposure: 38 percent of total loans and advances at end-2016.
  - Impairment figures in household loan books: about 1.5 percent of total loans and advances (broadly stable).
- Structural risk factors:
  - Limited diversification of Namibian economy increases correlation of defaults across households.
  - Aggregate assessments mask concentration of borrowers; microdata needed to capture heterogeneity.
- Preliminary survey findings (2009/10 NHIES):
  - NHIES includes 9,600 individual households as of 2009-2010.
  - Median DTI ratio in overall population is inferior to 0.01.
  - Average DTI ratio equals 0.44.
  - Debt largely concentrated among households with mortgages.
  - Territorial distribution: average DTI ratios of households with mortgage are equal or superior to one in all regions except Karas and Imusati.
  - Khomas province (including Windhoek) has the highest share of people with mortgage loans.
  - Caution: NHIES is not specifically designed to collect liabilities; survey limitations noted.

### Namibia application: database preparation and mapping methodology
- Data sources:
  - NHIES (2009-2010): gross income, expenditure items, outstanding debt levels, region, employment status.
  - Mortgage database (end-2014): 22,000 individual mortgage loans, including loan origination value, outstanding balance, monthly amortization payment, monthly interest payment, days overdue, property value, additional guaranties, region of property.
  - Note: 22,000 loans represent broadly one fourth of all outstanding mortgage loans.
- Temporal harmonization:
  - Update NHIES information to end-2014 by uniformly increasing individual household income based on national yearly growth rate reported in the Financial Stability Report of the Bank of Namibia; increase expenditures at average annual CPI rate reported by NSA.
  - Update is performed by extrapolating NHIES variables to the observation period of the mortgage database (not vice versa).
- Assumptions and caveats:
  - Merging implicitly assumes each loan corresponds to a different household; this can understate debt service for households with multiple mortgages. Calibration of distress thresholds aims to reduce ensuing estimation bias.
- Mapping approach:
  - Non-parametric mapping based on two matching keys: region (present in both sources) and positive relation between household income (NHIES) and amortization payment (mortgage database).
  - Partition both databases into 130 cells based on region and income/amortization deciles.
  - Distribution:
    - NHIES observations assigned within a grid box according to region of residence and gross income decile.
    - Mortgage data observations assigned within a grid box according to region of property and amortization payment decile.
  - Mapping rules applied differently for performing and non-performing loans:
    - i. Each performing loan belonging to cell (i, j) in the loan book grid box is paired with the average values of gross income and living costs of cell (i, j) in the NHIES grid box.
    - ii. Non-performing loans in cell (i, j) in the loan book grid box are paired with weighted averages of the minimum and average values of gross income and expenditures in cell (i, j) in the NHIES grid box; weights derived through a numerical procedure aimed at maximizing predictive performance for cell (i, j).
  - Rationale: non-performing loans likely correspond to households with lower income; weighted averages of the median and the minimum income enhance variability of financial margins and predictive performance.
- Definitions and variables:
  - Flow variables (income, expenditures, amortizations, debt payments) are annualized.
  - Living costs defined as sum of “basic” expenditure items (food, transport, health, education); exclude “non-necessary” items (travel, luxury goods, sport, entertainment, etc.).
  - A loan is considered non-performing if the monthly payment has an overdue superior to 30 days (i.e., household is at least one installment behind).
  - Internal bank guidelines commonly impose a 30-35 percent limit on the debt service to gross income ratio; guidelines allow flexibility for high net worth individuals.
- Cell-level calibration:
  - For non-performing loans, weighted averages use numerical optimization to maximize predictive performance of household vulnerability at the cell level.
  - Mapping enhances variability of financial margins in each cell to improve predictive performance.

*Source: wp17228 - 3. VALIDATION OF VULNERABILITY ESTIMATES*

### Section III.A.1., except for liquid assets, that, however, are not expected to be sizable in

### Section III.A.1., except for liquid assets, that, however, are not expected to be sizable in

### Methodology: construction of household-level indicators
- Individual relative financial margin (FM) at end-2014 is computed for each household h in cell (i,j) with separate formulas depending on loan performance status (performing / non-performing). Variables used:
  - )(,,2014jiYMean, )(,,2014jiYMin, )(,,2014jiLCMean, )(,,2014jiLCMin: households’ average and minimum gross income and living costs in cell (i, j) at end-2014 (mapped from the updated household survey).
  - 2014,hDP: debt payment of household h at end-2014 (from the mortgage book).
  - ji,α and ji,β: cell-specific weights to be derived through calibration.
- Debt servicing costs vary by household h; gross income and living costs are constant for all households within a given cell (i, j) and loan performance status.
- Two additional household-level measures:
  - 2014,hLTV: outstanding loan-to-value ratio (measure of household leverage).
  - 2014,hOTO: outstanding loan-to-loan-at-origination ratio.
- Note: household assets data are not available except for property value; property value used as proxy for gross wealth with limitations.

### Step 2 — Definition of household distress and validation of vulnerability estimates
- Objective: assess whether (2014,hFM, 2014,hLTV, 2014,hOTO) are good indicators of household distress (arrears).
- Binary logistic regression estimated to model relationship between arrears and vulnerability indices. Regression results (Table 2):
  - FM: Coefficient = -0.041; SE = 0.019; p-value = 0.0296
  - LTV: Coefficient = -0.681; SE = 0.167; p-value = 0.000
  - OTO: Coefficient = 0.0000; SE = 0.003; p-value = 0.958
  - Constant: Coefficient = -3.726; SE = 0.087; p-value = 0.000
- Interpretation of regression:
  - Relative financial margins (FM) have a negative and significant impact on probability of arrears.
  - LTV shows a significant negative coefficient; sign likely reflects reverse causality because banks set LTV based on repayment capacity.
  - OTO is not significant.
- Outcome: use only financial margins to derive household vulnerability estimates through a non-parametric binary (signal detection) approach. Calibration assumes ji,α and ji,β equal to zero in this preliminary analysis.

### Signal detection approach and distress threshold calibration
- Households defined as vulnerable when FM crosses a specified threshold. Thresholds are calibrated for each cell (i,j) using individual arrears information to balance type I and type II errors.
- Optimization objective: minimize noise-to-signal ratio (ratio of type II errors to 1 minus type I errors) and select ji,α and ji,β to maximize area under the Receiver Operating Characteristic (ROC) curve (AUC).
  - AUC interpretation: AUC = 0.5 indicates non-informative indicator; larger AUC (closer to 1) indicates more informative indicator.
- Data limitation: database includes loans with overdue payments in excess of 30 days only in 74 cells; in remaining 56 cells the procedure selects the lowest FM in the cell as critical threshold.
- Calibrated average distress thresholds by income decile (Table 3, first row in bold; values are in financial margin units):
  - Decile 1: -4.02
  - Decile 2: -1.18
  - Decile 3: -0.40
  - Decile 4: -0.01
  - Decile 5: 0.14
  - Decile 6: 0.39
  - Decile 7: 0.54
  - Decile 8: 0.59
  - Decile 9: 0.63
  - Decile 10: 0.66
- Alternative calibration (Calibration Using Average Share of Distressed Households, Table 3 second row in italic):
  - Decile 1: -5.11
  - Decile 2: -1.34
  - Decile 3: -0.51
  - Decile 4: -0.13
  - Decile 5: 0.07
  - Decile 6: 0.37
  - Decile 7: 0.50
  - Decile 8: 0.57
  - Decile 9: 0.60
  - Decile 10: 0.63

### Model comparison and in-sample predictive performance
- Three models compared:
  1. Signal detection calibrated thresholds (cell-specific).
  2. Calibration using average share of distressed households by decile.
  3. Fixed threshold equal to zero for all households.
- Findings:
  - Signal detection approach outperforms alternatives; goodness of fit very high in all deciles except decile 2.
    - Excluding decile 2, mean absolute percentage error = 3 percent.
    - In decile 2 financial margins are noisy; the algorithm selects relatively high thresholds to limit false alarms.
  - Calibration using average share of distressed households: average mean absolute percentage error = 20 percent; performs well when distress is uniformly distributed.
  - Fixed threshold = 0: extremely poor performance, especially in lowest deciles, because it does not correct for endogeneity and measurement issues.

### Step 3 — Stress testing: setup and scenarios
- Unified database updated to end-2016 for macro variables.
- One-period ahead analysis; baseline projections:
  - Individual household income projected to grow in line with non-mining GDP per capita (non-mining GDP projections from April 2017 IMF WEO database; population growth from linear projection of WB development indicators).
  - Individual household debt assumed to grow in line with non-mining GDP per capita (average household DTI ratio assumed constant).
  - Individual household expenditures projected to grow in line with inflation projections from April 2017 IMF WEO database.
  - Lending rate increases proxied by Jibar forward rates (due to peg with South African rand).
- Adverse scenarios:
  - Interest rate shocks of 200bp and 300bp.
  - Different assumptions on nominal gross income growth; shocks uniform across income deciles.
  - Household indebtedness grows in line with income; inflation projections as in baseline.
- Financial margins recomputed under baseline and adverse scenarios to count households below distress thresholds.

### Stress-test results and key statistics
- Under 300bp adverse shocks, share of distressed households ranges between 19.5 and 23 percent depending on income growth assumptions (Table 4).
- Table 4: Namibia: Share of Distressed Households (Baseline and Alternative Scenarios)
  - Nominal Gross Income Growth Rate (Percent) columns: Baseline | Adverse Scenarios: 5.2* | 5.0 | 4.5 | 4.0 | 3.5
  - Interest Rate Increase (bps): None | 2.8 (Baseline entry)
  - 200bps scenario: 13.0 | 14.1 | 15.2 | 16.3
  - 300bps scenario: 19.5 | 20.6 | 21.8 | 23.0
  - Note: *Nominal Gross Income Growth Rate is proxied by the growth rate in non-mining GDP per capita.
- Distributional results:
  - Most vulnerable households located in middle- and middle/upper-income deciles.
  - Lowest deciles less impacted because they rely on social transfers and subsidies not included in income definition.
  - Highest decile less vulnerable due to larger buffers despite higher indebtedness.
  - Decile 2 results may understate vulnerability because thresholds set relatively high to limit false alarms.
- Banking-sector implication:
  - Based on mortgage loan distribution across income deciles, banks’ mortgage arrears projected to increase up to 19.6 percent of total mortgage loans in the most adverse scenario.
- Key caveat:
  - Accuracy depends on assumption that relation between FM and household distress remains structurally unchanged between 2014 and 2017 (e.g., no changes in social benefits or tax rates). Distress thresholds validated with 2014 data assumed valid for 2017.

*Source: 2009/10 NHIES, commercial banks’ data, BON, and authors’ computations.*

### CONCLUSIONS

### CONCLUSIONS

### Framework and methodological contributions
- Reviewed and integrated best practices emergent in the literature on household vulnerability analysis into a coherent framework.
- Proposed analytical and estimation extensions aimed at:
  - improving the quality of estimates, and
  - allowing implementation in presence of data limitations.
- Result: a comprehensive framework with wide applicability to both advanced and developing economies.
- Methodology advantages:
  - Captures potential non-linear responses to shocks by taking into account the distributional aspects of the ability‐to‐pay of households.
  - Addresses a key weakness of traditional macro stress testing frameworks, which are unable to capture the non-linear effects associated with default correlations (Ampudia et al., 2014), particularly when the country under analysis has never experienced a crisis.

### Uses for stress testing and financial stability analysis
- The methodology may provide inputs for banks’ stress testing as an alternative to macroeconomic credit risk models for the computation of household average probability of default (see Holló and Papp, 2007; Ampudia et al., 2014; Bilston et al., 2015).
- By accounting for distributional heterogeneity, the approach can reveal non-linearities and default correlations that aggregate macro frameworks miss.

### Uses for macroprudential policy calibration
- Household vulnerability estimates can be used to calibrate macroprudential instruments such as LTV and DSTI limits.
- Observed practice: calibration in most jurisdictions has been based on average historical observation of these ratios and qualitative assessment.
- Risks of average-based calibration:
  - Imposing unneeded credit restrictions on some household segments (type II error).
  - Leaving systemic risk buildup undetected (type I error).
- Micro-based calibration benefits:
  - Allows a more precise assessment.
  - Permits consideration of both the benefits and costs associated with specific limits (Bańbuła et al., 2016).

### Uses for macroeconomic policy and welfare analysis
- Framework can inform macroeconomic policy decisions by assessing the potential impact of changes in policy variables on household financial positions and, consequently, on the economy.
- Empirical evidence cited:
  - Distribution of income, assets and debt across households plays a critical role in determining the economy’s overall response to policy changes and shocks (Bertrand and Morse, 2013; Bricker et al., 2014; Mian and Sufi, 2014a and 2014b; Devlin-Foltz and Sabelhaus, 2015).
- The methodology can assess impacts of policy decisions and shocks on household welfare, including effects on poverty and income distribution (Tiongson et al., 2010) — particularly relevant for developing countries.

### Practical implications and applicability
- The framework offers a helpful tool to support policy analysis and formulation across contexts:
  - Advanced economies: for banking stress tests and macroprudential tool calibration where detailed microdata may exist.
  - Developing economies: for welfare and poverty impacts where household-level distributional effects matter and data limitations may require the proposed estimation extensions.

*Source: wp17228 - CONCLUSIONS*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17228.pdf_