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### Institutional setup and ASN toolkit
- Macroprudential policy in Lithuania is conducted solely by the central bank (Bank of Lithuania).
- Bank of Lithuania’s macroprudential toolkit includes borrower-based measures (BBMs) enacted in 2011 through the Responsible Lending Regulations (Atsakingojo skolinimo nuostatai, or ASN).
- ASN scope and coverage:
  - Applies to all credit extended to natural persons and secured by real estate; summary focuses on residential housing loans.
  - Applies to profit-seeking credit providers including domestic banks and foreign branches, credit unions, peer-to-peer lending platform operators, and other non-bank financial intermediaries operating in Lithuanian jurisdiction.
  - Wide scope intended to minimize circumvention (leakage effects).
- ASN headline limits and timing:
  - LTV: 85 percent (implies a 15 percent minimum down payment requirement). — Applicable since 2011
  - LTV2: 70 percent (LTV limit for second and subsequent mortgage loans). — Applicable since 2022 (effective as of February 1, 2022). Note: applied only for borrowers whose first mortgage’s current LTV is above 50 percent at the inception of the secondary mortgage.
  - DSTI: 40 percent (limit on average monthly loan payments as a share of borrower’s monthly disposable income). — Applicable since 2011
  - DSTI*: 50 percent (stressed DSTI limit, computed with stressed interest rate to 5 percent). — Applicable since 2015
  - Maturity Limit: 30 years. — Applicable since 2015
- Operational details and exemptions:
  - Borrower must use own funds for down payment (borrowed funds disallowed).
  - Exemption: credit institutions may apply a DSTI limit of 60 percent for creditworthy customers, but such loans cannot exceed 5 percent of the institution’s annual mortgage flow.
  - DSTI* cannot be exceeded after applying a 5 percent interest rate sensitivity test.

### Intended functions and trade-offs of ASN measures
- Intended functions:
  - LTV cap: solvency requirement linked to borrower equity.
  - DSTI cap: liquidity measure limiting monthly debt service relative to disposable income.
  - DSTI* (stressed to 5 percent): mitigates interest rate risk given most mortgages have variable rates.
  - 30-year maturity limit: limits indebtedness relative to income (DTI) and enhances consumer protection by requiring amortization.
- Trade-offs and observed side effects:
  - LTV regulation can restrict housing access for financially constrained households, potentially increasing rental demand and wealth inequality.
  - Investors with greater funding may crowd out constrained buyers, potentially raising house prices and rental rates.
  - Observed market outcome: over the past decade since inception of ASN, rental prices have accelerated and grown, on average, 1 p.p. higher than house prices on an annual basis.

### Mortgage market dynamics and misalignment indicators
- Aggregate and misalignment indicators:
  - Peak year-on-year growth: house prices up to 26.8 percent; mortgage portfolio up to 12.3 percent.
  - By end-2022, home prices were up to 20 percent above fundamentals; mortgage credit overflow around 15 percent (two-market disequilibrium model).
  - Broad-based credit-to-GDP gap remains negative, but mortgage-stock-based gap is near zero (closed).
  - Recent interest-rate increases have begun to slow credit and house price growth; authorities should monitor systemic vulnerabilities.
- Loan-level trends (2020–mid-2022):
  - Median mortgage rate for new lending: dropped from 2.3 percent to 1.9 percent.
  - Average loan size rose from 60 thousand EUR to 90 thousand EUR.
  - Median LTV and DTI increased slightly; DSTI remained stable.
  - Variable-rate loans comprise more than 90 percent of the market; elevated policy rates have increased debt service burdens.
- Secondary mortgages:
  - Share in new lending flow rose from 9.9 percent to 12.9 percent during 2019–21; largest regional gains in Klaipėda, Palanga and Neringa.
  - Secondary mortgages often finance non-primary residences (leisure or rental).
  - DSTI distribution of secondary loans shifted rightward; LTV concentrated around 80 percent with more than half between 80 and 85 percent.
  - Historical default rates (2012–20): first mortgages ≈ 1 percent; secondary mortgages > 1.5 percent (≈ 50 percent higher).
  - Channels increasing secondary-mortgage risk: ability-to-pay (multiple debts), equity channel (higher LTVs), and correlated LGD in recourse systems.
- Policy response:
  - Bank of Lithuania imposed a 70 percent LTV2 limit for secondary mortgages effective February 1, 2022.
- Comparative BBM snapshot (selected jurisdictions, as of June 1, 2022):
  - Lithuania: LTV 85; DTI 40 (up to 60); Maturity 30; Effective DTI 7.8
  - Latvia: LTV 95; DTI 40; Maturity 30; LTI 66
  - Estonia: LTV 90; DTI 50; Maturity 30; Effective DTI 6.9
  - Poland: LTV 90; DTI 25 (up to 35); Maturity 7.9

### One-year PD model and lifetime risk framework
- One-year-ahead PD estimation:
  - Logistic regression: logit(PD_{k,t}) = β_0 + β_1^> x_{k,t} + β_2^> z_{k,t} + φ(oBBM_k).
  - Cubic splines φ(·) used for income-based debt ratios oD(S)TI_{(∗)} and oDTI; continuous variables winsorized (example caps: DSTI and LTV at 300 percent; DTI at 67).
  - Sample size: fitted on 4.8M observations.
  - Discriminatory power: AUROC of baseline model around 90 percent (five-fold cross-validation).
- Key one-year PD findings:
  - Residual maturity positively related to PD (defaults more likely at earlier stages).
  - Higher interest rates increase default risk.
  - Having more than one housing loan significantly increases default likelihood.
  - Historical defaults increase PD by 2.1 p.p.; being delinquent >60 days increases PD by ≈ 2.4 p.p.
  - PD is countercyclical; unemployment rate statistically significant.
  - BBM at origination: oLTV and oD(S)TI_{(∗)} significant; oDSTI measures have larger PD impact than oLTV; nonlinear effects evident.
- Lifetime PD, LGD, and ECL formulas (preserved exactly as presented):
  - Conditional one-year PD: PD_{k,t} = P(T_k ≤ t+1 | T_k > t).
  - Unconditional probability: P(T_k ≤ t+1, T_k > t) = PD_{k,t} ∏_{m=0}^{t−1} (1 − PD_{k,m}). (expression (2))
  - Lifetime PD over n years: PD_{LT_{k,n}} := 1 − ∏_{m=0}^{n−1} (1 − PD_{k,m}). (expression (3))
  - Alternative: PD_{LT_{k,n}} = ∑_{m=0}^{n−1} PD_{k,m} ∏_{t=0}^{m−1} (1 − PD_{k,t}). (expression (4))
  - LGD_{k,t} = max{EAD_{k,t} · (1 + C) − CLLT_{k,t}, 0}. (equation (5)) with C = 5% and example 25% collateral haircut for downturn LGD.
  - ECL_{k,t} := LGD_{k,t} · PD_{k,t} ∏_{m=0}^{t−1} (1 − PD_{k,m}). (equation (6))
  - ECL_{LT_{k,n}} := ∑_{t=1}^{n} (1 + i_k)^{−t} [ LGD_{k,t} · PD_{k,t} ∏_{l=0}^{t−1} (1 − PD_{k,l}) ]. (equation (7))
- Computational assumptions:
  - Mortgages issued between 2004 and 2020 modeled.
  - Annuity payment schedules assumed for all mortgages and other household loans.
  - Household characteristics and some loan variables kept constant over loan life; no worsening credit history assumed; oBBM_k kept constant.
  - Macroeconomic variables fixed at historic long-term averages (1996-2022).
  - No interest-rate forecasting for lifetime credit risk (interest rate dynamics assumed away for lifetime assessment).

### Efficacy of BBMs: counterfactuals and predictive power
- Pre-GFC counterfactual applying current ASN (maturity≤30y, DSTI≤40%, LTV≤85%) to pre-2011 loans:
  - Model estimates for mortgages issued around 2008:
    - Lifetime PD: 12 percent.
    - At-origination lifetime ECL rate: 0.6 percent.
  - Counterfactual effects:
    - Average lifetime PD lower by 2 p.p.
    - Lifetime ECL rate lower by 0.3 p.p.
    - BBM package would have reduced mortgage ECL rate by 78 percent in relative terms.
    - Mortgage portfolio would have been at least 24 percent smaller.
    - Aggregate mortgage portfolio losses would have been around 83 percent smaller.
  - Supplementary PD model (using factual cDSTI) yields even larger reductions (lifetime PD lower by 5 p.p.; ECL rate lower by 0.4 p.p.; implied mortgage portfolio losses 87 percent smaller).
  - Finding 1: Current ASN limits preceding the GFC would have substantially reduced individual and aggregate mortgage credit risk.
- Post-GFC and ASN effects:
  - Lenders self-corrected post-2009: LTV, DSTI, maturities declined; lifetime PDs and ECL rates declined versus pre-GFC.
  - Stress-test adverse scenario parameters: GDP −3 percent; disposable income −8 percent; house prices −36 percent; inflation 22 percent; unemployment +8 p.p.
  - Stress-test result: mortgage portfolio credit risk parameters less sensitive in 2019 versus 2009.
  - Finding 2: Mortgage quality increased in 2010s and borrowers more resilient, partly due to ASN.
- Predictive performance of BBM variables for one-year PD (AUROC, full model specification):
  - oDSTI: 0.9052
  - oDSTI*: 0.9050
  - oDTI: 0.9038
  - oLTV: 0.9017
  - oMaturity: 0.9017
  - Finding 3: Income-based measures (DSTI, DTI) have substantially higher discriminatory power for one-year PD than LTV or maturity; LTV more relevant for LGD.

### Recalibration toward tighter stance: assessment and options
- Assessment of ASN standing and international comparison:
  - Lithuania’s LTV limit of 85 percent ranks as the 2nd strictest among compared states; effective DTI places Lithuania among jurisdictions with more stringent limits but its effective DTI is the least stringent compared with Latvia and Estonia.
  - Cross-country comparisons partial; some countries compensate with higher macroprudential capital requirements (applied in Belgium, Germany, Liechtenstein, Slovenia, and Lithuania).
- Theoretical support for time-varying LTV caps:
  - Literature finds welfare gains from time-varying, countercyclical LTV caps; gains heterogeneous across borrowers and savers; high share of variable-rate mortgages can slightly diminish need to actively change LTV for Lithuania.
- Practical constraints on active BBM changes:
  - Procyclicality of loan-contract LTVs, data and implementation lags, uncertain effects of easing/tightening, social and political economy risks, and distortionary uncertainty from frequent changes.
  - Example: COVID-19 onset saw average and 1st quartile LTV ratios decrease as creditors became cautious.
- Bindingness and empirical distributions (October 2019–May 2022):
  - ≈ 37 percent of newly issued loans had a limiting LTV of 85 percent.
  - 48 percent had LTV in (80%,85%].
  - ≈ 31 percent of mortgages had maturities at the 30-year limit.
  - 64 percent of new loans would have been affected by tightening maturity cap to 25 years.
  - Only 1 percent would have been affected by tightening DSTI cap to 35 percent; tightening DSTI to 35 percent would affect around 16 percent of mortgage flow.
- Implications of tightening options:
  - Tightening LTV by 5 p.p. would impact roughly half of lending flow and disproportionately affect first-time buyers and young families, including many low-risk borrowers.
  - Tightening DSTI by 5 p.p. is less impactful but less distortionary; would affect around 15 percent of borrowers.
  - Targeting: DSTI (headline or stressed) more closely linked to PD; DSTI limit more effective than LTV cap for reducing household risk parameters with less pronounced macro feedback (Gross and Población, 2017).
- Quantitative recommendations (from iso-PD and iso-impact analysis):
  - One-year focus to reduce mortgage flow by 15 percent: options include {oDSTI = 28%, M = 30y} or {oDSTI = 35%, M = 22y} relative to current {40%, 30y}. Minimizing one-year PD while reducing flow by 15 percent suggests reducing DSTI to around 30 percent or stressed DSTI* to 40 percent while leaving maturity at 30y.
  - Lifetime focus: minimizing lifetime PD while targeting a 15 percent credit reduction favors joint reduction in DSTI(*) and maturity (example tangency: {34%, 23y} for DSTI and maturity; for DSTI* tangency {46%, 22y}).
  - Specific numerical suggestions:
    - Reduce stressed DSTI* cap from 50 percent to around 40 percent (one-year focus).
    - Or jointly tighten DSTI* and maturity to around 45 percent and 20y. respectively (joint option) — both reduce mortgage credit flow by ~15 percent and close the credit gap; joint tightening minimizes lifetime credit risk for individual loans.
- Interaction with rising mortgage rates:
  - A 3 p.p. increase in mortgage rates could translate into a 12 percent decrease in mortgage flow, eliminating 4/5 of the credit overflow (text broken across pages — preserve numeric fragments as presented).
  - Increasing rates have elevated average mortgage DSTIs from 27 percent to 30 percent, making the 40 percent cap binding for some borrowers.

### Secondary mortgage LTV calibration (micro-calibration exercise)
- Calibration objective:
  - Find personalized secondary LTV2_h such that aggregate ECL of a household with two mortgages equals ECL of a benchmark single mortgage with LTVH = 85%, DSTIH ≤ 40%, maturity 30 years, same collateral and features.
- Calibration methodology and LGD specification:
  - ECL_jh computed as discounted sum: ECL_jh := sum_{t=1}^{n_jh} [(1 + i_jh)^{-t} LGD_jh,t PD_jh,t ∏_{l=0}^{t-1} (1 − PD_jh,l)].
  - One-year horizon simplifies to LGD_jh,1 PD_jh,1.
  - PD_jh,t depends on DSTI_h,t, LTV_jh,t, Maturity_jh,t, LTV_{i≠j,h,t}, and indicator 1_{j=2}.
  - Downturn LGD: LGD_jh,t = max{ EAD_jh,t · [1 + C − (1 − ∆)/LTV_jh,t], 0 } with C (administrative costs) and ∆ (house price drop).
- Macroeconomic calibration scenarios (Table 4):
  - Scenario #1: ∆ = −15 ; GDP drop = −4.1 ; Unemployment change = +5.0 p.p.
  - Scenario #2: ∆ = −20 ; GDP drop = −6.9 ; Unemployment change = +6.4 p.p.
  - Scenario #3: ∆ = −25 ; GDP drop = −8.0 ; Unemployment change = +7.0 p.p.
  - Scenario #4: ∆ = −30 ; GDP drop = −10.7 ; Unemployment change = +8.5 p.p. (baseline; matches actual 2009 drop).
- One-year horizon calibration results (≈ 6,000 households, 2012–19):
  - Ineligible households: ≈ 1,500 households had no LTV2_h ∈ (0,85%) satisfying ECL-equalization (many had LTV1_h > 70%).
  - Personalized LTV2_h patterns:
    - Negative nonlinear relationship between LTV1_h and LTV2_h with kink around LTV1_h ≈ 70%.
    - Households with LTV1_h > 70%: average personalized LTV2_h around 70 percent (varies with ∆).
    - Households with LTV1_h < 70%: may borrow with LTV2_h up to 80 percent.
  - Aggregate calibration means and 90% confidence intervals (one-year horizon):
    - For cLTV1 >70%:
      - ∆ = −15%: 83 [82, 84]
      - ∆ = −20%: 80 [77, 82]
      - ∆ = −25%: 74 [71, 81]
      - ∆ = −30%: 70 [66, 78]
    - For cLTV1 ∈ (0,70]:
      - ∆ = −15%: 84 [83, 84]
      - ∆ = −20%: 82 [80, 83]
      - ∆ = −25%: 80 [78, 82]
      - ∆ = −30%: 79 [75, 81]
    - For cLTV1 = 0:
      - ∆ = −15%: 84 [83, 84]
      - ∆ = −20%: 82 [80, 83]
      - ∆ = −25%: 80 [76, 82]
      - ∆ = −30%: 78 [72, 81]
  - Interpretation: less severe house-price fall (∆ = 15%) supports LTV2 ≈ 83–84%; conservative baseline ∆ = 30% implies LTV2 substantially below headline 85%, especially when LTV1 > 70%.
- Lifetime horizon calibration (same sample):
  - Ineligible households: ≈ 1,300 households (≈ one-fifth) with personalized LTV2_h = 0.
  - LTV1_h = 70% remains a key eligibility threshold.
  - Personalized LTV2_h all < 85%; kinked relationship with LTV1_h persists.
  - Lifetime yields milder secondary LTV limits than one-year snapshot due to amortization effects (example for ∆ = 30%: average LTV2 for LTV1 >70% is 75% lifetime vs ~70% one-year).
- Key implications:
  - Regulatory LTV2 tightness depends critically on assumed ∆ and risk tolerance.
  - Personalized calibration can identify borrowers who should be ineligible and produce LTV2_h limits below headline 85% that vary with LTV1_h.
- Finding 7:
  - Secondary mortgage LTV limit should (1) be strictly lower than headline 85 percent; and (2) be differentiated by borrower’s first mortgage LTV (threshold around 70 percent in the model).

### Final remarks and policy recommendations on secondary mortgage LTV regulation
- Empirical summary:
  - Secondary mortgages historically issued with high LTVs (often ≥ 80%) and have higher lifetime PDs than single loans.
  - Issuance of a secondary mortgage increases the first loan's credit risk (negative externality).
  - Historical market behavior failed to internalize multi-loan risks, justifying restrictive regulation.
- Calibration-based policy suggestions:
  - Baseline calibration supports secondary LTV limit around 75 percent [67, 81] with a 70 percent first-mortgage threshold.
  - Bank of Lithuania enacted 70 percent secondary LTV with a 50 percent first-mortgage threshold; this lies within the lower end of estimated intervals but uses a lower first-mortgage threshold than model suggestion.
  - Reasons for stricter statutory thresholds may include broader macro-level concerns (market procyclicality, investor-driven boom risks, social side effects).
- Complementary measures and broader policy mix:
  - Macroprudential policy can target buy-to-let investors, but potency limited where many investor purchases financed with own funds (in Lithuania ~ half of housing transactions financed with credit).
  - Recommended complementary fiscal tools: appropriately progressive property taxation and stamp duty taxes to curb housing demand.
- Limitations and research directions:
  - Strength: granular loan-level data enable precise BBM evaluation.
  - Weakness: micro-level credit-risk framework is not general-equilibrium; does not capture macro feedbacks.
  - Suggested extensions: integrate micro-level lifetime credit-risk framework into micro-macro or semi-structural macroeconomic-banking setups.
- Concluding synthesis:
  - Secondary mortgages are riskier and impose negative externalities; calibration supports tighter, differentiated LTV2 regulation and complementary fiscal measures to address investor-fueled housing imbalances.

_Italic: Source: wpiea2023227-print-pdf_

### 2.1   Institutional Setup  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  

### 2.1 Institutional Setup

### Institutional framework
- Macroprudential policy in Lithuania is conducted solely by the central bank (Bank of Lithuania).
- Bank of Lithuania’s macroprudential toolkit includes borrower-based measures (BBMs) enacted in 2011 through the Responsible Lending Regulations (Atsakingojo skolinimo nuostatai, or ASN).
- The ASN framework applies to all credit extended to natural persons and secured by real estate; the summary here focuses on residential housing loans, which comprise the majority of loans under the regulation.
- The regulation applies to all credit providers that are profit-seeking legal persons, including domestic banks and foreign branches, credit unions, peer-to-peer lending platform operators, and other non-bank financial intermediaries that operate in Lithuanian jurisdiction.
- The wide scope of application of the ASN requirements aims to minimize the possibility of circumvention (leakage effects).

### ASN measures and headline limits
- LTV: 85 percent (implies a 15 percent minimum down payment requirement).
- LTV2: 70 percent (LTV limit for second and subsequent mortgage loans, effective as of February 1, 2022).
- DSTI: 40 percent (limit on average monthly loan payments as a share of borrower’s monthly disposable income).
- DSTI*: 50 percent (stressed DSTI limit, computed with stressed interest rate to 5 percent).
- Maturity Limit: 30 years.
- Applicable since:
  - LTV: 2011
  - LTV2: 2022
  - DSTI: 2011
  - DSTI*: 2015
  - Maturity Limit: 2015
- Note: LTV2 denotes the LTV limit for secondary mortgages, effective as of February 1, 2022. The 70 percent limit for LTV2 is applied only for borrowers whose first mortgage’s current LTV is above 50 percent at the inception of the secondary mortgage.

### Operational details and exemptions
- ASN disallows the use of borrowed funds for a down payment (borrower must use own funds).
- Credit institutions may use an exemption and apply a DSTI limit of 60 percent for creditworthy customers; however, the amount of loans issued with such exemptions cannot exceed 5 percent of the institution’s annual mortgage flow.
- DSTI* denotes the stressed DSTI limit, which cannot be exceeded after applying a 5 percent interest rate sensitivity test.
- The 70 percent LTV2 requirement is applied only when the borrower’s first mortgage current LTV is above 50 percent at the inception of the secondary mortgage; exemptions exist as noted.

### Intended functions of measures
- LTV cap functions as a solvency requirement linked to borrower equity (down payment).
- DSTI cap functions as a liquidity measure limiting monthly debt service relative to disposable income.
- DSTI* (stressed to 5 percent) mitigates interest rate risk given that almost all mortgage loans in Lithuania have variable rates.
- The 30-year maturity limit serves two functions:
  - Together with DSTI, it limits indebtedness relative to income (debt-to-income, DTI).
  - It enhances consumer protection by requiring amortization and disallowing perpetual interest-only structures, lowering cumulative interest paid.

### Trade-offs and observed side effects
- The ASN framework aims to increase resilience and smooth credit demand over the financial cycle, but may have social side effects:
  - LTV regulation can restrict access to housing and reduce home ownership for financially constrained households, potentially increasing rental demand and contributing to a vicious rental cycle.
  - More financially constrained buyers may be crowded out, allowing better-funded investors to purchase housing in bulk, potentially raising house prices, rental rates, and wealth inequality.
- Observed market outcome: over the past decade since inception of ASN, rental prices have accelerated and grown, on average, 1 p.p. higher than house prices on an annual basis.

*Source: wpiea2023227-print-pdf - 2.1 Institutional Setup.*

### 2.3   Mortgage Market Dynamics

### 2.3   Mortgage Market Dynamics

### Housing market dynamics and misalignment indicators
- House prices and mortgage portfolio grew at double-digit annual pace, with year-on-year growth rates peaking at 26.8 percent and 12.3 percent, respectively.
- The COVID-19 pandemic did little to slow the housing market; growth accelerated and reached 15-year heights.
- Measures of misalignments (based on a two-market disequilibrium model of Karmelavičius and others (2022)) indicate:
  - By end-2022, home prices were up to 20 percent above their fundamentals.
  - A mortgage credit overflow of around 15 percent.
- The current broad-based credit-to-GDP gap is still negative in Lithuania; however, the gap that is based on mortgage stock is closed, i.e., near zero.
- If the high flow of mortgage credit is sustained and the overflow gap does not close, it can invoke a positive mortgage credit-to-GDP gap.
- Although newer data suggest a slowdown in credit and house price growth due to sharply raised interest rates, the authorities should monitor the mortgage market carefully and be vigilant about systemic vulnerabilities.

### Trends in loan-level characteristics (2020–mid-2022)
- Mortgage interest rates for new lending experienced a deep fall:
  - Median rate dropped from 2.3 percent to 1.9 percent.
  - Rates became more compressed around the median, consistent with increased competitive pressures among lenders.
- Average loan size rose from 60 thousand EUR to 90 thousand EUR — a 40 percent increment over two years.
- Household disposable income growth lagged behind increasing home values, making down payments harder to accumulate.
- Median LTV and DTI ratios increased slightly as household indebtedness rose.
- DSTI ratios remained remarkably stable despite rising loan sizes — attributed to lower interest rate margins and somewhat longer maturities.
- Variable-rate loans comprise more than 90 percent of the market; debt service burdens have increased significantly with sharply elevated policy rates.

### Secondary mortgages: prevalence, characteristics, and risks
- Prevalence:
  - Share of secondary mortgages in new lending flow increased from 9.9 percent to 12.9 percent during 2019–21.
  - Increase is widespread across regions, with the biggest gains in the coastal region of Klaipėda, Palanga and Neringa (a resort area).
- Borrower and loan characteristics:
  - Secondary mortgages are commonly used to finance additional house purchases that are not primary residences (leisure or rental properties).
  - DSTI distribution of secondary loans is heavily shifted rightward relative to first mortgages, indicating higher liquidity strain.
  - LTV distribution of secondary mortgages is concentrated around 80 percent; more than half of such loans have LTVs between 80 and 85 percent.
- Historical delinquency and default evidence:
  - Throughout 2012–20, first mortgage average default rate was around 1 percent.
  - Throughout 2012–20, secondary mortgage default rate was over 1.5 percent — a 50 percent higher chance of nonperformance relative to first mortgages.
  - Empirical literature supports higher default risk for multi-loan borrowers and for second-home properties.
- Channels increasing risk for secondary mortgages:
  - Ability-to-pay channel: multiple mortgages increase difficulty to service debts; heightened sensitivity to interest rate changes and income loss.
  - Equity channel: higher LTVs for secondary mortgages increase PD and LGD; in partial/full recourse systems, LGDs on multiple loans can be correlated because recoveries derive from the same borrower’s income/assets.
- Macroprudential implications:
  - Secondary mortgages are procyclical and can amplify housing market activity and price cycles.
  - Prevalence of secondary mortgages can add fuel to housing price and credit flow gaps, generating negative externalities for less risky borrowers (e.g., first-time buyers) and other parts of the financial system.
  - Secondary mortgages can exacerbate side effects of macroprudential policy by inflating prices and reducing housing-for-purchase supply, accelerating rental cycles for financially constrained households.

### Policy response and regulatory settings
- Bank of Lithuania action:
  - Imposed a 70 percent LTV2 limit for secondary mortgages, which came into effect on February 1, 2022.
- International and comparative borrower-based measures (selected entries from Table 2):
  - Lithuania: LTV 85; DTI 40 (up to 60); Maturity 30; Effective DTI 7.8
  - Latvia: LTV 95; DTI 40; Maturity 30; LTI 66
  - Estonia: LTV 90; DTI 50; Maturity 30; Effective DTI 6.9
  - Poland: LTV 90; DTI 25 (up to 35); Maturity 7.9
  - Note: Table compiled and provided on June 1, 2022. The LTV limit reported is the maximum effective limit in each jurisdiction. The effective DTI limit is calculated by taking the DSTI, stressed DSTI and maturity limits into account, and assuming a 2 percent interest rate. For countries without maturity limits, 30 years is assumed; for countries without a DSTI limit, 40 percent DSTI is assumed.

### Empirical findings motivating further assessment
- Historical loan-level data in Lithuania indicate secondary mortgages exhibit a higher likelihood of default even when controlling for DSTI, LTV, borrower’s history, and other characteristics.
- Section 5 of the source document contains an assessment of the secondary mortgage LTV2 limit using pre-policy loan-level analysis.

*Source: wpiea2023227-print-pdf - 2.3   Mortgage Market Dynamics*

### 2.4   Tightening Options

### 2.4   Tightening Options

### Assessment of Lithuania’s ASN framework and comparative standing
- Recent interest rate hikes are already deflating mortgage market pressure, but exuberance and associated misalignments during the low-rate episode suggest that Lithuania’s macroprudential stance had been loose.
- BBMs are primarily aimed to boost resilience of lenders and debtors, but they are also desirable to work countercyclically and dampen formation of imbalances.
- When compared with BBMs in other European countries:
  - The LTV limit of 85 percent ranks as the 2nd strictest, while many states have an LTV of 90 percent, 95 percent, or even 100 percent.
  - In terms of the effective DTI requirement (calculated using a DSTI limit and maturity cap), Lithuania is among jurisdictions with more stringent limits.
  - Compared with Latvia and Estonia, Lithuania has the most restrictive LTV, while its effective DTI is the least stringent of the three.
- Cross-country comparisons are partial and must consider that some countries may compensate relatively loose BBM stance with higher macroprudential capital requirements; at the time of writing, such regulation is applied in Belgium, Germany, Liechtenstein, Slovenia, and also in Lithuania.

### Active changes in BBM policy: theoretical support and modeling evidence
- DSGE-based analyses and related literature find that time-varying LTV caps that respond to financial imbalances are welfare-improving:
  - Mendicino (2012), Lambertini and others (2013), Mendicino and Punzi (2014), Rubio and Carrasco-Gallego (2014), Bruneau and others (2018).
  - Gatt (2021) and Ferrero and others (2022) find LTV caps should be changed countercyclically; Gatt (2021) shows a time-varying LTV rule should react asymmetrically, tightening more aggressively during credit booms and allowing ample loosening during busts.
- Welfare gains from time-varying LTV rules are heterogeneous:
  - Actively changing the LTV limit is optimal from the borrower’s perspective; savers prefer keeping the LTV cap constant.
  - Aggregate macroeconomic and financial stability gains can be substantial despite this saver–borrower trade-off.
- Interest rate characteristics and mortgage contract features affect the extent and asymmetry of macroprudential policy effects:
  - A high share of variable-rate mortgages can slightly diminish the need to actively change the LTV limit for a country like Lithuania.
  - Interest payment type does not affect magnitude but can create strong asymmetries, with tightening having stronger effects than easing.

### Practical considerations, limitations, and risks of active BBM changes
- Aspects that complicate active, time-varying BBM implementation:
  - Loan-contract LTVs are highly procyclical: they increase with house prices in booms and drop in crises, making tightening/easing impacts asymmetric across the credit cycle.
  - Expansionary BBM policy during a bust may be ineffective because lenders become risk-averse and BBM-based requirements become less binding or obsolete.
  - Identifying the financial cycle phase is complex, using many indicators that often contradict; there are time lags in data acquisition, policy implementation, and delayed impact.
  - The effect of policy change is uncertain, particularly easing during busts—unclear which borrowers and which credit institutions would respond.
  - Frequent changes are distortionary and create uncertainty for creditors and households:
    - Unexpected tightening (e.g., LTV requirement) can force households to choose lower-quality homes, delay purchase, or incur financial loss.
    - Early announcement of future tightening can cause frontloading of mortgage demand, potentially accelerating imbalances.
  - Social sensitivity and political economy risks:
    - BBMs affect housing affordability; toolkit changes can become politicized, risking intrusion by politicians or lobbyists and jeopardizing independence of the policymaking institution.
- Empirical observations illustrating asymmetric lender behavior:
  - At onset of the COVID-19 pandemic in Lithuania, average and 1st quartile LTV ratios decreased as creditors became more cautious; LTV ratio dropped significantly during the GFC.

### Rationale for preferring occasional recalibration (a one-off tightening) over frequent active changes
- Operational issues caused by frequent BBM changes outweigh DSGE-based evidence favoring time variation; active changes (discretionary or rules-based) are rarely practiced.
- Longstanding BBM frameworks with fixed parameters can set standards and provide certainty; LTV and DSTI limits improve resilience and act countercyclically even if unchanged.
- Occasional discretionary recalibration is justified when strong evidence indicates the macroprudential stance is inappropriate (e.g., loose) and alterations are infrequent:
  - Empirical evidence (Brandao-Marques and others, 2020) finds tightening BBMs is particularly beneficial if financial vulnerabilities are rising.
  - Tightening during the low-rate heat would create space for later relaxation if steeply rising interest rates depress lending and burden the economy.

### How binding are Lithuania’s ASN parameters (empirical distribution and impact of tightening)
- Observed distributions for new housing loans (October 2019–May 2022) indicate:
  - Around 37 percent of newly issued loans had a limiting LTV of 85 percent.
  - 48 percent had an LTV that was just below the cap, i.e., LTV∈(80%,85%].
  - Around 31 percent of mortgages had maturities designated at the 30-year limit.
  - 64 percent of new loans would have been affected by tightening the mortgage duration cap to 25 years.
  - The corresponding figure for the DSTI cap of 40 percent would be only 1 percent.
  - Tightening the DSTI cap to 35 percent would have affected around 16 percent of the mortgage flow.
- Implications of tightening options:
  - BBM parameters are usually set in five-unit intervals; tightening LTV by 5 p.p. would have been the most impactful relative to setting the DSTI limit to 35 percent.
  - Tightening the LTV limit to 80 percent would impact roughly half of lending flow and would disproportionately affect first-time buyers and financially constrained young families, including many low-risk borrowers with high-quality collateral.
  - Tightening DSTI by 5 p.p. is less impactful but also less distortionary: it would have affected around 15 percent of borrowers (roughly the size of mortgage overflow) whose DSTI is on the righthand side of the distribution.
- Targeting and effectiveness considerations:
  - Stricter DSTI regulation—headline DSTI or stressed DSTI—would be more targeted to containment of risk because DSTI ratios are strongly related to the customer’s PD.
  - Gross and Población (2017) find that “DSTI limit is more effective than LTV cap from the perspective of reducing household risk parameters while implying less pronounced macro feedback effects.”

### Transition to quantitative assessment and modeling
- The chapter concludes the qualitative assessment and introduces the next steps:
  - Development of a micro credit risk model based on loan-level data.
  - In-depth assessment of the DSTI(*) cap from a quantitative perspective.
  - Calibration exercise of LTV limit for secondary mortgages.

_Italic: Source: Chapter 2.4, "Tightening Options," wpiea2023227-print-pdf._

### 3.2   One-Year-Ahead Probability of Default

### 3.2   One-Year-Ahead Probability of Default

### Model specification
- One-year-ahead PD for housing loan k at quarter t is estimated using a logistic regression (logit) model:
  - logit(PD_{k,t}) = ln(PD_{k,t}/(1−PD_{k,t})) = β_0 + β_1^> x_{k,t} + β_2^> z_{k,t} + φ(oBBM_k).
  - PD_{k,t} is the one-year-ahead PD for housing loan k at quarter t (t measured in years since origination).
  - x_{k,t}: vector of household and loan characteristics (time-varying).
  - z_{k,t}: macroeconomic variables (time-varying).
  - oBBM_k: BBM-related variables measured at origination of loan contract k.
- Income-based debt ratios oD(S)TI_{(∗)} and oDTI are transformed with restricted cubic splines φ(·) to capture nonlinear effects.
- Continuous variables are winsorized; example caps noted: DSTI and LTV ratios at 300 percent and DTI at 67.

### Estimation results (one-year-ahead PD)
- Estimation method: maximum likelihood logistic regression.
- Sample size: fitted on 4.8M observations.
- Discriminatory power:
  - AUROC of baseline model: around 90 percent (calculated using five-fold cross-validation).
  - Comparisons: Kelly and O’Toole (2018) AUROC up to 73 percent; Mihai and others (2018) up to 80 percent.
  - Higher AUROC attributed to inclusion of credit history variables; without them AUROC would be closer to Mihai and others (2018).
- Key parameter findings (Model 1, Table 5 summary):
  - Residual maturity of a loan is significant and positively related to one-year-ahead PD (default more likely at earlier stages of a housing loan’s lifespan).
  - Higher interest rates may significantly increase the risk of default throughout the life cycle of a loan.
  - Having more than one housing loan statistically significantly increases likelihood of mortgage default.
  - Borrowers with more dependents and lower income are more likely to default.
  - Historical defaults and short-term delinquency:
    - If a household had issues repaying its credit agreements over the past three years, its mortgage default probability is, on average, 2.1 p.p. higher than that of historically solvent borrowers.
    - If a housing loan is already delinquent for more than 60 days but not yet considered strictly in default, it is approximately 2.4 p.p. more likely that it will become nonperforming over a one year horizon.
  - Macroeconomic variables:
    - PD is countercyclical: PD is lower when the economy is growing and unemployment and inflation are low, though magnitudes are limited.
    - The unemployment rate is statistically significant even at conservative levels.
    - Loans granted before the GFC are statistically significantly riskier than those issued afterward (year-of-origination dummies included).
  - BBM-related variables at origination:
    - oLTV and oD(S)TI_{(∗)} are significant for mortgage default.
    - A loose BBM stance (allowance for high oBBM_k values) may increase individual mortgage default risk.
    - The magnitude of the impact of oDSTI measures on PD is higher compared with that of oLTV.
    - Cubic spline terms of oD(S)TI_{(∗)} are statistically significant, indicating nonlinear effects.
- Note on potential endogeneity: impact of interest rates on default may be slightly overestimated due to unobserved customer quality affecting both PD and interest rate.

### Transition to lifetime assessment (overview)
- Rationale: BBMs like LTV or DSTI caps, or limits on loan maturity, affect loan risk throughout lifetime, not only first year. Calibration should consider effects of origination BBM variables on successive loan evolution and LGD.
- Approach: Use one-year-ahead PD model to estimate lifetime PDs and loss rates via survival analysis.

### Lifetime PD, LGD, and ECL formulas and assumptions
- Conditional one-year PD interpretation:
  - PD_{k,t} = P(T_k ≤ t+1 | T_k > t), where T_k is time in years to first default.
- Unconditional probability of default in year t+1:
  - P(T_k ≤ t+1, T_k > t) = PD_{k,t} ∏_{m=0}^{t−1} (1 − PD_{k,m}). (expression (2))
- Lifetime PD over n-year maturity:
  - PD_{LT_{k,n}} := P(T_k ≤ n) = 1 − ∏_{m=0}^{n−1} (1 − PD_{k,m}). (expression (3))
  - Alternative representation: PD_{LT_{k,n}} = ∑_{m=0}^{n−1} PD_{k,m} ∏_{t=0}^{m−1} (1 − PD_{k,t}). (expression (4))
- Loss Given Default (LGD) at time t:
  - LGD_{k,t} = max{EAD_{k,t} · (1 + C) − CLLT_{k,t}, 0}. (equation (5))
  - C (administrative costs fraction) assumed to be C = 5%.
  - Assumes a 25 percent haircut to collateral value when computing downturn LGD in examples.
  - Testing indicated inclusion of 50 percent cure rate does not materially affect results; equation (5) implicitly assumes zero probability of loan recovery after default.
- Expected Credit Loss (period t) as product of unconditional PD and LGD:
  - ECL_{k,t} := LGD_{k,t} · PD_{k,t} ∏_{m=0}^{t−1} (1 − PD_{k,m}). (equation (6))
- Lifetime ECL (discounted sum over n years):
  - ECL_{LT_{k,n}} := ∑_{t=1}^{n} (1 + i_k)^{−t} [ LGD_{k,t} · PD_{k,t} ∏_{l=0}^{t−1} (1 − PD_{k,l}) ]. (equation (7))
  - Discount factor uses loan-specific interest rate i_k.
  - For lifetime credit risk at origination, assume away interest rate dynamics (no interest rate forecasting for long-term loans).

### Computational implementation and assumptions for lifetime estimates
- Data and sample:
  - Mortgages issued between 2004 and 2020 are modeled.
- Amortization and schedules:
  - Hypothetical amortization schedules constructed assuming annuity payment scheme for all mortgages and other household loans (including leases and consumer credits), so outstanding amounts and cLTV ratios adjust accordingly.
- Household and loan characteristic assumptions over loan life:
  - Household characteristics (family composition, economic activity type, income group) and some loan-specific variables (interest rates and creditor dummies) are kept constant over the loan’s lifetime.
  - Assume household credit history will not worsen and there will be no short-term delinquencies more than 60 days past due.
  - oBBM_k are kept constant (BBM-related variables measured at origination).
- Macroeconomic assumptions:
  - Macroeconomic variables (z_t: real GDP growth, inflation, unemployment rates) are fixed at their historic long-term averages obtained using 1996-2022 data.
- Procedure:
  - Construct loan payment schedule for each loan to obtain x_{k,t} and z_{k,t} sequences.
  - Use equation (1) estimates to compute one-year-ahead PDs PD_{k,t}.
  - Compute lifetime PDs and ECLs using equations (3) and (7).

*Italic: Source: "3.2   One-Year-Ahead Probability of Default" from wpiea2023227-print-pdf*

### 4.1   Efficacy of Borrower-Based Measures

### 4.1   Efficacy of Borrower-Based Measures

### 4.1.1 Mortgage Quality Preceding the GFC
- Household credit portfolio growth in the 2000s: 55 percent average annual rate.
- Market dynamics:
  - Around 2008, one quarter of new mortgage issuance had LTVs as high as 100 percent.
  - Borrowers increased DSTI ratios and maturities to compensate for worsening housing affordability.
- Model estimates at origination for mortgages issued around 2008:
  - Lifetime PD: 12 percent.
  - At-origination lifetime ECL rate: 0.6 percent (implying 0.6 EUR set aside per 100 EUR loan).
- Counterfactual exercise applying current ASN limits (maturity≤30 years, DSTI≤40 percent, LTV≤85 percent) to pre-2011 loans:
  - Average lifetime PD would have been lower by 2 p.p.
  - Lifetime ECL rate would have been lower by 0.3 p.p.
  - BBM package (ASN) would have reduced the mortgage ECL rate by 78 percent in relative terms.
  - Mortgage portfolio would have been at least 24 percent smaller.
  - Aggregate mortgage portfolio losses for the banking sector would have been around 83 percent smaller (= [1−(1−0.78)(1−0.24)]×100%).
- Supplementary alternative PD model (using factual cDSTI):
  - Counterfactual lifetime PD lower by 5 p.p. (instead of 2 p.p.).
  - ECL rate lower by 0.4 p.p. (instead of 0.3 p.p.).
  - Implied mortgage portfolio losses 87 percent smaller (= [1−(1−0.83)(1−0.24)]×100%).
- Finding 1: Had current ASN limits been imposed preceding the GFC, the credit risk of individual housing loans would have been significantly lower, and aggregate mortgage losses at least 83 percent smaller than those experienced by Lithuania’s banking sector during the crisis.

### 4.1.2 Post-GFC period: ASN Framework and Borrower Resilience
- Post-2009 lender behavior: LTV, DSTI ratios, and maturities declined sharply; lenders’ self-correction reduced the righthand tail of risk distribution.
- Role of ASN (implemented 2011):
  - Set a standard for market participants and limited growth in the 75th percentile of at-origination LTVs and maturities.
  - Helped anchor lifetime credit risk and improve borrower resilience.
- Observed changes in 2010s:
  - Lifetime PDs and ECL rates gradually declined and became significantly lower than pre-GFC levels.
  - Current (stock) DSTI and LTV metrics substantially declined between 2009 and 2019.
- Stress-test scenario used to assess resilience (adverse scenario parameters):
  - GDP drop: -3 percent.
  - Disposable income: -8 percent.
  - House prices: -36 percent.
  - Inflation: 22 percent.
  - Rise in unemployment rate: 8 p.p.
- Stress-test result: mortgage portfolio credit risk parameters are less sensitive to adverse economic changes in 2019 versus 2009.
- Finding 2: In the 2010s, mortgage quality increased and borrowers are now more resilient to adverse shocks compared with the pre-GFC period, at least partly due to the introduction of ASN regulations.

### 4.1.3 Comparison of Instruments in Predicting Default
- Purpose: assess which BBM-related variables best predict one-year-ahead mortgage default using AUROC statistics (five-fold cross-validation).
- BBM-related variables tested (at origination): oDSTI, oDSTI*, oDTI, oLTV, oMaturity.
- Key empirical insights:
  - Income-related indebtedness measures (oDSTI, oDSTI*, oDTI) have substantially higher discriminatory power than oLTV or oMaturity for one-year-ahead PD.
  - oLTV is more important for LGD; its effect on PD is significantly lower across specifications.
  - Maturity adds little predictive power for one-year-ahead default but may matter more for lifetime PD.
  - The stressed DSTI* cap of 50 percent (introduced in 2015) does not exhibit predictive advantage over the headline DSTI in the sample period (2012–2020); oDSTI shows at least marginally better AUROC performance.
  - Under the full model, the predictive superiority of income measures diminishes because the full model includes household income and credit history.
- AUROC statistics (Full model specification):
  - oDSTI: 0.9052
  - oDSTI*: 0.9050
  - oDTI: 0.9038
  - oLTV: 0.9017
  - oMaturity: 0.9017
- Finding 3: Effective containment of one-year-ahead probability of mortgage default can be achieved using income-based measures, especially the headline DSTI cap, whereby the LTV measure is more suitable for controlling the loss given default parameter.

*Source: wpiea2023227-print-pdf - 4.1   Efficacy of Borrower-Based Measures*

### 4.2   Recalibration Toward Tighter Stance

### 4.2   Recalibration Toward Tighter Stance

### Adequacy of DSTI(*) Regulation
- The DSTI(*) metric (oDSTI(*) at origination and stressed oDSTI*) enters the one-year-ahead PD model nonlinearly via a restricted cubic spline φ(·).
- Estimated marginal effects (average pointwise partial derivatives of one-year PD with respect to oDSTI(*), holding other predictors at means/modes) show:
  - The marginal effect curve lies above zero globally: oDSTI(*) variables positively affect mortgage PD.
  - At low oDSTI(*) levels (e.g., 0-10 percent) marginal effects are small; at very high oDSTI(*) (oDSTI(*)>60%) marginal effects are small because default risk is already large.
  - There exists an inflection region where the marginal impact on PD is highest:
    - oDSTI inflection point = 31 percent with confidence interval of [24, 39].
    - stressed oDSTI* inflection point = 35 percent with confidence interval of [28, 42].
- Robustness: replacing oDSTI(*) with current cDSTI(*) yields stronger marginal effects with a preserved nonlinear shape. Inflection estimates are similar:
  - cDSTI inflection = 32 [27, 41]; stressed cDSTI* inflection = 35 [31, 43].
- Current ASN parametrization:
  - oDSTI≤40% and oDSTI*≤50% are beyond those inflection points, suggesting room for tightening, especially for stressed DSTI*.
- Finding 4:
  - "The nonlinear relationship between DSTI(∗) variables and the estimated probability of mortgage default suggests that in the low-rate environment, the existing DSTI(∗) limits were loose, especially the stressed DSTI∗ cap, which could have been lowered from 50 percent to around 40 percent."

### Combination of DSTI(*) and Maturity Limits
- Rationale: tighter DSTI(*) caps incentivize borrowers to extend maturities; therefore DSTI(*) caps should be analyzed jointly with maturity limits to assess impact on PDs and ECL rates.
- Method: map iso-PD curves (combinations of DSTI(*) and maturity that yield equal PD) together with iso-impact curves (combinations that reduce new mortgage flow by a target percentage).
- Policy target example: closing a 15 percent credit overflow.
  - Iso-impact curve examples (one-year horizon) that reduce nominal credit flow by 15 percent include:
    - {28%,30y.} or {35%,22y.} would achieve the same reduction compared with current policy {40%,30y.}.
  - Policy-selection rule: choose a point on the iso-impact curve that lies nearest the origin {0%,0y.} on iso-PD maps (minimizes mortgage-level PD for given impact).
- One-year horizon implication:
  - Minimizing one-year PD while reducing credit flow by 15 percent suggests reducing DSTI limit to around 30 percent or stressed DSTI* to 40 percent, leaving maturity limit at 30 y.
  - Because DSTI≤40% is within confidence bounds of “optimal”, reducing stressed DSTI* to 40 percent would shadow the DSTI≤40% cap (DSTI*≤40% would be tighter).
- Lifetime-horizon implication:
  - Lifetime PD increases monotonically with maturity if DSTI(*) and other variables hold constant; iso-PD curves become flatter.
  - Minimizing lifetime PD while targeting a 15 percent credit reduction favors reducing both DSTI(*) cap and maturity limit.
  - Example tangency points:
    - For DSTI and maturity: {34%,23y.}.
    - For DSTI* cap: {46%,22y.}.
- Summary Finding 5:
  - "Since longer maturity loans may, ceteris paribus, have a higher chance of defaulting at least once during their lifespans, minimization of lifetime credit risk while achieving a desired policy impact can be accomplished through a joint reduction in both DSTI(∗) and maturity limits."
- Policy alternatives and numerical suggestions extracted from analysis:
  - Reduce stressed DSTI* cap from 50 percent to around 40 percent (one-year focus).
  - Or jointly tighten DSTI* and maturity to around 45 percent and 20y., respectively (joint option) — both options reduce mortgage credit flow by approximately 15 percent and close the credit gap; the joint tightening minimizes lifetime credit risk for individual loans.
- Interaction with rising mortgage rates:
  - A 3 p.p. increase in mortgage rates could translate into a 12 percent decrease in mortgage flow, essentially eliminating
    4
    5
    of the credit overflow.
  - Increasing rates are already elevating average mortgage DSTIs from 27 percent to 30 percent, making the 40 percent cap binding for some borrowers. As rates rise, ASN parametrization will become more binding and may render further tightening unnecessary.

### Loan-to-Value Limit for Secondary Mortgages — Probability of Default Differential
- Empirical evidence: secondary mortgages are riskier and tend to default around 50 percent more often (Section 2 reference).
- DSTI is a major determinant of PD; secondary mortgages typically have higher DSTI ratios. But even controlling for DSTI and other borrower/loan features, a loan being nonsingle or secondary increases PD.
- One-year PD model results:
  - The household having other active mortgage loans adds to the mortgage PD depending on other mortgages’ cLTV:
    - Sole fact of having other active mortgages adds up to 0.12 p.p. in PD, varying by cLTV of other mortgages.
    - If other mortgages’ cLTV ≈ 50 percent, PD differential = +0.07 p.p.
    - If other mortgages’ cLTV ≈ 75 percent, PD differential = +0.09 p.p.
    - Being not only nonsingle but also second in origination timing adds +0.02 p.p.
    - Example aggregation: a secondary loan whose predecessor cLTV is 75 percent may be 0.11 (= 0.09 + 0.02) p.p. more likely to default compared with an otherwise equivalent single mortgage.
  - Secondary mortgage origination also increases default likelihood of the predecessor (first) mortgage — a negative externality at household-portfolio level.
- Lifetime PD amplification:
  - At-origination lifetime PD averages:
    - Secondary mortgages’ lifetime PDs lie globally above first/single mortgages.
    - On average through history, lifetime PD has been 3 p.p. higher for secondary mortgages compared with first mortgage loans.
    - Secondary mortgages whose predecessor loans have cLTV ≥ 50 percent have an even higher chance to default during their lifespan, with PD difference equal to 3.5 p.p.
    - Lifetime PD differences declined post-GFC and after ASN inception in 2011, but over the past decade lifetime PD differences between first and secondary mortgages remain around 0.4 p.p.
- Finding 6:
  - "Secondary mortgages (1) are more likely to default over their lifetime compared with an otherwise equivalent but single mortgage loan; and (2) impose a negative externality in terms of heightened default rate on the existing housing loan portfolio."

*Source: wpiea2023227-print-pdf — Section 4.2 Recalibration Toward Tighter Stance*

### 5.2   Micro-Calibration Exercise

### 5.2   Micro-Calibration Exercise

### Calibration method
- Objective: find a secondary LTV2 limit that equalizes the aggregate Expected Credit Loss (ECL) of a household with two mortgages to the ECL of a hypothetical single mortgage (benchmark).
- Benchmark (hypothetical single mortgage) parametrization:
  - LTVH = 85%
  - DSTIH ≤40%
  - maturity of 30 years
  - same underlying collateral, interest rate, and other features as the actual secondary loan
- ECL computation for household h and loan j ∈ {1,2; H}:
  - ECL_jh := sum_{t=1}^{n_jh} [(1 + i_jh)^{-t} LGD_jh,t PD_jh,t ∏_{l=0}^{t-1} (1 − PD_jh,l)]
  - One-year horizon: set n_jh = 1 ⇒ ECL reduces to: LGD_jh,1 PD_jh,1
- One-year-ahead PDs:
  - PD_jh,t = PD(DSTI_h,t, LTV_jh,t, Maturity_jh,t, LTV_{i≠j,h,t}, 1_{j=2})
- LGD specification (downturn LGD with house price decline ∆):
  - LGD_jh,t = LGD(LTV_jh,t | ∆) = max{ EAD_jh,t · [1 + C − (1 − ∆)/LTV_jh,t], 0 }
  - Note: for sufficiently small administrative costs C and collateral haircut ∆, and low cLTV, LGD may equal zero.
- Calibration condition (personalized LTV2_h):
  - Find LTV2_h ∈ (0,85%) such that: ECL_1h(LTV1_h, LTV2_h) + ECL_2h(LTV2_h, LTV1_h) = ECL_Hh
- Implementation:
  - Calibration carried out at origination for each actual secondary mortgage
  - Two horizons evaluated: (1) one year; (2) lifetime
  - Computation accounts for full amortization schedules and interactions through common DSTI_h and other metrics
  - Assumption: zero probability of recovery/cure from default state

### Assumed macroeconomic scenarios used for calibration
- Table 4: Assumed Macroeconomic Scenarios for Calibration
  - Scenario #1: House price drop –∆(%) = −15 ; GDP drop (%) = −4.1 ; Change in unemployment rate (p.p.) = +5.0
  - Scenario #2: House price drop –∆(%) = −20 ; GDP drop (%) = −6.9 ; Change in unemployment rate (p.p.) = +6.4
  - Scenario #3: House price drop –∆(%) = −25 ; GDP drop (%) = −8.0 ; Change in unemployment rate (p.p.) = +7.0
  - Scenario #4: House price drop –∆(%) = −30 ; GDP drop (%) = −10.7 ; Change in unemployment rate (p.p.) = +8.5
- Rationale: Scenario #4 (∆ = 30%) matches the actual drop in 2009 in Lithuania during the GFC and is used as a conservative baseline.

### One-year horizon calibration results
- Sample: around 6,000 households that took out secondary loans during 2012–19.
- Ineligible households:
  - 1,500 households should not have been granted a secondary mortgage because no LTV2_h ∈ (0,85%) satisfied the ECL-equalization condition (their two-mortgage ECL exceeded the single-mortgage benchmark irrespective of LTV2_h).
  - Many of these ineligible households had first loan LTV1_h ratio above 70%.
- Eligibility threshold sensitivity:
  - The LTV1_h threshold of 70% is dependent on assumed ∆. Example: if ∆ = 15% then the LTV1_h threshold would be around 85%.
- Personalized LTV2_h patterns:
  - Clear negative and nonlinear relationship between LTV1_h and personalized LTV2_h, with a kink around LTV1_h ≈ 70%.
  - Households with LTV1_h >70%: average personalized LTV2_h limits around 70 percent (varies with ∆).
  - Households with LTV1_h <70%: may borrow with LTV2_h up to 80 percent.
- Aggregate calibration means and 90% confidence intervals (one-year horizon):
  - For cLTV1 >70%:
    - ∆ = −15%: 83 [82, 84]
    - ∆ = −20%: 80 [77, 82]
    - ∆ = −25%: 74 [71, 81]
    - ∆ = −30%: 70 [66, 78]
  - For cLTV1 ∈ (0,70]:
    - ∆ = −15%: 84 [83, 84]
    - ∆ = −20%: 82 [80, 83]
    - ∆ = −25%: 80 [78, 82]
    - ∆ = −30%: 79 [75, 81]
  - For cLTV1 = 0:
    - ∆ = −15%: 84 [83, 84]
    - ∆ = −20%: 82 [80, 83]
    - ∆ = −25%: 80 [76, 82]
    - ∆ = −30%: 78 [72, 81]
- Key interpretation:
  - Under less severe house price fall (∆ = 15%), secondary LTV2 limits around 83–84 percent.
  - Under baseline ∆ = 30% (most conservative), secondary LTV2 limits are substantially below the headline LTV limit of 85 percent, particularly for borrowers with higher LTV1_h.

### Lifetime horizon calibration results
- Sample: same ~6,000 households.
- Ineligible households:
  - Around 1,300 households (about one-fifth) should not have received a loan (personalized LTV2_h = 0).
  - LTV1_h = 70% remains a strong eligibility threshold.
- Personalized LTV2_h patterns:
  - All personalized LTV2_h < 85%.
  - Strong kinked relationship between LTV2_h and LTV1_h, dependent on ∆.
- Comparison with one-year results:
  - Lifetime horizon yields milder (less stringent) secondary LTV limits than one-year horizon.
  - Example under baseline ∆ = 30%:
    - Average LTV2 limit for households with LTV1 >70% is 75 percent under lifetime setting versus around 70 percent under one-year setting.
    - 90 percent confidence intervals overlap: [66, 78] (one-year) and [67, 81] (lifetime).
- Explanation for milder lifetime results:
  - Lifetime calibration accounts for amortization: if first loan residual maturity is short, the secondary loan will effectively be single for most of its lifetime, reducing aggregate multi-loan risk relative to the one-year snapshot.

### Key implications and policy-relevant findings
- The tightness of a general regulatory LTV2 limit depends critically on the assumed house price drop ∆ and regulator’s risk tolerance; historical volatility and current misalignment measures should inform ∆.
- Personalized calibration can produce:
  - A set of borrowers who should be ineligible for secondary mortgages (LTV2_h = 0).
  - Personalized LTV2_h limits that are strictly below the headline 85% cap, and that vary with the borrower’s first mortgage LTV1_h.

- Finding 7 (as summarized in the source):
  - To compensate for the elevated default probability of secondary mortgages, their regulatory LTV limit should be:
    1. strictly lower than the headline LTV limit of 85 percent; and
    2. differentiated by the borrower’s first mortgage LTV – whether it is below or above 70 percent.

*Source: 5.2 Micro-Calibration Exercise, wpiea2023227-print-pdf*

### 5.3   Final Remarks on Secondary Mortgage LTV Regulation

### 5.3   Final Remarks on Secondary Mortgage LTV Regulation

### Key empirical findings
- Secondary mortgages were historically issued with relatively high LTV ratios, often at least 80 percent.
- Secondary mortgages have lifetime PD rates significantly higher than those of single loans.
- The mere issuance of a secondary mortgage increases the corresponding first loan's credit risk (negative externality).
- Comparison of calibrated personalized LTV limits to actual historical LTVs (2012-19) shows a weak or lacking positive correlation between actual LTV2h and calibrated LTV2h limits (Figure 17(a)).
- Around 15 percent of all secondary mortgages should have been issued with lower LTV ratios compared with the calibrated personalized limits (represented by the red triangular area above the 45◦ angle).
- Panel (b) of Figure 17 reveals no correlation between actual secondary loan LTV ratio and corresponding first mortgage cLTV ratio; around 20 percent of loans throughout 2012-19 were granted too-high LTV ratios compared with the new regulation of 2022 (red rectangular area).
- Market behavior indicates many borrowers took secondary mortgages with relatively low LTVs in some cases (consistent with stringent personal limits or borrower choice), and many others took secondary mortgages with high LTVs even when first mortgages had LTV above 70 percent.

### Calibration approach and robustness checks
- Baseline calibration assumed lifetime ECLs and ∆ = 30% and used an objective function comparing ECLs of two loans to a single hypothetical mortgage (equation (8)).
- An alternative, laxer calibration equalized only the ECL of the secondary loan to the hypothetical single-mortgage case:
  - ECL2h(LTV2h, LTV1h) = ECLHh.
  - This alternative yields milder secondary LTV limits nearing 80 percent (Figure 18, Appendix A), closer to observed market practice.
  - The baseline approach is preferred because it accounts for the negative externality on the first mortgage; the alternative shows no clear negative relationship between first mortgage LTV and calibrated secondary LTV limit.

### Policy implications and recommendations
- The historical procyclicality and higher default risk of secondary mortgages imply a market failure to internalize these risks; this warrants restrictive regulation.
- Regulatory practice examples: Bank of Lithuania and regulators in Belgium, Ireland, Norway; Finland, Iceland, and Luxembourg have implicit similar regulations (exemptions for first-time buyers rather than explicit investor restrictions).
- Baseline calibration suggests a secondary mortgage LTV limit around 75 percent [67, 81] with a first mortgage LTV threshold of 70 percent.
- Bank of Lithuania enacted a 70 percent secondary mortgage LTV limit with a 50 percent first mortgage threshold:
  - 70 percent secondary LTV limit lies within the lower end of the estimated confidence interval.
  - 50 percent first-mortgage threshold is significantly lower than the 70 percent suggested by the model.
- Reasons for tighter statutory thresholds may include concerns beyond micro-level credit risk: wider impacts on housing credit market stability, market procyclicality, investor-driven boom and fire-sale risks, and social side effects on first-time buyers and young families.
- Macroprudential policy can target buy-to-let investors, but its potency is limited where a substantial share of investor purchases are funded with own funds (in Lithuania, only around half of housing transactions are financed with credit).
- Complementary fiscal measures recommended to curb housing demand:
  - Appropriately progressive property taxation.
  - Stamp duty taxes.
  - These fiscal tools can complement macroprudential measures to smooth the financial cycle.

### Relation to existing literature
- Findings that BBMs are effective in containing credit risk and boosting borrower resilience align with Gross and Población (2017), Jurča and others (2020), Giannoulakis and others (2023).
- DSTI calibration results differ quantitatively from Mihai and others (2018) and Nier and others (2019), but agree qualitatively on the nonlinear impact of DSTI cap on borrower default.
- The insight that secondary mortgages and multi-loan borrowers are riskier aligns with Kelly and O’Toole (2018) and Galán and Lamas (2019).
- Agent-based model results of Baptista and others (2016) and Tarne and others (2022) support the view that buy-to-let investors amplify credit and housing cycles and that differentiated BBMs for borrower classes can be welfare-improving.

### Limitations and directions for further research
- Strength: granular loan-level data enables precise evaluation of BBM instruments across market segments and borrower characteristics.
- Weakness: micro-level credit-risk framework is not general-equilibrium and does not capture wider feedback loops or economy-wide externalities.
- Suggested extensions:
  - Integrate loan-level lifetime credit risk framework into a micro-macro setup (e.g., Gross and Población (2017)).
  - Build a semi-structural framework with a full-fledged banking sector and macroeconomic block (similarities to Budnik and others (2020, 2023)) to capture spillovers between the mortgage market and the rest of the economy.
- Monetary policy context matters: analysis used low-interest-rate environment data on the cusp of changing monetary policy. Rapidly increasing interest rates and eroding purchasing power could change conclusions about appropriateness of DSTI and stressed DSTI limits; contingent macroprudential frameworks tied to monetary policy stance could be considered.

### Concluding summary
- Secondary mortgages display higher default probability and impose negative externalities on first mortgages; market behavior historically failed to internalize these risks.
- Baseline calibration supports a tighter secondary mortgage LTV limit (around 75 percent [67, 81]) with a 70 percent first-mortgage threshold, while Bank of Lithuania’s enacted 70 percent secondary and 50 percent first-mortgage thresholds err on the side of greater prudence given macro-level concerns.
- Complementary fiscal measures targeting residential real estate demand can enhance the effectiveness of macroprudential regulation in addressing investor-fueled housing market imbalances.

*Source: 5.3 Final Remarks on Secondary Mortgage LTV Regulation (wpiea2023227-print-pdf).*

### References

### wpiea2023227-print-pdf - References

### References coverage
- Lists empirical, modelling, and methodological literature on macroprudential policy, borrower-based measures, housing markets, mortgage default, and PD estimation, including working papers and journal articles by authors such as Acharya et al. (2022); Alam et al. (2019); Ampudia et al. (2021); Araujo et al. (2020); Baptista et al. (2016); Biljanovska et al. (2023); Brandao-Marques et al. (2020); Cerutti et al. (2017); Ferrero et al. (2022); Mendicino (2012); Mihai et al. (2018); Nier et al. (2019); Poghosyan (2019); Valderrama et al. (2023); and many country- and central bank-specific studies.
- Topics in the reference list include:
  - The effectiveness and transmission of macroprudential policies and borrower-based measures (oLTV, oDSTI, oDTI, cDSTI, cDSTI*, etc.).
  - Agent-based models, DSGE and integrated micro-macro simulation models for housing and mortgage markets.
  - Empirical evidence from loan-level data, cross-country analyses, and country case studies (including Lithuania, Spain, Portugal, Baltic countries).
  - ROC/AUROC methodology for model discrimination and validation (Mandrekar, 2010).

### Appendix A — Tables and Figures (key model estimation outputs)
- Table 5: One-Year-Ahead PD Estimation Results: Full Model (Models 1–3)
  - Observations: 4,842,974 (for Model 1, Model 2, Model 3).
  - AUROC: Model 1: 0.9052; Model 2: 0.9050; Model 3: 0.9038.
  - Selected coefficient magnitudes (coefficient (standard error)):
    - (Intercept): −7.08 (0.21) ∗∗∗; −7.10 (0.21) ∗∗∗; −7.07 (0.21) ∗∗∗.
    - Residual maturity: 0.01 (0.00) ∗∗∗ (all models).
    - Has interest rate: 0.25 (0.20); 0.26 (0.20); 0.19 (0.20).
    - Interest rate: 0.08 (0.00) ∗∗∗; 0.09 (0.00) ∗∗∗; 0.09 (0.00) ∗∗∗.
    - Income not reported: 2.01 (0.05) ∗∗∗ (all models).
    - Income group 1: 1.77 (0.04) ∗∗∗ (reported as 1.77 in Models 2–3; Model 1 shows "11.77(0.04)" in source—preserve as presented).
    - HH credit history (3 years): 2.52 (0.01) ∗∗∗; 2.52 (0.01) ∗∗∗; 2.55 (0.01) ∗∗∗.
    - Loan is delinquent for (60, 90) d.: 2.87 (0.02) ∗∗∗ (all models).
    - Annual real GDP growth: −0.02 (0.01) ∗ (all models).
    - Unemployment rate: 0.04 (0.00) ∗∗∗ (all models).
    - Annual inflation: 0.04 (0.00) ∗∗∗ (all models).
    - Has oLTV: −1.21 (0.02) ∗∗∗ (all models).
    - oLTV: 0.00 (0.00) ∗∗∗ (all models).
    - Has oDSTI: −0.82 (0.05) ∗∗∗ (Model 1); related oDSTI cubic spline terms listed (oDSTI cub1: 0.70 (0.03) ∗∗∗; oDSTI cub2: 0.96 (0.10) ∗∗∗; oDSTI cub3: 0.73 (0.02) ∗∗∗).
    - Has oDSTI*: −0.68 (0.05) ∗∗∗ with corresponding oDSTI* cubic spline terms (oDSTI* cub1: 0.61 (0.03) ∗∗∗; oDSTI* cub2: 0.67 (0.10) ∗∗∗; oDSTI* cub3: 0.65 (0.02) ∗∗∗).
    - Has oDTI: −0.73 (0.04) ∗∗∗ with oDTI cubic spline terms (oDTI cub1: 0.71 (0.02) ∗∗∗; oDTI cub2: 1.15 (0.07) ∗∗∗; oDTI cub3: 0.73 (0.02) ∗∗∗).
  - Significance notation: ∗∗∗ p < 0.001; ∗∗ p < 0.01; ∗ p < 0.05. Coefficients in bold have p-values lower than 10^−20.
  - Note: Terms oD(S)TI(∗) cub1-3 refer to cubic spline polynomials, as in Mihai and others (2018).

- Table 6: One-Year-Ahead PD Estimation Results: Full Model (c·– current) (Models 1–2)
  - Observations: 4,842,974 (both models).
  - AUROC: Model 1: 0.9125; Model 2: 0.9121.
  - Selected coefficient magnitudes (coefficient (standard error)):
    - (Intercept): −6.49 (0.21) ∗∗∗ (both models).
    - Residual maturity: 0.01 (0.00) ∗∗∗ (both models).
    - Has interest rate: 0.40 (0.20) ∗ (Model 1); 0.39 (0.20) (Model 2).
    - Interest rate: 0.08 (0.00) ∗∗∗; 0.09 (0.00) ∗∗∗.
    - Secondary mortgage (chron.): 0.09 (0.01) ∗∗∗; 0.11 (0.01) ∗∗∗.
    - Has other mortgages: 0.07 (0.01) ∗∗∗; 0.08 (0.01) ∗∗∗.
    - Adults and HH members ratio: −0.11 (0.02) ∗∗∗; −0.10 (0.02) ∗∗∗.
    - Income not reported: 1.29 (0.05) ∗∗∗; 1.28 (0.05) ∗∗∗.
    - Income group 1: 1.24 (0.04) ∗∗∗ (both models).
    - HH credit history (3 years): 2.44 (0.01) ∗∗∗; 2.45 (0.01) ∗∗∗.
    - Loan is delinquent for (60, 90) d.: 2.83 (0.02) ∗∗∗ (both models).
    - Annual real GDP growth: −0.02 (0.01) ∗ (both models).
    - Unemployment rate: 0.03 (0.00) ∗∗∗ (both models).
    - Annual inflation: 0.03 (0.00) ∗∗∗ (both models).
    - Has oLTV: −1.24 (0.02) ∗∗∗; −1.23 (0.02) ∗∗∗.
    - oLTV: 0.00 (0.00) ∗∗∗ (both models).
    - Has cDSTI: −1.64 (0.08) ∗∗∗ with cDSTI cubic spline terms (cDSTI cub1: 1.51 (0.04) ∗∗∗; cDSTI cub2: 1.53 (0.12) ∗∗∗; cDSTI cub3: 1.55 (0.03) ∗∗∗).
    - Has cDSTI*: −1.51 (0.07) ∗∗∗ with cDSTI* cubic spline terms (cDSTI* cub1: 1.40 (0.04) ∗∗∗; cDSTI* cub2: 1.18 (0.12) ∗∗∗; cDSTI* cub3: 1.46 (0.03) ∗∗∗).
  - Note: Terms cDSTI(∗) cub1-3 refer to cubic spline polynomials, as in Mihai and others (2018).

- Figure 18: Personalized Calibration of LTV2h — Alternative Objective Function
  - Calibration maps personalized LTV2h limits to first loan LTV1h ratios under different calibration horizons (one-year and lifetime) and house price drop assumptions: −15%, −20%, −25%, −30%.
  - Aggregate calibration results shown by subsets of households by LTV1h with explicit aggregated LTV2 limits and 90% confidence intervals:
    - For cLTV1 > 70: values presented as 83 [82, 84]; 81 [79, 82]; 79 [76, 81]; 77 [73, 80] (one-year horizon); and 84 [83, 84]; 82 [81, 83]; 81 [79, 82]; 80 [77, 82] (lifetime horizon).
    - For cLTV1 ∈ (0,70]: 84 [83, 84]; 82 [80, 83]; 80 [78, 82]; 79 [76, 81] (one-year); and 84 [83, 84]; 83 [82, 84]; 82 [80, 83]; 81 [79, 82] (lifetime).
    - For cLTV1 > 0: 83 [83, 84]; 82 [80, 83]; 80 [77, 82]; 78 [75, 81] (one-year); and 84 [83, 84]; 83 [81, 84]; 82 [79, 83]; 81 [78, 82] (lifetime).
  - Note: Objective function alternative used: ECL2h(LTV2h, LTV1h) = ECLHh. Vertical lines denote averaged LTV2 limits; light gray areas denote 90 percent confidence intervals.

### Appendix B — Model validation (ROC/AUROC details and cross-validation)
- Validation method:
  - Receiver Operating Characteristic (ROC) curve analysis used to measure discriminatory power for the dichotomous dependent variable (loan default “1” vs. non-default “0”).
  - True positive rate (TPRγ) and false positive rate (FPRγ) defined as:
    - TPRγ := TPγ / P = Number of correctly specified “1” cases / Total number of “1” cases.
    - FPRγ := FPγ / N = Number of incorrectly specified “0” cases / Total number of “0” cases.
  - ROC curve plots FPRγ (x-axis) against TPRγ (y-axis) for each threshold γ.
  - Area under the ROC curve (AUROC) computed as summary measure, with possible values in [0,1]. Statement: "70 percent level usually deemed satisfactory."
- Five-fold cross-validation procedure to avoid overfitting:
  - Model iteratively reestimated on each of five randomly selected training subsamples; AUROC obtained for each testing subsample.
  - Reported AUROC measures across folds (Figure 19):
    - Fold 1 AUROC: 0.9088
    - Fold 2 AUROC: 0.9028
    - Fold 3 AUROC: 0.9038
    - Fold 4 AUROC: 0.9048
    - Fold 5 AUROC: 0.9058
    - Average AUROC: 0.9052
  - Conclusion: The model discriminates nonperforming loans well (AUROC > 90 percent) and shows little variance across folds, indicating stability.

### Appendix C — Iso-impact curves and micro-level algorithm for policy tightening
- Definitions: iso-impact curves characterize combinations of borrower-based measure limits that produce the same percentage reduction in mortgage lending volume (∆D%).
  - When tightening oDSTI and maturity with oDSTI* fixed at 50:
    - Iso-impact_oDSTI(γ) = { {oDSTI, oDSTI*, M} | ∆D = γ, oDSTI* = 50 }.
  - When tightening oDSTI* and maturity with oDSTI fixed at 40:
    - Iso-impact_oDSTI*(γ) = { {oDSTI, oDSTI*, M} | ∆D = γ, oDSTI = 40 }.
  - Lending-volume reduction:
    - ∆D = 1 − (∑_{k=1}^n Ď_k) / (∑_{k=1}^n D_k), where D_k are initial loan amounts and Ď_k are post-intervention loan amounts.
- Assumptions for policy tightening cases (preserving exact numeric limits):
  - Considering policy tightening options with limits: M ≤ 30, oDSTI ≤ 40 and oDSTI* ≤ 50.
  - Initial mortgages: D_k, oDSTI_k ≤ 40%, oDSTI*_k ≤ 50%, M_k ≤ 30 years.
  - Household individual refusal or adjustment rule:
    - No household will take the mortgage if its initial size D_k would reduce more than 10 percent or its DSTI ratio would increase more than 10 p.p. due to the new regulatory framework.
    - Individual limits implied: D_k' = 0.9 D_k; oDSTI_k' = min{ oDSTI_k + 10 p.p., oDSTI }.
- Algorithm to obtain post-intervention mortgage features (Ď_k, ôDSTI_k, ôDSTI*_k, ˆM_k):
  - If M_k > M, set limiting maturity M_{0,k} = M, compute oDSTI_{0,k} and oDSTI*_{0,k} under M_{0,k}:
    - (I) If oDSTI_{0,k} ≤ oDSTI and oDSTI*_{0,k} ≤ oDSTI*, mortgage granted under shorter maturity M_{0,k} with initial amount D_k unchanged.
    - (II) If oDSTI_{0,k} > oDSTI or oDSTI*_{0,k} > oDSTI*, reduce D_k to D_{0,k} until oDSTI_{0,k} and oDSTI*_{0,k} are within limits. If D_{0,k} ≤ D_k (i.e., cannot satisfy), mortgage not issued.
  - If M_k ≤ M:
    - (I) If oDSTI_k ≤ oDSTI and oDSTI*_k ≤ oDSTI*, mortgage unchanged (D_k unchanged).
    - (II) If oDSTI_k > oDSTI or oDSTI*_k > oDSTI*, extend maturity to M_{0,k} until recalculated DSTI ratios oDSTI_{0,k} and oDSTI*_{0,k} are within limits:
      - If M_{0,k} ≤ M, mortgage granted under shorter maturity M_{0,k} and higher DSTI ratios with D_k unchanged.
      - If M_{0,k} > M, reduce D_k to D_{0,k} until oDSTI_k and oDSTI*_k are within limits with limiting maturity horizon M; if D_{0,k} ≤ D_k, mortgage not issued.
- Practical implication:
  - The iso-impact framework maps policy parameter combinations (maturity cap, oDSTI, oDSTI*) into aggregate lending-volume effects (∆D%) while accounting for micro-level household constraints (maximum 10 percent reduction in initial loan size or maximum 10 p.p. increase in DSTI tolerance).

*Micro-Assessment of Macroprudential Borrower-Based Measures in Lithuania — Working Paper No. WP/2023/227*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023227-print-pdf.pdf_