## _wp1226 ## Source details **Canonical URL:** [_wp1226](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp1226.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp1226.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp1226.pdf.json) --- ### Model and calibration - Extension of a standard incomplete market (SIM) model that introduces housing, house price risk, and mortgages. - Mortgages: - Modeled as long-term loans that can be refinanced or enter into default in any period. - Collateralized by a house. - No restriction on the initial down payment other than non-negativity in the benchmark. - Interest rates set endogenously and depend on the default probability. - House price and income processes: - House price: log(p_{t+1}) = (1−ρ_p) log(p̄) + ρ_p log(p_t) + ν_t. - Income (pre-retirement): log(y_t) = z_t + f_t + ε_t, with z_t = ρ_z z_{t−1} + e_t, ε ~ N(0, σ^2_ε), and (e, ν) jointly normal with correlation ρ_{e,ν}. - Housing specifics: - Agent must live in a house if he owns one and may own up to one house. - Purchase cost: ξ_B p_t; selling cost: ξ_S p_t. - Renting cost assumed constant r; disutility from renting denoted θ. - Mortgage features and lender pricing: - Constant payment b > 0 for n = T − t years; prepayment allowed by paying q^*(n). - Default: agent hands house to lender; house sold at p_t(1−ξ_S); income garnishment π(b,y,p,n) = min{max{y−φ,0}, q^*(n)b − p}. - Home-owner transfer: ω(b′,p,n) = max{0, (1−χ_n)/(1+ r̄) [E[p′|p](1−ξ_S) − q^*(n−1) max{b′,0}]}. - Mortgages priced by risk-neutral lenders with opportunity cost r. - Calibration (U.S. data, annual): - Ages: enter at 22, retire at 62, die no later than 82. - Survival rates: Centers for Disease Control and Prevention. - Initial asset b_0 matches mean net asset at age 22 in 2004 SCF. - Stochastic parameters targeted: - σ^2_ν = 0.302; ρ_{e,ν} = 0.115; ρ_p = 0.970. - σ^2_ε = 0.0630; σ^2_e = 0.0166; ρ_z = 0.990. - Targeted moments: σ_{Δp} = 0.115 and ρ_{Δp,Δy} = 0.027 from Campbell and Cocco (2003). - Other parameter values (selected): - r = 2%; γ = 2.000; ξ_B = 0.025; ξ_S (household) = 0.070; ξ_S (bank) = 0.220. - φ = ∞ for benchmark (no garnishment); r (rent) = 0. - Calibrated to match home ownership rate, mean price-to-income ratio, median home equity: θ = 0.105; p̄ = 5.699; β = 0.945. - Numerical solution: - b grid: 300 evenly spaced points between −20 and 20, and 200 between −120 and −20. - Shock grids: permanent income 15 points, transitory income 5 points, house price 11 points. - Simulate 20,000 agents; population weights from Census. ### Empirical fit and model validation - Benchmark moments (agents younger than 62): - Home ownership rate (%) Data 64.5 | Model 63.1 - Mean price-to-income ratio 2.6 | Model 2.6 - Median net-worth-to-income ratio 1.4 | Model 1.4 - Mean equity-to-price ratio (%) 50.0 | Model 65.7 - Default and mortgage dynamics: - Default rate in model: 0.6% (close to 0.5% benchmark in Jeske et al. (2010)). - Endogenous down payment distribution matches empirical origination (2000–2009) closely. - 51% of mortgages are less than five years old (agents use prepayment option often). - Only 6% of mortgages in default were acquired in the previous period (defaults accumulate over several periods of house price declines). ### Insurance, consumption, and inequality - Consumption inequality and life cycle: - Consumption inequality increases substantially over the life cycle but less than earnings inequality; the increase is approximately linear. - Insurance coefficients (μ_x = 1 − cov(Δ log(c), x) / var(x)): - Table 3 selected values: - Persistent shock (%) Benchmark 25.7 | No housing 25.3 | Kaplan and Violante 27.0, 30.0 | Blundell et al. 36.0 (9.0) - Transitory shock (%) Benchmark 81.9 | No housing 82.9 | Kaplan and Violante 82.0, 93.0 | Blundell et al. 95.0 (4.0) - House price shock (%) Benchmark 98.4 - Findings: - Introducing housing does not significantly change average insurance coefficients relative to a SIM without housing, but increases coefficients for younger agents. - Using the insurance coefficients proposed by Blundell et al. (2008), "98% of the variance of house price shocks does not translate into changes in consumption." - Cross-sectional variance of log consumption increases over the life cycle; most consumption inequality is explained by earning shocks rather than house price shocks. - Marginal propensity to consume housing wealth: - Findings support a low marginal propensity to consume housing wealth, consistent with agents’ need to consume housing services. ### Policy experiments — minimum down payment requirements - Experiments: minimum down payments of 15%, 20%, 25% (benchmark non-negative down payment). - Table 4 outcomes (perfectly elastic supply, p̄ fixed): - Benchmark Default rate (%) 0.6 | Home ownership (%) 63.1 - ≥15%: Default rate 0.4% | Home ownership 62.9% - ≥20%: Default rate 0.3% | Home ownership 62.5% - ≥25%: Default rate 0.2% | Home ownership 61.8% - Dynamics: - About half of long-run decline in default rate observed in implementation year; most remaining decline occurs over next 10 years. - For the highest requirement (25%), takes six years for home ownership to decline 1.3 percentage points to new long-run level. - Welfare and distributional effects: - Majority of agents benefit from minimum down payment requirements; welfare measured as consumption compensation (percent) shows positive gains for most percentiles. - Mechanism: higher down payment increases cost of defaulting → reduces default probability → lowers borrowing cost → allows homeowners to refinance at lower rates. Prospective buyers are typically worse off because buying becomes more difficult. - Housing supply response (upper bounds for long-run decline in mean house price when ownership held constant): - Minimum down payment = 15%: p̄ decline, % = 0.0 (perfectly elastic), 0.3 (intermediate), 0.7 (perfectly inelastic). - Minimum down payment = 20%: p̄ decline, % = 0.0, 1.0, 2.0 respectively. - Minimum down payment = 25%: p̄ decline, % = 0.0, 3.0, 4.9 respectively. - Rule of thumb: on average, a 1% decline in p̄ increases home ownership by 0.3 percentage points. - Ex-ante welfare declines from minimum down payments are smaller (or even slightly positive when p̄ declines) because agents entering without houses benefit from cheaper housing when p̄ falls. ### Policy experiments — income garnishment (reducing φ) - Benchmark φ = ∞ (no garnishment). Experiments with φ = 1.45, φ = 0.63, φ = 0.25. - Interpretation of φ (relative to median consumption): - φ = 1.45 → post-garnishment consumption = 100% of median consumption. - φ = 0.63 → 43% of median consumption. - φ = 0.25 → 17% of median consumption. - Table 6 outcomes (p̄ fixed unless otherwise noted): - Benchmark: Default rate 0.6% | Home ownership 63.1% | Median down payment 19.0% - φ = 1.45: Default rate 0.6% | Home ownership 63.7% | Median down payment 16.8% - φ = 0.63: Default rate 0.4% | Home ownership 67.4% | Median down payment 9.0% - φ = 0.25: Default rate 0.1% | Home ownership 69.8% | Median down payment 6.6% - Key quantitative effects: - Garnishing income in excess of 43% of median consumption for one year (φ = 0.63) reduces defaults by 30% (from 0.6% to 0.4%). - Median down payment reduced from 19.0% (benchmark) to 16.8% (φ = 1.45), 9.0% (φ = 0.63), 6.6% (φ = 0.25). - Home ownership increases up to 69.8% (φ = 0.25, p̄ fixed). - Potential house price increases due to garnishment up to 27.4% (φ = 0.25) if supply perfectly inelastic. - Insurance and consumption smoothing under garnishment (Table 7): - Var(log C) remains 0.4 across φ values. - Persistent-income-shock insurance coefficient (%) Benchmark 25.7 | φ = 1.45 24.9 | φ = 0.63 23.6 | φ = 0.25 23.2 - Transitory-income-shock insurance coefficient (%) Benchmark 81.9 | φ = 1.45 81.6 | φ = 0.63 80.3 | φ = 0.25 80.3 - Price-shock insurance coefficient (%) Benchmark 98.4 | small changes across φ (98.4, 98.4, 98.1) - Conclusion: strengthening garnishment has minimal effects on agents’ ability to self-insure; consumption smoothing is essentially unchanged. - Distributional and timing effects: - Announcement effect: when garnishment is announced to take effect one period after announcement and applies to existing loans, a spike in defaults occurs in announcement period as agents who would default prefer to do so before garnishment. - After initial spike, default rate falls drastically; in harshest case (φ = 0.25) default rate falls to zero. - Home ownership increases over time; for φ = 0.25 it takes up to 10 years for home ownership to rise 6.6 percentage points to long-run level. - Almost all agents benefit ex-ante from imposing income garnishment (consumption-equivalent welfare gains distribution shifted positive), but agents very likely to default are harmed when garnishment applies to existing debt. ### Housing supply response to garnishment (Table 8) - Reported p̄ increases and associated outcomes under supply scenarios: - φ = 1.45: p̄ increase, % = 0.0, 1.0, 2.0; corresponding home ownership 63.7%, 63.4%, 63.1%; ex-ante welfare gain (%) 0.16, 0.13, 0.10. - φ = 0.63: p̄ increase, % = 0.0, 9.4, 15.8; home ownership 67.4%, 65.0%, 63.1%; ex-ante welfare gain (%) 0.64, 0.34, 0.15. - φ = 0.25: p̄ increase, % = 0.0, 13.9, 27.4; home ownership 69.8%, 66.3%, 63.1%; ex-ante welfare gain (%) 0.85, 0.41, 0.04. - Interpretation: - Garnishment can imply large increases in house prices if housing supply does not adjust, which deteriorates affordability and can wash out welfare gains from garnishment. ### Mechanisms and interpretation - Minimum down payment requirements: - Raise borrower equity at origination → lower default probabilities → lower borrowing costs for homeowners → homeowners on average benefit; prospective buyers face higher saving requirements. - Aggregate house price response matters: if supply is inelastic and p̄ falls to keep ownership constant, welfare effects differ. - Income garnishment: - Increases cost of defaulting → lenders can offer mortgages at lower interest rates and allow lower down payments → borrowing constraints relax → home ownership and house prices can increase substantially if supply does not adjust. - Limited impact on consumption smoothing because (i) defaults are rare and concentrated among agents hit by large unexpected house price declines, (ii) debt forgiveness is not well targeted to low-income agents, and (iii) average consumption response to house price shocks is small. ### Main quantitative policy findings (exact reported values) - Minimum down payment experiments: - Default rate falls from 0.6% (benchmark) to 0.4% (≥15%), 0.3% (≥20%), 0.2% (≥25%). - Home ownership falls from 63.1% to 62.9% (≥15%), 62.5% (≥20%), 61.8% (≥25%) when assuming perfectly elastic supply (p̄ fixed). - Upper bounds for long-run decline in mean house price implied by minimum down payments: 0.7% (15%), 2.0% (20%), 4.9% (25%) when ownership held constant (perfectly inelastic supply). - Income garnishment experiments: - Garnishing income in excess of 43% of median consumption for one year (φ = 0.63) reduces defaults by 30% (from 0.6% to 0.4%). - Median down payment reduced from 19.0% (benchmark) to 16.8% (φ = 1.45), 9.0% (φ = 0.63), 6.6% (φ = 0.25). - Home ownership increases up to 69.8% (φ = 0.25, p̄ fixed). - Potential house price increases due to garnishment up to 27.4% (φ = 0.25) if supply perfectly inelastic. ### Conclusions - The life-cycle SIM model with house price risk and endogenous mortgages produces plausible implications for mortgage borrowing and default behavior. - Incorporating housing does not significantly change average income insurance coefficients from SIM models without housing, but raises insurance coefficients for young agents. - Consumption response to house price shocks is minimal (house price shock insurance coefficient 98.4% in benchmark). - Both policies studied—minimum down payment requirements and income garnishment—reduce mortgage default rates and benefit a majority of agents in baseline scenarios: - Down payment requirements reduce defaults by increasing borrower equity. - Garnishment reduces defaults by increasing the cost of default, while allowing lower down payments and expanding borrowing, which raises home ownership. - Aggregate house price response (housing supply elasticity) crucially affects welfare implications and affordability outcomes for both policies. *Source: IMF Working Paper _wp1226 (excerpted content provided).* ### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ### _wp1226 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ### Model and calibration - Proposes an extension of a standard incomplete market (SIM) model that introduces housing, house price risk, and mortgages. - Mortgages: - Modeled as long-term loans that can be refinanced or enter into default in any period. - Collateralized by a house. - No restriction on the initial down payment other than non-negativity in the benchmark. - Interest rates set endogenously and depend on the default probability. - Calibration targets: - Income and house price shocks. - Median net-worth. - Mean house price-to-income ratio. - Home ownership rate in the U.S. ### Empirical fit and model validation - The model generates an endogenous distribution of down payments similar to its empirical counterpart. - Predicts a life-cycle profile of home ownership and a mortgage default rate similar to their empirical counterparts. - Endogenous borrowing behavior in the model is plausible and important for policy experiments. ### Insurance, consumption, and inequality findings - Consumption inequality: - Increases substantially over the life cycle but less than earnings inequality. - The increase is approximately linear. - Insurance coefficients: - Average insurance coefficients for income shocks are very close to the coefficients obtained in the authors’ model without housing. - These average coefficients are very close to the ones reported by Kaplan and Violante (2010) from their SIM model without housing. - Incorporating housing increases insurance coefficient values for younger agents. - Housing narrows the gap between SIM-model implications and the data regarding life-cycle insurance profiles. - Role of house price shocks: - House price shocks are not an important source of consumption inequality (consistent with Li and Yao, 2007). - Using the insurance coefficients proposed by Blundell et al. (2008), "98% of the variance of house price shocks does not translate into changes in consumption." - Findings support a low marginal propensity to consume housing wealth, consistent with agents’ need to consume housing services. ### Policy experiments and main quantitative results - Two policy experiments studied: 1. Requiring a minimum down payment (benchmark has only non-negative down payment). 2. Allowing lenders to garnish defaulters’ income. - Minimum down payment experiment (as reported in the text): - "Requiring a minimum down payment of 15% of the house value reduces defaults on mortgages by 30%." - The same sentence in the source continues with an effect on home ownership rate but the provided content ends before that effect is fully reported. ### Relevance to policy debates - Context: - Qualified Residential Mortgage rules proposed by regulators in the U.S. would make higher down payments necessary to allow originators to fully securitize and sell the mortgage, potentially lowering interest rates for borrowers. - Critics argue such rules could have significant negative effects on the home ownership rate. - Proposals to allow mortgage creditors to take defaulters’ assets or income are part of the policy discussion. - This paper’s findings inform the potential effects of these mortgage default prevention policies by: - Quantifying the impact of a binding minimum down payment on defaults. - Assessing how housing in a life-cycle incomplete-markets model affects insurance and consumption dynamics relevant for welfare and policy evaluation. *Source: _wp1226 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (PDF).* ### 0.2 percentage points (if the aggregate house price level does not adjust), and may cause ### _wp1226 - 0.2 percentage points (if the aggregate house price level does not adjust), and may cause ### Model structure and key features - Life-cycle SIM model (agents live up to T periods, work until age W ≤ T) with: - Housing consumption in addition to non-durable goods. - Endogenous mortgage borrowing determined by lenders’ zero-profit conditions. - House price process: log(p_{t+1}) = (1−ρ_p) log(p̄) + ρ_p log(p_t) + ν_t. - Income process before retirement: log(y_t) = z_t + f_t + ε_t, with z_t = ρ_z z_{t−1} + e_t, ε ~ N(0, σ^2_ε), and (e, ν) jointly normal with correlation ρ_{e,ν}. - Housing specifics: - Agent must live in a house if he owns one and may own up to one house. - House purchase cost: ξ_B p_t; selling cost: ξ_S p_t. - Renting cost assumed constant r; disutility from renting denoted θ. - Mortgages: - Constant payment b > 0 for n = T − t years; prepayment allowed by paying q^*(n). - Default: agent hands house to lender; house sold at p_t(1−ξ_S); potential income garnishment π(b,y,p,n) = min{max{y−φ,0}, q^*(n)b − p}. - Home-owner transfer: ω(b′,p,n) = max{0, (1−χ_n)/(1+ r̄) [E[p′|p](1−ξ_S) − q^*(n−1) max{b′,0}]}. - Mortgages priced by risk-neutral lenders with opportunity cost r. ### Calibration (U.S. data, annual periods) - Ages: enter at 22, retire at 62, die no later than 82. - Survival rates: Centers for Disease Control and Prevention. - Initial asset position b_0 matches mean net asset at age 22 in 2004 SCF. - Stochastic parameters targeted to micro estimates: - σ^2_ν = 0.302; ρ_{e,ν} = 0.115; ρ_p = 0.970. - σ^2_ε = 0.0630; σ^2_e = 0.0166; ρ_z = 0.990. - Targeted moments: σ_{Δp} = 0.115 and ρ_{Δp,Δy} = 0.027 from Campbell and Cocco (2003). - Other parameter values (selected): - r = 2%; γ = 2.000; ξ_B = 0.025; ξ_S (household) = 0.070; ξ_S (bank) = 0.220. - φ = ∞ for benchmark (no garnishment); r (rent) = 0. - Calibrated to match home ownership rate, mean price-to-income ratio, median home equity: θ = 0.105; p̄ = 5.699; β = 0.945. - Numerical solution details: - b grid: 300 evenly spaced points between −20 and 20, and 200 between −120 and −20. - Shock grids: permanent income 15 points, transitory income 5 points, house price 11 points. - Simulate 20,000 agents; population weights from Census. ### Benchmark model fit and mortgage behavior - Table 2 moments (agents younger than 62): - Home ownership rate (%) Data 64.5 | Model 63.1 - Mean price-to-income ratio 2.6 | Model 2.6 - Median net-worth-to-income ratio 1.4 | Model 1.4 - Mean equity-to-price ratio (%) 50.0 | Model 65.7 - Default rate in model: 0.6% (close to 0.5% benchmark in Jeske et al. (2010)). - Endogenous down payment distribution matches empirical distribution for origination (2000–2009) closely. - Mortgage tenure and prepayment: - 51% of mortgages are less than five years old (agents use prepayment option often). - Only 6% of mortgages in default were acquired in the previous period (defaults accumulate over several periods of house price declines). ### Self-insurance and insurance coefficients - Insurance coefficient definition: μ_x = 1 − cov(Δ log(c), x) / var(x), interpreted as share of shock variance not transmitted to consumption growth. - Table 3 (selected values): - Persistent shock (%) Benchmark 25.7 | No housing 25.3 | Kaplan and Violante 27.0, 30.0 | Blundell et al. 36.0 (9.0) - Transitory shock (%) Benchmark 81.9 | No housing 82.9 | Kaplan and Violante 82.0, 93.0 | Blundell et al. 95.0 (4.0) - House price shock (%) Benchmark 98.4 - Findings: - Introducing housing does not significantly change average insurance coefficients relative to a SIM without housing, but increases coefficients for younger agents. - Response of consumption to house price shocks is minimal: 98.4% of variance of house price shocks does not translate into changes in consumption. - Cross-sectional variance of log consumption increases over the life cycle; most consumption inequality is explained by earning shocks rather than house price shocks. ### Effects of minimum down payment requirements - Experiments: minimum down payments of 15%, 20%, 25% (compared to benchmark with non-negative down payment). - Table 4 summary: - Benchmark Default rate (%) 0.6 | Home ownership (%) 63.1 - ≥15%: Default rate 0.4% | Home ownership 62.9% - ≥20%: Default rate 0.3% | Home ownership 62.5% - ≥25%: Default rate 0.2% | Home ownership 61.8% - Dynamics after imposition: - About half of long-run decline in default rate observed in implementation year; most remaining decline occurs over next 10 years. - For the highest requirement (25%), takes six years for home ownership to decline 1.3 percentage points to new long-run level. - Welfare and distributional effects: - Majority of agents benefit from minimum down payment requirements; welfare measured as consumption compensation (percent) shows positive gains for most percentiles. - Mechanism: higher down payment increases cost of defaulting → reduces default probability → lowers borrowing cost → allows homeowners to refinance at lower rates. Prospective buyers are typically worse off because buying becomes more difficult. - Interest rates and borrowing: - Minimum down payment requirement decreases interest rate spread for given borrower down payment choices (illustrated by Figure 9). - Housing supply response scenarios (Table 5): - For minimum down payment = 15%: p̄ decline, % = 0.0 (perfectly elastic), 0.3 (intermediate), 0.7 (perfectly inelastic). - For minimum down payment = 20%: p̄ decline, % = 0.0, 1.0, 2.0 respectively. - For minimum down payment = 25%: p̄ decline, % = 0.0, 3.0, 4.9 respectively. - Rule of thumb from calibration: on average, a 1% decline in p̄ increases home ownership by 0.3 percentage points. - Ex-ante welfare: declines from minimum down payments are smaller (or even slightly positive when p̄ declines) because agents entering without houses benefit from cheaper housing when p̄ falls. ### Effects of income garnishment (reducing φ) - Benchmark φ = ∞ (no garnishment). Experiments with φ = 1.45, φ = 0.63, φ = 0.25. - Interpretation: φ expressed relative to median consumption: - φ = 1.45 → post-garnishment consumption = 100% of median consumption. - φ = 0.63 → 43% of median consumption. - φ = 0.25 → 17% of median consumption. - Table 6 summary: - Benchmark: Default rate 0.6% | Home ownership 63.1% | Median down payment 19.0% - φ = 1.45: Default rate 0.6% | Home ownership 63.7% | Median down payment 16.8% - φ = 0.63: Default rate 0.4% | Home ownership 67.4% | Median down payment 9.0% - φ = 0.25: Default rate 0.1% | Home ownership 69.8% | Median down payment 6.6% - Key findings: - Garnishing defaulters’ income in excess of 43% of median consumption for one year (φ = 0.63) reduces mortgage defaults by 30% (from 0.6% to 0.4%). - Potential for garnishment reduces median down payment from 19% to 9% and can boost home ownership by up to 4.3 percentage points (if aggregate house price does not adjust). - Garnishment can increase house prices up to 16.1% (if home ownership does not adjust) in baseline experiment context. - Most agents benefit from garnishment because it relaxes borrowing constraints (allows lower down payments and lower interest rates); however, agents very likely to default are worse off when garnishment is applied to existing debt contracts. - Insurance and consumption smoothing under garnishment (Table 7): - Var(log C) remains 0.4 across φ values. - Persistent-income-shock insurance coefficient (%) Benchmark 25.7 | φ = 1.45 24.9 | φ = 0.63 23.6 | φ = 0.25 23.2 - Transitory-income-shock insurance coefficient (%) Benchmark 81.9 | φ = 1.45 81.6 | φ = 0.63 80.3 | φ = 0.25 80.3 - Price-shock insurance coefficient (%) Benchmark 98.4 | small changes across φ (98.4, 98.4, 98.1) - Conclusion: strengthening garnishment has minimal effects on agents’ ability to self-insure; consumption smoothing is essentially unchanged. - Distributional and timing effects: - Announcement effect: when garnishment is announced to take effect one period after announcement and applies to existing loans, a spike in defaults occurs in announcement period (agents who would default prefer to do so before garnishment). - After initial spike, default rate falls drastically; in the harshest case (φ = 0.25) default rate falls to zero. - Home ownership increases over time; for φ = 0.25 it takes up to 10 years for home ownership to rise 6.6 percentage points to long-run level. - Almost all agents benefit ex-ante from imposing income garnishment (consumption-equivalent welfare gains distribution shifted positive), but very likely defaulters (facing new garnishment on existing debt) can be harmed. ### Housing supply responses to garnishment (Table 8) - Perfectly elastic, intermediate, perfectly inelastic supply scenarios reported for each φ: - φ = 1.45: p̄ increase, % = 0.0, 1.0, 2.0; corresponding home ownership 63.7%, 63.4%, 63.1%; ex-ante welfare gain (%) 0.16, 0.13, 0.10. - φ = 0.63: p̄ increase, % = 0.0, 9.4, 15.8; home ownership 67.4%, 65.0%, 63.1%; ex-ante welfare gain (%) 0.64, 0.34, 0.15. - φ = 0.25: p̄ increase, % = 0.0, 13.9, 27.4; home ownership 69.8%, 66.3%, 63.1%; ex-ante welfare gain (%) 0.85, 0.41, 0.04. - Interpretation: - Garnishment can imply large increases in house prices if housing supply does not adjust, which deteriorates affordability and can wash out welfare gains from garnishment. ### Mechanisms and interpretation - Minimum down payment requirements: - Raise borrower equity at origination → lower default probabilities → lower borrowing costs for homeowners → homeowners on average benefit; prospective buyers face higher saving requirements. - Aggregate house price response matters: if supply is inelastic and p̄ falls to keep ownership constant, welfare effects differ. - Income garnishment: - Increases cost of defaulting → lenders can offer mortgages at lower interest rates and allow lower down payments → borrowing constraints relax → home ownership and house prices can increase substantially if supply does not adjust. - Limited impact on consumption smoothing because (i) defaults are rare and concentrated among agents hit by large unexpected house price declines, (ii) debt forgiveness is not well targeted to low-income agents, and (iii) average consumption response to house price shocks is small. ### Main quantitative policy findings (exact reported values) - Minimum down payment experiments: - Default rate falls from 0.6% (benchmark) to 0.4% (≥15%), 0.3% (≥20%), 0.2% (≥25%). - Home ownership falls from 63.1% to 62.9% (≥15%), 62.5% (≥20%), 61.8% (≥25%) when assuming perfectly elastic supply (p̄ fixed). - Upper bounds for long-run decline in mean house price implied by minimum down payments: 0.7% (15%), 2.0% (20%), 4.9% (25%) when ownership held constant (perfectly inelastic supply). - Income garnishment experiments: - Garnishing income in excess of 43% of median consumption for one year (φ = 0.63) reduces defaults by 30% (from 0.6% to 0.4%). - Median down payment reduced from 19.0% (benchmark) to 16.8% (φ = 1.45), 9.0% (φ = 0.63), 6.6% (φ = 0.25). - Home ownership increases up to 69.8% (φ = 0.25, p̄ fixed). - Potential house price increases due to garnishment up to 27.4% (φ = 0.25) if supply perfectly inelastic. ### Conclusions (as stated) - The life-cycle SIM model with house price risk and endogenous mortgages produces plausible implications for mortgage borrowing and default behavior. - Incorporating housing does not significantly change average income insurance coefficients from SIM models without housing, but raises insurance coefficients for young agents. - Consumption response to house price shocks is minimal. - Both policies studied—minimum down payment requirements and income garnishment—reduce mortgage default rates and benefit a majority of agents in baseline scenarios. - Down payment requirements reduce defaults by increasing borrower equity. - Garnishment reduces defaults by increasing the cost of default, while allowing lower down payments and expanding borrowing, which raises home ownership. - However, the aggregate house price response (housing supply elasticity) crucially affects welfare implications and affordability outcomes for both policies. *Source: IMF Working Paper _wp1226 (excerpted content provided).* ### References ### References ### Alphabetical listing - Aguiar, M. and Bils, M. 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