## wpiea2020089-print-pdf - 0.75 to 0.85. ## Source details **Canonical URL:** [wpiea2020089-print-pdf - 0.75 to 0.85.](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020089-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020089-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020089-print-pdf.pdf.json) --- ### Major findings - Long-run residential investment as a share of GDP increases from 3 to 5 percent of GDP in the model when real rates decline. - Empirical example: Sweden residential investment has risen from less than 2 percent after the housing crisis in the early 1990s to about 7 percent in 2017. - Main results: - The long-term output costs of all the macro-prudential actions in the study are moderate, regardless of whether the steady state has normal (mid-1990s) or elevated debt levels (the current state). - Short-term effects of macroprudential policy (MPP) depend critically on the initial debt level and the scope for central bank accommodation. - When monetary policy is unconstrained and initial debt is low, short-term output costs of an MPP tightening are small. - In an environment with elevated debt and little scope for central banks to cut rates, macroprudential actions may be associated with a significant drop in output and consumption. - An LTV tightening triggers a large decline in the house price and generates a negative feedback effect on debt capacity and aggregate demand because house prices are part of an LTV constraint. - LTI or DSTI tightenings are more efficient tools to curb household debt at low output cost; short-term effects on output and inflation are more than twice as large under an LTV tightening. - Welfare analysis: - An LTV at 70 percent, i.e. lower than the baseline calibration of 85 percent, is welfare maximizing in the nonlinear model with a ZLB. - Disregarding the ZLB constraint the optimal LTV is close to 85 percent. - The presence of a zero lower bound (ZLB) constraint is a crucial driver of the finding that tighter LTVs are welfare improving because the ZLB increases the economy’s vulnerability to disturbances. ### Mechanism: stylized two-period model (LTV vs LTI) - Setup and preferences: - Two-period economy; households borrow at rate R; receive wage normalized to one; consume housing services (h) and non-durable goods (c). - Preferences: sum_{t=1}^2 β^{t-1} [ c_t + log(h_t) - n_t^2/2 ] with 1/(1+R) < β < 1/R. - Budget constraint: c_t + q_t(h_t - h_{t-1}) + R b_{t-1} = n_t + b_t, with h_0, b_0 = 0 and b_2. - Borrowing constraints compared: - LTV: b_1 ≤ θ q_1 h_1. - LTI: b_1 ≤ θ LTI n_1. - To make long-run comparable, assume θ_LTI = θ and b_2 = θ. - Key equilibrium property: constraints bind and multiplier ϖ = 1 - β R > 0. - LTV tightening (permanent change θ' = x θ, x < 1): - House price response: - ∆q_{1;LTV} = - [ x θ (1 + β) ϖ ] / [ ϖ_H (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - Borrowing and consumption responses: - ∆b_{1;LTV} = - [ θ (1 + β) (1 - x) ] / [ (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - ∆c_{1;LTV} = ∆b_{1;LTV} - Drop in prices and consumption is larger the higher the level of initial debt (initial LTV). - LTI tightening: - House prices unaffected: ∆q_{1;LTI} = 0 - Labor supply falls: ∆n_{1;LTI} = - ϖ θ (1 - x) < 0 - Borrowing and consumption: - ∆b_{1;LTI} = - θ (1 - x) [ θ ϖ (1 + x) + 1 ] < 0 - ∆c_{1;LTI} = ∆n_{1;LTI} + ∆b_{1;LTI} - Comparison (first-period debt and consumption): - ∆b_{1;LTV} - ∆b_{1;LTI} = - (1 - x) θ [ θ^2 ϖ^2 ((1 - θ ϖ) x (1 + x) + 1) + β ] / [ (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - ∆c_{1;LTV} - ∆c_{1;LTI} = - (1 - x) θ [ Φ + β - ϖ + θ ϖ^2 / (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - Conclusion: deleveraging through LTV tightening has a larger negative impact on house prices, debt and consumption than an income-based constraint, particularly when house prices react more than labor supply. ### Quantitative model (overview and calibration) - Model framework and extensions: - Built on Iacoviello and Neri (2010) two-agent new Keynesian (TANK) with housing; extended to include housing transaction costs, long-term household debt, and a ZLB constraint for the policy rate. - Agents and mortgages: - Two household types: patient (P) and impatient (I); mass of unity; β_P > β_I. Patient households are savers; impatient households are borrowers. - Mortgage mechanics: mortgage payments M^P_t = [ r^M_{t-1} + δ ] D^P_{t-1} / P_t and debt stock evolves as D_t/P_t = (1 - δ) D_{t-1}/P_t + L_t/P_t. Effective mortgage rate r^M_t is weighted average with refinancing share ϑ. - Borrowing constraints in model: - Baseline collateral (LTV) constraint (eq. (8)) includes home equity extraction parameter μ and transition terms with ϵ_h and δ. - Alternative constraints: LTI (eq. (9)) and DSTI (eq. (10)) specified; for small shocks constraints bind with equality and one constraint binds at a time. - Calibration highlights (parameters preserved as in source): - Consumption habit parameters set to 0.7. - Output-gap weight in policy rule set to 0.25. - Share of savers β value: 0.67. - Speed of amortization set to yield 46 years of amortization. - Average interest rate fixation period: 1 year; refinancing share ϑ value: 0.3. - Calibration target for LTI based on Swedish FSA: 433% average for 2015-2017. - Steady-state residential investment target: 3% of GDP (4% of private sector absorption). - Housing transaction cost parameter θ_h set to match peak non-housing consumption response target 0.33% to a 25 bp monetary policy shock. - Accounting for increased household indebtedness (Swedish calibration): - Drivers and parameter changes from 1990s to 2010s: - Real interest rate in 2010s assumed 250bp lower than in 1990s. - Maximum LTV increased by 10 percentage points (bunching at 85% LTV in new loans 2015-2017). - Steady-state inflation: 1.5% in 2010s vs 2.0% in 1990s. - HEW share increased from 1.5% to 2.1% of available home equity. - Decomposition of increase in borrowers’ DTI: - Change in interest rate accounts for 54% of the increase. - Change in LTV ratio contributes 24%. - Change in HEW accounts for 12%. - Lower inflation accounts for 10%. - Steady-state implications (selected figures preserved exactly): - Doubling in LTI implies increase in real house prices of roughly one third. - Housing stock value relative to GDP rises by 110 percent. - Residential investment almost doubles between 1990s and 2010s (from 3.0 to 5.2 percent of GDP in Table 3). ### Empirical and literature connections (selected exact figures and findings) - Richter et al. (2018): a 10 percentage point tightening of the LTV induces a 1.1% reduction in output (output effects concentrated in emerging economies). - Alam et al. (2019): macroprudential tightening through LTV has a significant negative impact on house prices whereas a DSTI/LTI tightening does not entail any significant effects (sample of 63 countries over 1991 to 2016). - Mian and Sufi (2011): importance of home equity extraction for surge in U.S. mortgage debt. - Other findings: - Calza et al. (2013): more developed mortgage markets and high mortgage debt-to-GDP feature larger responses to monetary policy shocks. - Cloyne et al. (2018): mortgagors’ consumption reacts more strongly than other households’ consumption to monetary policy shocks. - Flodén et al. (2018): highly indebted Swedish households cut non-housing expenditures more than less indebted households following policy rate changes. - Alpanda and Zubairy (2018): monetary policy is less effective when debt is high (state-dependent local projections). - Walentin (2014): with general equilibrium effects, monetary policy impact is stronger when debt level is higher. ### Effects of macroprudential tightening — long-term effects (policy experiments and steady states) - Policy experiment: four borrower-based policies aimed at reducing aggregate loan-to-income ratio by 10.2%: - Tightening LTV, LTI, DSTI constraints, and reduction in MID (starting from MID = 30% in LTV-constrained economy). - Scaling and specific changes: - Reductions set to imply identical 10.2% decline in long-run aggregate loan-to-income ratio. - Low-indebtedness: LTV reduced from 0.75 to 0.65. - High-indebtedness: LTV reduced from 0.85 to 0.77. - In low debt environment, MID reduced to 6.35% to obtain 10.2% reduction in aggregate loan-to-income ratio. - Long-run aggregate effects (percent changes from Table 4, preserved exactly where given): - Aggregate LTI: -10.2 (repeated across scenarios). - Output (1990s): -0.23; -0.27; -0.34; -0.34 (LTV; LTI; DSTI; MID). - Output (2010s): -0.32; -0.37; -0.56; -0.56. - Consumption (1990s): -0.11; -0.12; -0.33; -0.34. - Consumption (2010s): -0.07; -0.08; -0.56; -0.56. - Residential investment (1990s): -2.72; -3.48; -0.37; -0.37. - Residential investment (2010s): -3.05; -3.56; -0.58; -0.58. - House prices (1990s): -1.06; -1.37; -0.04; -0.05. - House prices (2010s): -1.21; -1.41; -0.07; -0.07. - Borrowers’ housing (1990s): -7.03; -9.21; 0.42; 0.42. - Borrowers’ housing (2010s): -7.94; -9.30; -0.27; -0.27. - Mechanisms by constraint type: - Collateral constraints (LTV and MID tightening): strong contractions in housing investment and house prices; borrowers later allocate higher share of income to non-housing consumption, reducing labor supply and output. - Income-based constraints (LTI and DSTI): smaller falls in house prices and housing investment; borrowers reduce non-housing consumption and labor supply in high-debt economy; LTI and DSTI have basically identical long-run effects. ### Short-run effects (ZLB environment and simulations) - Baseline and shock setup: - Baseline: economy driven to the ZLB by adverse shocks; key state variable is shadow rate ^R_t. ZLB duration in baseline: two years (absent any MPP changes). Experiments report marginal effects with ZLB duration fixed at two years. - MPP changes modeled as highly persistent AR(1); MID modeled as AR(2) with _;1 = 0.9 and _;2 = 0.0000001 to produce near-permanent gradual decline. - Tightening of LTV: aggregate and disaggregate short-run effects - Key messages: - Transition after an LTV tightening implies large short-run costs in inflation and output when monetary policy is constrained by the ZLB. - These costs are roughly three times larger in the high debt economy versus the low debt economy. - Quantitative short-run impacts (high debt economy, ZLB binds for 8 quarters): - GDP initially falls by more than 3 percent. - Inflation initially falls by less than 1 percent. - These responses correspond to an LTV tightening that reduces LTI by 10.2% in the long run (example: LTI reduction from 433 to about 390 percentage points). - Quantitative short-run impacts (low debt economy, same LTV tightening): - GDP initially falls by 0.8 percent. - Inflation initially falls by 0.3 percent. - Disaggregate drivers (high debt economy): - House prices fall by more than 5 percent on impact (vs. 2.6 percent in the low debt economy). - Borrowers’ housing stock falls by roughly 1 percent on impact. - All three main components of aggregate demand fall: residential investment (most), aggregate non-housing consumption (next), non-residential investment. - Borrowers’ consumption contraction is four times as large in the high debt regime versus the low debt regime. - Two forces explaining three-fold larger GDP contraction in high debt regime: - LTV tightening requires more monetary accommodation in a high debt economy; unconstrained policy rate response is three times larger compared to low debt economy. - Monetary policy is more potent in a high debt environment: output responds roughly 50% stronger to monetary policy shocks in the high debt regime (policy shock example: 25 basis points hike). - Short-run effects of income-based MPP tools (LTI and DSTI) - When indebtedness is high and monetary policy cannot accommodate (ZLB), income-based tightenings impose substantially lower short-term macroeconomic costs than an LTV tightening. - Figure 7 experiment: for same long-term LTI reduction and ZLB binding for two years, output response is more than twice as strong for an LTV tightening compared to LTI/DSTI tightening. - Mechanism: LTV tightening transmits through house prices reducing collateral and aggregate demand; LTI/DSTI transmit via income which is less volatile and households can increase labor supply to smooth consumption. - Short-run effects of MID removal - Gradual removal of mortgage interest deductibility (MID) can entail significant macroeconomic costs when interest rates are low and LTV constraints bind. - MID removal increases effective user cost of debt-financed housing, putting immediate downward pressure on house prices because asset prices are forward-looking, reducing borrowing capacity under LTV constraints and leading to substantial macroeconomic contraction almost as strong as for an LTV tightening. - Removing MID under LTI or DSTI constraints would require no monetary accommodation and would only gradually reduce output. ### Welfare implications - Objective and method: - Compute unconditional welfare of household groups and social welfare W_S = (1 - _P) W_P + (1 - _I) W_I in the high debt economy. - Use second-order approximation around non-stochastic steady state; simulate pruned system for 5,000 periods for different steady state LTV values; identical innovations across LTV values. - Two monetary assumptions: unconstrained central bank and central bank constrained by ZLB (handled using Hebden et al. (2010) method). - Calibration adjustments for low interest environment: - Steady state nominal interest rate in model set to 2 percent. - Standard deviation of monetary policy shock shrunk to about 34 percent of the value estimated in Iacoviello and Neri (2010). - Welfare results (Figure 9 summaries and exact values where provided): - Unconstrained monetary policy: - Unconditional social welfare maximized at an LTV of about 0.85 (maximum welfare obtained for an LTV of 0.84). - Savers’ welfare monotonically increasing in LTV. - Borrowers' welfare deteriorates when steady state LTV exceeds 0.77. - ZLB imposed: - Total welfare maximized at LTV = 0.71. - Lower optimal LTV driven entirely by lower welfare of borrowers at higher LTV values under ZLB. - A tightening from LTV = 0.85 to LTV = 0.75 can be rationalized on unconditional welfare grounds with the ZLB. - Distributional effects and frequency of ZLB: - For LTV fixed at 0.70, economy is at ZLB in about 300 out of 5,000 simulated periods (probability 0.06). - ZLB introduces severe downward skew for output gap and borrowers’ non-housing consumption, costly for welfare; savers largely unaffected. - Caveats: - Analysis assumes neither unconventional monetary policy (UMP) nor fiscal policy tools are available when ZLB binds; availability of UMP/fiscal tools may bias results toward a lower optimal LTV in this analysis. ### Policy implications and recommendations - When selecting macroprudential tools to reduce household indebtedness, consider differing needs for monetary policy accommodation: - LTV tightenings are more contractionary in the short term and require larger monetary accommodation, especially when monetary policy is constrained by the ZLB or when initial debt is elevated. - LTI or DSTI tightenings are generally more efficient at curbing household debt at lower short-term output cost. - ZLB considerations: - The ZLB amplifies the welfare rationale for lower LTV limits because it raises the economy’s vulnerability to disturbances. - Optimal average LTV depends on whether the ZLB is active: with ZLB, optimal LTV ~ 70 percent; without ZLB, optimal LTV ~ 85 percent (baseline calibration). - Quantitative assessment of trade-offs should account for initial debt levels, potential need for central bank accommodation, and relative sensitivity of house prices versus labor supply to policy changes. - Policy design implication: account for interactions between macroprudential tools and monetary policy when reducing household debt; in ZLB environments prioritize income-based constraints (LTI/DSTI) over collateral-based constraints (LTV) or MID removal to lower short-run macroeconomic costs. - Suggested extension: incorporate borrower heterogeneity to examine robustness and potential combinations of tools that bind for different borrowers. ### Key calibrated and steady-state numeric highlights (selected exact values) - Share of patient households β value: 0.67. - Consumption habit parameters value: 0.70. - Steady-state nominal interest rate used in welfare exercises: 2 percent. - Calibration targets and parameters: - Target steady-state residential investment: 3% of GDP. - LTI calibration target for borrowers (median loan-size-weighted, Swedish FSA): 433% average for 2015-2017. - Decomposition of increase in borrowers’ DTI: 54% real rate change; 24% LTV change; 12% HEW change; 10% lower inflation. - Long-run policy experiment magnitude: aggregate LTI targeted reduction = -10.2 percent (aggregate LTI: -10.2 across MPP experiments). - Table 4 steady-state percent changes (2010s high-debt economy, LTV; LTI; DSTI; MID): - Output: -0.32; -0.37; -0.56; -0.56 - Consumption: -0.07; -0.08; -0.56; -0.56 - Residential investment: -3.05; -3.56; -0.58; -0.58 - House prices: -1.21; -1.41; -0.07; -0.07 - Borrowers’ housing: -7.94; -9.30; -0.27; -0.27 - Short-run LTV tightening (high debt, ZLB binds 8 quarters) impacts: - GDP initially falls by more than 3 percent. - Inflation initially falls by less than 1 percent. - House prices fall by more than 5 percent on impact. - Short-run LTV tightening (low debt) impacts: - GDP initially falls by 0.8 percent. - Inflation initially falls by 0.3 percent. - House prices fall by 2.6 percent on impact. - Welfare panel (Figure 9 axis values preserved): - LTV axis: 0.65, 0.70, 0.75, 0.80, 0.85, 0.90. - Total Welfare panel values (example points): -2.605, -2.6, -2.595, -2.59. - Savers Welfare panel values (example points): -628, -626, -624, -622, -620. - Borrowers Welfare panel values (example sequence): -76.9, -76.8, -76.7, -76.6, -76.5, -76.4, -76.3, -76.2. *Italic source: Excerpt from wpiea2020089-print-pdf - 0.75 to 0.85.* ### 0.75 to 0.85. ### wpiea2020089-print-pdf - 0.75 to 0.85. ### Major findings - Long-run residential investment as a share of GDP increases from 3 to 5 percent of GDP in the model when real rates decline. - Empirical example: Sweden residential investment has risen from less than 2 percent after the housing crisis in the early 1990s to about 7 percent in 2017. - Main results summarized: - The long-term output costs of all the macro-prudential actions in the study are moderate, regardless of whether the steady state has normal (mid-1990s) or elevated debt levels (the current state). - Short-term effects of macroprudential policy (MPP) depend critically on the initial debt level and the scope for central bank accommodation. - When monetary policy is unconstrained and initial debt is low, short-term output costs of an MPP tightening are small. - In an environment with elevated debt and little scope for central banks to cut rates, macroprudential actions may be associated with a significant drop in output and consumption. - An LTV tightening triggers a large decline in the house price and generates a negative feedback effect on debt capacity and aggregate demand because house prices are part of an LTV constraint. - LTI or DSTI tightenings are more efficient tools to curb household debt at low output cost; short-term effects on output and inflation are more than twice as large under an LTV tightening. - Welfare analysis: - An LTV at 70 percent, i.e. lower than the baseline calibration of 85 percent, is welfare maximizing in the nonlinear model with a ZLB. - Disregarding the ZLB constraint the optimal LTV is close to 85 percent. - The presence of a zero lower bound (ZLB) constraint is a crucial driver of the finding that tighter LTVs are welfare improving because the ZLB increases the economy’s vulnerability to disturbances. ### Mechanism: stylized two-period model (LTV vs LTI) - Setup: - Two-period economy; households borrow at rate R; receive wage normalized to one; consume housing services (h) and non-durable goods (c). - Preferences: sum_{t=1}^2 β^{t-1} [ c_t + log(h_t) - n_t^2/2 ] with 1/(1+R) < β < 1/R. - Budget constraint: c_t + q_t(h_t - h_{t-1}) + R b_{t-1} = n_t + b_t, with h_0, b_0 = 0 and b_2. - Borrowing constraints compared: - LTV: b_1 ≤ θ q_1 h_1. - LTI: b_1 ≤ θ LTI n_1. - To make long-run comparable, assume θ_LTI = θ and b_2 = θ. - Key equilibrium property: constraints bind and multiplier ϖ = 1 - β R > 0. - LTV tightening (permanent change θ' = x θ, x < 1): - House price response: - ∆q_{1;LTV} = - [ x θ (1 + β) ϖ ] / [ ϖ_H (1 - ϖ x θ) (1 - ϖ θ) ] < 0 (where ∆q ≡ q' - q) - Borrowing and consumption responses: - ∆b_{1;LTV} = - [ θ (1 + β) (1 - x) ] / [ (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - ∆c_{1;LTV} = ∆b_{1;LTV} - Drop in prices and consumption is larger the higher the level of initial debt (initial LTV). - LTI tightening: - House prices unaffected: ∆q_{1;LTI} = 0 - Labor supply falls: ∆n_{1;LTI} = - ϖ θ (1 - x) < 0 - Borrowing and consumption: - ∆b_{1;LTI} = - θ (1 - x) [ θ ϖ (1 + x) + 1 ] < 0 - ∆c_{1;LTI} = ∆n_{1;LTI} + ∆b_{1;LTI} - Comparison (first-period debt and consumption): - ∆b_{1;LTV} - ∆b_{1;LTI} = - (1 - x) θ [ θ^2 ϖ^2 ((1 - θ ϖ) x (1 + x) + 1) + β ] / [ (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - ∆c_{1;LTV} - ∆c_{1;LTI} = (∆b_{LTV} - ∆b_{LTI}) - ∆n_{1;LTI} = - (1 - x) θ [ Φ + β - ϖ + θ ϖ^2 / (1 - ϖ x θ) (1 - ϖ θ) ] < 0 - Conclusion: deleveraging through LTV tightening has a larger negative impact on house prices, debt and consumption than an income-based constraint, particularly when house prices react more than labor supply. ### Quantitative model (overview) - Built on the Iacoviello and Neri (2010) two-agent new Keynesian (TANK) economy with housing; extended to include: - housing transaction costs, - long-term household debt, - a ZLB constraint for the policy rate. - Agents: - Two types of households: patient (P) and impatient (I); mass of unity. Discount factors satisfy β_P > β_I. Patient households are savers; impatient households are borrowers. - Patient households: - Expected lifetime utility: - E_0 ∑_{t=0}^∞ (β_P)^t z_t [ - c ln(c^P_t - ε c^P_{t-1}) + j_{P,t} ln(h_{P,t}) - v_t (n^{1+ϕ}_{...})/(1+ϕ) ] (as specified in eq. (1)) - Budget constraint and detailed income and return components given (see eq. (2)). - Mortgages: savers receive mortgage payments M^P_t = [ r^M_{t-1} + δ ] D^P_{t-1} / P_t (eq. (4)); debt stock evolves as D_t/P_t = (1 - δ) D_{t-1}/P_t + L_t/P_t (eq. (5)). - Effective mortgage rate r^M_t is weighted average of past and new rates with refinancing share ϑ (eq. (6)). - Impatient households: - Utility form analogous to patient households but with β_I < β_P and j_I > j_P. They do not accumulate physical capital and borrow the remainder after a down payment (budget constraint eq. (7)). - Baseline collateral (LTV) borrowing constraint (eq. (8)): - L_t/P_t ≤ θ_{LTV,t} q_t [ h_{I,t} - (1 - ϵ_h) h_{I,t-1} ] + μ q_t (1 - ϵ_h) h_{I,t-1} - (1 - δ) D_{t-1}/P_t ] - Includes home equity extraction parameter μ. - Alternative constraints considered: - LTI (eq. (9)): - L_t/P_t ≤ θ_{LTI,t} [ w_{c,I,t} n_{c,I,t} + w_{h,I,t} n_{h,I,t} ] + μ q_t (1 - ϵ_h) h_{I,t-1} - (1 - δ) D_{t-1}/P_t - DSTI (eq. (10)): - L_t/P_t ≤ θ_{DSTI,t} [ w_{c,I,t} n_{c,I,t} + w_{h,I,t} n_{h,I,t} ] (1 - τ_t) r^F_t + δ + μ q_t (1 - ϵ_h) h_{I,t-1} - (1 - δ) D_{t-1}/P_t - For small shocks around steady state, constraints bind with equality; analysis assumes one constraint binds at a time. ### Empirical and literature connections (selected exact figures and findings) - Microdata evidence: Mian and Sufi (2011) on the importance of home equity extraction for the surge in U.S. mortgage debt. - Richter et al. (2018): a 10 percentage point tightening of the LTV induces a 1.1% reduction in output (output effects concentrated in emerging economies). - Alam et al. (2019): macroprudential tightening through LTV has a significant negative impact on house prices whereas a DSTI/LTI tightening does not entail any significant effects (sample of 63 countries over 1991 to 2016). - Other empirical findings summarized: - Calza et al. (2013): countries with more developed mortgage markets and high mortgage debt-to-GDP feature larger responses to monetary policy shocks. - Cloyne et al. (2018): mortgagors’ consumption reacts more strongly than other households’ consumption to monetary policy shocks (US and UK household data). - Flodén et al. (2018): highly indebted Swedish households cut non-housing expenditures more than less indebted households following policy rate changes. - Alpanda and Zubairy (2018): using state-dependent local projections, monetary policy is less effective when debt is high (partial equilibrium reasoning). - Walentin (2014): taking general equilibrium effects into account, monetary policy impact is stronger when debt level is higher. ### Policy implications and guidance - When selecting macroprudential tools to reduce household indebtedness, consider differing needs for monetary policy accommodation: - LTV tightenings are more contractionary in the short term and require larger monetary accommodation, especially when monetary policy is constrained by the ZLB or when initial debt is elevated. - LTI or DSTI tightenings are generally more efficient at curbing household debt at lower short-term output cost. - ZLB considerations: - The ZLB amplifies the welfare rationale for lower LTV limits because it raises the economy’s vulnerability to disturbances. - Optimal average LTV depends on whether the ZLB is an active constraint: with ZLB, optimal LTV ~ 70 percent; without ZLB, optimal LTV ~ 85 percent (baseline calibration). - Quantitative assessment of trade-offs should account for initial debt levels, the potential need for central bank accommodation, and the relative sensitivity of house prices versus labor supply to policy changes. *Italic source: Excerpt from wpiea2020089-print-pdf - 0.75 to 0.85.* ### 3.2 Firms and technology ### 3.2 Firms and technology ### Wholesale sector - Competitive wholesale sector: capital and labor produce the non-housing good Yt; new houses IHt are produced with capital, labor, land and an intermediate input. - Firms maximize profit function given in equation (11) subject to production technologies: - Non-housing production (eq. (12)): Yt = Ac t · n_{c;P;t}^β (n_{c;I;t})^{1-β} · (z_{ct} k_{ct-1})^{ϑ_c} - Housing production (eq. (13)): IHt = Ah t · n_{h;P;t}^β (n_{h;I;t})^{1-β} · (z_{ht} k_{ht-1})^{ϑ_h} k_{bt}^{ϑ_b} l_{t-1}^{ϑ_l} - Ac t and Ah t are productivity levels in the non-housing and housing sectors, respectively. - β is the labor income share of patient households. - Production specification implies complementarity across labor skills from the two types of households. ### Retailers - Monopolistically competitive retailers differentiate the homogeneous non-housing good; they buy at price Pw t and sell at Pt = Xt Pw t where Xt is the markup. - Price-setting frictions: - Calvo pricing with probability 1−ξ_p each quarter to reoptimize. - Remaining fraction ξ_p partially index prices by fraction ι_p to past inflation. - Resulting Phillips curve for net inflation π (where π = ln ...) (eq. (14)): - π_t − ι_p π_{t-1} = κ_p (E_t π_{t+1} − ι_p π_t) − λ_p ln(X_t/X̄) + ε_{π;t} - λ_p ≡ (1−β ξ_p) (1−ξ_p)/ξ_p - ε_{π;t} is an i.i.d. markup shock. - Nominal wages are sticky; four wage Phillips curves (one for each sector-household pair) documented in the Appendix. ### Monetary, fiscal and macroprudential policy - Monetary policy: - Nominal gross interest rate Rt follows a Taylor-type rule with ZLB: Rt = max(1, R̂t) (eq. (15)) - Shadow gross rate R̂t defined in eq. (16): - R̂t = R̄ R̂_{t-1}^{ρ_R} [ (π_t / π̄)^{φ_r} (Y_t / Y^{flex}_t)^{φ_Y} (Y_t / Y_{t-1})^{φ_{ΔY}} ]^{1−ρ_R} exp(ε_{r;t}) - R̂t denotes gross notional (shadow) rate; ε_{r;t} is an i.i.d. monetary shock. - Y^{flex}_t measures flex-price-wage output (so ln(Y_t/Y^{flex}_t) is the model-consistent output gap). - ρ_R is the steady state gross nominal interest rate parameter. - Central bank internalizes policy changes that affect potential output via the output gap term. - Government budget: - Balances period-by-period; finances interest rate deductions with lump-sum taxes paid by impatient households: - Tt = τ_t r_M t−1 D_{t−1} / P_t ### Market clearing - Non-housing goods market clearing: - c^P_t + c^I_t + i_{ct} + A_{kt} + i_{ht} + k_{bt} = Y_t - Housing market clearing: - h^P_t + h^I_t − (1−δ_h)(h^P_{t−1} + h^I_{t−1}) = IH_t ### Calibration - General approach: - Parameters affecting steady state (markups, factor shares, depreciation) set to conventional literature values. - Dynamic parameters set to estimated values in Iacoviello and Neri (2010) except investment adjustment costs from Walentin (2014). - Key deviations and choices: - Consumption habit parameters set to 0.7 (higher than Iacoviello and Neri (2010) estimates of 0.32 and 0.58). - Higher degree of price stickiness than Iacoviello and Neri, motivated by Del Negro et al. (2015) and Lindé et al. (2016). - Output-gap weight in policy rule set to 0.25 to reflect a liquidity trap and to approximate optimal policy in NK environments. - Stronger response of policy rate to inflation than in Iacoviello and Neri (2010). - Share of savers β set to 0.67 (two thirds); implies a larger share of borrowers (1−β) than in Iacoviello and Neri priors, aiming to match total debt-to-income ratio in data. - Borrower and saver behavior parameters: - Speed of amortization parameter set to yield 46 years of amortization (matching Riksbank calculations for Sweden). - Average interest rate fixation period set to 1 year (matches Swedish mortgage average). - Calibration target for LTI based on median loan-size-weighted LTI for new mortgage loans from Swedish FSA: 433% average for 2015-2017. - Steady-state residential investment target: 3% of GDP (4% of private sector absorption); LTI of borrowers in 1990s set to 433/2% via weights j_P and j_I. - LTI (Ξ_LTI_t) and DSTI (Ξ_DSTI_t) parameters set to match same borrower LTI as in LTV constrained economy accounting for real rate and inflation changes. - Housing transactions and HEW: - Housing transaction cost parameter θ_h set to match peak non-housing consumption response to a 25 bp monetary policy shock for the 1990s: target 0.33% response (average of U.S. and U.K. peak responses per Cloyne et al. (2018)). ### Accounting for the increased household indebtedness - Four assumed drivers of increase in household indebtedness from 1990s to 2010s: - Lower real interest rates - Easier credit conditions (higher maximum LTV) - Lower inflationary pressures - Increase in home equity withdrawal (HEW) - Calibration for Swedish case to explain doubling of aggregate LTI from 217% to 433%: - Real interest rate in 2010s assumed 250bp lower than in 1990s. - Maximum LTV increased by 10 percentage points (evidenced by bunching at 85% LTV in new loans 2015-2017). - Steady-state inflation in 2010s calibrated to 1.5% instead of 2.0% in 1990s. - HEW share increased from 1.5% to 2.1% of available home equity (consistent with US evidence ~1.7%). - Decomposition of drivers for increase in borrowers’ DTI: - Change in interest rate accounts for 54% of the increase. - Change in LTV ratio contributes an additional 24%. - Change in HEW accounts for 12%. - Lower inflation accounts for 10%. - Long-run equilibrium comparisons (Table 3 highlights): - DSTI ratios of borrowers increase substantially less than DTI and LTI. - Pure interest payment over income decreases slightly despite higher debt. - Lower real rates increase non-residential and residential investment as share of GDP; residential investment almost doubles between 1990s and 2010s. - Doubling in LTI implies increase in real house prices of roughly one third in the model; housing stock value relative to GDP rises by 110 percent. - Steady state properties broadly invariant to type of borrowing constraint. ### Effects of macroprudential tightening — long-term effects - Policy experiment: characterize effects of four borrower-based policies aimed at reducing aggregate loan-to-income ratio by 10.2%: - Tightening LTV, LTI, DSTI constraints, and reduction in MID (starting from MID = 30% in LTV-constrained economy). - Scaling of reductions: - Reductions in LTV, LTI and DSTI set to imply identical 10.2% decline in long-run aggregate loan-to-income ratio as obtained when removing MID; scaling applied separately for low- and high-indebtedness regimes. - Low-indebtedness: LTV reduced from 0.75 to 0.65. - High-indebtedness: LTV reduced from 0.85 to 0.77. - In low debt environment, mortgage deductibility (MID) is reduced to 6.35% to obtain 10.2% reduction in aggregate loan-to-income ratio. - Long-term aggregate effects: - All four debt-reducing policies cause moderate falls in output and consumption. - Mechanisms differ by constraint type: - Collateral constraints binding (LTV and MID tightening): - Reducing debt capacity has a small, positive long-run effect on borrowers’ consumption. - Strong contractions in housing investment and house prices. - Tighter LTV reduces usefulness of housing as collateral; removing MID makes debt-financed housing effectively more expensive after tax; borrowers reduce housing stock and later allocate higher share of income to non-housing consumption, reducing labor supply and output. - Income-based constraints (LTI and DSTI tightening): - Smaller falls in house prices and housing investment. - In high-debt economy, borrowers reduce non-housing consumption and decrease labor supply because labor income loses part of its “collateral” value. - LTI and DSTI tightenings have basically identical long-run effects on all variables (DSTI differs only via accounting for time-variation in nominal interest rate; neither LTI nor DSTI affects nominal rate in long run). - Long-term aggregate effects (in percentage terms) are roughly invariant to the initial debt level; basic long-run mechanisms do not depend on initial debt. *Italic: Source content unit "wpiea2020089-print-pdf - 3.2 Firms and technology" from the supplied PDF content.* ### 5.2 Short-run e§ects ### 5.2 Short-run e§ects ### Simulations set-up - Baseline: economy driven to the zero lower bound (ZLB) by adverse shocks that lower ináation below the central bankís target and output below potential. The key state variable is the notional (shadow) rate ^R_t, which determines the expected duration of the ZLB. - ZLB duration in the baseline: two years (absent any MPP changes). - Experiments report marginal e§ects with ZLB duration Öxed at two years (central bank assumed able to cut rates as needed after the two years). - MPP parameter dynamics: - Changes in LTV, LTI and DSTI modelled as AR(1) with coe¢cient arbitrarily close to unity (treated as structural changes). - Mortgage interest deductibility (MID) modelled as AR(2) to obtain a gradual reduction in MID (_t in eq. (7)): - _;1 = 0.9 - _;2 = 0.0000001 - Result: near-permanent gradual decline in  (MID). ### Tightening of LTV: aggregate and disaggregate short-run e§ects - Key messages: - The transition after an LTV tightening implies large short-run costs in terms of ináation and output when monetary policy is constrained by the ZLB. - These costs are roughly three times larger in the high debt economy versus the low debt economy. - Quantitative short-run impacts (high debt economy, ZLB binds for 8 quarters): - GDP initially falls by more than 3 percent. - Ináation initially falls by less than 1 percent. - These responses correspond to an LTV tightening that reduces LTI by 10.2% in the long run. - Long-run LTI example: reduction from 433 to about 390 percentage points in the high debt economy. - Quantitative short-run impacts (low debt economy, same LTV tightening): - GDP initially falls by 0.8 percent. - Ináation initially falls by 0.3 percent. - Disaggregate drivers in the high debt economy: - House prices fall by more than 5 percent on impact (vs. 2.6 percent in the low debt economy). - Borrowersí housing stock falls by roughly 1 percent on impact (and then gradually more). - All three main components of aggregate demand fall: residential investment (most), aggregate non-housing consumption (next), non-residential investment (also falls). - Borrowersí consumption contraction is four times as large in the high debt regime versus the low debt regime; borrowersí housing stock reduction is similar across regimes. - Housing transaction costs matter for borrowersí willingness to o§-load housing to savers in the short run. - The tightened LTV applies only to new loans, driving gradual decline in borrowersí debt and housing stock. - Two forces explaining the roughly three-fold larger GDP contraction in high debt regime: - LTV tightening requires more monetary accommodation in a high debt economy. When monetary policy is unconstrained, the unconstrained policy rate response is three times larger compared to the low debt economy. - Monetary policy is more potent in a high debt environment: output responds roughly 50% stronger to monetary policy shocks in the high debt regime (policy shock example: 25 basis points hike), driven by stronger contributions from residential investment and borrowersí consumption. - Note: both forms of investment constitute a substantially larger share of GDP in the high debt regime. ### Short-run e§ects of income-based MPP tools (LTI and DSTI) - When indebtedness is high and monetary policy cannot accommodate (ZLB), income-based MPP tightenings (LTI or DSTI) impose substantially lower short-term macroeconomic costs than an LTV tightening. - Figure 7 experiment: various MPP tools sized to achieve the same long-term LTI reduction, with ZLB binding for two years and indebtedness high. - Output response: more than twice as strong for an LTV tightening compared to tightening LTI/DSTI. - Mechanism: - LTV tightening transmits strongly through house prices, reducing borrowing capacity via the collateral constraint and feeding back to housing and non-housing consumption. - LTI/DSTI tightenings generate weaker negative feedback because income is less volatile than house prices. - Borrowers can increase short-term labor supply in response to an LTI/DSTI tightening to smooth consumption, muting income declines. - Interpretation: LTV-induced amplification is an instance of the Önancial accelerator (references in text). ### Short-run e§ects of MID removal - Gradual removal of mortgage interest deductibility (MID) can entail significant macroeconomic costs when interest rates are low and LTV constraints bind. - Mechanism and quantitative behavior: - MID removal increases the e§ective (after tax) user cost of debt-Önanced housing, putting immediate downward pressure on house prices because asset prices are forward-looking, even if MID is removed gradually. - Falling house prices reduce borrowing capacity under LTV constraints, leading to substantial macroeconomic contraction almost as strong as for an LTV tightening. - Contrastingly, removal of MID under LTI or DSTI constraints would require no monetary accommodation and would only gradually reduce output (as shown in Appendix Figure A.2). - Take-away: removing MID under binding LTVs can cause large short-run costs if households are forward-looking and expect interest rates to rise within a foreseeable future; LTI or DSTI constraints produce more favorable short-term outcomes when deleveraging. ### Welfare implications of reducing debt limits - Objective: compute unconditional welfare of the two household groups and social welfare W_S = (1 - _P) W_P + (1 - _I) W_I in the high debt (low steady state real and nominal rate) economy. - Method: - Second-order approximation of lifetime utility around non-stochastic steady state (Schmitt-Grohe and Uribe (2007)); simulate pruned system for 5,000 periods for di§erent steady state LTV values (_LTV). - Use identical innovations for all shock processes across LTV values to isolate partial derivative with respect to LTV. - Two monetary policy assumptions: - Unconstrained central bank (can always set policy rate per interest rate rule). - Central bank constrained by ZLB (imposed on second-order system using Hebden et al. (2010), with positive current and anticipated monetary shocks when ZLB binds so current and expected policy rate non-negative). - Calibration adjustments for low interest environment: - Steady state nominal interest rate in model: 2 percent (instead of 5 percent in Iacoviello and Neri (2010)). - Standard deviation of monetary policy shock shrunk by ratio of steady state nominal rate in model to the average Federal funds rate in Iacoviello and Neri (2010) sample (1965-2006), yielding a modiÖed standard deviation of about 34 percent of the value estimated in that paper. - Authors note using historical estimated value would increase welfare costs of ZLB and lower optimal unconditional LTV. - Welfare results (Figure 9): - Unconstrained monetary policy: - Unconditional social welfare maximized at an LTV of about 0.85 (to be exact, maximum welfare is obtained for an LTV of 0.84). - Sayers: saversí welfare monotonically increasing in LTV. - Borrowers: welfare deteriorates when steady state LTV exceeds 0.77. - Trade-o§: higher LTV benefits savers but increases consumption volatility and reduces welfare for borrowers at higher LTVs. - ZLB imposed: - Total welfare maximized at a notably lower LTV value: 0.71. - Lower optimal LTV driven entirely by lower welfare of borrowers at higher LTV values under ZLB. - A tightening of macroprudential policy from an LTV value of 0.85 to 0.75 can be rationalized on unconditional welfare grounds when the ZLB is taken into account. - Distributional e§ects and ZLB: - For LTV fixed at 0.70, simulated distributions show ZLB introduces a severe downward skew for the output gap and borrowersí non-housing consumption, which is very costly for welfare. - Saversí non-housing consumption largely una§ected by ZLB; savers can use savings to smooth consumption and buy cheaper houses from borrowers when ZLB binds. - Frequency of ZLB in simulations: - Economy at ZLB in about 300 out of 5,000 simulated periods when LTV equals 0.7 (i.e., probability 0.06). - Caveats: - Analysis assumes neither unconventional monetary policy (UMP) nor Öscal policy tools are available to stabilize the economy when ZLB binds. Availability of UMP/Öscal policy may bias results toward a lower optimal LTV in this analysis. - Even given UMP/Öscal policy, effectiveness and timeliness are debated; results may hold unless those tools are designed to put money directly in the hands of constrained borrowers. ### Conclusions (policy-relevant findings and recommendations) - Four factors documented in paper can account for a doubling of household indebtedness between the 1990ís and 2010ís in several advanced economies, with lower real mortgage rates as the main driver. - In presence of an e§ective lower bound on policy rates, limiting household indebtedness is welfare-improving even if house prices are consistent with fundamentals. - When policy rate close to ZLB, model implies unconditional welfare maximized when LTV is capped around 70 percent. - Long-term output costs of tightening LTV, LTI, DSTI, or reducing mortgage interest deductibility are moderate. - Short-term costs depend critically on the choice of MPP tool when indebtedness is high and monetary policy constrained: - LTV tightening and MID reduction can produce significant near-term drops in output and consumption via large housing price declines and collateral feedback. - LTI or DSTI tightenings are more e¢cient for deleveraging at lower short-term output cost because they avoid strong collateral feedback and are less dependent on monetary accommodation. - When initial debt is lower and monetary policy unconstrained, short-term costs are smaller and any of the four MPP tools can be used to reduce indebtedness at low output cost. - Policy design implication: account for interactions between macroprudential tools and monetary policy when reducing household debt; in ZLB environments prioritize income-based constraints (LTI/DSTI) over collateral-based constraints (LTV) or MID removal to lower short-run macroeconomic costs. - Suggested extension: incorporate borrower heterogeneity to examine robustness and potential combinations of tools that bind for di§erent borrowers; such extensions may refine but are unlikely to overturn main results. *Italic: Source: wpiea2020089-print-pdf - 5.2 Short-run e§ects* ### References ### wpiea2020089-print-pdf - References ### References - Alam, Zohair, Adrian Alter, Jesse Eiseman, Gaston Gelos, Heedon Kang, Machiko Narita, Erlend Nier, Naixi Wang, 2019, ìDigging DeeperñEvidence on the E§ects of Macroprudential Policies from a New Database,îIMF Working Papers WP/19/66. - Alpanda, Sami and Sarah Zubairy, 2017, ìAddressing household indebtedness: Monetary, Öscal or macroprudential policy?,îEuropean Economic Review, 92(C), 47ñ73. - Alpanda, Sami and Sarah Zubairy, 2019, ìHousehold Debt Overhang and Transmission of Monetary Policy,îJournal of Money, Credit and Banking, 51(5), 1265ñ1307. - Andreasen. 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The Role of the Relative Price of Investment Goodsî,IMF Economic Review64(4), 635ñ659. - Schmitt-Grohe, Stefanie and Martin Uribe, 2007, ìOptimal Simple and Implementable Monetary and Fiscal Rules,îJournal of Monetary Economics,54, 1702ñ1725. - Smets, Frank and Rafael Wouters, 2007, ìShocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,îAmerican Economic Review, 97(3), 586ñ606. - Walentin, Karl, 2014, ìHousing Collateral and the Monetary Transmission Mechanismî,Scandinavian Journal of Economics,116(3), 635ñ668. *References section from wpiea2020089-print-pdf* ### Tables and Figures (captions, parameter lists and selected statistics) - Table 1: Calibrated structural parameters. - Capital share in the goods production function symbol:  c value: 0.35 - Capital share in the housing production function symbol:  h value: 0.10 - Land share in the housing production function symbol:  l value: 0.10 - Intermediate share in the housing production function symbol:  o value: 0.10 - Gross markup in prices and wages X;X wh ;X wc value: 1.15 - Housing depreciation  h value: 0.005 - Capital depreciation, non-housing sector  kc value: 0.025 - Capital depreciation, housing sector  kh value: 0.03 - Taylor rule coe¢ cient on ináation r  value: 2.00 - Taylor rule coe¢ cient on output gap r  y value: 0.50 - Taylor rule coe¢ cient on output r y value: 0.25 - Taylor rule smoothing  R value: 0.75 - Calvo price rigidity   value: 0.9200 - Calvo wage rigidity, non-housing sector  wc value: 0.7920 - Calvo wage rigidity, housing sector  wh value: 0.9118 - Price indexation   value: 0.6911 - Wage indexation, non-housing sector  wc ;0.08301 - Wage indexation, housing sector  wh value: 0.41186 - Share of patient hhs value: 0.67 - Consumption habit " P ;" I value: 0.70 - Capital utilization cost  value: 0.70 - Investment adjustment costs non-housing sector S 00 c value: 5.316 - Investment adjustment costs, housing sector S 00 h value: 7.485 - Inverse Frisch elasticity, patient hhs  P value: 0.5238 - Inverse Frisch elasticity, impatient hhs  I value: 0.5060 - Sectorial labor mobility, patient hhs  P value: 0.6833 - Sectorial labor mobility, impatient hhs  I value: 0.9654 - Amortization rate on hhs loans  value: 0.0075 - Share reÖnancing  value: 0.3 - Housing preference weight, patient hhs j P value: 0.1235 - Housing preference weight, impatient hhs j I value: 0.2316 - Housing transaction costs  h value: 10 - Table 2: Parameters that drive the change in indebtedness. - Parameter: Moment 1990ís Value Target 2010ís Value Target - P Real rate 0.9925 3% 0.99875 0.5% -  LTV LTV 0.7575% 0.8585% -   Ináation rate 0.005 2% 0.00375 1.5% - HEW fraction 0.015 -0.02095 LTI=433% - Table 3: Long-run equilibrium in low debt vs. high debt economy (in percent) - Columns: 1990ís (LTV LTI DSTI) and 2010ís (LTV LTI DSTI) - LTI borrowers: 217 217 217 | 433 433 433 - DSTI (after tax) borrowers: 14.2 14.2 14.2 | 19.1 19.1 19.1 - Interest (after tax)/income of borrowers: 7.67 7.67 7.66 | 6.08 6.08 6.07 - Non-residential investment /GDP: 17.1 17.2 17.2 | 20.9 20.9 21.0 - Residential investment /GDP: 3.0 2.6 2.6 | 5.2 4.4 4.4 - House prices (%from 1990ís to 2010í): 36.5 34.4 34.4 - Table 4: Steady state e§ects of MPP in the two indebtedness regimes (percent change). - Layout shows results for 1990ís and 2010ís under LTV, LTI, DSTI, MID regimes. - Aggregate LTI: -10.2 (repeated across scenarios) - Output: -0.23; -0.27; -0.34; -0.34 | -0.32; -0.37; -0.56; -0.56 - Consumption: -0.11; -0.12; -0.33; -0.34 | -0.07; -0.08; -0.56; -0.56 - Non-residential investment: -0.17; -0.20; -0.34; -0.34 | -0.20; -0.24; -0.56; -0.56 - Residential investment: -2.72; -3.48; -0.37; -0.37 | -3.05; -3.56; -0.58; -0.58 - House prices: -1.06; -1.37; -0.04; -0.05 | -1.21; -1.41; -0.07; -0.07 - DSTI (after tax) of borrowers: -10.2; 6.24; -10.2; -10.2 | -10.2; 2.09; -10.2; -10.2 - Interest/income (after tax) of borrowers: -10.2; 20.2; -10.2; -10.2 | -10.2; 28.32; -10.2; -10.2 - Consumption of borrowers: 1.07; 1.20; 0.37; 0.38 | 0.98; 1.11; -0.33; -0.33 - Housing of borrowers: -7.03; -9.21; 0.42; 0.42 | -7.94; -9.30; -0.27; -0.27 - Hours worked of borrowers: -1.05; -1.23; -1.31; -1.31 | -1.11; -1.27; -1.79; -1.79 - Income of borrowers: -0.26; -0.32; -0.34; ñ0.34 | -0.38; -0.44; -0.56; -0.56 - Note: In the high debt environment, mortgage interest deductibility (MID) is completely removed. In the low debt environment, MID is reduced to 6.35% to obtain the same reduction in LTI. - Figures (captions and panel notes) - Figure 1: International Evidence — panels include: Households’ debt-to-income ratio; Real mortgage rate; House prices; Residential investment; Annual rate of inflation. Countries identified in legend: Sweden Norway Denmark UK USA Australia Canada. - Figure 2: LTV in Sweden. - Figure 3: LTI and LTV in Sweden. Source: Swedish FSA Mortgage Survey, average 2015-2017. - Figure 4: Aggregate e§ects of LTV tightening under alternative household leverage assumptions. - Panel A: Monetary policy constrained by ZLB for 8 quarters — series plotted include: Nom Policy Rate (APR, dev from baseline); Inflation (APR); Output (Dev from Trend). - Panel B: Monetary policy unconstrained — series plotted include: Nom Policy Rate (APR, dev from baseline); Inflation (APR); Output (Dev from Trend). - Lines shown for Low Initial Debt and High Initial Debt. - Figure 5: Disaggregate e§ects of permamental LTV tightening in a liquidity trap under alternative household leverage assumptions — series (by quarter): Aggegate Consumption; Savers Consumption; Borrowers Consumption; Non-residential Investment; Residential Investment; Housing Price; Savers Housing; Borrowers Housing; DTI of borrowers (Perc. Points). Lines for Low Initial Debt and High Initial Debt. - Figure 6: E§ects of a contractionary monetary policy shock under alternative household leverage assumptions in the LTV model — series: Nominal Policy Rate (APR); Yearly Inflation (4q-change); GDP; House Price; Aggegate Consumption (GDP Contrib.); Borrowers Consumption; Non-residential Investment (GDP Contrib.); Residential Investment (GDP Contrib.). Lines for Low Indebtedness and High Indebtedness. - Figure 7: Aggregate E§ects of LTV, LTI, DSTI and MID tightening in a liquidity trap under high indebtedness — series: Nom Policy Rate (APR, dev from baseline); Inflation (APR); Output (Dev from Trend). Lines for LTV tightening, LTI tightening, DSTI tightening, MID tightening. - Figure 8: Disaggregate e§ects of LTV, LTI, DSTI and MID tightening in a liquidity trap under high indebtedness — series: Aggegate Consumption; Savers Consumption; Borrowers Consumption; Non-residential Investment; Residential Investment; Housing Price; Savers Housing; Borrowers Housing. Lines for LTV tightening, LTI tightening, DSTI tightening, MID tightening. *Tables and Figures section from wpiea2020089-print-pdf* ### 9. LTI of borrowers (Perc. Points) ### 9. LTI of borrowers (Perc. Points) ### Unconditional welfare and simulated distributions (Figure 9) - LTV axis values shown: 0.65, 0.70, 0.75, 0.80, 0.85, 0.90. - Total Welfare values (panel): -2.605, -2.6, -2.595, -2.59 (plotted across LTV). - Savers Welfare values (panel): -628, -626, -624, -622, -620 (plotted across LTV). - Borrowers Welfare values (panel): -76.9, -76.8, -76.7, -76.6, -76.5, -76.4, -76.3, -76.2 (plotted across LTV). - Distribution panels (for LTV = 0.7): - Output Gap frequency axis: 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3. - Output Gap outcome axis: -40, -30, -20, -10, 0, 10. - Savers Consumption (in levels) frequency axis: 0, 2, 4, 6, 8, 10; outcome axis: 1.3, 1.4, 1.5, 1.6, 1.7, 1.8. - Borrowers Consumption (in levels) frequency axis: 0, 5, 10, 15; outcome axis: 0.2, 0.3, 0.4, 0.5, 0.6, 0.7. - Methodology note: Welfare is computed using second order approximation of the model and using the method of Hebden, LindÈ and Svensson (2010) to handle the ZLB. - Definition: Total welfare refers to W_S = (1 P)W_p + (1 I)W_I, following Lambertini et al. (2013). ### Two-period model (A.1) — setup and first-order conditions - Representative-agent problem (as stated): - Max 2 Σ_{t=1} ^{t-1} [ c_t + log(h_t) n_t^2/2 ] subject to budget and borrowing limit. - Borrowing-limit specifications considered: - LTV: B_1 =  q_1 h_1 - LTI: B_1 =  n_1 - Compact form of the problem: - Max 2 Σ_{t=1} ^{t-1} [ n_t R b_{t-1} + b_t q_t (h_t h_{t-1}) + log(h_t) n_t^2/2 ] s.t. LTV: b_1   q_1 h_1 or LTI: b_1   n_1. - First-order conditions (as given): - b_t: 1 = R +  (LTV constraint) - h_1 (LTV): q_1 = 1/h_1 + q_2 +   q_1 h_2 ; q_2 = 1/h_2 ; n_t = 1 for t = 1,2 - h_1 (LTI): q_1 = 1/h_1 + q_2 h_2 ; q_2 = 1/h_2 ; n_1 = 1 +   ### Equilibrium in the two-period model - Market clearing: h_t =  H for t = 1,2. - LTV limit equilibrium (expressions as given): - q_1 = (1 + ) / (1(1 R) ) 1/ H - q_2 = 1/ H - q_1 q_2 = 1/ H [ + (1 R)  ] / [ 1(1 R)  ] > 0 - b_2 =  ; b_1 =  q_1  H =  (1 + ) / [ 1(1 R)  ] - b_1 b_2 =  [ + (1 R)  ] / [ 1(1 R)  ] > 0 - Consumption: - c_2 = 1R  (1 + ) / (1 ) +  = 1^2  R  / (1 ) = (1 ) (1 + ) R  (1 + ) / (1 ) = 1 ^2  R  / (1 ) ; c_1 = 1 + b_1 = 1 +  (1 + ) / [ 1(1 R)  ]. - Positivity condition for c_2: 1^2  R  / (1 ) > 0; given assumption  < < 1 the denominator positive and numerator positive (algebra in text). - LTI limit equilibrium (expressions as given): - q_1 = 1/ H + q_2 ; q_2 = 1/ H - Labor supply: n_1 = 1 +  (1 R) ; n_2 = 1 - Debt: b_1 =  (1 +  (1 R)) ; b_2 =  - Consumption: - c_2 = 1R  (1 +  (1 R)) +  = 1 +  R  (1 +  ) =  (1R  ) + (1R ) - c_1 = (1 + ) (1 +  (1 R)) - Positivity condition:  < is sufficient as stated. ### Macroprudential experiment (A.1.2) - Initial equality: b_{2;LTI} = b_{2;LTV} = . - Permanent cut in debt by fraction x < 1: 0 = x . - LTV contraction (expressions as given): - q'_1 = (1 + ) / (1(1 R)  x) 1/ H - q'_2 = 1/ H - b'_1 =  x q'_1  H = x  (1 + ) / (1(1 R)  x) - Consumption: - c'_2 = 1R x  (1 + ) / (1(1 R)  x) + x  - c'_1 = 1 + b'_1 = 1 + x  (1 + ) / (1(1 R) x ) - LTI contraction (expressions as given): - q'_1 = 1/ H + q'_2 ; q'_2 = 1/ H - Labor supply: - n'_1 = 1 + x  (1 R) ; n'_2 = 1 - Debt: - b'_1 =  x (1 + x  (1 R)) ; b'_2 = x  - Consumption: - c'_2 = 1R  x (1 + x  (1 R)) + x  - c'_1 = (1 +  x (1 R)) (1 +  x) ### Comparison LTV vs LTI (A.1.3) — main analytical findings - Reduction in period-1 debt in LTV economy: - Δ b_{1;LTV} = b'_{1;LTV} b_{1;LTV} =  (1 + ) [ x / (1(1 R) x ) 1 / (1(1 R) ) ] - Algebra yields Δ b_{1;LTV} =  (1 + ) (1x) / [ (1 x ) (1 ) ] where  = (1 R). - Reduction in period-1 debt in LTI economy: - Δ b_{1;LTI} = b'_{1;LTI} b_{1;LTI} =  x (1 +  x )  (1 +  ) =  (1x) (  (1 + x) + 1). - Net comparison: - Δ b_{LTV} Δ b_{LTI} = (1x)  [ ^2 ^2 ((1  ) x (1 + x) + 1) + ] / [ (1 x ) (1 ) ] < 0. - Interpretation: Debt decreases more in the LTV economy; house prices respond more than labor supply to the policy change. - Consumption implications: - Period 2: Δ c_{2;LTV} Δ c_{2;LTI} = R (Δ b_{1;LTI} Δ b_{1;LTV}) > 0 ⇒ consumption falls more under LTV. - Period 1 comparison derived showing Δ c_{1;LTV} Δ c_{1;LTI} < 0 given assumed parameter inequalities, concluding the drop in consumption is higher in the LTV case. Q.E.D. ### DSGE model — first-order conditions and structure (A.2) - Aggregated first-order conditions and equilibrium relations reproduced exactly as in the source (selected equations and relations include): - Household optimality, production, capital and investment conditions (equations (17)–(24), (41)–(48) as listed). - Price, wage, and monetary policy relations (equations (19)–(22), (49)–(50), (54)–(57)). - Capital accumulation and utilization: k_{c,t} = (1_{kc}) k_{c,t-1} + (1S_{c,t}) i_{c,t} ; k_{h,t} = (1_{kh}) k_{h,t-1} + (1S_{h,t}) i_{h,t} (equations (60)–(61)). - Investment adjustment cost specification: F(i_t;i_{t-1}) = Σ_{s={K,H}} (1~S) [ i_t / i_{t-1} ]^{~S} with ~S(x) = 1/2 [ exp(p S_{00}^s (x _s)) + exp(- p S_{00}^s (x _s)) 2 ]. - Capital utilization cost: a(z_{s,t}) = R_s [ 1/2 /(1) z_{s,t}^2 + (1)/(1) z_{s,t} + (1/2 /(1) 1) ] for s = {c,h}. - LTV-related terms appear through ltv_t, m_ltv_t and related terms in the impatient household conditions (equations (34)–(36)). ### Shocks and processes (A.2.1–A.2.2) - Preference shocks (AR(1)): - log z_t = _z log z_{t-1} + "_{z;t} - log j_{c;t} = _j log j_{c;t} + (1_j) log j_c + "_{j;c;t} ; c = {P,I} - log v_t = _v log v_{t-1} + "_{v;t} - LTV, LTI and DSTI requirement shocks () are very persistent AR(1) processes (described in main text). - Interest rate deductibility () follows an AR(2) process (described in main text). - Cost-push shock ";t and monetary policy shock "r;t are i.i.d. - Technology shocks (AR(1)): - log a_{c,t} = _{AC} log a_{c,t-1} + "_{c,t} - log a_{h,t} = _{AH} log a_{h,t-1} + "_{h,t} - log a_{k,t} = _{AK} log a_{k,t-1} + "_{k,t} ### Appendix figures (A.3) — summarized panel effects - Figure A.1: Effects of a contractionary monetary policy shock under different borrowing constraints (LTV, LTI, DSTI) across 18 quarters: - 1. Nominal Policy Rate (APR) — vertical axis 0 to 0.25 (in steps shown 0, 0.05, 0.1, 0.15, 0.2, 0.25). - 2. Yearly Inflation (4q-change) — vertical axis -0.03 to 0.01 (ticks as shown). - 3. GDP — vertical axis -0.15 to 0 (percent). - 4. House Price — vertical axis -0.25 to 0 (percent). - 5. Aggregate Consumption (GDP Contrib.) — vertical axis -0.1 to 0 (percent). - 6. Borrowers Consumption — vertical axis -0.5 to 0 (percent). - 7. Non-residential Investment (GDP Contrib.) — vertical axis -20 to 5 (percent) and -0.06 to 0 (percent) in another panel as shown. - 8. Residential Investment (GDP Contrib.) — vertical axis -0.06 to 0 (percent). - Figure A.2: Aggregate effects of MID removal across different borrowing constraints with unconstrained monetary policy and high indebtedness across 36 quarters: - 1. Nom Policy Rate (APR, dev from baseline) — vertical axis -0.6 to 0 (percent). - 2. Inflation (APR) — vertical axis 0.01 to 0.08 (percent). - 3. Output (Dev from Trend) — vertical axis -0.6 to 0 (percent). - Series compared: LTV, LTI, DSTI. *Source: wpiea2020089-print-pdf - 9. LTI of borrowers (Perc. Points).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020089-print-pdf.pdf_