## _wp16104 — 3.1 Patient households (and related model & empirical findings) ## Source details **Canonical URL:** [_wp16104 — 3.1 Patient households (and related model & empirical findings)](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16104.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16104.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16104.pdf.json) --- ### Empirical revisitation: private/public debt and future growth (Section 2) — key findings - Data and sample: - Unbalanced panel annual dataset covering 30 advanced and emerging market countries. - Sample stretching from 1960 to 2014. - Empirical specification: - Baseline dependent variable: future output growth over three years, 3yit+3. - Main regressors: change in total private debt-to-GDP ratio in the previous three years, 3(PRD/Y)it−1, and change in public debt-to-GDP ratio in the previous three years, 3(PUD/Y)it−1. - Levels of debt-to-GDP ratios (lagged one year) and subsamples by public debt level (cutoff at 95 percent of GDP) also analyzed. - Detrended real GDP (HP-filtered) used as alternative dependent variable: ˆyit+3. - Quantified empirical effects: - A one standard deviation increase in the change in total private debt-to-GDP ratio (14 percentage points) is associated with a 1.8% lower output growth in subsequent years on average. - Coefficients on 3(PRD/Y)it−1 reported: -0.128*** and -0.143*** with standard errors (0.014) and (0.016). - Change in public debt 3(PUD/Y)it−1 is not significant when change in private debt is included: 3(PUD/Y)it−1 = -0.014 (0.019) (Table 1, column 2). - Lagged levels of private debt PRD/Yit−1 significantly correlated with subsequent GDP change: reported coefficients include -0.086*** (0.005), -0.095*** (-0.006), -0.087*** (0.006), and -0.212*** (0.030). - Lagged level of public debt PUD/Yit−1 generally not significant for full sample, but regime-dependent: - For PUD/Y ≤ 95%: PUD/Yit−1 = 0.057*** (0.015) (Table 1, column 5). - For PUD/Y > 95%: PUD/Yit−1 = -0.119*** (0.032) (Table 1, column 6). - Cyclical (detrended) output results (Table 2): - PRD/Yit coefficients: -0.007*** (0.003), -0.012*** (0.003), -0.012*** (0.003), -0.043*** (0.013) across columns 1–4 respectively. - PUD/Yit insignificantly related for full sample and PUD/Y ≤ 95%; negative and significant for PUD/Y > 95%: PUD/Yit = -0.029** (0.013) (Table 2, column 4). - Interpretation: - Countries with more “fiscal space” (lower public debt) are better positioned to weather financial crises because automatic stabilizers and targeted government assistance can alleviate private deleveraging; high public debt impairs these stabilizing mechanisms. - Panel descriptive stat sample (selected examples): - Australia — Private debt: Years 1960-2014 Average 110.62 Std. dev. 47.21; Public debt: Years 1989-2014 Average 21.75 Std. dev. 8.03 - Greece — Private debt: Years 1970-2014 Average 62.28 Std. dev. 33.17; Public debt: Years 1980-2014 Average 91.52 Std. dev. 45.06 - Japan — Private debt: Years 1964-2014 Average 169.53 Std. dev. 30.98; Public debt: Years 1980-2014 Average 132.25 Std. dev. 66.72 - United States — Private debt: Years 1952-2014 Average 110.83 Std. dev. 29.93; Public debt: Years 1947-2014 Average 85.54 Std. dev. 15.25 ### Model setup (Section 3) — purpose, agents, and mechanisms - Objective: - Derive a minimum model structure that reproduces leverage cycles, captures interactions between private and public debt, and is suitable for policy analysis of crisis-style events featuring high private leverage and government intervention. - Core structure and enrichments: - Closed-economy Kiyotaki and Moore (1997) backbone with Iacoviello (2005) housing-market borrowing constraints embedded in a New-Keynesian setting. - Enrichments: fiscal policy, government indebtedness, sovereign risk premium (Corsetti et al., 2013), government intermediation of funds (Gertler and Karadi, 2011). - Agents and frictions: - Patient households: work, consume, buy housing, invest in riskless private bonds and government bonds. - Impatient households: work, consume, borrow subject to collateral constraints. - Entrepreneurs: borrow subject to collateral constraint and produce in monopolistic competition. - Government: finances expenditures via lump-sum and distortionary taxes and issuing government bonds; government debt subject to sovereign default risk and calibrated fiscal limit (calibrated on real-world default cases, namely Greece). - Central bank: monetary policy follows a Taylor-type rule. - No banks explicitly modeled. - Definitions: - Leverage cycle: increase (decrease) in private indebtedness caused by loosening (tightening) of borrowing constraints when debt collateral appreciates (depreciates). - Deleveraging: reduction in liabilities via cuts to borrowing. - Crisis: a drop in collateral value reducing credit availability out of future income. - Public intervention: credit extended by government to financially-constrained agents to alleviate collateral-driven borrowing constraints. - Two key links between private and public indebtedness captured: - Financial accelerator: private deleveraging reduces output and prices, depressing government revenues. - Government interventions increase public debt to mitigate private deleveraging but can raise sovereign risk and necessitate fiscal consolidation. ### Patient households — preferences, budget, and first-order conditions (Section 3.1 and Appendix B.1) - Preferences and utility (as provided): - Households maximize expected lifetime utility: - U_t = E_t sum_{s=0}^{1} δ^{t+s} [ ln X'_{t+s} + e^H_{t+s} ( ln h'_{t+s} - L'_{t+s} ) ], - where δ ∈ (0,1) is the discount factor; - X'_t is habit-adjusted consumption; - e^H_t is a housing shock; - h'_t are housing holdings; - L'_t is labor supply; - ζ is a housing preference parameter; - η measures the elasticity of labor with respect to the real wage. - Habit-adjusted consumption: - X'_t = C'_t - θ C'_{t-1}, with θ ∈ (0,1). - Baseline calibration: patient households’ discount factor calibrated to =0.99 (Table 3). - Choices and traded assets: - Choices: consumption C'_t, housing h'_t, labor L'_t. - Assets traded: riskless private bonds B_t and nominal government bonds B^G_t. - Taxes: lump-sum τ^L_t; distortionary τ^C_t on consumption and τ^W_t on labor income. - Returns and transfers: wage W'_t; nominal return on private bonds R_t; nominal return on government bonds R^G_t discounted at the ex-ante expected haircut rate ̄g_t; government transfers Ξ_t. - Flow budget constraint (as stated in the source): - (1+τ^C_t)^{-1} C'_t + q_t h'_t + B'_t / P_t + B^G_t / P_t + τ^L_t = (1-τ^W_t) W'_t L'_t / P_t + R_{t-1} B'_{t-1} / P_t + (1-̄g_t) R^G_{t-1} B^G_{t-1} / P_t + Ξ_t. - Selected first-order conditions (Appendix B.1, patient households): - μ0t = 1/(1 + τCt) X0t, (B.1) - (1 − τWt) W0t/Pt = (L0t)^{η−1} − 1+τCt X0t, (B.2) - 1/(1 + τCt) X0t = −Et[ Rt − 1+τCt+1 X0t+1 Πt+1 ], (B.3) - 1/(1 + τCt) X0t = −Et[ 1/ΓGt+1 − RGt − 1+τCt+1 X0t+1 Πt+1 ], (B.4) - qt (1 + τCt) X0t = ζe Ht h0t + Et[ qt+1 − 1+τCt+1 X0t+1 ], (B.5) - Non-arbitrage and sovereign spread implication: RGt = Et[ 1/ΓGt+1 − 1 ] Rt. ### Experiments: leverage-cycle shock and comparative statics (Section 5.1) - Shock and calibration: - Downward phase triggered by temporary negative house price shock: house prices fall by one percent. - Model calibrated on average euro area data. - Numerical example comparison: example cited that a 24% house price fall and a 3.2% output gap are consistent with model-scaled relation ≈0.15×24 = 3.7. - Mechanisms linking private deleveraging to public finances: - Fall in output reduces government revenues and raises public debt-to-GDP via debt deflation, higher sovereign risk premium, and endogenous government support costs (equations (19) and (20) referenced). - High-private-debt scenario (parameterization): - Steady-state public debt at baseline; private debt higher because LTV ratios set at high-range euro-area values m00 = 0.99 and m = 0.44. - Result: stronger financial accelerator → deeper deleveraging, deeper GDP contraction, deflation, larger increase in public debt/GDP. - High-public-debt scenario: - Baseline private debt, but public debt/GDP set high (top percentiles of cross-country averages; still below fiscal limit ̄=1). - Result: recession milder yet more persistent; more protracted recession driven by higher sovereign risk premium, higher interest payments, and anticipated higher future tax rates. - If public debt sufficiently below fiscal limit, government borrowing to absorb negative shock can be optimal (Ostry et al. (2015) resemblance). ### Systematic sensitivity (Figure 4) — varied parameters and robust results - Experiments vary: - Caps on LTV ratio m, m00 vary between 0.375 and 0.95; x-axis reports resulting private debt/GDP. - Long-run steady-state public debt/GDP ratio varies between 0.6 and 1.2. - Main findings: 1. Economic contraction worsens as the LTV ratio increases. 2. Initial public debt has little bearing on contraction severity if below ≈100% of annual GDP in the calibrated model. 3. Post-shock public debt/GDP is positively correlated with initial private debt: larger pre-shock private liabilities → worse public debt legacy. 4. Higher caps on LTV cause more deleveraging; magnitude of deleveraging marginally depends on public debt level. 5. Deflationary effects stronger the higher the LTV ratio; inflation barely affected by steady-state public debt level. ### Policy question: government financial assistance to constrained agents (Section 5.2) — trade-offs and numerical experiments - Government instrument modeled: lend directly to private borrowers during deleveraging to relax borrowing constraints and smooth spending (real-world analogues: mortgage relief, targeted government credit, “Cash-for-Clunkers”-type programs, indirect support via financial intermediaries). - Two main trade-offs: 1. Intervention benefits (support to output and revenues) versus costs (higher public debt and subsequent fiscal consolidation effects). 2. Fiscal space constraint: capacity to intervene depends on distance between initial government debt stock and fiscal limit; higher public debt narrows capacity and worsens the trade-off. - Channels to instability from intervention: 1. Higher sovereign risk premia with higher public debt (raising RGt). 2. Direct intermediation: government borrows at RGt to lend at Rt (< RGt), incurring efficiency loss κ and fiscal cost. - Numerical experiment setup: - Baseline: private debt high (m00 = 0.99 and m = 0.44); government indebtedness baseline = 0.68; fiscal stance ρB = 0.05 to guarantee public debt stability. - Comparative statics over government reaction parameter ε ∈ [0,1] and inefficiency κ ∈ {0, 0.1, 0.2}. - Key numerical results: - There exists a non-zero level of government intervention that minimizes output losses. - Lower κ (more efficient intervention) implies a higher output-loss-minimizing ε. - Stronger intervention mitigates private deleveraging and deflation virtually irrespective of κ. - There exists a non-zero intervention level that minimizes the surge in government debt/GDP; this optimal level increases with intervention efficiency. - Fiscal space, stability, and optimal intervention (Figure 6): - As government debt rises above ≈100% of GDP, the model’s region of stability shrinks and allowable financial assistance becomes constrained. - For debt below 90% of GDP, desirable intervention level ε* stays virtually constant. - ε* declines monotonically as debt increases above 90% and from about 110% of GDP onward coincides with the maximum allowed by the stability condition. - High government debt makes direct intermediation costly: even small efficiency losses can make intervention lead to instability due to large sovereign risk premia. ### Overall conclusions and policy implications (Sections 2, 3, 5.1–5.2) - Do private and public debt levels amplify swings? Yes, with qualifications: - Private debt booms increase recession severity; larger booms produce worse recessions. - Public debt exacerbates downturns mainly when particularly high because it impairs fiscal accommodation during private deleveraging. - Accelerations in private debt are as, or possibly more, worrisome than accelerations in public debt. - On government intervention: - Targeted financial assistance to credit-constrained agents during rapid deleveraging is desirable when fiscal space exists and interventions are reasonably efficient. - Limits: intervention is constrained by debt sustainability, fiscal limits (calibrated with reference to Greece), distortionary taxation, sovereign risk premia, and possible inefficiencies from direct intermediation. - Excessive or inefficient intervention is self-defeating. - Policy recommendations highlighted: - Cap LTV ratios at safer levels to reduce macrofinancial vulnerabilities from credit booms. - Surveillance should pay greater attention to private indebtedness risks, not only public debt metrics. - Maintain fiscal space before crises to preserve countercyclical capacity. - Fiscal rules could be adjusted to recognize government’s mitigating role during deleveraging (debt consolidations should be more gradual amid deleveraging). *Source: IMF Working Paper _wp16104 (sections 1–5, Tables 1–2, Appendix B as reproduced in the supplied content).* ### 3.1 Patient households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 ### _wp16104 - 3.1 Patient households ### Introduction and motivation - The global financial crisis followed an extraordinary upward swing in the leverage cycle; when the bubble burst, massive private-sector debt accumulation triggered debt deflation dynamics that propelled the ratio of public debt-to-GDP very rapidly. - Recent empirical literature documents that credit growth predicts financial crises and that, conditional on having a recession, stronger credit growth predicts deeper recessions. - Existing models do not fully reproduce empirical macro-financial links between private and public balance sheets or the dynamic interaction between fiscal and private agents during leverage cycles. - Objective: derive a minimum model structure that reproduces leverage cycles, captures interactions between private and public debt, and is suitable for policy analysis of crisis-style events featuring high private leverage and government intervention. ### Empirical revisitation: link between private/public debt and economic activity (Section 2) - Data and sample: - Unbalanced panel annual dataset covering 30 advanced and emerging market countries. - Sample stretching from 1960 to 2014. - Empirical specification: - Baseline dependent variable: future output growth over three years, 3yit+3. - Main regressors: change in total private debt-to-GDP ratio in the previous three years, 3(PRD/Y)it−1, and change in public debt-to-GDP ratio in the previous three years, 3(PUD/Y)it−1. - Also analyze levels of debt-to-GDP ratios (lagged one year) and subsamples by public debt level (cutoff at 95 percent of GDP). - Detrended real GDP (HP-filtered) used as alternative dependent variable: ˆyit+3. - Key empirical findings: - Change in private debt and subsequent growth: - A one standard deviation increase in the change in total private debt-to-GDP ratio (14 percentage points) is associated with a 1.8% lower output growth in subsequent years on average. - Table 1 (columns 1–2) reports coefficients on 3(PRD/Y)it−1 of -0.128*** and -0.143*** (standard errors in parentheses: (0.014) and (0.016)). - Change in public debt and subsequent growth: - The change in the public debt-to-GDP ratio is not a significant predictor of changes in future output when the change in private debt is included (Table 1, column 2, 3(PUD/Y)it−1 = -0.014 with (0.019)). - Levels of debt-to-GDP and subsequent growth: - Lagged level of private debt PRD/Yit−1 is significantly correlated with subsequent GDP change: coefficients reported in Table 1 (columns 3–4 and 5–6) include -0.086*** (0.005), -0.095*** (-0.006), -0.087*** (0.006), and -0.212*** (0.030). - Lagged level of public debt PUD/Yit−1 is generally not significant for the full sample (Table 1), but its effect depends on the public-debt regime. - Nonlinearities by public-debt regime: - When public debt is low or medium (≤ 95 percent of GDP), the level of the public-debt-to-GDP ratio becomes positively correlated with subsequent growth (Table 1, column 5: PUD/Yit−1 = 0.057*** (0.015)), suggesting fiscal expansions can attenuate deleveraging if fiscal space exists. - When public debt is high (> 95 percent of GDP), the negative relationship between changes in private debt and subsequent GDP growth is exacerbated and the coefficient on public debt changes sign and is significant (Table 1, column 6: PUD/Yit−1 = -0.119*** (0.032)). - Quantified effect: in low-to-medium public debt environments, the negative impact of a change to private debt-to-GDP is reduced by one tenth; whereas it doubles when public debt is high. - Cyclical (detrended) output results (Table 2): - PRD/Yit has negative correlations with detrended output three years later: - Table 2 coefficients: PRD/Yit = -0.007*** (0.003) in column 1; -0.012*** (0.003) in column 2; -0.012*** (0.003) in column 3; -0.043*** (0.013) in column 4. - PUD/Yit is insignificantly related to detrended output for the full sample or for PUD/Yit ≤ 95% subsample; it becomes negative and significant for PUD/Yit > 95% (Table 2, column 4: PUD/Yit = -0.029** (0.013)). - Interpretation: - Empirical evidence suggests countries with more “fiscal space” are better positioned to weather a financial crisis because automatic stabilizers and targeted government financial assistance can alleviate private deleveraging, whereas high public debt impairs these stabilizing mechanisms. ### Model setup (Section 3) - Model purpose: reproduce observed relationships between debt and output and analyze government intervention as lender of last resort providing financial assistance to credit-constrained agents. - Core structure: - Closed-economy, Kiyotaki and Moore (1997) backbone with Iacoviello (2005) modifications for housing-market borrowing constraints, embedded into a New-Keynesian setting. - Enrichments: fiscal policy, government indebtedness, sovereign risk premium (in line with Corsetti et al., 2013), and government intermediation of funds (in line with Gertler and Karadi, 2011). - Agents and frictions: - Patient households: work, consume, buy housing, invest in riskless private bonds and government bonds. - Impatient households: work, consume, borrow subject to collateral constraints. - Entrepreneurs: borrow subject to collateral constraint and produce in monopolistic competition. - Government: finances expenditures via lump-sum and distortionary taxes and issuing government bonds; government debt subject to sovereign default risk and calibrated fiscal limit (calibrated on real-world default cases, namely Greece). - Central bank: monetary policy follows a Taylor-type rule. - No banks are explicitly modeled (to keep model simple without loss of generality). - Definitions and mechanisms: - Leverage cycle: increase (decrease) in private indebtedness caused by loosening (tightening) of borrowing constraints when debt collateral appreciates (depreciates). - Deleveraging: reduction in liabilities via cuts to borrowing. - Crisis: a drop in collateral value reducing credit availability out of future income. - Public intervention: credit extended by government to financially-constrained agents to alleviate collateral-driven borrowing constraints. - Fiscal and monetary interaction: - Fiscal rule: government expenditures and taxes react to stabilize public debt compatibly with fiscal limits. - Model captures two key links between private and public indebtedness: - Through the financial accelerator, private deleveraging reduces output and prices, depressing government revenues. - Public debt increases due to government interventions to alleviate private borrowing constraints, which mitigates private deleveraging but can raise sovereign risk and necessitate fiscal consolidation. - Model calibration and empirical alignment: - Shocks and steady-state ratios calibrated on average euro area data. - Model reproduces empirical findings that: (i) higher private leverage leads to more severe recessions and worse public finances, and (ii) initially high public debt exacerbates recessions because of lack of fiscal space. - Model shows that financial assistance to credit-constrained agents during rapid deleveraging is desirable, but assistance is constrained by debt sustainability, distortionary taxation, sovereign risk premia, and possible inefficiencies from direct government intermediation. ### Policy implications and caveats (from the model and empirical results) - Policy recommendations supported by the analysis: - It is desirable for policymakers to provide targeted financial assistance to credit-constrained agents during phases of rapid private deleveraging, to alleviate credit constraints and stabilize output and prices. - Maintaining fiscal space prior to crises improves the government’s ability to act countercyclically and to intervene effectively in private deleveraging episodes. - Caveats and trade-offs: - Financial assistance is limited by debt sustainability constraints and the government’s fiscal limit (calibrated with reference to Greece in the model). - Direct government intermediation may create inefficiencies and interact adversely with distortionary taxation and sovereign risk premia; these costs must be weighed against stabilizing benefits. - High initial public debt can double the adverse effect of private deleveraging on growth relative to lower public-debt regimes. *Source: IMF Working Paper _wp16104 (sections 1–3, Tables 1–2 as reported in the provided content).* ### 3.1 Patient households ### 3.1 Patient households ### Preferences and objective - Households are infinitely-lived and solve an intertemporal utility maximization problem with expected lifetime utility: - U_t = E_t sum_{s=0}^{1} δ^{t+s} [ ln X'_ {t+s} + e^H_{t+s} ( ln h'_{t+s} - L'_{t+s} ) ], - where δ ∈ (0,1) is the discount factor; - X'_t is habit-adjusted consumption; - e^H_t is a housing shock (as in Iacoviello (2015)); - h'_t are housing holdings; - L'_t is labor supply; - ζ is a housing preference parameter; - η measures the elasticity of labor with respect to the real wage. - Habit-adjusted consumption: - X'_t = C'_t - θ C'_{t-1}, - where C'_t is consumption and θ ∈ (0,1) is the degree of habit formation. ### Choices and assets - Patient households choose consumption C'_t, housing h'_t, and labor L'_t. - They trade: - riskless private bonds B_t; - nominal government bonds B^G_t. - They pay: - lump-sum taxes τ^L_t; - distortionary taxes τ^C_t on consumption and τ^W_t on labor income. - They receive: - hourly wage W'_t; - nominal return on private bonds R_t; - nominal return on government bonds R^G_t discounted at the ex-ante expected haircut rate ̄g_t; - government transfers Ξ_t. ### Flow budget constraint (as stated) - Patient households’ budget constraint reads as: - (1+τ^C_t)^{-1} C'_t + q_t h'_t + B'_t / P_t + B^G_t / P_t + τ^L_t = (1-τ^W_t) W'_t L'_t / P_t + R_{t-1} B'_{t-1} / P_t + (1-̄g_t) R^G_{t-1} B^G_{t-1} / P_t + Ξ_t. - (The model text presents the constraint in the form shown in equation (4).) ### Role in the model - Patient households supply labor, hold housing, save in private and government bonds, and are the ultimate lenders to impatient households and entrepreneurs. - The patient households’ discount factor is calibrated in the baseline to =0.99 (Table 3). *Source: _wp16104 - 3.1 Patient households* ### 5.1 Do the levels of private and public debt amplify swings ### 5.1 Do the levels of private and public debt amplify swings in economic activity over the leverage cycle? ### Experimental setup and shock - The downward phase of the leverage cycle is triggered by a temporary negative house price shock: house prices fall by one percent. - The shock depresses the value of housing collateral, tightening borrowing constraints for constrained agents and forcing private deleveraging via cuts to consumption and investment. - Resulting dynamics include a protracted output contraction and deflation. The model’s response matches observed relationships between changes in house prices and the output gap (example cited: in 2009q1, the S&P/Case-Shiller Home Price Index fell by about 24% from its trend and by the end of 2009 the U.S. output gap had reached 3.2%, a level close to what the model would suggest, ⇡0.15⇥24 = 3.7). ### Mechanisms linking private deleveraging to public finances - Fall in output reduces government revenues and raises the public debt-to-GDP ratio. - Mechanisms amplifying public debt increases: - debt deflation; - higher public indebtedness boosts the sovereign risk premium and government financing costs; - government reacts endogenously (via equations (19) and (20)) to partially mitigate private deleveraging, entailing payment of premium RGt − Rt in financial markets and efficiency losses (government intervention is small in baseline calibration; effects disentangled in Subsection 5.2). ### Role of high private vs. high public debt (Figure 3 scenarios) - High private debt scenario: - Steady-state public debt at baseline; private debt higher because LTV ratios set at high-range euro-area values (m00 = 0.99 and m = 0.44). - Stronger financial accelerator leads to deeper and stronger deleveraging than baseline, causing a more severe fall in aggregate demand, deeper GDP contraction, and deflation. - Stronger fall in government revenues and debt deflation produce a more pronounced increase in public debt/GDP. - High public debt scenario: - Baseline private debt, but public debt/GDP set high (top percentiles of cross-country averages; still below fiscal limit ̄=1). - Recession is milder yet more persistent relative to high private debt case. - Effects on deleveraging and inflation are negligible compared to baseline because government can borrow more to partially absorb the shock despite smaller fiscal buffers and higher financing costs. - More protracted recession driven by higher-than-baseline sovereign risk premium, higher interest payments, and anticipated higher future tax rates. - If public debt is sufficiently below fiscal limit, government is better off increasing debt to absorb a negative shock (reminiscent of Ostry et al. (2015)). ### Systematic sensitivity across parameter ranges (Figure 4) - Experiments vary: - Caps on LTV ratio (m, m00 vary between 0.375 and 0.95); x-axis reports resulting private debt/GDP for comparison. - Long-run steady-state public debt/GDP ratio ( varies between 0.6 and 1.2). - Four additional findings: 1. Economic contraction is increasingly worse the higher the LTV ratio. 2. Initial level of public debt has no bearing on contraction severity if public debt is below a certain level (approximately 100% of annual GDP in the calibrated model), consistent with panel regression results. 3. Public debt/GDP ratio after a shock is positively correlated with the initial level of private debt: larger private liabilities pre-shock lead to worse public debt legacy because of faster deleveraging and greater government support. 4. Higher caps on the LTV ratio cause more deleveraging; the amount of deleveraging after the shock marginally depends on the level of public debt. 5. Deflationary effects of the negative house price shock are stronger the higher the LTV ratio; inflation is barely affected by steady-state public debt level. ### Policy question: Should governments extend financial assistance to credit-constrained agents? (Section 5.2) - Government instrument modeled: lend money directly to private borrowers (impatient households and entrepreneurs) during deleveraging to relax borrowing constraints and smooth spending. - Real-world analogues: mortgage relief programs, government credit for home renovation, “Cash-for-Clunkers”-type programs, and indirect support via financial intermediaries. - Two main trade-offs for government intervention: 1. Intervention costs versus benefits: output/fiscal revenue support must outweigh adverse impact on output (and revenues) from subsequent fiscal consolidations needed to finance the intervention (government assistance increases public debt). 2. Fiscal space constraint: room for intervention depends on distance between initial government debt stock and fiscal limit; higher public debt narrows capacity to intervene and worsens the first trade-off. ### Channels to instability from government intervention - Two mechanisms through which government debt may become unstable: 1. Higher sovereign risk premia associated with higher public debt stocks (raising borrowing costs RGt). 2. Direct intermediation: government borrows at RGt to lend to private sector at Rt (< RGt), incurring efficiency loss κ and additional fiscal cost. ### Numerical experiments on intervention magnitude and efficiency (Figure 5) - Baseline experiment: private debt high (m00 = 0.99 and m = 0.44); government indebtedness baseline ( = 0.68); fiscal stance ρB = 0.05 to guarantee public debt stability. - Comparative statics over government reaction parameter ε ∈ [0,1] and inefficiency κ ∈ {0, 0.1, 0.2}. - Key results: - There exists a non-zero level of government intervention that minimizes output losses. - The more efficient the intervention (lower κ), the bolder the output-loss-minimizing degree of intervention (higher ε). - Stronger intervention mitigates private deleveraging and deflation virtually irrespective of κ. - There exists a non-zero intervention level that minimizes the surge in government debt/GDP; this optimal level is an increasing function of intervention efficiency. ### Fiscal space, stability, and optimal intervention (Figure 6) - As government debt rises above values around 100% of GDP, the model’s region of stability shrinks and allowable financial assistance becomes constrained. - At high government debt levels, even small efficiency losses make direct intermediation costly due to large sovereign risk premia, making government debt prone to instability. - Trough-minimizing level of intervention ε* as function of government debt Γ: - For debt below 90% of GDP, desirable intervention level stays virtually constant. - ε* declines monotonically as debt increases above 90% and from about 110% of GDP onward coincides with the maximum allowed by stability condition. ### Overall conclusions from Sections 5.1–5.2 - Do private and public debt levels amplify swings? Yes, with caveats: - Private debt booms raise the severity of recessions; larger booms produce worse recessions. - Public debt exacerbates downturns mainly when its level is especially high because high public debt impairs fiscal accommodation during private deleveraging. - Accelerations in private debt are as, or possibly more, worrisome than accelerations in public debt. - Fiscal buffers increase macroeconomic resilience to financial shocks after high-leverage phases; under mild leverage cycles, buffers are less valuable but still important. - Should governments extend targeted financial assistance to credit-constrained agents? Yes, conditional on: - Targeted lending to constrained agents (not blanket fiscal stimulus) can mitigate deleveraging and improve output and revenues. - Limits exist due to debt sustainability; trade-offs rise with higher public debt and with greater inefficiency of intervention. - If fiscal space exists and interventions are reasonably efficient, moderate targeted intervention is desirable; excessive or inefficient intervention is self-defeating. - Policy implications highlighted: - Capping LTV ratios at safer levels reduces macrofinancial vulnerabilities from credit booms. - Surveillance should pay greater attention to private indebtedness risks, not only public debt metrics. - Fiscal rules could be adjusted to recognize the government’s mitigating role during deleveraging phases (debt consolidations should be more gradual amid deleveraging). - Restricting above-safe LTV loan options would likely limit realizations of deep and prolonged recessions. *Source: IMF working paper section 5.1–5.2 (as reproduced in the supplied content).* ### References ### _wp16104 - References ### Major thematic areas in the cited literature - Financial accelerator, credit channels, and house prices - Aoki, K., Proudman, J., and Vlieghe, G. (2004). House prices, consumption, and monetary policy: A financial accelerator approach. - Bernanke, B. and Gertler, M. (1995). Inside the black box: the credit channel of monetary policy transmission. - Bernanke, B., Gertler, M., and Gilchrist, S. (1999). The financial accelerator in a quantitative business cycle model. - Iacoviello, M. (2005). House prices, borrowing constraints, and monetary policy in the business cycle. - Gertler, M. and Karadi, P. (2011). A model of unconventional monetary policy. - Axtell, Geanakoplos et al. (2012). Agent-based model of the housing market and systemic risk. - Credit booms, private credit, and macrofinancial stability - Schularick, M. and Taylor, A. M. (2012a, 2012b). Credit booms gone bust: Monetary policy, leverage cycles, and financial crises, 1870-2008. - Jordà, Ò., Schularick, M., and Taylor, A. M. (2013, 2014). When credit bites back; Private credit and public debt in financial crises. - Dell’Ariccia, G., Igan, D., Laeven, L., Tong, H., Bakker, B., and Vandenbussche, J. (2012). Policies for macrofinancial stability: How to deal with credit booms. - Sovereign risk, public debt, and fiscal limits - Corsetti, G., Kuester, K., Meier, A., and Müller, G. J. (2013). Sovereign risk, fiscal policy and macroeconomic stability. - Bi, H. and Traum, N. (2014). Estimating fiscal limits: The case of Greece. - Ostry, J. D., Ghosh, A. R., and Espinoza, R. A. (2015). When should public debt be reduced? - Leverage, liquidity traps, and crises - Eggertsson, G. B. and Krugman, P. (2012). Debt, deleveraging, and the liquidity trap: A Fisher-Minsky-Koo approach. - Korinek, A. and Simsek, A. (2014). Liquidity trap and excessive leverage. - Guerrieri, V. and Lorenzoni, G. (2015). Credit crises, precautionary savings, and the liquidity trap. - Farhi, E. and Werning, I. (2015). A theory of macroprudential policies in the presence of nominal rigidities. - Historical perspectives and broader syntheses - Fisher, I. (1933). The debt-deflation theory of great depressions. - Minsky, H. P. (1982). Can it happen again? Essays on Instability and Finance. - Mian, A. R. and Sufi, A. (2014). House of debt: how they (and you) caused the Great Recession and how we can prevent it from happening again. - Taylor, A. M. (2012). Review of This Time Is Different: Eight Centuries of Financial Folly. - Empirical methods and models referenced - Smets, F. and Wouters, R. (2003). An estimated dynamic stochastic general equilibrium model of the euro area. - Westerlund, J. (2007). Testing for error correction in panel data. - Christiano, L., Motto, R., and Rostagno, M. (2010). Financial factors in economic fluctuations. ### Table A.1: Countries in Panel Regressions and Descriptive Statistics (private and public debt) - Australia — Private debt: Years 1960-2014 Average 110.62 Std. dev. 47.21; Public debt: Years 1989-2014 Average 21.75 Std. dev. 8.03 - Austria — Private debt: Years 1960-2014 Average 92.29 Std. dev. 38.36; Public debt: Years 1988-2014 Average 68.27 Std. dev. 9.28 - Belgium — Private debt: Years 1970-2014 Average 120.52 Std. dev. 45.38; Public debt: Years 1980-2014 Average 111.33 Std. dev. 16.01 - Canada — Private debt: Years 1955-2014 Average 126.49 Std. dev. 36.49; Public debt: Years 1980-2014 Average 78.12 Std. dev. 14.39 - Czech Republic — Private debt: Years 1993-2014 Average 77.25 Std. dev. 10.07; Public debt: Years 1995-2014 Average 27.92 Std. dev. 11.11 - Denmark — Private debt: Years 1966-2014 Average 162.54 Std. dev. 48.05; Public debt: Years 1992-2014 Average 51.00 Std. dev. 13.89 - Finland — Private debt: Years 1970-2014 Average 120.34 Std. dev. 31.20; Public debt: Years 1980-2014 Average 36.61 Std. dev. 16.67 - France — Private debt: Years 1969-2014 Average 125.86 Std. dev. 25.73; Public debt: Years 1980-2014 Average 54.93 Std. dev. 22.21 - Germany — Private debt: Years 1960-2014 Average 100.24 Std. dev. 19.14; Public debt: Years 1991-2014 Average 62.37 Std. dev. 11.61 - Greece — Private debt: Years 1970-2014 Average 62.28 Std. dev. 33.17; Public debt: Years 1980-2014 Average 91.52 Std. dev. 45.06 - Hong Kong — Private debt: Years 1978-2014 Average 163.28 Std. dev. 48.74; Public debt: Years 2001-2014 Average 1.18 Std. dev. 1.00 - Hungary — Private debt: Years 1989-2014 Average 81.49 Std. dev. 33.96; Public debt: Years 1997-2014 Average 66.83 Std. dev. 10.04 - Indonesia — Private debt: Years 1976-2014 Average 35.96 Std. dev. 15.05; Public debt: Years 2000-2014 Average 40.31 Std. dev. 20.11 - Ireland — Private debt: Years 1971-2014 Average 135.17 Std. dev. 85.22; Public debt: Years 1995-2014 Average 61.43 Std. dev. 33.97 - Italy — Private debt: Years 1960-2014 Average 79.55 Std. dev. 21.70; Public debt: Years 1988-2014 Average 109.02 Std. dev. 11.61 - Japan — Private debt: Years 1964-2014 Average 169.53 Std. dev. 30.98; Public debt: Years 1980-2014 Average 132.25 Std. dev. 66.72 - Korea, Rep. — Private debt: Years 1962-2014 Average 107.75 Std. dev. 52.29; Public debt: Years 1990-2014 Average 21.63 Std. dev. 9.58 - Mexico — Private debt: Years 1980-2014 Average 28.30 Std. dev. 10.07; Public debt: Years 1980-2014 Average 34.92 Std. dev. 23.07 - Netherlands — Private debt: Years 1961-2014 Average 141.13 Std. dev. 70.35; Public debt: Years 1980-2014 Average 63.21 Std. dev. 10.56 - Norway — Private debt: Years 1960-2014 Average 144.30 Std. dev. 36.05; Public debt: Years 1980-2014 Average 36.63 Std. dev. 8.53 - Poland — Private debt: Years 1992-2014 Average 50.17 Std. dev. 21.06; Public debt: Years 1995-2014 Average 46.61 Std. dev. 5.70 - Portugal — Private debt: Years 1960-2014 Average 124.69 Std. dev. 49.46; Public debt: Years 1990-2014 Average 72.27 Std. dev. 28.40 - Singapore — Private debt: Years 1970-2014 Average 98.78 Std. dev. 19.75; Public debt: Years 1963-2014 Average 67.57 Std. dev. 25.84 - Spain — Private debt: Years 1970-2014 Average 123.53 Std. dev. 44.86; Public debt: Years 1980-2014 Average 52.09 Std. dev. 19.57 - Sweden — Private debt: Years 1961-2014 Average 138.07 Std. dev. 44.74; Public debt: Years 1993-2014 Average 50.70 Std. dev. 12.56 - Switzerland — Private debt: Years 1960-2014 Average 156.31 Std. dev. 33.05; Public debt: Years 1983-2014 Average 48.33 Std. dev. 11.11 - Thailand — Private debt: Years 1970-2014 Average 86.46 Std. dev. 40.24; Public debt: Years 1996-2014 Average 43.65 Std. dev. 9.64 - Turkey — Private debt: Years 1986-2014 Average 31.74 Std. dev. 18.82; Public debt: Years 1987-2014 Average 40.45 Std. dev. 12.38 - United Kingdom — Private debt: Years 1963-2014 Average 110.19 Std. dev. 46.68; Public debt: Years 1980-2014 Average 49.87 Std. dev. 17.12 - United States — Private debt: Years 1952-2014 Average 110.83 Std. dev. 29.93; Public debt: Years 1947-2014 Average 85.54 Std. dev. 15.25 ### Appendix B: Equilibrium conditions (selected first-order conditions and defining relations) B.1 Patient households - Intertemporal maximization yields the following first-order conditions with respect to C0t, L0t, B0t, BGt and h0t: - μ0t = 1/(1 + τCt) X0t, (B.1) - (1 − τWt) W0t/Pt = (L0t)^{η−1} − 1+τCt X0t, (B.2) - 1/(1 + τCt) X0t = −Et[ Rt − 1+τCt+1 X0t+1 Πt+1 ], (B.3) - 1/(1 + τCt) X0t = −Et[ 1/ΓGt+1 − RGt − 1+τCt+1 X0t+1 Πt+1 ], (B.4) - qt (1 + τCt) X0t = ζe Ht h0t + Et[ qt+1 − 1+τCt+1 X0t+1 ], (B.5) - Definitions and implications: - μ0t is the Lagrange multiplier associated to the budget constraint and Πt+1 ≡ Pt+1/Pt represents the gross inflation rate. - Equations (B.3) and (B.4) imply a non-arbitrage condition between the riskless interest rate and that on government bonds, whereby a sovereign risk spread arises, i.e. RGt = Et[ 1/ΓGt+1 − 1 ] Rt. B.2 Impatient households - Intertemporal maximization yields the following first-order conditions with respect to C00t, L00t, B00t and h00t: - μ00t = 1/(1 + τCt) X00t, (B.6) - (1 − τWt) W00t/Pt = (L00t)^{η−1} − 1+τCt X00t, (B.7) - 1/(1 + τCt) X00t = −λ00Et[ Rt − 1+τCt+1 X00t+1 Πt+1 ] + λ00t Rt, (B.8) - qt (1 + τCt) X00t = ζe Ht h00t + Et[ λ00 qt+1 − 1+τCt+1 X00t + λ00t m00 qt+1 Πt+1 ], (B.9) - Definitions: - μ00t is the Lagrange multiplier associated to the flow of funds and λ00t is the Lagrange multiplier associated with the borrowing constraint. B.3 Entrepreneurs - Maximization of function (11) subject to constraints (9), (10), (12), (13), (14), (15) and the two quadratic adjustment costs yields the following first-order conditions evaluated at the symmetric equilibrium: - μt = 1/(1 + τCt) Xt, (B.10) - μt = −λt Rt + Et[ μt+1 Rt/Πt+1 ], (B.11) - ut = μt [ 1 + (K̄) ( I t/Kt−1 − ) ], (B.12) - ut = Et[ μt+1 ( K̄ ( I t+1/Kt ) I t+1/Kt − K̄^2 ( I t+1/Kt )^2 + h ( μt+1 MCt+1 ) Yt+1/Kt + (1 − δ) ut+1 ) ], (B.13) - μt qt = Et[ −μt+1 ( qt+1 + MCt+1 ν Yt+1 h t − + mt qt+1 Πt+1 ) ], (B.14) - w0t = MCt α (1 − ω − ν) Yt L0t, (B.15) - w00t = MCt (1 − α) (1 − ω − ν) Yt L00t, (B.16) - 0 = 1 + e Pt − (MCt − 1) − φP (Πt − 1) Πt + φP Et[ −μt+1/μt (Πt+1 − 1) Πt+1 Yt+1/Yt ], (B.17) - Definitions and notation as in the source: - λt is the Lagrange multiplier associated with the borrowing constraint, MCt is the firm’s marginal cost, and ut is Tobin’s q. *Italic: Content derived from _wp16104 - References and Appendix as provided in the source PDF.* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16104.pdf_