## wpiea2020237-print-pdf

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---

### Pre- and Post-GFC Policy Multipliers (summary of Section 1)
- Purpose: estimate change in U.S. policy multipliers relative to pre-2008 financial crisis levels using an augmented Blanchard-Perotti framework that allows dynamic effects of shocks to the central bank balance sheet, real interest rates and debt levels on economic activity.
- Key empirical findings:
  - Expenditure multipliers have fallen post-2008 because of higher government debt, implying reduced effectiveness of fiscal policy.
  - Quantitative easing (QE) is beneficial but requires sizable balance sheet interventions to lead to noticeable effects on real GDP.
  - Rising debt stocks make dealing with a crisis increasingly costly despite the current low interest rate environment.
- Use case: results used to assess impact of policy packages to address COVID-19.
- Context: G7 response to the 2008 crisis combined expansionary fiscal and accommodative monetary policies, resulting in elevated public debt and substantially larger central bank balance sheets.

### Model, identification, and estimation approach (Sections 1–2)
- Baseline reduced-form VAR:
  - Y_t = μ + Σ_{j=1}^p A_j Y_{t-j} + U_t where Y_t = [T_t, G_t, X_t]' are logs of quarterly taxes, primary expenditure and GDP, measured in real, per capita terms.
- Structural form and identification:
  - Structural VAR: Ω U_t = Φ V_t with V_t = [e_t^t, e_t^g, e_t^x]'.
  - Identification follows Blanchard and Perotti (2002); the paper takes a_3 = 2.08 (quarterly data) as the elasticity of taxes to an output shock for baseline and assesses sensitivity.
  - Example identifying matrices provided (Ω and Φ) and the paper notes initial under-identification resolved by Blanchard and Perotti via setting either a5 or b4 to zero.
- Expanded (augmented) VAR to guard against omitted variable bias:
  - Augmentation includes central bank balance sheet size relative to GDP (BS_t), real interest rate (R_t), and debt-to-GDP ratio (D_t) as exogenous/deterministic regressors.
  - Augmented reduced-form: Y_t = μ + Σ_{j=1}^p A_j Y_{t-j} + Σ_{i=0}^k C_i D_{t-i} + U_t with Y_t = [T_t, G_t, X_t, BS_t, R_t]'.
- Data and sample:
  - U.S. quarterly data, 1966Q1-2019Q4.
  - Endogenous variables: real revenue per capita, real expenditure per capita, real GDP per capita, Federal Reserve balance sheet assets (relative to GDP), and the real interest rate.
  - Exogenous variable: debt-to-GDP ratio (outstanding debt of the general government divided by nominal GDP).
  - Real interest rate defined as the 10-year bond yield less the inflation rate measured by the GDP deflator.
  - Federal Reserve asset holdings measured at end of each quarter.
- Notable level movements:
  - Debt ratio increased from 63 percent at the end of 2007 to approximately 107 percent by the end of 2019.
  - Federal Reserve asset holdings increased from 6 to 19 percent of GDP over the same period.
  - Footnote: Federal Reserve asset ratio relative to GDP peaked at 25 percent at the end of 2014.
- Estimation strategy:
  - Unconstrained VAR in levels with a single lag (lag length chosen by Schwarz Information Criterion); unit roots detected and one cointegrating vector found.
  - Structural vector error correction model (SVECM) estimated using Pagan and Pesaran (2008) approach; with one cointegrating vector, four structural shocks assumed to have permanent effects and one transitory shock.
  - SVECM estimated by maximum likelihood; model treated as non-linear by construction.

### Empirical results: multipliers and counterfactual scenarios (Sections 2–3)
- General pre/post comparison:
  - Pre-crisis (up to 2007Q4) expenditure multipliers are stronger than post-crisis (up to 2019Q4).
  - After eight quarters, the impulse response of real GDP per capita to an expenditure shock is more than four times larger using the model estimated up to 2007 than using data up to 2019.
  - After eight quarters, the impulse response to a tax shock is more negative (almost 40 percent larger in absolute terms) for the pre-GFC estimation than for the post-GFC estimation.
  - Conclusion: both the expenditure multiplier and the tax multiplier for the U.S. have fallen since the onset of the GFC.
- Shock timing and response horizon used for comparisons:
  - Pre-crisis shock at 2006Q1; post-crisis shock at 2018Q1; responses traced for 8 quarters; shocks are unit percentage changes with responses expressed as percentage changes in real GDP per capita relative to baseline.

- Scenario 1 — one percentage point increase in the debt ratio:
  - Immediate response: real GDP per capita decreases initially both pre- and post-crisis, with the negative effect slightly larger pre-crisis (Panel A).
  - After 4 periods: impact still negative but declining toward zero; negative impact larger post-crisis compared to pre-crisis in absolute terms.
  - Accumulated impact: overall impact of higher government debt on real GDP is negative.
  - Contextual numeric level: U.S. debt level reached 107 percent by March 2020.
  - Channels: expectations of higher taxes, private saving responses, public investment (debt overhang), total factor productivity effects, and long-term interest rates (crowding out).

- Scenario 2 — one percentage point increase in government expenditure (deficit-financed):
  - Both pre- and post-crisis multipliers show a positive response in real GDP per capita.
  - The fiscal multiplier has declined post 2008Q1 — sensitivity of real GDP per capita to increases in government expenditure is significantly lower post-GFC.
  - Mechanism: larger negative coefficient on the debt ratio in the real GDP per capita equation using post-crisis data implies stronger negative feedback from expenditure-driven debt accumulation.

- Scenario 3 — one percentage point increase in government taxes:
  - Both pre- and post-crisis tax multipliers show a negative response in real GDP per capita.
  - Estimated elasticity of taxes in the real GDP per capita equation increased slightly (in absolute terms) post-crisis.
  - Effect partly offset by reduction in the debt ratio due to higher taxes.
  - Note: transitory versus permanent nature of tax policy affects consumption/saving behavior and ultimately real GDP.

- Scenario 4 — one-time one percentage point increase in Federal Reserve balance sheet relative to GDP (not reversed):
  - Both pre- and post-crisis responses of real GDP per capita to the balance sheet shock are positive but small.
  - Conclusion: sizable increases (e.g., 10 times) in the balance sheet are needed to have similar effects on GDP per capita as a comparable increase in primary expenditure.
  - Impact is relatively weaker in post-crisis years than pre-crisis years.

- Scenario 5 — 100 basis points increase in the interest rate:
  - Increase in interest rates has negative impact pre- and post-GFC.
  - Initially the negative impact is weaker in post-crisis years in absolute terms; after the second period the post-crisis impact is larger in absolute terms.
  - Possible cause: higher government debt in the post-crisis period implies higher interest payments, faster accumulation of debt, and larger drag on real GDP given a larger post-crisis negative coefficient on the debt ratio.

- Conversion factors and average shares (used to convert elasticity to dollar terms; multipliers expressed in elasticity terms in paper):
  - Real Primary Expenditure per capita:
    - Average Shares 2004Q1-2007Q4 = 0.30; Conversion Factor 2004Q1-2007Q4 = 3.3.
    - Average Shares 2016Q1-2019Q4 = 0.31; Conversion Factor 2016Q1-2019Q4 = 3.2.
  - Real Taxes:
    - Average Shares 2004Q1-2007Q4 = 0.28; Conversion Factor 2004Q1-2007Q4 = 3.6.
    - Average Shares 2016Q1-2019Q4 = 0.28; Conversion Factor 2016Q1-2019Q4 = 3.6.
  - Federal Reserve Asset holdings relative to GDP:
    - Average Shares 2004Q1-2007Q4 = 0.06; Conversion Factor 2004Q1-2007Q4 = 16.6.
    - Average Shares 2016Q1-2019Q4 = 0.23; Conversion Factor 2016Q1-2019Q4 = 4.4.
  - Note: conversion factors are sensitive to sample period; multipliers therefore expressed in elasticity terms in the paper.

### Statistical tests, historical decomposition, and robustness (Section 3)
- Tests of equality of impulse response functions pre- and post-GFC (Table 1 — F-statistics and p-values):
  - Primary Expenditure: F-statistic 262.6048, p-Value 0.0000
  - Taxes: F-statistic 164.6404, p-Value 0.0000
  - Federal Reserve Assets Ratio: F-statistic 164.0191, p-Value 0.0000
  - Real Interest Rate (basis points): F-statistic 162.4467, p-Value 0.0000
  - Debt-to-GDP Ratio (percent): F-statistic 247.5926, p-Value 0.0000
  - Conclusion: the null hypothesis of no change is rejected convincingly for all policy multipliers.
- Historical decomposition (ranked average contributors to real GDP per capita):
  - 2002-2004: shocks to debt (negative), taxes (positive), real interest rate (negative).
  - 2005-2007: shocks to taxes (negative), debt-ratio (positive), Federal Reserve asset holdings (negative).
  - 2014-2016: shocks to real interest rate (negative), taxes (positive), Federal Reserve asset holdings (negative).
  - 2017-2019: shocks to taxes (positive), Federal Reserve asset holdings (negative), debt (negative).
- Regression of historical decomposition on structural shocks (Table 2 — estimates and p-values, Chow test with break at 2008Q1):
  - Primary Expenditure: 1996Q1-2007Q4 = 0.1396; 2008Q1-2019Q4 = 0.0759; p-Value 0.0000 *
  - Taxes: 1996Q1-2007Q4 = -0.1162; 2008Q1-2019Q4 = -0.1054; p-Value 0.0000 *
  - Federal Reserve Assets Ratio: 1996Q1-2007Q4 = 0.0422; 2008Q1-2019Q4 = 0.0360; p-Value 0.0000 *
  - Real Interest Rate (basis points): 1996Q1-2007Q4 = 0.0011; 2008Q1-2019Q4 = 0.0025; p-Value 0.0001 *
  - Debt-to-GDP Ratio (percent): 1996Q1-2007Q4 = -0.0021; 2008Q1-2019Q4 = -0.0007; p-Value 0.1686
  - An asterisk indicates statistically significant difference across the two periods.
- Simple averages of structural shocks (Table 3) and contributions (Table 4) reported in scientific notation; Table 4 implies:
  - Pre-crisis strongest drivers of real GDP per capita: shocks to debt-to-GDP ratio (positive), taxes (negative), primary expenditure (negative).
  - Post-crisis dominant drivers: shocks to taxes (positive), Federal Reserve asset holdings (positive), debt-ratio (negative).
- Robustness to alternative identifying assumptions:
  - Allowing b3 ≠ 0 and alternative zero restrictions (relaxing Blanchard and Perotti (2003) assumption that government expenditure does not respond within one quarter to changes in real per capita GDP) does not change the main finding that policy multipliers have fallen post-GFC.
  - Authors note empirical results for alternatives available upon request.

### Impact of COVID-19 policy measures (Section 3 — as of May 21, 2020)
- Modeled policy actions:
  - U.S. federal government announced a debt-financed stimulus package of approximately 2.4 trillion dollars, representing a 27 percent increase in government expenditure (or 9 percent of GDP).
  - Federal Reserve asset purchases raised assets relative to GDP from 18 percent at the end of 2019 to 19.2 percent by the end of the first quarter of 2020.
  - Modeling assumptions: increase in government expenditure spread equally over the first 4 quarters; Federal Reserve actions occurred entirely in the first quarter.
- Estimated incremental impact on real GDP per capita using post-crisis estimates:
  - Combined effect (staggered government expenditure + Federal Reserve asset purchases):
    - Less than 0.65 percentage points in the first quarter using the post-crisis model.
    - Rising to 2.5 percent after 5 quarters using the post-crisis model.
  - Corresponding pre-crisis increments:
    - Around 1 percent in the first quarter.
    - Around 3 percent after 5 quarters.
  - Implication: reduced effectiveness of the COVID-19 stimulus measures using post-GFC multipliers compared with pre-crisis multipliers.

### Unconventional monetary policy, fiscal policy, and debt dynamics (Section 4)
- Federal Reserve unconventional actions (2012–2015) summarized:
  - Fed reinvested principal payments on agency debt and MBS into agency MBS; Operation Twist expired December 2012; open-ended purchases of long-term Treasuries at $45 billion a month and MBS at $40 billion a month (beginning September 2012).
  - December 2012 FOMC commitment: keep federal funds rate close to zero at least as long as unemployment > 6½ percent, inflation projected 1–2 years not above 2½ percent, and longer-term inflation expectations well-anchored.
  - Staff estimates: unconventional policies equivalent to a federal funds rate easing of roughly 250 basis points as of end-2012.
  - 2015: Fed’s first rate increase in almost nine years; subsequent pace of increases slowed amid weak activity and global concerns.
  - 2017: plans for gradual and predictable decline in Fed holdings of securities; federal funds rate primary instrument.
- Fiscal consolidation and legislative actions (2013–2017):
  - 2013: structural primary withdrawal estimated to have increased to about 2½ percent of GDP in 2013 from 1¼ percent in 2012.
  - Fiscal consolidation in 2011–13 stronger than anticipated: federal primary structural deficit declined by 1¼ percent of GDP more than predicted in 2011.
  - Bipartisan Budget Act of 2015 suspended debt ceiling until March 2017; Protecting Americans from Tax Hikes Act lowered tax revenues by 3½ percent of GDP over the next 10 years; Fixing America’s Surface Transportation Act commits US$305 billion to surface transportation for 4 years.
  - Administration’s budget (circa 2017) projects federal primary balance moving from a 1.9 percent of GDP deficit to a 2.1 percent of GDP surplus over 10 years under specified policy changes.
- Fiscal stimulus, tax reform, and projected debt dynamics (2018–2024):
  - Combined effect of Tax Cuts and Jobs Act and increased discretionary spending projected to push federal government deficit to exceed 4.5 percent of GDP by 2019.
  - Demand stimulus expected to raise output cumulatively by 1½ percent by 2020, pushing unemployment below 3½ percent.
  - Even with modest consolidation scheduled to start in 2020, federal debt projected to continue climbing, exceeding 90 percent of GDP by 2024.

### Conclusions (Section 3 and Section 8)
- Main conclusions:
  - Elevated debt levels and significantly larger central bank balance sheets affect the strength of fiscal and monetary multipliers.
  - Evidence that expenditure and tax multipliers have fallen post-crisis in the U.S., implying reduced effectiveness of fiscal policy.
  - Effectiveness of unconventional monetary policy via asset purchases is smaller than comparable fiscal measures; large balance-sheet interventions needed for noticeable GDP effects.
  - Dealing with a crisis is becoming more costly, despite the low interest rate environment.

*Source: wpiea2020237-print-pdf*

### Section 1

### Pre- and Post-GFC Policy Multipliers

### Abstract and primary findings
- Paper estimates change in policy multipliers in the U.S. relative to pre-2008 financial crisis levels using an augmented Blanchard-Perotti model that allows dynamic effects of shocks to the central bank balance sheet, real interest rates and debt levels on economic activity.
- Key empirical findings:
  - Expenditure multipliers have fallen post-2008 crisis because of higher government debt, implying that the effectiveness of fiscal policy has declined.
  - Quantitative easing (QE) is beneficial but requires sizable balance sheet interventions to lead to noticeable effects on real GDP.
  - The results imply that, because of rising debt stocks, dealing with a crisis is becoming more costly despite the current low interest rate environment.
- Use case: results are used to assess the impact of the policy packages to address COVID-19.

### Context and motivation
- G7 response to the 2008 global financial crisis combined expansionary fiscal and accommodative monetary policies, plus structural policies.
- Consequence: elevated public debt in nearly all G7 countries (Figure 1) and substantially larger central bank balance sheets (Figure 2), potentially constraining future countercyclical fiscal and monetary policy.
- Example: the 2008 U.S. stimulus package of over 1 percent of GDP mainly comprised tax rebates targeted at low- and middle-income individuals.

### Model and identification (methodology)
- Baseline reduced-form VAR:
  - Y_t = μ + Σ_{j=1}^p A_j Y_{t-j} + U_t
  - Y_t = [T_t, G_t, X_t]' are logs of quarterly taxes, primary expenditure and GDP, measured in real, per capita terms.
- Structural VAR written as Ω U_t = Φ V_t with structural shocks V_t = [e_t^t, e_t^g, e_t^x]'.
- Identification follows Blanchard and Perotti (2002) using quarterly data and institutional information about tax and transfer systems, central bank communication on QE, and debt trajectory.
- Identification specifics provided:
  - The paper takes the Blanchard-Perotti estimate of the elasticity of taxes to an output shock, a_3 = 2.08 (quarterly data), as a starting point and assesses sensitivity to deviations in a_3.
  - Example Ω and Φ matrices (identifying restrictions suggested):
    - Ω = [ [1, 0, -2.0000]; [0, 1, 0]; [-c1, -c2, 1] ]
    - Φ = [ [a4, a5, 0]; [b4, b5, 0]; [0, 0, c6] ]
  - The model as initially presented is under-identified (seven unknown parameters in Ω and Φ combined vs. six estimable from the VAR); Blanchard and Perotti achieve exact identification by setting either a5 or b4 to zero.

### Standard Blanchard-Perotti results (U.S., pre- and post-GFC)
- Data: quarterly observations; sample windows used for pre-crisis estimation up to 2007Q4 and extended estimation up to 2019Q4.
- Impulse-response experiments:
  - Use a one-dollar (unit) deficit-financed shock in expenditure to compute the expenditure multiplier; use a unit shock to taxes to compute the tax multiplier.
  - Shocks are one-period shocks.
- Empirical results (qualitative and comparative):
  - Pre-crisis (up to 2007Q4) expenditure multipliers are stronger than post-crisis (up to 2019Q4) multipliers.
  - After eight quarters, the impulse response of real GDP per capita to an expenditure shock is more than four times larger using the model estimated up to 2007 than using data up to 2019.
  - After eight quarters, the impulse response to a tax shock is more negative (almost 40 percent larger in absolute terms) for the pre-GFC estimation than for the post-GFC estimation.
  - Conclusion: both the expenditure multiplier and the tax multiplier for the U.S. have fallen since the onset of the GFC.

### Expanded model (augmented VAR) and rationale
- To guard against omitted variable bias, the standard model is augmented with:
  - central bank balance sheet size relative to GDP (BS_t),
  - real interest rate (R_t),
  - debt-to-GDP ratio (D_t) included as exogenous/deterministic regressors.
- Augmented reduced-form VAR specification:
  - Y_t = μ + Σ_{j=1}^p A_j Y_{t-j} + Σ_{i=0}^k C_i D_{t-i} + U_t
  - Y_t = [T_t, G_t, X_t, BS_t, R_t]' are logs of quarterly taxes, primary spending, GDP (per capita, real), central bank balance sheet size relative to GDP, and the real interest rate; D_t is the debt-to-GDP ratio.
- Purpose: assess how higher debt levels, QE (via central bank balance sheet), and lower real interest rates affect fiscal multipliers and determine magnitudes required for policy interventions to achieve desired real-economy support.

### Interpretation of channels and policy implications
- Two complementary angles explain multiplier changes:
  - Interest rate angle: substantial decline in real interest rates since end-2007 likely increased fiscal multipliers in the short run.
  - Debt angle: increased debt accumulation since the GFC exerts a negative drag on real growth and hence on fiscal multipliers in both the short and long run.
- Net effect in the model: despite low interest rates, large debt accumulation dominates and leads to lower multipliers post-GFC.
- QE assessment: QE has relatively small effects on the real economy compared to fiscal measures; meaningful effects on real GDP require sizable balance sheet interventions.
- Policy implication highlighted for COVID-19 context: rising debt stocks make crisis response increasingly costly even in a low interest rate environment.

### Supporting empirical and theoretical context
- Literature consensus cited: debt has a negative impact on the macro economy in the long run, especially when debt-to-GDP exceeds a threshold.
- Main channels through which debt affects the macroeconomy:
  - private saving (via taxes to finance interest payments affecting household consumption and saving),
  - public investment (debt overhang),
  - total factor productivity (incentives for work and use of capital and labor),
  - long-term interest rates (crowding out of private investment).

*Prepared by Sam Ouliaris and Celine Rochon; IMF Working Paper WP/20/237 (Section 1).*

### Section 2

### wpiea2020237-print-pdf - Section 2

### Model specification and identification
- Debt-to-GDP identity (non-linear) used to treat 퐷퐷t as exogenous for estimation:
  - 퐷퐷t = (1 + 푅푅t)(1 + ∆푋푋t)퐷퐷t−1 + 푃푃퐵퐵t
  - ∆푋푋t denotes the real growth rate in GDP; 푃푃퐵퐵t denotes the primary balance.
- VAR/SVAR setup:
  - Reduced-form residual vector: 푈푈t = [푡푡t, 푔푔t, 푥푥t, 푏푏ss t, 푟푟t]′ (5 variables).
  - Expanded structural VAR written as: Ω Ut = Φ Vt or Ω푌푌t = 휇휇′ + Σ퐴퐴′j 푌푌t−j + Σ퐶퐶′i 퐷퐷t−i + 훷훷 Vt, with structural shocks Vt = [푒푒ttt, 푒푒tg g, 푒푒tx x, 푒푒tbbb, 푒푒tr r]′.
  - Variance-covariance identification: with n = 5 endogenous variables, a maximum of 15 parameters can be estimated (since variance-covariance matrix has n(n+1)/2 unique values).
- Identification restrictions proposed (exact identification):
  - Specific zero restrictions and parameter settings in Ω and Φ matrices (examples in source), including:
    - Set 푏푏3 = 0 (following Blanchard and Perotti (2002)).
    - Set elasticity of taxes to a shock in output, 푎푎3, to 2.08 (for quarterly data).
    - Assume diagonal Φ (structural shocks are uncorrelated).
    - Assume changes in the debt-to-GDP ratio affect only GDP per capita contemporaneously (3rd element of 퐶퐶0′ non-zero; others contemporaneously invariant).
  - The chosen identification allows contemporaneous two-way responses between taxes and expenditure (non-zero 푎푎2 and 푏푏1), in contrast to Blanchard-Perotti (2002) which sets 푎푎2 = 0 and 푏푏1 = 0.
- Additional identifying assumptions:
  - Unexpected movements in the balance sheet or the interest rate are not subject to movements in taxes and expenditure contemporaneously, but only to their structural shocks and to output movements.
  - Unexpected movements in taxes and expenditure are not subject to contemporaneous movements in the balance sheet.

### Data and estimation approach
- Sample and variables:
  - U.S. quarterly data, 1966Q1-2019Q4.
  - Endogenous variables: real revenue per capita, real expenditure per capita, real GDP per capita, Federal Reserve balance sheet assets (relative to GDP), and the real interest rate.
  - Exogenous variable: debt-to-GDP ratio (outstanding debt of the general government divided by nominal GDP).
  - Real interest rate defined as the 10-year bond yield less the inflation rate measured by the GDP deflator.
  - Federal Reserve asset holdings measured as at the end of each quarter.
- Notable level movements (end-of-period comparisons reported):
  - Debt ratio increased from 63 percent at the end of 2007 to approximately 107 percent by the end of 2019.
  - Federal Reserve asset holdings increased from 6 to 19 percent of GDP over the same period.
  - Footnote: Federal Reserve asset ratio relative to GDP peaked at 25 percent at the end of 2014.
- Estimation strategy:
  - Unconstrained VAR in levels estimated with a single lag of the 5 endogenous variables and debt-to-GDP as exogenous; lag length chosen by Schwarz Information Criterion.
  - Unit root tests indicated presence of unit roots; cointegration testing detected a single cointegrating vector.
  - Therefore estimate a structural vector error correction model (SVECM).
  - SVECM estimated using method of Pagan and Pesaran (2008): rewrite SVAR in terms of a subset of endogenous variables and residuals of cointegrating vectors, treating those residuals as transitory shocks.
  - With a single cointegrating vector, setup implies four structural shocks with permanent effects (assumed to be 푒푒ttt, 푒푒tg g, 푒푒tx x, 푒푒tr r) and one transitory shock.
  - SVECM remains exactly identified with these long-run constraints; model is non-linear by construction and estimated by maximum likelihood.
- Growth-rate behavior:
  - Growth rates of Federal Reserve balance sheet, debt-to-GDP ratio, and real interest rate are shown relative to growth rate in real GDP per capita (Figure 5 panels A–C in source).
  - Variables changed significantly after the start of the financial crisis in 2007, especially government debt accumulation and asset purchases by the Federal Reserve.

### Results: multipliers pre- and post-GFC
- Estimation strategy for policy scenarios:
  - Two datasets used to measure sensitivity of real GDP per capita:
    - (a) SVECM estimated with full sample: 1966Q1 to 2019Q4.
    - (b) Same model estimated with pre-crisis data: 1966Q1-2007Q4.
  - Shock timing assumed without loss of generality:
    - Pre-crisis shock at 2006Q1.
    - Post-crisis shock at 2018Q1.
  - Responses traced for 8 quarters after the shock; shocks are unit percentage changes and responses are expressed as percentage changes in real GDP per capita relative to baseline.
- Scenario 1 — one percentage point increase in the debt ratio:
  - Immediate response: real GDP per capita decreases initially both pre- and post-crisis, with the negative effect being slightly larger pre-crisis (Panel A).
  - After 4 periods: impact still negative but declining toward zero; negative impact larger post-crisis compared to pre-crisis in absolute terms.
  - Accumulated impact (Panel B): overall impact of higher government debt on real GDP is negative.
  - Interpretation and channels: negative expectations (including expectations of higher taxes), private saving effects, public investment via debt overhang, total factor productivity, and long-term interest rates via crowding out.
  - Contextual numeric level: U.S. debt level reached 107 percent by March 2020 (noted as potentially approaching thresholds where debt negatively affects real growth).
- Scenario 2 — one percentage point increase in government expenditure (deficit-financed):
  - Both pre- and post-crisis multipliers show a consistent positive response in real GDP per capita.
  - The fiscal multiplier has declined post 2008Q1 — estimated sensitivity of real GDP per capita to increases in government expenditure is significantly lower post-GFC.
  - Contributing mechanism: larger negative coefficient on the debt ratio in the real GDP per capita equation using post-crisis data, implying a stronger negative feedback from increases in expenditure to debt accumulation and slower future growth.
  - Low interest rate environment caveat: despite low rates, estimated larger negative debt coefficient suggests debt accumulation remains economically consequential.
- Scenario 3 — one percentage point increase in government taxes:
  - Both pre- and post-crisis tax multipliers show a consistent negative response in real GDP per capita.
  - Estimated elasticity of taxes in the real GDP per capita equation increased slightly (in absolute terms) post-crisis.
  - Effect partly offset by reduction in the debt ratio owing to higher taxes.
  - Note on uncertainty: transitory versus permanent nature of tax policy affects consumption/saving behavior and ultimately real GDP.
- Scenario 4 — one-time one percentage point increase in the Federal Reserve’s balance sheet relative to GDP (not reversed later):
  - Both pre- and post-crisis responses of real GDP per capita to the balance sheet shock are positive but small.
  - Conclusion: sizable increases (e.g., 10 times) in the balance sheet are needed to have similar effects on GDP per capita as a comparable increase in primary expenditure.
  - Impact is relatively weaker in post-crisis years than pre-crisis years.
  - Possible explanation: large amount of liquidity needed after the crisis; pre-crisis period had less need for liquidity injections.
  - Interpretation: quantitative easing is beneficial but requires sizable balance sheet interventions to produce noticeable effects on GDP.

- Conversion factors and average shares (reported for sample windows; used to convert elasticity to dollar terms; multipliers expressed in elasticity terms in paper):
  - Variable average shares and conversion factors:
    - Real Primary Expenditure per capita: Average Shares 2004Q1-2007Q4 = 0.30; Conversion Factor 2004Q1-2007Q4 = 3.3. Average Shares 2016Q1-2019Q4 = 0.31; Conversion Factor 2016Q1-2019Q4 = 3.2.
    - Real Taxes: Average Shares 2004Q1-2007Q4 = 0.28; Conversion Factor 2004Q1-2007Q4 = 3.6. Average Shares 2016Q1-2019Q4 = 0.28; Conversion Factor 2016Q1-2019Q4 = 3.6.
    - Federal Reserve Asset holdings relative to GDP: Average Shares 2004Q1-2007Q4 = 0.06; Conversion Factor 2004Q1-2007Q4 = 16.6. Average Shares 2016Q1-2019Q4 = 0.23; Conversion Factor 2016Q1-2019Q4 = 4.4.
  - Note from source: conversion factors are sensitive to sample period; multipliers are therefore expressed in elasticity terms.

*italics: Source — wpiea2020237-print-pdf - Section 2*

### Section 3

### Section 3

### Changes in Policy Multipliers Pre- and Post-GFC
- The parameter estimates on the government debt ratio are statistically different pre- and post-GFC.
- Expenditure and Federal Reserve asset holding multipliers are inversely related to the value of the elasticity of GDP in the tax equation (i.e., 2.08).
- Estimated coefficients:
  - GDP equation: coefficients on balance sheet variable are positive pre- and post-crisis, with the post-crisis coefficient slightly lower.
  - Balance sheet equation: coefficients on output are negative pre- and post-crisis, with the post-crisis coefficient three times lower.
- Implication: these coefficient changes may explain the need for more quantitative easing post-crisis.
- Fifth scenario (real GDP per capita response to a 100 basis points increase in the interest rate):
  - Increase in interest rates has negative impact pre- and post-GFC.
  - Initially the negative impact is weaker in the post-crisis years in absolute terms; after the second period the post-crisis impact is larger in absolute terms.
  - Possible cause: higher government debt in the post-crisis period implying higher interest payments, faster accumulation of debt, and a larger drag on real GDP given a larger post-crisis negative coefficient on the debt-ratio in the real GDP equation.
  - Consistent with the debt multiplier in Figure 6, which suggests a delayed differential pre- and post-crisis response of GDP to a debt shock and debt accumulation.
- Table 1 (F-statistics for null that impulse response functions are the same pre- and post-GFC):
  - Primary Expenditure: F-statistic 262.6048, p-Value 0.0000
  - Taxes: F-statistic 164.6404, p-Value 0.0000
  - Federal Reserve Assets Ratio: F-statistic 164.0191, p-Value 0.0000
  - Real Interest Rate (basis points): F-statistic 162.4467, p-Value 0.0000
  - Debt-to-GDP Ratio (percent): F-statistic 247.5926, p-Value 0.0000
  - An asterisk in Table 1 indicates a statistically significant difference in the impulse response functions (i.e. the multipliers) pre- and post-GFC.
- Conclusion: The null hypothesis of no change is rejected convincingly for all the policy multipliers.

### Historical Decomposition Results
- Method: Historical decomposition of the SVECM (Burbridge and Harrison (1985)) uses estimated impulse response functions to decompose within-sample structural errors of endogenous variables, including debt-to-GDP.
- The decomposition identifies contribution of each structural error to deviations from the baseline; cumulative responses of real GDP per capita are obtained by accumulating changes each quarter.
- Changes across sample periods reflect differences in size and importance of structural errors and changes in estimated impulse response functions pre- and post-crisis.
- Ranked average contributors to real GDP per capita in absolute terms:
  - 2002-2004 (Figure 8, Panel A): historical shocks to debt (negative), taxes (positive), and the real interest rate (negative).
  - 2005-2007 (Figure 8, Panel B): shocks to taxes (negative), the debt-ratio (positive), and Federal Reserve asset holdings (negative).
  - 2014-2016 (Figure 9, Panel A): shocks to the real interest rate (negative contribution), taxes (positive), and Federal Reserve asset holdings (negative).
  - 2017-2019 (Figure 9, Panel B): shocks to taxes (positive), Federal Reserve asset holdings (negative), and debt (negative).
- Regression of historical decomposition on structural shocks (Table 2) — estimates and p-values:
  - Primary Expenditure: 1996Q1-2007Q4 = 0.1396; 2008Q1-2019Q4 = 0.0759; p-Value 0.0000 *
  - Taxes: 1996Q1-2007Q4 = -0.1162; 2008Q1-2019Q4 = -0.1054; p-Value 0.0000 *
  - Federal Reserve Assets Ratio: 1996Q1-2007Q4 = 0.0422; 2008Q1-2019Q4 = 0.0360; p-Value 0.0000 *
  - Real Interest Rate (basis points): 1996Q1-2007Q4 = 0.0011; 2008Q1-2019Q4 = 0.0025; p-Value 0.0001 *
  - Debt-to-GDP Ratio (percent): 1996Q1-2007Q4 = -0.0021; 2008Q1-2019Q4 = -0.0007; p-Value 0.1686
  - An asterisk in Table 2 indicates a statistically significant difference in the estimates across the two periods (Chow test with break point at 2008Q1).
- Simple averages of structural shocks (logarithm) (Table 3):
  - Primary Expenditure: 1996Q1-2007Q4 = -1.1860E-03; 2008Q1-2019Q4 = -1.6360E-03
  - Taxes: 1996Q1-2007Q4 = 2.1590E-03; 2008Q1-2019Q4 = -7.0010E-03
  - Federal Reserve Assets Ratio: 1996Q1-2007Q4 = 6.2800E-04; 2008Q1-2019Q4 = 2.0276E-02
  - Real Interest Rate (basis points): 1996Q1-2007Q4 = 1.7182E-02; 2008Q1-2019Q4 = -9.1598E-02
  - Debt-to-GDP Ratio (percent): 1996Q1-2007Q4 = -4.2229E-01; 2008Q1-2019Q4 = 6.9703E-01
  - Note: estimated structural shocks are defined as the actual value of the variable minus its baseline value.
- Contribution of average structural shocks to real GDP per capita (Table 4) — obtained by multiplying Table 2 and Table 3:
  - Primary Expenditure: 1996Q1-2007Q4 = -1.6558E-04; 2008Q1-2019Q4 = -1.2424E-04
  - Taxes: 1996Q1-2007Q4 = -2.5087E-04; 2008Q1-2019Q4 = 7.3791E-04
  - Federal Reserve Assets Ratio: 1996Q1-2007Q4 = 2.6483E-05; 2008Q1-2019Q4 = 7.2982E-04
  - Real Interest Rate (basis points): 1996Q1-2007Q4 = 1.8724E-05; 2008Q1-2019Q4 = -2.2609E-04
  - Debt-to-GDP Ratio (percent): 1996Q1-2007Q4 = 8.8374E-04; 2008Q1-2019Q4 = -4.7848E-04
- Table 4 implication:
  - Pre-crisis strongest drivers of real GDP per capita: shocks to the debt-to-GDP ratio (positive), taxes (negative), and primary expenditure (negative).
  - Post-crisis dominant drivers: shocks to taxes (positive), Federal Reserve asset holdings (positive), and the debt-ratio (negative).

### Robustness and Identification
- Alternative identifying assumptions estimated for the SVECM:
  - 푏푏3 ≠ 0; 푎푎5 = 0 and 푏푏3 ≠ 0; 푏푏5 = 0 — both relax Blanchard and Perotti (2003) assumption that government expenditure does not respond within one quarter to changes in real per capita GDP.
  - Key finding that policy multipliers have fallen post-GFC is robust to these alternative identifying assumptions.
  - Empirical results for these alternatives are available from the authors upon request.

### Impact of COVID-19 Measures (as of May 21, 2020)
- Policy actions modeled:
  - U.S. federal government announced a debt-financed stimulus package of approximately 2.4 trillion dollars, representing a 27 percent increase in government expenditure (or 9 percent of GDP).
  - Federal Reserve asset purchases raised assets relative to GDP from 18 percent at the end of 2019 to 19.2 percent by the end of the first quarter of 2020.
  - Modeling assumptions: increase in government expenditure spread equally over the first 4 quarters; Federal Reserve’s actions occurred entirely in the first quarter.
- Estimated incremental impact on real GDP per capita for 8 quarters using post-crisis estimates (Figure 10):
  - Combined effect (staggered government expenditure + Federal Reserve asset purchases) on real GDP per capita:
    - Less than 0.65 percentage points in the first quarter using the post-crisis model.
    - Rising to 2.5 percent after 5 quarters using the post-crisis model.
  - Corresponding pre-crisis increments:
    - Around 1 percent in the first quarter.
    - Around 3 percent after 5 quarters.
  - Implication: reduced effectiveness of the COVID-19 stimulus measures using post-GFC multipliers compared with pre-crisis multipliers.

### Conclusion (Section VIII)
- Study approach: expanded Blanchard-Perotti model allowing for dynamic effects of central bank balance sheet, real interest rates, and debt levels on real GDP per capita.
- Main findings:
  - Elevated debt levels and significantly larger central bank balance sheets impact the strength of fiscal and monetary multipliers.
  - Evidence that expenditure and tax multipliers have fallen post-crisis in the U.S., implying reduced effectiveness of fiscal policy.
  - Effectiveness of unconventional monetary policy via asset purchases is not as strong as expected.
  - Dealing with a crisis is becoming more costly, despite the current low interest rate environment.

*Source: wpiea2020237-print-pdf - Section 3*

### Section 4

### Section 4

### Unconventional monetary policy and Federal Reserve actions (2012–2015)
- Fed reinvested principal payments on agency debt and MBS into agency MBS.
- 2012: Fed stated that economic conditions were likely to warrant low rates at least through late 2014.
- Operation Twist expired in December 2012.
- On June 20, 2012 the Fed announced continuation through end-2012 of its program to extend the average maturity of its securities holdings, entailing sales or redemptions of about $267 billion in shorter-term securities, and purchases of longer-maturity Treasury securities of an equal amount, by the end of 2012.
- Once the maturity extension program was completed, the Federal Reserve would hold almost no securities maturing through January 2016.
- Fed announced open-ended outright purchases of long-term Treasuries at an initial pace of $45 billion a month; purchases were in addition to open-ended purchases of mortgage backed securities (MBS) at a pace of $40 billion a month, which began in September 2012.
- December 2012 FOMC commitment: keep the federal funds rate close to zero at least as long as the unemployment rate remains above 6½ percent, inflation projected 1–2 years ahead is not above 2½ percent, and longer-term inflation expectations remain well-anchored.
- Staff estimates: lower long-term yields from unconventional policies resulted in a stimulus equivalent to a federal funds rate easing of roughly 250 basis points as of end-2012.
- 2014: Median forecast of FOMC participants indicated the fed funds rate was expected to lift-off from zero by mid-2015, with a gradual path upward toward a 3.75 percent longterm level; however, full employment expected to be reached slowly and inflation pressures forecast to remain muted, leaving scope for policy rates to stay at zero for longer while still keeping inflation under 2 percent.
- 2015: Fed’s first rate increase in almost nine years, carefully prepared and telegraphed.
- 2016–2017: Since the first rate increase in December 2015, the predicted pace of subsequent rate increases slowed in both FOMC and market expectations amid concerns about weak activity, jobs data, recurrent financial market volatility, and diminishing global prospects.
- 2017: Fed holdings of securities expected to decline in a gradual and predictable manner; federal funds rate to be the primary means for adjusting monetary policy; a material reduction in the economic outlook could be accompanied by a resumption of reinvestment of principal payments, but under the baseline outlook changes to the balance sheet are intended to operate quietly with minimal effects on financial conditions.
- Future level of reserves expected to be appreciably below recent years but larger than before the financial crisis.

### Fiscal consolidation, budget policy, and legislative actions (2013–2017)
- 2013: Pace of fiscal consolidation accelerated; Congress allowed the automatic across-the-board spending cuts (“sequester”) to materialize from March.
- Structural primary withdrawal estimated to have increased to about 2½ percent of GDP in 2013, from 1¼ percent in 2012, in combination with higher marginal rates for upper-income taxpayers, expiration of the payroll tax cut, and stronger-than-expected revenue collections.
- Consolidation in 2011–13 stronger than earlier anticipated: the federal primary structural deficit declined by 1¼ percent of GDP more than predicted in 2011.
- The outlook for potential growth worsened, lowering future federal revenues and compounding the long-term fiscal sustainability challenge.
- Under current policies, after stabilizing in 2015–18, the debt-to-GDP ratio expected to begin rising again as aging-related pressures assert themselves and interest rates normalize.
- Budget proposals for FY2016 (Office of Management and Budget forecast): deliver a stable federal government deficit of around 2½ percent of GDP through the 10 year budget window and stabilize the federal debt at about 73 percent of GDP by 2025; proposals include savings in healthcare spending, increased revenues from lower personal income tax deductions for higher income individuals, changes to the business tax code, an end to sequestration, funds to augment education and infrastructure programs, and immigration reform.
- Congressional budget blueprint aims to balance the budget in 10 years without revenue increases and through significant cuts to discretionary, non-defense spending.
- Near-term fiscal policy characterized as well-calibrated to prevailing economic circumstances: change in the structural primary balance expected to be -½ and 0.1 percent of GDP in 2016 and 2017, respectively.
- Fiscal uncertainties diminished by passage of:
  - The Bipartisan Budget Act of 2015 which suspended the debt ceiling until March 2017 and locked in appropriations for 2016 and 2017.
  - Protecting Americans from Tax Hikes Act that lowered tax revenues by 3½ percent of GDP over the next 10 years and made permanent multiple tax provisions (enhanced child tax credit, American Opportunity tax credit, improvements to the earned income tax credit, research and experimentation credit for corporations).
  - Fixing America’s Surface Transportation Act that commits US$305 billion to surface transportation for the next 4 years.
- Administration’s budget (circa 2017) proposes an expenditure-based medium-term fiscal consolidation: federal primary balance forecast to go from a 1.9 percent of GDP deficit to a 2.1 percent of GDP surplus over the next 10 years, including:
  - Reduction in both non-defense spending and defense outlays as a share of GDP; nondefense reductions concentrated in downsizing of line agencies and reductions in safety net programs (including funding for Medicaid and food stamps and tightening eligibility for earned income and child tax credits and disability insurance).
  - A tax reform designed to improve efficiency, lower marginal rates, and broaden the base while leaving the federal revenue-GDP ratio broadly unchanged.
  - An extremely optimistic real GDP growth assumption that rises to 3 percent by 2021 and remains at that level over the medium term.
- Administration committed to increasing defense, infrastructure and security spending while lowering most other spending items outside of social security and Medicare; scope to reduce or eliminate programs with limited effect on outcomes to address inefficiency and duplication and to devolve responsibilities to states for greater flexibility (including Medicaid, social assistance programs, and infrastructure provision).

### Fiscal stimulus, tax reform, and projected debt dynamics (2018–2024)
- 2018: Given planned fiscal stimulus, the Federal Reserve would need to raise policy rates at a faster pace to achieve its dual mandate; Fed’s adherence to data dependence and clear communication emphasized.
- Combination of revenue losses from the Tax Cuts and Jobs Act and approved increase in spending projected to create a significant increase in the fiscal deficit in the next few years, adding to an already-unsustainable public debt, contributing to a rise in global imbalances, and increasing risks of future recession with possible negative outward spillovers.
- The combined effect of the administration’s tax cuts and increased defense and non-defense discretionary spending policies projected to cause the federal government deficit to exceed 4.5 percent of GDP by 2019.
- The demand stimulus expected to raise output, cumulatively, by 1½ percent by 2020, pushing the unemployment rate below 3½ percent.
- The increase in the federal deficit expected to exacerbate an already unsustainable upward dynamic in the public debt-to-GDP ratio.
- Even with planned, modest fiscal consolidation scheduled to start in 2020, the federal debt projected to continue to climb, exceeding 90 percent of annual GDP by 2024.

*Source: wpiea2020237-print-pdf - Section 4*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020237-print-pdf.pdf_