## Policy Multipliers in Japan Under QQE

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---

### Introduction and objective
- Objective: assess effects of high debt levels and prolonged low interest rates on key policy multipliers (fiscal and monetary) in Japan before and after the introduction of Qualitative and Quantitative Easing (QQE) in 2013 (henceforth, “pre- and post-QQE”).
- Empirical approach: augmented Blanchard-Perotti structural VAR model introduced in Ouliaris and Rochon (2021); allows dynamic effects of shocks in central bank asset holdings, interest rates, and debt levels relative to GDP on economic activity.
- Research question: test for a structural break in key multipliers following QQE in 2013 by allowing the coefficient on the debt ratio to change.
- Motivation: since 2013 Japan experienced elevated debt-to-GDP and significantly larger central bank balance sheets, potentially reducing preparedness for future recessions or crises.
- Fiscal context: growing debt-to-GDP has made the cost of servicing public debt Japan’s second-largest budget line; main fiscal adjustment options—higher taxes or lower public spending—threaten near-term growth and potential GDP.

### Model specification and identification
- Core reduced-form VAR (levels) specification: Y_t = μ + Σ_{j=1}^p A_j Y_{t−j} + Σ_{i=0}^k (C_i + E_i Q_t) D_{t−i} + U_t, where
  - Y_t = [T_t, G_t, X_t, BS_t, R_t]' are logs of quarterly taxes, primary spending, GDP, central bank balance sheet (real, per capita), and real interest rate.
  - D_t is the debt-to-GDP ratio; Q_t is an indicator equal to 0 for t ≤ 2012Q4 and 1 for t ≥ 2013Q1.
- Debt identity (non-linear): D_t = (1 + R_t)(1 + ΔX_t) D_{t−1} + PB_t, where ΔX_t is real GDP growth and PB_t is the primary balance.
- Estimation strategy:
  - “Pre-QQE model”: set E_i = 0 for all i (no structural break).
  - “Post-QQE model”: allow E_i ≠ 0 (structural break in relationship between Y_t and D_t).
  - Impulse responses derived as percentage deviations from the baseline by applying unit percentage shocks to T_t, G_t, X_t, BS_t, R_t and solving the SVAR together with the non-linear debt equation.
- Structural representation: Ω Y_t = μ' + Σ A'_j Y_{t−j} + Σ (C'_i + E'_i Q_t) D_{t−i} + Φ V_t, with structural shocks V_t = [e_{t}^t, e_{t}^g, e_{t}^x, e_{t}^{bb}, e_{t}^r]'.
- Identification:
  - Φ chosen diagonal (structural shocks uncorrelated).
  - Suggested identification restrictions: n(n−1)/2 = 10 restrictions for Ω.
  - With specified restrictions, model has 15 unknown parameters and is exactly identified (15 unique values in reduced-form covariance matrix used to infer Ω and Φ).
- Specific parameter choices and identifying assumptions:
  - taxes respond to output with coefficient a_3 = 1.18 (quarterly elasticity of taxes to a shock in expenditure/output).
  - use quarterly data to justify constraint b_3 = 0 (no discretionary fiscal response within quarter).
  - model allows contemporaneous mutual responses of taxes and expenditure (a_2 and b_1 potentially non-zero).

### Data and estimation approach
- Sample: quarterly data for Japan over 1981Q3-2020Q3.
- Endogenous variables: real expenditure per capita, real revenue per capita, real GDP per capita, BoJ balance sheet assets (end of quarter), real interest rate.
- Real interest rate definition: 10-year bond yield less the inflation rate measured by the GDP deflator.
- Debt-to-GDP ratio: outstanding debt of the general government divided by nominal GDP.
- Estimation details:
  - First estimated an unconstrained VAR in levels with a single lag of the 5 endogenous variables and the debt-to-GDP ratio as a separate variable.
  - Lag length p chosen using the Schwarz Information Criterion.
  - All variables confirmed to possess unit roots; no single cointegrating vector detected.
  - Estimation implemented as a structural VAR in first differences.

### Main results — shock experiments and multipliers
- Experiment design:
  - Shock timing: assumed the shock occurs in 2017Q3 for both pre- and post-QQE models.
  - Horizon: response functions over 12 quarters.
  - Shock size: shock each variable by one percentage point; responses in GDP expressed as percentage changes relative to baseline.
- Debt shock (one percentage point increase in debt ratio):
  - Following the one percentage point shock to the debt ratio, real GDP decreases initially both pre- and post-QQE.
  - Magnitude: the negative effect is larger post-QQE in absolute terms compared to pre-QQE.
  - Structural break test: Wald statistic for null hypothesis E_i' = 0 is 44.8 with a p-value of zero, allowing rejection of no structural break.
  - Interpretation: large initial negative impact may reflect negative expectations (including expectations of higher taxes) arising from higher debt.
  - Mechanisms: private saving effects, public investment (debt overhang), total factor productivity, and long-term interest rates (crowding out).
- Fiscal multipliers and monetary policy efficacy (summary):
  - Estimated government expenditure shocks have a positive effect on output; tax shocks have a negative effect.
  - Both the expenditure and tax multipliers of Japan have fallen since the start of QQE, implying reduced effectiveness of fiscal policy following the change in monetary policy.
  - Efficacy of quantitative easing is small—requiring huge interventions to have a significant effect on real GDP—and the effectiveness of quantitative easing has declined since 2013.
  - Authors argue the reduction in policy multipliers can be attributed in part to the upward trend in government debt relative to GDP which, despite historically low interest rates, has increased Japan’s structural deficit and the likelihood of reduced expenditures and higher taxes going forward.

### Scenario analysis — detailed findings
- Scenario 1 — One percentage point increase in government expenditure:
  - Both pre-QQE and post-QQE models display a positive response in real GDP per capita.
  - The fiscal multiplier has clearly declined since the onset of QQE in 2013Q1.
  - The estimated coefficient on the debt ratio in the real GDP per capita equation is negative pre- and post-QQE; the post-QQE estimate is significantly more negative.
  - Mechanism: increases in expenditure raise government debt, leading to higher interest payments, larger fiscal deficits, and further debt accumulation that drag on GDP.
- Scenario 2 — One percentage point increase in government taxes:
  - Both pre-QQE and post-QQE multipliers show a negative response in real GDP per capita.
  - The pre-QQE tax multiplier is larger in absolute value than the post-QQE tax multiplier.
  - Channels: increased taxes affect consumption/saving and leverage behavior of households; uncertainty about whether tax changes are transitory versus permanent also affects consumption/saving and leverage.
  - Robustness: findings are robust to the specific setting of the tax elasticity parameter (i.e., 1.18). Both the expenditure and BoJ asset holding multipliers are inversely related to the value of the tax elasticity parameter.
- Scenario 3 — One-time percentage point increase in the central bank’s balance sheet relative to GDP (not reversed):
  - Both pre-QQE and post-QQE multipliers are positive but rather small.
  - The post-QQE multiplier is slightly smaller than the pre-QQE multiplier for the first 8 periods after the shock, but the difference is not significant.
  - Interpretation: raises doubt about the effectiveness of quantitative easing; reduced efficacy after QQE can be attributed in part to the increased debt stock.
- Scenario 4 — 100 basis points increase in the interest rate (then reverts next quarter):
  - The interest rate increase produces the expected negative impact on real GDP per capita in both models.
  - The negative impact is notably stronger in the post-QQE model compared to the pre-QQE for all quarters.
  - Interpretation: higher government debt in the post-QQE period implies higher interest payments on the debt and, other things equal, faster debt accumulation and a larger drag on real GDP per capita from positive shocks to the real interest rate.

### Quantitative, robustness, and comparative notes
- Structural break and robustness:
  - Structural break: introduction of QQE as break (2013Q1); using 2016Q4 as the break point (QQE with YCC) does not change conclusions.
  - Alternative structural break test: the null hypothesis of no structural break is rejected; the Wald statistic for this null is 18.5, with a p-value of zero.
- Comparison to other literature:
  - Goode, Lui and Nguyen (2021) report significantly larger cumulative fiscal responses for Japan using a structural VAR without debt that conditions on the zero-lower bound (ZLB) period (1995-2020). Their estimate of the cumulative fiscal multiplier for 10 quarters after the fiscal shock is greater than 1 for the ZLB period.
  - The paper notes that inclusion of the debt-ratio in such structural VARs may reduce those estimated multipliers because of the drag from the debt stock via the interest rate channel.

### Key statistics and exact numeric values
- Sample period: 1981Q3-2020Q3.
- Structural break indicator: Q_t = 0 for t ≤ 2012Q4; Q_t = 1 for t ≥ 2013Q1.
- Shock timing for reported impulse responses: 2017Q3.
- Response horizon: 12 quarters.
- Unit shock magnitude: one percentage point applied to each policy variable.
- Elasticity used: a_3 = 1.18 (quarterly elasticity of taxes to a shock in expenditure/output).
- Identification counts: n(n−1)/2 = 10 identification restrictions; 15 unknown parameters; 15 unique values in reduced-form covariance matrix.
- Structural break test: Wald statistic = 44.8 with a p-value of zero.
- Alternative structural break test: Wald statistic = 18.5 with a p-value of zero.

### Conclusions and policy implications
- Empirical findings indicate a significant decline in both expenditure and tax multipliers in Japan after QQE (2013), reducing fiscal policy effectiveness in the post-QQE environment.
- Quantitative easing has limited efficacy on real GDP; its effectiveness has declined since 2013, implying that large-scale balance sheet interventions are required to materially affect output.
- The upward trend in the government debt-to-GDP ratio has increased the structural deficit and raised the probability of future fiscal consolidation (reduced expenditures and higher taxes), which in turn can lower near-term growth and potential GDP.
- Policy implication: elevated debt and large central bank balance sheets constrain the effectiveness of both fiscal and monetary policy interventions and complicate the management of future recessions or crises.

*Prepared by Sam Ouliaris and Celine Rochon; WP/24/113, June 2024.*

### Section 1

### Policy Multipliers in Japan Under QQE

### Introduction
- Objective: assess effects of high debt levels and prolonged low interest rates on key policy multipliers (fiscal and monetary) in Japan before and after the introduction of Qualitative and Quantitative Easing (QQE) in 2013 (henceforth, “pre- and post-QQE”).
- Empirical approach: augmented Blanchard-Perotti structural VAR model introduced in Ouliaris and Rochon (2021); allows dynamic effects of shocks in central bank asset holdings, interest rates, and debt levels relative to GDP on economic activity.
- Research question: test for a structural break in key multipliers following QQE in 2013 by allowing the coefficient on the debt ratio to change.
- Motivation: since 2013 Japan experienced elevated debt-to-GDP and significantly larger central bank balance sheets, potentially reducing preparedness for future recessions or crises.
- Fiscal context: the growing debt-to-GDP ratio has made the cost of servicing public debt Japan’s second-largest budget line; main fiscal adjustment options—higher taxes or lower public spending—threaten near-term growth and potential GDP.

### Model
- Core reduced-form VAR (levels) specification: Y_t = μ + Σ_{j=1}^p A_j Y_{t−j} + Σ_{i=0}^k (C_i + E_i Q_t) D_{t−i} + U_t, where
  - Y_t = [T_t, G_t, X_t, BS_t, R_t]' are logs of quarterly taxes, primary spending, GDP, central bank balance sheet (real, per capita), and real interest rate.
  - D_t is the debt-to-GDP ratio; Q_t is an indicator equal to 0 for t ≤ 2012Q4 and 1 for t ≥ 2013Q1.
- Debt identity (non-linear): D_t = (1 + R_t)(1 + ΔX_t) D_{t−1} + PB_t, where ΔX_t is real GDP growth and PB_t is the primary balance.
- Estimation strategy:
  - “Pre-QQE model”: set E_i = 0 for all i (no structural break).
  - “Post-QQE model”: allow E_i ≠ 0 (structural break in relationship between Y_t and D_t).
  - Impulse responses derived as percentage deviations from the baseline by applying unit percentage shocks to T_t, G_t, X_t, BS_t, R_t and solving the SVAR together with the non-linear debt equation.
- Structural representation: Ω Y_t = μ' + Σ A'_j Y_{t−j} + Σ (C'_i + E'_i Q_t) D_{t−i} + Φ V_t, with structural shocks V_t = [e_{t}^t, e_{t}^g, e_{t}^x, e_{t}^{bb}, e_{t}^r]'.
- Identification:
  - Φ chosen diagonal (structural shocks uncorrelated).
  - Suggested identification restrictions: n(n−1)/2 = 10 restrictions for Ω.
  - With specified restrictions, model has 15 unknown parameters and is exactly identified (15 unique values in reduced-form covariance matrix used to infer Ω and Φ).
- Specific parameter choices and identifying assumptions preserved from Blanchard-Perotti tradition:
  - taxes respond to output with coefficient a_3 = 1.18 (quarterly elasticity of taxes to a shock in expenditure/output).
  - use quarterly data to justify constraint b_3 = 0 (no discretionary fiscal response within quarter).
  - model allows contemporaneous mutual responses of taxes and expenditure (a_2 and b_1 potentially non-zero), unlike some implementations that set them to 0.

### Data and Estimation Approach
- Sample: quarterly data for Japan over 1981Q3-2020Q3.
- Endogenous variables: real expenditure per capita, real revenue per capita, real GDP per capita, BoJ balance sheet assets (end of quarter), real interest rate.
- Real interest rate definition: 10-year bond yield less the inflation rate measured by the GDP deflator.
- Debt-to-GDP ratio: outstanding debt of the general government divided by nominal GDP.
- Estimation details:
  - First estimated an unconstrained VAR in levels with a single lag of the 5 endogenous variables and the debt-to-GDP ratio as a separate variable.
  - Lag length p chosen using the Schwarz Information Criterion.
  - All variables confirmed to possess unit roots; no single cointegrating vector detected.
  - Estimation implemented as a structural VAR in first differences.

### Results
- Experiment design:
  - Shock timing: without loss of generality assumed the shock occurs in 2017Q3 for both pre- and post-QQE models.
  - Horizon: response functions over 12 quarters.
  - Shock size: shock each variable by one percentage point; responses in GDP expressed as percentage changes relative to baseline.
- Debt shock experiment (one percentage point increase in debt ratio, possibly from a negative one-time exogenous shock):
  - Result: following the one percentage point shock to the debt ratio, real GDP decreases initially both pre- and post-QQE.
  - Magnitude: the negative effect is larger post-QQE in absolute terms compared to pre-QQE.
  - Structural break test: Wald statistic for null hypothesis E_i' = 0 is 44.8 with a p-value of zero, allowing rejection of no structural break.
  - Interpretation: large initial negative impact may reflect negative expectations (including expectations of higher taxes) arising from higher debt.
  - Mechanisms cited: private saving effects (tax financing of interest payments), public investment (debt overhang), total factor productivity (incentives for work and use of capital and labor), and long-term interest rates (crowding out).
- Fiscal multipliers and monetary policy efficacy (summary statements from the abstract and results section):
  - Estimated government expenditure shocks have a positive effect on output; tax shocks have a negative effect.
  - Both the expenditure and tax multipliers of Japan have fallen since the start of QQE, implying reduced effectiveness of fiscal policy following the change in monetary policy.
  - Efficacy of quantitative easing is small—requiring huge interventions to have a significant effect on real GDP—and the effectiveness of quantitative easing has declined since 2013.
  - Authors argue the reduction in policy multipliers can be attributed in part to the upward trend in government debt relative to GDP which, despite historically low interest rates, has increased Japan’s structural deficit and the likelihood of reduced expenditures and higher taxes going forward.

### Key statistics and exact numeric values reported
- Sample period: 1981Q3-2020Q3.
- Structural break indicator: Q_t = 0 for t ≤ 2012Q4; Q_t = 1 for t ≥ 2013Q1.
- Shock timing for reported impulse responses: 2017Q3.
- Response horizon: 12 quarters.
- Unit shock magnitude: one percentage point applied to each policy variable.
- Elasticity used: a_3 = 1.18 (quarterly elasticity of taxes to a shock in expenditure/output).
- Identification counts: n(n−1)/2 = 10 identification restrictions; 15 unknown parameters; 15 unique values in reduced-form covariance matrix.
- Structural break test: Wald statistic = 44.8 with a p-value of zero.

### Conclusions and policy implications (as presented)
- Empirical findings indicate a significant decline in both expenditure and tax multipliers in Japan after QQE (2013), reducing fiscal policy effectiveness in the post-QQE environment.
- Quantitative easing has limited efficacy on real GDP; its effectiveness has declined since 2013, implying that large-scale balance sheet interventions are required to materially affect output.
- The upward trend in the government debt-to-GDP ratio has increased the structural deficit and raised the probability of future fiscal consolidation (reduced expenditures and higher taxes), which in turn can lower near-term growth and potential GDP.
- Policy implication: elevated debt and large central bank balance sheets constrain the effectiveness of both fiscal and monetary policy interventions and complicate the management of future recessions or crises.

*Prepared by Sam Ouliaris and Celine Rochon; WP/24/113, June 2024.*

### Section 2

### Policy Multipliers in Japan Under QQE — Section 2

### Scenario analysis and main findings
- Scenario 1 — One percentage point increase in government expenditure:
  - Both pre-QQE and post-QQE models display a positive response in real GDP per capita (fiscal multiplier).
  - The fiscal multiplier has clearly declined since the onset of QQE in 2013Q1.
  - The estimated coefficient on the debt ratio in the real GDP per capita equation is negative pre- and post-QQE; the post-QQE estimate is significantly more negative, indicating larger negative feedback effects from increases in the stock of government debt.
  - Mechanism highlighted: increases in expenditure raise government debt, which leads to higher interest payments, larger fiscal deficits, and further debt accumulation that drag on GDP.

- Scenario 2 — One percentage point increase in government taxes:
  - Following the tax shock, both pre-QQE and post-QQE multipliers show a negative response in real GDP per capita.
  - The pre-QQE tax multiplier is larger in absolute value than the post-QQE tax multiplier.
  - Possible channels: increased taxes affect consumption/saving and leverage behavior of households; uncertainty about whether tax changes are transitory versus permanent also affects consumption/saving and leverage, and thus GDP.
  - Robustness: findings are robust to the specific setting of the tax elasticity parameter (i.e., 1.18). It is noted that both the expenditure and BoJ asset holding multipliers are inversely related to the value of the tax elasticity parameter.

- Scenario 3 — One-time percentage point increase in the central bank’s balance sheet relative to GDP (not reversed):
  - Both pre-QQE and post-QQE multipliers are positive but rather small.
  - The post-QQE multiplier is slightly smaller than the pre-QQE multiplier for the first 8 periods after the shock, but the difference is not significant.
  - Raises doubt about the effectiveness of quantitative easing; reduced efficacy after QQE can be attributed in part to the increased debt stock.

- Scenario 4 — 100 basis points increase in the interest rate (then reverts next quarter):
  - The interest rate increase produces the expected negative impact on real GDP per capita in both models.
  - The negative impact is notably stronger in the post-QQE model compared to the pre-QQE for all quarters.
  - Interpretation: higher government debt in the post-QQE period implies higher interest payments on the debt and, other things equal, faster debt accumulation and a larger drag on real GDP per capita from positive shocks to the real interest rate.

### Quantitative and econometric notes
- Structural break choice and robustness:
  - The paper uses the introduction of QQE as the structural break (2013Q1); using 2016Q4 as the break point (QQE with YCC) does not change the conclusions.
  - The null hypothesis of no structural break is rejected; the Wald statistic for this null is 18.5, with a p-value of zero.
- Comparison to other literature:
  - Goode, Lui and Nguyen (2021) report significantly larger cumulative fiscal responses for Japan using a structural VAR without debt that conditions on the zero-lower bound (ZLB) period (1995-2020). Their estimate of the cumulative fiscal multiplier for 10 quarters after the fiscal shock is greater than 1 for the ZLB period.
  - The paper notes that inclusion of the debt-ratio in such structural VARs may reduce those estimated multipliers because of the drag from the debt stock via the interest rate channel.

### Synthesis and interpretation
- Overall evidence:
  - Expenditure and tax multipliers have fallen under QQE relative to pre-QQE levels.
  - The effectiveness of fiscal policy has declined under QQE.
  - Unconventional monetary policy via central bank asset purchases (QQE) shows limited efficacy: the estimated QQE multiplier is not strong and appears to have declined post 2013.
- Mechanisms emphasized:
  - Increased government debt amplifies the negative feedback from fiscal expansion through higher interest payments and subsequent debt accumulation.
  - Higher debt also increases vulnerability to interest rate increases, producing larger negative GDP responses to rate shocks in the post-QQE period.

*Source: Policy Multipliers in Japan Under QQE — Section 2 (IMF Working Paper).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024113-print-pdf.pdf_