## _wp0507 - 7. Impulse Responses of Financing Methods in Models 1 and 2

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### I. Purpose and key hypothesis
- Examine whether the effectiveness of fiscal policy (increases in government spending) is asymmetric across different levels of real interest rates.
- Central hypothesis:
  - The size of the Ricardian effect depends positively on the level of real interest rates.
  - When real rates are low, deficit-financed spending is less likely to threaten debt sustainability and thus has stronger stimulative effects.
  - When real rates are high, the same spending is more likely to push the debt-output ratio toward a political upper limit, inducing expected future tax increases and dampening consumption and investment.

### II. Empirical approach and models
- Sample: U.S. quarterly time series, 1959:1–2001:4.
- Switching index:
  - Lagged ex post real interest rate rr_{t-1} = 400*(R_{t-1}/P_{t-1} − 1) (three-month Treasury bill rate minus actual inflation).
  - Alternative: ex ante real rate (three-month Treasury bill minus expected inflation from Livingston Survey).
- Regimes: three regimes defined by two thresholds on the switching index — "low-rate", "moderate-rate", and "high-rate".
- Econometric framework:
  - Threshold vector autoregression (TVAR) with up to two thresholds (three regimes).
  - Thresholds estimated by grid search and refinement estimator.
  - Nonlinearity tested using Hansen (1999, 2000) methods with bootstrap p-values (J=1,000).
- Identification: Choleski decomposition with government spending ordered first (assumption: fiscal shocks contemporaneously affect but do not respond contemporaneously to macro variables).
- Two model specifications:
  - Model 1 ordering: {∆ ln G_t, ∆ ln D_t, ∆ ln Z_t, ∆ ln X_t, ∆R_t}, where Z_t is private consumption C_t or private investment I_t; R_t = three-month T-bill rate.
  - Model 2 ordering: {∆ ln G_t, ∆ ln M_t, ∆ ln Z_t, ∆ ln X_t, ∆ ln P_t, R_t}, where M = monetary base, P = GDP deflator.
- Lag lengths: lag order set at 2 for model 1 with investment growth and at 3 for other models (Akaike information criterion).

### III. Nonlinearity and threshold evidence
- Linearity testing for single threshold (F1):
  - Rejection (significant) in interest rate and inflation equations (p < 0.01).
  - Mild evidence for investment growth (p < 0.10) and output growth (p < 0.15).
  - Weak or no evidence for consumption growth in some specifications (p > 0.40).
- Tests for double threshold (F2):
  - Reject one threshold in favor of two thresholds at the 5 percent level for the interest rate and inflation equations in both models.
- Confidence intervals for thresholds are sometimes wide or half-open due to sample size.
- Regime sample splits example (model 1 with investment growth):
  - Estimated thresholds (0.223, 3.485) with number of observations (33, 93, 42) for low, moderate, high regimes.
- Regime means (model 1 with investment growth, regime-mean real rates and output growth):
  - Real rate means: low-rate = –0.97 percent; moderate-rate = 1.92 percent; high-rate = 4.94 percent.
  - Output growth means: low-rate = 3.89 percent; moderate-rate = 3.45 percent; high-rate = 2.59 percent.

### IV. Impulse-response experiment design
- Shock: positive government spending shock of 1 percentage point to the rate of government spending growth (annualized).
- Analysis conditioned on the economy staying within its initial regime (small regime shifts unlikely given typical peak responses).
- Bootstrap inference: empirical standard errors via bootstrap with 1,000 replications.

### V. Main empirical findings — real activity (consumption, investment, output)
- General pattern across specifications:
  - Low-rate regime: largest immediate stimulative effect of a 1 percentage point government spending growth shock on real activity.
  - Moderate-rate regime: initial positive responses smaller and sometimes insignificant.
  - High-rate regime: responses of consumption, investment, and output weaker and often insignificantly different from zero; investment response can be negative.
- Quantified output responses (Table 4; averages in basis points; numbers in parentheses are empirical standard errors):
  - Model 1 with ∆ ln C_t (first 1-2 quarters): Low = 33.4 (9.4), Moderate = 15.2 (5.5), High = 1.2 (10.5), Whole = 10.6 (3.9).
  - Model 1 with ∆ ln I_t (first 1-2 quarters): Low = 28.8 (15.5), Moderate = 8.5 (3.9), High = 8.4 (8.5), Whole = 7.7 (3.5).
  - Model 2 with ∆ ln C_t (first 1-2 quarters): Low = 23.9 (11.2), Moderate = 7.9 (4.6), High = 2.9 (11.9), Whole = 11.3 (4.9).
  - Model 2 with ∆ ln I_t (first 1-2 quarters): Low = 14.1 (12.3), Moderate = 6.5 (4.6), High = 6.0 (6.6), Whole = 10.8 (4.4).
- Investment growth:
  - Low-rate regime: investment growth responses significantly positive initially (productivity-enhancing effect dominates).
  - High-rate regime: investment growth responses tend to be weakly negative or insignificant (Ricardian/expectation of future taxes and crowding-out dominate).
- Output response heterogeneity:
  - Low-rate regime shows the most pronounced positive initial output response.
  - High-rate regime shows statistically insignificant output responses in the first half-year and thereafter.

### VI. Interest rates, inflation, and Mankiw effect
- Nominal interest rates (Model 2) responses to the government spending shock:
  - Significantly positive under the low-rate regime after two to three quarters.
  - Small or insignificant under the moderate-rate regime.
  - Significantly or insignificantly negative under the high-rate regime and for the whole sample.
- Inflation responses (Model 2):
  - Significant positive inflation response under the low-rate regime with a lag.
  - No or much smaller positive inflation responses under the high-rate regime and for the whole sample.
- Real interest rates (Model 2′, ex post real rate used in place of R_t):
  - Real rate response larger and positive under the low-rate regime (insignificant initial response followed by significant positive responses).
  - Insignificant or negative real rate responses under moderate- and high-rate regimes.
- Interpretation:
  - Positive nominal and real rate responses under low-rate regime align with Keynesian demand effects (higher aggregate demand raises inflation and nominal interest rates).
  - Negative or non-positive nominal rate responses under high-rate regime consistent with stronger Ricardian/Mankiw-type effects where expected future tax liabilities reduce consumption, lowering real rates.

### VII. Financing methods — debt vs. money creation
- Model 1 (debt growth) and Model 2 (money growth) responses to the shock:
  - Initial financing of additional spending is via increased debt issuance across regimes.
  - Low-rate regime:
    - Debt growth is significantly positive initially but declines as real returns on bonds rise.
  - High-rate regime:
    - Money growth rises significantly after a short lag (hump-shaped response), indicating substitution toward money creation when debt financing is costly.
  - Moderate-rate regime:
    - Brief initial increase in money growth.
- Interpretation: substitution between debt issuance and money creation depends on financing cost; when debt financing is expensive (high real rates), governments rely relatively more on money creation.

### VIII. Robustness checks and alternative specifications
- Alternative variables and orderings:
  - Using real money stock M1 instead of monetary base, using real interest rates instead of nominal, and different variable orderings do not qualitatively alter main results.
- Alternative switching index:
  - Using ex ante real interest rate yields similar double-threshold evidence but often less pronounced asymmetries in dynamic responses.
- Switching index using debt-output ratio:
  - No evidence of asymmetric effects on consumption/investment/output; suggests dynamics of debt accumulation and financing costs (real rate) are more relevant than current debt level for agents’ expectations.
- Use of national defense spending as the fiscal shock:
  - Similar but less marked asymmetric effects; defense shocks tend to have a greater crowding-out effect irrespective of regime.

### IX. Policy implications and interpretation
- Fiscal expansions are more effective at stimulating real activity in the short run when real interest rates are low.
- When real interest rates are high, fiscal expansions are less effective and can be counterproductive for consumption and investment because of stronger perceived fiscal sustainability risks and larger Ricardian effects.
- Financing composition matters:
  - Low real rates favor debt financing with stimulative effects.
  - High real rates encourage money creation to finance spending, with different macro implications (e.g., inflation dynamics).
- Trade-offs and caveats:
  - Persistent, expansionary fiscal policy can raise real rates and accelerate debt accumulation, potentially shifting the economy into a higher-rate regime and undermining future fiscal effectiveness.
  - Fiscal austerity can provide a stronger foundation for future fiscal efficacy by reducing the probability that spending shocks push debt toward politically tolerable upper bounds.
  - Aggressive fiscal policy increases macroeconomic volatility, which may lower growth (referenced result: Fatás and Mihov, 2003).

### X. Conclusion (authors’ summary)
- Government spending has a significant positive short-run impact on aggregate spending when real interest rates are low but not when real interest rates are relatively high.
- Additional asymmetric findings:
  - Government spending raises inflation and nominal interest rates only when real interest rates are relatively low.
  - At low real rates, government spending tends to raise real rates; at high real rates, it can lower them.
  - Government spending induces debt issuance at low real rates and money creation at high real rates.
- Overall interpretation: fiscal policy is likely more conducive to short-run growth when real interest rates are low, but sustained deficits can erode this effectiveness; fiscal austerity may be needed to preserve fiscal policy potency in times of need.

*Source: _wp0507 - 7. Impulse Responses of Financing Methods in Models 1 and 2 (IMF Working Paper PDF).*

### References..............................................................................................................

### _wp0507 - References..............................................................................................................

### Tables
- 1. Tests for a Single Threshold and Threshold Estimates ........................................................15
- 2. Tests for a Double Threshold and Threshold Estimates ......................................................16
- 3. Specification Tests for Asymmetry in TVARs ....................................................................18
- 4. Output Growth Responses ...................................................................................................23
- 5. Output Growth Responses with Ex Ante Real Rates as Switching Index ...........................30

### Figures
- 1. Real Interest Rates, Debt-to-GDP Ratio, and Growth in Government Spending ................12
- 2. Regime Type Index, Real Interest Rates, and Output Growth ............................................19
- 3. Impulse Responses of Real Activity in Model 1 .................................................................21
- 4. Impulse Responses of Real Activity in Model 2 .................................................................22
- 5. Impulse Responses of Nominal Interest Rates and Inflation in Model 2 ............................25
- 6. Impulse Responses of Real Interest Rates in Model 2′...............................................26

*Source: _wp0507 - References..............................................................................................................*

### 7. Impulse Responses of Financing Methods in Models 1 and 2 ............................................28

### 7. Impulse Responses of Financing Methods in Models 1 and 2

### I. Purpose and key hypothesis
- Examine whether the effectiveness of fiscal policy (increases in government spending) is asymmetric across different levels of real interest rates.
- Central hypothesis: the size of the Ricardian effect depends positively on the level of real interest rates; when real rates are low, deficit-financed spending is less likely to threaten debt sustainability and thus has stronger stimulative effects; when real rates are high, the same spending is more likely to push the debt-output ratio toward a political upper limit, inducing expected future tax increases and dampening consumption and investment.

### II. Empirical approach and models
- Sample: U.S. quarterly time series, 1959:1–2001:4.
- Switching index: lagged ex post real interest rate rr_{t-1} = 400*(R_{t-1}/P_{t-1} − 1) (three-month Treasury bill rate minus actual inflation), with an alternative using ex ante real rate (three-month Treasury bill minus expected inflation from Livingston Survey).
- Regimes: three regimes defined by two thresholds on the switching index — "low-rate", "moderate-rate", and "high-rate".
- Econometric framework: threshold vector autoregression (TVAR) with up to two thresholds (three regimes); thresholds estimated by grid search and refinement estimator; nonlinearity tested using Hansen (1999, 2000) methods with bootstrap p-values (J=1,000).
- Identification: Choleski decomposition with government spending ordered first (assumption: fiscal shocks contemporaneously affect but do not respond contemporaneously to macro variables).
- Two model specifications:
  - Model 1 ordering: {∆ ln G_t, ∆ ln D_t, ∆ ln Z_t, ∆ ln X_t, ∆R_t}, where Z_t is private consumption C_t or private investment I_t; R_t = three-month T-bill rate.
  - Model 2 ordering: {∆ ln G_t, ∆ ln M_t, ∆ ln Z_t, ∆ ln X_t, ∆ ln P_t, R_t}, where M = monetary base, P = GDP deflator.
- Lag lengths: lag order set at 2 for model 1 with investment growth and at 3 for other models (Akaike information criterion).

### III. Nonlinearity and threshold evidence
- Linearity testing for single threshold (F1) finds rejection (significant) in interest rate and inflation equations (p < 0.01), mild evidence for investment growth (p < 0.10) and output growth (p < 0.15); weak or no evidence for consumption growth in some specifications (p > 0.40).
- Tests for double threshold (F2) reject one threshold in favor of two thresholds at the 5 percent level for the interest rate and inflation equations in both models.
- Confidence intervals for thresholds are sometimes wide or half-open due to sample size.
- Regime sample splits example (model 1 with investment growth): estimated thresholds (0.223, 3.485) with number of observations (33, 93, 42) for low, moderate, high regimes (see Figures 3 notes).
- Regime means (model 1 with investment growth, regime-mean real rates and output growth):
  - Real rate means: low-rate = –0.97 percent; moderate-rate = 1.92 percent; high-rate = 4.94 percent.
  - Output growth means: low-rate = 3.89 percent; moderate-rate = 3.45 percent; high-rate = 2.59 percent.

### IV. Impulse-response experiments
- Shock: positive government spending shock of 1 percentage point to the rate of government spending growth (annualized).
- Analysis conditioned on the economy staying within its initial regime (small regime shifts unlikely given typical peak responses).
- Bootstrap inference: empirical standard errors via bootstrap with 1,000 replications.

### V. Main empirical findings — real activity (consumption, investment, output)
- General pattern across specifications:
  - Under the low-rate regime, the immediate stimulative effect of a 1 percentage point government spending growth shock on real activity is largest.
  - Under moderate-rate regime, initial positive responses are smaller and sometimes insignificant.
  - Under high-rate regime, responses of consumption, investment, and output are weaker and often insignificantly different from zero; investment response can be negative.
- Quantified output responses (Table 4; averages in basis points):
  - Model 1 with ∆ ln C_t (first 1-2 quarters): Low = 33.4 (9.4), Moderate = 15.2 (5.5), High = 1.2 (10.5), Whole = 10.6 (3.9).
  - Model 1 with ∆ ln I_t (first 1-2 quarters): Low = 28.8 (15.5), Moderate = 8.5 (3.9), High = 8.4 (8.5), Whole = 7.7 (3.5).
  - Model 2 with ∆ ln C_t (first 1-2 quarters): Low = 23.9 (11.2), Moderate = 7.9 (4.6), High = 2.9 (11.9), Whole = 11.3 (4.9).
  - Model 2 with ∆ ln I_t (first 1-2 quarters): Low = 14.1 (12.3), Moderate = 6.5 (4.6), High = 6.0 (6.6), Whole = 10.8 (4.4).
- Investment growth:
  - Under low-rate regime, investment growth responses are significantly positive initially (productivity-enhancing effect dominates).
  - Under high-rate regime, investment growth responses tend to be weakly negative or insignificant (Ricardian/expectation of future taxes and crowding-out dominate).
- Output response heterogeneity:
  - The low-rate regime shows the most pronounced positive initial output response; high-rate regime shows statistically insignificant output responses in the first half-year and thereafter.

### VI. Interest rates, inflation, and Mankiw effect
- Nominal interest rates (Model 2) responses to the government spending shock:
  - Significantly positive under the low-rate regime after two to three quarters.
  - Small or insignificant under the moderate-rate regime.
  - Significantly or insignificantly negative under the high-rate regime and for the whole sample.
- Inflation responses (Model 2):
  - Significant positive inflation response under the low-rate regime with a lag.
  - No or much smaller positive inflation responses under the high-rate regime and for the whole sample.
- Real interest rates (Model 2′, ex post real rate used in place of R_t):
  - Real rate response is larger and positive under the low-rate regime (insignificant initial response followed by significant positive responses).
  - Insignificant or negative real rate responses under moderate- and high-rate regimes.
- Interpretation:
  - Positive nominal and real rate responses under low-rate regime align with Keynesian demand effects; higher aggregate demand raises inflation and nominal interest rates.
  - Negative or non-positive nominal rate responses under high-rate regime are consistent with stronger Ricardian/Mankiw-type effects where expected future tax liabilities reduce consumption, lowering real rates.

### VII. Financing methods — debt vs. money creation
- Model 1 (debt growth) and Model 2 (money growth) responses to the shock:
  - Initial financing of additional spending is via increased debt issuance across regimes.
  - Under low-rate regime: debt growth is significantly positive initially but declines as real returns on bonds rise.
  - Under high-rate regime: money growth rises significantly after a short lag (hump-shaped response), indicating substitution toward money creation when debt financing is costly.
  - Under moderate-rate regime: brief initial increase in money growth.
- Interpretation: substitution between debt issuance and money creation depends on the financing cost; when debt financing is expensive (high real rates), governments rely relatively more on money creation.

### VIII. Robustness checks and alternative specifications
- Alternative variables and orderings: using real money stock M1 instead of monetary base, using real interest rates instead of nominal, and different variable orderings do not qualitatively alter main results.
- Alternative switching index: using ex ante real interest rate yields similar double-threshold evidence but often less pronounced asymmetries in dynamic responses.
- Alternative switching index using debt-output ratio: no evidence of asymmetric effects on consumption/investment/output; suggests dynamics of debt accumulation and financing costs (real rate) are more relevant than current debt level for agents’ expectations.
- Use of national defense spending as the fiscal shock: similar but less marked asymmetric effects; defense shocks tend to have a greater crowding-out effect irrespective of regime.

### IX. Policy implications and interpretation
- Fiscal expansions are more effective at stimulating real activity in the short run when real interest rates are low.
- When real interest rates are high, fiscal expansions are less effective and can be counterproductive for consumption and investment because of stronger perceived fiscal sustainability risks and larger Ricardian effects.
- Financing composition matters: low real rates favor debt financing with stimulative effects; high real rates encourage money creation to finance spending, with different macro implications (e.g., inflation dynamics).
- Trade-off and caveats:
  - Persistent, expansionary fiscal policy can raise real rates and accelerate debt accumulation, potentially shifting the economy into a higher-rate regime and undermining future fiscal effectiveness.
  - Fiscal austerity can provide a stronger foundation for future fiscal efficacy by reducing the probability that spending shocks push debt toward politically tolerable upper bounds.
  - Aggressive fiscal policy increases macroeconomic volatility, which may lower growth (referenced result: Fatás and Mihov, 2003).

### X. Conclusion (authors’ summary)
- New empirical evidence shows government spending has a significant positive short-run impact on aggregate spending when real interest rates are low but not when real interest rates are relatively high.
- Additional asymmetric findings:
  - Government spending raises inflation and nominal interest rates only when real interest rates are relatively low.
  - At low real rates, government spending tends to raise real rates; at high real rates, it can lower them.
  - Government spending induces debt issuance at low real rates and money creation at high real rates.
- Overall interpretation: fiscal policy is likely more conducive to short-run growth when real interest rates are low, but sustained deficits can erode this effectiveness; fiscal austerity may be needed to preserve fiscal policy potency in times of need.

*Source: _wp0507 - 7. Impulse Responses of Financing Methods in Models 1 and 2 (IMF Working Paper PDF).*

### References

### References

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*Source: _wp0507 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0507.pdf_