## 2.1 Structural Shocks and Historical Decompositions

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---

### Major findings and substantive conclusions
- Global average public debt-to-GDP ratio rose to nearly 100% in 2020—a 15-percentage-point increase from the previous year.
- Debt-to-GDP ratios contracted in 2021 and 2022, reversing approximately half of the 2020 surge.
- The structural shocks considered jointly account for around 60% of the variations in the debt-to-GDP ratio.
- GDP growth shocks explain roughly 40% of the yearly variation in debt-to-GDP ratios for the median advanced economy.
- Discretionary policy shocks explain less than a fifth of the yearly variation in debt-to-GDP ratios in the baseline model.
- The baseline SVAR does not explicitly incorporate monetary policy shocks, but an extension allowing for monetary policy shocks leaves the main results unchanged.
- Unexpected inflation has been important for debt-to-GDP in certain periods and countries (including the US), though for the sample period considered this has been less relevant.
- The study finds a small impact of discretionary fiscal consolidations on GDP growth (i.e., a small primary balance multiplier), and reports a "zero multiplier" effect in robustness checks using alternative approaches (local projections and IVs derived from SVAR shocks).

### Interpretation and policy-relevant implications
- The macroeconomic reaction to GDP shocks and the comovements of GDP with other macro and fiscal variables are the principal drivers of observed changes in debt-to-GDP ratios.
- Given high debt-to-GDP ratios, the results suggest reassessing policy calibrations and implicit policy reactions to shocks.
- Fiscal consolidations have limited direct impact on debt-to-GDP in this framework; debt reduction during periods of growth is highlighted as significant.
- Methodological implication: addressing endogeneity and the foresight problem is crucial to obtain reliable estimates of fiscal multipliers and debt dynamics.

### Key statistics and quantitative statements (preserved exactly)
- "nearly 100% in 2020"
- "a 15-percentage-point increase"
- "reversing approximately half of the 2020 surge"
- "jointly account for around 60% of the variations in the debt-to-GDP ratio"
- "GDP shocks explain roughly 40% of the yearly variation in debt to GDP ratios for the median advanced economy"
- "discretionary policy shocks on the other hand explain less than a fifth"
- "six variables: GDP growth, government revenues, primary balance, debt to GDP, inflation, and the effective interest rate on debt"
- "three distinct shocks: a demand-driven GDP growth shock, a supply-driven GDP growth shock, and a primary balance shock orthogonal to the others"
- Sample: "a panel of yearly data covering seventeen advanced economies from 1981-2019"
- Data sources: "Historical Public Finance Database (HPFD)" (pre-2011), "Global Debt Database (GDD)" and "WEO" (post-2011)

### Conceptual and methodological points
- Model: Structural Vector Autoregression (SVAR) with structural parameters Θ = (A0, A+) and reduced-form parameters B and Σ.
  - Structural form: y′t A0 = Σ_{l=1}^p y′t−l Al + c + ε′t  (equation (2.1))
  - Reduced form: y′t = x′t B + u′t  (equation (2.3))
  - Structural shocks: ε′t(Θ) = y′t A0 − x′t A+  (equation (2.4))
- Historical decomposition: Hi,j,t,t+h(Θ) = Σ_{l=0}^h e′i,n L l(Θ) e j,n e′j,n ε t+h−l(Θ)  (equation (2.5))
- Identification: narrative sign restrictions impose S j F(θ) e j,n > 0 for 1≤j≤n (equation (2.6)), combining sign restrictions with narrative constraints on primary balance shocks.

---

### 3.1 Model Specification

### Model overview and variables
- Six-variable SVAR: (1) Real GDP growth; (2) Growth rate of real government revenues; (3) change in primary balance to GDP; (4) change in debt to GDP; (5) nominal effective interest rate on public debt; (6) GDP deflator inflation.
- Sign restrictions (Table 1) summarized identification across shocks.

### Identification strategy and narrative restrictions
- Isolate three structural shocks:
  - Two GDP shocks: supply and demand.
  - One discretionary primary balance shock orthogonal to growth shocks.
- Demand shock sign restrictions:
  - Output and inflation move in the same direction on impact.
  - Government revenues react procyclically.
- Supply shock sign restrictions:
  - Output and inflation move in opposite directions on impact.
  - Government revenues react procyclically.
- Narrative restrictions:
  - Imposed only in the first year of multi-year consecutive narrative episodes.
  - Additional narrative restriction: impose a negative demand shock in 2008.
  - Predictability check of narrative shocks: regression yields an R square around 0.4 for first-year episodes; 95 percent of first-year narrative shocks have positive residuals; positive-residual share drops to around 70 percent when considering all narrative shocks.

### Estimation approach and inference
- VAR estimated country by country with two lags using Bayesian Methods.
- Minnesota Prior applied to reduced-form VAR; shrinkage parameters chosen to maximize marginal data density.
- Structural identification uses Antolín-Díaz and Rubio-Ramírez (2018) approach with Haar prior for rotation matrices.
- Aggregation: country-by-country estimates summarized by medians across 17 advanced economies.
- Impulse responses summarized as medians over six years; 68 percent highest posterior density credible sets used; inverse variance weights used to aggregate country-level impulse responses.

### Notable data/contextual points
- Frequency: Annual.
- Fiscal aggregation: General government.
- Sample: Seventeen advanced economies, 1981-2019.
- Data sources: HPFD (pre-2011), GDD and IMF WEO (post-2011).
- Anomalies in 2014–2015: model does not fit non-economic fluctuations arising from large statistical recalibrations that inflated GDP by over 20%.

---

### 4.3 The Value of Narrative Restrictions

### Narrative restrictions sharpen identification and precision
- Narrative information, even when sparse, tightens posterior distributions and HPD credible sets, especially for the primary balance shock.
- US 1990 example (Figure 9 described):
  - Mean of the shock without narrative restrictions: -0.07
  - Mean with narrative restriction: 0.3
  - Narrative database actual value (Guajardo et al. (2014)): 0.36
  - Note: estimation uses only sign from narrative restriction, not magnitude.
- Table 6 evidence: narrative information reduces HPD widths for many impulse responses; e.g., Primary Balance Shock: GDP Growth -3.49, Primary Balance -5.19, Debt -2.16 (percent differences in HPD widths cumulated over 6-year horizon; negative denotes smaller HPD sets with narrative-sign restrictions).

### Narrative restrictions can change qualitative inference
- Introducing narrative information can alter signs and magnitudes of inferred impacts:
  - With narrative sign restrictions: impact of a primary balance shock on GDP and debt ratios is negative but small.
  - Without narrative restrictions: impact on GDP is positive (still small) and debt ratios show a much sharper negative impact.
- Conclusion: narrative sign restrictions improve shock identification and can materially change substantive conclusions.

---

### 5 Reconciliation with Contractionary Austerity Results in the Literature

### Two main sources of divergence with prior literature
- Explicit modeling of GDP shocks and combining SVARs with narrative information better addresses foresight and endogeneity.
- Heterogeneity across countries: country-by-country SVAR avoids dynamic homogeneity assumptions that can bias panel regressions.

### External validation checks
- Applying identification method to US tax revenue shocks reproduces a large negative tax multiplier found by Mertens and Ravn (2013).
- Fiscal expansion shocks identified by the method align with Ben Zeev et al. (2023) military spending news episodes despite no direct narrative restrictions on expansions.

---

### 5.1 The Problem of Foresight and Invertibility

### Diagnostics and findings
- Foresight can render VAR representations non-fundamental; diagnostic approach uses R-squared from regressing candidate structural shocks on observables.
- Simulation threshold: R-squared below 0.25 suggests non-invertibility may be present but practically insignificant.
- Table 7 diagnostics:
  - Narrative Shocks: 0.471 (cont./lags); 0.582 (plus forecasts)
  - SVAR (Sign-narrative): 0.104; 0.156 (plus forecasts)
  - SVAR (sign-only): 0.239; 0.424 (plus forecasts)
- Interpretation: non-fundamentalness likely limited in baseline VARs that combine sign and narrative restrictions.

### Orthogonality and local projections comparison
- VAR (sign-narrative) shocks are orthogonal to one- and five-year-ahead forecasts of GDP growth and changes in debt to GDP; narrative shocks correlate systematically with forecasts.
- Local projections using two-way fixed effects:
  - Using narrative shocks directly reproduces sharp persistent negative GDP response found in prior local projection literature.
  - Replacing narrative shocks with SVAR-extracted shocks (sign-only or sign-narrative) yields a zero fiscal multiplier.
  - Instrumenting narrative shocks with sign-narrative VAR shocks: first-stage F statistic of 15; IV estimates similar to baseline VAR results.
- Conclusion: biases from relying solely on narrative data can explain differences; identification method, not sample size, drives differences.

---

### 5.2 The Role of Heterogeneity

### Findings on heterogeneity versus exogeneity
- Country-by-country SVAR accommodates cross-country heterogeneity.
- Country-level local projections (three-year horizon):
  - Distribution of primary balance multipliers centered around zero when heterogeneity is allowed.
  - Baseline SVAR cross-country distribution qualitatively similar.
- Correlation analysis:
  - Correlation between country-by-country local projection coefficients using narrative shocks and corresponding sign-narrative VAR estimates is essentially zero.
  - Replacing narrative shocks with VAR-derived sign-narrative shocks produces much higher correlation (correlation =0.7 in another comparison).
- Interpretation: exogeneity of shocks, rather than heterogeneity, is the key issue; VAR-derived shocks recover VAR results even under homogeneity-imposing two-way fixed effects.

---

### 5.3 Proxy SVARs and the Tax Multiplier

### US evidence and external validation
- US government revenue shocks (1981-2019 with narrative information): GDP growth declines in response to a revenue increase shock, but response has a wide confidence band and is not statistically significant (Figure 14 described).
- Using Mertens and Ravn (2013) narrative data (1950-2006) focusing on tax increases:
  - Statistically significant negative multiplier found.
  - Magnitude: multiplier peaks at about 3.
  - Comparisons: Mertens and Ravn (2013) peak multiplier 2.5; Mountford and Uhlig (2009) revenue multiplier peaks at 5.
- Interpretation: method reproduces established negative tax multiplier results under appropriate sample and narrative data, supporting validity.

---

### 6 Robustness: Priors, Global Shocks, Unexpected Inflation, and Predictability

### Priors and main ratio
- Baseline: Minnesota priors; alternate: Jeffrey’s prior.
- Main result robust: ratio of contribution of growth to discretionary shocks remains around 2.5 under either prior (Growth Shocks/Primary Balance Shock ratios: 2.56, 2.50).

### Global shocks and monetary policy
- Augmenting SVAR with US 10 year nominal yield as an exogenous variable (VAR-X) increases accounted fraction of movements in debt ratios and strengthens finding that growth shocks are main driver.
- Identifying an additional monetary policy shock via impact sign restrictions leaves relative contribution of growth vs discretionary fiscal shocks largely unchanged.

### Predictability of narrative information
- Strategy: use only presence/absence (sign) of narrative shocks in sign restrictions, not actual narrative shock values.
- Filtering narrative information by residuals (keeping only non-predictable component) yields results essentially the same as baseline.

---

### 7 Conclusion — Key Takeaways

### Framework and main empirical findings
- Framework: SVAR augmented with narrative sign restrictions.
- Main empirical findings:
  - Exogenous demand and supply growth shocks account for approximately forty percent of the variations in the debt-to-GDP ratio.
  - Discretionary policy shocks contribute less than a fifth of these variations.
  - Discretionary primary balance consolidations have a modest influence on the debt-to-GDP ratio and, on average, an insignificant impact on GDP.

### Reasons for divergence from prior contractionary-austerity literature
- SVAR combined with narrative sign restrictions better addresses foresight and endogeneity; invertibility concerns appear quantitatively limited in this framework.
- Country-by-country SVAR estimation accommodates cross-country heterogeneity and avoids biases from imposing coefficient homogeneity.

### External validation and future research avenues
- External validation:
  - Tax multiplier estimates for the US align with Mertens and Ravn (2013).
  - Correct identification of 1990 US consolidation magnitude in Guajardo et al. (2014) using only sign information.
- Suggested future research:
  - Extend analysis to emerging economies.
  - Investigate potential non-linearities in debt dynamics and heterogeneous impacts of consolidations on GDP growth.
  - Decompose primary balance into revenues and expenditures and subcomponents for select countries with data.

---

### Key empirical decomposition statistics (preserved exactly)
- Contribution shares (medians across countries) to debt dynamics (Table 3):
  - Growth Shocks: 41
  - Demand Shock: 24
  - Supply Shock: 17
  - Primary Balance Shock: 16
  - Total: Identified Shocks: 57
- Contribution shares conditional on debt ratio changes (Table 3):
  - Debt to GDP Increase: Growth Shocks 40, Demand Shock 25, Supply Shock 15, Primary Balance Shock 14, Total: Identified Shocks 54
  - Debt to GDP decrease: Growth Shocks 43, Demand Shock 25, Supply Shock 18, Primary Balance Shock 18, Total: Identified Shocks 61
- Forecast Error Variance Decomposition (Table 5): Growth Shocks 38, Demand Shock 22, Supply Shock 16, Primary Balance Shock 15, Total: Identified Shocks 53
- Historical Decomposition (Table 5): Growth Shocks 41, Demand Shock 24, Supply Shock 17, Primary Balance Shock 16, Total: Identified Shocks 57
- Table 9 selected entries (baseline / Jeffrey’s prior / VAR-X / Monetary policy shock):
  - Growth Shocks: 41 35 18 39
  - Demand Shock: 24 21 11 22
  - Supply Shock: 17 14 7 17
  - Primary Balance Shock: 16 14 7 14
  - Growth Shocks/Primary Balance Shock ratios: 2.56 2.50 2.57 2.78
- R squared diagnostic for Non-Fundamentalness (Table 7):
  - Narrative Shocks: 0.471; plus forecasts: 0.582
  - SVAR (Sign-narrative): 0.104; plus forecasts: 0.156
  - SVAR (sign-only): 0.239; plus forecasts: 0.424

*Source: wpiea2024087-print-pdf - 2.1 Structural Shocks and Historical Decompositions.*

### 2.1  Structural Shocks and Historical Decompositions  . . . . . . . . . . . . . . .    6

### 2.1 Structural Shocks and Historical Decompositions

### Major findings and substantive conclusions
- Global average public debt-to-GDP ratio rose to nearly 100% in 2020—a 15-percentage-point increase from the previous year.
- Debt-to-GDP ratios contracted in 2021 and 2022, reversing approximately half of the 2020 surge.
- The structural shocks considered jointly account for around 60% of the variations in the debt-to-GDP ratio.
- GDP growth shocks explain roughly 40% of the yearly variation in debt-to-GDP ratios for the median advanced economy.
- Discretionary policy shocks explain less than a fifth of the yearly variation in debt-to-GDP ratios in the baseline model.
- The baseline SVAR does not explicitly incorporate monetary policy shocks, but an extension allowing for monetary policy shocks leaves the main results unchanged.
- Unexpected inflation has been important for debt-to-GDP in certain periods and countries (including the US), though for the sample period considered this has been less relevant.
- The study finds a small impact of discretionary fiscal consolidations on GDP growth (i.e., a small primary balance multiplier), and reports a "zero multiplier" effect in robustness checks using alternative approaches (local projections and IVs derived from SVAR shocks).

### Interpretation and policy-relevant implications
- The macroeconomic reaction to GDP shocks and the comovements of GDP with other macro and fiscal variables are the principal drivers of observed changes in debt-to-GDP ratios.
- Given high debt-to-GDP ratios, the results suggest reassessing policy calibrations and implicit policy reactions to shocks.
- Fiscal consolidations have limited direct impact on debt-to-GDP in this framework; debt reduction during periods of growth is highlighted as significant.
- Methodological implications: addressing endogeneity and the foresight problem is crucial to obtain reliable estimates of fiscal multipliers and debt dynamics.

### Key statistics and quantitative statements (preserved exactly)
- "nearly 100% in 2020"
- "a 15-percentage-point increase"
- "reversing approximately half of the 2020 surge"
- "jointly account for around 60% of the variations in the debt-to-GDP ratio"
- "GDP shocks explain roughly 40% of the yearly variation in debt to GDP ratios for the median advanced economy"
- "discretionary policy shocks on the other hand explain less than a fifth"
- "six variables: GDP growth, government revenues, primary balance, debt to GDP, inflation, and the effective interest rate on debt"
- "three distinct shocks: a demand-driven GDP growth shock, a supply-driven GDP growth shock, and a primary balance shock orthogonal to the others"
- Sample: "a panel of yearly data covering seventeen advanced economies from 1981-2019"
- Data sources: "Historical Public Finance Database (HPFD)" (pre-2011), "Global Debt Database (GDD)" and "WEO" (post-2011)

### Conceptual and methodological points
- Model: Structural Vector Autoregression (SVAR) with structural parameters Θ = (A0, A+) and reduced-form parameters B and Σ, following the standard representation:
  - Structural form: y′t A0 = Σ_{l=1}^p y′t−l Al + c + ε′t  (equation (2.1))
  - Reduced form: y′t = x′t B + u′t  (equation (2.3))
  - Structural shocks: ε′t(Θ) = y′t A0 − x′t A+  (equation (2.4))
- Historical decomposition: contribution of jth structural shock to ith variable between t and t+h:
  - Hi,j,t,t+h(Θ) = Σ_{l=0}^h e′i,n L l(Θ) e j,n e′j,n ε t+h−l(Θ)  (equation (2.5))
- Identification: narrative sign restrictions impose constraints so that structural shocks are of a particular sign on certain dates, framed as S j F(θ) e j,n > 0 for 1≤j≤n (equation (2.6)), where S j is an s j by n matrix of full row rank.
- The narrative sign restriction approach combines sign restrictions (Mountford and Uhlig (2009) style for growth and fiscal shocks) with narrative constraints on the primary balance shock (Antolín-Díaz and Rubio-Ramírez (2018) style), using cross-country narrative information on primary balance consolidations from the literature (e.g., Guajardo et al. (2014), Gunter et al. (2021), Carrière-Swallow et al. (2021)).

### Robustness, validation, and comparison to literature
- The methodology addresses the "foresight problem" and non-invertibility concerns articulated in Ramey (2016) and diagnostics from Beaudry et al. (2019).
- External validation exercises:
  - Reproducing the high negative tax multiplier found by Mertens and Ravn (2013) when applying the method to US tax increases.
  - Periods of exogenous fiscal expansions identified by the method align with Ben Zeev et al. (2023) military spending news episodes, despite no narrative restrictions on fiscal expansions in estimation.
- Cross-country heterogeneity is explicitly allowed for, differing from panel regression approaches that assume homogeneity.
- Applying country-specific local projections with narrative data yields a distribution of primary balance multipliers centered around zero, consistent with the baseline SVAR.
- Using structurally-identified SVAR shocks in local projections or as instruments for narrative shocks yields a null multiplier, consistent with baseline estimates.

### Data and estimation (concise)
- Frequency: Annual (to maximize country-year coverage).
- Fiscal aggregation: General government (not central government).
- Sample: Seventeen advanced economies, 1981-2019.
- Data sources: HPFD (pre-2011), GDD and IMF WEO (post-2011).

*Source: wpiea2024087-print-pdf - 2.1 Structural Shocks and Historical Decompositions.*

### 3.1  Model Specification

### 3.1  Model Specification

### Model overview and variables
- The SVAR consists of the following six variables: (1) Real GDP growth; (2) Growth rate of real government revenues; (3) change in primary balance to GDP; (4) change in debt to GDP; (5) nominal effective interest rate on public debt; and (6) GDP deflator inflation.
- Table 1 in the source summarizes the variables used as well as the sign restrictions that are imposed.

### Identification strategy
- Identification is based on sign restrictions to isolate three structural shocks:
  - Two GDP shocks: supply and demand.
  - One discretionary primary balance shock orthogonal to the growth shocks.
- Narrative restrictions are used to sharpen identification of the discretionary primary balance shock using updated measures (up till 2019) based on the methodology in Guajardo et al. (2014).
- Demand shock sign restrictions:
  - Output and inflation move in the same direction on impact.
  - Government revenues react procyclically.
- Supply shock sign restrictions:
  - Output and inflation move in opposite directions on impact.
  - Government revenues react procyclically.
- Key deviations from Mountford and Uhlig (2009):
  - Two separate GDP shocks (supply and demand) are identified rather than a single GDP shock.
  - Focus is on the primary balance to GDP ratio rather than on revenues alone.
  - Sign restrictions are imposed for a single period consistent with annual frequency of the data rather than for four quarters.

### Use of narrative restrictions
- Narrative restrictions are imposed only in the first year of multi-year consecutive narrative episodes (e.g., Austria coded positive consolidation shocks in 2000 and 2001 → restriction imposed only in 2000).
- An additional narrative restriction: impose a negative demand shock in 2008.
- Rationale for first-year restriction:
  - Increasing the number of narrative restrictions reduces the set of candidate solutions that satisfy all sign and narrative restrictions.
  - Fiscal adjustments are often multi-year plans; information beyond the first year may be pre-announced or revised and can confound estimation of exogenous shifts (Alesina et al. (2015) reasoning).
- Predictability check of narrative shocks:
  - Regression of actual magnitudes of narrative shocks on lagged values of output gap, level of debt to GDP, GDP growth, and narrative shocks (plus country fixed effects) yields an R square around 0.4.
  - For almost all (95 percent) of the narrative shocks incorporated as narrative restrictions, the regression yields a positive residual, indicating an unexplained fiscal consolidation component not predictable by lagged macroeconomic variables.
  - This positive-residual share drops to around 70 percent when considering all narrative shocks rather than only first-year episodes, supporting the first-year restriction approach.

### Estimation approach
- VAR estimated country by country with two lags using Bayesian Methods.
- Minnesota Prior applied to the reduced-form VAR, following the version discussed in Sims and Zha (1998) and Del Negro (2011); shrinkage parameters chosen to maximize marginal data density.
- Structural identification with sign and narrative sign restrictions uses the Antolín-Díaz and Rubio-Ramírez (2018) approach, building on Rubio-Ramirez et al. (2010) and the Haar prior for rotation matrices.
- Justification for Haar prior:
  - Influence of Haar prior argued to be negligible in tightly sign-identified SVARs, especially when augmented with multiple shocks and narrative restrictions.
  - Uniform prior over orthogonal matrices is necessary for uniform joint prior and posterior over the identified set for impulse responses when identifying multiple shocks.

### Aggregation choice
- Model estimated country-by-country and medians summarized across 17 advanced economies.
- Country-by-country approach chosen over panel VAR to avoid imposing dynamic homogeneity across heterogeneous countries.

### Inference details
- Impulse responses summarized as medians over six years.
- Credible sets: 68 percent highest posterior density credible sets used; inverse variance weights used to aggregate country-level impulse responses.

### Notable data/contextual points
- Anomalies in 2014 and 2015: large residuals corresponding to substantial declines in debt-to-GDP driven by ‘below-the-line’ fiscal operations and statistical recalibrations that inflated GDP by over 20%; model appropriately does not fit these non-economic fluctuations.

*Source: IMF working paper chapter section 3.1 and adjoining exposition*

### 4.3  The Value of Narrative Restrictions

### 4.3  The Value of Narrative Restrictions

### Narrative restrictions sharpen identification and precision
- Estimating the SVAR with only sign restrictions versus with narrative sign restrictions shows that narrative information, even when sparse, is valuable (consistent with Antolín-Díaz and Rubio-Ramírez (2018)).
- Figure 9 (described) compares the posterior distribution of the primary balance shock during narrative periods:
  - Entire sample and a specific episode (the 1990 consolidation in the US) are contrasted.
  - Narrative data imply all shock draws should be positive; sign-restriction-only identification includes several negative values that should not exist, illustrating the sharpening effect of narrative information.
  - For the US in 1990:
    - Mean of the shock without narrative restrictions: -0.07
    - Mean with narrative restriction: 0.3
    - Narrative database actual value (Guajardo et al. (2014)): 0.36
  - Note: only the sign and not the magnitude from the narrative restriction is used in estimation.

- Table 6 (described) shows that narrative information tightens Highest Posterior Density (HPD) credible sets for most impulse responses; the impact is especially noticeable for the primary balance shock.
  - Confidence interval width differences are expressed as percentage differences; negative values indicate smaller confidence intervals for the VAR with narrative restrictions.

### Narrative restrictions can change qualitative inference
- Figure 10 (described) shows the introduction of narrative information leads to significant changes in conclusions about the impact of a primary balance shock:
  - With narrative sign restrictions: impact on GDP and debt ratios is negative but small.
  - Without narrative restrictions (VAR only): impact on GDP is positive (albeit still small) and debt ratios show a much sharper negative impact.
- Conclusion: narrative restrictions sharpen shock identification, improve HPD credible set accuracy, and can alter substantive conclusions.

---

### 5  Towards a Reconciliation with Contractionary Austerity Results in the Literature

### Two main sources of divergence with prior literature
- First source: explicit modeling of GDP shocks and combining SVARs with narrative information better addresses foresight and endogeneity.
- Second source: heterogeneity across countries—conventional panel regressions often impose homogeneity across countries (even with country and time fixed effects), which can introduce substantial biases in dynamic settings (see Pesaran and Smith (1995)).

### External validation checks
- Applying the identification method based on narrative sign restrictions to US tax revenue shocks reproduces a large negative tax multiplier found by Mertens and Ravn (2013).
- Fiscal expansion shocks for the US identified by the method agree with military spending shocks of Ben Zeev et al. (2023), despite not incorporating that narrative data.

---

### 5.1  The Problem of Foresight and Invertibility
- Foresight by agents can render VAR representations non-fundamental and prevent recovery of true shocks (Ramey (2016)).
- Invertibility is a property of disturbances of a structural model and cannot be fully tested in a purely data-driven way.
- Diagnostic approach (Beaudry et al. (2019)):
  - Compute R-squared from regressing candidate structural shocks on observables not in the empirical model.
  - Simulations indicate an R-squared value below 0.25 suggests non-invertibility may be theoretically present but practically insignificant.
- Findings from Table 7 (described):
  - Regressions of narrative shocks on macro variables and forecasts: R-squares in excess of 0.25.
  - SVAR shocks: explanatory power much lower, with R-squares well below 0.10.
  - Interpretation: quantitative importance of non-fundamentalness likely limited in baseline VARs that combine narrative and sign restrictions, relative to SVARs with only sign restrictions and local projections using narrative shocks directly.

- Cochrane (2004) insight applied to fiscal shocks:
  - For inference on GDP and debt-to-GDP forecasts (Table 8 described):
    - VAR (sign-narrative) shocks are orthogonal to one- and five-year-ahead forecasts of GDP growth and changes in debt to GDP (no significant predictive power).
    - Narrative shocks are systematically correlated with forecasts for changes in debt to GDP.

- Local projections comparison (Figure 11 described):
  - Using two-way fixed effects with narrative shocks directly reproduces sharp persistent negative GDP response found in prior local projection literature.
  - Replacing narrative shocks with SVAR-extracted shocks (sign restrictions only) or SVAR with narrative-sign restrictions yields:
    - Using SVAR-extracted shocks: zero fiscal multiplier emerges (consistent with baseline).
    - Bottom-right panel: instrumenting narrative shocks with sign-narrative VAR shocks (IV approach) yields:
      - VAR shocks are strong instruments for narrative shocks (first-stage F statistic of 15).
      - Estimated GDP response via IV almost identical to baseline.
  - Conclusion: biases from relying solely on narrative data can explain differences; identification method drives differences in results, not sample size.

- Symmetry concern:
  - Narrative restrictions correspond solely to fiscal consolidations, while the linear SVAR assumes symmetry between expansions and recessions.
  - For the US, the method correctly identifies positive primary balance shocks in years overlapping Ben Zeev et al. (2023) (1999 and 2003), agreeing with spending news shocks.

---

### 5.2  The Role of Heterogeneity
- Country-by-country SVAR framework accommodates cross-country heterogeneity, avoiding homogeneity assumptions that can bias panel estimates (Favero et al. (2011)).
- Country-level local projections over a three year horizon:
  - Left panel of Figure 12: distribution of primary balance multipliers centered around zero when heterogeneity is allowed.
  - Right panel of Figure 12: cross-country distribution from baseline SVAR estimates is qualitatively similar.
- Correlation analysis (Figure 13):
  - Correlation between country-by-country local projection coefficients using narrative shocks and corresponding sign-narrative VAR estimates is essentially zero.
  - Replacing narrative shocks with VAR-derived sign-narrative shocks produces much higher correlation with VAR estimates.
  - Interpretation: exogeneity of shocks, rather than heterogeneity, is the key issue; VAR-derived shocks recover VAR results even under homogeneity-imposing two-way fixed effects.

---

### 5.3  Proxy SVARs and the Tax Multiplier
- Method applied to US government revenue shocks:
  - With sample 1981-2019 and narrative information: GDP growth declines in response to a revenue increase shock, but response has a wide confidence band and is not statistically significant (Figure 14 described).
- Using Mertens and Ravn (2013) narrative data and sample 1950-2006:
  - Focusing on tax increases, the approach finds a statistically significant negative multiplier (Figure 15 described).
  - Magnitude: multiplier peaks at about 3.
    - Comparison: Mertens and Ravn (2013) peak multiplier 2.5; Mountford and Uhlig (2009) revenue multiplier peaks at 5.
  - Interpretation: external validation consistent with MR findings, reassures validity of methods.

---

### 6  Robustness: Priors, Global Shocks, Unexpected Inflation, and Predictability of Narrative Data
- Priors:
  - Baseline uses Minnesota priors due to short sample; second column in Table 9 uses Jeffrey’s prior.
  - Main result on relative importance of growth versus discretionary primary balance shocks in historical decomposition of debt to GDP is robust:
    - Ratio of contribution of growth to discretionary shocks remains around 2.5 under either prior.
- Global shocks:
  - Augmenting the SVAR with the 10 year nominal yield on US government bonds as an exogenous variable (Column 3, Table 9):
    - This variable accounts for a large fraction of movements in debt ratios.
    - New estimates further strengthen main finding that growth shocks (luck) are the main driver of debt ratios, contrasted with discretionary fiscal policy.
- Additional monetary policy shock identification (last column in Table 9):
  - Identifying an additional monetary policy shock via impact sign restrictions leaves the relative contribution of growth vs discretionary fiscal shocks largely unchanged.
- Predictability of narrative information:
  - Jordà and Taylor (2016) document narrative shocks are predictable from past debt values.
  - Strategy here: use only presence/absence (sign) of narrative shocks in sign restrictions, not actual narrative shock values.
  - Reproducing Jordà and Taylor (2016) regression and filtering narrative information by residuals (keeping only non-predictable component) yields results essentially the same as baseline.

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### 7  Conclusion — Key Takeaways
- Framework: Structural Vector Autoregression (SVAR) augmented with narrative sign restrictions.
- Main empirical findings:
  - Exogenous demand and supply growth shocks account for approximately forty percent of the variations in the debt-to-GDP ratio.
  - Discretionary policy shocks contribute less than a fifth of these variations.
  - Discretionary primary balance consolidations have a modest influence on the debt-to-GDP ratio and, on average, an insignificant impact on GDP.
- Two primary reasons results differ from prior literature finding contractionary austerity:
  - The SVAR combined with narrative sign restrictions better addresses foresight and endogeneity (invertibility concerns appear quantitatively limited in this framework).
  - Country-by-country SVAR estimation accommodates cross-country heterogeneity and avoids biases from imposing coefficient homogeneity.
- External validation:
  - Tax multiplier estimates for the US are quantitatively in line with Mertens and Ravn (2013).
  - Correct identification of 1990 US consolidation magnitude in Guajardo et al. (2014) using only sign information.
- Suggested avenues for future research:
  - Extend analysis to emerging economies.
  - Investigate potential non-linearities in debt dynamics and heterogeneous impacts of consolidations on GDP growth.
  - For select countries with data, decompose primary balance into revenues and expenditures and subcomponents (different types of taxes, government consumption vs investment).

*Source: wpiea2024087-print-pdf - 4.3  The Value of Narrative Restrictions*

### References

### wpiea2024087-print-pdf - References

### Key empirical findings and decomposition results
- Contribution shares (medians across countries) to debt dynamics (Table 3):
  - Growth Shocks: 41
  - Demand Shock: 24
  - Supply Shock: 17
  - Primary Balance Shock: 16
  - Total: Identified Shocks: 57
- Contribution shares conditional on debt ratio changes (Table 3):
  - Overall: Growth Shocks 41, Demand Shock 24, Supply Shock 17, Primary Balance Shock 16, Total: Identified Shocks 57
  - Debt to GDP Increase: Growth Shocks 40, Demand Shock 25, Supply Shock 15, Primary Balance Shock 14, Total: Identified Shocks 54
  - Debt to GDP decrease: Growth Shocks 43, Demand Shock 25, Supply Shock 18, Primary Balance Shock 18, Total: Identified Shocks 61
- Sample-average versus years with large changes in debt ratios (Table 4):
  - Overall: Growth Shocks 41, Demand Shock 24, Supply Shock 17, Primary Balance Shock 16, Total: Identified Shocks 57
  - Years with Large Changes in Debt to GDP: Growth Shocks 39, Demand Shock 24, Supply Shock 15, Primary Balance Shock 15, Total: Identified Shocks 54
- Historical decomposition means by country (Table 2 — values listed per growth/demand/supply/primary balance rows; column headers abbreviated):
  - Growth Shocks row (example entries): 41 36 38 42 45 44 42 43 35 37 43 46 (as shown across countries)
  - Demand row (example entries): 24 19 19 25 28 25 29 26 26 23 22 22 27
  - Supply row (example entries): 17 17 19 17 17 19 13 17 12 15 21 19
  - Primary Balance Shock row (example entries): 16 17 23 17 11 11 16 15 13 18 16 11
  - Total: Identified Shocks row (example entries): 57 53 61 59 56 55 58 58 48 53 59 57
- Forecast error variance versus historical decomposition (Table 5):
  - Forecast Error Variance Decomposition: Growth Shocks 38, Demand Shock 22, Supply Shock 16, Primary Balance Shock 15, Total: Identified Shocks 53
  - Historical Decomposition: Growth Shocks 41, Demand Shock 24, Supply Shock 17, Primary Balance Shock 16, Total: Identified Shocks 57

### Impulse responses and narrative shock effects
- Impulse responses presented with medians and 68th percentile confidence intervals; responses are weighted using inverse variance weights and based on an annual sample of 17 advanced economies from 1981-2019 (Figures 6, 7, 8).
- Primary balance narrative information tightens credible sets (Table 6: % difference between HPD sets cumulated over 6-year horizon; negative denotes smaller HPD sets with narrative-sign restrictions relative to sign-only):
  - Demand Shock: GDP Growth 0.01, Revenue Growth -0.65, Primary Balance -12.62, Debt -0.77, Interest Rate 0.22, Inflation -0.1
  - Supply Shock: GDP Growth -1.32, Revenue Growth -1.78, Primary Balance -7.96, Debt -2.55, Interest Rate -2.09, Inflation -2.69
  - Primary Balance Shock: GDP Growth -3.49, Revenue Growth -1.62, Primary Balance -5.19, Debt -2.16, Interest Rate -1.26, Inflation -1.14
- Impulse response examples for the US:
  - Government Revenue Shock for the US (1981-2019): median and 16-84th percentile confidence intervals provided (Figure 14).
  - Government Revenue Shock for the US (1952-2006) using Mertens and Ravn (2013) shocks as narrative restrictions: median and 16-84th percentile confidence intervals; tax increase shocks from Mertens and Ravn (2013) database imposed as narrative restrictions (Figure 15).

### Identification, sign restrictions, and VAR specification
- Sign restrictions imposed on the VAR impulse responses (Table 1):
  - Demand Shock: GDP Growth +++ (positive on impact)
  - Supply Shock: GDP Growth ++- (positive then negative sign pattern)
  - Discretionary Primary Balance Shock: Primary Balance/GDP +
  - Notes: Empty cells imply no sign restriction for that shock/variable pair. Primary balance to GDP and debt to GDP ratios included in first difference in the VAR.
- Baseline VAR specification details and robustness checks (Table 9 notes):
  - Baseline: six-variable VAR, estimated with two lags using the Minnesota prior.
  - Alternate: Jeffrey’s prior instead of Minnesota.
  - VAR-X: adds US nominal 10 year yields as an exogenous variable.
  - Additional specification: adds an additional monetary shock identified with inflation and the effective interest rate moving in opposite directions on impact.
  - Selected reported entries (Table 9):
    - Growth Shocks (columns show values under Baseline, Jeffrey’s Prior, VAR-X, Monetary Policy Shock): 41 35 18 39
    - Demand Shock: 24 21 11 22
    - Supply Shock: 17 14 7 17
    - Primary Balance Shock: 16 14 7 14
    - US (10 year) Nominal Rate: 00 40 (reported as "0040" under one column)
    - Monetary Policy Shock: 14
    - Residual: 44 50 35 33
    - Growth Shocks/Primary Balance Shock ratios: 2.56 2.50 2.57 2.78

### Diagnostics on non-fundamentalness and orthogonality
- R squared diagnostic for Non-Fundamentalness (Table 7; R squared values reported):
  - Narrative Shocks: Contemporaneous and lagged controls: 0.471; plus forecasts: 0.582
  - SVAR (Sign-narrative): 0.104; plus forecasts: 0.156
  - SVAR (sign-only): 0.239; plus forecasts: 0.424
  - Observations: 476 407
  - Notes: Based on panel regressions of shocks on explanatory variables including two lags of several macro variables and, in the forecasts column, one and five year ahead forecasts of debt to GDP, GDP growth and primary balance to GDP. Sample: 17 countries from 1990-2019.
- Orthogonality of shocks with respect to macroeconomic forecasts (Table 8; selected coefficients and statistics):
  - Regressions use sample of 17 countries from 1995-2019; all regressions include country fixed effects; standard errors clustered by country.
  - Narrative Shocks coefficients (selected): △Debt/GDP f t−1,t+4 = 3.38*** (standard error 1.07)
  - VAR shocks coefficients (selected): △Debt/GDP f t−1,t+4 = 1.17 (standard error 0.69)
  - Constants show various significant intercepts (e.g., 0.086***, 0.11***, 0.22***, 0.25***, 0.040***, -0.33**, -4.97***, -6.18*** in corresponding regressions)
  - Observations per regression: 408 or 407; R-squared values range from 0.001 to 0.070
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.

### Figures and visual decomposition notes
- Figure captions and notes highlight data and sample coverage:
  - Figure 1: Evolution of Debt to GDP Ratios. Source: IMF World Economic Outlook (WEO) Database.
  - Figure 2: Narrative Shocks in Advanced Economies. Notes: Green and blue denote positive and negative narrative primary balance shocks. Sources: Guajardo et al. (2014).
  - Figures 3 and 5: Historical Decomposition of Debt to GDP year-on-year Changes in the US and Ireland respectively. Notes: Based on the baseline VAR with narrative sign restrictions; the "other" category combines unidentified VAR shocks and the initial condition.
  - Figure 11: Panel Fixed Effects Local Projections comparing Narrative Shocks, VAR Shocks (with sign restrictions only), VAR Shocks (with sign-narrative), and Narrative Shocks instrumented with VAR Shocks (with sign-narrative). Notes: Impulse response of GDP growth to primary balance consolidation shocks; regression controls for lagged dependent variable and country and time fixed effects; standard errors clustered by country; sample of 17 advanced economies from 1983-2019.
  - Figure 12–13: Cross-country heterogeneity and correlations across methods (local projections and VAR medians); scatter plots and histograms illustrate heterogeneity and method concordance (correlation <0.1 in one comparison, correlation =0.7 in another).

*Public Debt Dynamics and the Impact of Fiscal Policy — Working Paper No. WP/2024/087*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024087-print-pdf.pdf_