## Annex I. Panel Regressions on Fiscal Responsiveness

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---

### Description and methodology
- Role: Technical annex presenting panel-regression analysis used to assess fiscal responsiveness for 16 Advanced Economies (AEs) over 1880–2022.
- Two empirical tests following Bohn (1998) and Mauro et al. (2015):
  - Test 1 (equation (3)): pb_t = ρ1 · d_{t−1} + α1 (Q_t − Q_t^*) + ε_t — estimate ρ1 (response of primary balance to lagged debt ratio).
  - Test 2 (equation (5)): pb_t = ρ2 · pb_t^{DS} + α2 (Q_t − Q_t^*) + ε_t — estimate ρ2 (response of primary balance to debt-stabilizing primary balance, DSPB).
- Debt-stabilizing primary balance definition (equation (4)):
  - pb_t^{DS} = (r_t^* − g̅_t) / (1 + π̅ + g̅_t) · d_{t−1}.
- Regressions include time and country fixed effects; three subperiods analyzed: Pre-GFC (1880-2008), GFC/post-GFC (2009-2019), Pandemic (2020-2022).
- Robust standard errors clustered by year; primary balances are highly autocorrelated and results robust to including lagged dependent variables.

### Regression specifications (Annex)
- Equation (A.1):
  - pb_{i,t} = ρ1 · d_{i,t−1} + ω1 · otherperiod_t · d_{i,t−1} + α1 · Q_gap_{i,t} + δ_t + β_i + ε_{i,t}
  - otherperiod_t equals 1 if year t does not fall within the period of interest and 0 otherwise.58
- Equation (A.2):
  - pb_{i,t} = ρ2 · pb_{i,t}^{DS} + ω2 · otherperiod_t · pb_{i,t}^{DS} + α2 · Q_gap_{i,t} + δ_t + β_i + ε_{i,t}
- Sample and data:
  - 16 AEs; primary balances and debt: Public Finance in Modern History database (Mauro et al., 2015).
  - Trend growth and monetary r-star for DSPB: Platzer et al. (2013).
  - Inflation set at 2 percent for DSPB construction.
  - Full sample period in regressions: 1880-2022.
- Note 58: For the pre-GFC, GFC, and Covid regressions, the dummy otherperiod_t equals 1 if the years fall within 2009-2022, 1880-2008 and 2020-2022 and 1880-2019, respectively.

### Annex Table 1 — Key regression estimates (Responsiveness of Fiscal Policy)
- Response to Lagged Debt Level (columns (1) pre-GFC, (2) GFC, (3) COVID):
  - Lagged Debt Level:
    - pre-GFC: 0.031*** (0.003)
    - GFC: -0.015*** (0.003)
    - COVID: -0.035*** (0.006)
  - Lagged Debt Level * Other Period:
    - pre-GFC: -0.053*** (0.006)
    - GFC: 0.041*** (0.006)
    - COVID: 0.058*** (0.007)
  - Output Gap:
    - pre-GFC: 0.014 (0.019)
    - GFC: 0.018 (0.020)
    - COVID: 0.013 (0.020)
  - Observations: 1796 (all columns)
  - R-squared:
    - pre-GFC: 0.40
    - GFC: 0.37
    - COVID: 0.37
- Response to Debt-Stabilizing Primary Balance (DSPB) (columns (4) pre-GFC, (5) GFC, (6) COVID):
  - Debt Stabilizing Primary Balance (DSPB):
    - pre-GFC: 1.37*** (0.16)
    - GFC: 0.49*** (0.15)
    - COVID: 0.67*** (0.20)
  - DSPB * Other Period:
    - pre-GFC: -0.86 (0.21)
    - GFC: 0.75*** (0.21)
    - COVID: 0.46* (0.24)
  - Output Gap:
    - pre-GFC: 0.005 (0.019)
    - GFC: 0.004 (0.020)
    - COVID: 0.005 (0.020)
  - Observations: 1796 (all columns)
  - R-squared: 0.36 (all columns)
- Notes:
  - Robust standard errors, clustered by year, reported in parentheses.
  - Significance: *** p<0.01, ** p<0.05, * p<0.1

### Main empirical findings on fiscal responsiveness (stylized)
- Pre-GFC (1880-2008):
  - Primary balances respond positively to lagged debt ratio: a 1 percentage point higher debt ratio associated with a rise in the primary balance of 0.03 percentage points (0.031***).
  - ρ1 positive and statistically significant; ρ2 > 1 (DSPB coefficient 1.37***).
  - Interpretation: Fiscal policy characterized as passive (consistent with Bohn, 1998).
- GFC / Post-GFC (2009-2019):
  - Response of primary balance to lagged debt becomes negative but statistically significant (−0.015***), indicating attenuation of fiscal responsiveness relative to pre-GFC.
  - ρ2 substantially smaller than one (DSPB coefficient 0.49***).
- Pandemic (2020-2022):
  - Response of primary balance to lagged debt is negative and statistically significant (−0.035***).
  - ρ2 remains significantly smaller than one (DSPB coefficient 0.67***).
  - Interpretation: Fiscal policy became more “active” during the pandemic; primary balances failed to move toward debt-stabilizing levels.
- Robustness:
  - Results robust to inclusion of lagged dependent variable given high autocorrelation in primary balances.
  - Statistical significance indicated by solid lines in related figures at 10 percent level (robust SEs clustered by year).

### Interpretation, mechanisms, and implications
- Active vs passive fiscal policy:
  - Passive fiscal policy: primary balance adjusts endogenously to debt — reduces fiscal-monetary tensions and permits active monetary policy.
  - Active fiscal policy: primary balance set exogenously to debt — increases the relevance of the real interest rate for debt dynamics and raises potential fiscal-monetary tensions.
- Suggested drivers of increasing activeness:
  - Discretionary spending pressures (e.g., pandemic relief).
  - Waning social and political cohesion and lack of viable deficit-reduction coalitions.
  - Longer-term structural spending pressures (aging entitlements, green transition, supply-chain diversification).
- Consequences of increased fiscal activeness:
  - Rising debt levels combined with potentially higher-for-longer interest rates can undermine fiscal sustainability.
  - Larger required fiscal consolidations or accommodation by monetary policy (posing price-stability and financial-stability tradeoffs).

### Theoretical framework and key equations (as presented)
- Debt law of motion and valuation:
  - Debt dynamics (equation (1) / A.9): Δd_t = (r_t − g_t) / (1 + π_t + g_t) · d_{t−1} − pb_t.
  - Interest-growth differential (A.3): Γt ≡ (r_t − g_t) / (1 + π_t + g_t).
  - Law of motion with fiscal reaction (A.4): d_t = [Γ_t + (1 − ρ1)] · d_{t−1} − α1 (Q_t − Q_t^*) − ε_t.
- Debt-stabilizing primary balance and fiscal r-star:
  - Fiscal r-star (closed-economy) (A.10 / main text equation (6)):
    - r_f^* = g̅ + (1 + π̅ + g̅) · p̅b / d̅.
  - Debt accumulation relative to fiscal r-star (equation (7) / A.13):
    - Δd_t / d̅ = (r_t − r_f^*) / (1 + π̅ + g̅) − (pb_t − p̅b) / d̅.
- Fiscal-monetary gap (equation (11)):
  - r_m^* − r_f^* = Δd_t / d̅ · (1 + π̅ + g̅) + (1/φ) · (Δπ_t − Φ_t) + (pb_t − p̅b) / d̅ · (1 + π̅ + g̅) − τ_t^*,
    where τ_t^* ≡ r_t − r_t^P (spread between real effective interest rate on government debt and the real policy rate).
  - Interpretation of terms:
    - First term: debt growth contribution to the gap.
    - Second term: inflation deviation contribution (monetary accommodation leads to higher inflation).
    - Third term: fiscal consolidation (raising pb_t toward p̅b) closes the gap.
    - Fourth term: reductions in τ_t^* (e.g., via financial repression or debt-mix changes) can close the gap by lowering government borrowing costs.

### Policy levers and trade-offs (as discussed)
- Levers to close a positive fiscal-monetary gap:
  - Fiscal consolidation: adjust primary balances upward toward debt-stabilizing levels.
  - Monetary accommodation: keep policy rates below monetary r-star to ease fiscal costs (risks higher inflation or financial-stability consequences).
  - Lower τ_t^* via:
    - Financial repression (official and unofficial taxes on savings; debt-liquidation through lower real rates and higher inflation).
    - Changes in debt issuance strategy to reduce term premia (e.g., shorter maturities).
- Trade-offs and constraints:
  - Fiscal consolidation may be pro-cyclical under higher policy rates and weak growth.
  - Monetary accommodation can impair price stability and entail financial-stability and inflation risks.
  - Financial repression has historically been used, but entails adverse spillovers to households, firms, and capital formation.

### Box 1 — Fiscal R-Star in an Open Economy (summary)
- Phase diagram intuition:
  - Balanced debt accumulation schedule: positive function between real interest rates and the primary balance (debt-stabilizing r_f^* for a given primary balance).
  - Flat schedule: monetary r-star (real interest rate at which inflation is stable).
  - Four areas described: I (inflation falling, debt accumulation positive), II (both debt and inflation growing), III (inflation rising, debt falling), IV (both inflation and debt falling).
- Comparative statics (qualitative):
  - Panel A — Monetary r-star increases: fiscal-monetary gap larger; trade-off between stabilizing debt and inflation target increases.
  - Panel B — Potential growth increases: eases debt sustainability; reduces trade-off.
  - Panel C — Inflation target increases: reduces fiscal-monetary tensions for a given gap.
  - Panel D — Spread τ_t^* increases: raises fiscal-monetary tensions.
- Open-economy equations (Box eqs):
  - Open-economy inflation (Box eq.1):
    - Δπ_t = Φ_t − φ (r_t^P − r_m^*) + η (q_t − q^*).
  - Debt dynamics with FX debt share (Box eq.2):
    - Δd_t = [α_{t−1} r_t^f + (1−α_{t−1}) r_t^d − g_t + α_{t−1} Δq_t (1 + r_t^f) / (1 + g_t)] d_{t−1} − pb_t.
  - Open-economy fiscal r-star (Box eq.3), with ζ ≡ 1/(1−α):
    - r_f^* = ζ g̅ + ζ (1 + g̅) p̅b / d̅ − ζ α r_f.
  - Key implication: open-economy fiscal r-star is decreasing in the foreign interest rate; effect larger for higher shares of foreign-currency debt.
- Open-economy risks and limits:
  - Capital outflows and real exchange rate depreciation can raise debt ratios via valuation effects and lower fiscal r-star.
  - Closed-economy policy tools (e.g., financial repression, surprise inflation) are less effective when foreign currency debt shares are large or nonresident holdings are substantial.
- Data and estimation:
  - Annual data over 140 years for 16 AEs; JST and PFMH databases used; monetary r-star from Platzer et al. (2023).
  - Variable construction: HP-filtered long-term primary balance; debt target d̅ as five-year moving average of public debt to GDP; inflation expectations via official target or five-year moving average.
- Historical patterns:
  - Fiscal-monetary gap peaked during World War II; fiscal-monetary gap in 2020 highest since early 1950s.
  - Fiscal-monetary gap on upward trajectory since mid-2000s.
  - Fiscal r-star is generally faster-moving and more volatile than monetary r-star.
- Correlates of fiscal r-star (quantitative associations as presented):
  - Terminal debt level d̅: "falling by 0.04 to 0.02 percentage points for every 1 percentage point of debt to GDP."
  - Long-term primary balance p̅b: "A one percentage point higher long-term primary balance is associated with a more than two percentage point higher fiscal r-star."
  - Trend growth rate g̅: "A one percentage point higher trend growth rate is associated with a 1.2 to 1.4 percentage point higher fiscal r-star."
  - Monetary r-star: "fiscal r-star increasing by 0.75 to 0.90 percentage points for a one percentage point higher monetary r-star."
- Empirical associations linking a 1 percentage point higher fiscal-monetary gap to macro-financial outcomes (selected quantitative results as reported):
  - Debt ratio and price level: rise by around 1.5 percentage points after ten years.
  - Cumulative nominal depreciation:
    - relative to the U.S. dollar: around 2 percent after ten years.
    - relative to a commodity basket: around 1.5 percent after ten years.
  - Fiscal consolidation (cumulative primary balance): 0.02 cumulative percentage points after ten years.
  - Cumulative debt liquidation: 0.6 percentage points ten years later.
  - Asset prices and returns (Figure 8 text verbatim): "A one percentage point higher fiscal-monetary gap is associated with 2 and 1 and percentage points and lower returns on bonds (Figure 8A) and real cash (Figure 8D) after ten years, respectively."
  - Real housing returns: fall initially but are relatively unchanged after ten years.
  - Real equity returns: higher risk premia than bonds; limited vulnerability to an increase in the fiscal-monetary gap.
  - Crisis probabilities (cumulative within ten years), for a 1 percentage point higher gap:
    - External debt crisis: 0.7 percentage points higher.
    - Domestic debt crisis: 1.1 percentage points higher.
    - Inflation crisis: 1.6 percentage points higher.
    - Currency crisis: 1.3 percentage points higher.
    - Systemic financial crisis: almost 2 percentage points more likely.
    - Bond crisis (real bond returns < −10 percent): significantly more likely.
    - Housing crisis (real asset returns < −10 percent): probability increases.
    - Sharp drops in real equity returns: increase somewhat in first few years but association insignificant after ten years.
    - Recessions: about 1 percentage point more likely.
  - Interpretation: higher fiscal-monetary gaps are associated with rising debt, higher inflation, currency depreciation, low real fixed-income returns, elevated crisis risks, and some evidence of debt liquidation and financial repression.

### Policy implications, scenarios, and guidance (from projections and scenarios)
- WEO-derived 5-year-ahead projection approach (2014–2023 sample; expanded to 37 EMEs in some specifications) — variables mapped from WEO 5-year-ahead projections for g̅, p̅b, d̅, and monetary r-star.
- Recent estimates (WEO-derived):
  - AEs: fiscal r-star declined from around 4 percent in 2014 to around 1 percent in 2023; monetary r-star increased recently; fiscal-monetary gap rose to historically high levels.
  - EMs: fiscal r-star decline more gradual; monetary r-star relatively stable; fiscal-monetary gap increased more moderately.
  - Forecast-error adjustment: after adjusting for historical forecast errors, fiscal r-star estimates are even lower and fiscal-monetary gap estimates even higher.
- Scenario matrix (Figure 12 logic):
  - Quadrants by monetary r-star (lower-for-longer vs higher-for-longer) and fiscal r-star (low vs high):
    - Lower-for-longer monetary r-star & Low fiscal r-star: I. Weak fiscal adjustment; backloaded.
    - Higher-for-longer monetary r-star & Low fiscal r-star: II. Strong fiscal adjustment; front-loaded (with temptation for financial repression).
    - Lower-for-longer monetary r-star & High fiscal r-star: III. No adjustment needed.
    - Higher-for-longer monetary r-star & High fiscal r-star: IV. Potential fiscal adjustment needed.
- Policy levers emphasized:
  - Fiscal consolidation.
  - Growth-enhancing structural reforms to raise fiscal and monetary space.
  - Other actions including financial repression historically, with significant adverse spillovers.
- Political economy and institutional guidance:
  - Fiscal consolidation implementation constrained by political polarization and social cohesion; central bank independence important to preserve price stability and reduce inflation risk premia on government debt.
  - Financial repression faces modern limits due to organized financial interests and global capital mobility; but may be used if fiscal-monetary tensions persist and political cohesion is lacking.
- Practical implication: Without policy action, higher inflation and continued increases in debt levels are more likely; growth-enhancing structural reforms and preserving central bank independence are emphasized to ease policy tradeoffs.

*Source: wpiea2024174-print-pdf — Annex I. Panel Regressions on Fiscal Responsiveness, Annex Table 1, and Box 1 excerpts from IMF Working Paper "Fiscal R-Star: Fiscal-Monetary Tensions and Implications for Policy".*

### Annex I. Panel Regressions on Fiscal Responsiveness ....................................................................

### Annex I. Panel Regressions on Fiscal Responsiveness

### Description
- Title: Annex I. Panel Regressions on Fiscal Responsiveness
- Location in source: page 43

### Role within the working paper
- Part of the IMF Working Paper "Fiscal R-Star: Fiscal-Monetary Tensions and Implications for Policy"
- Serves as the technical annex presenting panel-regression analysis used to assess fiscal responsiveness (exact regression specifications, variables, and results are contained in the annex itself).

*Source: wpiea2024174-print-pdf - Annex I. Panel Regressions on Fiscal Responsiveness, IMF Working Paper "Fiscal R-Star: Fiscal-Monetary Tensions and Implications for Policy".*

### Annex Table 1. Responsiveness of Fiscal Policy to Debt and Debt-Stabilizing Primary Balances ..................... 44

### Annex Table 1. Responsiveness of Fiscal Policy to Debt and Debt-Stabilizing Primary Balances

### Key empirical context and data
- Sample: 16 Advanced Economies (AEs) over the period 1880 to 2022 (over 140 years of data).
- Subperiods analyzed: Pre-GFC (1880-2008), GFC/post-GFC (2009-2019), Pandemic (2020-2022).
- Stylized facts motivating the analysis:
  - Primary balances in AEs have been declining since the Global Financial Crisis (GFC).
  - Mean and median public debt ratios reached almost 120 and 90 percent of GDP in 2022, respectively.
- Empirical approach:
  - Two panel regression exercises following Bohn (1998) and Mauro et al. (2015):
    - Test 1 (equation (3)): pb_t = ρ1 · d_{t−1} + α1 (Q_t − Q_t^*) + ε_t — estimate ρ1 (response of primary balance to lagged debt ratio).
    - Test 2 (equation (5)): pb_t = ρ2 · pb_t^{DS} + α2 (Q_t − Q_t^*) + ε_t — estimate ρ2 (response of primary balance to debt-stabilizing primary balance).
  - Debt-stabilizing primary balance defined (equation (4)) as pb_t^{DS} = (r_t^* − g̅_t) / (1 + π̅ + g̅_t) · d_{t−1}.
  - Regressions include time and country fixed effects; results shown for three subperiods.

### Main empirical findings on fiscal responsiveness
- Pre-GFC (1880-2008):
  - Primary balances respond positively to lagged debt ratio: a 1 percentage point higher debt ratio associated with a rise in the primary balance of 0.03 percentage points.
  - ρ1 positive and statistically significant; ρ2 > 1 (primary balance moved more than one-for-one with the debt-stabilizing primary balance).
  - Interpretation: Fiscal policy characterized as passive (consistent with Bohn, 1998).
- GFC / Post-GFC (2009-2019):
  - Response of primary balance to lagged debt becomes negative but statistically insignificant.
  - ρ2 substantially smaller than one.
  - Interpretation: Attenuation of fiscal responsiveness relative to pre-GFC.
- Pandemic (2020-2022):
  - Response of primary balance to lagged debt is negative and statistically significant.
  - ρ2 remains significantly smaller than one.
  - Interpretation: Fiscal policy became more “active” during the pandemic; primary balances failed to move toward debt-stabilizing levels.
- Robustness notes:
  - Primary balances are highly autocorrelated; exercises including the lagged dependent variable find results robust.
  - Solid lines in Figure 2 indicate statistical significance at the 10 percent level; robust standard errors clustered by year are used.

### Interpretation and mechanisms
- Active versus passive fiscal policy:
  - Passive fiscal policy: primary balance adjusts endogenously to debt (reduces fiscal-monetary tensions; permits active monetary policy).
  - Active fiscal policy: primary balance set exogenously to debt (increases relevance of real interest rate for debt dynamics; raises potential fiscal-monetary tensions).
- Drivers of increasing activeness (suggested in text):
  - Discretionary spending pressures (e.g., pandemic relief).
  - Waning social and political cohesion and lack of viable deficit-reduction coalitions.
  - Longer-term structural spending pressures (aging entitlements, green transition, supply-chain diversification).
- Consequences of increased fiscal activeness:
  - Rising debt levels combined with potentially higher-for-longer interest rates can undermine fiscal sustainability.
  - Larger required fiscal consolidations or accommodation by monetary policy (which can pose price-stability and financial-stability tradeoffs).

### Theoretical framework linking fiscal responsiveness to policy tensions
- Debt law of motion and valuation:
  - Debt dynamics (equation (1)): Δd_t = (r_t − g_t) / (1 + π_t + g_t) · d_{t−1} − pb_t.
  - Debt valuation and intertemporal solvency conditions summarized in equation (2).
- Fiscal r-star (fiscal r*):
  - Defined as the debt-stabilizing real interest rate for a given constant expected primary balance pb̅, inflation target π̅, trend growth g̅, and terminal debt ratio d̅ (equation (6)):
    - r_f^* = g̅ + (1 + π̅ + g̅) · pb̅ / d̅.
  - Debt accumulation expressed relative to fiscal r-star (equation (7)):
    - Δd_t / d̅ = (r_t − r_f^*) / (1 + π̅ + g̅) − (pb_t − pb̅) / d̅.
- Fiscal-monetary gap:
  - Defined as monetary r-star minus fiscal r-star: r_m^* − r_f^*.
  - Closed-form relation (equation (11)):
    - r_m^* − r_f^* = Δd_t / d̅ · (1 + π̅ + g̅) + (1/φ) · (Δπ_t − Φ_t) + (pb_t − pb̅) / d̅ · (1 + π̅ + g̅) − τ_t^*,
      where τ_t^* ≡ r_t − r_t^P (spread between real effective interest rate on government debt and the real policy rate).
  - Interpretation of terms in equation (11):
    - First term: debt growth contribution to the gap.
    - Second term: inflation deviation contribution (monetary accommodation leads to higher inflation).
    - Third term: fiscal consolidation (raising pb_t toward pb̅) closes the gap.
    - Fourth term: reductions in τ_t^* (e.g., via financial repression or debt-mix changes) can close the gap by lowering government borrowing costs.

### Implications and policy levers (as discussed)
- Closing a positive fiscal-monetary gap can involve:
  - Fiscal consolidation: adjust primary balances upward toward debt-stabilizing levels.
  - Monetary accommodation: keep policy rates below monetary r-star to ease fiscal costs (risking higher inflation or financial-stability consequences).
  - Lowering τ_t^* via:
    - Financial repression (official and unofficial taxes on savings; debt-liquidation through lower real rates and higher inflation).
    - Changes in debt issuance strategy to reduce term premia (e.g., shorter maturities).
- Trade-offs:
  - Fiscal consolidation could be pro-cyclical under higher policy rates and weak growth.
  - Monetary accommodation can impair price stability and may entail financial-stability and inflation risks.
  - Financial repression historically used as one option when high debt and constrained primary-balance adjustments co-occur.

*International Monetary Fund — Annex Table 1. Responsiveness of Fiscal Policy to Debt and Debt-Stabilizing Primary Balances (excerpt).*

### Box 1).

### Box 1. Fiscal R-Star in an Open Economy

### Graphical representations and comparative statics (phase diagram intuition)
- The phase diagram uses axes for the primary balance and real interest rates and is composed of two schedules:
  - Balanced debt accumulation schedule: positive function between real interest rates and the primary balance; the debt-stabilizing real interest rate for a given level of the primary balance. For simplicity, it is assumed that the real effective interest rate on government debt equals the real policy rate, such that 휏=0.
  - Flat schedule: follows from the IS and Phillips curves and represents the exogenously given real interest rate at which inflation is stable (monetary r-star).
- The diagram yields four areas describing joint inflation and debt dynamics:
  - Area I: inflation is falling while debt accumulation is positive.
  - Area II: both debt and inflation are growing.
  - Area III: inflation is rising while debt is falling.
  - Area IV: both inflation and debt are falling.
- Interpretation for a given primary balance (푝푏
̅̅̅
):
  - If monetary policy rate is less than 푟
푚
∗ and the effective fiscal financing cost equals 푟
푓
∗, the primary balance level would lead to an increase in inflation without an increase in debt stocks.
  - If the real interest rate faced by the fiscal authority is greater than 푟
푓
∗ (with monetary policy rate still less than 푟
푚
∗), then inflation and debt stocks would both increase.
  - Moving left on the phase diagram (toward larger primary deficits) enlarges the locus of region II, making these challenges more acute.

### Comparative statics (Figure 4 panels and implications)
- Panel A — Monetary r-star exogenously increases:
  - The inflation target curve shifts upward; for any given primary balance, the fiscal-monetary gap is larger, ceteris paribus.
  - Rising global neutral interest rates increase the trade-off between stabilizing debt and achieving the inflation target.
- Panel B — Potential growth increases:
  - The y-intercept of the debt accumulation line rises (direct effect of faster nominal GDP growth = inflation target + real growth), easing debt sustainability via more favorable r - g dynamics.
  - The slope of the debt accumulation line pivots leftward toward the y-axis (elasticity of the primary balance with respect to borrowing costs goes down).
  - Overall, higher potential growth makes the trade-off between stabilizing debt and achieving the inflation target less acute.
- Panel C — Inflation target increases:
  - The zero debt accumulation line becomes steeper, decreasing the elasticity of balanced debt relative to the primary balance.
  - For a given fiscal-monetary gap, a higher inflation target would reduce fiscal-monetary tensions.
- Panel D — Spread (휏
푡
∗
) increases:
  - A higher spread increases the real interest rate on government debt relative to the real policy rate, pivoting the debt accumulation equation downward.
  - For a given fiscal-monetary gap, a higher spread increases fiscal-monetary tensions.

### Non-linear dynamics and expectations
- Inflation expectations anchoring requires commitment by the monetary authority to set the nominal policy rate such that the real policy rate tracks monetary r-star.
- If fiscal-monetary tensions cause repeated misses of the inflation target (due to rising monetary r-star, fiscal dominance, lack of central bank independence, or concerns after large-scale asset purchases), long-term inflation expectations can move up.
- To re-anchor expectations, the real policy rate must be moved above monetary r-star for a sustained period; without complementary fiscal adjustment, this worsens debt dynamics and increases pressure on the central bank.
- High fiscal-monetary tensions can create adverse feedback loops that culminate in fiscal dominance or erosion of central bank independence.

### Policy options to close the fiscal-monetary gap
- Fiscal primary balance adjustment to make fiscal policy passive and raise fiscal r-star.
- Debt management operations, for example shortening weighted-average maturity of debt issuance when faced with an upward-sloping term structure (lowers effective cost of debt but may raise rollover risks).
- Financial engineering and financial repression (macroprudential and capital flow measures to increase the captive pool of savings and reduce effective fiscal borrowing costs), recognizing the trade-offs and limits:
  - Financial repression tools include interest rate caps, capital controls, moral suasion, and reserve and capital requirements.
  - Financial repression can be viewed as lowering the real stochastic discount factor of debt holders, generating a bubble-like fiscal resource (see discussion referencing Brunnermeier et al., 2020).
- If the interest rate paid by the government is substantially lower than the interest rate faced by the private sector, monetary and fiscal authorities can achieve their goals even if the fiscal-monetary gap is substantially positive and neither policy adjusts.

### Open economy formulation and key equations
- Open economy inflation equation (Box equation (1)), where 푞
푡
−푞
∗
 is the real exchange rate gap and 휂 is the elasticity of inflation with respect to this gap:
  - (Box eq.1) Δ휋
푡
=Φ
푡
−휙
(
푟
푡
푃
−푟
푚
∗
)
+휂(푞
푡
−푞
∗
)
- Debt dynamics accounting for foreign- and local-currency debt (Box equation (2)), where 훼
푡−1
 is the share of foreign currency debt, 푟
푡
푓
 is the foreign currency real interest rate, and Δ푞
푡
 is the growth rate of the real exchange rate (positive = real depreciation):
  - (Box eq.2) Δ푑
푡
=
훼
푡−1
푟
푡
푓
+
(
1−훼
푡−1
)
푟
푡
푑
−푔
푡
+훼
푡−1
Δ푞
푡
(1+푟
푡
푓
)
1+푔
푡
푑
푡−1
−푝푏
푡
- Open-economy fiscal r-star (Box equation (3)), with long-run share of foreign currency debt 훼 and 휁≡
1
1−훼
:
  - (Box eq.3)  푟
푓
∗
=휁푔
̅
+휁
(
1+푔
̅
)
푝푏
̅̅̅
푑
̅
−휁훼푟
푓
- Key implication: open economy fiscal r-star is decreasing in the foreign interest rate; the importance of the foreign interest rate is greater for countries with higher shares of foreign currency debt. When the share of foreign currency debt is zero, Box equation (3) collapses to the closed-economy counterpart.

*Source: IMF working paper text (Box 1). *

### Box 1. Fiscal R-Star in an Open Economy (cont.)

### Box 1. Fiscal R-Star in an Open Economy (cont.)

### Open-economy dynamics and risks
- Open financial accounts can exacerbate fiscal-monetary tensions and trigger nonlinearities when domestic real interest rates diverge from foreign real interest rates.
- If policymakers accommodate active fiscal policy and allow substantially large interest rate differentials to exist:
  - capital outflows could trigger a real exchange rate depreciation, further pushing up the debt ratio through exchange rate valuation effects;
  - this can lower fiscal r-star and further increase the fiscal-monetary gap.
- Market perception of additional risk associated with investing in foreign assets (the additional compensation demanded by investors to hold foreign assets) could push up the country’s risk premium.
- The risk premium is influenced by active fiscal policy, adversely impacting investors’ perceptions about the riskiness of a country’s institutions (e.g., central bank independence), including through fears of fiscal dominance.

### Limits to closed-economy policy tools in an open economy
- Some policy actions available in a closed economy become less effective in an open economy, which could tempt policymakers to revert to nonconventional tools.
- Key constraints and consequences:
  - Accommodative monetary policy cannot fully offset a higher interest burden if a large share of debt is denominated in foreign currency.
  - The impact of surprise inflation on the debt ratio is smaller if it is offset by a nominal currency depreciation that pushes up the stock of FX-denominated debt.
  - Forcing domestic savers to hold government debt through financial repression is less effective if:
    - a larger share of the debt stock is held by nonresidents; or
    - domestic savers can substitute foreign assets for domestic assets.
  - As domestic-focused policy actions become less effective, policymakers may be tempted to distort capital flows, including foreign exchange intervention (FXI) and capital flow measures (CFMs).

### Data and methodology for estimating fiscal r-star and the fiscal-monetary gap
- Sample and data:
  - Annual data over the last 140 years.
  - Sample consists of 16 AEs: Australia, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, Switzerland, United Kingdom, and United States.
  - JST (Jordà-Schularick-Taylor) database provides macroeconomic data for these 16 countries from 1878 to 2020.
  - Fiscal data complemented with Public Finances in Modern History (PFMH) database on government expenditures, revenues, interest expenses, and public debt.
  - Monetary r-star data source: Platzer et al. (2023), who apply Laubach and Williams (2003) methodology using the JST database.
- Variable construction (baseline):
  - Long-term primary balance: Hodrick-Prescott (HP) filter applied to the primary balance series.
  - Output growth: estimates from Platzer et al. (2023).
  - Debt target (푑̅): five-year moving average of the public debt to GDP ratio.
  - Inflation expectations: official inflation target where applicable; otherwise five-year moving average of country inflation.
- Advantages:
  - JST dataset and simple filtering techniques enable documentation of fiscal r-star and fiscal-monetary gap evolution over more than one hundred and fifty years, covering episodes such as the Great Depression and World War II.

### Estimation results and historical patterns
- Fiscal-monetary gap dynamics:
  - The fiscal-monetary gap peaked during World War II amid war-era fiscal strains.
  - The fiscal-monetary gap in 2020 is the highest measured since the early 1950s (post–World War II debt overhang).
  - The gap hit a historic low in the mid-1970s during the post-war boom and demobilization.
  - After the 1970s low, the gap remained low and relatively constant from the early 1980s through the mid-2000s, primarily due to the decline in monetary r-star after the early 1980s disinflation.
  - The fiscal-monetary gap has been on an upward trajectory since the mid-2000s.
- Relative volatilities:
  - Fiscal r-star is generally faster-moving and more volatile than monetary r-star (fiscal r-star is a function of the policy-discretionary primary balance; monetary r-star is a function of the market for loanable funds).
- Decomposition of changes in fiscal r-star (equation (12)):
  - Change in fiscal r-star decomposed into: impact of change in potential growth rate; impact of change in ratio of primary balance to debt level; and their covariance.
  - Historical decomposition findings:
    - Decline in fiscal r-star during the first half of the Twentieth Century coincided with significant spending needs associated with the two World Wars, with primary balances and debt accounting for most of this increase.
    - From the early 1930s to late 1960s, trend growth positively contributed to the increase in fiscal r-star.
    - Post-2000 decline in fiscal r-star was due to both declining potential growth and deteriorating debt and primary balance dynamics.
    - Fiscal policy (debt and deficits) was less of a drag on fiscal r-star from the early 1970s through the late 1990s.

### Correlates of fiscal r-star (key quantitative associations)
- Terminal debt level 푑̅:
  - Fiscal r-star is negatively associated with higher terminal debt levels, "falling by 0.04 to 0.02 percentage points for every 1 percentage point of debt to GDP."
- Long-term primary balance 푝푏̅:
  - Fiscal r-star is positively associated with the long-term primary balance.
  - "A one percentage point higher long-term primary balance is associated with a more than two percentage point higher fiscal r-star."
- Trend growth rate 푔̅:
  - "A one percentage point higher trend growth rate is associated with a 1.2 to 1.4 percentage point higher fiscal r-star."
- Monetary r-star:
  - Fiscal r-star co-moves with monetary r-star: "fiscal r-star increasing by 0.75 to 0.90 percentage points for a one percentage point higher monetary r-star."
- Notes on statistical significance and collinearity:
  - Debt stock negatively associated with fiscal r-star but not always statistically significant, possibly due to collinearity between primary balance (flow) dynamics and debt (stock) levels.

### Empirical strategy linking fiscal-monetary gap to macroeconomic outcomes
- Local projections (Jordà, 2005) estimated:
  - Outcome response specification (equation (13)) relates horizon-h response of outcome variable to initial fiscal-monetary gap, includes:
    - country-specific fixed effects;
    - three lags of the outcome variable;
    - controls: lags of debt level, trend output growth, inflation, primary balance, real policy rate, and monetary r-star.
  - Robust standard errors account for heteroskedasticity, cross-sectional correlation, and serial correlation (Driscoll and Kraay, 1998).
  - Estimates reflect predictive relationships and dynamic impulse responses; they do not necessarily carry a causal interpretation.

### Associations between a higher fiscal-monetary gap and macro-financial outcomes (selected quantitative results)
- General macro indicators (conditional on controls), for a 1 percentage point higher fiscal-monetary gap:
  - Debt ratio (Figure 7A) and price level (Figure 7B): rise by around 1.5 percentage points after ten years.
  - Cumulative nominal depreciation:
    - relative to the U.S. dollar (Figure 7C): around 2 percent after ten years.
    - relative to a commodity basket (Figure 7D): around 1.5 percent after ten years.
  - Fiscal consolidation (Figure 7E): 0.02 cumulative percentage points after ten years (measured as cumulative sum of the primary balance).
  - Cumulative debt liquidation (Figure 7F): a 1 percentage point higher gap is associated with cumulative liquidation of government debt by 0.6 percentage points ten years later.
- Asset prices and returns (Figure 8), for a 1 percentage point higher fiscal-monetary gap:
  - "A one percentage point higher fiscal-monetary gap is associated with 2 and 1 and percentage points and lower returns on bonds (Figure 8A) and real cash (Figure 8D) after ten years, respectively" (text as presented).
  - Real housing returns (Figure 8C): fall initially but are relatively unchanged after ten years.
  - Real equity returns (Figure 8B): higher risk premia than bonds, associated with better performance relative to bonds; equity returns show limited vulnerability to an increase in the fiscal-monetary gap.
- Crisis probabilities (Figure 9), for a 1 percentage point higher fiscal-monetary gap (cumulative probabilities within ten years unless otherwise specified):
  - External debt crisis (Figure 9A): 0.7 percentage points higher.
  - Domestic debt crisis (Figure 9B): 1.1 percentage points higher.
  - Inflation crisis (Figure 9D): 1.6 percentage points higher.
  - Currency crisis (Figure 9E): 1.3 percentage points higher.
  - Systemic financial crisis (Figure 9F): almost 2 percentage points more likely.
  - Bond crisis (Figure 9G): significantly more likely (bond crisis defined as years in which real bond returns are less than negative 10 percent).
  - Housing crisis (Figure 9H): probability increases (housing crisis defined as real asset returns less than negative 10 percent).
  - Sharp drops in real equity returns (Figure 9I): increase somewhat in first few years but association insignificant after ten years.
  - Recessions (Figure 9J): about 1 percentage points more likely.
- Interpretation:
  - Results indicate that as the fiscal-monetary gap rises, fixed-income assets underperform, the likelihood of various crises increases, and there is some evidence of greater propensity toward debt liquidation and financial repression.

*Source: Box 1. Fiscal R-Star in an Open Economy (cont.), IMF Working Paper content provided in the supplied PDF excerpt.*

### 2023. The underlying assumption is that these projections serve as reasonable approximations of their long-

### wpiea2024174-print-pdf - 2023. The underlying assumption is that these projections serve as reasonable approximations of their long-

### Estimation approach and data
- Sample period: 2014-2023.
- Cross-country sample: 16 AEs in Section V sample; expanded to include 37 EMEs in this section.
- Projection horizon used: 5-year ahead projections from the WEO dataset.
- Variables mapped from WEO 5-year-ahead projections:
  - 푔̅ measured by 5-year ahead GDP growth projections.
  - 푝푏
̅̅̅ measured by 5-year ahead government primary balance projections.
  - 푑
̅ measured by 5-year ahead debt level projections.
  - Monetary r-star measured by 5-year ahead projections of the policy rate minus 휋̅.
  - For countries lacking an official inflation target, inflation (휋̅) is measured in the same manner as projected; otherwise the official inflation target is used.
- Rationale: forward-looking, model-free approach using WEO projections is robust to endpoint problems of filtering techniques used in Section III and focuses on recent endpoint estimates.
- Forecast-error adjustment: results are also estimated after correcting for historical forecast errors for potential growth, primary balances, and debt levels (Annex Figure 1).

### Recent estimates and key empirical findings
- Fiscal r-star and the fiscal-monetary gap are at historic levels based on WEO-derived 5-year-ahead projections.
- Advanced Economies (AEs):
  - Fiscal r-star exhibits a significant downward trend from around 4 percent in 2014 to around 1 percent in 2023.
  - Drivers of the decline (left-hand panel of Figure 11): combination of lower potential GDP growth, higher terminal debt, and notably the declining primary balance (especially during the COVID-19 pandemic).
  - Monetary r-star has increased recently on the back of rising global interest rates.
  - Result: a corresponding rise in the fiscal-monetary gap to historically high levels (left-hand panel of Figure 10).
- Emerging Markets (EMs):
  - Fiscal r-star decline is more gradual, driven by a moderate fall in potential GDP growth and inflation target, and a moderate post-Covid increase in terminal debt.
  - Monetary r-star relatively stable.
  - Result: fiscal-monetary gap has increased at a more measured pace than in AEs.
- Forecast-error adjustment implication:
  - After adjusting for historical forecast errors, recent estimates for fiscal r-star are even lower for both AEs and EMs, and fiscal-monetary gap estimates are even higher than shown in Figure 10.
  - Implication: WEO-derived baseline results may understate the ultimate level of the fiscal-monetary gap today.

### Policy implications and adjustment scenarios
- Conceptual use: fiscal r-star and the fiscal-monetary gap provide a framework for assessing appropriate fiscal-monetary policy mixes and the timing/pace of fiscal adjustment.
- Policymaking requires ex-ante assessment of likely trajectories of fiscal and monetary r-star to choose adjustment paths.
- Scenarios matrix (Figure 12):
  - Monetary r-star: lower-for-longer vs. higher-for-longer.
  - Fiscal r-star: low vs. high.
  - Example quadrant outcomes:
    - Lower-for-longer monetary r-star & Low fiscal r-star: I. Weak fiscal adjustment; backloaded.
    - Higher-for-longer monetary r-star & Low fiscal r-star: II. Strong fiscal adjustment; front-loaded (with temptation for financial repression).
    - Lower-for-longer monetary r-star & High fiscal r-star: III. No adjustment needed.
    - Higher-for-longer monetary r-star & High fiscal r-star: IV. Potential fiscal adjustment needed.
- Policy levers (referenced via equation (13)):
  - Fiscal consolidation.
  - Growth-enhancing structural reforms to raise both fiscal and monetary space.
  - Other actions, including (historically) financial repression, though with significant adverse spillovers.
- Guidance:
  - If monetary r-star remains lower-for-longer, large upfront fiscal adjustment may be mitigated.
  - If monetary r-star is higher-for-longer, fiscal adjustment may be needed depending on primary balance trends and debt stock.

### Political economy, central bank independence, and risks
- Political economy constraints:
  - Fiscal consolidation implementation may be limited by political polarization and social cohesion.
  - Example (cited): Jamaica’s sustained debt reduction achieved via fiscal responsibility mechanisms, consensus-building, and reduced polarization.
- Co-movement of polarization and fiscal-monetary gap:
  - Political polarization in the AE sample is at highs not seen since the 1940s (Figure 13).
  - Historical association: higher polarization makes fiscal adjustment harder; fiscal pressures can feed back into polarization.
- Central bank independence:
  - Monetary accommodation historically associated with higher fiscal-monetary tensions; episodes where policy rates deviated below Taylor-rule-based equilibrium coincide with heightened tensions (Figure 14).
  - Safeguarding central bank independence is important to preserve price stability and to reduce inflation risk premia on government debt, thereby enhancing fiscal sustainability.
  - Risk: de-anchoring of inflation expectations from overly accommodative policy could necessitate even tighter policy later, increasing fiscal-monetary tensions.

### Financial repression, safe assets, and international considerations
- Financial repression:
  - Historically used to lower fiscal financing costs during large fiscal-monetary gaps.
  - Today, the efficacy of financial repression is limited by organized financial interests that would lobby against suppressed returns and by global capital mobility that makes capital “lock-in” difficult.
  - If fiscal-monetary tensions remain elevated and political cohesion is lacking, financial repression may become a preferred tool in some countries despite adverse spillovers to households, firms, and capital formation.
- Global demand and supply for safe assets:
  - The impact of fiscal-monetary tensions in AEs depends on global absorptive capacity for additional government debt issuance.
  - Although official foreign demand for safe assets has fallen, private sector demand has offset much of that decline; the additional spread (yield) demanded by savers relative to monetary r-star determines adverse financing dynamics.
  - Sustainability of large fiscal-monetary gaps may depend on global savers’ willingness to accept negative real returns on safe assets and the stability of the international monetary system (IMS) and reserve currency composition.

### Conclusions and avenues for further research
- Conceptual contributions:
  - Introduction of fiscal r-star: the implied debt-stabilizing real interest rate at which output is at potential and inflation is at target.
  - Definition of the fiscal-monetary gap: fiscal r-star relative to monetary r-star.
- Empirical conclusions:
  - High fiscal-monetary gaps have historically been associated with rising debt levels, higher inflation, currency depreciation, low real asset returns, and elevated crisis risks.
- Caveats and needed extensions:
  - Theoretical framework treats trend growth and monetary r-star as exogenous; in reality fiscal policy can affect trend growth and equilibrium real interest rates. Endogeneity needs further work.
  - More refined empirical identification strategies are needed to establish causality between fiscal-monetary gaps and macro outcomes.
  - Potential theoretical extensions: incorporate fiscal r-star into micro-founded DSGE models, derive open-economy versions, and account for active fiscal policy in computing market-clearing r-star.
  - Potential empirical extensions: study the relationship between interest-growth differentials ("r-g"), active fiscal policy, fiscal consolidation, role of financial repression, mapping fiscal-monetary gaps to sovereign stress indicators, and decomposing changes in the gap into monetary r-star vs. fiscal r-star contributions.
- Policy instruments and integration:
  - Fiscal r-star complements monetary r-star and r-double-star; interactions among these "star" rates can inform holistic policy advice on fiscal-monetary-financial policy mixes.
  - IMF operationalization: estimates of fiscal r-star, monetary r-star, and the fiscal-monetary gap could be integrated into existing assessments such as the IMF’s Consistent Policy Assessment (CPA) to add a proxy for fiscal-monetary tensions.
- Practical implication:
  - Without policy action, higher inflation and continued increases in debt levels are more likely; growth-enhancing structural reforms and preserving central bank independence are emphasized to ease policy tradeoffs.

*Source: IMF Working Paper (excerpts provided).*

### Annex I. Panel Regressions on Fiscal

### Annex I. Panel Regressions on Fiscal Responsiveness

### Regression specifications
- Equation (A.1): 푝푏푖,푡 = 휌1 ⋅ 푑푖,푡−1 + 휔1 ⋅ 표푡ℎ푒푟푝푒푟푖표푑푡 ⋅ 푑푖,푡−1 + 훼1 ⋅ 푄_푔푎푝푖,푡 + 훿푡 + 훽푖 + 휖푖,푡
  - 푄_푔푎푝푖,푡 ≡ 푄푖,푡 − 푄푖,푡∗
  - 훿푡 and 훽푖 are time and country fixed effects.
  - 표푡ℎ푒푟푝푒푟푖표푑푡 equals 1 if the year 푡 does not fall within the period of interest, and 0 otherwise.58
  - Under this specification, 휌1 is interpreted as the responsiveness of fiscal policy during the sub-period of interest.

- Equation (A.2): 푝푏푖,푡 = 휌2 ⋅ 푝푏푖,푡퐷푆 + 휔2 ⋅ 표푡ℎ푒푟푝푒푟푖표푑푡 ⋅ 푝푏푖,푡퐷푆 + 훼2 ⋅ 푄_푔푎푝푖,푡 + 훿푡 + 훽푖 + 휖푖,푡
  - 푝푏푖,푡퐷푆 is the debt-stabilizing primary balance (DSPB) as defined in Section III.
  - Under this specification, 휌2 is interpreted as the responsiveness of fiscal policy during the sub-period of interest.

58
- More specifically, for the pre-GFC, GFC, and Covid regressions, the dummy variable 표푡ℎ푒푟푝푒푟푖표푑푡 equals 1 if the years fall within 2009-2022, 1880-2008 and 2020-2022 and 1880-2019, respectively.

### Sample and data
- Sample: 16 AEs (same as Section VI).
- Data sources:
  - Primary balances and debt levels: Public Finance in Modern History database (Mauro et al., 2015).
  - Trend growth and monetary r-star for constructing 푝푏푖,푡퐷푆: Platzer et al. (2013).
- For the debt-stabilizing balance, inflation is set at 2 percent for all countries.
- Full sample period in regressions: 1880-2022.

### Regression results — Annex Table 1 (Responsiveness of Fiscal Policy)
- Response to Debt Levels (columns (1) pre-GFC, (2) GFC, (3) COVID)
  - Lagged Debt Level:
    - pre-GFC: 0.031*** (0.003)
    - GFC: -0.015*** (0.003)
    - COVID: -0.035*** (0.006)
  - Lagged Debt Level * Other Period:
    - pre-GFC: -0.053*** (0.006)
    - GFC: 0.041*** (0.006)
    - COVID: 0.058*** (0.007)
  - Output Gap:
    - pre-GFC: 0.014 (0.019)
    - GFC: 0.018 (0.020)
    - COVID: 0.013 (0.020)
  - Time FEs: Yes (all columns)
  - Country FEs: Yes (all columns)
  - Observations: 1796 (all columns)
  - R-squared:
    - pre-GFC: 0.40
    - GFC: 0.37
    - COVID: 0.37

- Response to Debt-Stabilizing Primary Balances (DSPB) (columns (4) pre-GFC, (5) GFC, (6) COVID)
  - Debt Stabilizing Primary Balance (DSPB):
    - pre-GFC: 1.37*** (0.16)
    - GFC: 0.49*** (0.15)
    - COVID: 0.67*** (0.20)
  - DSPB * Other Period:
    - pre-GFC: -0.86 (0.21)
    - GFC: 0.75*** (0.21)
    - COVID: 0.46* (0.24)
  - Output Gap:
    - pre-GFC: 0.005 (0.019)
    - GFC: 0.004 (0.020)
    - COVID: 0.005 (0.020)
  - Time FEs: Yes (all columns)
  - Country FEs: Yes (all columns)
  - Observations: 1796 (all columns)
  - R-squared: 0.36 (all columns)

- Notes:
  - Robust standard errors, clustered by year, are reported in parentheses.
  - Significance: *** p<0.01, ** p<0.05, * p<0.1

### Interpretation of panel results
- The responsiveness of primary balances to lagged debt levels differs across sub-periods:
  - Positive and statistically significant coefficient in pre-GFC (0.031***).
  - Negative and statistically significant coefficients in GFC (-0.015***) and COVID (-0.035***).
- When using the debt-stabilizing primary balance (DSPB):
  - Strong positive responsiveness in pre-GFC (1.37***), lower but positive responsiveness in GFC (0.49***) and COVID (0.67***).
  - Interaction terms (DSPB * Other Period) indicate shifts in responsiveness across periods:
    - pre-GFC: -0.86 (not significant at conventional levels),
    - GFC: 0.75***,
    - COVID: 0.46*.

### Theoretical derivations and tests (Bohn’s tests and Fiscal R-Star)
- Interest-growth differential (A.3):
  - Γt ≡ (rt − gt) / (1 + πt + gt)
- Law of motion with fiscal reaction (A.4):
  - dt = [Γt + (1 − ρ1)] ⋅ dt−1 − α1 (Qt − Qt∗) − εt
  - Debt ratio stationary if:
    - (i) Γk is stationary, and
    - (ii) ρ1 > E[Γt].
  - If conditions hold, the debt ratio is expected to converge to zero.

- Test 2 (permanent component changes):
  - Γ̅t ≡ (rt∗ − g̅t) / (1 + π̅ + g̅t) (A.5)
  - Law of motion with DSPB reaction (A.6):
    - dt = [Γt + (1 − ρ2 ⋅ Γ̅t)] ⋅ dt−1 − α1 (Qt − Qt∗) − εt
  - Debt ratio stationary if:
    - (i) E[Γt] = Γ̅t and positive, and
    - (ii) ρ2 > 1.
  - If conditions hold, the debt ratio is expected to converge to zero.

- Fiscal r-star derivation
  - Debt law using primary balance (A.7): Dt = (1 + it−1) Dt−1 − PBt
  - Scaled by nominal GDP (A.8): dt = (1 + it−1)/((1+πt)(1+gt)) dt−1 − pb_t
  - Change in debt-to-GDP (A.9): Δdt = (rt − gt)/(1 + πt + gt) dt−1 − pbt + 표t
    - 표t is a residual term approximating zero for sufficiently low nominal GDP growth.
  - Fiscal r-star (A.10), solving Δdt = 0 for steady state (d̅, g̅, π̅, p̅b):
    - r_f^* = g̅ + (1+π̅+g̅) p̅b̅ / d̅

- Fiscal-monetary gap derivation
  - Starting from (A.9) and inserting (A.10) leads to (A.11).
  - Under simplifying assumptions (gt = g̅, dt−1 = d̅, (πt − π̅) p̅b̅ / d̅ ≈ 0), (A.12):
    - Δdt = (rt − g̅)/(r_f^* − g̅) p̅b̅ − pbt
  - Rearranged and divided by d̅ gives (A.13):
    - Δdt/d̅ = (rt − r_f^*)/(1+π̅+g̅) − (pbt − p̅b)/d̅
  - Using τt ≡ rt − r_t^P and equation (10) yields the fiscal-monetary gap in equation (11).

*Source: Authors’ calculations*

### References

### References (Fiscal R-Star: Fiscal-Monetary Tensions and Implications for Policy)

### Core literature topics represented
- Fiscal-monetary interactions and the fiscal theory of the price level
  - Works: Leeper 1991; Cochrane 2001; Cochrane 2018; Cochrane 2023; Bianchi & Melosi 2019; Bianchi, Faccini, & Melosi 2023; Brunnermeier, Merkel, & Sannikov 2020.
- Natural rate of interest (r*, neutral rate) and long-term interest dynamics
  - Works: Laubach & Williams 2003; Holston, Laubach, & Williams 2017; Benigno et al. 2024; Lubik, Merone & Robino 2024; Platzer & Peruffo 2022; Platzer, Tietz & Linde 2022; Rachel & Summers 2019; Akinci et al. 2020.
- Debt sustainability, public debt valuation, and fiscal capacity
  - Works: Ghosh et al. 2013; Jiang et al. (2019, 2022); Reinhart & Rogoff 2014; Reinhart & Sbrancia 2015; Bohn 1998; Bohn 2005; Reis 2022; Jeanne 2023.
- Fiscal space, consolidation, and fiscal policy design
  - Works: Ostry et al. 2010; IMF 2016; IMF 2018; Balasundharam et al. 2023 (IMF Working Papers 2023/063); Chen et al. 2023 (IMF WP 23/260); Budina et al. 2023 (SDN/2023/007).
- Inflation dynamics, inflation targeting, and central bank strategy
  - Works: Blanchard 2022 (Fiscal Policy under Low Interest Rates; also FT piece), Gagnon 2022; Gagnon & Collins 2019; Schnabel 2022; Gaspar, Smets & Vestin 2010.
- Financial stability, banking crises, and market events
  - Works: BIS 2023 Report on the 2023 banking turmoil; Caprio et al. 2005 Banking Crisis Database; Chen & Kemp 2023 (IMF WP 2023/210).
- Political economy, redistribution, and social/political costs of fiscal actions
  - Works: Alesina (1990, 1991, 1992); Gabriel, Klein & Pessoa 2023; Hübscher, Sattler & Wagner 2023; Sargent et al. 2019.

### Representative authors, institutions, and publications frequently cited
- Individuals: Olivier Blanchard; Eric M. Leeper; John H. Cochrane; Francesco Bianchi; Carmen Reinhart; Kenneth Rogoff; Gita Gopinath; Lawrence H. Summers; Thomas Laubach; John C. Williams; Benigno, Hofmann, Nuño, Sandri.
- Institutions and outlets: International Monetary Fund (IMF Working Papers, Staff Notes, Fiscal Monitor, World Economic Outlook), National Bureau of Economic Research (NBER Working Papers), Brookings Papers on Economic Activity, BIS Quarterly Review, Journal of Monetary Economics, Quarterly Journal of Economics, American Economic Review, Journal of Economic Perspectives.
- Datasets and empirical tools: Varieties of Democracy dataset (V-Dem v13); Jordà (2005) local projections methodology; Driscoll & Kraay (1998) covariance estimation for spatial panels.

### Methodologies and technical approaches referenced
- Fiscal and monetary policy interaction models and classifications (e.g., “active” vs “passive” policy regimes): Leeper 1991; Leeper, Plante & Traum 2010; Chung, Davig & Leeper 2007.
- Natural rate estimation and measurement techniques: Laubach & Williams 2003; Holston, Laubach & Williams 2017; Lubik, Merone & Robino 2024.
- Empirical macrofinancial history and business-cycle analysis: Jordà, Schularick & Taylor 2017; Reinhart & Rogoff 2014.
- Fiscal valuation and discounted cash flow approaches to fiscal capacity: Jiang et al. (2019, 2022).
- Panel and time-series econometric tools: Jordà 2005; Driscoll & Kraay 1998.

### Policy-relevant themes and guidance signaled by sources
- The necessity of fiscal-monetary coordination to avoid fiscal dominance and preserve price stability (multiple theoretical and empirical contributions: Woodford 1995, 1998, 2001; Leeper 1991; Bianchi & Melosi 2019, 2022; Blanchard 2010).
- Assessing fiscal space, debt sustainability, and debt-reduction strategies in high-debt environments (IMF 2016; IMF 2018; IMF 2022; Arslanalp & Eichengreen 2023; Arslanalp, Eichengreen & Henry 2024).
- Importance of structural reforms and growth-enhancing policies to ease fiscal trade-offs and support green transitions (Budina et al. 2023; Balasundharam et al. 2023).
- Considerations for central bank strategy in light of evolving r* estimates and high public debt (Benigno et al. 2024; Platzer et al. 2022; Gopinath 2022, 2023a, 2023b; Schnabel 2022).

*References as listed in the source document: wpiea2024174-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024174-print-pdf.pdf_