## 1. Number of Countries Constrained by ZLB

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---

### I. Introduction — crisis, policy response, and limits
- Global contraction in 2020: output 3 percent below the 2019 level.
- Global fiscal measures to support the economy summed to US$16.9 trillion (IMF 2021).
- Advanced economies (AEs) implemented extensive spending, revenue measures, lending and loan guarantee programs, and expanded asset purchase programs.
- Central banks moved policy rates closer to Effective Lower Bounds (ELB) and expanded asset purchases.
- Near-term complications: the war in Ukraine, soaring commodity prices, elevated geopolitical risk, and supply disruptions.
- Constraints highlighted:
  - Interest rates were already low in many AEs prior to COVID-19.
  - Many EM central banks faced similar constraints (Figure 1: Number of Countries Constrained by ZLB).
  - Public debt levels rose sharply across regions during the pandemic.
- Conceptual framing:
  - Traditional separation of fiscal (debt/deficits, structural objectives) and monetary (price stability) roles can fail under ELB and high debt.
  - “Interactions between fiscal policy and monetary policy” defined as direct or indirect effects actions by one authority have on the policy space and effectiveness of the other.
  - Interaction need not imply a single joint instrument; independence and mandates (price stability, debt sustainability) should be preserved.
- Institutional constraints:
  - Central bank independence is a prerequisite to prevent fiscal dominance.
  - Country-specific factors (financial market structure, inflation history, monetary credibility) determine appropriate interaction scope.

### II. Context — limited policy space and low demand (pre- and post-pandemic)
- Long-run factors lowering equilibrium real interest rate: demographics and low productivity.
- Some central banks faced low inflation (example: euro zone).
- Central banks created new instruments such as large-scale asset purchases.
- COVID-19 effects:
  - Output and inflation fell sharply on onset.
  - Heightened uncertainty may have further lowered the equilibrium real interest rate.
  - Fiscal policy was heavily used, including guarantee programs and subsidized loans.
  - With supply-driven inflation pressures (commodity prices, disruptions), anchoring inflation remains critical.

### III. Dynamics of closer interaction — model setup and mechanisms
- Model basis and features:
  - Based on Erceg and Linde (2013) NK-DSGE, augmented with discounting to address the forward guidance puzzle (Del Negro, Giannoni and Patterson, 2015).
  - Two-country model: home = typical small open EM; foreign = large, relatively closed AE.
  - Features: habit in consumption, convex investment adjustment costs, Bernanke-Gertler-Gilchrist financial accelerator, nominal rigidities in import/consumer prices and wages, permanent and mean-reverting productivity shocks.
  - Central bank follows a Taylor rule with ELB constraint; model allows unconventional monetary policy (forward guidance, average inflation targeting).
  - Fiscal authority: distortionary taxes, public consumption, long-term government debt issuance.
  - Exchange rates flexible; countries not in currency union.
- Baseline construction:
  - Baseline matches IMF WEO April 2020 projections to generate a severe recession with a persistent negative output gap and below-target inflation.
  - Shocks include large negative supply shocks, negative consumption demand shocks (AR(1) persistence 0.9), and exchange rate risk premium shocks for EM (around 10 percent average depreciation).
  - Calibration symmetric except for capital flow shock and higher policy rate ELB in EM.

### III.1 Severe Recession Scenario — fit to WEO
- Baseline closely matches April 2020 WEO output gap for both regions and matches AE inflation forecasts; EM inflation match is less precise due to exchange rate pass-through offsetting recessionary forces.
- Baseline features protracted inflation below target — relevant for average inflation targeting scenarios.

### III.2 What central banks can do alone (limits of UMP)
- Empirical evidence:
  - Asset purchases of 15-20 percent of GDP required to lower 10-year yields by 100 basis points in U.S. and euro area (Fabo et al. 2020).
  - Such purchases cumulatively boost GDP roughly 1-2 percent, with considerable uncertainty.
- Example calibrated effects:
  - QE that reduces 10-year term premia by 25 basis points yields an output boost less than 0.5 percent after 2 years.
  - Complementing QE with forward guidance (later ELB liftoff) can boost output by about 1 percent relative to baseline.
  - Inflation effects in calibrated small open economies are small: only about 0.1 - 0.2 percent.
- Positive fiscal side-effect:
  - UMP can create fiscal space through higher nominal GDP, lower interest payments, and higher tax revenues; government debt-to-GDP ratio may fall.

### III.3 Fiscal stimulus with alternative monetary strategies
- Fiscal shock simulated:
  - Transient discretionary government spending equal to 1 percent of GDP for 2 years, declining thereafter with AR(1) root 0.65.
  - Total fiscal package ≈ 2.5 percent of baseline GDP over 3-4 years.
- Assumptions for stimulus effectiveness:
  - Credible communication that stimulus is temporary.
  - Country is fiscally solvent so spreads do not rise.
  - Central bank can credibly keep policy rate at ELB despite fiscal stimulus (if inflation remains at or below target).
- Results in liquidity trap (policy rate at ELB):
  - Output increases by about 1.25 percent on average in the first two years — fiscal multiplier ≈ 1.25 (cumulated two-year output response divided by cumulated spending increase).
  - Higher government consumption crowds in private consumption and investment at the ELB.
  - Debt-to-GDP ratio falls persistently when the central bank maintains accommodative monetary policy (due to higher nominal GDP and low interest rates).
  - If the central bank leans against stimulus (tightens), the debt-to-GDP decline is short-lived (higher debt service and smaller GDP gain).
  - Net exports are crowded out as the real exchange rate appreciates.
- Comparison when economy at potential and inflation at target:
  - Central bank would tighten as inflation rises, reducing positive fiscal effects on output and inflation, and raising fiscal cost.

### III.4 Alternative monetary strategy — Average Inflation Targeting (AIT)
- AIT specification:
  - Central bank targets a 5-year average annual inflation rate; initial average inflation gap assumed minus 0.5 percent.
- Effects under AIT:
  - Central bank keeps nominal rate at the ELB longer, producing higher actual inflation and inflation expectations, reducing real rates, amplifying output and inflation response to fiscal stimulus.
  - Under AIT in simulations, nominal GDP rises enough that debt-to-GDP falls and returns to baseline (described as a “fiscal free lunch” in the liquidity trap).
  - Drivers: elevated multiplier, modest rise in debt service costs, modest contribution from primary balance.
- Sensitivity:
  - Favorable AIT effects depend on initial negative AIT gap and inflation outlook; absent an initial negative AIT gap, AIT impact on debt dynamics is much weaker.

### III.5 Credible monetary and fiscal stimulus under financial stress
- Stress scenario:
  - Self-fulfilling financial stress raises domestic long-term interest rates well above foreign rates, amplifying recession and lowering inflation further.
- Policy response simulated:
  - Central bank large-scale asset purchases reduce 5-year term-premium by about 100 basis points in the simulation.
- Combined credible QE and fiscal stimulus:
  - Output expansion almost twice as large as fiscal-only case.
  - Primary deficit rises somewhat, but government debt-to-GDP falls due to higher nominal GDP.
  - Decisive and credible central bank expansion can ease financial tensions and avoid self-fulfilling sovereign default risk, provided the government commits to fiscal consolidation subsequently.

### IV. Country-specific considerations — case studies and implementation risks
- Five country cases (mid-2021): Belgium, Iceland (AEs); Botswana, South Africa, Thailand (EMs).
- Purpose: illustrate how country-specific characteristics shape scope of fiscal-monetary interaction.
- General case-study findings:
  - Fiscal-monetary interaction was warranted on several occasions during COVID-19, supported by model findings and country characteristics.
  - In some instances, the case for interaction became limited as conditions evolved.
  - Risks limiting interaction included threats to central bank independence and credibility.
  - The paper favors “arms-length” interaction: authorities aware of cross-effects but operationally independent.

#### Selected country pre-crisis and pandemic statistics (preserved exactly as presented)
- Belgium:
  - Debt declining path reaching 98 percent of GDP in 2019.
  - Inflation fell to 1.5 percent on average since the global financial crisis.
  - Growth averaged 1.4 percent over 2010-2019.
  - ECB policy rate zero from 2016 onwards.
- Iceland:
  - Growth averaged just over 4 percent during 2013-2019.
  - Public debt about 66 percent in 2019.
  - Policy rate stood at 3 percent at end-2019.
- Botswana:
  - Policy rate stood at 4.75 percent as of end-2019.
  - Headline and core inflation at lower end of target range; inflation expectations anchored around the midpoint.
- Thailand:
  - Policy rate stood at 1.25 percent at end-2019.
  - Government debt around 40 percent of GDP.
  - Inflation and inflation expectations declined below the lower end of the target band pre-pandemic.
- South Africa:
  - Real GDP almost stagnated with per-capita GDP growth negative for a fifth consecutive year in 2019.
  - Policy rate stood at 6.5 percent at end-2019.
  - Public debt rising trajectory; central bank official reserves relatively low.
  - Inflation stable within the official target range; inflation expectations well anchored.

#### Pandemic impacts (selected exact figures)
- Belgium:
  - GDP fell by 6.3 percent in 2020.
  - Inflation dropped to 0.4 percent in 2020.
  - Current account: small deficit of 0.2 percent of GDP.
- Iceland:
  - Output fell by 6.5 percent in 2020.
  - Average inflation rose to 2.9 percent in 2020 (target 2.5 percent).
  - Currency depreciated by well over 10 percent against the euro relative to end-2019.
- Botswana:
  - Economy contracted by 8.5 percent in 2020.
  - Current account deficit deteriorated to over 10 percent of GDP.
  - Foreign exchange reserves declined amid portfolio outflows in 2020Q2-Q3 but remained above adequate levels.
- South Africa:
  - Real GDP contracted by 6.4 percent in 2020.
  - Annual average inflation declined to 3.3 percent in 2020.
  - Currency depreciated by nearly 40 percent against the U.S. dollar relative to end-2019.
  - Public debt moved from 56 percent in 2019 to 69 percent in 2020.
- Thailand:
  - Real GDP contracted by 6.1 percent in 2020.
  - Headline inflation decelerated to -0.9 percent in 2020.
  - Tourism accounts for more than 15 percent of GDP.

#### Country policy assessments and operational notes (selected)
- Belgium:
  - Fiscal support measures about 5 percent of GDP in 2020.
  - Debt jumped by 16 percentage points to 114 percent of GDP in 2020.
  - ECB expanded quantitative easing under PEPP; ECB net purchases of Belgian government debt in 2020 equivalent to around 80 percent of net debt issued by the Belgian government in the primary market.
  - Asset purchases judged warranted to provide fiscal space; favorable impact could reverse if interest rates increase.
- Botswana:
  - Initial stimulus package of 2.6 percent of GDP plus supplementary budget and loan facility amounting to 1.3 percent of GDP.
  - Public debt increased by 3.2 percent of GDP to 19.5 percent in FY2020; debt ceiling 40 percent.
  - BoB cut policy rate by 100 bps to 3.75 percent between April and October 2020.
  - Inflation dropped to 1.9 percent in 2020.
  - Secondary market underdeveloped; BoB could consider temporary government asset purchases (to be repaid within six months) under BoB Act in severe market dysfunction, with clear communication.
- Iceland:
  - Fiscal support measures amounted to 6.6 percent of GDP in 2020.
  - Public debt increased to around 77 percent of GDP in 2020 from 66 percent in 2019.
  - CBI announced an asset purchase program authorized for up to 5 percent of GDP (ISK150 billion); only one percent of the envelope had been used five months after announcement.
  - 10-year government bond yield moved from a low of 2.6 percent in June 2020 to 3 percent in July 2021.
  - Asset purchase program judged not clearly warranted given inflation above target and sufficient policy space, but retained as a permanent tool.
- South Africa:
  - Fiscal package of about 5 percent of GDP; public debt rose to 69 percent in 2020 from 56 percent in 2019.
  - SARB cut policy rate by 275 basis points between March and July 2020 to a historic low of 3.5 percent.
  - SARB launched a government bond purchase program to ensure market functioning; purchases presented as liquidity support rather than economic stimulus.
  - Asset purchase program size: 1.5 percent of GDP.
  - 10-year government yield eased to around 9 percent in April 2021 from peak above 12 percent at the height of the pandemic.
  - Policy judgement: accommodative stance appropriate; avoid direct financing of government deficits to preserve credibility.
- Thailand:
  - Fiscal package: 8 percent of GDP (figure excludes equity injections, loans, asset purchases, debt assumptions, guarantees, and quasi-fiscal measures).
  - Public debt increased from 41 percent in 2019 to almost 50 percent of GDP in 2020; remained below 60 percent debt ceiling.
  - 10-year government bond yield about 1.3 percent in 2020, rose to 1.7 percent in April 2021.
  - BoT policy rate cut cumulatively by 75 bps between February and May 2020 to 0.5 percent.
  - BoT asset purchases: government assets equivalent to 0.6 percent of GDP purchased in March 2020.
  - Transmission constrained; credit guarantees and on-lending used to improve transmission.
  - Model-consistent assessment: further fiscal support/credit guarantees warranted; asset purchases could support fiscal policy in downside scenarios if credible.

### Cross-country synthesis (Table 1 excerpts preserved exactly)
- Belgium
  - Assessment: asset purchases warranted
  - Country-specific: ECB’s monetary policy aligned with Belgium’s cycle enabling countercyclical fiscal policy.
- Botswana
  - General: Y N N N Y
  - Assessment: asset purchases not warranted
  - Country-specific: buffers from the government investment account; small secondary market limits scope for asset purchases.
- Iceland
  - General: Y N N N Y
  - Assessment: asset purchases not warranted
  - Country-specific: moderate public debt; policy rate not at the ELB but inflation above target. Assessment: further asset purchases not warranted (but useful policy tool).
- South Africa
  - General: Y N Y Y Y
  - Assessment: asset purchases warranted
  - Country-specific: high public debt and credit rating downgrade reduce fiscal space; concerns over fiscal risks constrain monetary policy space. Assessment: further asset purchases not warranted due to risks.
- Thailand
  - General: Y (Y) N Y Y
  - Assessment: further fiscal support/credit guarantees warranted
  - Country-specific: long-standing fiscal discipline, low borrowing costs, and large domestic investor base generate fiscal space. Assessment: further fiscal support/credit guarantees warranted.

### V. Conclusions and policy implications
- Core messages:
  - Close fiscal–monetary interactions can improve macroeconomic outcomes when ELB and high debt bind and when authorities have credible frameworks.
  - Expansionary fiscal policy can raise the neutral rate, easing monetary constraints; expansionary monetary policy can create fiscal space via higher GDP and lower interest burdens.
- Practical prescriptions (as implied by analysis):
  - When policy rate at ELB and monetary tools limited, credible temporary fiscal stimulus can have multipliers > 1 (example: multiplier ≈ 1.25).
  - Central banks can enhance fiscal effectiveness by credibly committing to accommodative policies (including AIT where credible).
  - Large-scale QE can be necessary to materially lower long-term yields (empirical estimates: 15-20 percent of GDP to lower 10-year yields by 100 basis points), but UMP alone unlikely to fully offset severe demand shortfalls.
  - Where sovereign spreads risk constraining fiscal policy, credible central bank asset purchases can prevent self-fulfilling rises in borrowing costs and support fiscal countercyclical response — conditional on government commitment to fiscal sustainability.
  - Safeguards: preserve central bank independence and prioritize anchoring inflation if conflicts arise between inflation objectives and supporting fiscal space.
- Institutional caveats:
  - Ability to leverage interactions differs across countries due to institutional setup, inflation history, pre-pandemic environment, and pandemic impact.
  - Risks include perceptions of inconsistent price stability mandates and adverse market reactions, especially in EMs.
  - Safeguards and credibility are crucial.

### Appendix A — The Open Economy DSGE Model (overview and calibration highlights)
- Model features:
  - Two-country DSGE with endogenous investment, HM and FL households, sticky wages and prices (Calvo), trade adjustment costs, incomplete financial markets, optional financial accelerator.
- Key calibrated parameters and exact values preserved:
  - Quarterly frequency.
  - Trade share of the small open economy: 24 percent of GDP.
  - ρ_C = ρ_I = 2.5.
  - Price markup θ_p = 0.2.
  - Import adjustment cost parameters: φ_{M_C} = φ_{M_I} = 1.
  - Financial intermediation parameter φ_b = 0.01.
  - Relative risk aversion σ = 2.
  - Habit persistence א = 0.8.
  - μ_0 ψ = 0.65.
  - Investment adjustment cost φ_I = 3.
  - Depreciation rate δ = 0.03.
  - CES parameter ρ (in production) set to −1 (Leontief).
  - Price markup θ_P = 0.2 and steady-state investment to output ratio of [20] percent.
  - Financial accelerator: monitoring cost μ = [0.12]; default rate = [3] percent per year; variance = [0.28].
  - Calvo parameters: ξ_p = 0.92; ξ_m = 0.90; ξ_w = 0.88.
  - Indexation: ι_p = 1; ι_w = ι_m = 0.5.
  - Wage markup θ_W = 1/3.
  - Behavioral expectations discount φ = 0.9.
  - Monetary rule parameters: γ_i = 0.9; γ_π = 1.5; γ_x = 0.125; γ_Δx = 0.25.
  - Discount factor β = 0.99875.
  - Inflation target = 2 percent implies steady state nominal interest rate = 2.5 percent.
  - Fiscal parameters: government spending share = 20 percent of steady state output; government debt to annualized GDP ratio b_G = 0.90; transfers to GDP ratio = 7 percent; τ_C = 10 percent; τ_K = 20 percent; τ_N = 0.35.
  - Tax adjustment rule: υ_1 = 0.985; υ_2 = υ_3 = 0.1.
  - Bond maturity probability ϖ = 0.125.
  - Price inflation steady-state parameter π = 0.005 used in approximation for ϖ_{long}.
- Solution method:
  - Log-linearize around non-stochastic steady state; render nominal variables stationary; unconstrained model solved via Anderson and Moore (1985) implementing Blanchard and Kahn (1980) solution method.

*Source: wpiea2022170-print-pdf (Working Paper No.: WP/2022/170).*

### 1. Number of Countries Constrained by ZLB ..............................................................................

### 1. Number of Countries Constrained by ZLB

### Major sections and topics (as listed in the source)
- 1. Number of Countries Constrained by ZLB ............................................................................................................5
- 2. A Severe Recession Scenario ............................................................................................................................. 12
- 3. What can monetary policy do alone to fight the recession .............................................................................. 14
- 4. Transient government spending hike of 1 percent of baseline GDP for two years ...................................... 16
- 5. Transient government spending hike in liquidity trap under alternative monetary ....................................... 17
- 6. Monetary and fiscal stimulus at the ELB with elevated spreads..................................................................... 19
- 7. Impact of the pandemic on output and inflation ................................................................................................ 23
- 8. Public debt and asset purchases in Belgium and peer countries................................................................... 24
- 9. Public debt and monetary policy rate in Botswana and peer countries. ........................................................ 24
- 10. Public debt and monetary policy rate in Iceland and peer countries. .......................................................... 26
- 11. Public debt and monetary policy rate in South Africa and peer countries................................................... 27
- 12. Public debt and monetary policy rate in Thailand and peer countries. ........................................................ 29
- TABLE
  - 1. Overview of findings from general considerations reflecting model implications ......................................... 29
- APPENDICES
  - A. The Open Economy DSGE Model...................................................................................................................... 35
  - B.1. Robustness with respect to initial AIT gap ..................................................................................................... 46

### Implicit focal points (based strictly on section headings)
- Measurement and enumeration of countries at the zero lower bound (ZLB).
- Scenario analysis of a severe recession and policy responses.
- Effectiveness and limits of monetary policy acting alone in recessions.
- Fiscal stimulus experiments: transient government spending hikes of "1 percent of baseline GDP" and variations under liquidity-trap conditions.
- Combined monetary and fiscal stimulus at the effective lower bound (ELB) in presence of elevated spreads.
- Pandemic-era impacts on output and inflation.
- Cross-country comparisons of public debt, monetary policy rates, and asset purchases for Belgium, Botswana, Iceland, South Africa, and Thailand.
- Model documentation and robustness checks: "The Open Economy DSGE Model" and robustness with respect to "initial AIT gap."

*Source: wpiea2022170-print-pdf - 1. Number of Countries Constrained by ZLB (IMF).*

### REFERENCES .............................................................................................................

### REFERENCES

### I. Introduction — crisis, policy response, and limits
- The global economy shrunk sharply in 2020, with output 3 percent below the 2019 level.
- Global fiscal measures to support the economy summed to US$16.9 trillion (IMF 2021).
- Advanced economies (AEs) implemented the most far-reaching responses, including spending, revenue measures, lending and loan guarantee programs, and expanded asset purchase programs.
- Central banks brought policy rates closer to Effective Lower Bounds (ELB); many engaged in or expanded asset purchase programs.
- Key near-term complications: the war in Ukraine, soaring commodity prices, elevated geopolitical risk, and supply disruptions.
- Constraints:
  - Interest rates were already low in many AEs prior to COVID-19, limiting further cuts.
  - Many EM central banks faced similar constraints (Figure 1: Number of Countries Constrained by ZLB).
  - Public debt levels rose sharply across regions during the pandemic.

- Conceptual framing:
  - Traditional “consensus assignment” separates fiscal focus (debt/deficits, structural objectives) and monetary focus (price stability, flexible inflation targeting).
  - Under ELB and high debt, strict separation may fail; fiscal-monetary interaction becomes more central.
  - “Interactions between fiscal policy and monetary policy” are defined as direct or indirect effects actions by one authority have on the policy space and effectiveness of the other.
  - Interaction can include central bank internalizing fiscal effectiveness and fiscal authority recognizing that expansionary fiscal policy can raise the neutral rate.
  - Interaction stops short of treating fiscal and monetary policy as a single joint instrument.

- Institutional and credibility constraints:
  - Central bank independence is a prerequisite to prevent fiscal dominance.
  - Greater interaction should preserve traditional mandates (price stability, debt sustainability).
  - Country-specific factors (financial market structure, inflation history, monetary credibility) determine appropriate interaction scope.

### II. Context — limited policy space and low demand (pre- and post-pandemic)
- Pre-COVID factors reducing reliance on conventional monetary policy:
  - Demographics and low productivity pushed down the real equilibrium interest rate over the last decade.
  - Some central banks faced low inflation (e.g., euro zone).
  - Central banks created new instruments (large-scale asset purchases).
- COVID-19 exacerbated constraints:
  - Output and inflation fell sharply on onset (IMF 2020 WEO).
  - Heightened uncertainty may have further lowered the equilibrium real interest rate.
  - Fiscal policy was heavily used, including guarantee programs and subsidized loans.
  - With supply-driven inflation pressures (commodity prices, disruptions), anchoring inflation is critical (IMF 2021 WEO).

### III. Dynamics of closer interaction — model setup and mechanisms
- Model used:
  - Based on Erceg and Linde (2013) NK-DSGE, augmented with discounting to address forward guidance puzzle (Del Negro, Giannoni and Patterson, 2015).
  - Two-country model: home = typical small open EM; foreign = large, relatively closed AE.
  - Features: habit in consumption, convex investment adjustment costs, Bernanke-Gertler-Gilchrist financial accelerator, nominal rigidities in import/consumer prices and wages, permanent and mean-reverting productivity shocks.
  - Central bank follows a Taylor rule with ELB constraint; model allows unconventional monetary policy (forward guidance, average inflation targeting).
  - Fiscal authority: distortionary taxes, public consumption (affects aggregate demand), long-term government debt issuance.
  - Exchange rates are assumed flexible; countries are not in a currency union.

- Baseline construction:
  - Baseline matches IMF WEO April 2020 projections to generate a severe recession with a persistent negative output gap and below-target inflation.
  - Shocks include large negative supply shocks, negative consumption demand shocks (AR(1) persistence 0.9), and exchange rate risk premium shocks for EM (around 10 percent average depreciation).
  - Calibration symmetric across economies except for capital flow shock and higher policy rate ELB in EM.

III.1 Severe Recession Scenario — fit to WEO
- Baseline closely matches April 2020 WEO output gap for both regions and matches AE inflation forecasts; EM inflation match is less precise due to exchange rate pass-through offsetting recessionary forces.
- Baseline features protracted inflation below target — relevant for average inflation targeting scenarios.

III.2 What central banks can do alone (UMP limits)
- Empirical evidence referenced: asset purchases of 15-20 percent of GDP required to lower 10-year yields by 100 basis points in U.S. and euro area; such purchases cumulatively boost GDP roughly 1-2 percent (Fabo et al. 2020), with considerable uncertainty.
- Given already-low long-term rates, scope of unconventional monetary policy (UMP) is limited.
- Example scenario: QE reduces 10-year term premia by 25 basis points — output boost is less than 0.5 percent after 2 years.
- Complementing QE with forward guidance (later ELB liftoff) can boost output by about 1 percent relative to baseline.
- Inflation effects in calibrated small open economies (fairly flat Phillips curves) are small: only about 0.1 - 0.2 percent.
- Positive side-effect: UMP can create fiscal space through higher nominal GDP, lower interest payments, and higher tax revenues (government debt-to-GDP ratio may fall).

III.3 Fiscal stimulus with alternative monetary strategies
- Fiscal shock simulated: transient discretionary government spending equal to 1 percent of GDP for 2 years, declining thereafter with AR(1) root 0.65 — total fiscal package ≈ 2.5 percent of baseline GDP over 3-4 years.
- Key assumptions for stimulus effectiveness:
  - Credible communication that stimulus is temporary.
  - Country is fiscally solvent so spreads do not rise.
  - Central bank can credibly keep policy rate at ELB despite fiscal stimulus (if inflation remains at or below target).
- Results (liquidity trap: policy rate at ELB):
  - Output increases by about 1.25 percent on average in the first two years — fiscal multiplier ≈ 1.25 (cumulated two-year output response divided by cumulated spending increase).
  - Higher government consumption crowds in private consumption and investment when monetary policy is at the ELB.
  - Debt-to-GDP ratio falls persistently when the central bank maintains accommodative monetary policy (due to higher nominal GDP and low interest rates); if the central bank leans against stimulus (tightens), the debt-to-GDP decline is short-lived (higher debt service and smaller GDP gain).
  - Net exports are crowded out as the real exchange rate appreciates.

- Comparison case: fiscal expansion when economy is at potential and inflation at target:
  - Central bank would tighten monetary policy as inflation rises, reducing positive fiscal effects on output and inflation, and raising the fiscal cost.

- Alternative monetary strategy — Average Inflation Targeting (AIT):
  - AIT: central bank targets a 5-year average annual inflation rate; initial average inflation gap assumed minus 0.5 percent.
  - Under AIT, central bank keeps nominal rate at the ELB longer, producing higher actual inflation and inflation expectations, reducing real rates, amplifying output and inflation response to fiscal stimulus.
  - Under AIT in simulations, nominal GDP rises enough that debt-to-GDP falls and returns to baseline (a “fiscal free lunch” in the liquidity trap).
  - Drivers: elevated multiplier, modest rise in debt service costs, modest contribution from primary balance.
  - Sensitivity: favorable AIT effects depend on initial negative AIT gap and inflation outlook; absent an initial negative AIT gap, AIT impact on debt dynamics is much weaker.

III.4 Credible monetary and fiscal stimulus under financial stress
- Scenario: self-fulfilling financial stress raises domestic long-term interest rates well above foreign rates, amplifying recession and lowering inflation further.
- Central bank large-scale asset purchases reduce 5-year term-premium by about 100 basis points in the simulation, easing financial conditions.
- Combined credible QE and fiscal stimulus:
  - Output expansion almost twice as large as fiscal-only case.
  - Primary deficit rises somewhat, but government debt-to-GDP falls due to higher nominal GDP.
  - Conclusion: decisive and credible central bank expansion can ease financial tensions and avoid self-fulfilling sovereign default risk, provided the government commits to fiscal consolidation subsequently.

### IV. Country-specific considerations — case studies and implementation risks
- Case studies: five countries analyzed as of mid-2021 — two AEs (Belgium, Iceland) and three EMs (Botswana, South Africa, Thailand).
- Case study purpose: illustrate how country-specific characteristics shape the appropriate scope of fiscal-monetary interaction (financial market structure, inflation history, monetary credibility).
- General findings from case studies:
  - On multiple occasions during COVID-19, fiscal-monetary interaction was warranted and supported by both general model-based considerations and country characteristics.
  - In some instances, the case for interaction was limited a few months into the pandemic due to evolving conditions.
  - Risks limited the use of interaction in several cases — notably risks to central bank independence and credibility.
  - Table 1 (not reproduced here) presents an overview of findings.
- Monetary policy frameworks in case-study countries:
  - Belgium: member of euro area since 1999; ECB objective is “inflation rates below, but close to, 2 percent over the medium term.”
  - Iceland: Central Bank of Iceland adopted an inflation target of 2.5 percent (text truncated here).
- Operational principle emphasized:
  - The paper favors “arms-length” interaction where authorities are aware of cross-effects but remain operationally independent — this is distinct from formal coordination or joint planning.

### V. Conclusions and policy implications (synthesized)
- Interaction rationale:
  - Fiscal-monetary interactions can improve macroeconomic outcomes when policy constraints (ELB, high debt) are binding and when authorities have credible frameworks.
  - Expansionary fiscal policy can raise the neutral rate, easing monetary constraints; expansionary monetary policy can create fiscal space via higher GDP and lower interest burdens.
- Practical policy prescriptions implicit in analysis:
  - When the policy rate is at the ELB and monetary tools are limited, credible temporary fiscal stimulus can have multipliers > 1 (example: multiplier ≈ 1.25 in calibrated scenario).
  - Central banks can enhance fiscal effectiveness by credibly committing to accommodative policies (including AIT where credible).
  - Large-scale QE can be necessary to lower long-term yields materially (empirical estimates: 15-20 percent of GDP to lower 10-year yields by 100 basis points in some AEs), but UMP alone is unlikely to fully offset severe demand shortfalls.
  - Where sovereign spreads risk constraining fiscal policy, credible central bank asset purchases can prevent self-fulfilling rises in borrowing costs and support fiscal countercyclical response — conditional on government commitment to fiscal sustainability.
  - Safeguards: preserve central bank independence and prioritize anchoring inflation if conflicts arise between inflation objectives and supporting fiscal space.

*Italic: Content derived from wpiea2022170-print-pdf (IMF working paper content provided above).*

### 2001. With the move to inflation targeting, it also abolished its former focus on the exchange rate.

### wpiea2022170-print-pdf - 2001. With the move to inflation targeting, it also abolished its former focus on the exchange rate.

### Monetary frameworks and inflation targeting
- The South African Reserve Bank (SARB) and the Bank of Thailand (BoT) adopted inflation targeting regimes in 2000 with current target ranges of 3-6 percent and 1-3 percent, respectively.
- The SARB publicly expressed a preference for inflation and inflation expectations to durably move toward 4.5 percent over time; in June 2021 the governor suggested there may be a case for reducing the inflation target.
- The BoT described its inflation targeting regime as flexible and suitable to achieve multiple objectives.
- The Bank of Botswana’s (BoB) primary objective is price stability, defined as inflation between 3-6 percent; it has also maintained a stable real exchange rate against a basket of the South African rand and the SDR.

### Pre-Crisis macroeconomic conditions (selected country findings)
- Belgium:
  - Debt was on a declining path reaching 98 percent of GDP in 2019.
  - Inflation fell to 1.5 percent on average since the global financial crisis.
  - Growth averaged 1.4 percent over 2010-2019.
  - ECB policy rate had been zero from 2016 onwards.
- Iceland:
  - Growth averaged just over 4 percent during 2013-2019.
  - Public debt amounted to about 66 percent in 2019.
  - Policy rate stood at 3 percent at end-2019.
- Botswana:
  - Policy rate stood at 4.75 percent as of end-2019.
  - Headline and core inflation remained at the lower end of the target range; inflation expectations anchored around the midpoint.
- Thailand:
  - Policy rate stood at 1.25 percent at end-2019.
  - Government debt around 40 percent of GDP.
  - Inflation and inflation expectations declined below the lower end of the target band pre-pandemic.
- South Africa:
  - Real GDP almost stagnated with per-capita GDP growth negative for a fifth consecutive year in 2019.
  - Policy rate stood at 6.5 percent at end-2019.
  - Public debt rising trajectory; central bank official reserves relatively low.
  - Inflation stable within the official target range; inflation expectations well anchored.

### Impact of the COVID-19 pandemic: output and inflation (selected statistics)
- General:
  - Output gaps turned negative; magnitude of economic contraction similar across countries.
- Belgium:
  - GDP fell by 6.3 percent in 2020.
  - Inflation dropped to 0.4 percent in 2020.
  - Current account turned to a small deficit of 0.2 percent of GDP.
- Iceland:
  - Output fell by 6.5 percent in 2020.
  - Average inflation rose to 2.9 percent in 2020 (target 2.5 percent).
  - Currency depreciated by well over 10 percent against the euro relative to end-2019.
- Botswana:
  - Economy contracted by 8.5 percent in 2020.
  - Current account deficit deteriorated to over 10 percent of GDP.
  - Foreign exchange reserves declined amid portfolio outflows in 2020Q2-Q3 but remained above adequate levels.
- South Africa:
  - Real GDP contracted by 6.4 percent in 2020 (steepest decline since 1946).
  - Annual average inflation declined to 3.3 percent in 2020.
  - Currency depreciated by nearly 40 percent against the U.S. dollar relative to end-2019.
  - Public debt moved from 56 percent in 2019 to 69 percent in 2020.
- Thailand:
  - Real GDP contracted by 6.1 percent in 2020.
  - Headline inflation decelerated to -0.9 percent in 2020.
  - Tourism accounts for more than 15 percent of GDP.

### Fiscal-monetary policy mix: constraints, actions, and assessments
- Cross-cutting:
  - All case study countries experienced elevated gross financing needs, larger deficits, and increased public debt; fiscal and monetary constraints varied by country.
  - Some countries had both policy levers unconstrained (Botswana, Iceland); others had one constrained (Thailand) or both constrained (Belgium, South Africa).
- Belgium:
  - Fiscal support measures about 5 percent of GDP in 2020.
  - Debt jumped by 16 percentage points to 114 percent of GDP in 2020.
  - ECB expanded quantitative easing under PEPP; ECB net purchases of Belgian government debt in 2020 were equivalent to around 80 percent of net debt issued by the Belgian government in the primary market.
  - Asset purchases were judged warranted to provide fiscal space; favorable impact could reverse if interest rates increase.
- Botswana:
  - Initial stimulus package of 2.6 percent of GDP plus supplementary budget and loan facility amounting to 1.3 percent of GDP.
  - Public debt increased by 3.2 percent of GDP to 19.5 percent in FY2020; debt ceiling 40 percent.
  - BoB cut policy rate by 100 bps to 3.75 percent between April and October 2020.
  - Inflation dropped to 1.9 percent in 2020.
  - Secondary market underdeveloped; BoB could consider temporary government asset purchases (to be repaid within six months) under BoB Act in severe market dysfunction, with clear communication.
- Iceland:
  - Fiscal support measures amounted to 6.6 percent of GDP in 2020.
  - Public debt increased to around 77 percent of GDP in 2020 from 66 percent in 2019.
  - Central Bank of Iceland (CBI) announced an asset purchase program authorized for up to 5 percent of GDP (ISK150 billion); only one percent of the envelope had been used five months after announcement.
  - 10-year government bond yield moved from a low of 2.6 percent in June 2020 to 3 percent in July 2021.
  - The asset purchase program was judged not clearly warranted given inflation above target and sufficient policy space, but retained as a permanent tool.
- South Africa:
  - Fiscal package of about 5 percent of GDP; public debt rose to 69 percent in 2020 from 56 percent in 2019.
  - SARB cut policy rate by 275 basis points between March and July 2020 to a historic low of 3.5 percent.
  - SARB launched a government bond purchase program to ensure market functioning; purchases were presented as liquidity support rather than economic stimulus.

*Source: wpiea2022170-print-pdf - 2001. With the move to inflation targeting, it also abolished its former focus on the exchange rate.*

### 1.5 percent of GDP. While the program was smaller than those implemented in many other EMs, it sent a

### 1.5 percent of GDP. While the program was smaller than those implemented in many other EMs, it sent a strong signal that the SARB stood ready to smooth undue volatility in the government bond market.

### South Africa — case study findings and policy assessment
- Program and market response:
  - Asset purchase program size: 1.5 percent of GDP.
  - 10-year government yield: eased to around 9 percent in April 2021 from its peak of above 12 percent at the height of the pandemic.
- Central bank stance and rationale:
  - The SARB resisted calls for larger government bond purchases; the governor cautioned that a larger program would mean the domestic currency “will no longer be issued by a credible, inflation-targeting central bank, but by one that is fully financing the public sector instead”.
  - Concern that larger-scale asset purchases “would imply that the SARB would be buying, more or less, all new debt for the foreseeable future” and “such interventions would crowd pension funds and other institutional investors out of the bond market”.
- Model-consistent assessment:
  - General considerations suggest fiscal–monetary interaction could have benefitted the economy given a sluggish recovery and inflation below target.
  - Monetary policy constrained by fiscal risk; upside inflationary risks from a potentially large currency depreciation should fiscal risks materialize.
  - Conclusion: greater conventional or unconventional monetary easing would not have been warranted under these fiscal risk considerations.
- Policy judgement:
  - The accommodative monetary policy stance, with the negative real policy rate significantly below the estimated neutral real rate of around 2 percent, was appropriate.
  - A favorable sovereign debt composition, including long average maturities, provides near-term resilience.
  - Medium-term: debt sustainability concerns need to be addressed through fiscal consolidation supported by structural reforms to boost growth.
  - In acute government bond market stress, additional secondary market asset purchases could be considered to normalize liquidity while monitoring potential negative effects on price stability and central bank credibility.
  - The SARB should continue to avoid direct financing of government deficits to preserve monetary policy credibility.

### Thailand — case study findings and policy assessment
- Fiscal and monetary response:
  - Fiscal package: 8 percent of GDP, financed mostly by domestic debt issuance and some expenditure reprioritization. (Note: figure excludes equity injections, loans, asset purchases, debt assumptions, guarantees, and quasi-fiscal measures.)
  - Public debt: increased from 41 percent in 2019 to almost 50 percent of GDP in 2020; remained below the 60 percent of GDP debt ceiling.
  - 10-year government bond yield: about 1.3 percent in 2020, rose to 1.7 percent in April 2021 amid rising U.S. 10-year treasury yields and global inflation fears.
  - BoT policy rate: cut cumulatively by 75bps between February and May 2020 to a historic low of 0.5 percent.
  - BoT asset purchases: government assets equivalent to 0.6 percent of GDP purchased in March 2020 to support bond market functioning.
- Transmission constraints and supporting measures:
  - Monetary policy transmission was constrained; bank lending to SMEs declined despite policy easing due to elevated credit risk and tighter bank lending standards.
  - Authorities deployed credit guarantees and on-lending through state-owned and private banks at favorable rates to improve transmission.
- Model-consistent assessment:
  - Some fiscal space combined with constrained monetary policy presented an opportunity for more accommodation and closer interaction.
  - Provision of government guarantees was key to enhancing monetary policy transmission and channeling liquidity to the private sector.
  - Fiscal policy could boost demand without creating financial stability risks, supporting monetary policy when transmission is limited.
  - In a downside scenario with financial market stress, an asset purchase program could:
    - counter market pressures,
    - support fiscal policy by avoiding surges in government borrowing costs amid elevated gross financing needs,
    - ease financial conditions for households and firms.
  - If credible, further asset purchases could be coupled with forward guidance on the evolution of policy support.

### Cross-country synthesis from Table 1 (mid-2021 baseline)
- General considerations categories used:
  - Output gap: negative
  - Inflation: below target (in most cases)
  - Fiscal policy: constrained (varies by country)
  - Monetary policy space: constrained (varies)
  - Elevated gross financing needs: common across cases
- Selected country assessments preserved exactly as presented:
  - Belgium
    - Assessment: asset purchases warranted
    - Country-specific: ECB’s monetary policy aligned with Belgium’s cycle enabling countercyclical fiscal policy.
  - Botswana
    - General: Y N N N Y
    - Assessment: asset purchases not warranted
    - Country-specific: buffers from the government investment account; small secondary market limits scope for asset purchases.
  - Iceland
    - General: Y N N N Y
    - Assessment: asset purchases not warranted
    - Country-specific: moderate public debt; policy rate not at the ELB but inflation above target. Assessment: further asset purchases not warranted (but useful policy tool).
  - South Africa
    - General: Y N Y Y Y
    - Assessment: asset purchases warranted
    - Country-specific: high public debt and credit rating downgrade reduce fiscal space; concerns over fiscal risks constrain monetary policy space. Assessment: further asset purchases not warranted due to risks.
  - Thailand
    - General: Y (Y) N Y Y
    - Assessment: further fiscal support/credit guarantees warranted
    - Country-specific: long-standing fiscal discipline, low borrowing costs, and large domestic investor base generate fiscal space; fiscal policy can support aggregate demand without creating financial stability risks and can support monetary policy transmission. Assessment: further fiscal support/credit guarantees warranted.

### Conclusions and broader policy implications
- Core messages:
  - Close fiscal–monetary interactions can improve tradeoffs faced by each policy, especially in severe downturns like COVID that reduce conventional policy space.
  - Model results indicate forceful interaction (including quantitative easing) can moderate sovereign spread increases, creating space for fiscal action if debt remains sustainable.
  - Active fiscal policy is particularly powerful for output stabilization when monetary policy is constrained.
  - Average inflation targeting combined with credible monetary–fiscal frameworks can reinforce fiscal effects and counter negative demand shocks.
  - Key caveat: fiscal stimulus must be properly sized; central bank accommodation is feasible only if it does not overheat the economy and push inflation above target.
- Institutional and country-specific constraints:
  - Ability to leverage interactions differs across countries due to institutional setup, inflation history, pre-pandemic environment, and pandemic impact.
  - Risks from greater interaction include potential perceptions of inconsistent central bank price stability mandates, risking adverse market reactions—especially in EMs.
  - Institutional credibility is crucial; safeguards are needed if authorities pursue greater interaction.
- Areas for further research (not covered in this paper):
  - Specific modalities of an effective fiscal–monetary mix.
  - Interactions outside recessions and with other policy levers such as macroprudential policy.
  - Dynamic effects of interactions on institutional credibility.
  - Policy mixes under adverse supply disruptions that raise inflation while output falls; preliminary suggestion that a mix of tight fiscal policy and loose monetary policy may be preferable from a public finance perspective when many countries have elevated government debt post-COVID.

*Source: IMF staff analysis and case studies (mid-2021 baseline).*

### Appendix A. The Open Economy DSGE Model

### Appendix A. The Open Economy DSGE Model

### Model overview
- Two-country (or two-region) DSGE model closely follows the Erceg and Lindé (2013) variant of the Erceg, Guerrieri and Gust (2006) SIGMA model, with the main difference that the pricing block allows for discounting to address the forward-guidance puzzle.
- Features:
  - Countries can differ in size.
  - Endogenous investment.
  - Hand-to-mouth (HM) and forward-looking (FL) households.
  - Sticky wages and sticky prices (Calvo-style contracts).
  - Trade adjustment costs.
  - Incomplete financial markets across countries.
  - Optional financial accelerator channel (Bernanke, Gertler, and Gilchrist (1999); Christiano, Motto, and Rostagno (2008)) described in Section A.6.
- For exposition, focus is on one economy since blocks are isomorphic.

### A.1 Firms and price setting
- Differentiated intermediate goods indexed by i ∈ [0,1]; each produced by a monopolistically competitive firm.
- Domestic demand for firm i:
  - Y_Dt(i) = [P_Dt(i) / P_Dt]^{-(1+θ_p)/θ_p} Y_Dt (A.1) with θ_p > 0.
- Export demand:
  - X_t(i) = [P_Mt^*(i) / P_Mt^*]^{-(1+θ_p)/θ_p} M_t^* (A.2).
- Production function (CES) for firm i:
  - Y_t(i) = [ω_K^{ρ/(1+ρ)} K_t(i)^{1/(1+ρ)} + ω_L^{ρ/(1+ρ)} (Z_t L_t(i))^{1/(1+ρ)}]^{1+ρ} (A.3).
  - Technology shock (log-linearized): z_t = ρ_z z_{t−1} + ε_{z,t} (A.4).
- Price setting:
  - Calvo probability of reoptimizing: 1 − ξ_t (domestic); non-optimizing firms reset domestic price as P_Dt(i) = π_{t−1}^{ι_p} π^{1−ι_p} P_Dt−1(i) with indexation parameter ι_p.
  - Optimal price maximization problem (when allowed) involves state-contingent discount factor ψ_{t,t+j} and Calvo survival ξ_p^j (A.5).
  - First-order condition (A.6).
- Export pricing assumes local currency pricing (LCP); log-linear deviation from law of one price:
  - δ_t^* = −p_{M,t}^* − s_t + p_{X,t} where p_{X,t} = p_{D,t} (A.7).
- Aggregation:
  - Domestic intermediate goods aggregator: Y_Dt = [∫_0^1 Y_Dt(i)^{1/(1+θ_p)} di]^{1+θ_p} (A.8).
  - Domestic price index: P_Dt = [∫_0^1 P_Dt(i)^{−θ_p} di]^{−1/θ_p} (A.9).
  - Foreign import index: M_t^* = [∫_0^1 X_t(i)^{1/(1+θ_p)} di]^{1+θ_p} (A.10) and price P_Mt^* (A.11).
- Final consumption and investment goods:
  - Final consumption CES aggregator (A.12): C_At = (ω_C^{ρ_C/(1+ρ_C)} C_Dt^{1/(1+ρ_C)} + (1−ω_C)^{ρ_C/(1+ρ_C)} (φ_Ct M_Ct)^{1/(1+ρ_C)})^{1+ρ_C}.
  - Consumption import adjustment cost φ_Ct quadratic form (A.13); adjustment costs depend on distributor’s import ratio relative to economy-wide ratio (external to distributors).
  - Distributor minimizes discounted expected costs to supply C_At (A.14).
  - Investment goods produced analogously with weight ω_I possibly different from ω_C.

### A.2 Households and wage setting
- Labor aggregation (Dixit-Stiglitz):
  - L_t = [∫_0^1 (ζ N_t(h))^{1/(1+θ_w)} dh]^{1+θ_w} (A.15); wage index W_t = [∫_0^1 W_t(h)^{−θ_w} dh]^{1/θ_w} (A.16).
  - Household-specific labor demand: N_t(h) = [W_t(h) / W_t]^{−(1+θ_w)/θ_w} L_t / ζ (A.17).
- Two household types:
  - Forward-looking (FL) households share = 1 − ω (denoted 1−ψ in text where HM share is ψ).
  - Hand-to-mouth (HM) households share = ψ.
- FL household preferences (utility functional):
  - Π_t ∑ β^j { 1/(1−σ) (C_{t+j}^O(h) − א C_{t+j−1}^O − C^O_v c_{t+j})^{1−σ} + χ_0 Z_{t+j}^{1−ρ}/(1−χ) (1−N_{t+j}(h))^{1−χ} + μ_0 F(MB_{t+j+1}(h) / P_{C,t+j}) } (A.18).
  - External habit around lagged aggregate consumption per capita of forward-looking agents C_{t−1}^O.
  - Consumption demand shock: v_{c,t} = ρ_v v_{c,t−1} + ε_{v_c,t} (A.19).
- FL household budget constraint (A.20) includes:
  - Consumption tax τ_{C,t}; investment price P_{I,t}; money balances MB; state-contingent bonds B_D; domestic and foreign government bonds B_G and B_F; nominal exchange rate S_t; taxes τ_{N,t} and τ_{K,t}; transfers TR_t; profit share Γ_t(h); adjustment cost on investment φ_{I,t}(h) (A.20–A.23).
- Capital accumulation: K_{t+1}(h) = (1−δ) K_t(h) + I_t(h) (A.21).
- Financial markets:
  - Domestic state-contingent bonds B_D are available (complete domestically); cross-border trade restricted to a single non-state contingent foreign bond.
  - Foreign bond intermediation cost depends on economy-wide net foreign assets ratio (A.22): φ_{b,t} = exp(−φ_b (B_{F,t+1} / (P_Dt Y_Dt))).
  - Price faced by home residents satisfies P_{B,t} = P_{B,t}^* φ_{b,t}; nominal interest rate i_t = 1/P_{B,t} − 1.
- Wage setting:
  - FL households set wages in Calvo-style staggered contracts with probability of reoptimization 1 − ξ_w; non-optimizing reset: W_t(h) = ω_{t−1}^{ι_w} ω^{1−ι_w} W_{t−1}(h) (A.24) with indexation parameter ι_w.
- HM households:
  - Nominal consumption spending equals current after-tax disposable income: P_{C,t} (1+τ_{C,t}) C_t^{HM}(h) = (1−τ_{N,t}) W_t(h) N_t(h) + TR_t(h) (A.25).
  - HM households set wage equal to average wage of optimizing households and work same hours as average FL household.

### A.3 Monetary policy
- Central bank policy rule with effective lower bound (ELB):
  - i_t = max[i_t^{SHADOW}, −i^{ELB}], where i_t is nominal policy rate measured as deviation from ELB.
  - Shadow policy rule:
    - i_t^{SHADOW} = (1−γ_i)[γ_π (π_{C,t} − π_C) + γ_x x_t + γ_Δx Δx_t] + γ_i i_{t−1}^{SHADOW} + ε_{i,t} (A.26).
  - x_t is model-consistent employment gap (percent deviation of actual employment from flexible-wage-and-price employment); ε_{i,t} is monetary policy shock.

### A.4 Fiscal policy
- Government debt evolution (aggregate end of period t debt D_{G,t+1}):
  - D_{G,t+1} = P_{C,t} G_t + TR_t^O + TR_t^{HM} − τ_{N,t} W_t L_t − τ_{C,t} P_{C,t} C_t − τ_{K,t} (R_{K,t} − δ P_{I,t}) K_t + (1 + i_{G,t−1}) D_{G,t} − (MB_{t+1} − MB_t) (A.27).
- Government spending process: (g_t − g) = ρ_G (g_{t−1} − g) + ε_{g,t} (A.28) with ε_{g,t} ~ N(0, σ_G).
- Labor income tax adjustment rule to stabilize debt/GDP and deficit:
  - τ_{N,t} − τ_N = υ_1 (τ_{N,t−1} − τ_N) + (1−υ_1)[υ_2 (d_{G,t} − d_G) + υ_3 (Δ d_{G,t+1} − Δ d_{G,t})] (A.29).
  - d_{G,t} = D_{G,t} / (4 P_t Ȳ) i.e., government debt as share of annualized nominal trend output.
- Government purchases do not directly affect household utility or private production technology.
- Long-term government debt approach following Krause and Moyen (2016); effective interest rate on newly issued debt:
  - i_{G,t}^{new} = ϖ_{new} i_t + (1−ϖ_{new}) E_t i_{G,t+1}^{new}, with ϖ_{new} = (i + ϖ)/(1 + i). Effective interest rate on debt stock updates with ϖ_{long} = 1 − (1−λ)/(1+π) approximately equals λ when π is low (π = 0.005 in calibration).

### A.5 Resource constraint and net foreign assets
- Aggregate resource constraint:
  - Y_{D,t} = C_{D,t} + I_{D,t} + φ_{I,t} + ζ^* ζ M_t^* (A.30).
- Final consumption allocation:
  - C_{A,t} = C_t + G_t (A.31).
- Private consumption per capita:
  - C_t = (1−ψ) C_t^O + ψ C_t^{HM} (A.32).
- Foreign imports split: M_t^* = M_{C,t}^* + M_{I,t}^* (A.33).
- Net foreign assets evolution:
  - P_{B,t}^* B_{F,t+1} φ_{b,t} = B_{F,t} + P_{M,t}^* ζ^* ζ M_t^* − P_{M,t} M_t (A.34).
- Foreign block assumed isomorphic to domestic block.

### A.6 Financial accelerator (capital services production)
- Augmented model includes financial accelerator following Bernanke, Gertler and Gilchrist (1999) and Christiano, Motto and Rostagno (2008):
  - Intermediate goods producers rent capital services from entrepreneurs at price R_{K,t} rather than from households.
  - Entrepreneurs purchase physical capital from competitive capital goods producers; to finance capital acquisition, entrepreneurs combine net worth with a bank loan and pay an external finance premium due to an agency problem.
  - Banks fund lending by issuing deposits to households at the central-bank set interest rate; households bear no credit risk.
  - Equilibrium: shocks to entrepreneurial net worth (leverage) induce fluctuations in corporate finance premium.
  - Debt contract is written in nominal terms (following Christiano, Motto and Rostagno (2008)).

### A.7 Solution method and calibration
- Frequency: calibrated at a quarterly frequency.
- Domestic country size parameter ζ_s set to a very small number so domestic economy is arbitrarily small relative to foreign country.
- Trade share of the small open economy set to 24 percent of GDP; pins down ω_C and ω_I under assumption that import intensity of consumption equals 1/2 that of investment.
- Parameters and calibration values (preserve exact numbers as in source):
  - ρ_C = ρ_I = 2.5.
  - Price markup θ_p = 0.2.
  - Import adjustment cost parameters: φ_{M_C} = φ_{M_I} = 1.
  - Financial intermediation parameter φ_b = 0.01.
  - Relative risk aversion parameter σ = 2.
  - Habit persistence parameter א = 0.8.
  - Labor market utility parameter χ_0 set so labor market activity comprises half of household time endowment; Frisch elasticity targeted to equal 1/2 implies χ = 4.
  - μ_0 ψ = 0.65 (as reported).
  - Investment adjustment cost parameter φ_I = 3.
  - Depreciation rate δ = 0.03 (consistent with annual depreciation rate of 12 percent).
  - CES parameter ρ (in production) set to −1 implying Leontief technology (zero elasticity of substitution).
  - Price markup θ_P = 0.2 and steady-state investment to output ratio of [20] percent (bracketed as in source).
  - Financial accelerator calibration (following Bernanke, Gertler and Gilchrist (1999)):
    - Monitoring cost μ = [0.12].
    - Default rate of entrepreneurs = [3] percent per year.
    - Variance of idiosyncratic productivity shocks to entrepreneurs = [0.28].
  - Calvo parameters:
    - Domestic price contract duration ξ_p = 0.92.
    - Import/export contract ξ_m = 0.90.
    - Wage contract duration ξ_w = 0.88.
  - Indexation:
    - Degree of price indexation ι_p = 1.
    - Wage and import price indexation ι_w = ι_m = 0.5.
  - Wage markup θ_W = 1/3.
  - Behavioral expectations for wage/price setting (Gabaix-style bounded rationality):
    - Cognitive discount parameter φ = 0.9 (replace forward-looking X_{t+1|t} with φ X_{t+1|t} in linearized Phillips curves).
  - Monetary rule parameters (A.26):
    - γ_i = 0.9.
    - γ_π = 1.5.
    - γ_x = 0.125.
    - γ_Δx = 0.25.
  - Discount factor β = 0.99875.
  - Inflation target = 2 percent implies steady state nominal interest rate = 2.5 percent.
  - Fiscal parameters:
    - Government spending share = 20 percent of steady state output.
    - Government debt to annualized GDP ratio b_G = 0.90.
    - Transfers to GDP ratio = 7 percent.
    - Steady state sales (VAT) tax rate τ_C = 10 percent.
    - Capital tax rate τ_K = 20 percent.
    - Given annualized steady state real interest rate of 0.5 percent, steady state labor income tax rate τ_N = 0.35.
    - Tax adjustment rule: υ_1 = 0.985, υ_2 = υ_3 = 0.1.
    - Bond maturity probability ϖ = 0.125 (two-year steady state maturity structure).
  - Price inflation steady-state parameter π = 0.005 used in approximation for ϖ_{long}.
- Solution approach:
  - Log-linearize model around non-stochastic steady state.
  - Render nominal variables stationary by suitable transformations.
  - Unconstrained model solved via Anderson and Moore (1985) algorithm implementing Blanchard and Kahn (1980) solution method.

*Source: Appendix A. The Open Economy DSGE Model (wpiea2022170-print-pdf).*

### Appendix B

### Appendix B

### Figure B.1 — Robustness with respect to initial AIT gap
- The appendix contains a figure titled "Figure B.1. Robustness with respect to initial AIT gap."
- No numeric details, chart data, or figure panels are present in the supplied content for this figure.

### Document identifiers and location
- Page: 47
- Report title: Effective Fiscal-Monetary Interactions in Severe Recessions
- Working Paper No.: WP/2022/170

*Source: wpiea2022170-print-pdf - Appendix B*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022170-print-pdf.pdf_