## wpiea2022222-print-pdf — Introduction

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---

### Macroeconomic impact of the COVID-19 pandemic
- Lockdowns, travel restrictions and containment measures in 2020 produced a rapid drop in economic activity larger than after the Global Financial Crisis (GFC) of 2008.
- Employment losses were significant, particularly in the U.S.; the in-person services sector was hardest hit.
- Labor market adjustment in the euro area occurred mainly through the intensive margin via Job Retention Schemes.

### Monetary and fiscal policy responses (magnitudes and instruments)
- U.S. monetary policy:
  - Federal Funds Rate (FFR) cut to the range of 0 to 0.25 percent, close to the Effective Lower Bound (ELB).
  - Fed expanded balance sheet and re-commenced asset purchases.
- Euro area monetary policy:
  - Deposit Facility Rate (DFR) at -0.5 percent.
  - ECB introduced the Pandemic Emergency Purchase Program (PEPP) and expanded Asset Purchase Programs (APP).
- Fiscal policy:
  - U.S. cumulative fiscal stimulus during 2020–21 around 15 percent of GDP (difference between recorded fiscal balance and pre-pandemic projection in the 2019 WEO).
  - Euro area fiscal stimulus during 2020–21 around 13 percent of GDP by the same metric.
  - U.S. Congress approved US$1.9 trillion in pandemic-related spending in March 2021 (American Rescue Plan, ARP).
  - Next Generation EU (NGEU) package of €800 billion (loans and grants) to be distributed during 2021–27.
  - U.S. Bipartisan Infrastructure Framework (BIF) in November 2021 adds close to US$600 billion (3 percent of GDP) of public investment.
  - Preliminary estimates: close to 77 percent of NGEU will finance additional fiscal spending in the euro area with 80 percent for public investments.

### Changes in monetary policy frameworks
- United States:
  - Shift from Flexible Inflation Targeting (FIT) to Flexible Average Inflation Targeting (FAIT) in August 2020.
  - Policy guidance: maintain FFR at 0–0.25 percent until labor market conditions reach levels consistent with maximum employment and inflation has risen to 2 percent and is on track to moderately exceed 2 percent for some time.
- Euro area:
  - ECB Strategy Review concluded July 2021 formalized symmetry around the two percent inflation objective and removed ambiguity of “below, but close to, two percent.”
  - Revised forward guidance underscores tolerance for inflation temporarily above two percent and commitment to current key policy rates until inflation is forecast to durably reach two percent within the medium-term projection horizon.
- Both central banks cited a decline in the neutral policy rate as motivation for strategy changes; a lower neutral rate implies less scope to lower policy rates before being constrained by the ELB.

### Planned public investment (nominal amounts and shares)
- U.S. BIF: close to US$600 billion (3 percent of GDP) in public investment for transportation, water, broadband, and maintenance.
- NGEU: around €800 billion (around 6 percent of euro area GDP) in grants and loans during 2021–27; significant public investment component.
- Additional legislative proposals noted: Build Back Better Act (BBB) around 7½ percent of GDP proposed but not passed; a smaller Inflation Reduction Act approved August 2022 (note: described in a footnote).

### Modelling framework and scope
- Framework: variant of Erceg and Lindé (2013) two-country New Keynesian model (Fed’s SIGMA), calibrated to the U.S. and the euro area.
- Model features:
  - Open-economy, general equilibrium.
  - Subjective discounting in price setting to address the forward-guidance puzzle.
  - Analyzes interactions between fiscal and monetary policies across domestic and foreign economies.
- Exclusions: short-time work schemes or various moratoria are beyond the scope.

### Key model findings and quantitative impacts (selected)
- FAIT in the U.S. (given an initially negative AIT gap):
  - Adoption of FAIT delayed the FFR liftoff by at least two quarters.
  - Weakened the U.S. dollar.
  - Higher quarterly U.S. output and core inflation over the medium term, with peak impacts of 1.5 percent and 0.3 percentage points respectively, relative to FIT.
  - Spillovers to the euro area boost quarterly output by up to 0.4 percent over the medium term.
  - By late 2021, the U.S. AIT gap had fallen to zero (with expansionary fiscal and monetary policy contributing to closing that gap).
- Euro area strategy scenarios:
  - Adopting fully symmetric FIT in the euro area implies ECB liftoff would be delayed by one–two quarters relative to the previous regime, boosting median inflation by a peak of 0.2 percentage points over the medium term and output by 1.6 percent.
  - If the ECB had adopted a FAIT approach similar to the Fed, the model indicates this would have further boosted core inflation by a peak of 0.3 percentage points and output by 1.75 percent.

### Peak-impact scenario highlights (preserved entries)
- FIT to FAIT in the U.S.: U.S. output peak impact 1.5 percent; U.S. inflation 0.3 percentage points; euro area output 0.4 percent; euro area inflation 0.1 percentage points.
- Asymmetric to symmetric in the euro area: euro area output peak 1.6 percent; euro area inflation peak 0.2 percentage points.
- FIT to FAIT in the euro area: euro area output 1.7 percent; euro area inflation 0.35 percentage points; U.S. output 0.3 percent; U.S. inflation 0.03 percentage points.
- FAIT in the U.S. with ARP: U.S. output peak 4 percent; U.S. inflation peak 0.35 percentage points; euro area output 0.6 percent; euro area inflation 0.1 percentage points.
- US Fiscal package BIF (incremental): U.S. output 0.75 percent; U.S. inflation 0.1 percentage points; euro area output 0.1 percent; euro area inflation 0.03 percentage points.
- Euro area NGEU and slower consolidation combined: U.S. output 4 percent; euro area output 3.5 percent; U.S. inflation 0.4 percentage points; euro area inflation 0.5 percentage points.

### Fiscal–monetary interaction and ELB role
- Binding ELB increases the macroeconomic impact of fiscal policy compared to an unconstrained monetary policy environment.
- A more accommodative monetary policy reduces the debt burden and prevents crowding-out of private investment from fiscal stimulus.
- Combined monetary regime changes (FAIT and FIT) and fiscal expansion are mutually reinforcing, producing larger output gains with modest additional inflation and limited adverse international spillovers when AIT gaps are negative.

### Model limitations and interpretation
- Baseline Phillips curve slopes imply fiscal stimulus and new monetary regimes explain around one third of the unexpected inflation in the U.S. during 2021 and around one quarter in the euro area.
- If the price and wage Phillips curves are assumed twice as steep, the model explains around 70 percent of the U.S. unexpected inflation.
- Exchange rate and external balance impacts of combined policies are relatively modest in the model.

### Policy implications and considerations (policy-relevant bullets)
- Adopting FAIT in the U.S. and FIT/asymmetric targeting changes in the euro area can provide meaningful output support when AIT gaps are negative, with only mild inflationary effects.
- Fiscal stimulus is more effective when monetary policy is constrained by the ELB; coordination of accommodative monetary regimes with fiscal investment amplifies output gains and mitigates hysteresis.
- Composition matters: government investment yields larger output multipliers than untargeted transfers; splitting stimulus evenly between investment and transfers roughly halves the output impact.
- Monitoring Phillips curve slopes and cost-push factors is critical, as steeper slopes materially increase the demand-side contribution of policy to inflation outcomes.

---

### Box 1. The Slope of the New Keynesian Phillips Curve — Calibration and implications

### Calibration choices
- Baseline slope of domestic price Phillips curve = 0.007.
- Alternative (steeper) slope = 0.014 (twice as steep).
- Estimation motivation: Smets and Wouters (2007) estimated over 1985Q1–2021Q4 yields a slope nearly double that estimated over 1985Q1–2019Q4.

### Implications under steeper Phillips curve
- U.S.:
  - Combined ARP and BIF raise quarterly U.S. core inflation by around 0.2-0.3 percentage points in the near term under the steeper slope.
  - U.S. fiscal stimulus can explain around 0.5 percentage points of average unexpected core inflation in 2021 and 0.8 percentage points of the difference at end-2021.
- Euro area:
  - Slower fiscal consolidation (government consumption +1 percentage point per year for two years) changes core inflation by around 0.2-0.3 percentage points under the steeper slope.
  - Adding U.S. fiscal packages with slower euro consolidation boosts euro area quarterly output up to 3.5 percent and core inflation by 0.5 percentage points.
- Monetary regime effects:
  - Peak impact of introducing FAIT on core inflation would be around 1-1.1 percentage points higher in the near term under the steeper Phillips Curve.
- Contribution to 2021 inflation surprise:
  - Baseline: combined fiscal and monetary changes explain around 30 percent of U.S. unexpected inflation in 2021 and around 24 percent in the euro area.
  - Steeper Phillips curve: policy measures account for 70 percent of the surprise in 2021.

### Conclusion from Box 1
- FAIT boosted output and inflation in the U.S. and could have similar effects in the euro area.
- Significant fiscal support in 2021 had substantial macroeconomic impact and reinforced monetary accommodation, especially when the ELB binds.
- Even with steeper Phillips curves, substantial unexplained factors remain for the 2021 inflation surge.

---

### Appendix I. Technical Appendix — Model structure, calibration and key parameters

### Model structure (core features)
- Variant of Erceg and Lindé (2013) SIGMA model with discounting in pricing block to address forward-guidance puzzle.
- Two-country model (U.S. and euro area), equally sized; endogenous investment; hand-to-mouth households; sticky wages and prices; trade adjustment costs; incomplete international financial markets.
- Optional financial accelerator paralleling Bernanke, Gertler and Gilchrist (1999) and Christiano, Motto and Rostagno (2008).

### Fiscal instruments and calibration notes
- Taxes on capital τ_Kt, consumption τ_Ct, labor income τ_N,t; government purchases g_t; transfers to HM households tr_t^HM; general transfers tr_t^O.
- Government investment proxied via link: one percentage point increase in government capital stock has a direct impact on output of around three percent (accounting for time to build).

### Baseline initial conditions and exit timing
- Initial AIT gaps: U.S. = -0.5 percent (annualized); euro area = -0.8 percent (annualized).
- Steady state nominal interest rates i̅_US and i̅_EA set to 2.5 percent annually.
- Baseline implies exit from ELB after 15 quarters (U.S., mid-2024) and 17 quarters (euro area, late 2024).

### Selected quantitative calibration entries (values preserved)
- Trade share 9.3% of GDP.
- Share of HM agents χ = 0.55.
- Investment adjustment cost φI = 3.
- Depreciation δ = 0.025 (annual depreciation rate of 10 percent).
- Calvo domestic price contract duration ξp = 0.92; ξm = 0.90; ξw = 0.88.
- Degree of price indexation ιp = 1; ιw = ιm = 0.5.
- Cognitive discounting φ = 0.95 in expectations.
- Interest rate smoothing γEA = γUS = 0.92.
- AIT/FIT gap coefficients γπ: US = 4.3; ECB = 5.
- Discount factor β = 0.99875.
- Bond maturing probability ϖ = 0.055.
- Steady state gov’t debt/GDP (%) bG: US: 130; EA: 100.
- Gov’t consumption/GDP (%) gy: US: 19; EA: 25.
- Steady state transfers/GDP (%) trtO = 6.75; trtHM = 8.25.
- Steady state labor income tax rate (%) τN: US: 32; EA: 30.
- Steady state consumption tax rate (%) τC: US: 7; EA: 20.
- Steady state capital tax rate (%) τK: US: 21; EA: 26.
- Steady state inflation target π̄ = 2 (annual, %); steady state nominal interest rate i = 2.5 (annual, %).

### Modeling implications and solution method
- Log-linearization around non-stochastic steady state; Anderson and Moore (1985) algorithm used for unconstrained model solution.
- Accurate accounting for market prices of expected ELB episodes in early 2021 requires aggressive inflation response coefficients in the policy rules; without them the model cannot replicate those priced expectations.

---

*IMF Working Paper — U.S. and Euro Area Monetary and Fiscal Interactions During the Pandemic: A Structural Analysis (wpiea2022222-print-pdf).*

### Introduction ...........................................................................................................

### wpiea2022222-print-pdf - Introduction ...........................................................................................................

### Macroeconomic impact of the COVID-19 pandemic
- Lockdowns, travel restrictions and containment measures in 2020 produced a rapid drop in economic activity larger than after the Global Financial Crisis (GFC) of 2008.
- Employment losses were significant, particularly in the U.S.; the in-person services sector was hardest hit.
- Labor market adjustment in the euro area occurred mainly through the intensive margin via Job Retention Schemes.

### Monetary and fiscal policy responses
- U.S. monetary policy:
  - Federal Funds Rate (FFR) cut to the range of 0 to 0.25 percent, close to the Effective Lower Bound (ELB).
  - Fed expanded balance sheet and re-commenced asset purchases.
- Euro area monetary policy:
  - Deposit Facility Rate (DFR) at -0.5 percent.
  - ECB introduced the Pandemic Emergency Purchase Program (PEPP) and expanded Asset Purchase Programs (APP).
- Fiscal policy:
  - U.S. cumulative fiscal stimulus during 2020–21 around 15 percent of GDP (difference between recorded fiscal balance and pre-pandemic projection in the 2019 WEO).
  - Euro area fiscal stimulus during 2020–21 around 13 percent of GDP by the same metric.
  - U.S. Congress approved US$1.9 trillion in pandemic-related spending in March 2021 (American Rescue Plan, ARP).
  - Next Generation EU (NGEU) package of €800 billion (loans and grants) to be distributed during 2021–27.
  - U.S. Bipartisan Infrastructure Framework (BIF) in November 2021 adds close to US$600 billion (3 percent of GDP) of public investment.
  - Preliminary estimates: close to 77 percent of NGEU will finance additional fiscal spending in the euro area with 80 percent for public investments.

### Changes in monetary policy frameworks
- United States:
  - Shift from Flexible Inflation Targeting (FIT) to Flexible Average Inflation Targeting (FAIT) in August 2020.
  - Policy guidance: maintain FFR at 0–0.25 percent until labor market conditions reach levels consistent with maximum employment and inflation has risen to 2 percent and is on track to moderately exceed 2 percent for some time.
- Euro area:
  - ECB Strategy Review concluded July 2021 formalized symmetry around the two percent inflation objective and removed ambiguity of “below, but close to, two percent.”
  - Revised forward guidance underscores tolerance for inflation temporarily above two percent and commitment to current key policy rates until inflation is forecast to durably reach two percent within the medium-term projection horizon.
- Both central banks cited a decline in the neutral policy rate as motivation for strategy changes; a lower neutral rate implies less scope to lower policy rates before being constrained by the ELB.

### Planned public investment
- U.S. BIF: close to US$600 billion (3 percent of GDP) in public investment for transportation, water, broadband, and maintenance.
- NGEU: around €800 billion (around 6 percent of euro area GDP) in grants and loans during 2021–27; significant public investment component.
- Additional legislative proposals noted: Build Back Better Act (BBB) around 7½ percent of GDP proposed but not passed; a smaller Inflation Reduction Act approved August 2022 (note: described in a footnote).

### Modelling framework and scope
- Framework: variant of Erceg and Lindé (2013) two-country New Keynesian model (Fed’s SIGMA), calibrated to the U.S. and the euro area.
- Model features:
  - Open-economy, general equilibrium.
  - Subjective discounting in price setting to address the forward-guidance puzzle.
  - Analyzes interactions between fiscal and monetary policies across domestic and foreign economies.
- Exclusions: short-time work schemes or various moratoria are beyond the scope.

### Key model findings and quantitative impacts
- FAIT in the U.S. (given an initially negative AIT gap defined as the difference between the 2 percent target and average inflation over the past 60 months):
  - Adoption of FAIT delayed the FFR liftoff by at least two quarters.
  - Weakened the U.S. dollar.
  - Higher quarterly U.S. output and core inflation over the medium term, with peak impacts of 1.5 percent and 0.3 percentage points respectively, relative to FIT.
  - Spillovers to the euro area through trade and financial channels boost quarterly output by up to 0.4 percent over the medium term.
  - By late 2021, the U.S. AIT gap had fallen to zero (with expansionary fiscal and monetary policy contributing to closing that gap).
- Euro area strategy scenarios:
  - ECB’s prior strategy of “inflation rates below, but close to, 2 percent over the medium term” is modeled by assuming stronger ECB reactions when projected inflation one year ahead exceeds 2.5 percent.
  - Under stochastic shock uncertainty, adopting fully symmetric FIT in the euro area implies ECB liftoff would be delayed by one–two quarters relative to the previous regime, boosting median inflation by a peak of 0.2 percentage points over the medium term and output by 1.6 percent.
  - If the ECB had adopted a FAIT approach similar to the Fed, the model indicates this would have further boosted core inflation by a peak of 0.3 percentage points and output by

*Source: IMF Working Paper — Introduction section of "U.S. and Euro Area Monetary and Fiscal Interactions During the Pandemic: A Structural Analysis" (wpiea2022222-print-pdf).*

### 1.75 percent. This improvement in inflation and activity outcomes were due to the sizeable initial euro area AIT

### U.S. and Euro Area Monetary and Fiscal Interactions During the Pandemic: A Structural Analysis

### Key findings and summary impacts
- Adopting FAIT in the U.S. raises quarterly U.S. output by up to 1.5 percent and U.S. core inflation by up to 0.3 percentage points over the medium term, relative to FIT, given negative initial AIT gaps and an ELB constraint.
- FAIT in the U.S. produces positive spillovers to the euro area, boosting euro area quarterly output by up to 0.4 percent and euro area core inflation slightly (up to 0.1 percentage points), via a weaker U.S. dollar and trade channel effects.
- The ARP (U.S.) is shown to boost U.S. output by 4 percent during its first year of implementation, with core inflation higher by 0.3 percentage points.
- Implementing the U.S. BIF would boost quarterly U.S. output by 0.75 percent (additional to the impact of the ARP) and U.S. core inflation by 0.1 percentage points; it would also boost euro area output and core inflation both by an additional 0.1 percentage points via the trade channel.
- The NGEU package in the euro area added around 0.5 percentage points to quarterly output in its first year of implementation, with the impact on quarterly output projected to peak in the third year at around 1.3 percent; impact on core inflation is 0.15 percentage points.
- A two-year hike in government consumption and investment spending by one percent of GDP per year in the euro area boosts euro area quarterly output by an average of over 1 percent and core inflation by 0.1 percentage points during the two years; if the same amount is split evenly between government investment and untargeted transfers, the impact would be roughly halved.
- The combination of FAIT in the U.S., FIT in the euro area, additional government investment in both regions, the BIF, and a slower fiscal consolidation in the euro area produces combined peak impacts: euro area output peaking at around 3½ percent with core inflation higher by around 0.5 percentage points; U.S. output peak impact of 1¼ percent with peak inflationary impact of 0.2 percentage points.
- The implementation of fiscal stimulus and new monetary regimes can explain around one third of the unexpected inflation in the U.S. during 2021 and around one quarter in the euro area; this fraction rises to around 70 percent if the price and wage Phillips curves are assumed to be twice as steep.

### Monetary policy regime changes and mechanisms
- FAIT versus FIT:
  - FAIT in the U.S. uses a 5-year trailing average of core inflation (AIT) in the shadow rate rule; negative AIT gaps lead to more accommodative policy to offset past undershooting of the 2 percent target.
  - Under FAIT in the U.S., the negative AIT term lowers the shadow rate relative to FIT, delaying liftoff from the ELB by two quarters.
  - Under FAIT, the model’s U.S. shadow rate decomposition shows weaker near-term shadow rates (teal area in figures) and higher medium-term output and inflation relative to FIT.
- ELB specification:
  - U.S. ELB treated as the lower point of the actual FFR 0--0.25 target range; FFR formula used: FFR_t = max[4 i_t^US, 0].
  - Euro area conditional ELB assumed at -1/2 (i.e., -50 basis points); EONIA_t = max[4 i_t^EA, −1/2].
- Eurosystem policy rule nonlinearities:
  - Euro area shadow rate rule augmented by a penalty term triggered when expected inflation exceeds the two percent target by more than ½ percentage points, producing nonlinearity.

### Fiscal packages: magnitudes, composition, and interactions
- U.S. fiscal measures:
  - ARP: peak U.S. output boost of 4 percent in its first year; core inflation +0.3 percentage points.
  - BIF (incremental on top of ARP): quarterly U.S. output +0.75 percent; U.S. core inflation +0.1 percentage points; brings forward FFR liftoff by an additional quarter under FAIT.
- Euro area fiscal measures:
  - NGEU: +0.5 percentage points to quarterly output in year 1; peak quarterly output ~1.3 percent in year 3; core inflation +0.15 percentage points.
  - Slower fiscal consolidation (two-year hike in gov consumption and investment of 1 percent of GDP per year): euro area quarterly output + over 1 percent on average during the two years; core inflation +0.1 percentage points.
- Fiscal–monetary complementarities:
  - Binding ELB increases the macroeconomic impact of fiscal policy compared to an unconstrained monetary policy environment.
  - A more accommodative monetary policy reduces the debt burden and prevents crowding-out of private investment from fiscal stimulus.
  - Combined monetary regime changes (FAIT and FIT) and fiscal expansion are mutually reinforcing, producing larger output gains with modest additional inflation and limited adverse international spillovers when AIT gaps are negative.

### Model structure, calibration, and baseline assumptions
- Model type and features:
  - Two-country general equilibrium New Keynesian model with endogenous capital and labor supply; closely follows Erceg, Guerrieri and Gust (2006) and Erceg and Lindé (2013).
  - Features sticky nominal wages and prices, habit persistence in consumption, investment adjustment costs, a financial accelerator, and hand-to-mouth households to match fiscal transmission.
  - Open-economy channels: trade and financial links; trade share set at about 9 percent of GDP for each region; import intensity of consumption goods set to 3/4 of that of investment goods.
  - Exchange rate determined by an uncovered interest parity (UIP) condition with local currency pricing.
- Fiscal instruments and calibration:
  - Taxes on capital τ_Kt, consumption τ_Ct, and labor income τ_N,t; government purchases g_t; transfers to hand-to-mouth households tr_t^HM; general transfers tr_t^O.
  - Government investment proxied by link from some government purchases to medium-term productivity: a one percentage point increase in government capital stock has a direct impact on output of around three percent (accounting for time to build).
- Baseline initial conditions and outlook:
  - Initial AIT gaps set to -0.5 percent (U.S.) and -0.8 percent (euro area) in annualized terms; both central banks constrained by the ELB.
  - Steady state nominal interest rates i̅_US and i̅_EA set to 2.5 percent annually.
  - Baseline implies exit from ELB after 15 quarters (U.S., mid-2024) and 17 quarters (euro area, late 2024).
  - Baseline calibrated to IMF staff outlook early 2021; includes negative consumption preference shocks, persistent negative technology shocks, and supply-chain related price markup shocks; counterfactual without NGEU is shown.

### Quantitative scenario and peak-impact table (selected entries preserved)
- FIT to FAIT in the U.S. (initial AIT gap, ELB): Peak impact on U.S. output 1.5 percent; on U.S. inflation 0.3 percentage points; euro area output 0.4 percent; euro area inflation 0.1 percentage points.
- Asymmetric to symmetric in the euro area (initial AIT gap, ELB, stochastic simulation, modal result): Peak impact on euro area output 1.6 percent; peak impact on euro area inflation 0.2 percentage points.
- FIT to FAIT in the euro area (initial AIT gap, ELB): Peak impact on euro area output 1.7 percent; euro area inflation 0.35 percentage points; U.S. impacts smaller (U.S. output 0.3 percent; U.S. inflation 0.03 percentage points).
- FAIT in the U.S. with ARP: U.S. output peak 4 percent; U.S. inflation peak 0.35 percentage points; euro area output 0.6 percent; euro area inflation 0.1 percentage points.
- US Fiscal package BIF (incremental): U.S. output 0.75 percent; U.S. inflation 0.1 percentage points; euro area output 0.1 percent; euro area inflation 0.03 percentage points.
- Euro area NGEU and slower consolidation combined: (4)+(6) yields peak impacts of U.S. output 4 percent; euro area output 3.5 percent; U.S. inflation 0.4 percentage points; euro area inflation 0.5 percentage points.

### Model limitations and interpretation
- The model implies fiscal stimulus and new monetary regimes are insufficient to explain the full unexpected rise in inflation in 2021; only around one third (U.S.) and one quarter (euro area) of unexpected inflation is explained under baseline Phillips curve slopes.
- If the price and wage Phillips curves are assumed twice as steep, the model explains around 70 percent of the U.S. unexpected inflation and a larger share overall, with stronger resonance in the U.S. than the euro area due to subdued wage growth in the euro area and energy-driven inflation there.
- Exchange rate and external balance impacts of combined policies are relatively modest in the model.

### Policy implications and considerations
- Adopting FAIT in the U.S. and FIT/asymmetric targeting changes in the euro area can provide meaningful output support when AIT gaps are negative, with only mild inflationary effects.
- Fiscal stimulus is more effective when monetary policy is constrained by the ELB; coordination of accommodative monetary regimes with fiscal investment amplifies output gains and mitigates hysteresis.
- Composition of fiscal spending matters: government investment yields larger output multipliers than untargeted transfers; splitting stimulus evenly between investment and transfers roughly halves the output impact.
- Monitoring Phillips curve slopes and cost-push factors is critical, as steeper slopes materially increase the demand-side contribution of policy to inflation outcomes.

*IMF Working Papers — U.S. and Euro Area Monetary and Fiscal Interactions During the Pandemic: A Structural Analysis*

### 0.1 percentage points, roughly 15–20 percent of the domestic impact in the U.S.

### wpiea2022222-print-pdf - 0.1 percentage points, roughly 15–20 percent of the domestic impact in the U.S.

### Changing the Euro Area monetary regime: symmetric FIT vs. asymmetric AIT
- Stochastic simulations show adoption of a symmetric FIT rule in the euro area would delay the median liftoff date by one-two quarters relative to a market-perceived asymmetric inflation targeting framework.
- Comparing symmetric FIT to asymmetric targeting (median vs. baseline) implies peak medium-term impacts of:
  - Up to 1.6 percent to quarterly euro area output.
  - 0.2 percentage points to quarterly euro area core inflation.
- A symmetric FIT regime limits downside GDP risk and contains deflation risk relative to an asymmetric rule that responds more aggressively to expected inflation impulses exceeding 2.5 percent per annum.
- When the U.S. regime remains FAIT, shifting the euro area from FIT to AIT (given a large negative AIT gap of -0.8 percent) puts downward pressure on the euro area shadow rate in the near term; conversely, adopting FAIT would:
  - Boost euro area quarterly output by a peak of 1.7 percent over the medium term beyond the FIT vs. “below, but close to” regime switch.
  - Boost euro area core inflation by a peak of 0.35 percentage points over the medium term beyond the FIT switch.
- The euro area’s larger negative initial AIT gap (around -0.8 percent vs. - -0.5 percent in the U.S.) implies in principle larger gains from a regime shift, but ECB’s more limited policy-rate maneuvering space constrains those gains.
- If the ELB is not binding, the larger negative euro AIT gap yields a larger unconstrained boost to output (peak effect 2.5 percent in euro area versus 2 percent in the U.S.).

### Spillovers between U.S. and euro area under alternative monetary regimes
- A more accommodative euro area policy under FAIT weakens the euro relative to the U.S. dollar.
- Net spillovers to U.S. output and inflation from euro area FAIT remain positive but relatively small.

### U.S. fiscal packages in 2020–2021: composition and modeled treatment
- Pandemic relief (ARP and earlier acts):
  - ARP: US$1.9 trillion (around 8½ percent of GDP), March 2021.
    - Composition highlighted in the model:
      - Stimulus checks: 2 percent of GDP.
      - Expanded unemployment benefits: 1.5 percent of GDP.
      - Expansions of Child Tax Credit and Earned Income Tax Credit: 0.5 percent of GDP.
      - Government consumption (health expenditure and state/local government expenditure): over 1.5 percent of GDP.
  - CARES Act: US$2.2 trillion (around 10 percent of GDP), March 2020.
  - Appropriations Bill: US$900 billion (around 4 percent of GDP), December 2020.
- Public investment and structural proposals:
  - BIF (Infrastructure Investment and Jobs Act): US$1.2 trillion, November 2021.
    - Includes around US$600 billion in newly planned public investment in transportation, broadband and water infrastructure.
  - BBB Act (House-passed version): US$1.75 trillion (8 percent of GDP), November 2021; would fund social spending and climate initiatives up to ten years (subject to spending items).
    - House-passed BBB composition includes transfers to households (1.5 percent of 2021 GDP), paid family leave (0.9 percent of 2021 GDP), universal pre-school (0.5 percent of 2021 GDP), childcare (1.2 percent of GDP), home care (0.6 percent of GDP), and climate-related measures (2.4 percent of 2021 GDP).
    - The model assumes a one-year lag in BBB implementation relative to the House schedule due to Senate delays.
  - Tax measures in BIF/House BBB are modeled as modest; no increases to tax rates are included in model simulations.

### Modeled impacts of U.S. fiscal packages on U.S. output, monetary policy, and spillovers
- ARP impacts:
  - Quarterly output boosted by up to 4 percent over the medium term (reflecting size, frontloaded phasing, and transfers to ‘hand to mouth’ households).
  - Implied cumulative fiscal multiplier from the ARP: 0.8 after one year and 0.8 after three years.
- BIF impacts:
  - Peak additional quarterly output effect of 0.75 percent.
  - Implied cumulative fiscal multiplier from the BIF: 1.3 after three years (reflecting longer horizon and public investment share).
- BBB (if passed and implemented) impacts:
  - Would boost quarterly output by a further 0.6 percent further out in the medium term.
- ELB interaction:
  - Impact on output from fiscal packages is larger than in a model without an ELB constraint, reflecting added benefits when monetary policy is constrained.
  - Fiscal multipliers reported are consistent with literature estimates above 1 when monetary policy is at the ELB.
- Monetary policy responses and inflation:
  - Implementing ARP+BIF brings forward the FFR liftoff date by 2 quarters according to the FAIT rule in the model.
  - Inflation is higher by 0.35 percentage points in the near term relative to a scenario without the 2021 U.S. fiscal packages.
  - BBB would steepen monetary tightening, with a peak impact on inflation of around 0.1 percentage points.
- Spillovers to euro area from U.S. fiscal packages:
  - U.S. packages tighten U.S. monetary policy and strengthen the U.S. dollar.
  - Euro area exports rise due to euro depreciation and stronger U.S. demand, deteriorating the U.S.–euro area bilateral trade balance.
  - Peak euro area impacts:
    - Output: 0.6 percent.
    - Inflation: 0.1 percentage points.

### Euro area fiscal trajectory: NGEU and higher government investment
- NGEU package assumptions and modeled effects:
  - NGEU: €800 billion (or 6 percent of GDP).
  - Assumed that 77 percent of €800 billion will lead to additional fiscal measures; of that, 80 percent is via public investment.
  - Without NGEU, quarterly output and inflation would have been around 0.5 and 0.05 percentage points lower in the first year of implementation.
  - By the third year of implementation, the NGEU’s impact on quarterly output rises to over one percentage point, with the impact on inflation reaching almost 0.15 percentage points.
  - The implied cumulative fiscal multiplier from NGEU over the first three years: 1.4.
  - NGEU brings forward liftoff of the ECB policy rate by around one quarter in the model, all else equal.
- Alternative higher government spending scenario:
  - If government spending (public consumption and investment) is higher by 1 percent of GDP each year for two years (quarters 4 through 12):
    - Quarterly peak of euro area output would be higher by 1.4 percent.
    - Implied cumulative multiplier over this two-year period: 1.3.
- Composition effects:
  - Changing composition to half government spending and half untargeted transfers to all households lowers the implied fiscal multiplier from 1.3 to 0.6.
  - That composition change reduces peak quarterly output impact to up to 0.6 percent and peak core inflation impact to 0.1 percentage points.
- ELB interaction in euro area:
  - Additional spending has a larger impact on output when monetary policy is constrained by the ELB than when it is not.
  - Higher output and inflation coincide with an earlier liftoff of the ECB policy rate by around two quarters in the case of higher investment.

### Synchronized fiscal policy changes (U.S. and euro area)
- Combining U.S. ARP and BIF with a slower pace of fiscal consolidation in the euro area (1 percent of GDP per year higher spending for two years, quarters 4 through 12) yields mutually reinforcing effects:
  - The combined impact on U.S. and euro area output and inflation is larger than the sum of individual impacts from these policies simulated separately.
  - Effects are particularly pronounced in the euro area.

### Spillovers from euro area fiscal stimulus to the U.S.
- Spillovers to the U.S. from euro area slower consolidation or higher investment are small:
  - Peak impact on U.S. output around ¼ percent.
  - Impact on U.S. inflation effectively zero.
- Note: As the euro area is treated as a single entity in the model, these spillovers do not account for heterogeneity across member states; more stimulus in countries with stronger ties to the U.S. could generate larger spillovers.

*IMF Working Papers — U.S. and Euro Area Monetary and Fiscal Interactions During the Pandemic: A Structural Analysis*

### Box 1. The Slope of the New Keynesian Phillips Curve

### Box 1. The Slope of the New Keynesian Phillips Curve

### Calibration and empirical motivation
- Baseline calibration: estimated slope (coefficient on current marginal cost) of the domestic price Phillips curve equals 0.007.
- Alternative (steeper) calibration: slope set to 0.014 (twice as steep).
- Motivation: estimating the Smets and Wouters (2007) model over 1985Q1–2021Q4 (including post-COVID) yields an estimated slope nearly double that estimated using only the pre-COVID sample (1985Q1–2019Q4).
- Literature evidence: non-linear Phillips Curves that steepen when inflation is higher (Forbes, Collins and Gagnon, 2021; Linde and Trabandt, 2019).

### Inflationary impact of fiscal policy (model findings)
- U.S.:
  - Combined impact of the ARP and BIF on quarterly U.S. core inflation would be around 0.2-0.3 percentage points higher in the near term under the steeper Phillips Curve.
  - U.S. fiscal stimulus can explain around 0.5 percentage points of the average unexpected core inflation in 2021 and 0.8 percentage points of the difference at the end of the year.
- Euro area:
  - Slower fiscal consolidation in the euro area (government consumption higher by one percentage point per year for two years) would change core inflation by a similar amount (around 0.2-0.3 percentage points under the steeper Phillips Curve).
  - Adding the U.S. fiscal packages to a simulation with slower euro area consolidation boosts euro area quarterly output by up to 3.5 percent over the medium term, while core inflation is higher by 0.5 percentage points.
- Cumulative fiscal multipliers implied by the model from implementing the ARP, BIF and NGEU programs and having a slower pace of euro area fiscal consolidation are above one.
- The impact of fiscal support is larger for as long as the ELB is binding.

### Inflationary impact of new monetary regimes (model findings)
- Peak impact of introducing FAIT on core inflation would be around 1-1.1 percentage points higher in the near term under the steeper Phillips Curve, in both the U.S. and the euro area.
- Under baseline calibration:
  - Introduction of FAIT in the U.S. and symmetric FIT in the euro area can explain around 0.2 percentage points on average of the difference between U.S. core inflation and the October 2020 WEO.
  - For the euro area, the amount of unexpected core inflation in 2021 explained by the new monetary regimes is small, at less than 0.02 percentage points.
- FAIT creates an upward move in near-term inflation expectations, lowering the ex-ante real interest rate, boosting demand, and helping return the economy to full employment and 2 percent inflation more quickly.
- Formalizing a symmetric inflation target in the euro area (instead of “below, but close to, 2 percent”) yields more limited gains than full adoption of FAIT.

### Combined effects, ELB interaction, and spillovers
- Fiscal stimulus has an added impact because monetary policy is constrained by the ELB: comparing model results with and without a binding ELB constraint shows larger effects when the ELB binds.
- The bilateral U.S. trade balance increases significantly despite a somewhat stronger U.S. dollar when fiscal stimulus is implemented.
- The net effect of combined policies brings forward liftoff from the ELB in both the U.S. and euro area by around a year, relative to a scenario without these fiscal policies.
- Synchronized fiscal stimulus in both regions creates positive spillovers to output in each region via the trade channel without exacerbating trade imbalances and results in a larger multiplier for both fiscal packages.
- The greater accommodation provided by an FAIT framework in the U.S. can help maximize these spillover effects.

### Contribution of fiscal and monetary policies to the 2021 inflation surprise
- Under the baseline calibration:
  - The combination of fiscal stimulus packages and the introduction of the two new monetary regimes can explain around 30 percent of the unexpected inflation in the U.S. during 2021 and around 24 percent in the euro area.
- Under the steeper Phillips Curve calibration (slopes twice as steep):
  - The monetary and fiscal stimulus account for 70 percent of the surprise in inflation in 2021.
  - The alternative calibration magnifies the policy impact on aggregate demand and inflation but still indicates that combined policy measures are insufficient to fully explain the large and unexpected pick-up in 2021 core inflation.
- Fiscal stimulus likely had a greater impact on inflation than the change in monetary regimes in 2021.

### Sources of the unexplained inflation and model limitations
- Even with the steeper Phillips curve, other factors must play a substantial role in the 2021 inflation surge.
- Potential additional factors (not exhaustive) include supply-demand imbalances not captured by the model, including a shift in the composition of consumption toward goods during the pandemic that strained supply chains.

### Conclusion (model-based synthesis)
- Adoption of FAIT boosted output and inflation in the U.S. and had the potential to do so in the euro area, strengthening monetary policy effectiveness and creating positive international spillovers.
- Significant fiscal support implemented during 2021 had a significant macroeconomic impact and was mutually reinforcing with monetary accommodation, particularly when the ELB is binding.
- The model indicates that the introduction of new monetary regimes and fiscal stimulus in 2021 that were not assumed in IMF staff 2020 forecasts cannot fully explain the unexpected rise in inflation during 2021:
  - Combined impact explains less than one third of the unexpected inflation in the U.S., and a smaller amount in the euro area, with fiscal stimulus contributing significantly more than new monetary regimes.
  - The explained amount increases to 70 percent if the Phillips curve in the model is steeper, but substantial unexplained factors remain.

*IMF Working Paper — Box 1. The Slope of the New Keynesian Phillips Curve*

### Appendix I. Technical Appendix: The Open

### Appendix I. Technical Appendix: The Open Economy New Keynesian Model

### Model structure and purpose
- Variant of Erceg and Lindé (2013) version of the Erceg, Guerrieri and Gust (2006) SIGMA model; main modification is discounting in the pricing block to address the forward-guidance puzzle.
- Two-country (U.S. and euro area), equally sized economies; features endogenous investment, hand-to-mouth (HM) households, sticky wages and sticky prices, trade adjustment costs, and incomplete international financial markets.
- Model can be run without the financial accelerator for exposition; Section A.6 describes inclusion of a financial accelerator that parallels Bernanke, Gertler, and Gilchrist (1999) and Christiano, Motto, and Rostagno (2008).

### Firms and price setting (Section A.1)
- Continuum of differentiated intermediate goods i ∈ [0,1], each produced by a monopolistically competitive firm.
- Domestic demand for firm i: YDt(i) = [PDt(i)/PDt]−(1+θp) θp YDt. (A.1)
- Export demand: Xt(i) = [PMt*(i)/PMt*]−(1+θp) θp Mt*. (A.2)
- Production uses capital services Kt(i) and labor index Lt(i) with CES technology:
  Yt(i) = [ωK ρ/(1+ρ) Kt(i)1/(1+ρ) + ωL ρ/(1+ρ) (Zt Lt(i))1/(1+ρ)]1+ρ. (A.3)
- Technology shock (log-linearized) follows AR(2): ∆zt = ρz,1 ∆zt−1 − ρz,2 zt−1 + εz,t. (A.4)
- Calvo-style price contracts: firms can reoptimize with probability 1−ξp; non-optimizing firms reset domestic price as PDt(i) = πt−1 ιp π ιp PDt−1(i) allowing structural persistence when ιp > 0.
- Optimization problem for reoptimizing firm and FOC yield expected discounted profit condition (A.5)–(A.6).
- Export pricing assumes local currency pricing (LCP); deviations from law of one price (log-linear): δt* = −pM,t* − st + pX,t where pX,t = pD,t. (A.7)
- Final domestic output aggregator (Dixit-Stiglitz):
  YDt = [∫0^1 YDt(i)1/(1+θp) di]1+θp. (A.8)
  Price index: PDt = [∫0^1 PDt(i)−1 θp di]−θp. (A.9)
- Foreign import aggregator and price index analogs (A.10)–(A.11).
- Consumption goods distributor CES combining domestic and imported goods:
  CAt = (ωC ρC/(1+ρC) CDt1/(1+ρC) + (1−ωC) ρC/(1+ρC) (φCt MCt)1/(1+ρC))1+ρC. (A.12)
- Consumption import adjustment cost φCt quadratic form (A.13); distributors minimize expected discounted production cost (A.14).
- Final investment goods produced analogously with possibly different weight ωI.

### Households and wage setting (Section A.2)
- Continuum of monopolistically competitive households supplying differentiated labor; aggregate labor index:
  Lt = [∫0^1 (ζ Nt(h))1/(1+θw) dh]1+θw. (A.15)
- Labor aggregator cost and wage index: Wt = [∫0^1 Wt(h)−1 θw dh]θw. (A.16)
- Household labor demand: Nt(h) = [Wt(h)/Wt]−(1+θw)/θw Lt ζ−1. (A.17)
- Two household types:
  - Forward-looking (FL) households (share 1−χ) maximize expected utility (A.18) with external habit (parameter א), leisure, real money balances, and preference shock vc,t. Real-balance subutility F has a satiation point to account for zero nominal interest rate possibility.
  - Hand-to-mouth (HM) households (share χ) consume disposable income each period and receive no capital income; HM wage set equal to average optimizing wage; consumption condition: PCt (1+τCt) C t HM(h) = (1−τN,t) Wt(h) Nt(h) + TRt(h). (A.25)
- Consumption demand shock vc,t follows AR(1): vc,t = ρv v vc,t−1 + εv c,t. (A.19)
- FL household budget constraint (A.20) includes consumption tax τCt, investment price PI t, money balances, contingent claims BDt+1, domestic government bonds BGt+1, foreign bond BFt+1, nominal exchange rate St, transaction cost on foreign bond φbt, wages net of labor tax (1−τN,t), transfers TRt, capital rental (1−τK,t) RKt Kt(h), depreciation write-off PI t τK,t δ Kt(h), investment adjustment cost −PD t φIt(h), and other asset terms.
- Capital accumulation Kt+1(h) = (1−δ) Kt(h) + It(h). (A.21)
- Investment acceleration (adjustment cost): φIt(h) = 1/2 φI (It(h) − It−1)2 / It−1. (A.23)
- FL households set nominal wages in Calvo fashion: reoptimize with probability 1−ξw; non-optimizing reset: Wt(h) = ωt−1 ιw ω1−ιw Wt−1(h). (A.24)
- Cross-border bond trade is restricted to single non-state-contingent foreign bond; transaction cost φbt depends on economy-wide net foreign assets ratio:
  φbt = exp(−φb (BFt+1 / (PDt YDt))). (A.22)
- Effective nominal interest rate it = 1/PBt − 1.

### Monetary and fiscal policy (Section A.3)
- Governments do not balance budget each period; government end-of-period debt evolution:
  DGt+1 = PCt Gt + TRt O + TRt HM − τN,t Wt Lt − τCt PCt Ct − τK,t (RKt − δ PI t) Kt + (1+ iGt−1) DGt − (MBt+1 − MBt). (A.26)
- Taxes τK,t, τC,t, τN,t and ratio trt HM = TRt HM / (Pt Y) are fixed.
- Government spending process (log of g): (gt − g) = ρG (gt−1 − g) + εg,t with εg,t ~ N(0, σG). (A.27)
- When studying government investment impact, technology shock augmented: ∆zt = 0.7 ∆zt−1 − 0.005 zt−1 + εz,t + 0.003 gt (links transient government investment to stationary technology).
- Labor income tax rule to stabilize debt/GDP and deficit:
  τN,t − τN = υ1 (τN,t−1 − τN) − (1−υ1)[ υ2 (bGt − bG) + υ3 (∆bGt+1 − ∆bGt) ]. (A.28)
- Debt measure bGt = BGt / (4 P̄t Y) (government debt as share of annualized nominal trend output).
- Long-term government debt modeled using Krause and Moyen (2016) style stochastic maturity:
  iGt new = ϖnew it + (1−ϖnew) Et iGt+1 new, with ϖnew = (i + ϖ)/(1+i). Effective debt-rate iGt = ϖlong iGt new + (1−ϖlong) iGt−1 where ϖlong = 1−(1−λ)/(1+π) approximates λ when π is low (π = 0.005 in calibration). Setting λ = 0 nests one-period debt (iGt = it).

### Resource constraint and net foreign assets (Section A.4)
- Aggregate resource constraint: YDt = CDt + IDt + φIt + ζ∗/ζ M t *. (A.29)
- Final consumption allocation: CAt = Ct + Gt. (A.30)
- Aggregate private consumption: Ct = (1−χ) CO t + χ CHM t. (A.31)
- Exports split: Mt* = MCt* + MIt*. (A.32)
- Net foreign assets evolution:
  PB,t* BF,t+1 φbt = BF,t + PMt* ζ∗/ζ M t* − PMt Mt. (A.33)
- Foreign economy is isomorphic to domestic economy.

### Financial accelerator (Section A.5)
- Augmented model follows Bernanke, Gertler and Gilchrist (1999): intermediate producers rent capital from entrepreneurs who buy physical capital from capital goods producers and finance with net worth plus bank loans.
- Entrepreneurs face external finance premium due to agency problem; banks obtain funds by issuing deposits to households at central bank rate; corporate finance premium fluctuates with entrepreneurial net worth and leverage.
- Debt contract between entrepreneurs and banks specified in nominal terms (following Christiano, Motto and Rostagno (2008)).

### Calibration and solution method (Section A.6)
- Quarterly frequency calibration.
- Country size parameter ζ = 1 (equal-sized countries).
- Trade share of U.S. economy set to 9.3 percent of GDP to match U.S.-euro area trade and indirect linkages.
- Parameters: ρC = ρI = 2.75; θp = 0.1; φMC = φMI = 1; φb (financial intermediation parameter) set to a very small value (0.001) to ensure unique steady state.
- Preference and household parameters:
  - Relative risk aversion σ = 2.
  - Habit persistence א = 0.8.
  - Share of HM agents χ = 0.55 (implies HM agents account for about one third of aggregate private consumption).
  - Utility parameter χ0 set to target labor time share of one half; Frisch elasticity targeted to equal 1/2 implying χ = 4.
  - μ0 on real-balance subutility set arbitrarily low.
- Investment and capital parameters:
  - Investment adjustment cost φI = 3.
  - Depreciation rate δ = 0.025 (annual depreciation rate of 10 percent).
  - CES parameter ρ = −1 implying Leontief production between capital and labor (zero elasticity of substitution).
  - Quasi-capital share ωK = 0.3; price markup θP = 0.1 chosen to imply steady state investment/output ≈ 20 percent.
- Financial accelerator calibration (augmented model):
  - Monitoring cost μ = 0.12 (proportion of entrepreneurs’ gross revenue).
  - Default rate of entrepreneurs = 3 percent per year.
  - Variance of idiosyncratic productivity shocks to entrepreneurs = 0.28.
- Calvo and indexation parameters:
  - Domestic price contract duration ξp = 0.92.
  - Import/export contract parameter ξm = 0.90.
  - Wage contract duration ξw = 0.88.
  - Degree of price indexation ιp = 1.
  - Wage and import price indexation parameters ιw = ιm = 0.5.
  - Wage markup θW = 1/3.
- Expectations and forward-guidance adjustment:
  - Behavioral expectations following Gabaix (2020) via cognitive discount φ = 0.95 replacing X t+1|t with φ X t+1|t in linearized wage and price Phillips curves to dampen role of expectations in price and wage setting.
- Monetary rule calibration to match early-2021 outlooks:
  - Interest smoothing parameters γEA = γUS = 0.92.
  - Employment growth parameters γ∆e,EA = γ∆e,US = 0.25.
  - Employment gap coefficient γe set slightly higher for U.S. (0.25 annualized) than ECB (0.125 annualized).
  - AIT gap coefficient for Fed γπ,US = 4.3; inflation coefficient for ECB γπ,EA set (value truncated in source).

*Source: Appendix I. Technical Appendix: The Open Economy New Keynesian Model (wpiea2022222-print-pdf).*

### 5. Without these aggressive response coefficients on inflation, our model cannot account for the long-lived

### 5. Without these aggressive response coefficients on inflation, our model cannot account for the long-lived

### Model calibration and fiscal parametrization
- Discount factor 훽 = 0.99875; inflation target = 2 percent → steady state nominal interest rate = 2.5 percent.
- Share of government spending on goods and services:
  - US = 19 percent of steady state output.
  - EA = 25 percent of steady state output.
- Government debt to GDP ratio 푏퐺:
  - US = 130 percent of annualized GDP.
  - EA = 100 percent of annualized GDP.
- Ratio of transfers to GDP = 15 percent (model assumption for transfers; steady state transfers detailed in table below).
- Steady state sales (VAT) tax rate 휏퐶:
  - US = 7 percent.
  - EA = 20 percent.
- Steady state capital tax 휏퐾:
  - US = 0.21.
  - EA = 0.26.
- Full tax-deduction of capital depreciation assumed (i.e. 훿휏 = 훿).
- Given annualized steady state real interest rate = 0.5 percent, the government’s intertemporal budget constraint implies average labor income tax rate 휏푁:
  - US = 0.30 percent in text (table reports US: 32; EA: 30 — see Summary Table of Parameters below).
- Tax adjustment rule (equation A.29) parameters chosen to represent an unaggressive tax adjustment:
  - 휐1 = 0.985, 휐2 = 휐3 = 0.1.
- Following Krause and Moyen (2016), bond maturing probability 휗 = 0.055, consistent with a 4.5 year steady state maturity structure of government debt.
- Wage-setting includes strategic complementarities; the wage markup 휃W influences the slope of the wage Phillips Curve.

### Steady state, solution method, and model linearization
- Log-linearization: The model’s equations are log-linearized around the non-stochastic steady state.
- Stationarity: Nominal variables are rendered stationary by suitable transformations.
- Solution algorithm:
  - The unconstrained version of the model is solved by computing the reduced-form solution using the numerical algorithm of Anderson and Moore (1985), which implements the Blanchard and Kahn (1980) solution method.
- Comment on model fit: Aggressive response coefficients on inflation are required for the model to account for the long-lived expected ELB episodes priced in markets in early 2021.

### Summary Table of Parameters — selected entries (values preserved exactly as in source)
- Relative country size 휁 = 1
- Trade share 1-휔C = 0.095, 1-휔I = 0.136 => trade share 9.3% of GDP
- Trade price elasticity 1+휌C/휌C = 1+휌I/휌I = 1.5
- Price markup 휃p = 0.1
- Import adjustment cost 휑MC = 휑MI = 1
- Financial intermediation cost abroad 휙b = 0.001
- Relative risk aversion 휎 = 2
- Habit persistence א = 0.8
- Leisure in utility 휒0 = 1
- Share of work to time endowment se = 0.5
- Labor utility curvature parameter 휒 = 4
- Real money balance utility 휇0 = 0.001
- Share of hand-to-mouth agents 휍 = 0.55
- Investment adjustment cost 휙I = 3
- Capital depreciation (10% per year) 훿 = 0.025
- Elasticity of substitution between intermediate goods 휌 = -1
- Quasi-capital share 휔K = 0.3
- Monitoring cost 휇 = 0.12
- Default rate for entrepreneurs 퐹(휔̅) = 3 percent / year
- Variance of idiosyncratic productivity shock var(log휔) = 0.28
- Calvo domestic price contract duration 휉p = 0.92
- Calvo Import/export contract duration 휉m = 0.9
- Calvo wage contract duration 휉w = 0.88
- Wage and import price indexation 휄w = 휄m = 0.5
- Wage markup 휃W = 1/3
- Cognitive discounting in price setting 휑 = 0.95
- Interest rate smoothing 훾EA = 훾US = 0.92
- Employment growth 훾∆e,EA = 훾∆e,US = 0.25
- Employment gap 훾e: US = 0.25/4, ECB = 0.125/4
- AIT/FIT gap coefficients 훾π: US = 4.3, ECB = 5
- Discount factor 훽 = 0.99875
- Bond maturing probability 휗 = 0.055
- Tax adjustment rule 휐1, 휐2, 휐3: 휐1 = 0.985, 휐2 = 휐3 = 0.1
- Steady state gov’t debt/GDP (%) 푏퐺: US: 130, EA: 100
- Gov’t consumption/GDP (%) gy: US: 19, EA: 25
- Steady state transfers/GDP (%) 푡푟tO, 푡푟tHM: 푡푟tO = 6.75, 푡푟tHM = 8.25
- Steady state labor income tax rate (%) 휏N: US: 32, EA: 30
- Steady state consumption tax rate (%) 휏C: US: 7, EA: 20
- Steady state capital tax rate (%) 휏K: US: 21, EA: 26
- Steady state inflation, inflation target (annual, %) 휋̅ = 2
- Steady state nominal interest rate (annual, %) i = 2.5

### Key modeling implications
- The combination of fiscal parameter choices (debt, tax rates, transfers, government consumption shares) and monetary calibration (훽, inflation target, steady state real interest rate) pins down steady state tax rates and the steady state nominal interest rate.
- The assumed bond maturity structure (휗 = 0.055) and unaggressive tax adjustment rule (휐1 = 0.985; 휐2 = 휐3 = 0.1) are intended to reflect empirical features of U.S. and EA fiscal positions without imposing aggressive fiscal policy feedback.
- Accurate accounting for market prices of expected ELB episodes in early 2021 requires aggressive inflation response coefficients in the model’s policy rules; without them the model cannot replicate those priced expectations.

*IMF Working Paper No. WP/2022/222 — U.S. and Euro Area Monetary and Fiscal Interactions During the Pandemic: A Structural Analysis*

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