## 1. Overlapping Generations (OLG) Households

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### Model context, timing, and population
- Time periods represent years.
- World technology growth: g = T_t / T_{t−1}.
- World population growth rate: n.
- Two household types in each region z:
  - Liquidity-constrained households (LIQ): share ψ(z) of the population.
  - Overlapping generations households with finite planning horizons (OLG): share 1−ψ(z) of the population.
- In each period:
  - LIQ individuals born: N(z) n_t ψ(z) (1−θ^n).
  - OLG individuals born: N(z) n_t (1−ψ(z)) (1−θ^n).
- OLG constant probability of death each period: (1−θ) ⇒ average planning horizon 1/(1−θ).
- Labor productivity for households declines at constant rate χ < 1 over lifetimes.
- Perfect foresight version presented in overview.

### Liquidity constraints, non-Ricardian behavior, and fiscal transmission
- LIQ households:
  - No access to financial markets; consume after-tax income each period (rule-of-thumb / hand-to-mouth behavior).
  - High marginal propensity to consume out of income.
- OLG households:
  - Finite horizons (Blanchard (1985) specification).
  - Higher government debt implies non-zero net worth for these households in the long run.
- Roles in fiscal policy transmission:
  - LIQ presence strongly affects short-run fiscal multipliers: transfers and tax changes directly affect LIQ consumption.
  - Finite-horizon OLG households crucial for long-run crowding-out: government debt accumulates as net wealth for finite-horizon households, crowding out physical capital and foreign asset holdings long run.
  - These non-Ricardian features enable non-trivial short-run stimulus effects and long-run debt-induced crowding-out.

### Asset markets, ownership, and aggregation
- Asset markets incomplete.
- Complete home bias in government debt: nominally non-contingent one-period domestic-currency bonds.
- International asset trade limited to nominally non-contingent one-period bonds denominated in U.S. dollars.
- Complete home bias in ownership of domestic firms; equity not traded; households receive lump-sum dividends.
- Per capita variables considered at disaggregated household level.
- Real aggregate variables x_t rescaled: ˇx_t = x_t / (T_t n_t).
- Steady state of ˇx_t denoted by x.

---

### OLG household preferences, consumption, and assets
- Lifetime expected utility (parameters preserved as in source):
  - Discount factor: β.
  - Survival parameter: θ < 1.
  - Coefficient of relative risk aversion: γ > 0.
  - Share parameter: 0 < η_OLG < 1.
  - Intertemporal structure includes external consumption habit h_OLG a,t = c_OLG t−1 / N(1−ψ)^v with habit persistence parameter v.
- Consumption: c_OLG a,t is a Dixit-Stiglitz CES aggregate across retail varieties with elasticity σ_R.
- Money: cashless limit assumed (Woodford (2003)).
- Assets available:
  - Domestic government bonds: B_a,t.
  - Bank-issued bonds to entrepreneurs: B_N a,t + B_T a,t.
  - Foreign (U.S. dollar) bonds: F_a,t.
- Exchange rate: E_t; gross nominal interest rates: i_t (domestic) and i*_t (U.S. dollar) with foreign exchange risk premium ξ_f t.
- Insurance contract: entering financial markets requires premium (1−θ)/θ on financial wealth each period alive; entire financial wealth encashed at death.
- Taxes: labor income tax τ_L,t, consumption tax τ_c,t, lump-sum taxes τ_ls a,t; transfers Υ_OLG a,t.
- Real variables:
  - Real wage: w_t = W_t / P_t.
  - Final consumption inflation: π_t = P_t / P_t−1.
  - Gross nominal exchange rate depreciation: ε_t = E_t / E_t−1.
  - Real exchange rate versus U.S.: e_t = (E_t P*_t) / P_t.
  - Real domestic bonds: b_t = B_t / P_t; real internationally traded bonds: f_t = F_t / P*_t.
  - Real interest rate: r_t = i_t / π_t+1.
  - Uncovered interest parity: i_t = i*_t ξ_t ε_t+1.

### Budget constraint (nominal) — preserved structure
- Full nominal budget constraint as presented in source (variables and terms preserved exactly in structure).

### Aggregate consumption rule and wealth decomposition (after rescaling by technology)
- Optimal aggregate consumption rule:
  - ˇc_OLG t / Θ_t = ˇfw_t + ˇhw_L t + ˇhw_K t. (Equation 4)
- Financial wealth component:
  - ˇfw_t = 1 / π_t g n [ i_t−1 ( ˇb_t−1 + ˇb_N t−1 + ˇb_T t−1 ) + i*_t−1 ε_t (1+ξ_f t−1) ˇf_t−1 e_t−1 ]. (Equation 5)
- Human wealth from labor:
  - ˇhw_L t = ( N(1−ψ) ( ˇw_t (1−τ_L,t) ) ) + θχ g r_t ˇhw_L t+1. (Equation 6)
- Human wealth from capital/dividends:
  - ˇhw_K t = [ Σ_j ˇd_j t + r ˇbr_t − ˇτ_ls,OLG t + ˇΥ_OLG t ] + θ g r_t ˇhw_K t+1. (Equation 7)
- Marginal propensity to consume denominator:
  - Θ_t = p_R t + τ_c,t η_OLG + θ j_t r_t Θ_t+1. (Equation 8)
- Auxiliary expression j_t given explicitly in Equation (9) in source.
- Key implications:
  - Government debt adds to agents’ net worth.
  - Time profile of tax changes affects consumption time profile.
  - In long run government debt crowds out private capital and net foreign assets.
- Intuition on finite horizons and interest rate effects preserved as in source:
  - Finite-horizon agents discount distant future taxes more heavily at rates r_t / θ and r_t / θχ than market rate r_t, so debt-financed stimulus that tilts taxes into the future raises perceived human wealth and consumption.
  - When γ > 1, income effect of an increase in real interest rate dominates substitution effect, increasing marginal propensity to consume 1/Θ_t and partly offsetting contractionary effects of higher r_t.

---

### 2. Liquidity-Constrained (LIQ) Households and Aggregation

### LIQ household behavior and budget constraint
- Objective function identical to OLG households.
- Consumption constraint: consume at most current income (after-tax wage income plus net government transfers).
- Rescaled budget constraint:
  - ˇc_LIQ t ( p_R t + τ_c,t ) = ˇw_t ℓ_LIQ t (1−τ_L,t ) + ˇΥ_LIQ t − ˇτ_ls,LIQ t. (Equation 10)
- High marginal propensity to consume out of income ⇒ fiscal multipliers of revenue-based stimulus measures particularly high when LIQ population share is high.

### Aggregation
- Aggregate consumption: ˇC_t = ˇc_OLG t + ˇc_LIQ t.
- Aggregate labor supply: ˇL_t = ˇℓ_OLG t + ˇℓ_LIQ t.

---

### 3. Firms — Entrepreneurs and Banks (Financial Accelerator Sector)

### Financial accelerator setup and mechanisms
- Entrepreneurs (tradables and nontradables) purchase capital, rent to manufacturers, choose utilization.
- Financing via net worth and bank loans.
- Capital productivity subject to idiosyncratic risk; entrepreneurs risk-neutral and bear aggregate risk.
- Loan contracts specify state-contingent gross interest schedule with cutoff productivity; below cutoff firms default and surrender capital.
- Bankruptcy monitoring costs rbr_t: banks recover only fraction of capital value on default.
- Banks borrow from households and pay depositors nominal rate i_t (non-state-contingent).
- Bank profit condition: debt contract parameters chosen to maximize entrepreneurial profits subject to zero bank profits in each state.
- External finance premium: difference between rate entrepreneurs pay banks and rate banks pay depositors.
- Dividends and net worth:
  - Zero bank profits ⇒ surplus between aggregate returns to capital net of bankruptcy costs and deposit interest goes to entrepreneurs and accumulates.
  - Entrepreneurs follow fixed dividend policy to prevent excessive net worth accumulation.
- Key implication: upward-sloping relationship between external finance premium and entrepreneurs’ debt-to-equity ratio (leverage).
- Model retains full nonlinear setup, important when shocks to net worth are large.

---

### 4. Governmental Authorities

### Fiscal instruments, budget constraint, and stabilization rule
- Fiscal instruments:
  - Government spending: G_t = G_cons t + G_inv t.
  - Lump-sum taxes: τ_ls,t = τ_ls,OLG t + τ_ls,LIQ t.
  - Lump-sum transfers: Υ_t = Υ_OLG t + Υ_LIQ t.
  - Tax rates: τ_L,t, τ_c,t, τ_k,t.
- Public infrastructure capital depreciates at rate δ_G.
- Tax revenue τ_t is sum of labor, consumption, capital and lump-sum taxes.
- Government budget constraint (rescaled):
  - ˇb_t = i_t−1 / π_t g n ˇb_t−1 + ˇG_t + ˇΥ_t − ˇτ_t = i_t−1 / π_t g n ˇb_t−1 − ˇs_t. (Equation 11)
  - ˇs_t is the primary surplus.

### Fiscal policy targeting rule
- Objectives:
  1. Stabilize interest-inclusive government deficit-to-GDP ratio gd_rat_t at long-run level gdss_rat_t.
  2. Stabilize business cycle by letting deficit fall with output gap.
- Targeting rule:
  - gd_rat_t = gdss_rat_t − d_gdp ln ( g ˇdp_t / g ˇdp_pot ). (Equation 12)
  - d_gdp ≥ 0.
- Definitions:
  - gd_rat_t = 100 ( ( i_t−1 − 1 ) ˇb_t−1 / π_t g n − ˇs_t ) / g ˇdp_t = 100 ( ˇb_t − ˇb_t−1 / π_t g n ) / g ˇdp_t. (Equation 13)
  - Long-run debt relation:
    - bss_rat_t = ( π g n ) / ( π g n − 1 ) gdss_rat_t. (Equation 14)
    - π is central bank inflation target.
    - Implied long-run autoregressive coefficient on debt is 1/( π g n ), close to one.
- Additional features:
  - Model allows permanent shocks to technology and private saving, producing permanent effects on potential GDP due to non-Ricardian features.
  - Potential output g ˇdp_pot modeled as arithmetic moving average of past actual GDP.
  - Characterization includes degree of automatic stabilizers (d_gdp) with OECD estimates used.
- Implementation: Rule (12) is a targeting rule; default instrument in paper is general transfers ˇΥ_t.

---

### 3. Monetary Policy

### Monetary policy rule and calibration highlights
- Interest rate rule stabilizes inflation; responds to one-year-ahead inflation with steady-state real interest rate formulated as geometric moving average.
- Calibration (parameters preserved exactly):
  - Real per capita growth rate: 1.5 percent.
  - World population growth rate: 1 percent.
  - Long-run real interest rate: 3 percent.
  - Intertemporal elasticity of substitution: 0.25 (γ = 4).
  - Wage elasticity of labor supply: 0.5.
  - Shares of liquidity-constrained agents: 25 percent in US, EU and JA; 50 percent in AS and RC.
  - Average remaining time at work: 20 years (χ = 0.95).
  - Planning horizon: 20 years (θ = 0.95).
  - Calibration target: long-run crowding-out effect of higher government debt ~ one basis point per one percentage point increase in government debt to GDP ratio.
  - Elasticities of substitution: 1 between capital and labor; 0.75 between domestic and foreign goods; 0.5 between tradables and nontradables.
  - Steady state gross markups: 1.1 in manufacturing and wage setting; 1.05 in retailing, investment and consumption goods production; 1.025 for import agents.
  - Public capital stock depreciation (δG): 4 percent per year.
  - Elasticity of aggregate output w.r.t. public capital: 0.14.
  - Financial accelerator calibration: leverage (corporate debt to corporate equity) = 100; steady state external finance premium = 2.5 percent.
  - Monetary rule parameters: conventional for an annual model.
  - Fiscal rule parameters: target deficit to GDP ratios consistent with historical debt to GDP ratios; OECD dgdp used.
  - Model variants: GIMF without financial accelerator and with separate financial accelerator sectors; calibration identical for common sectors.

---

### Shock experiments, financial accelerator, and policy regimes

### Financial accelerator mechanism (summary)
- Firms borrow to finance capital; external finance premium rises with leverage.
- Declines in net worth raise external finance premium → lower investment.
- Lower earnings and rebuilding net worth → lower dividends → reduce household income, wealth, and consumption.
- At Zero Lower Bound (ZIF) central banks unable to lower nominal rates further; real rates rise as inflation falls.
- Three policy interest rate scenarios used in impulse responses:
  - Immediate Policy Interest Rate Response (policy can drop immediately) — red line.
  - Unchanged Policy Interest Rate for One Year — blue line.
  - Unchanged Policy Interest Rate for Two Years — green line.

### A. Decline in Productivity Growth (shock specification)
- Shock: reduction in sector-wide productivity growth of 0.25 percentage points for 10 years in both tradables and non-tradables, then return to baseline.
- Financing of deficit changes: financed by changes in general transfers; automatic stabilizers function normally.
- Key comparative findings (two-year fixed rates vs adjustable):
  - Without financial accelerator:
    - Two-year fixed rates produce considerably larger declines in real GDP, inflation, consumption and investment than immediate adjustment.
  - With financial accelerator:
    - For two-year fixed rates effects substantially larger due to large increase in external finance premium from higher leverage → lower investment and dividends → lower consumption.
    - Quantified comparisons for two-year fixed rates:
      - Consumption decline: about 2.5 percent with financial accelerator vs less than 1.5 percent without.
      - Investment reduction in year two: 4.5 percent with financial accelerator vs about 2 percent without.
    - Rest of world (RW) spillovers: little when policy can adjust or held fixed one year; with two-year fixed rates, spillovers to RW considerably higher with financial accelerator.

### B. Increase in Borrower Riskiness (shock specification)
- Shock: temporary but persistent increase in idiosyncratic project risk of U.S. corporate borrowers; shock phases out with annual decay factor 0.95.
- With financial accelerator:
  - External finance premium increases between 70 and 90 basis points in year one, depending on nominal interest rate flexibility.
  - Effects:
    - Some effect on consumption.
    - Very considerable and persistent effect on investment even when rates can adjust or fixed one year.
    - Much larger effects when interest rates unchanged for two years, partly due to larger initial jump in external finance premium and larger increase in riskless real interest rate.
    - Spillovers to RW miniscule when rates can adjust or fixed one year, but very significant when rates unchanged for two years.

---

### V. Short-Run Fiscal Multipliers (design and results)

### Shock design and multiplier definition
- Four temporary fiscal stimulus types simulated (discretionary stimulative actions equal to 1 percent of pre-shock GDP for two years):
  - (i) Increase in government investment expenditures.
  - (ii) Increase in general lump-sum transfers to all households.
  - (iii) Increase in lump-sum transfers targeted at liquidity-constrained households.
  - (iv) Decrease in tax rates on labor income.
- Fiscal multiplier defined as percentage change in GDP in the same years (stimulus equals exactly 1 percent of baseline GDP in first two years).
- Monetary accommodation scenarios: no accommodation (rates follow rule) vs rates unchanged for one year vs rates unchanged for two years.
- Monetary accommodation lowers real interest rates via higher inflation, stimulating consumption and investment and depreciating real exchange rates.
- Comparisons made between model with and without financial accelerator.

### A. Increase in Government Investment Expenditures — average two-year U.S. GDP effects
- Model without financial accelerator:
  - No monetary accommodation: 1.2 percent increase.
  - One year of monetary accommodation: 1.4 percent increase.
  - Two years of monetary accommodation: 1.8 percent increase.
- Model with financial accelerator:
  - No monetary accommodation: 1.3 percent.
  - One year: 1.5 percent.
  - Two years: 2.2 percent.
- Mechanisms:
  - Direct demand injection and small supply-side effect.
  - Under two-year monetary accommodation with financial accelerator, riskless real interest rates below baseline by around 1.2 percentage points in years 1 and 2, boosting private investment and consumption.
  - Corporate net worth increases → external finance premium declines → further investment increases.
- Fiscal accounts:
  - Automatic stabilizers offset considerable part of stimulus, especially under accommodation.
  - Two-year monetary accommodation with financial accelerator: fiscal accounts move back into balance in year 3; government debt to GDP ratio below baseline for several years.
- RW spillovers:
  - Small with no accommodation and one-year accommodation.
  - With two-year accommodation: about 0.6 percent average increase in RW real GDP with financial accelerator vs about 0.3 percent without.

### B. Increase in General Lump-Sum Transfers
- Effects on U.S. GDP are small:
  - Model without financial accelerator, no accommodation: GDP increases by less than 0.2 percent.
  - One-year accommodation: similar.
  - Two-year accommodation: real GDP rises by about 0.3 percent.
- Reason: LIQ households only 25 percent of U.S. households; others treat transfer as two-year windfall and spend little.
- With financial accelerator:
  - Very small increase in multiplier for no accommodation and one-year accommodation.
  - With two-year accommodation: real GDP rises by about 0.4 percent on average over two years.
  - Spillovers to RW noticeable only with financial accelerator and two-year accommodation.

### C. Increase in Targeted Lump-Sum Transfers (to LIQ households)
- Targeted transfers to LIQ (one quarter of U.S. households) produce much larger effects:
  - Aggregate consumption increase much higher than untargeted transfers.
  - U.S. GDP effects almost four times larger than general lump-sum transfers.
  - Two-year monetary accommodation:
    - Model without financial accelerator: U.S. GDP = 1.1 percent.
    - Model with financial accelerator: U.S. GDP = 1.5 percent.
    - Comparable general transfers: 0.3 percent (without accelerator) and 0.4 percent (with accelerator).
- Spillovers:
  - Larger U.S. demand raises U.S. and RW inflation.
  - With financial accelerator and monetary accommodation, higher RW inflation lowers RW real interest rates → improves RW corporate balance sheets and external finance premia → significantly larger RW GDP increase (about four times larger than for general lump-sum transfers with two-year accommodation and financial accelerator).

### D. Decrease of the Labor Income Tax Rate
- A discretionary reduction of about 1.7 percentage points in the tax rate on labor income required to achieve a discretionary increase of 1 percent in the government deficit to GDP ratio.
- Effects:
  - U.S. GDP effect slightly larger than general lump-sum transfers under no accommodation and one-year accommodation, and slightly smaller under two-year accommodation.
  - Mechanisms:
    - Labor income tax cut increases labor supply → increases potential and actual output.
    - Increase in potential GDP reduces inflationary pressure → less decline in real interest rate → less monetary stimulus compared with general transfers.
    - Example: two-year accommodation and no accelerator — riskless real interest rates fall on average by about 0.3 percentage points with general lump-sum transfers but are virtually unchanged with labor income tax cut.
  - Smaller changes in real interest rates imply less propagation via financial accelerator to external finance premium.

---

### VI. Effects of Announced G20 Fiscal Stimulus Packages (simulation highlights)
- Simulations based on announced G20 fiscal stimulus packages implemented over 2009 and 2010; monetary assumption: two years of accommodation.
- Regional package features:
  - Largest packages: Japan, emerging Asia and the United States.
  - Composition by region:
    - Japan: general and targeted transfers dominate.
    - Emerging Asia: government investment spending dominates.
    - United States: general and targeted transfers and labor income taxes dominate.
    - Euro area, Africa and Latin America: smaller packages with relatively large role for corporate income tax cuts in 2010.
  - Government consumption expenditures do not predominate in any region.
- Simulation outcomes:
  - Both model versions show considerable GDP impact from announced packages.
  - Model with financial accelerator: effects up to 50 percent larger due to favorable effects on corporate net worth and external finance premium.
- Data: stimulus package estimates based on IMF staff data as of April 20, 2009.

- Representative numeric results (Table 1, preserved structure):
  - Model without Financial Accelerator — Effects on GDP Level in 2009:
    - World: 1.6
    - United States: 1.4
    - Japan: 1.8
    - Emerging Asia: 2.6
    - Remaining Countries: 1.4
  - Model with Financial Accelerator — Effects on GDP Level in 2009:
    - World: 2.1
    - United States: 1.9
    - Japan: 2.4
    - Emerging Asia: 3.1
    - Remaining Countries: 2.0

---

### VII. Long-Run Effects of the Accumulation of Public Debt

### Permanent deficit scenario and assumptions
- Scenario: permanent 0.5 percentage point increase in U.S. government deficit to GDP ratio ⇒ ultimately a 10 percentage point increase in U.S. government debt to GDP ratio.
- Deficits initially driven by stimulus measures based on higher lump-sum transfers or lower taxes on labor income, consumption and capital income.
- As debt and real interest rates increase, transfers lowered or taxes increased, but not enough to reverse 0.5 percentage point deficit increase.
- Analysis restricted to model version with financial accelerator.

### Transitional dynamics and long-run channels
- Example (stimulus based on lower labor income tax rates):
  - First 10 years: U.S. GDP, consumption, and investment increase.
  - Higher aggregate demand → deteriorating trade balance and real appreciation.
  - Inflation and nominal interest rates rise; real interest rates rise except first two periods.
  - Longer run: real GDP declines relative to baseline by ultimately about 0.4 percent.
- Two long-run channels causing GDP decline:
  1. Higher fiscal deficits → lower U.S. saving → lower world saving → higher world real interest rate → crowding out of U.S. investment in physical capital → lower real output; crowding out of U.S. investment in net foreign assets → progressive deterioration in U.S. current account imbalances and need for real effective exchange rate depreciation above baseline.
  2. Distortionary labor income taxes: initially fall to stimulate GDP, but must rise above baseline in the longer run to service larger public debt with higher real interest rate.
- Long-run international effects: higher world real interest rates reduce capital ratios and hence GDP globally.

### Long-run quantitative results (Table 2, preserved exactly)
- Permanent 10 percentage point increase in the U.S. government debt to GDP ratio — selected outcomes by financing instrument (Deviation from Baseline):
  - Financed by a Cut in General Transfers:
    - Real GDP (Percent): U.S. -0.27; RoW -0.20; Global -0.21
    - Real Interest Rate (Percentage points): U.S. 0.10; RoW 0.10; Global 0.10
    - Current Account to GDP (Percentage points): U.S. -0.32; RoW 0.10
    - Investment (Percent): U.S. -0.54; RoW -0.47; Global -0.48
    - Government Deficit to GDP (Percentage points): U.S. 0.48; RoW 0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. 0.12; RoW 0.05; Global 0.06
  - Financed by an Increase in Labor Income Taxes:
    - Real GDP (Percent): U.S. -0.43; RoW -0.24; Global -0.28
    - Real Interest Rate (Percentage points): U.S. 0.11; RoW 0.11; Global 0.11
    - Current Account to GDP (Percentage points): U.S. -0.36; RoW 0.12
    - Investment (Percent): U.S. -0.73; RoW -0.54; Global -0.58
    - Government Deficit to GDP (Percentage points): U.S. 0.48; RoW 0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. 0.07; RoW 0.05; Global 0.06
    - Labor Income Tax Rate (Percentage points): U.S. 0.41; RoW 0.00; Global 0.09
  - Financed by an Increase in Capital Taxes:
    - Real GDP (Percent): U.S. -0.64; RoW -0.25; Global -0.34
    - Real Interest Rate (Percentage points): U.S. 0.10; RoW 0.10; Global 0.10
    - Current Account to GDP (Percentage points): U.S. -0.30; RoW 0.10
    - Investment (Percent): U.S. -1.80; RoW -0.50; Global -0.79
    - Government Deficit to GDP (Percentage points): U.S. 0.48; RoW -0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. -0.02; RoW 0.05; Global 0.03
    - Capital Tax Rate (Percentage points): U.S. 1.25; RoW 0.00; Global 0.28
  - Financed by an Increase in Consumption Taxes:
    - Real GDP (Percent): U.S. -0.34; RoW -0.21; Global -0.24
    - Real Interest Rate (Percentage points): U.S. 0.10; RoW 0.10; Global 0.10
    - Current Account to GDP (Percentage points): U.S. -0.33; RoW 0.11
    - Investment (Percent): U.S. -0.61; RoW -0.49; Global -0.51
    - Government Deficit to GDP (Percentage points): U.S. 0.48; RoW -0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. 0.11; RoW 0.05; Global 0.06
    - Consumption Tax Rate (Percentage points): U.S. 0.32; RoW 0.00; Global 0.07

---

### Key quantitative findings, mechanisms, and policy implications

### Key quantitative findings (preserved)
- Corresponding figures for global real GDP are 0.21 percent, 0.24 percent, 0.28 percent and 0.34 percent (context preserved from source).
- Multipliers of a two-year fiscal stimulus package range from 1.3 for government investment to 0.2 for general transfers.
- In the presence of monetary accommodation and a financial accelerator multipliers are up to twice as large.
- A permanent 0.5 percentage points increase in the U.S. deficit to GDP ratio leads to a 10 percentage points increase in the U.S. debt to GDP ratio in the long run.
- Servicing this higher debt eventually reduces U.S. output by between 0.3 and 0.6 percent, with output losses larger for more distortionary fiscal instruments.
- The real interest rate effect (but not the tax burden effect) affects the rest of the world equally and accounts for output losses of around 0.2 percent.

### Mechanisms and channels (concise)
- Non-Ricardian household behavior (LIQ and finite-horizon OLG) raises world real interest rates under higher deficits, crowding out investment and reducing potential output worldwide.
- Financial accelerator amplifies transmission: monetary accommodation lowers real interest rates → improves corporate balance sheets → reduces external finance premium → amplifies fiscal multipliers.
- More distortionary taxes (labor, capital) produce greater negative long-run effects on potential GDP.
- Short-run benefits of stimulus can be substantial (especially government investment and targeted transfers), but permanent deficits impose lasting costs via higher real rates and distortionary taxation.

### Policy implications and recommendations (preserved language)
- A carefully chosen package of fiscal and supporting monetary stimulus measures can significantly support domestic and global economies during acute stress.
- Such stimulus measures should be embedded in a conservative medium-term fiscal framework to ensure that deficits and debt do not drift upwards permanently when the economy recovers.
- In the absence of a credible medium-term fiscal framework, the long-run costs of permanently higher deficits would far exceed the short-run benefits.

*Source: _wp09255 - 1. Overlapping Generations (OLG) Households (IMF working paper content preserved exactly as provided).*

### 1. Overlapping Generations (OLG) Households . . . . . . . . . . . . .    9

### 1. Overlapping Generations (OLG) Households

### Model context and timing
- Time periods represent years.
- World technology grows at the constant rate g = T_t / T_{t−1}, where T_t is the level of labor augmenting world technology.
- World population grows at the constant rate n.
- Perfect foresight version of the model is presented in the overview.

### Household types and population shares
- Two household types in each region z:
  - Liquidity-constrained households (LIQ): share ψ(z) of the population.
  - Overlapping generations households with finite planning horizons (OLG): share 1−ψ(z) of the population.
- In each period:
  - Number of LIQ individuals born: N(z) n_t ψ(z) (1−θ^n).
  - Number of OLG individuals born: N(z) n_t (1−ψ(z)) (1−θ^n).
- OLG households face a constant probability of death (1−θ) each period, implying an average planning horizon of 1/(1−θ).
- Households experience labor productivity that declines at a constant rate χ < 1 over their lifetimes.

### Liquidity constraint and non-Ricardian behavior
- LIQ households have no access to financial markets and consume their after-tax income each period (rule-of-thumb / hand-to-mouth behavior, as in Galí and others (2007)).
- OLG households have finite horizons (Blanchard (1985) specification) and thus higher government debt implies a non-zero net worth for these households in the long run.
- Both household types are subject to uniform labor income, consumption, and lump-sum taxes.

### Roles in fiscal policy transmission
- Presence of LIQ households strongly affects short-run fiscal multipliers:
  - Fiscal transfers and tax changes directly affect LIQ household consumption because they consume current after-tax income.
- Finite-horizon OLG households are critical for long-run crowding-out effects:
  - Accumulation of government debt represents net wealth for finite-horizon households and can crowd out physical capital and foreign asset holdings in the long run.
- These two non-Ricardian features allow the model to generate non-trivial short-run stimulus effects and long-run debt-induced crowding-out, unlike infinite-horizon representative-agent models.

### Asset markets, government debt, and openness
- Asset markets are incomplete.
- Complete home bias in government debt: nominally non-contingent one-period bonds denominated in domestic currency.
- International asset trade is limited to nominally non-contingent one-period bonds denominated in U.S. dollars.
- Complete home bias in ownership of domestic firms; equity is not traded and households receive lump-sum dividend payments.

### Aggregation and notation
- Per capita variables are considered only at the level of disaggregated households.
- Real aggregate variables x_t are rescaled by technology T_t and by population n_t: ˇx_t = x_t / (T_t n_t).
- Steady state of ˇx_t is denoted by x.

*Source: _wp09255 - 1. Overlapping Generations (OLG) Households . . . . . . . . . . . . .    9*

### 1.  Overlapping Generations (OLG) Households

### 1.  Overlapping Generations (OLG) Households

### OLG household preferences and consumption
- Lifetime expected utility:
  - ∞
    Σ
    s=0
    (βθ)
    s
    [
    1
    1−γ
    (
    (c
    OLG
    a+s,t+s
    / h
    OLG
    a+s,t+s
    )
    η
    OLG
    (1−ℓ
    OLG
    a+s,t+s
    )
    1−η
    OLG
    )
    1−γ
    ]
  - Parameters: β is the discount factor, θ < 1 determines the planning horizon, γ > 0 is the coefficient of relative risk aversion, 0 < η
    OLG
    < 1.
- Consumption specification:
  - c
    OLG
    a,t
    is a Dixit-Stiglitz CES aggregate over retailed consumption goods varieties c
    OLG
    a,t
    (i), with elasticity of substitution σ
    R
  - External consumption habit:
    - h
      OLG
      a,t
      =
      c
      OLG
      t−1
      /
      N(1−ψ)
      v
    - v parameterizes habit persistence.
- Money: cashless limit assumed (Woodford (2003)).

### Assets, returns, and taxes
- Assets households can hold:
  - Domestic government bonds: B
    a,t
  - Bank-issued bonds to nontradables and tradables entrepreneurs: B
    N
    a,t
    + B
    T
    a,t
  - Foreign (U.S. dollar) bonds: F
    a,t
- Exchange rate and interest rates:
  - Nominal exchange rate versus U.S. dollar: E
    t
  - Gross nominal interest rates on domestic and foreign assets held from t to t+1: i
    t
    and i
    t
    ∗
    (1+ξ
    f
    t
    )
    - i
      ∗
      t
      is the U.S. dollar nominal interest rate
      - ξ
        f
        t
        is a foreign exchange risk premium external to household decisions
- Insurance contract requirement:
  - Households entering financial markets pay a premium of (1−θ)/θ on financial wealth each period alive; companies encash entire financial wealth at death.
- Income and taxes:
  - Pre-tax nominal labor income: W
    t
    Φ
    a,t
    ℓ
    a,t
    , with Φ
    a,t
    = Φ
    a
    = κχ
    a
    and χ < 1
  - Lump-sum remuneration for bankruptcy monitoring: P
    t
    rbr
    a,t
  - Lump-sum after-tax nominal dividends from firm/union i in sector j: D
    j
    a,t
    (i)
  - Labor income tax rate: τ
    L,t
  - Consumption tax rate: τ
    c,t
  - Lump-sum taxes: τ
    ls
    a,t
  - Transfers to/from government: Υ
    OLG
    a,t
- Consumption tax payable on price P
  t
    (chosen as numeraire).
- Retail sales price: P
  R
  t

### Prices, real variables, and rates
- Real wage: w
  t
  = W
  t
  / P
  t
- Price level, relative price, and inflation:
  - For any good x: P
    x
    t
    , p
    x
    t
    = P
    x
    t
    / P
    t
    , π
    x
    t
    = P
    x
    t
    / P
    x
    t−1
  - Gross final consumption goods inflation: π
    t
    = P
    t
    / P
    t−1
- Exchange and real exchange:
  - Gross nominal exchange rate depreciation: ε
    t
    = E
    t
    / E
    t−1
  - Real exchange rate versus the United States: e
    t
    = (E
    t
    P
    ∗
    t
    ) / P
    t
- Real bonds and interest:
  - Real domestic bonds: b
    t
    = B
    t
    / P
    t
  - Real internationally traded bonds: f
    t
    = F
    t
    / P
    ∗
    t
  - Real interest rate in terms of final consumption goods: r
    t
    = i
    t
    / π
    t+1
- Uncovered interest parity: i
  t
  = i
  ∗
  t
  ξ
  t
  ε
  t+1

### Budget constraint (nominal)
- P
  R
  t
  c
  OLG
  a,t
  + P
  t
  c
  OLG
  a,t
  τ
  c,t
  + P
  t
  τ
  ls
  a,t
  + B
  a,t
  + B
  N
  a,t
  + B
  T
  a,t
  + E
  t
  F
  a,t
  =
  1
  θ
  [
  i
  t−1
  ( B
  a−1,t−1
  + B
  N
  a−1,t−1
  + B
  T
  a−1,t−1
  )
  + i
  ∗
  t−1
  E
  t
  F
  a−1,t−1
  ]
  (1+ξ
  f
  t−1
  )
  + W
  t
  Φ
  a,t
  ℓ
  OLG
  a,t
  (1−τ
  L,t
  )
  +
  Σ
  j
  ∫
  0
  1
  D
  j
  a,t
  (i) di + P
  t
  rbr
  a,t
  + P
  t
  Υ
  OLG
  a,t

### Optimal aggregate consumption rule and wealth decomposition
- Aggregate consumption rule (after rescaling by technology):
  - ˇc
    OLG
    t
    / Θ
    t
    =
    ˇ
    fw
    t
    +
    ˇ
    hw
    L
    t
    +
    ˇ
    hw
    K
    t
    . (Equation 4)
- Financial wealth component:
  - ˇ
    fw
    t
    =
    1
    π
    t
    gn
    [ i
    t−1
    ( ˇ
    b
    t−1
    + ˇ
    b
    N
    t−1
    + ˇ
    b
    T
    t−1
    ) + i
    ∗
    t−1
    ε
    t
    (1+ξ
    f
    t−1
    )
    ˇ
    f
    t−1
    e
    t−1
    ] . (Equation 5)
- Human wealth from labor:
  - ˇ
    hw
    L
    t
    = ( N(1−ψ) ( ˇw
    t
    (1−τ
    L,t
    )) ) + θχ g
    r
    t
    ˇ
    hw
    L
    t+1
    . (Equation 6)
- Human wealth from capital/dividends:
  - ˇ
    hw
    K
    t
    = [ Σ
    j
    ˇ
    d
    j
    t
    + r
    ˇ
    br
    t
    − ˇτ
    ls,OLG
    t
    + ˇ
    Υ
    OLG
    t
    ] + θ g
    r
    t
    ˇ
    hw
    K
    t+1
    . (Equation 7)
- Marginal propensity to consume denominator:
  - Θ
    t
    =
    p
    R
    t
    + τ
    c,t
    η
    OLG
    +
    θ j
    t
    r
    t
    Θ
    t+1
    . (Equation 8)
- Auxiliary expression for j
  t
    (relating to intertemporal substitution, habits, and taxes) given explicitly in Equation (9) in the source.
- Key model implications:
  - Government debt adds to agents’ net worth.
  - Time profile of tax changes affects consumption time profile.
  - In the long run government debt crowds out private capital and net foreign assets.
- Intuition:
  - Households with finite planning horizons discount distant future taxes more heavily (at rates r
    t
    / θ and r
    t
    / θχ) than the market rate r
    t
    , so a tilt of tax payments into the distant future (via debt-financed stimulus) raises perceived human wealth and consumption.
  - When γ > 1 (conventional assumption), the income effect of an increase in the real interest rate is stronger than the substitution effect, increasing the marginal propensity to consume 1/Θ
    t
    and partly offsetting contractionary effects of higher r
    t
    . Larger γ therefore requires larger interest rate changes to clear markets after fiscal shocks.

---

### 2.  Liquidity-Constrained (LIQ) Households and Aggregate Households

### LIQ household behavior and budget constraint
- Objective function identical to that of OLG households.
- Consumption constraint: can consume at most current income (after-tax wage income plus net government transfers).
- Rescaled budget constraint:
  - ˇc
    LIQ
    t
    ( p
    R
    t
    + τ
    c,t
    ) = ˇw
    t
    ℓ
    LIQ
    t
    (1−τ
    L,t
    ) + ˇ
    Υ
    LIQ
    t
    − ˇτ
    ls,LIQ
    t
    . (Equation 10)
- High marginal propensity to consume out of income, implying:
  - Fiscal multipliers of revenue-based stimulus measures (e.g., tax cuts, increases in transfers) are particularly high when LIQ agents have a high population share.

### Aggregation
- Aggregate consumption and labor supply:
  - ˇ
    C
    t
    = ˇc
    OLG
    t
    + ˇc
    LIQ
    t
  - ˇ
    L
    t
    = ˇ
    ℓ
    OLG
    t
    + ˇ
    ℓ
    LIQ
    t

---

### 3.  Firms — Entrepreneurs and Banks (Financial Accelerator Sector)

### General setup
- Entrepreneurs in tradables and nontradables purchase capital from capital goods producers, rent to manufacturers, and choose capital utilization.
- Financing: combination of net worth and bank loans.
- Productivity risk: capital productivity subject to idiosyncratic risk; entrepreneurs are risk-neutral and bear aggregate risk.
- Loan contracts: specify loan amount and state-contingent schedule of gross interest rates with a cutoff productivity level; entrepreneurs below cutoff go bankrupt and surrender capital to bank.
- Bankruptcy monitoring costs: rbr
  t
  means bank recovers only a fraction of capital value when firms default.
- Banks finance loans by borrowing from households and pay depositors nominal rate i
  t
  (non-state-contingent).
- Bank profit condition:
  - Parameters of debt contract chosen to maximize entrepreneurial profits subject to zero bank profits in each state.
  - Zero profits require the non-stochastic payment to depositors to equal the stochastic payoff to lending in each state (interest from non-bankrupt firms + liquidation value of bankrupt firms − monitoring costs).
- External finance premium:
  - Entrepreneurs pay an external finance premium equal to the difference between the rate entrepreneurs pay banks and the rate banks pay depositors.
- Dividends and net worth:
  - Given banks make zero profits, the difference between aggregate returns to capital net of bankruptcy costs and deposit interest paid goes to entrepreneurs and accumulates.
  - To prevent entrepreneurs from accumulating enough net worth to avoid loans, entrepreneurs follow a fixed dividend policy and regularly pay out dividends to households.
- Key implication:
  - Upward-sloping relationship between external finance premium and entrepreneurs’ debt-to-equity ratio (leverage).
  - Model retains full nonlinear setup (not linearized) generating important nonlinearities when shocks to net worth are large.

---

### 4.  Governmental Authorities

### Budget constraint
- Fiscal policy instruments:
  - Government spending: G
    t
    = G
    cons
    t
    + G
    inv
    t
  - Lump-sum taxes: τ
    ls,t
    = τ
    ls,OLG
    t
    + τ
    ls,LIQ
    t
  - Lump-sum transfers: Υ
    t
    = Υ
    OLG
    t
    + Υ
    LIQ
    t
  - Tax rates: τ
    L,t
    , τ
    c,t
    , τ
    k,t
- Government investment augments public infrastructure capital, which depreciates at rate δ
  G
- Tax revenue τ
  t
  is the sum of labor, consumption, capital and lump-sum taxes.
- Government budget constraint (rescaled):
  - ˇ
    b
    t
    =
    i
    t−1
    /
    π
    t
    gn
    ˇ
    b
    t−1
    + ˇ
    G
    t
    + ˇ
    Υ
    t
    − ˇτ
    t
    =
    i
    t−1
    /
    π
    t
    gn
    ˇ
    b
    t−1
    − ˇs
    t
    . (Equation 11)
  - ˇs
    t
    is the primary surplus.

### Fiscal policy rule and stabilization
- Fiscal policy rule objectives:
  1. Stabilize the interest-inclusive government deficit-to-GDP ratio gd
    rat
    t
    at a long-run level gdss
    rat
    (rules out default and fiscal dominance).
  2. Stabilize business cycle by letting the deficit fall with the output gap.
- Targeting rule:
  - gd
    rat
    t
    = gdss
    rat
    t
    − d
    gdp
    ln ( g
    ˇ
    dp
    t
    / g
    ˇ
    dp
    pot
    ) . (Equation 12)
  - d
    gdp
    ≥ 0
- Definitions and expressions:
  - gd
    rat
    t
    = 100 ( ( i
    t−1
    − 1 ) ˇ
    b
    t−1
    / π
    t
    gn − ˇs
    t
    ) / g
    ˇ
    dp
    t
    = 100 ( ˇ
    b
    t
    − ˇ
    b
    t−1
    / π
    t
    gn ) / g
    ˇ
    dp
    t
    . (Equation 13)
  - Long-run target deficit-to-GDP: gdss
    rat
    t
  - Current and long-run government debt-to-GDP: ˇ
    b
    rat
    t
    and ˇ
    bss
    rat
    t
  - Relationship from government budget constraint:
    - bss
      rat
      t
      =
      ( π gn ) / ( π gn − 1 ) gdss
      rat
      t
      . (Equation 14)
    - π is the inflation target of the central bank.
    - Implied long-run autoregressive coefficient on debt is 1/( π gn ), which is quite close to one.
- Additional model features:
  - Model allows for permanent shocks to technology and private saving, producing permanent effects on potential GDP due to non-Ricardian features.
  - Potential output g
    ˇ
    dp
    pot
    is modeled as an arithmetic moving average of past actual GDP to allow the gap to close over time.
  - Fiscal policy characterization includes the degree to which automatic stabilizers work (d
    gdp
    ), with OECD estimates available for various countries.
- Implementation:
  - Rule (12) is a targeting rule, not an instrument rule; any tax or spending instruments can be used to implement it.
  - Default instrument in the paper: general transfers ˇ
    Υ
    t
    (transfers not targeted at a specific household group).

*Source: _wp09255 - 1.  Overlapping Generations (OLG) Households*

### 3.  Monetary Policy

### 3.  Monetary Policy

### Monetary policy rule
- Monetary policy uses an interest rate rule to stabilize inflation.
- The rule is similar to a conventional inflation forecast based rule that responds to one-year-ahead inflation, with the important exception that the “steady state” of the real interest rate is formulated as a (geometric) moving average.

### Calibration
- Real per capita growth rate: 1.5 percent.
- World population growth rate: 1 percent.
- Long-run real interest rate: 3 percent.
- Household utility functions equal across countries.
- Intertemporal elasticity of substitution: 0.25 (γ = 4).
- Wage elasticity of labor supply: 0.5.
- Shares of liquidity-constrained agents: 25 percent in US, EU and JA; 50 percent in AS and RC.
- Average remaining time at work: 20 years (χ = 0.95).
- Planning horizon: 20 years (θ = 0.95).
- Calibration targets long-run crowding-out effect of higher government debt at around one basis point per one percentage point increase in government debt to GDP ratio.
- Elasticities of substitution: 1 between capital and labor; 0.75 between domestic and foreign goods; 0.5 between tradables and nontradables.
- Steady state gross markups: 1.1 in manufacturing and wage setting; 1.05 in retailing, investment and consumption goods production; 1.025 for import agents.
- Public capital stock depreciation estimate (δG): 4 percent per year.
- Elasticity of aggregate output with respect to public capital: 0.14 (reproduced via productivity of public capital in distribution sector).
- Financial accelerator calibration:
  - Leverage (corporate debt to corporate equity): 100 in all sectors and regions.
  - Steady state external finance premium: 2.5 percent.
- Monetary rule parameters: conventional for an annual model.
- Fiscal rule parameters: target deficit to GDP ratios consistent with historically observed government debt to GDP ratios; OECD estimates of output gap coefficients dgdp used.
- Paper compares two model variants: GIMF without a financial accelerator and a variant with separate financial accelerator sectors in tradables and nontradables; calibration identical for common sectors.

### Financial accelerator mechanism and shock design
- Financial accelerator: firms borrow to finance physical capital and face an external finance premium increasing in leverage (debt to net worth). Declines in net worth raise the real interest rate faced by corporate sector.
- Corporate net worth = market value of physical capital − value of financial liabilities.
- Physical capital value declines with negative technology shocks, higher bankruptcy costs, higher borrower riskiness, or higher depreciation; nominal indebtedness value can rise due to a decline in the price level.
- Two main transmission channels from deteriorated corporate balance sheets:
  - Higher leverage → higher external finance premium → reduced investment.
  - Lower earnings and need to rebuild net worth → lower dividend distributions → reduced household income, wealth and consumption.
- Zero lower bound (ZIF) implications: when central banks reach the zero lower bound, inability to lower nominal rates causes real interest rates to rise faster when inflation falls; simulations compare three policy environments:
  - Interest rate follows reaction function (policy can drop immediately) — red line.
  - Policy rates unchanged for one year (ZIF or delayed) — blue line.
  - Policy rates unchanged for two years (ZIF or delayed) — green line.

### A. Decline in Productivity Growth (shock specification and effects)
- Shock: reduction in sector-wide productivity growth of 0.25 percentage points for 10 years in both tradables and non-tradables sectors, followed by a return to baseline.
- Financing of deficit changes: financed by changes in general transfers; automatic stabilizers function normally.
- Model without financial accelerator:
  - Interest rates able to adjust (red): short- to medium-run decline in real GDP and inflation; central bank reduces policy rate; real interest rate eventually falls below baseline.
  - Interest rates unchanged for one year (blue): slightly lower real GDP, inflation, consumption and investment relative to red.
  - Interest rates unchanged for two years (green): considerably larger declines in real GDP, inflation, consumption and investment due to prolonged inability to offset downward pressure and substantial rise in real interest rate.
  - Rest of world (RW) spillovers limited; real GDP barely moves due to U.S. dollar appreciation strengthening RW trade balance.
- Model with financial accelerator:
  - For red and blue cases: negative effects slightly larger than without accelerator.
  - For green case (two-year fixed rates): substantially larger negative effects due to:
    - Large increase in external finance premium from higher leverage (lower net worth) → lower investment and lower dividends → lower consumption.
    - Declines in GDP and inflation raise riskless real interest rate further → further reduces investment and consumption.
  - Quantified comparisons for two-year fixed rates:
    - Consumption decline: about 2.5 percent with financial accelerator vs less than 1.5 percent without.
    - Investment reduction in year two: 4.5 percent with financial accelerator vs about 2 percent without.
  - RW effects: little impact when policy can adjust or held fixed one year; with two-year fixed rates, spillovers to RW considerably higher in model with financial accelerator due to propagated increases in RW real interest rates harming RW corporate balance sheets and external finance premia.

### B. Increase in Borrower Riskiness (shock and effects)
- Shock: temporary but persistent increase in idiosyncratic project risk of U.S. corporate borrowers in both tradables and non-tradables; shock phases out with annual decay factor 0.95.
- Model without financial accelerator: shock not present.
- Model with financial accelerator:
  - External finance premium increases between 70 and 90 basis points in year one, depending on nominal interest rate flexibility.
  - Effects:
    - Some effect on consumption.
    - Very considerable and persistent effect on investment even when rates can adjust or are fixed for one year.
    - Much larger effects when interest rates unchanged for two years, due partly to larger initial jump in external finance premium and mainly due to much greater increase in riskless real interest rate.
    - Spillovers to RW miniscule when rates can adjust or fixed for one year, but very significant when rates unchanged for two years for reasons analogous to the productivity shock.

### V. Short-Run Fiscal Multipliers (design and general mechanisms)
- Four types of temporary fiscal stimulus measures simulated:
  - (i) Increase in government investment expenditures.
  - (ii) Increase in general lump-sum transfers to all households.
  - (iii) Increase in lump-sum transfers targeted specifically at liquidity-constrained households.
  - (iv) Decrease in tax rates on labor income.
- Fiscal shock size: discretionary stimulative actions equal to 1 percent of pre-shock GDP for two years.
- Resulting government deficits smaller than shock size because automatic stabilizers (dgdp > 0) react to positive GDP movements.
- “Fiscal multiplier” defined as percentage change in GDP in the same years (stimulus equals exactly 1 percent of baseline GDP in first two years).
- Demand effects: direct injection into aggregate demand or increased real disposable incomes; magnitude depends on share of liquidity-constrained households.
- Supply effects: government investment raises potential output over time; temporary decreases in distortionary labor income taxes increase labor supply and potential output, reducing inflationary effects.
- Monetary accommodation scenarios: no accommodation (rates follow rule) vs monetary accommodation for one or two years (rates unchanged). Monetary accommodation lowers real interest rates via higher inflation, stimulating consumption and investment and depreciating real exchange rates.
- Model comparisons made with and without financial accelerator; monetary accommodation amplifies fiscal multipliers and interacts with financial accelerator effects.

### A. Increase in Government Investment Expenditures (short-run results)
- Average effects on U.S. GDP over two years (model without financial accelerator):
  - No monetary accommodation: 1.2 percent increase.
  - One year of monetary accommodation: 1.4 percent increase.
  - Two years of monetary accommodation: 1.8 percent increase.
- Corresponding effects (model with financial accelerator):
  - No monetary accommodation: 1.3 percent.
  - One year: 1.5 percent.
  - Two years: 2.2 percent.
- Mechanisms:
  - Direct demand injection.
  - Small but appreciable supply-side effect (greater private production efficiency).
  - Under two-year monetary accommodation with financial accelerator, riskless real interest rates are below baseline by around 1.2 percentage points in years 1 and 2, boosting private investment and consumption.
  - Corporate net worth increases, raising value of physical capital and reducing real value of corporate debt → external finance premium declines → further investment increases.
- Fiscal accounts:
  - Automatic stabilizers offset a considerable part of stimulus effect on deficits, especially under monetary accommodation.
  - In the case of two-year monetary accommodation with financial accelerator, fiscal accounts move back into balance in year 3; government debt to GDP ratio below baseline for several years.
  - Caveat: ongoing deliberate use of inflation to reduce debt could raise interest rate risk premia, not captured by model.
- RW spillovers:
  - Small with no accommodation and one-year accommodation.
  - With two-year accommodation, spillovers larger: about 0.6 percent average increase in RW real GDP with financial accelerator vs about 0.3 percent without.

### B. Increase in General Lump-Sum Transfers
- Effects on U.S. GDP are small:
  - Model without financial accelerator, no accommodation: GDP increases by less than 0.2 percent (consumption rises somewhat; investment falls).
  - One-year accommodation: similar.
  - Two-year accommodation: real GDP rises by about 0.3 percent.
- Main reason: liquidity-constrained households comprise only one quarter of U.S. households; other households treat transfer as a two-year windfall and spend little.
- Small initial demand increase → minimal secondary effects and minimal decline in real interest rates under accommodation.
- Adding financial accelerator:
  - Very small increase in multiplier for no accommodation and one-year accommodation.
  - With two-year accommodation, somewhat larger effects on corporate net worth and external finance premium; real GDP rises by about 0.4 percent on average over two years.
  - Spillovers to RW more noticeable only in the case with financial accelerator and two-year accommodation.

### C. Increase in Targeted Lump-Sum Transfers
- Targeted transfers directed at liquidity-constrained households (one quarter of U.S. households).
- Effects:
  - Aggregate increase in consumption much higher than untargeted transfers.
  - U.S. GDP effects almost four times larger than general lump-sum transfers.
  - Two-year monetary accommodation:
    - Model without financial accelerator: U.S. GDP = 1.1 percent.
    - Model with financial accelerator: U.S. GDP = 1.5 percent.
    - Comparable general transfers: 0.3 percent (without accelerator) and 0.4 percent (with accelerator).
- Spillovers:
  - Larger increase in U.S. demand raises inflation in both U.S. and RW.
  - With financial accelerator and monetary accommodation, higher RW inflation lowers RW real interest rates → improves RW corporate balance sheets and external finance premia → significantly larger RW GDP increase (about four times larger than for general lump-sum transfers with two-year accommodation and financial accelerator).

### D. Decrease of the Labor Income Tax Rate
- A discretionary reduction of about 1.7 percentage points in the tax rate on labor income is needed to achieve a discretionary increase of 1 percent in the ratio of the government deficit to GDP.
- Effects:
  - For both models (with and without financial accelerator), U.S. GDP effect is slightly larger than general lump-sum transfers under no accommodation and one-year accommodation, and slightly smaller under two-year accommodation.
  - Mechanisms:
    - Labor income tax cut increases labor supply → increases potential and actual output.
    - Increase in potential GDP reduces inflationary pressure → less decline in real interest rate → less monetary stimulus to aggregate demand compared with general transfers.
    - Example: two-year accommodation and no accelerator — riskless real interest rates fall on average by about 0.3 percentage points with general lump-sum transfers but are virtually unchanged with labor income tax cut.
  - Smaller changes in real interest rates imply less propagation via financial accelerator effects on the external finance premium.

### VI. Effects of Announced G20 Fiscal Stimulus Packages
- Simulations based on announced G20 fiscal stimulus packages implemented over 2009 and 2010; monetary policy assumption: two years of accommodation.
- Regional package features:
  - Japan, emerging Asia and the United States announced the largest fiscal packages.
  - Composition:
    - Japan: general and targeted transfers dominate.
    - Emerging Asia: government investment spending dominates.
    - United States: general and targeted transfers and labor income taxes dominate.
    - Euro area, Africa and Latin America: smaller packages with a relatively large role for corporate income tax cuts in 2010.
  - Government consumption expenditures do not predominate in any region.
- Simulation outcomes:
  - Both model versions show considerable GDP impact from announced packages.
  - Regional decomposition reflects package sizes and higher multipliers of government investment (e.g., emerging Asia).
  - Even tax- and transfer-dominated packages have sizeable effects.
  - Effects in model with financial accelerator are up to 50 percent larger due to favorable effects on corporate net worth and external financing premium from stimulus-induced economic improvement.
- Data: stimulus package estimates based on IMF staff data as of April 20, 2009.

### VII. Long-Run Effects of the Accumulation of Public Debt
- Scenario: permanent 0.5 percentage point increase in the U.S. government deficit to GDP ratio, ultimately resulting in a 10 percentage point increase in the U.S. government debt to GDP ratio.
- Assumptions:
  - Deficits initially driven by stimulus measures based on higher lump-sum transfers or lower taxes on labor income, consumption and capital income.
  - As debt and real interest rates increase, transfers are lowered or taxes increased, but not enough to reverse the 0.5 percentage point deficit increase.
  - Analysis restricted to the model version with a financial accelerator.
- Transitional dynamics (illustrated for stimulus based on lower labor income tax rates):
  - First 10 years: U.S. GDP, consumption, and investment increase.
  - Higher aggregate demand → deteriorating trade balance and real appreciation.
  - Inflation and nominal interest rates rise; real interest rates rise except for the first two periods.
  - Longer run: real GDP declines relative to baseline by ultimately about 0.4 percent.
- Two long-run channels causing GDP decline:
  1. Higher fiscal deficits → lower U.S. saving → lower world saving → higher world real interest rate → crowding out of investment in U.S. physical capital → lower real output; also crowding out of U.S. investment in net foreign assets → progressive deterioration in U.S. current account imbalances and need for real effective exchange rate depreciation above baseline.
  2. Evolution of distortionary labor income taxes: initially fall to stimulate GDP, but in the longer run they must rise above baseline to service larger public debt with higher real interest rate.
- Long-run international effects: significant negative effect on GDP in other regions as higher world real interest rates reduce capital ratios and hence GDP globally.
- Long-run quantitative result preview:
  - Higher debt results in a decline in long-run U.S. real GDP of 0.27 percent for general transfers (Table 2 referenced for regional breakdown).

*Source: _wp09255 - 3.  Monetary Policy*

### 0.34 percent for consumption taxes, 0.43 percent for labor income taxes and 0.64 percent

### _wp09255 - 0.34 percent for consumption taxes, 0.43 percent for labor income taxes and 0.64 percent

### Key quantitative findings
- The corresponding figures for global real GDP are 0.21 percent, 0.24 percent, 0.28 percent and 0.34 percent.
- The multipliers of a two-year fiscal stimulus package range from 1.3 for government investment to 0.2 for general transfers.
- In the presence of monetary accommodation and a financial accelerator mechanism multipliers are up to twice as large.
- A permanent 0.5 percentage points increase in the U.S. deficit to GDP ratio leads to a 10 percentage points increase in the U.S. debt to GDP ratio in the long run.
- Servicing this higher debt eventually reduces U.S. output by between 0.3 and 0.6 percent, with output losses larger for more distortionary fiscal instruments.
- The real interest rate effect (but not the tax burden effect) affects the rest of the world equally and accounts for output losses of around 0.2 percent.

### Mechanisms and channels
- Non-Ricardian household behavior raises world real interest rates, crowding out investment and reducing potential output worldwide.
- The U.S. faces worse outcomes for all instruments because it must finance a higher debt stock from higher distortionary taxes.
- More distortionary taxes produce greater negative effects on potential GDP.
- Monetary accommodation lowers real interest rates, which improves corporate balance sheets and reduces the external finance premium; this amplifies fiscal multipliers when combined with a financial accelerator.

### Short-run versus long-run trade-offs
- Short- and medium-run: Fiscal stimulus can produce favorable domestic outcomes (positive GDP multipliers, up to 1.3 for government investment; transfers and tax cuts have lower multipliers).
- Long-run: Permanently higher deficits and debt lead to higher distortionary taxes and higher real interest rates, producing very unfavorable long-run consequences for domestic and global output.
- The long-run output losses from higher debt are permanent and can exceed the short-run stimulus effects for the same instruments.

### Policy implications and recommendations
- A carefully chosen package of fiscal and supporting monetary stimulus measures can significantly support domestic and global economies during acute stress.
- Such stimulus measures should be embedded in a conservative medium-term fiscal framework to ensure that deficits and debt do not drift upwards permanently when the economy recovers.
- In the absence of a credible medium-term fiscal framework, the long-run costs of permanently higher deficits would far exceed the short-run benefits.

*Source: IMF working paper content from _wp09255 - 0.34 percent for consumption taxes, 0.43 percent for labor income taxes and 0.64 percent*

### References

### _wp09255 - References

### References (Selected citations from the unit)
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- Chari, V.V. and Kehoe, P.J. (1999), “Optimal Fiscal and Monetary Policy”, Chapter 26 in Taylor, J.B. and Woodford, M., eds., Handbook of Macroeconomics, Volume 1C, Elsevier.
- Christiano, L., Motto, R. and Rostagno, M. (2009), “Financial Factors in Business Cycles”, Working Paper, Northwestern University and European Central Bank.
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- Engen, E.M. and R.G. Hubbard (2004), “Federal Government Debt and Interest Rates”, NBER Macroeconomics Annual, 19, 83-138.
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- Freedman, C., M. Kumhof, D. Laxton, and J. Lee (2009a), “The Case for Global Fiscal Stimulus”, IMF Staff Position Paper No. 09/04 (Washington, DC.: International Monetary Fund).
- Freedman, C., M. Kumhof, D. Laxton, D. Muir and S. Mursula (2009b), “Fiscal Multipliers Galore”, forthcoming IMF Working Paper.
- Friedman, M. (1957), A Theory of the Consumption Function, Princeton, NJ: National Bureau of Economic Research.
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- Gramlich, E.M. (1999), “Remarks by Governor Edward M. Gramlich before the Wharton Public Policy Forum Series, Philadelphia, Pennsylvania”.
- International Monetary Fund (2009), “Global Economic Slump Challenges Policies”, World Economic Outlook Update, January, World Economics and Financial Surveys (Washington).
- Ireland, P. (2001), “Sticky-Price Models of the Business Cycle: Specification and Stability”, Journal of Monetary Economics, 47, 3-18.
- Kamps, C. (2004), “New Estimates of Government Net Capital Stocks for 22 OECD Countries 1960-2001”, IMF Working Paper Series, WP/04/67.
- Kumhof, M. and D. Laxton (2009a), “Simple, Implementable Fiscal Policy Rules”, IMF Working Papers, WP/09/76.
- Kumhof, M. and D. Laxton (2009b), “Fiscal Deficits and Current Account Deficits”, IMF Working Papers, WP/09/237.
- Kumhof, M., D. Laxton, D. Muir, and S. Mursula (2009), “The Global Integrated Monetary and Fiscal Model - Theoretical Structure”, IMF Working Papers (forthcoming).
- Laubach, T. (2003), “New Evidence on the Interest Rate Effects of Budget Deficits and Debt”, Finance and Economics Discussion Series 2003-12, Board of Governors of the Federal Reserve System.
- Laxton, D. and P. Pesenti (2003), “Monetary Rules for Small, Open, Emerging Economies”, Journal of Monetary Economics, 50(5), 1109-1152.
- Ligthart, J.E. and Suárez, R.M.M. (2005), “The Productivity of Public Capital: A Meta Analysis”, Working Paper, Tilburg University.
- Lucas, R.E. (1972), “Expectations and the Neutrality of Money”, Journal of Economic Theory, 4, 103-124.
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### Figures (captions and variables illustrated)
- Figure 1: WEO Revisions to US GDP, Inflation and Interest Rates since April 2007
  - Panels: Real GDP (Index; 2006=1), CPI Inflation (In percent), Fed Funds Rate / Fed Funds Futures / 3-Month T-Bill (WEO) and Fed Funds Rates (In percentage points), Long-Term Interest Rate (In percentage points).
  - Comparison series: WEO Apr. 2007 and WEO Oct. 2009 across years 2006, 2008, 2010, 2012, 2014 with index values and percentage scales shown (range examples include 0.95–1.30 for Real GDP index; -1–4 for CPI Inflation; 0–6 for interest rates).

- Figure 2: United States: Net Worth, Liabilities, and Risky Spread
  - Panels: Nonfarm Business Net Worth and Housing Equity (In trillions of U.S. dollars; years 2006–2009 with scales 0–35), Liabilities to Net Worth Ratio (In percent; scales 60–160), Risky Spread: Difference Between Corporate BAA and 10-Year Government Bond Yield (In percentage points; scales 1–6).
  - Series: Nonfarm Business Net Worth, Housing Equity, Nonfarm Business Sector, Housing Sector, Total.

- Figures 3–8: Model impulse-response visualizations for shocks and fiscal instruments
  - Common elements: Three policy interest rate response scenarios (Immediate Policy Interest Rate Response; Unchanged Policy Interest Rate for One Year; Unchanged Policy Interest Rate for Two Years).
  - Variables displayed across figures include: Real GDP (In percent), Inflation (In percentage points), Nominal Interest Rate (In percentage points), Real Interest Rate (In percentage points), Consumption (In percent), Investment (In percent), External Financing Premium (In percentage points), Corporate Net Worth (In percent), Real GDP for Rest of the World, and other model-specific variables. Figures distinguish "Model With Financial Accelerator" and "Model Without Financial Accelerator".
  - Figure-specific focuses:
    - Figure 3: U.S. Persistent Productivity Growth Shock (Deviation from Baseline).
    - Figure 4: U.S. Persistent Increase in Borrower Riskiness (Deviation from Baseline).
    - Figure 5: U.S. Fiscal Stimulus, Instrument = Gov’t Investment (Deviation from Baseline).
    - Figure 6: U.S. Fiscal Stimulus, Instrument = General Transfers (Deviation from Baseline).
    - Figure 7: U.S. Fiscal Stimulus, Instrument = Targeted Transfers (Deviation from Baseline).
    - Figure 8: U.S. Fiscal Stimulus, Instrument = Labor Income Tax (Deviation from Baseline).

- Figure 9: Dynamic Effects of a 10 Percentage Point Increase in the Debt to GDP Ratio
  - Panels and variables include: Real GDP (% Difference), Nominal Policy Rate and CPI Inflation (Difference), Consumption and Investment (% Difference), Real Interest Rate (Difference), Real Gov’t Spending (% Difference), Real Effective Exchange Rate (% Difference; + = Depreciation), TB/GDP and CA/GDP (Difference), Labor Income Tax Rates (Difference), Government Deficit/GDP (Difference), Government Debt Ratio (Difference), Private Savings/GDP (% Difference), Capital/GDP and NFA/GDP (Difference).
  - Time horizon labels include periods 0 2 4 6 8 10 20 30 40 50 LR.

### Tables (key numeric results preserved exactly)

- Table 1: GDP Effects of G-20 Fiscal Stimulus (Percent Deviation from Baseline)
  - Model without Financial Accelerator
    - Effects on GDP Level in 2009
      - World: 1.6
      - All U.S.: 0.4 0.1 0.1 0.7 0.3
      - United States: 1.4 1.0 0.0 0.0 0.2 0.1
      - Euro Area: 0.7 0.0 0.5 0.0 0.1 0.1
      - Japan: 1.8 0.1 0.0 1.5 0.2 0.0
      - Emerging Asia: 2.6 0.4 0.1 0.1 2.0 0.2
      - Remaining Countries: 1.4 0.2 0.1 0.1 0.4 0.8
    - Effects on GDP Level in 2010
      - World: 1.3
      - United States: 1.2 1.0 0.0 0.0 0.2 0.1
      - Euro Area: 0.6 0.0 0.3 0.0 0.1 0.1
      - Japan: 1.6 0.1 0.0 1.3 0.3 0.0
      - Emerging Asia: 2.2 0.4 0.1 0.1 1.7 0.1
      - Remaining Countries: 1.1 0.2 0.1 0.1 0.5 0.5
  - Model with Financial Accelerator
    - Effects on GDP Level in 2009
      - World: 2.1
      - United States: 1.9 1.5 0.1 0.1 0.3 0.2
      - Euro Area: 0.9 0.1 0.6 0.0 0.2 0.2
      - Japan: 2.4 0.2 0.0 1.8 0.4 0.1
      - Emerging Asia: 3.1 0.8 0.1 0.1 2.1 0.3
      - Remaining Countries: 2.0 0.5 0.2 0.1 0.7 1.0
    - Effects on GDP Level in 2010
      - World: 1.9
      - United States: 1.8 1.4 0.1 0.1 0.3 0.2
      - Euro Area: 0.7 0.1 0.4 0.0 0.2 0.1
      - Japan: 2.2 0.2 0.1 1.6 0.4 0.1
      - Emerging Asia: 2.7 0.8 0.1 0.1 1.7 0.2
      - Remaining Countries: 1.8 0.5 0.2 0.1 0.7 0.7

- Table 2: Effects of a Permanent 10 Percentage Point Increase in the U.S. Government Debt to GDP Ratio (Deviation from Baseline)
  - Financed by a Cut in General Transfers
    - Real GDP (Percent): U.S. -0.27; RoW -0.20; Global -0.21
    - Real Interest Rate (Percentage points): U.S. 0.10; RoW 0.10; Global 0.10
    - Current Account to GDP (Percentage points): U.S. -0.32; RoW 0.10
    - Investment (Percent): U.S. -0.54; RoW -0.47; Global -0.48
    - Goverment Deficit to GDP (Percentage points): U.S. 0.48; RoW 0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. 0.12; RoW 0.05; Global 0.06
  - Financed by an Increase in Labor Income Taxes
    - Real GDP (Percent): U.S. -0.43; RoW -0.24; Global -0.28
    - Real Interest Rate (Percentage points): U.S. 0.11; RoW 0.11; Global 0.11
    - Current Account to GDP (Percentage points): U.S. -0.36; RoW 0.12
    - Investment (Percent): U.S. -0.73; RoW -0.54; Global -0.58
    - Goverment Deficit to GDP (Percentage points): U.S. 0.48; RoW 0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. 0.07; RoW 0.05; Global 0.06
    - Labor Income Tax Rate (Percentage points): U.S. 0.41; RoW 0.00; Global 0.09
  - Financed by an Increase in Capital Taxes
    - Real GDP (Percent): U.S. -0.64; RoW -0.25; Global -0.34
    - Real Interest Rate (Percentage points): U.S. 0.10; RoW 0.10; Global 0.10
    - Current Account to GDP (Percentage points): U.S. -0.30; RoW 0.10
    - Investment (Percent): U.S. -1.80; RoW -0.50; Global -0.79
    - Goverment Deficit to GDP (Percentage points): U.S. 0.48; RoW -0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. -0.02; RoW 0.05; Global 0.03
    - Capital Tax Rate (Percentage points): U.S. 1.25; RoW 0.00; Global 0.28
  - Financed by an Increase in Consumption Taxes
    - Real GDP (Percent): U.S. -0.34; RoW -0.21; Global -0.24
    - Real Interest Rate (Percentage points): U.S. 0.10; RoW 0.10; Global 0.10
    - Current Account to GDP (Percentage points): U.S. -0.33; RoW 0.11
    - Investment (Percent): U.S. -0.61; RoW -0.49; Global -0.51
    - Goverment Deficit to GDP (Percentage points): U.S. 0.48; RoW -0.00; Global 0.11
    - Private Saving to GDP (Percentage points): U.S. 0.11; RoW 0.05; Global 0.06
    - Consumption Tax Rate (Percentage points): U.S. 0.32; RoW 0.00; Global 0.07

*Content derived from the PDF unit "_wp09255 - References" (figures and tables captions and numeric results preserved exactly as in source).*

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