## 1. Manufacturers

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### Manufacturers: production, technology, and optimization
- Production:
  - Homogenous output Z_Ht sold at price P_Ht.
  - Cobb-Douglas production technology: Z_Ht = (K_t)^(1−α_L) (T_t L_t)^(α_L). (18)
- Capital and investment:
  - Law of motion of capital: K_{t+1} = (1−δ) K_t + I_t. (19)
  - Investment adjustment costs (quadratic): G_{I,t} = φ_I / 2 I_t [ (I_t / g − I_{t−1}) / I_{t−1} ]^2. (20)
- Nominal dividends and firm objective:
  - D_Ht = P_Ht Z_Ht − (W_t L_t + P_t I_t + P_t G_{I,t}).
  - Firm maximizes discounted nominal dividends: Max_{P_H{t+s}, L_{t+s}, I_{t+s}, K_{t+s+1}} Σ_{s=0}^{∞} ˜R_{t,s} D_{H,t+s}. (21)
  - Discount factor includes θ terms: ˜R_{t,s} = Π_{l=1}^{s} θ_{i,t+l−1} for s>0 (= 1 for s=0). (22)
- Key modelling implications:
  - Cobb-Douglas with labor share α_L; depreciation δ; adjustment cost parameters φ_I enter Euler and FOC conditions through θ in discounting.
  - Capital accumulation channel is a principal mechanism for fiscal-debt crowding-out.

### Distributors: demand, technology, and prices
- Demand and aggregation:
  - Final output is a CES aggregate of distributed varieties with elasticity σ_D; Z_{D,t}(i) = [ P_t(i) / P_t ]^{−σ_D} Z_{D,t}. (23)
- Domestic/foreign input mix and adjustment costs:
  - CES production combining domestic Y_{H,t}(i) and foreign Y_{F,t}(i) with elasticity ξ_D and quasi-share α_{H,t}.
  - Foreign-share adjustment cost: G_{F,t}(i) embedded in production aggregator (equation (24)).
  - G_{F,t}(i) = φ_F / 2 (R_t − 1)^2 / [ 1 + (R_t − 1)^2 ], with R_t = [Y_{F,t}(i)/Z_{D,t}(i)] / [Y_{F,t−1}/Z_{D,t−1}]. (25)
  - Purpose: limit excessive short-term responsiveness of international trade to the real exchange rate.
- Price and inflation adjustment:
  - Inflation adjustment costs: G_{P,t}(i) = φ_P / 2 Z_{D,t} [ P_t(i)/P_{t−1}(i) / (P_{t−1}/P_{t−2}) − 1 ]^2. (26)
  - Nominal dividends: D_{D,t}(i) = P_t(i) Z_{D,t}(i) − [ P_{H,t} Y_{H,t}(i) + P_{F,t} Y_{F,t}(i) + P_t G_{P,t}(i) + P_t T_t ω_D ].
  - Foreign input price under PPP: P_{F,t} = P^*_{H,t} E_t. (27)
- Phillips curve for final goods inflation:
  - Markup 9 = σ_D / (σ_D − 1).
  - Phillips-curve specification (as in source): 9 p^D_{t−1} = φ_P (9−1) [ π_t / π_{t−1} ] [ π_t / π_{t−1} − 1 ] − θ g r_t φ_P (9−1) β̄ Z_{D,t+1} / Z_{D,t} [ π_{t+1} / π_t ] [ π_{t+1} / π_t − 1 ] . (28)

### Retailers: demand and adjustment costs
- Demand and objective:
  - Household demand for retailer varieties C_t(i) given by (7) in source.
  - Retailer maximizes present discounted nominal revenue minus input costs and quantity adjustment costs.
- Quantity adjustment costs:
  - G_{C,t}(i) = φ_C / 2 C_t [ (C_t(i) / g − C_{t−1}(i)) / C_{t−1}(i) ]^2. (29)
- Normalized first-order condition:
  - σ_R − 1 / σ_R p_{R,t−1} = φ_C [ (β̄ C_t − β̄ C_{t−1}) / β̄ C_{t−1} ] (β̄ C_t / β̄ C_{t−1}) − θ g r_t φ_C [ (β̄ C_{t+1} − β̄ C_t) / β̄ C_t ] [ (β̄ C_{t+1} / β̄ C_t) ]^2. (30)
- Model note: retailer adjustment-cost specification materially affects consumption dynamics primarily in the first two to three years after shocks.

### Government: budget, fiscal policy targets, and dynamics
- Instruments and budget constraint:
  - Instruments: nominal one-period debt B_t, lump-sum taxes τ_t, government spending G_t.
  - Normalized debt: β̄ b_t = B_t / P_t T_t.
  - Real government budget constraint: β̄ b_t = (i_{t−1} / π_t g) β̄ b_{t−1} + β̄ G_t − β̄ τ_t. (31)
- Fiscal policy rule and targets:
  - Government targets a government-deficit-to-GDP ratio β̄ gd_rat_tgt; relationships given by equations (32) and (33).
  - Relationship between deficit target and long-run government-debt-to-GDP ratio:
    - β̄ b_rat_tgt = β̄ gd_rat_tgt π_tgt g / (π_tgt g − 1). (33)
  - Implication: debt dynamics are tied to the economy’s nominal growth rate; an autoregressive coefficient on debt at 1 / (π_tgt g) is very close to one → debt takes several decades to reach long-run value after a permanent deficit change.

### Monetary policy: rule and calibration role
- Interest-rate rule:
  - i_t = (i_{t−1})^{δ_i} [ r^{filt}_t , π^{avg}_t ]^{1−δ_i} (π^{avg}_t / π^{tgt}_t)^{(1−δ_i)δ_π}
  - r^{filt}_t = Π_{j=0}^κ (r_{t−j})^{1/(κ+1)} ; π^{avg}_t = π_{ι,t} π_{1−ι,t+1}.
- Calibration parameters:
  - δ_i = δ^∗_i = 0.4; δ_π = 1.0 (overall inflation-feedback coefficients of 2); ι = 0.5; κ = 3 (four-year moving average for r^{filt}_t).
- Role in simulations:
  - Monetary policy mainly affects short-run dynamics; long-run steady states determined by fiscal policy and household horizons.

### Equilibrium and balance of payments (key relations)
- Market clearing for manufacturing and final output and net foreign asset evolution as specified in source:
  - e_t ˇf_t = i^∗_{t−1} ξ_{t−1} ε_t π_t g e_{t−1} ˇf_{t−1} + p_H_t ˇY_F^∗_t − p_F_t ˇY_F_t
  - Market clearing for international bonds: ˇf_t + ˇf^∗_t = 0
  - GDP identity: g ˇdp_t = ˇC_t + ˇI_t + ˇG_t + p_H_t ˇY_F^∗_t − p_F_t ˇY_F_t
- Current-account and long-run net foreign liabilities relation:
  - cˇad_rat_t = −100 e_t ˇf_t − e_{t−1} ˇf_{t−1}/(π_t g g ˇdp_t)
  - ˇfl_t = − e_t ˇf_t
  - Long-run relationship: nˇfl_rat_LR = cˇad_rat_LR π_tgt g / (π_tgt g − 1)

### Calibration: key parameter values used in simulations
- Country sizes:
  - HO (home, United States) = 25 percent of world GDP.
  - RW (small open economy) = 0.5 percent of world GDP.
- Initial fiscal and external positions:
  - Initial government-debt-to-GDP ratios: 60 percent (both countries).
  - Initial U.S. net-foreign-liabilities-to-GDP ratio: 40 percent.
  - U.S. imports-to-GDP ratio targeted at 15 percent.
- Growth, inflation, and rates:
  - World technology trend growth rate g = 3% per annum.
  - Targeted inflation rate π_tgt = 2% per annum.
  - Long-run real interest rate r = 4% per annum (equalized across countries).
- Household horizons and preferences:
  - Planning horizon 1/(1−θ) evaluated with θ ranging from θ = 0.8 (5 year horizon) to θ = 0.98 (50 year horizon).
  - Baseline intertemporal elasticity γ = 4 (elasticity = 0.25); sensitivity case γ = 2.
  - Labor supply elasticity targeted at 1 via parameter η.
- Other structural parameters:
  - ξ_D = 1.5; distribution-sector variety elasticity = 6; retail-sector variety elasticity = 11.
  - Adjustment-cost parameters: φ_P = 20, φ_C = 5, φ_I = 10, φ_F = 2.
  - Annual depreciation rate = 10 percent.
- INF model differences:
  - θ = 1 (infinite horizon), 50% liquidity-constrained agents; foreign exchange risk premium parameters ζ = 0.01 and nfa = 0.1333; liquidity-constrained agents receive 25% of aggregate dividends via lump-sum redistribution.
- Small open economy (RW) specifics:
  - Size = 0.5% of world economy, zero net foreign liabilities, imports-to-GDP = 30%.

### Link to fiscal-deficit shocks: mapping and interpretation
- Shock modeled: permanent 1% increase in targeted fiscal-deficit-to-GDP ratio (ˇgd_rat_tgt), implemented via reductions in lump-sum taxes in the baseline U.S. case.
- Mapping to debt: under a 5% annual nominal growth rate, a permanent 1% increase in the fiscal-deficit-/current-account-deficit-to-GDP ratio corresponds to a 20% increase in the long-run government-debt-/net-foreign-liabilities-to-GDP ratio.

### Model variants and core mechanism differences
- INF model (infinite-horizon representative agent with 50% liquidity-constrained agents):
  - Additional saving by unconstrained consumers offsets reduced government saving → zero long-run national saving effect and zero long-run effect on real interest rate and current account.
- FIN model (finite-horizon agents with constant death probability θ):
  - Households perceive government debt as net wealth; do not fully offset fiscal deficits → long-run crowding-out of capital and foreign assets; long-run positive relationship from higher government debt to higher current account deficits.

### Quantitative simulation findings (permanent 1 percentage point increase in deficit-to-GDP)
- FIN model (representative results):
  - Short-run current account deterioration: around 0.5% of GDP.
  - Long-run current account deterioration:
    - around 0.75% of GDP for a country the size of the United States.
    - around 1% of GDP for a small open economy.
  - Long-run effects independent of fiscal instrument (lump-sum taxes or government spending).
- INF model (50% liquidity-constrained / 50% infinite-lived):
  - Short-run current account deterioration:
    - around 0.1% of GDP for lump-sum tax cuts.
    - around 0.4% of GDP for spending increases.
  - Long-run current account deterioration: zero by construction.
- U.S. tax-cut simulation highlights:
  - Tax cut of 1% of GDP raises primary and overall deficits by 1% of GDP on impact; long-run debt rises from 60% to 80% of GDP (increase of 20 percentage points).
  - INF responses:
    - Consumption rises ~0.2% in first few years; liquidity-constrained agents increase consumption ~0.6% initially; infinitely lived agents’ consumption falls ~0.2% initially.
    - Small current account deterioration ~0.1% of GDP on impact; long-run effects on real interest rate and current account = zero.
  - FIN responses (5-year horizon θ = 0.8 vs 10-year horizon θ ≈ 0.9):
    - 5-year horizon: initial consumption +2.2%, output +0.5% on impact; current account deteriorates 0.3%–0.5% of GDP starting year two; long-run deterioration ≈ 0.75% of GDP for U.S.-sized economy.
    - Long-run real interest rate rise up to 90 basis points (5-year horizon) vs 20 basis points (10-year horizon).
    - Investment declines: 0.7% of GDP (5-year horizon) vs 0.2% (10-year horizon).
    - Capital stock crowded out by almost 5% of GDP (5-year horizon); net foreign assets crowded out by ~15% of GDP (stock counterpart of long-run CA deterioration).
- Robustness to planning horizon:
  - Current account deterioration remains positive at all finite horizons; at 50-year horizon it ≈ 0.4% of GDP (declines with longer horizons but only vanishes in infinite-horizon limit).
  - To replicate INF implications within FIN framework would require planning horizons of several hundred years.
- Sensitivity analysis:
  - Lower γ (γ = 2): real interest rate increase roughly half baseline; investment drop roughly half; change in current-account-to-GDP virtually identical to baseline at 5- and 10-year horizons.
  - Fiscal instrument = government spending: larger initial GDP stimulus (INF: 0.5%; FIN 5-year: 1.0%); longer-run FIN real interest rates and current accounts similar to tax-cut baseline; INF current account deteriorates by 0.4% of GDP on impact with slow reversion to zero.
  - Coordinated worldwide deficits (HO and RW both +1% of GDP):
    - Short-run GDP stimulus stronger in FIN; worldwide saving reduction ~4 times larger → world real interest rates rise more and worldwide investment/GDP fall roughly four times more.
    - Current account effects smaller for a net international debtor: U.S. experiences a small improvement in current-account-to-GDP ratio by between 0.1 percentage points (10-year horizon) and 0.2 percentage points (5-year horizon).
- Small open economy results (size 0.5% of world GDP, zero initial net foreign assets, imports-to-GDP = 30%):
  - Country too small to affect world real interest rate long-run; FIN model: initial real rates rise ~5–10 basis points due to monetary response, long-run real rate effect ≈ zero.
  - Consumption rises on impact but GDP contracts 0.3%–0.4% because of import leakage.
  - Long-run current account deterioration ≈ 1% of GDP (one-for-one with fiscal deficit deterioration); foreigners acquire nearly all additional government debt.
  - Result sensitive to international capital-flow frictions (not pursued here).

### Policy implications and recommendations (as in source)
- The long-run international implications of permanent fiscal stimulus depend critically on:
  - Household planning horizons (finite vs infinite horizon assumptions).
  - Market openness and country size.
  - Whether fiscal expansions are global or country-specific.
- Modeling recommendation:
  - Incorporate finite-horizon (overlapping generations) or non-Ricardian microfoundations into open economy monetary business-cycle models to analyze long-run fiscal issues while preserving monetary and nominal rigidity features.
- Practical policy implications:
  - Permanent increases in deficits can materially worsen current account deficits in finite-horizon settings: up to 0.75% of GDP long-run for U.S.-sized economies and up to 1% of GDP for small open economies for a permanent 1% of GDP deficit increase.
  - Infinite-horizon representative-agent models may understate long-run external effects of permanent fiscal drift; policy evaluations of long-run global current-account rebalancing should account for non-Ricardian behavior and finite planning horizons.

*Source: _wp09237 - 1. Manufacturers . . . . . . . . . . . . . . . . . . . . .  13 (PDF).*

### 1. Manufacturers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13

### _wp09237 - 1. Manufacturers . . . . . . . . . . . . . . . . . . . . . . . . .  13

### Sections and major themes
- 1. Manufacturers — page 13
- 2. Distributors — page 13
- 3. Retailers — page 14
- C. Government — page 15
  - 1. Budget Constraint — page 15
  - 2. Fiscal Policy — page 15
  - 3. Monetary Policy — page 15
- D. Equilibrium and Balance of Payments — page 16
- III. Calibration — page 16
- IV. Permanent Increases in Fiscal Deficits — page 18
  - A. U.S. Fiscal Deficits — page 19
  - B. Sensitivity Analysis — page 21
  - C. Small Open Economies — page 22
- V. Conclusion — page 23
- References — page 25
- Tables
- Figures

### Figures listed
- 1. IMF WEO and CBO Baseline Deficit and Debt Projections for the United States — page 28
- 2. CBO Long-Term Projections for U.S. Fiscal Deficits and Debt — page 28
- 3. Dissaving and the Role of the Planning Horizon — page 29
- 4. One Percentage Point Deficit Shock, Instrument = Taxation, Part I — page 30
- 5. One Percentage Point Deficit Shock, Instrument = Taxation, Part II — page 31
- 6. One Percentage Point Deficit Shock, Instrument = Taxation, Part III — page 32
- 7. Current Account Deficit and the Planning Horizon — page 33
- 8. Real Interest Rate and the Planning Horizon — page 33
- 9. One Percentage Point Deficit Shock in a Small Open Economy — page 34
- 10. Large Open Economy Dissaving — page 35

*Source: _wp09237 - 1. Manufacturers . . . . . . . . . . . . . . . . . . . . . . .  13 (PDF).*

### 11.  Small Open Economy Dissaving . . . . . . . . . . . . . . . . . . . . . . . . . .  35

### 11.  Small Open Economy Dissaving

### I. Introduction and policy context
- Many governments announced sizeable expansionary fiscal stimulus packages in response to the recent financial crisis; these packages are large as a share of GDP and differ greatly across countries.
- Concern: a significant share of these increases in government deficits may represent a permanent drift to higher deficits rather than a temporary spike, raising long-run fiscal sustainability issues.
- U.S. example cited: Auerbach and Gale (2009) argue extensions of stimulus measures and Bush tax cuts could worsen deficits materially; IMF WEO projection shows U.S. debt-to-GDP ratio expected to reach 100 percent over the next decade.
- Long-run risks are compounded by demographics, medical costs, and increased uncertainty about the long-run sustainable growth rate of potential output.
- Central question of the paper: can deteriorations in fiscal deficits be a major contributing factor to deteriorations in current account deficits, and conversely, would fiscal consolidation among major deficit spenders materially help resolve global current account imbalances?

### II. Methodological approach and model class
- Approach: use an open economy dynamic general equilibrium model with microfoundations to simulate effects of fiscal deficit shocks and explore sensitivity to model assumptions.
- Rationale: reduced-form empirical literature on fiscal–external links is mixed; permanent deficit effects can take years or decades to materialize and may be missed in empirical work.
- Key modeling insight: standard open-economy monetary business cycle models with infinite-horizon agents predict very small medium-run and zero long-run effects of fiscal deficits on the current account because they mechanically force net foreign assets to return to baseline in the long run.
- Alternative: finite-horizon (overlapping generations / Blanchard (1985)) models allow households and firms to have finite planning horizons, generating non-Ricardian behavior and allowing long-run crowding-out effects of permanent increases in government debt, including endogenous net foreign liability positions.
- Two model variants used:
  - FIN: finite-horizon model where agents face a constant probability of death (θ < 1) and average planning horizon 1/(1−θ).
  - INF: infinite-horizon representative agent model with a 50% share of liquidity-constrained agents (horizon effectively zero) and 50% infinitely lived agents, with a small external risk premium ξt to allow determination of steady-state net foreign assets.

### III. Key model features and mechanisms
- Households:
  - Utility over consumption Ca,t, leisure (1−La,t), and real balances (Ma,t/PRt) with discount factor β and finite-horizon parameter θ.
  - Consumption aggregates via CES retail varieties with elasticity σR; endogenous labor supply; CRRA preferences with relative risk aversion γ.
  - Financial assets: domestic nominal one-period government bonds (home bias) and foreign bonds denominated in HO currency. Only nominally non-contingent one-period bonds traded internationally in HO currency.
  - Insurance contract assumption: households pay a premium of (1−θ)/θ on financial wealth each period and financial wealth is encashed at death.
  - Aggregation across cohorts yields aggregate consumption system where consumption responds to aggregate real financial wealth fw t and human wealth hw t with marginal propensity to consume 1/Θt.
  - Marginal propensity to consume steady-state relationship (for calibration insight):
    - mpc = η / (p̄R) * ( (1−θβ) / (1/γ) * g^( (1−η)(1−1/γ) ) ) / ( r̄^(1/γ − 1) )
    - (Equation (15) in text; highlights roles of θ, γ, η, g, r̄, and p̄R)
  - Intuition: government debt can be perceived as net wealth by finite-horizon households because households discount distant future taxes (which service debt) more heavily than the government does.
- Firms and markets:
  - Manufacturing (competitive), distribution and retail (monopolistic competition) sectors; distributors face nominal price rigidities, retailers face quantity adjustment costs generating consumption inertia.
  - Capital accumulation subject to adjustment costs; capital provides a key channel for government debt crowding-out.
  - Asset markets incomplete; complete home bias in ownership of domestic firms and government debt.
  - Uncovered interest parity: it = i* t ξt εt+1, with ξt equal to one in FIN model and a small function of net foreign liabilities in INF variant.
- Policy rules:
  - Monetary policy: standard reaction function to stabilize inflation (state-of-the-art monetary specification preserved).
  - Fiscal policy: stabilizes government deficit and government debt; longer-run dynamics depend only on fiscal policy.

### IV. Quantitative findings and comparisons
- Main simulation: permanent 1 percentage point increase in the government-deficit-to-GDP ratio (1% of GDP).
- FIN model results:
  - Short-run current account deterioration: around 0.5% of GDP.
  - Long-run current account deterioration:
    - around 0.75% of GDP for a country the size of the United States.
    - around 1% of GDP for a small open economy.
  - Long-run effects are independent of whether fiscal instrument is lump-sum taxes or government spending.
- INF model (50% infinitely lived, 50% liquidity-constrained) results, otherwise identical calibration:
  - Short-run current account deterioration:
    - around 0.1% of GDP for lump-sum tax cuts.
    - around 0.4% of GDP for spending increases.
  - Long-run current account deterioration: zero by construction (reflecting infinite-horizon Ricardian forces and model assumptions).
- Interpretation:
  - Even moderate departures from the infinite-horizon assumption (e.g., finite horizons as long as 50 years) produce radically different long-run results.
  - The FIN model can generate significantly larger immediate and sustained current account effects of permanent deficit increases than the INF model.
  - The liquidity-constrained (zero-horizon) limit produces strong short-run consumption effects but cannot capture the long-run steady-state net foreign asset determination that finite-horizon models provide.

### V. Policy implications and economic intuition
- Fiscal stimulus premised on non-Ricardian behavior (households not offsetting lower government saving by raising private saving) is consistent with finite-horizon and liquidity-constrained interpretations; these same non-Ricardian features imply longer-run external adjustment implications when deficits are made permanent.
- Shorter household planning horizons (lower θ):
  - Increase marginal propensity to consume.
  - Reduce sensitivity of consumption to real interest rate changes.
  - Lead to larger increases in real interest rates and larger reductions in private saving and investment following permanent deficit increases, potentially amplifying external deficits.
- Implication for global imbalances:
  - Permanent increases in deficits in small open economies can produce material and persistent current account deteriorations (up to 1% of GDP for a 1% of GDP deficit increase).
  - Infinite-horizon model assumptions may understate the long-run external implications of permanent fiscal drift.
- Modeling recommendation:
  - Integrate finite-horizon (overlapping generations) or otherwise non-Ricardian microfoundations into open economy monetary business cycle models to analyze longer-run fiscal issues without losing monetary and nominal rigidity features.

*Source: _wp09237 - 11.  Small Open Economy Dissaving (excerpts from the chapter text)*

### 1.  Manufacturers

### 1.  Manufacturers

### Manufacturers: production, technology, and optimization
- Manufacturers produce homogenous output Z_Ht and sell it at price P_Ht.
- Production technology (Cobb-Douglas in capital K_t and labor L_t, labor share parameter α_L):
  - Z_Ht = (K_t)^(1−α_L) (T_t L_t)^(α_L). (18)
- Capital accumulation and investment adjustment costs:
  - Law of motion of capital: K_{t+1} = (1−δ) K_t + I_t. (19)
  - Investment adjustment costs (quadratic in gross investment growth):
    - G_{I,t} = φ_I / 2 I_t [ (I_t / g − I_{t−1}) / I_{t−1} ]^2. (20)
- Nominal dividends D_Ht:
  - D_Ht = P_Ht Z_Ht − (W_t L_t + P_t I_t + P_t G_{I,t}) (nominal cash outflows).
- Firm optimization problem (maximization of discounted nominal dividends):
  - Max_{P_H{t+s}, L_{t+s}, I_{t+s}, K_{t+s+1}} Σ_{s=0}^{∞} ˜R_{t,s} D_{H,t+s}. (21)
  - Discounting term:
    - ˜R_{t,s} = Π_{l=1}^{s} θ_{i,t+l−1} for s>0 (= 1 for s=0). (22)
- First-order conditions for labor, investment, and capital are standard except for the presence of the term θ in the discount factor (details in Technical Appendix).

### Key model features for manufacturers
- Cobb-Douglas production with explicit labor share α_L.
- Capital evolves with depreciation rate δ and faces quadratic adjustment costs parameterized by φ_I.
- Discounting includes θ terms, altering standard Euler conditions.

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### 2.  Distributors

### Demand and aggregation
- Final output produced by distributors; customers demand a CES aggregate of distributed varieties with elasticity of substitution σ_D.
- Aggregate demand for variety i:
  - Z_{D,t}(i) = [ P_t(i) / P_t ]^{−σ_D} Z_{D,t}. (23)
- Numeraire price index P_t is defined analogously to equation (4) (as in source).

### Distributor technology and adjustment costs
- CES production in domestic and foreign manufactures Y_{H,t}(i) and Y_{F,t}(i), with elasticity of substitution ξ_D and domestic goods quasi-share α_{H,t}.
- Production subject to an adjustment cost G_{F,t}(i) that makes rapid changes in the share of foreign tradables costly:
  - Z_{D,t}(i) =
    (α_{H,t})^{1/ξ_D} [ Y_{H,t}(i) ]^{(ξ_D−1)/ξ_D} + (1−α_{H,t})^{1/ξ_D} [ Y_{F,t}(i) (1−G_{F,t}(i)) ]^{(ξ_D−1)/ξ_D}
    all raised to the ξ_D/(ξ_D−1) power. (24)
  - G_{F,t}(i) = φ_F / 2 (R_t − 1)^2 / [ 1 + (R_t − 1)^2 ], where R_t = [Y_{F,t}(i)/Z_{D,t}(i)] / [Y_{F,t−1}/Z_{D,t−1}]. (25)
  - (Footnote: this assumption addresses potential excessive short-term responsiveness of international trade to the real exchange rate.)

### Prices, costs, and inflation adjustment
- Prices of inputs and marginal cost: P_Ht, P_Ft, and P_Dt.
- Inflation adjustment costs G_{P,t}(i) (quadratic in changes in the rate of inflation):
  - G_{P,t}(i) = φ_P / 2 Z_{D,t} [ P_t(i)/P_{t−1}(i) / (P_{t−1}/P_{t−2}) − 1 ]^2. (26)
- Nominal dividends D_{D,t}(i):
  - D_{D,t}(i) = P_t(i) Z_{D,t}(i) − [ P_{H,t} Y_{H,t}(i) + P_{F,t} Y_{F,t}(i) + P_t G_{P,t}(i) + P_t T_t ω_D ].
  - Fixed resource cost P_t T_t ω_D applies as long as the firm produces positive output; net output = max(0, Z_{D,t}(i) − T_t ω_D).
- Price of foreign inputs under purchasing power parity:
  - P_{F,t} = P^*_{H,t} E_t. (27)

### Phillips curve for final goods inflation
- Markup parameter 9 = σ_D / (σ_D − 1).
- Phillips curve for final goods inflation π_t:
  - 9 p^D_{t−1} = φ_P (9−1) [ π_t / π_{t−1} ] [ π_t / π_{t−1} − 1 ]
    − θ g r_t φ_P (9−1) β̄ Z_{D,t+1} / Z_{D,t} [ π_{t+1} / π_t ] [ π_{t+1} / π_t − 1 ] . (28)
  - (Equation as presented in source; first-order conditions for input demands listed in Technical Appendix.)

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### 3.  Retailers

### Demand, costs, and optimization
- Household demand for retailer-supplied varieties C_t(i) is given by (7) (as in source).
- Retailers maximize present discounted nominal revenue P_{R,t}(i) C_t(i) minus nominal input costs P_t C_t(i) and quantity adjustment costs P_t G_{C,t}(i).
- Quantity adjustment costs:
  - G_{C,t}(i) = φ_C / 2 C_t [ (C_t(i) / g − C_{t−1}(i)) / C_{t−1}(i) ]^2. (29)

### First-order condition (normalized)
- Normalized first-order condition for retailer’s problem:
  - σ_R − 1 / σ_R p_{R,t−1} = φ_C [ (β̄ C_t − β̄ C_{t−1}) / β̄ C_{t−1} ] (β̄ C_t / β̄ C_{t−1})
    − θ g r_t φ_C [ (β̄ C_{t+1} − β̄ C_t) / β̄ C_t ] [ (β̄ C_{t+1} / β̄ C_t) ]^2. (30)
- Model note: this specification only has a significant effect on consumption dynamics in the first two to three years following a shock, leaving longer-run results largely unaffected.

---

### C. Government

### 1.  Budget Constraint
- Government instruments: nominal one-period debt B_t (interest rate i_t), lump-sum taxes τ_t, government spending G_t.
- Normalized real debt: β̄ b_t = B_t / P_t T_t.
- Real government budget constraint:
  - β̄ b_t = (i_{t−1} / π_t g) β̄ b_{t−1} + β̄ G_t − β̄ τ_t. (31)

### 2.  Fiscal Policy
- Government sets a target β̄ gd_rat_tgt for the government-deficit-to-GDP ratio β̄ gd_rat_t:
  - β̄ gd_rat_t = 100 ( (i_{t−1} − 1) β̄ b_{t−1} / π_t g + β̄ G_t − β̄ τ_t ) / g
  - β̄ dp_t = 100 ( β̄ b_t − β̄ b_{t−1} / π_t g ) / g
  - β̄ dp_t = β̄ gd_rat_tgt. (32)
- Relationship between deficit target and long-run government-debt-to-GDP ratio β̄ b_rat_tgt:
  - β̄ b_rat_tgt = β̄ gd_rat_tgt π_tgt g / (π_tgt g − 1). (33)
  - π_tgt is the central bank’s inflation target.
- Implications:
  - A target for the government-deficit ratio ensures a non-explosive government debt ratio; the ratio between the two is given by the economy’s nominal growth rate.
  - The autoregressive coefficient on debt, at 1 / (π_tgt g), is very close to one, implying that following a permanent change in the deficit target, debt takes several decades to reach its long-run value.

*Source: _wp09237 - 1.  Manufacturers*

### 3.  Monetary Policy

### 3.  Monetary Policy

### Monetary policy rule and rationale
- Monetary policy relies on an interest rate rule to stabilize inflation. The rule is similar to conventional inflation-forecast-based rules, but the “steady state” value of the real interest rate is proxied by a moving average of past actual real interest rates to reflect permanent changes in equilibrium real interest rates induced by permanent saving shocks.
- Targeted inflation rate is a geometric weighted average of current year and one-year-ahead inflation with weight ι on current-year inflation and target π_tgt. The rule as stated in the source:
  - i_t = (i_{t−1})^{δ_i} [ r^{filt}_t , π^{avg}_t ]^{1−δ_i} (π^{avg}_t / π^{tgt}_t)^{(1−δ_i)δ_π}
  - r^{filt}_t = Π_{j=0}^κ (r_{t−j})^{1/(κ+1)}
  - π^{avg}_t = π_{ι,t} π_{1−ι,t+1}
- Monetary policy, like adjustment costs, only affects the short run of simulations.

### Equilibrium and balance of payments (key relations)
- Market clearing (manufacturing and final output):
  - ˇZ_H_t = ˇY_H_t + ˇY_F^∗_t
  - ˇZ_D_t = ˇC_t + ˇI_t + ˇG_t + ω_D + ˇG_{I,t} + ˇG_{P,t} + ˇG_{C,t}
- Net foreign asset evolution:
  - e_t ˇf_t = i^∗_{t−1} ξ_{t−1} ε_t π_t g e_{t−1} ˇf_{t−1} + p_H_t ˇY_F^∗_t − p_F_t ˇY_F_t
- Market clearing condition for international bonds: ˇf_t + ˇf^∗_t = 0
- Level of GDP: g ˇdp_t = ˇC_t + ˇI_t + ˇG_t + p_H_t ˇY_F^∗_t − p_F_t ˇY_F_t
- Current-account-deficit-to-GDP ratio and net foreign liabilities (definitions and long-run relationship):
  - cˇad_rat_t = −100 (i^∗_{t−1} ξ_{t−1} ε_{t−1}) e_{t−1} ˇf_{t−1} / (π_t g) + p_H_t ˇY_F^∗_t − p_F_t ˇY_F_t / g ˇdp_t = −100 e_t ˇf_t − e_{t−1} ˇf_{t−1}/(π_t g g ˇdp_t)
  - ˇfl_t = − e_t ˇf_t
  - Long-run relationship (time subscript t replaced with LR): nˇfl_rat_LR = cˇad_rat_LR π_tgt g / (π_tgt g − 1)

### Monetary policy calibration within the model
- Interest rate smoothing parameters: δ_i = δ^∗_i = 0.4 (annual model).
- Coefficients on inflation: δ_π = 1.0, resulting in overall inflation-feedback coefficients of 2.
- Targeted inflation weighting: ι = 0.5 (equal weight on current and one-year-ahead inflation).
- Equilibrium real interest rate proxied by a four year moving average (κ = 3 implied).
- Monetary policy affects mainly short-run dynamics in simulations.

---

### Calibration (model-wide key parameter values)
- HO (home) represents the United States and accounts for 25 percent of world GDP. RW (one alternative) represents a small open economy and accounts for 0.5 percent of world GDP.
- International bonds denominated in HO currency.
- Initial government-debt-to-GDP ratios: 60 percent (both countries).
- Initial U.S. net-foreign-liabilities-to-GDP ratio: 40 percent.
- U.S. imports-to-GDP ratio targeted at 15 percent via α_H and α^∗_H.
- World technology trend growth rate g = 3% per annum.
- Targeted inflation rate π_tgt in each country = 2% per annum.
- Long-run real interest rate r is equalized across countries at 4% per annum.
- Planning horizon 1/(1−θ) evaluated with θ ranging from θ = 0.8 (5 year horizon) to θ = 0.98 (50 year horizon). Empirical evidence suggests θ between 0.8 and 0.9 is required to match interest-rate sensitivity to government debt.
- Intertemporal elasticity of substitution: baseline γ = 4 (i.e., elasticity = 0.25); sensitivity case γ = 2 considered.
- Labor supply elasticity targeted at 1 via leisure share parameter η.
- Elasticity of substitution between domestic and foreign goods ξ_D = 1.5.
- Elasticities of substitution between varieties: distribution sector = 6, retail sector = 11.
- Real and inflation adjustment cost parameters chosen to yield reasonable dynamics; calibrated values for adjustment cost parameters referenced as φ_P = 20, φ_C = 5, φ_I = 10, φ_F = 2.
- Technology share α_L, fixed cost ω_D, and initial government spending set to obtain initial shares of labor income, investment and government spending in GDP of 60 percent, 19 percent and 18 percent, respectively.
- Annual depreciation rate = 10 percent.
- INF model calibration differences:
  - θ = 1 (infinite horizon), 50% share of liquidity-constrained agents.
  - Foreign exchange risk premium function for RW with ζ = 0.01 and nfa = 0.1333 (corresponding to assumed 40% U.S. net-foreign-liabilities-to-GDP ratio).
  - Liquidity-constrained agents receive 25% share of aggregate dividends via lump-sum tax redistribution.
- Small open economy (RW) assumptions: size = 0.5% of world economy, international debt denominated in HO currency, zero net foreign liabilities, imports-to-GDP ratio = 30%.

---

### IV.  Permanent Increases in Fiscal Deficits

### Shock design and mapping to debt changes
- Shock: permanent 1% increase in targeted fiscal-deficit-to-GDP ratio ˇgd_rat_tgt (simulated via reductions in lump-sum taxes τ in baseline U.S. case).
- Under assumption of 5% annual nominal growth rate, a permanent 1% increase in the fiscal-deficit-/current-account-deficit-to-GDP ratio corresponds to a 20% increase in the long-run government-debt-/net-foreign-liabilities-to-GDP ratio.
- Comparison across model variants:
  - INF model with 50% liquidity-constrained agents.
  - FIN model with 10-year planning horizon (θ ≈ 0.9).
  - FIN model with 5-year planning horizon (θ = 0.8).

### Main mechanisms and model differences
- INF models: additional saving by unconstrained consumers offsets reduced government saving in the long run → zero long-run effects on national saving, zero long-run effect on real interest rate and current account (long run net foreign liabilities specified independently of government debt).
- FIN models: households do not fully offset fiscal deficits; increased government debt crowds out physical capital and foreign assets → long-run causal relationship from higher government debt to higher current account deficits via stock-flow dynamics.

### U.S. fiscal deficits — simulation highlights
- Tax cut of 1% of GDP on impact raises primary and overall deficits by 1% of GDP; debt rises over decades, long-run debt reaches 80% of GDP (increase of 20 percentage points from 60%).
- INF model responses:
  - Overall consumption rises by around 0.2% in first few years.
  - Liquidity-constrained agents increase consumption ~0.6% initially; infinitely lived agents’ consumption falls ~0.2% initially due to monetary policy tightening.
  - Output drops slightly on impact; small current account deficit ~0.1% of GDP on impact.
  - Long-run effects on real interest rate and current account are zero.
- FIN model responses:
  - All households respond to full profile of future deficits; consumption increases depend on planning horizon.
  - For 5-year horizon: initial consumption increase 2.2%, output up 0.5% on impact; stronger inflation leads to larger real interest rate increase and stronger real appreciation -> higher imports and depressed exports.
  - Current account deteriorates by between 0.3% and 0.5% of GDP starting in year two; long-run deterioration ≈ 0.75% of GDP for U.S.-sized economy.
  - Long-run: higher real interest rates (up to 90 basis points for 5-year horizon vs 20 basis points for 10-year horizon) and larger investment declines (0.7% of GDP for 5-year horizon vs 0.2% for 10-year horizon).
  - Stocks: domestic private capital crowded out (capital stock drops by almost 5% of GDP for 5-year horizon); net holdings of foreign assets crowded out by around 15% of GDP (stock counterpart of long-run current account deterioration).

### Robustness to planning horizon
- Current account deterioration remains positive across planning horizons; even at 50-year horizon it equals around 0.4% of GDP (long-run deterioration declines with longer horizons but does not vanish except in infinite-horizon limit).
- To replicate INF model implications, FIN model would require planning horizons of several hundred years.

### Sensitivity analysis
- Increasing intertemporal elasticity of substitution (lower γ): with γ = 2, increase in real interest rate is roughly half of baseline; drop in investment likewise about half. At 5- and 10-year horizons, change in current-account-to-GDP ratio is virtually identical to baseline.
- Using government spending rather than taxation as fiscal instrument: larger initial GDP stimulus (0.5% for INF model; 1.0% for FIN model with 5-year horizon); longer-run real interest rates and current accounts in FIN model similar to baseline; INF model current account deteriorates by 0.4% of GDP on impact with slow reversion to zero.
- Coordinated worldwide fiscal stimulus (HO and RW both increase deficits by 1% of GDP):
  - Short-run GDP stimulus stronger in FIN model; but reduction in worldwide saving is four times larger → longer-run increase in world real interest rates and decrease in worldwide investment and GDP roughly four times larger.
  - Current account effects smaller when all countries run equal deficits; a net international debtor (e.g., U.S.) experiences a small improvement in current-account-to-GDP ratio by between 0.1 percentage points (10-year horizon) and 0.2 percentage points (5-year horizon).
- Small open economy (size 0.5% of world GDP, zero net foreign assets, imports-to-GDP = 30%):
  - Country is too small to affect world real interest rate in long run.
  - In FIN model, initial real rates rise ~5-10 basis points due to monetary policy response; long-run real rate effect virtually zero.
  - Consumption rises on impact but GDP contracts 0.3%-0.4% because of import leakage.
  - Long-run current account deterioration equals almost exactly 1% of GDP (i.e., equals the fiscal deficit deterioration); foreigners acquire nearly all additional government debt.
  - Result sensitive to frictions in international capital flows; with such frictions higher fiscal deficits could increase domestic real interest rates and change private saving/investment responses, reducing current account deterioration (not pursued here).

---

### V.  Conclusion — Key findings and implications
- A permanent increase in fiscal deficits equal to 1% of GDP, if not mirrored by rest-of-world increases, leads to:
  - Short-run current account deterioration of around 0.5% of GDP.
  - Long-run deterioration of about 0.75% of GDP for a country the size of the United States, and 1% of GDP for a small open economy.
- Contrast with infinite-horizon (INF) model:
  - INF model predicts small short-run current account effects (0.1% of GDP for tax cuts; 0.4% for spending increases) and zero long-run effect by construction.
  - INF model thus cannot capture long-run stock-flow dynamics of permanent saving shocks.
- Finite-horizon (FIN) model advantages:
  - Generates empirically plausible increases in real interest rates in response to higher government-debt-to-GDP ratios with realistic planning horizons (5–10 years).
  - Produces substantially larger short-run stimulus effects and sustained long-run current account and debt implications than INF models.
- Practical policy implication:
  - The long-run international implications of permanent fiscal stimulus depend critically on household planning horizons, market openness, and whether fiscal expansions are global or country-specific; small open economies are likely to finance most of permanent deficits externally, producing near one-for-one current account deterioration.

*Source: _wp09237 - 3.  Monetary Policy (IMF working paper chapter).*

### References

### _wp09237 - References

### Major referenced topics and literature
- Methods for simulating forward-looking models and nominal rigidity analyses:
  - Armstrong, J., R. Black, D. Laxton, and D. Rose, 1998, “A Robust Method for Simulating Forward-Looking Models”.
  - Christiano, L.J., M. Eichenbaum and C. Evans (2005), “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy”.
  - Ireland, P., 2001, “Sticky-Price Models of the Business Cycle: Specification and Stability”.
  - Woodford, M., 2003, Interest and Prices: Foundations of a Theory of Monetary Policy.
- Fiscal policy, deficits, debt, and fiscal multipliers in intertemporal and open-economy frameworks:
  - Auerbach, A.J. and W.G. Gale, 2009, “The Economic Crisis and the Fiscal Crisis: 2009 and Beyond”.
  - Bayoumi, T. and S. Sgherri, 2006, “Mr. Ricardo’s Great Adventure: Estimating Fiscal Multipliers in a Truly Intertemporal Model”, WP/06/168.
  - Blanchard, O.J., 1985, “Debt, Deficits, and Finite Horizons”.
  - Blanchard, O.J. and R. Perotti, 2002, “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output”.
  - Kumhof, M. and D. Laxton, 2007, “A Party without a Hangover? On the Effects of U.S. Government Deficits”, WP/07/202.
  - Ganelli, G., 2005, “The New Open Economy Macroeconomics of Government Debt”.
  - Kopcke, R., G. Tootell and R. Triest, eds., 2006, The Macroeconomics of Fiscal Policy.
- Current account, saving glut, and global rebalancing:
  - Chinn, M. and H. Ito, 2005, “Current Account Balances, Financial Development and Institutions: Assaying the World ’Saving Glut’”, NBER No. 11761.
  - Chinn, M. and J. Lee, 2005, “Three Current Account Balances: A ‘Semi-Structuralist’ Interpretation”, NBER No. 11853.
  - Faruqee, H., D. Laxton, D. Muir and P. Pesenti, 2005, “Smooth Landing or Crash? Model-Based Scenarios of Global Current Account Rebalancing”, NBER No. 11583.
  - Frenkel, J.A., and A. Razin, 1992, Fiscal Policies and the World Economy, Second Edition.
- Debt, interest rates, and long-term fiscal outlook:
  - Engen, E.M. and R.G. Hubbard, 2004, “Federal Government Debt and Interest Rates”.
  - Laubach, T., 2003, “New Evidence on the Interest Rate Effects of Budget Deficits and Debt”.
  - Government Accountability Office, 2009, “The Nation’s Long-Term Fiscal Outlook - March 2009 Update”, GAO-09-405SP.
  - Kamenik, O., D. Laxton, J. Lee, G.M. Milesi-Ferretti, P. Rabanal, T. Tressel, and O. Celasun, 2009, “Rising U.S. Public Debt: Consequences for Bond Yields”, IMF Staff Position Paper No. 09/XX.
- Consumption, employment, and saving behavior under fiscal policy:
  - Fatas, A., and I. Mihov, 2001, “The Effects of Fiscal Policy on Consumption and Employment: Theory and Evidence”.
  - Gali, J., J.D. López-Salido and J. Vallés, 2007, “Understanding the Effects of Government Spending on Consumption”.
  - Bernheim, D.B., 1987, “Budget Deficits and the Balance of Trade”.
  - Buiter, W.H., 1981, “Time Preference and International Lending and Borrowing in an Overlapping Generations Model”.
- Model development and policy analysis tools:
  - Erceg, C., L. Guerrieri and C. Gust, 2005b, “SIGMA: A New Open Economy Model for Policy Analysis”.
  - Kumhof, M., D. Laxton, D. Muir, and S. Mursula, 2009, “The Global Integrated Monetary and Fiscal Model - Theoretical Structure” (forthcoming).
  - Laxton, D. and P. Pesenti, 2003, “Monetary Rules for Small, Open, Emerging Economies”.

### Figures, projections, and model results presented
- Figure 1: IMF WEO and CBO Baseline Deficit and Debt Projections for the United States
  - Horizontal axis years (as labeled): 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
  - Vertical axes (left and right) include numeric ticks: 0 20 40 60 80 100 120 and -2 0 2 4 6 8 10 12 14 16
  - Series labeled: WEO: Debt Held by the Public/GDP (left axis); WEO: Budget Deficit/GDP (right axis); WEO: Primary Deficit/GDP (right axis); CBO: President's Budget Deficit/GDP (right axis)
- Figure 2: CBO Long-Term Projections for U.S. Fiscal Deficits and Debt
  - Horizontal axis years (as labeled): 2007 2011 2015 2019 2023 2027 2031 2035 2039 2043 2047 2051 2055 2059 2063 2067 2071 2075 2079
  - Vertical axes numeric ticks: 0 100 200 300 400 500 600 700 800 and 0 5 10 15 20 25 30 35 40 45
  - Series labeled: Debt/GDP: Extended Baseline; Debt/GDP: Alternative Fiscal; Deficit/GDP: Extended Baseline; Deficit/GDP: Alternative Fiscal
- Figure 3: Dissaving and the Role of the Planning Horizon
  - Axes and labeled points include: Real Interest Rate; Investment, Saving; Investment; Saving (short horizon); Saving (long horizon); points A, A’, B, C
- Figures 4–6: One Percentage Point Deficit Shock, Instrument = Taxation (Parts I–III)
  - Planning horizons compared: Infinite = . . . , 10-years = ___, 5-years = - - -
  - Fiscal accounts (Figure 4) variables and plotted ranges include:
    - Tax Revenue/GDP (Difference): numeric ticks from -1.5 to 1.5
    - Gov. Spending/GDP (Difference): ticks from -0.2 to 0.5
    - Primary Deficit/GDP (Difference): ticks from -1.0 to 1.5
    - Interest Expenditure/GDP (Difference): ticks from -0.5 to 2.0
    - Government Deficit/GDP (Difference): ticks from 0.0 to 1.2
    - Government Debt/GDP (Difference): ticks from 0 to 20
    - Time horizon axis ticks: 0 5 10 15 20 25 30 35 40 45 50 (horizontal)
  - Macroeconomic aggregates (Figure 5) variables and plotted ranges include:
    - GDP (% Difference): ticks -3 -2 -1 0 1
    - Consumption (% Difference): ticks -3 -2 -1 0 1 2 3
    - Investment (% Difference): ticks -6 -4 -2 0 2
    - Government Spending (% Difference): ticks -0.1 0.1
    - Exports (% Difference): ticks -3 -2 -1 0 1
    - Imports (% Difference): ticks -6 -4 -2 0 2
    - Government Deficit/GDP (Difference): ticks 0.0 0.2 0.4 0.6 0.8 1.0 1.2
    - Current Account/GDP (Difference): ticks -0.8 -0.6 -0.4 -0.2 0.0 0.2
    - Real Interest Rate (Difference): ticks 0.0 0.2 0.4 0.6 0.8 1.0
    - Real Exchange Rate (% Difference; + = Depreciation): ticks -2 -1 0 1 2
    - Time horizon axis ticks: 0 5 10 15 20 25 30 35 40 45 50
  - Flow of funds (Figure 6) variables and plotted ranges include:
    - Government Savings / GDP (Difference): ticks -1.2 to 0.2
    - Government Debt / GDP (Difference): ticks 0 5 10 15 20
    - Private Savings / GDP (Difference): ticks -0.5 to 1.5
    - Private Financial Wealth / GDP (Difference): ticks -5 to 20
    - Investment / GDP (Difference): ticks -0.7 to 0.1
    - Capital / GDP (Difference): ticks -5 to 1
    - Current Account / GDP (Difference): ticks -0.8 to 0.2
    - Net Foreign Assets / GDP (Difference): ticks -14 to 2
    - Time horizon axis ticks: 0 5 10 15 20 25 30 35 40 45 50
- Figure 7: Current Account Deficit and the Planning Horizon
  - Vertical axis ticks: 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
  - Horizontal axis ticks: 25 10 25 50? (figure labels show: 25 10 25 50 and 25102550 with caption "Number of Years into the Future")
  - Series labeled by planning horizons: 5 years, 10 years, 15 years, 20 years, 30 years, 50 years, Infinite
  - Series plotted: CA B/GDP
- Figure 8: Real Interest Rate and the Planning Horizon
  - Vertical axis ticks: 0 10 20 30 40 50 60 70 80 90 (RR in Basis Points)
  - Horizontal axis ticks: 25 10 25 50? (25102550 with caption "Years into the Future")
  - Series labeled by planning horizons: 5 years, 10 years, 15 years, 20 years, 30 years, 50 years, Infinite
- Figure 9: One Percentage Point Deficit Shock in a Small Open Economy
  - Planning horizons compared: Infinite = . . . , 10-years = ___, 5-years = - - -
  - Macroeconomic aggregates and plotted ranges include:
    - GDP (% Difference): ticks -0.4 to 0.1
    - Consumption (% Difference): ticks -0.5 to 1.5
    - Investment (% Difference): ticks -0.5 to 0.1
    - Government Spending (% Difference): ticks -0.1 to 0.1
    - Exports (% Difference): ticks -2.0 to 0.5
    - Imports (% Difference): ticks -0.5 to 2.0
    - Government Deficit/GDP (Difference): ticks 0.0 to 1.2
    - Current Account/GDP (Difference): ticks -1.5 to 0.5
    - Real Interest Rate (Difference): ticks 0.00 0.02 0.04 0.06 0.08 0.10
    - Real Exchange Rate (% Difference; + = Depreciation): ticks -1.5 to 0.5
    - Time horizon axis ticks: 0 5 10 15 20 25 30 35 40 45 50
- Figures 10–11: Large and Small Open Economy Dissaving (schematic)
  - Labeled schematic elements include: r, S,I, S, I, I, S, 0, S0, S1, r0, r1, CA Deficit, Home, Rest of the World, World

### Key numeric labels and horizons repeatedly used across figures
- Planning horizons explicitly enumerated: 5 years, 10 years, 15 years, 20 years, 30 years, 50 years, Infinite
- Time-series and projection horizons in figures: year ranges including 2007 through 2019, and long-run horizons through 2079 with intermediate ticks at 4-year intervals in Figure 2 (2007, 2011, 2015, ..., 2079)
- Deficit and debt axes numeric ticks preserved as shown: e.g., 0 20 40 60 80 100 120 (debt scale); -2 0 2 4 6 8 10 12 14 16 (deficit scale); long-term debt axis 0 100 200 300 400 500 600 700 800; long-term deficit axis 0 5 10 15 20 25 30 35 40 45

*Italic: Source PDF filename: _wp09237 - References*

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