## _wp10199 - 1. Manufacturers

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---

### I. Introduction — purpose and main findings
- Context: Policy of “starving the beast” (STB) — cutting taxes to induce deficits that force reductions in government spending.
- Research question: Systematic analysis of macroeconomic and welfare trade-offs of STB using a two-country New Keynesian overlapping-generations model where Ricardian equivalence does not hold (finite planning horizons).
- Key high-level conclusions:
  - STB yields welfare gains only under restrictive conditions: cuts to particularly distortionary taxes, successful and rapid implementation of spending cuts, and correct identification of spending categories that reduce neither welfare nor productivity.
  - If spending cuts are aborted or come very late, impact on output and welfare becomes negative and large.
  - If government spending directly raises household welfare or aggregate productivity, STB is likely to be costly.

### II. Model structure — agents, sectors, and markets
- Geography:
  - Two countries: the United States and the rest of the world (RW).
- Households:
  - Overlapping generations with finite planning horizons: in each period N* (1−θ) and N (1−θ) individuals born in the United States and RW, respectively.
  - Constant probability of death (1−θ) each period; average planning horizon 1/(1−θ).
  - Labor productivity declines at constant rate χ over lifetimes.
  - Utility specification:
    - ∑_{s=0}^{∞} (βθ)^s [ 1/(1−γ) ((C_{a+s,t+s})^η (1−L_{a+s,t+s})^{1−η})^{1−γ} ]
    - Parameters: β, θ<1, γ>0, 0<η<1.
  - Cashless limit for money demand (Woodford, 2003).
  - Consumption C_{a,t} is a CES aggregate over retailed varieties with elasticity σ_R.
  - Financial assets: domestic government bonds B_{a,t} (domestic currency) and foreign bonds F_{a,t} (U.S. currency); gross nominal interest rates i^*_t and i_t.
  - Insurance contracts pay premium (1−θ)/θ on financial wealth each period and encash wealth at death.
  - Pre-tax nominal labor income: W_t Φ_{a,t} L_{a,t} with Φ_{a,t}=κ χ^a; aggregate average productivity normalized to one.
  - Taxes: labor tax τ_{L,t}; consumption tax τ_{C,t} payable on distributors’ sales price P_t; lump-sum tax τ_{ls,a,t}; capital income taxes proportional.
  - Household nominal budget constraint (as presented):
    - P^R_t C_{a,t} + P_t C_{a,t} τ_{C,t} + B_{a,t} + E_t F_{a,t} =
      (1/θ)[ i_{t−1} B_{a−1,t−1} + i^*_ {t−1} E_t F_{a−1,t−1} ] + W_t Φ_a L_{a,t} (1−τ_{L,t}) +
      ∫_0^1 D^M_{a,t}(i) di + ∫_0^1 D^D_{a,t}(i) di + ∫_0^1 D^R_{a,t}(i) di − P_t τ_{ls,a,t}.
- Aggregate consumption and wealth:
  - ˇC_t / Θ_t = ˇfw_t + ˇhw^L_t + ˇhw^K_t (financial wealth and human wealth components).
  - Marginal propensity to consume: mpc_t = 1/Θ_t with Θ_t given in model (equation (6)).
  - Steady-state relation (equation (11) as presented):
    - mpc = η / [p^R ( (1−θβ^{1/γ} g (1−η) (1−1/γ) r (1/γ −1) ) ) ]
  - Intuition: shorter planning horizons (lower θ) raise the mpc and decrease its sensitivity to r_t.
- Asset markets and open-economy features:
  - Asset markets incomplete.
  - Complete home bias in government debt and ownership of domestic firms.
  - Only international assets traded are nominal one-period bonds denominated in U.S. currency.
  - Uncovered interest parity: i_t = i^*_t ε_{t+1} with ε_t = E_t / E_{t−1}.
- Firms and production:
  - Firms managed according to owners’ finite planning horizons (discounting includes θ).
  - Manufacturing uses labor and capital accumulation with adjustment costs; distribution combines domestic and foreign goods with import adjustment cost.
  - Publicly provided capital stock (infrastructure) is essential input; government investment funds K^G_t.
  - Nominal rigidities in price-setting and retailer sales-volume adjustment costs produce inertial consumption dynamics.

### III. Mechanisms linking STB to macro and welfare outcomes
- Non-Ricardian channel:
  - Finite planning horizons (θ<1) and declining productivity (χ<1) cause debt-financed tax cuts to appear as net wealth to some households.
- Marginal propensity to consume and fiscal policy:
  - mpc depends on η, θ, γ, consumption tax path, and the real interest rate.
  - For γ=1 and exogenous labor supply with no consumption taxes, mpc = (1−βθ).
  - With γ>1 (benchmark γ=4 cited), income effects dominate substitution effects: higher real interest rates can increase mpc via income effects.
- Trade-offs specific to STB:
  - Potential benefits: cutting distortionary taxes reduces tax distortions and frees resources for private consumption.
  - Potential costs:
    - Delayed spending cuts → permanently higher government debt → higher real interest rates → lower welfare.
    - Cutting government spending that raises household utility or productivity reduces welfare or productivity.
  - Political economy risks: empirical evidence suggests STB often fails; tax cuts can increase spending or lead to later tax increases.

### IV. Government fiscal structure and STB experiment specification
- Fiscal instruments: τ_{L,t}, τ_{C,t}, τ_{K,t}, lump-sum τ^{ls}_t, government consumption G^{cons}_t and government investment G^{inv}_t.
- Government investment law of motion:
  - ˇK^G_{t+1|g} = (1 − ∆_G) ˇK^G_t + ˇG^{inv}_t. (Equation (13))
- Debt issuance: nominal one-period debt B_t at gross nominal interest rate i_t; normalized ˇb_t = B_t / (P_t T_t).
- Government budget constraint (normalized):
  - ˇb_t = (i_{t−1} / π_t^g) ˇb_{t−1} − ˇs_t. (Equation (14))
  - ˇs_t = ˇτ_t − ˇG_t. (Equation (15))
- Tax revenue definition (equation (16)):
  - ˇτ_t = τ_{L,t} ˇw_t L_t + τ_{C,t} ˇC_t + ˇτ^{ls}_t + τ_{K,t} (r_{k,t} − ∆_K q_t)) ˇK_t.
- STB specification:
  - Instantaneous cut in tax revenue to GDP ratio τ^{rat}_t = ˇτ_t / g ˇdp_t and gradual cut in government spending to GDP ratio G^{rat}_t = ˇG_t / g ˇdp_t.
  - Taxation rule: τ^{rat}_t = τ^{rat} + ǫ_τ. (Equation (17))
    - Baseline: endogenous adjustment of labor tax rate τ_{L,t}.
  - Alternative tax experiment: τ_{K,t} − τ̄_K = τ_{L,t} − τ̄_L. (Equation (18))
- STB spending protocol (transition):
  1. Fiscal authority allows increase in debt-to-GDP during transition; long-run level equals original b^{rat} + ǫ_b.
  2. Long-run target for government spending to GDP ratio:
     - ˜G^{rat}_t = (τ^{rat} + ǫ_τ) − (b^{rat} + ǫ_b) (˜r_t^g − 1). (Equation (19))
  3. Gradual convergence with autoregressive coefficient ρ_G and small debt-correction term:
     - G^{rat}_t = (1 − ρ_G) ˜G^{rat}_t + ρ_G G^{rat}_{t−1} − ξ (b^{rat}_t − b^{rat} − ǫ_b). (Equation (20))
- Calibration/sensitivity note: to obtain a smooth path for G^{rat}_t given ǫ_τ, choose ρ_G and ǫ_b consistently; doubling the time to reach new lower spending level roughly doubles the increase in long-run government debt to GDP relative to baseline.
- Government spending adjustments can be implemented via government consumption, government investment, or a combination.

### V. Model calibration and evaluation approach
- Model: two-country New Keynesian with menu of fiscal tools and nominal/real rigidities; perfect-foresight results presented.
- Welfare: compensating consumption variation statistic; sensitivity to discounting of future generations.
- Sensitivity experiments vary:
  - Speed of expenditure adjustment.
  - Government investment cuts.
  - Capital income tax cuts.
  - Planning horizons.
  - Labor supply elasticity.
  - Reversibility of tax cuts.
- Scenarios enumerated: Base Case; Slower Expenditure Adjustment; Government Investment Cut; Capital Income Tax Cut; Longer Planning Horizons; Inelastic Labor Supply; Undoing the Tax Cut.
- Reporting: impulse responses in percent deviations from initial steady state; welfare tables with 50-year horizon values.

### VI. Monetary policy: rule and calibration (model-wide key parameters and steady-state targets)
- Monetary policy rule: interest rate rule similar to Orphanides (2003) with moving-average term to track permanent changes in steady state real interest rate; κ_r = 3 to reflect major portion of long-lived change within 3 to 5 years.
- Model frequency: annual.
- Key steady-state/calibration targets and parameters:
  - Bond denomination: U.S. currency.
  - United States share of world GDP: 25 percent.
  - U.S. steady-state government debt to GDP: 50 percent.
  - U.S. steady-state net foreign liabilities to GDP: 30 percent.
  - Rest of world (RW) government debt to GDP: 50 percent.
  - U.S. imports to GDP ratio: 12 percent.
  - Steady state world real growth rate: 2.5 percent per annum.
  - Steady state inflation rate in each country: 2 percent per annum.
  - Long-run real interest rate (equalized across countries): 3 percent per annum.
  - Intertemporal elasticity of substitution: 0.25 (γ = 5).
  - Planning horizon: 10 years, implying θ = 0.9.
  - Labor productivity decline rate: χ = 0.95.
  - Fiscal crowding calibration: 1 percentage point increase in government debt to GDP in the United States → approximately 2 basis points increase in U.S. (and world) real interest rate.
  - Labor supply elasticity target: 0.5 (η chosen accordingly).
  - Elasticity of substitution: 1 between capital and labor; 1.5 between domestic and foreign manufactures.
  - Steady state price markups: 20 percent in manufacturing; 5 percent in retailing.
  - Manufacturing labor share parameters set to ensure labor income share of 60 percent.
  - Depreciation rate of capital: 10 percent per annum.
  - Steady state share of government spending in GDP: 18 percent.
  - Steady state investment to GDP ratio: 16 percent.
  - Public spending decomposition (U.S. national accounts): infrastructure investment = 3 percent of GDP; other public spending = 15 percent of GDP.
  - Depreciation rate of public capital: 4 percent per annum.
  - Elasticity of aggregate output with respect to public capital (α_G adjusted): 0.14.
  - Monetary policy parameters: interest rate smoothing δ_i = 0.25; inflation coefficient δ_π = 0.6; output growth coefficient δ_y = 0.25.
  - Overall coefficient on inflation noted as equal to 1.6.
  - κ_r = 3.
- Adjustment cost parameters and nominal rigidities chosen for plausible short-run dynamics (not numerically specified).

### VII. Experiments design and baseline quantitative results
- Baseline experiment design:
  - Immediate and permanent cut in labor income tax-to-GDP ratio of 2 percentage points.
  - Gradual cuts in government consumption to offset bulk of tax cuts within about 6 years.
  - Transition fiscal deficits raise government debt-to-GDP by 5 percentage points.
  - Long-run balancing requires government consumption to decline by somewhat more than 2 percent of GDP due to higher interest expenses.
  - The 2 percentage point labor income tax-to-GDP cut is broadly consistent with estimated size of the 2001–03 U.S. tax cuts.
- Short-run responses (baseline):
  - Aggregate consumption rises gradually by about 3.5 percent over 6 years.
  - Real interest rates increase by up to 50 basis points on impact.
  - Investment contracts by around 2 percent.
  - U.S. real dollar appreciates by 1.7 percent on impact.
  - U.S. net foreign liabilities increase eventually by around 3 percent of GDP.
  - After first 4 years, decline in investment and net exports combined with reduction in real government consumption result in a modest, temporary decline in output below initial steady state.
- Long-run responses (baseline):
  - Global interest rates rise by around 8 basis points in the long run.
  - Crowding out reduces private investment and aggregate capital stock.
  - Increase in hours worked more than offsets lower capital, leaving long-run U.S. GDP around 0.2 percent higher.
  - U.S. real exchange rate depreciates over the long run by just under 0.5 percent.
  - Real interest rates driven by monetary policy first five years, almost exclusively by fiscal policy thereafter.
- Welfare outcomes (baseline):
  - Benchmark (government consumption excluded from utility):
    - U.S. welfare improves by more than 3.0 percent of initial steady state consumption at all discount rates considered.
    - At the 3 percent discount rate, welfare increase = 3.2 percent of initial steady state consumption.
    - Welfare increase slightly stronger at smaller discount rates.
  - Alternative (government consumption included in utility; α calibrated to mrs = −1):
    - At a 3 percent discount rate, welfare loss = 1.2 percent of initial steady state consumption.
    - Net welfare change remains negative unless mrs declines in absolute value to 0.72 or less.
    - Only at discount rates of 20 percent or more would overall welfare effect become positive (outside reported range).
  - Rest of world (RW):
    - RW output declines eventually by 0.2 percent.
    - RW household welfare declines by around 0.05 percent at all social discount rates considered.

### VIII. Sensitivity: Slower Expenditure Adjustment (principal alternative scenario)
- Scenario description:
  - Bulk of tax cuts offset after around 12 rather than 6 years.
  - Public debt eventually increases by 10 rather than 5 percentage points of GDP.
- Macroeconomic outcomes:
  - U.S. net foreign liabilities to GDP ratio increases by between 5 and 6 percentage points.
  - Long-run real interest rates increase by 15 basis points (U.S. and world).
  - Long-run contraction in U.S. GDP of around 2.6 percent.
  - RW GDP contracts by around 0.7 percent.
- Welfare effects (exact reported values):
  - Under wasteful government spending assumption (mrs = 0):
    - At 3 percent discount rate, U.S. welfare improves by 1.4 percent of steady state consumption (compared with 3.2 percent in baseline).
    - RW welfare deteriorates by 0.15 percent of steady state consumption.
  - Under alternative assumption mrs = −1:
    - At 3 percent discount rate, U.S. welfare declines by 2.7 percent of steady state consumption.
    - RW welfare outcomes are significantly worse than in baseline (text reports deterioration larger than under mrs = 0).
- Interpretation:
  - Slower implementation of expenditure cuts substantially reduces or reverses positive output and welfare effects of baseline STB.
  - Stronger crowding out from higher long-run interest rates is dominant channel producing worse macroeconomic and welfare outcomes.
- Model caveat:
  - Computations favor STB because assumed elasticity of real interest rates with respect to debt is at the lower end of empirical estimates.

### IX. Policy-relevant implications extracted from analysis
- Conditions under which STB can be welfare-improving:
  - Spending cuts must be implemented quickly (rapid expenditure adjustment).
  - Cuts must target spending categories that do not reduce household welfare or aggregate productivity.
  - Tax cuts should be directed at particularly distortionary taxes.
- Risks making STB costly:
  - Delayed or aborted spending cuts → permanent higher government debt → higher real interest rates → harm to output and welfare.
  - If government spending directly increases household utility or productivity, cuts reduce welfare and damage aggregate outcomes.
- Empirical and political considerations:
  - Empirical studies cited suggest tax cuts frequently do not lead to spending restraint, and can increase spending or lead to later tax increases.

*Source: _wp10199 - 1. Manufacturers (excerpts from provided chapter/section).*

### 1. Manufacturers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    9

### 1. Manufacturers

### I. Introduction — purpose and main findings
- Context: For thirty years, prominent voices have endorsed a policy of “starving the beast” (STB) — cutting taxes to induce budget deficits so that deficits force reductions in government spending.
- Debate:
  - Proponents include Milton Friedman (2003) and Gary Becker; historical examples cited include President Reagan (1981) and the 2001 tax cuts introduced by President Bush.
  - Opposing evidence: Romer and Romer (2007) find “no support for the hypothesis that tax cuts restrain government spending; indeed, [the findings] suggest that tax cuts may actually increase spending. The results also indicate that the main effect of tax cuts on the government budget is to induce subsequent legislated tax increases.”
- Research question: Systematic analysis of macroeconomic and welfare trade-offs of STB using a two-country New Keynesian overlapping-generations model where Ricardian equivalence does not hold because consumers have finite lifetimes (finite planning horizons).
- Key high-level conclusions:
  - STB yields welfare gains only under ideal circumstances: cuts to particularly distortionary taxes, successful and rapid implementation of spending cuts, and correct identification of spending categories that reduce neither welfare nor productivity.
  - If spending cuts are aborted or come very late, the impact on output and welfare becomes negative and large.
  - If government spending directly raises household welfare or aggregate productivity, STB is likely to be costly.

### II. Model structure — agents, sectors, and markets
- Geography: Two countries — the United States and the rest of the world (RW). When needed, the United States is marked with an asterisk.
- Households:
  - Overlapping generations with finite planning horizons. In each period, N* (1−θ) and N (1−θ) individuals are born in the United States and RW, respectively.
  - Each agent faces a constant probability of death (1−θ) in each period, implying an average planning horizon of 1/(1−θ).
  - Labor productivity declines at a constant rate χ over households’ lifetimes.
  - Utility for a household of age a at time t:
    ∑_{s=0}^{∞} (βθ)^s [ 1/(1−γ) ((C_{a+s,t+s})^η (1−L_{a+s,t+s})^{1−η})^{1−γ} ]
    where β is the discount factor, θ<1 determines planning horizon, γ>0 is RRA coefficient, 0<η<1.
  - Cashless limit for money demand (Woodford, 2003).
  - Consumption C_{a,t} is a CES aggregate over retailed varieties with elasticity σ_R.
  - Households can hold domestic government bonds B_{a,t} (domestic currency) and foreign bonds F_{a,t} (U.S. currency). Gross nominal interest rates on U.S. and RW currency assets: i*_t and i_t.
  - Households enter insurance contracts that pay a premium of (1−θ)/θ on financial wealth each period and encash wealth at death.
  - Pre-tax nominal labor income: W_t Φ_{a,t} L_{a,t}, with productivity Φ_{a,t}=κ χ^a and aggregate average productivity normalized to one.
  - Taxes: labor tax τ_{L,t}; consumption tax τ_{C,t} payable on distributors’ sales price P_t (chosen as numeraire); lump-sum tax τ_{ls,a,t}. Capital income taxes assumed proportional.
  - Household budget constraint (nominal):
    P^R_t C_{a,t} + P_t C_{a,t} τ_{C,t} + B_{a,t} + E_t F_{a,t} =
    (1/θ)[ i_{t−1} B_{a−1,t−1} + i^*_ {t−1} E_t F_{a−1,t−1} ] + W_t Φ_a L_{a,t} (1−τ_{L,t}) +
    ∫_0^1 D^M_{a,t}(i) di + ∫_0^1 D^D_{a,t}(i) di + ∫_0^1 D^R_{a,t}(i) di − P_t τ_{ls,a,t}.
- Aggregate consumption and wealth relationships:
  - Aggregate consumption relation after rescaling by technology:
    ˇC_t / Θ_t = ˇfw_t + ˇhw^L_t + ˇhw^K_t
    where ˇfw_t is financial wealth, ˇhw^L_t is human wealth from labor discounted at after-tax real wage, ˇhw^K_t is human wealth from dividends and lump-sum transfers.
  - Marginal propensity to consume: mpc_t = 1/Θ_t with Θ_t given explicitly in the model (equation (6) in the source).
  - Steady-state relationship between mpc, steady-state real interest rate r, and θ:
    mpc = η / [p^R ( (1−θβ^{1/γ} g (1−η) (1−1/γ) r (1/γ −1) ) ) ]
    (equation (11) as presented).
  - Intuition: Households discount future tax liabilities at rates higher than the market real interest rate r_t (discount factors include θ and χ), so government debt can appear as net wealth to myopic households; shorter planning horizons (lower θ) raise the mpc and decrease its sensitivity to r_t.
- Asset markets and open-economy features:
  - Asset markets are incomplete.
  - Complete home bias in government debt (nominal one-period domestic-currency bonds).
  - Only international assets traded are nominal one-period bonds denominated in U.S. currency.
  - Complete home bias in ownership of domestic firms; equity is not traded domestically; households receive lump-sum dividends.
  - Uncovered interest parity (arbitrage for foreign bonds):
    i_t = i^*_t ε_{t+1}
    where ε_t = E_t / E_{t−1} is gross nominal exchange rate depreciation.
- Firms and production structure:
  - Firms are managed according to owners’ preferences (finitely-lived households) and therefore have finite planning horizons; discounting in firm valuation includes θ.
  - Production: manufacturing sector employs labor and accumulates capital subject to investment adjustment costs.
  - Distribution sector combines domestic and foreign goods subject to an import adjustment cost.
  - Publicly provided capital stock (infrastructure) is an essential input; government investment maintains this capital stock financed by tax revenue.
  - Price setting for final output subject to nominal rigidities; retailers face costs to rapidly adjust sales volumes, generating inertial consumption dynamics at short horizons.
  - Firms maximize present discounted value of dividends; technical details provided in a Technical Appendix.

### III. Mechanisms linking STB to macro and welfare outcomes
- Non-Ricardian channel:
  - Finite planning horizons (θ<1) and declining lifetime productivity (χ<1) create non-Ricardian effects; households may treat debt-financed tax cuts as net wealth because they may not be alive to pay future taxes.
- Marginal propensity to consume and fiscal policy:
  - mpc depends on η, θ, γ, the consumption tax path, and the real interest rate; balanced-budget shifts of consumption taxes from present to future increase mpc.
  - For γ=1 (log utility) and exogenous labor supply with no consumption taxes, mpc simplifies to (1−βθ).
  - With γ>1 (benchmark γ=4 cited), income effects dominate substitution effects: higher real interest rates can increase mpc by income effects, partially offsetting contractionary impacts of higher r on human wealth.
- Trade-offs specific to STB:
  - Potential benefits: cutting distortionary taxes frees resources for private consumption and reduces tax distortions.
  - Potential costs:
    - If spending cuts are delayed, government debt rises permanently, raising real interest rates and lowering welfare.
    - If government spending contributes to household utility or productivity, cuts reduce welfare or productivity.
  - Political economy risks: evidence suggests STB often fails (Romer and Romer (2007), Krugman (2003), Niskanen (2006), Bayoumi and Goncalves (2007)); tax cuts may induce subsequent legislated tax increases.

### IV. Model calibration and evaluation approach (descriptive)
- The model is calibrated as a two-country New Keynesian model with a menu of fiscal tools and standard nominal and real rigidities to generate plausible short-run impulse responses.
- Perfect-foresight results are presented; log-linear extensions are straightforward.
- Welfare is evaluated with a compensating consumption variation statistic and sensitivity to discounting of future generations is examined.
- The paper conducts baseline experiments and sensitivity analyses varying:
  - Speed of expenditure adjustment,
  - Government investment cuts,
  - Capital income tax cuts,
  - Planning horizons,
  - Labor supply elasticity,
  - Reversibility (undoing) of tax cuts.

### V. Experimental design and principal scenarios (as described)
- Experiments assess:
  - Macroeconomic responses (GDP, consumption) in the United States and RW to STB.
  - Social welfare effects through compensating consumption variation.
  - Sensitivity of welfare to the discount rate applied to future generations and to whether government spending enters the utility function or productivity.
- Scenarios noted in table of contents and figures include:
  - Base Case.
  - Slower Expenditure Adjustment.
  - Government Investment Cut.
  - Capital Income Tax Cut.
  - Longer Planning Horizons.
  - Inelastic Labor Supply.
  - Undoing the Tax Cut.
- Outcomes reported in figures and tables include:
  - Macroeconomic effects (in percent deviation from initial steady state).
  - Benchmark Welfare — No Government Spending in Utility Function.
  - Alternative Welfare — With Government Spending in Utility Function.

### VI. Policy-relevant implications extracted from analysis
- STB can be welfare-improving only under restrictive conditions:
  - Spending cuts must be implemented quickly (rapid expenditure adjustment).
  - Cuts must target spending categories that do not reduce household welfare or aggregate productivity.
  - Tax cuts should be directed at particularly distortionary taxes.
- Risks that make STB costly:
  - Delayed or aborted spending cuts lead to permanent higher government debt and higher real interest rates, harming output and welfare.
  - If government spending directly increases household utility or productivity, cuts reduce welfare and damage aggregate outcomes.
- Empirical and political considerations:
  - Empirical studies cited suggest tax cuts frequently do not lead to spending restraint, and can increase spending or lead to later tax increases.

*Source: _wp10199 - 1. Manufacturers (excerpts from provided chapter/section).*

### 1.  Manufacturers

### 1.  Manufacturers

### Manufacturing sector: technology, accumulation, and payouts
- Output of manufacturing firms: M_t (denoted M_t in source as M_t).
- Production function: CES in capital K_t, labor L_t, and labor augmenting technology T_t.
- Capital accumulation:
  - Follows the usual accumulation equation with depreciation rate ∆_K.
  - Subject to quadratic adjustment costs in gross investment I_t.
- Dividends: D^M_t equal nominal revenue minus nominal cash outflows (wage bill, investment, adjustment costs and capital income taxation).
- Capital income taxation: levied on the return to capital net of depreciation (R_{k,t} − P_t ∆_K q_t) K_t.
- Additional model structure: Standard optimality conditions for labor, capital and investment are derived and shown in the Technical Appendix.

### Key model variables and notation (as used in the source)
- R_{k,t}: nominal rental rate of capital.
- q_t: shadow price of capital (Tobin’s q).
- ∆_K: depreciation rate on private capital.
- I_t: gross investment.

---

### 2.  Distributors

### Two-stage production and pricing structure
- Firms: indexed by i ∈ [0,1]; perfectly competitive in input markets, monopolistically competitive in output market.
- Stage 1: Manufacturing output composite Y^M_t(i) produced by combining foreign and domestic manufactured goods.
  - Includes an adjustment cost that makes rapid changes in the share of foreign goods costly.
- Stage 2: Final output produced by combining Y^M_t(i) with publicly provided infrastructure capital K^G_t:
  - Z^D_t(i) = Y^M_t(i) (K^G_t / T_t)^{α_G S}. (Equation (12) in source)
- Public infrastructure:
  - K^G_t is identical for all firms and provided free to end users.
  - Enters similarly to technology but with decreasing returns α_G < 1.
  - T is a normalization factor used to set Z̄^D = Ȳ^M.
- Firm profit maximization:
  - Maximize present discounted value of nominal revenue minus nominal input costs.
  - Input costs include cost of foreign and domestic manufactured goods, a fixed cost, and inflation adjustment costs.
  - Inflation adjustment costs: quadratic in changes in the rate of inflation (following Ireland (2001) and Laxton and Pesenti (2003)).
  - Fixed cost: P_t T_t ω arises when firm produces positive output.
  - Net output: max(0, Z^D_t(i) − T_t ω).
- Optimality conditions:
  - Include input demand equations and a New Keynesian Phillips curve for final goods inflation.

---

### 3.  Retailers

### Retailer demand and adjustment costs
- Households demand a CES aggregate of consumption goods varieties from retailers.
- Retailers face quantity adjustment costs: quadratic in the rate of change of consumption.
- Retailer optimization:
  - Maximize present discounted value of revenue minus input costs and quantity adjustment costs.
  - First order condition features a steady state markup over the price of final goods and adjustment cost terms depending on the rate of change of consumption.

---

### C.  Government

### 1.  Fiscal Policy: instruments and constraints
- Fiscal instruments: tax rates τ_{L,t}, τ_{C,t}, τ_{K,t}, lump-sum taxes/transfers τ^{ls}_t, government consumption G^{cons}_t and government investment G^{inv}_t.
- Government consumption: G^{cons}_t is exogenous and unproductive.
- Government investment: G^{inv}_t augments publicly provided infrastructure capital K^G_t with law of motion:
  - ˇK^G_{t+1|g} = (1 − ∆_G) ˇK^G_t + ˇG^{inv}_t. (Equation (13) in source)
- Debt issuance: nominally non-contingent one-period debt B_t at gross nominal interest rate i_t.
- Normalized debt variable: ˇb_t = B_t / (P_t T_t).
- Government budget constraint (in normalized terms):
  - ˇb_t = (i_{t−1} / π_t^g) ˇb_{t−1} − ˇs_t. (Equation (14) in source)
  - ˇs_t = ˇτ_t − ˇG_t. (Equation (15) in source)
- Tax revenue definition:
  - ˇτ_t = τ_{L,t} ˇw_t L_t + τ_{C,t} ˇC_t + ˇτ^{ls}_t + τ_{K,t} (r_{k,t} − ∆_K q_t)) ˇK_t. (Equation (16) in source)
- Additional notation:
  - ˇG_t = ˇG^{cons}_t + ˇG^{inv}_t.
  - r^J_{k,t} = R^J_{k,t} / P_t.
  - Government debt to GDP ratio: b^{rat}_t = ˇb_t / g ˇdp_t.

### 2.  Starving-the-Beast (STB): policy experiment specification
- STB specified as:
  - Instantaneous cut in the tax revenue to GDP ratio τ^{rat}_t = ˇτ_t / g ˇdp_t.
  - Subsequent, more gradual cut in the government spending to GDP ratio G^{rat}_t = ˇG_t / g ˇdp_t.
- Taxation rule for STB:
  - τ^{rat}_t = τ^{rat} + ǫ_τ. (Equation (17) in source)
    - τ^{rat}: original steady state tax revenue to GDP ratio.
    - ǫ_τ: (negative) shock to that ratio.
  - Implementation: endogenous adjustment of one tax rate (baseline: labor tax rate τ_{L,t}).
  - Alternative experiment: labor and capital income tax rates change by equal amounts:
    - τ_{K,t} − τ̄_K = τ_{L,t} − τ̄_L. (Equation (18) in source)
    - τ̄_L and τ̄_K are labor and capital income tax rates in original steady state.

### 3.  STB spending protocol and transition dynamics
- Three assumptions for spending policy under STB:
  1. The fiscal authority allows an increase in the debt to GDP ratio during the transition to a lower spending to GDP ratio; the stock adjustment is not instantaneous. Long-run level of the ratio equals original value b^{rat} plus shock ǫ_b.
  2. Long-run target for government spending to GDP ratio ˜G^{rat}_t given by:
     - ˜G^{rat}_t = (τ^{rat} + ǫ_τ) − (b^{rat} + ǫ_b) (˜r_t^g − 1). (Equation (19) in source)
       - ˜r_t: term that converges to long-run equilibrium real interest rate (endogenous).
  3. Gradual convergence of G^{rat}_t with autoregressive coefficient ρ_G and small correction term for debt deviations:
     - G^{rat}_t = (1 − ρ_G) ˜G^{rat}_t + ρ_G G^{rat}_{t−1} − ξ (b^{rat}_t − b^{rat} − ǫ_b). (Equation (20) in source)
- Calibration and sensitivity notes:
  - To obtain a smooth path of government spending given shock ǫ_τ, choose convergence rate ρ_G and shock to debt level ǫ_b in a mutually consistent way.
  - Example: in sensitivity analysis, roughly doubling the time for government spending to reach its new lower level is accompanied by roughly doubling the increase in long-run government debt to GDP ratio relative to baseline.
  - Government spending to GDP ratio can be adjusted through government consumption, government investment, or a combination; both possibilities are explored in sensitivity analysis.

*Source: IMF Working Paper content unit "_wp10199 - 1.  Manufacturers"*

### 3.  Monetary Policy

### 3. Monetary Policy

### Monetary policy rule and role
- Monetary policy uses an interest rate rule similar to Orphanides (2003) but with a moving-average term to track permanent changes in the steady state real interest rate in an overlapping generations model.
- The steady state nominal interest rate proxy ̃r_t includes a moving average of past real interest rates to reflect evolution of the equilibrium real interest rate over time.
- κ_r is set to 3 in the moving-average expression to ensure that ̃r_t "starts to reflect the major portion of a long-lived change in r_t within a period of 3 to 5 years."

### Calibration (model-wide key parameters and steady-state targets)
- Model frequency: annual.
- Bond denomination: U.S. currency.
- United States share of world GDP: 25 percent.
- U.S. steady-state government debt to GDP: 50 percent.
- U.S. steady-state net foreign liabilities to GDP: 30 percent.
- Rest of world (RW) government debt to GDP: 50 percent.
- U.S. imports to GDP ratio: 12 percent.
- Steady state world real growth rate: 2.5 percent per annum.
- Steady state inflation rate in each country: 2 percent per annum.
- Long-run real interest rate (equalized across countries): 3 percent per annum.
- Intertemporal elasticity of substitution: 0.25 (γ = 5).
- Planning horizon: 10 years, implying θ = 0.9.
- Labor productivity decline rate: χ = 0.95.
- Calibration target for fiscal crowding: a one percentage point increase in government debt to GDP in the United States leads to approximately two basis points increase in the U.S. (and world) real interest rate.
- Labor supply elasticity target: 0.5 (η chosen accordingly).
- Elasticity of substitution: 1 between capital and labor; 1.5 between domestic and foreign manufactures.
- Steady state price markups: 20 percent in manufacturing; 5 percent in retailing.
- Manufacturing labor share parameters set to ensure labor income share of 60 percent.
- Depreciation rate of capital: 10 percent per annum.
- Steady state share of government spending in GDP: 18 percent.
- Steady state investment to GDP ratio: 16 percent (fixed via fraction of economic profits remaining after fixed costs in distribution).
- Public spending decomposition (U.S. national accounts): infrastructure investment = 3 percent of GDP; other public spending = 15 percent of GDP.
- Depreciation rate of public capital: 4 percent per annum.
- Elasticity of aggregate output with respect to public capital (α_G adjusted): 0.14.
- Investment, consumption and trade adjustment cost parameters and nominal rigidities chosen for plausible short-run dynamics (not numerically specified in source).
- Monetary policy parameters: interest rate smoothing δ_i = 0.25; inflation coefficient δ_π = 0.6; output growth coefficient δ_y = 0.25.
- Overall coefficient on inflation noted as equal to 1.6.
- κ_r = 3 (moving average real interest rate parameter).

### Welfare metrics and procedures
- Two welfare metrics:
  - Benchmark metric: government consumption does not directly contribute to household utility.
  - Alternative metric: government consumption per capita enters the utility function separably with weight α and same functional form parameter γ as private consumption.
- Benchmark welfare aggregation in overlapping generations: use household utility function with generation-specific consumption and leisure replaced by corresponding average per capita values; allow policymaker discount factor D to vary.
- Benchmark discount choices:
  - Baseline social discount rate set equal to the market rate of interest (3 percent), with sensitivity analysis over the range 0.1 percent to 10 percent per year.
- Compensating consumption variation (ccv): percentage increase in original steady state consumption (holding original leisure) that yields the same change in welfare as the policy change; computed for discount rates from 0.1 percent to 10 percent.
- Inclusion of government consumption in utility:
  - Utility augmented by α/(1−γ) (  G_cons_t )^{1−γ} term, where G_cons_t denotes domestic government consumption per capita.
  - Baseline calibration chooses α to obtain marginal rate of substitution mrs = −1 between private and government consumption in steady state.
  - Threshold mrs values are computed that would make the policy (STB) welfare-neutral for each discount rate (0.1 percent to 10 percent).

### Experiments and design
- Seven experiments: baseline + six variations.
- Baseline experiment:
  - Immediate and permanent cut in labor income tax-to-GDP ratio of 2 percentage points.
  - Gradual cuts in government consumption to offset the bulk of the tax cuts within about 6 years.
  - Transition fiscal deficits raise government debt-to-GDP by 5 percentage points.
  - Long-run balancing requires government consumption to decline by somewhat more than 2 percent of GDP due to higher interest expenses.
  - The 2 percentage point labor income tax-to-GDP cut is broadly consistent with estimated size of the 2001–03 U.S. tax cuts.
- Six variations test sensitivity to:
  1. Reduced speed of government spending cuts.
  2. Replacing cut in government consumption with equal percentage cuts in government consumption and government investment.
  3. Replacing cut in labor income taxes with equal percentage point cuts in labor and capital income taxes.
  4. Increasing households’ planning horizon.
  5. Reducing labor supply elasticity.
  6. Assuming spending cuts never materialize so tax cuts must be reversed.
- Reporting: impulse responses in Figures 1–7 (top panels) in deviations from initial steady state; welfare results in bottom panels; Tables 1–3 record precise numerical values including 50-year horizon values to capture long stock-flow dynamics.

### Baseline experiment quantitative results and dynamics
- Short-run responses:
  - Aggregate consumption rises gradually by about 3.5 percent over 6 years.
  - Monetary policy raises nominal interest rates in response to inflationary pressure; real interest rates increase by up to 50 basis points on impact.
  - Investment contracts by around 2 percent.
  - U.S. real dollar appreciates by 1.7 percent on impact.
  - U.S. net foreign liabilities increase eventually by around 3 percent of GDP.
  - After first 4 years, decline in investment and net exports combined with reduction in real government consumption result in a modest, temporary decline in output below initial steady state.
- Long-run responses:
  - Aggregate saving decreases (lower government saving and lower private saving due to non-Ricardian behavior).
  - Global interest rates rise by around 8 basis points in the long run (United States represents 25 percent of world GDP, so U.S. saving behavior significantly affects world saving supply).
  - Crowding out reduces private investment and the aggregate capital stock.
  - Increase in hours worked due to the tax cut more than offsets lower capital, leaving long-run U.S. GDP around 0.2 percent higher.
  - U.S. real exchange rate depreciates over the long run by just under 0.5 percent to allow higher exports to finance permanently higher imports and larger interest obligations.
  - Real interest rates are mostly driven by monetary policy over the first five years, and almost exclusively by fiscal policy thereafter.
- Welfare outcomes (baseline experiment):
  - With government consumption excluded from utility (benchmark):
    - U.S. welfare improves by more than 3.0 percent of initial steady state consumption at all discount rates considered.
    - At the 3 percent discount rate, the increase in welfare equals 3.2 percent of initial steady state consumption.
    - Welfare increase is slightly stronger at smaller discount rates.
  - With government consumption included in utility (baseline α calibrated to mrs = −1):
    - Losses from lower government consumption and higher real interest rates more than offset gains from higher private consumption and tax relief at all but the highest discount rates.
    - At a discount rate of 3 percent, the welfare loss equals 1.2 percent of initial steady state consumption.
    - The net welfare change remains negative unless mrs declines in absolute value to a threshold value of 0.72 or less.
    - Only at discount rates of 20 percent or more (not in reported range) would the overall welfare effect become positive because that heavily weights the near-term period before the government spending cut is complete.
- Rest of world (RW) effects:
  - RW output declines by eventually 0.2 percent due to higher global interest rates.
  - RW household welfare declines by around 0.05 percent at all social discount rates considered.

*Source: _wp10199 - 3.  Monetary Policy*

### 1.  Slower Expenditure Adjustment

### 1.  Slower Expenditure Adjustment

### Macroeconomic outcomes
- If the bulk of the tax cuts is offset after around 12 rather than 6 years:
  - Public debt eventually increases by 10 rather than 5 percentage points of GDP.
  - U.S. net foreign liabilities to GDP ratio increases by between 5 and 6 percentage points.
  - Long-run real interest rates increase by 15 basis points (U.S. and world).
  - Long-run contraction in U.S. GDP of around 2.6 percent.
  - Rest of the World (RW) GDP contracts by around 0.7 percent.
- Model caveat:
  - These computations favor STB because the assumed elasticity of real interest rates with respect to debt are at the lower end of the range of empirical estimates.

### Mechanism and comparison with baseline
- Key trade-off:
  - Baseline: tax reductions lower distortions enough to raise long-run output despite higher real interest rates.
  - Slower expenditure adjustment: higher public debt pushes real interest rates up so much that the net effect is a significant long-run output decline.
- Relative importance:
  - The balance between lower tax distortions and higher real interest rates is critical for the long-run output response.

### Welfare effects (exact reported values)
- Under the assumption of wasteful government spending (mrs = 0):
  - At the 3 percent discount rate, U.S. welfare improves by 1.4 percent of steady state consumption, compared with 3.2 percent in the baseline.
  - RW welfare deteriorates by 0.15 percent of steady state consumption.
- Under the alternative assumption mrs = −1:
  - At the 3 percent discount rate, U.S. welfare declines by 2.7 percent of steady state consumption (almost two and a half times larger than in the baseline).
  - RW welfare outcomes are significantly worse than in the baseline (quantified above as a deterioration of 0.15 percent under mrs = 0; with mrs = −1 the text reports U.S. decline but RW is “significantly worse than in the baseline”).

### Summary interpretation
- Slower implementation of expenditure cuts substantially reduces or reverses the positive output and welfare effects seen in the baseline STB experiment.
- Stronger crowding out from higher long-run interest rates is the dominant channel producing worse macroeconomic and welfare outcomes. 

*Source: _wp10199 - 1.  Slower Expenditure Adjustment*

### References

### _wp10199 - References

### Fiscal policy, deficits, and public finance
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### Monetary policy, rules, and interactions with fiscal policy
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### Consumption, taxes, rebates, and labor supply
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### Open economy, capital mobility, and exchange rate regimes
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### Price stickiness, wage/contract dynamics, and business cycle models
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### Public capital, productivity, and sectoral studies
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### Historical and theoretical foundations of stabilization policy
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*References list as presented in the source PDF.*

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