## _wp16146

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---

### Purpose and scope
- Uses a theoretical endogenous growth model to study design of fiscal policy reform packages and their potential to boost trend growth and welfare.
- Reform packages studied involve:
  - cuts to distortionary capital and labor income tax rates; and
  - increases in public investment.
- To keep public debt sustainable, packages include offsetting measures: reductions in unproductive government spending or increases in non-distortionary consumption taxes.
- Model limitations:
  - Consumers are homogeneous; no income or wealth inequality.
  - Does not study progressive marginal income tax changes or targeted transfers requiring heterogeneous-agent models.

### Key model features
- Integrates three features from endogenous growth literature:
  - investment in technology (human capital) offsets diminishing marginal productivity of private capital, allowing perpetual growth in output per capita;
  - cuts to distortionary tax rates change investment behavior and thus impact long-run growth;
  - public capital influences total factor productivity and growth via a congestion effect (productivity depends on the ratio of aggregate public to private capital stocks).
- Structure:
  - Two-sector, investment-based endogenous growth framework (private physical capital and human capital produced by consumers).
  - Public capital affects total factor productivity in both final output and human-capital sectors.
  - Agents: homogeneous consumers, perfectly competitive firms, and government financing productive public capital investment G_t^I and unproductive spending g_t via taxes (τ^c_t, τ^K_t, τ^L_t) and one-period bonds.
- Fiscal instruments:
  - Capital income tax τ^K_t and labor income tax τ^L_t distort accumulation and inter-sectoral allocation.
  - Consumption tax τ^c_t is non-distortionary for consumption/saving under model assumptions if levied at a constant rate over time.

### Analytical approach
- Theoretical analysis:
  - Derives relationship between fiscal policy variables (e.g., τ^K, τ^L) and steady-state growth rate.
  - Characterizes transition path of macro variables as economy converges to new steady state (Balanced Growth Path, BGP).
  - Proves unique, locally stable BGP for the functional forms used.
  - Presents closed-form expression for BGP growth rate (expression (26)/(47) in source) showing dependence on A, C, α, ϕ, γ, ε, σ, β, δ, τ^K, τ^L and function Φ.
- Numerical simulation:
  - Uses specified functional forms (6),(24),(25) and parameter assignments (Table 1).
  - Welfare metric: W = Σ_{t=0}^∞ β^t (c_t^{1-σ} − 1)/(1−σ) (equation (28)); welfare effect expressed as constant percent consumption change making consumer indifferent between reform and pre-reform BGP.
  - Two simulated reform families:
    1. Cuts to τ^K and/or τ^L offset by reductions in unproductive spending g_t or increases in consumption tax τ^c_t.
    2. Increases in public investment raising targeted G/K, with same offsetting measures.

### Baseline parameterization and fiscal baseline
- Depreciation rate: human capital = 0.1
- Depreciation rate: private physical capital = 0.1
- Depreciation rate: public capital = 0.1
- Elasticity of final output to public capital = 0.05
- Elasticity of human capital to public capital = 0.05
- Capital share in final output = 0.36
- Capital share in schooling = 0.36
- Scale factor = 13.6%
- Unproductive government spending: share of final output = 13.6%
- Labor income tax rate = 17.5%
- Capital tax rate = 17.5%
- Consumption tax rate = 7%
- Public investment: share of final output mk = 4.63% (table entries use 4.6 or 4.7; baseline growth figures use 4.6%)
- Growth rate of GDP per capita (baseline) = 4.6%
- Government debt (% of final output) (baseline) = 44.5%
- Revenue on benchmark BGP = 19.8% of final output

### Reform definitions (reference scale: a 5 percentage point cut in capital income tax rate τ^K)
- Common reform definitions:
  1. A 5 percentage point cut in the capital income tax rate τ^K.
  2. A cut to the labor income tax rate τ^L that generates the same discounted present value of total government revenue as the capital tax cut.
  3. Cuts to both τ^K and τ^L of equal magnitude that together generate the same discounted present value of revenue as the 5 percentage point τ^K cut.
  4. An increase in public investment by 1 percentage point of final output (sufficient to increase the BGP ratio of public to private capital G/K by around 10 percent).

### Quantitative outcomes — Reform Packages 1–4 (compensated by cuts to unproductive spending)
Baseline repeated:
- K_τ Rate (%) = 17.5
- L_τ Rate (%) = 17.5
- C_τ Rate (%) = 7
- Public Investment (% of final output) = 4.6
- Growth Rate of GDP per Capita (%) = 4.6
- Govt. Debt (% of final output) = 44.5

Reform outcomes (changes reported exactly):
- Reform 1 — Capital Income Tax Cut:
  - K_τ (%) = 12.5
  - L_τ (%) = 17.5
  - C_τ (%) = 7
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 4.84
- Reform 2 — Labor Income Tax Cut (revenue-equivalent to 5 percentage point capital tax cut):
  - K_τ (%) = 17.5
  - L_τ (%) = 15.08
  - C_τ (%) = 7
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.06
  - Change in Consumer Welfare (%) = 4.31
- Reform 3 — Capital and Labor Tax Cut (equal magnitude, revenue-equivalent):
  - K_τ (%) = 15.86
  - L_τ (%) = 15.86
  - C_τ (%) = 7
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 4.63
- Reform 4 — Public Investment Increase:
  - K_τ (%) = 17.5
  - L_τ (%) = 17.5
  - C_τ (%) = 7
  - Public Investment (% of final output) = 5.6
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 3.23

Additional fiscal facts (exact):
- Following a 5 percentage point capital income tax cut (or revenue-equivalent labor tax cut), revenue is lower on the post-reform BGP by around 2 percentage point of final output. Unproductive government spending must be around 2 percentage points of final output lower on the new BGP compared with the benchmark BGP to keep government debt at its level on the original BGP.

Mechanics (Reforms 1–4, summarized with exact outcomes):
- Reform 1: reduces distortions, raises post-tax return to capital, stimulates private physical capital accumulation; welfare increases by around 4.8 percent.
- Reform 2: raises post-tax wage, requires higher rental rate on private capital to avoid arbitrage through resource reallocation; welfare increases by around 4.31 percent.
- Reform 3: growth effects similar to Reform 1 and welfare effect between Reforms 1 and 2 (4.63 percent).
- Reform 4: raises G/K, boosts total factor productivity across sectors; welfare increases by around 3.23 percent.

### Quantitative outcomes — Reform Packages 5–8 (compensated by consumption tax increases)
Baseline repeated:
- K_τ Rate (%) = 17.5
- L_τ Rate (%) = 17.5
- C_τ Rate (%) = 7
- Public Investment (% of final output) = 4.6
- Growth Rate of GDP per Capita (%) = 4.6

Reform outcomes (exact figures):
- Reform 5 — Capital Income Tax Cut with C_τ increase:
  - K_τ (%) = 12.5
  - L_τ (%) = 17.5
  - C_τ (%) = 12.2
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 0.14
- Reform 6 — Labor Income Tax Cut with C_τ increase:
  - K_τ (%) = 17.5
  - L_τ (%) = 15.08
  - C_τ (%) = 13.6
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.06
  - Change in Consumer Welfare (%) = -0.48
- Reform 7 — Capital and Labor Tax Cut with C_τ increase:
  - K_τ (%) = 15.86
  - L_τ (%) = 15.86
  - C_τ (%) = 12.2
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = -0.08
- Reform 8 — Public Investment and Consumption Tax Rise:
  - K_τ (%) = 17.5
  - L_τ (%) = 17.5
  - C_τ (%) = 10.33
  - Public Investment (% of final output) = 5.6
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 0.22

Mechanics and welfare implications (Reforms 5–8, exact statements):
- Replacing lost revenue with higher consumption taxation causes an initial slowdown in consumption growth and imposes short-run welfare costs relative to offsetting revenue loss via cuts to unproductive spending.
- Reform 5 yields same long-run growth effect as Reform 1 but much smaller welfare gain (0.14% vs. 4.84%).
- Reform 6 yields a larger short-run consumption slowdown and an overall small welfare loss (-0.48%).
- Reform 7 yields a small overall welfare reduction (-0.08%).
- Reform 8 yields a positive welfare gain (0.22%) despite the consumption tax rise.

### Key quantitative takeaways (numeric fidelity preserved)
- Moderately sized distortionary tax cuts or public investment increases generate small permanent increases in annual growth of output per capita: typical reported change in growth rate of GDP per capita = 0.06–0.07 percentage points across reforms.
- Welfare effects differ markedly by financing:
  - Largest welfare gains occur when fiscal costs are offset by cuts to unproductive government spending (examples: 4.84%, 4.31%, 4.63%, ~3¼ percent).
  - Welfare gains are much smaller or negative when fiscal costs are offset by permanent consumption tax increases (examples: 0.14%, -0.48%, -0.08%, 0.22%).
- Revenue impact: a 5 percentage point capital income tax cut reduces revenue on the post-reform BGP by around 2 percentage point of final output; requires unproductive spending cuts of ~2 percentage points of final output to maintain pre-reform debt ratio.
- Interest-rate channel: interest rate on government bonds increases following capital tax cuts, expanding the interest-rate–growth differential (r_t^b − H̄) on the post-reform BGP under the calibration used, which can render sustaining the prior debt ratio infeasible without fiscal adjustment.

### Mechanisms driving long-run growth and transition dynamics (select propositions and implications)
- BGP existence and uniqueness: model admits a unique BGP when tax rates and G/K are constant (Proposition 2).
- Closed-form BGP growth rate: H^∘ given by expression (26)/(47) (source) and:
  - increases with higher G/K because public capital raises total factor productivity in both sectors;
  - decreases with higher τ^K and τ^L because these taxes distort accumulation and inter-sector allocation;
  - is unaffected by τ^c under model assumptions (τ^c constant and no leisure/labor supply choice).
- Transition dynamics:
  - Consumers choose sectoral shares v_t and u_t; Proposition 4: u_t is increasing in v_t (u'_t(v_t) > 0).
  - Cutting τ^K (or τ^L under calibration) raises BGP growth rate and BGP physical-to-human capital ratio K^∘; initial reallocation favors final output shares u_t and v_t, which fall as the economy approaches new BGP.
  - Increasing targeted G/K raises BGP growth rate and K^∘ under stated sufficient conditions (γ = ε and ε sufficiently small).

### Robustness highlights (selected rows from Table 4, numeric fidelity preserved)
- Higher pre-reform tax rates scenario:
  - Baseline: K_τ = 25; L_τ = 25; C_τ = 15; Total gov rev & spend = 29.24 & 27.66; Growth Rate of GDP per Capita (%) = 1.42.
  - Reform (offset by unproductive spending cut): K_τ = 20; L_τ = 25; C_τ = 15; Total = 27.54 & 25.93; Growth Rate = 1.5; Change in Consumer Welfare = 5.29
  - Reform (offset by cons. tax rise): K_τ = 20; L_τ = 25; C_τ = 21.25; Total = 29.04 & 27.42; Growth Rate = 1.5; Change in Consumer Welfare = 0.05
- Lower intertemporal elasticity (σ = 4 vs σ = 2):
  - Reform (offset by unproductive spending cut): K_τ = 12.5; L_τ = 17.5; C_τ = 7; Growth Rate = 1.47; Change in Consumer Welfare = 3.29
- Variation in human capital exponent φ:
  - φ = 0.45, Reform (offset by unproductive spending cut): Growth Rate = 1.51; Change in Consumer Welfare = 5.55
  - φ = 0.35, Reform (offset by unproductive spending cut): Growth Rate = 1.46; Change in Consumer Welfare = 3.75
- Increased public capital productivity (γ, ε = 0.15) and public investment rise from 4½ to 5½ %:
  - Reform (offset by unproductive spending cut): Growth Rate = 1.66; Change in Consumer Welfare = 10.7

### Policy implications (as stated in source)
- Cuts to distortionary tax rates remove distortions to private investment, spurring faster output growth via endogenous investment choices and resource reallocation between final output and human capital sectors.
- Public investment increases can raise total factor productivity and growth by increasing the ratio of public to private physical capital.
- The design of fiscal reform packages critically determines welfare outcomes: offsetting tax cuts or public investment increases with cuts to unproductive spending yields substantially larger welfare gains than financing them via higher consumption taxes.
- Quantitative results rely on representative-agent framework; allowing for heterogeneous agents (income/wealth inequality, progressive taxes, targeted transfers) could change growth and welfare effects and is left for future research.

*Source: _wp16146 (PDF chapter/section provided).*

### Introduction  ______________________________________________________________4

### _wp16146 - Introduction  ______________________________________________________________4

### Fiscal Reform in Theoretical Macroeconomic Models: Neoclassical and Endogenous Growth Theory _____________________________________________________________5
- A. Overview  _______________________________________________________________5
- B. Neoclassical Growth Theory  ________________________________________________6
- C. Endogenous Growth Models  ________________________________________________8

### The Model ______________________________________________________________9
- A. Consumers ______________________________________________________________9
- B. Firms__________________________________________________________________11
- C. The Government _________________________________________________________12
- D. Competitive Equilibrium __________________________________________________12
- E. Steady State Growth: The Balanced Growth Path _______________________________16
- F. The Mechanism Driving Long Run Growth ____________________________________16
- G. Stability of the Balanced Growth Path ________________________________________18

### Fiscal Reform Packages: The Transition Path to a New BGP _____________________18
- A. A Numerical Simulation  __________________________________________________21

### Conclusion _____________________________________________________________33

### Figures
- 1. Convergence in the Neoclassical Growth Model _________________________________7
- 2. Packages 1 and 5: Capital Income Tax Cut  ____________________________________26
- 3. Packages 2 and 6: Labor Income Tax Cut  _____________________________________31
- 4. Packages 4 and 8: Public Investment Increase __________________________________32

### Tables
- 1. Parameter Values  ________________________________________________________22
- 2. Reform Packages 1-4: Compensated by Unproductive Government Spending Cuts _____25
- 3. Reforms 5-8: Compensated by Consumption Tax Rate Increases ___________________28
- 4. Robustness Tests: Effect of Fiscal Policy Reforms under Different Assumptions  ______47

### Appendices
- I. The Competitive Equilibrium  _______________________________________________34
- II. Solving for the Balanced Growth Path ________________________________________36
- III. The Growth Mechanism __________________________________________________39
- IV. The Transition Path ______________________________________________________41
- V. A Numerical Example ____________________________________________________44
- VI. Robustness of Numerical Solutions _________________________________________46

### References ________________________________________________________________48

*Source: _wp16146 - Introduction (page listing and table of contents).*

### INTRODUCTION

### _wp16146 - INTRODUCTION

### Purpose and scope
- The paper uses a theoretical endogenous growth model to study the design of fiscal policy reform packages and their potential to boost trend growth and welfare.
- Reform packages studied involve:
  - cuts to distortionary capital and labor income tax rates; and
  - increases in public investment.
- To keep public debt sustainable, packages include offsetting measures: reductions in unproductive government spending or increases in non-distortionary consumption taxes.

### Key model features
- The model integrates three features from the endogenous growth literature:
  - investment in technology (human capital) offsets diminishing marginal productivity of private capital, allowing perpetual growth in output per capita;
  - cuts to distortionary tax rates change investment behavior and thus impact long-run growth;
  - public capital influences total factor productivity and growth.
- Structure:
  - Two-sector, investment-based endogenous growth framework (private physical capital and human capital produced by consumers).
  - Public capital affects total factor productivity through a "congestion" effect (productivity depends on the ratio of aggregate public to private capital stocks).
  - Agents: consumers (homogeneous), firms (perfectly competitive), and government.
  - Government finances productive public capital investment GtI and unproductive spending gt via distortionary taxes (τc,t, τK,t, τL,t) and one-period government bonds.
- Important modelling assumptions and limits:
  - Consumers are homogeneous; the model does not allow for income or wealth inequality.
  - The paper does not study progressive marginal income tax changes or targeted transfers that require heterogeneous-agent models.

### Analytical approach
- Theoretical analysis:
  - Mathematical derivation of model properties, including the relationship between fiscal policy variables (e.g., distortionary tax rates) and the trend (steady state) economic growth rate.
  - Characterization of the transition path of macroeconomic variables as the economy converges to a new steady state with a higher trend growth rate.
  - The model has a unique, locally stable steady state (balanced growth path) along which macro variables grow at a constant rate in the long run.
- Numerical simulation:
  - Uses reasonable parameter values to illustrate reform effects.
  - Two main simulated reform types:
    1. Cuts to capital and/or labor income tax rates, offset by reductions in unproductive government expenditure or increases in consumption tax rates to maintain public debt at its pre-reform level.
    2. Increases in public investment in productive infrastructure, with the same offsetting fiscal measures.

### Numerical simulation results and quantitative findings
- Tax cuts:
  - Modest cuts to capital income taxation and/or labor income taxation (of 5 percentage points or less) improve welfare significantly when offset by cuts to unproductive government spending, although the impact on long-run per capita growth rates is small.
  - Modest capital income tax cuts have positive (albeit small) growth effects and non-trivial welfare effects even when compensated for by increases in consumption taxation; this is not necessarily the case for labor income tax cuts.
  - There is a small welfare loss from a fiscal reform package involving modest labor income tax cuts offset by higher consumption taxes.
- Public investment:
  - Raising public investment (e.g., by 1 percentage point of GDP) has similar growth and welfare effects to tax cuts when accompanied by cuts to unproductive spending, under conservative assumptions about the productivity of public capital.
  - Increases in public investment can increase per capita growth and produce a non-trivial boost to welfare even under conservative public capital productivity assumptions.
- Offsetting by consumption taxes versus spending cuts:
  - Modest capital income tax cuts and public investment increases have smaller welfare benefits when offset by higher consumption tax rates, although growth effects are the same as when offsets are achieved via cuts to unproductive spending.

### Contributions and implications
- The paper’s key contributions are:
  - studying both the transition path and the new steady state post-reform in a theoretical growth model that integrates endogenous technological progress, productive public capital, several types of distortionary taxation, and public debt;
  - numerically verifying that cuts to capital income taxation can yield positive growth and non-trivial welfare effects even when offset by increases in consumption taxation, though this result is less robust for labor income tax cuts;
  - numerically verifying that increases in public investment can raise per capita growth and boost welfare under conservative assumptions about public capital productivity.
- Caveat for policy interpretation:
  - Results may differ in models with heterogeneous agents; extensions to include progressive taxation or targeted transfers are left for future research due to numerical solution challenges.

*Source: _wp16146 - INTRODUCTION*

### Section IV. The budget constraint for the government each period is

### Section IV. The budget constraint for the government each period is

### Government budget constraint and primary balance
- Government period budget constraint (equation (10)) is expressed in the model (see source for full algebraic form and variables).  
- The primary balance pb_t is defined as the difference between non-interest revenue and non-interest expenditure (equation (11)).  
- The primary balance expression aggregates taxes and non-interest expenditures, capturing the fiscal stance net of interest payments.

### Competitive equilibrium — firms’ optimizing conditions
- Firms choose inputs private capital v_{t-1}K_{t-1} and human-capital-augmented labor u_{t-1}H_{t-1} until marginal products equal market prices:  
  - Capital rental condition: equation (12).  
  - Labor (human-capital-augmented) wage condition: equation (13).

### Competitive equilibrium — consumers’ optimizing behavior and Euler equations
- Consumers make three choices: (i) consume or save current income; (ii) allocate new savings across physical capital K_t and government bonds B_t; (iii) allocate existing physical and human capital between human-capital production and final output (fractions v_t and u_t).  
- Consumption/saving and asset-allocation conditions:
  - Euler equation for private physical capital: equation (14).
  - Euler equation for the human capital good: equation (15), where p_t is the relative price of human capital goods.
  - Euler equation for government bond holdings: equation (16).
- In equilibrium, marginal returns on private physical capital, human capital, and government bonds are equal (prevents arbitrage).
- Tax distortion roles:
  - Capital income tax τ^K_t introduces a wedge in the Euler equation (14), distorting consumption/saving.
  - Consumption tax τ^c_t is non-distortionary for consumption/saving if levied at a constant rate over time (it cancels in (14) and (16)).
  - Labor income tax τ^L_t does not distort consumption/saving directly (deferred consumption cannot be saved directly in human capital) but does distort inter-sectoral allocation.

### Allocating resources across sectors (final output vs human-capital production)
- Consumers choose v_t and u_t to equate marginal products across sectors subject to taxation (equations (17) and (18)). Rental rate r_t and wage rate w_t equal marginal products as per firm optimality (12) and (13).  
- Tax wedges τ^K_t and τ^L_t distort inter-sectoral allocation because taxes apply to income from the final output sector but not to the (untaxed) human-capital sector in this model.  
- Combining (17) and (18) implies equality of the marginal rate of technical substitution across sectors up to taxation distortions (equation (19)).

### Definition of Competitive Equilibrium and transversality conditions
- Definition 1: Competitive Equilibrium is a sequence {c_t, K_t, H_t, B_t, v_t, u_t}∞_{t=0}, prices {r^b_t, r_t, w_t, p_t}∞_{t=0}, fiscal variables {g_t, τ^c_t, τ^K_t, τ^L_t}∞_{t=0}, and initial conditions {G_{t-1}, K_{t-1}, H_{t-1}, B_{t-1}} that satisfy market clearing, optimality conditions (12)-(18), consumer (4) and government (10) budget constraints, and transversality conditions (20)-(23).  
- Transversality conditions (preventing unused resources or Ponzi schemes):
  - Private physical capital: lim_{t→∞} β^t (1+τ^c_t) u_{c,t} K_t = 0 (equation (20)).
  - Human capital: lim_{t→∞} β^t p_t H_t = 0 (equation (21)).
  - Public capital: lim_{t→∞} β^t (1+τ^c_t) u_{c,t} G_t = 0 (equation (22)).
  - Government bonds: lim_{t→∞} β^t (1+τ^c_t) u_{c,t} B_t = 0 (equation (23)).

### Steady state growth — Balanced Growth Path (BGP)
- Definition 2: A Competitive Equilibrium admits a BGP if for some t* ≥ 0, {c_t, K_t, H_t, B_t, G_t, g_t} grow at constant rates for all t ≥ t*, while all other variables are constant, given initial conditions {G_{t-1}, K_{t-1}, H_{t-1}, B_{t-1}}.  
- Normalization: growing variables are normalized by H_{t-1} to obtain stationary variables (notation with superscript ◦).  
- Proposition 2: The model has a unique BGP (proof in Appendix II).

### Mechanism driving long-run growth and closed-form BGP growth rate
- Specific functional forms assumed for tractability:
  - Final output production: equation (24) with parameters A, α, γ, etc.
  - Human capital production: equation (25) with parameters C, ϕ, ε, etc.
  - Parameter restrictions: γ, ε ≥ 0; 0 ≤ α, ϕ ≤ 1.
- Proposition 3: Closed-form BGP growth rate Ḣ^◦ (denoted in source) is given by expression (26) (see source for full algebraic expression involving A, C, α, ϕ, γ, ε, σ, β, δ, τ^K, τ^L, and function Φ).
- Key qualitative dependencies:
  - Steady-state growth (income per capita) is possible because human-capital accumulation  u_{t-1}H_{t-1} offsets diminishing returns to private physical capital v_{t-1}K_{t-1}.
  - Constant returns to scale in reproducible factors at aggregate level occurs if government sets public investment to keep G/K constant.
  - BGP growth rate increases with a higher ratio of public to private physical capital (G/K) because public capital raises total factor productivity in both sectors.
  - BGP growth rate is decreasing in τ^K (capital income tax) and τ^L (labor income tax): these taxes distort accumulation and inter-sectoral allocation, slowing growth.
  - Consumption tax τ^c_t is non-distortionary for growth under model assumptions (no leisure/labor supply choice and τ^c constant over time).

### Stability of the BGP
- The BGP is locally stable for the model with specific functional forms (6), (24), (25): normalized variables converge to the BGP given initial conditions sufficiently close to the BGP.  
- Stability determined by linear system x_{t+1} = A x_t + D 1_t and eigenvalues of D A^{-1}: number of eigenvalues with absolute value < 1 must match the number of non-exogenous forward-looking variables {c^◦_t, u^◦_t, v^◦_t, p^◦_t, r^{b◦}_t}.

### Fiscal reform packages and transition to a new BGP
- Two main fiscal reform types analyzed:
  1. Permanent reduction in distortionary private capital income tax τ^K_t or labor income tax τ^L_t.
  2. Permanent increase in public investment, raising the targeted constant ratio G/K on the post-reform BGP.
- Financing options to keep government debt/GDP sustainable at pre-reform BGP level:
  a. Reduction in unproductive government spending g_t.  
  b. Increase in consumption tax τ^c_t.
- Reform is modeled as a permanent shock causing a unique transition path from the pre-reform BGP to a new post-reform BGP.

### Dynamics of resources across sectors during transition
- Consumers adjust fractions v_t (physical capital to final output) and u_t (human capital to final output); physical and human capital must move together across sectors.
- Proposition 4: Using specific functional forms (6), (24), (25), u_t is an increasing function of v_t (u'_t(v_t) > 0) (equation (27)) — private physical and human capital move in the same direction across sectors.
- The ratio of private physical capital to human capital K^◦ (defined as K_{t-1}/H_{t-1} in normalized form) drives allocation choices: an inverse relationship between K^◦ and sectoral shares u, v (detailed derivation in Proposition 5, Appendix IV).
- Proposition 6 (comparative statics on BGP physical-to-human capital ratio K^◦):
  1. An increase in τ^K lowers the BGP physical-to-human capital ratio: ∂K^◦/∂τ^K < 0.
  2. An increase in τ^L has an ambiguous effect; under parameter choices used for numerical simulation in Section IV, the effect is negative: ∂K^◦/∂τ^L < 0.
  3. An increase in the public-to-private capital ratio G^◦ = G/K raises the BGP physical-to-human capital ratio ∂K^◦/∂G^◦ > 0, provided γ = ε and ε is sufficiently small (sufficient but not necessary conditions).

- Summary of qualitative transition effects:
  - Cutting τ^K (or τ^L under reasonable calibration) raises the BGP growth rate (per (26)) and the BGP physical-to-human capital ratio K^◦.
  - Initially after tax cuts, sectoral shares u_t and v_t devoted to final output are relatively high, but they fall as the economy moves to the new BGP.
  - Increasing targeted G/K raises the BGP growth rate and K^◦ (under conditions in Proposition 6).

### Numerical simulation setup and welfare metric
- Numerical solution uses specific functional forms (6), (24), (25) and parameter assignments (see Table 1 in source). Key parameter calibrations mentioned:
  - Productivity of public capital parameters γ and ε are both set to 0.05.
  - Parameter ϕ on private physical capital in human-capital production is set to 0.55.
  - Parameter α on private physical capital in final output production is set to 0.36.
  - The source notes these choices are within literature ranges and robustness to parameter changes is discussed in Appendix VI.
- Welfare metric: consumer welfare following a reform approximated by W = Σ_{t=0}^∞ β^t (c_t^{1-σ} − 1)/(1−σ) (equation (28)), with welfare effect of a reform expressed as the constant percentage of consumption each period that makes the consumer indifferent between the reform and the pre-reform BGP (further details in Appendix V).

*Source: _wp16146 - Section IV. The budget constraint for the government each period is*

### 0.1           Depreciation           rate:

### _wp16146 - 0.1           Depreciation           rate:

### Model parameters and fiscal baseline
- Depreciation rate: human capital = 0.1
- Depreciation rate: private physical capital = 0.1
- Depreciation rate: public capital = 0.1
- Elasticity of intertemporal substitution (inverse): (symbol present, no numeric value given)
- Elasticity of final output to public capital = 0.05
- Elasticity of human capital to public capital = 0.05
- Capital share in final output = 0.36
- Capital share in schooling = 0.36
- Scale factor = 13.6%
- Unproductive government spending: share of final output = 13.6%
- Labor income tax rate = 17.5%
- Capital tax rate = 17.5%
- Consumption tax rate = 7%
- Public investment: share of final output mk = 4.63%
- Public investment: (% of final output) baseline = 4.63% (table entries use 4.6 or 4.7; baseline growth figures use 4.6%)
- Growth rate of GDP per capita (baseline) = 4.6%
- Government debt (% of final output) (baseline) = 44.5%
- Revenue on benchmark BGP = 19.8% of final output

### Reform design: eight fiscal reform packages
- Reform Packages 1–4: fiscal cost compensated by cutting unproductive government spending t_g so that government debt (% of final output) remains the same on the post-reform BGP as on the pre-reform BGP.
- Reform Packages 5–8: fiscal cost compensated by increasing consumption tax rate C_t permanently so that the discounted present value of tax revenue from the point of reform equals the pre-reform BGP; additional adjustments in unproductive spending may be required to keep the debt ratio unchanged.
- Common reform definitions (reference scale: a 5 percentage point cut in capital income tax rate K_t τ):
  1. A 5 percentage point cut in the capital income tax rate K_t τ.
  2. A cut to the labor income tax rate L_t τ that generates the same discounted present value of total government revenue as the capital tax cut.
  3. Cuts to both K_t τ and L_t τ of equal magnitude that together generate the same discounted present value of revenue as the 5 percentage point capital tax cut.
  4. An increase in public investment by 1 percentage point of final output (sufficient to increase the BGP ratio of public to private capital G/K by around 10 percent).

### Budget sustainability condition (normalized steady state)
- Government budget constraint in normalized steady state implies: b̄ = (r̄ + 1) / (H̄) * (± p̄b)  (expression symbolically presented in the source as equation (29); symbols preserved as presented).
- A fiscal reform that causes a permanent reduction in the primary balance (as a share of final output) and an increase in the interest rate–growth differential (r̄ − H̄) implies the pre-reform ratio of government debt to final output cannot be sustained on the new BGP unless fiscal adjustment prevents the decline in the primary balance.

### Quantitative outcomes: Reform Packages 1–4 (compensated by cuts to unproductive spending)
Baseline fiscal policy (table summary):
- K_τ Rate (%) = 17.5
- L_τ Rate (%) = 17.5
- C_τ Rate (%) = 7
- Public Investment (% of final output) = 4.6 (table baseline)
- Growth Rate of GDP per Capita (%) = 4.6
- Govt. Debt (% of final output) = 44.5

Reform outcomes (Tax Policy Reform Packages 1–3; change in growth and welfare):
- Capital Income Tax Cut (Reform 1):
  - K_τ (%) = 12.5
  - L_τ (%) = 17.5
  - C_τ (%) = 7
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 4.84
- Labor Income Tax Cut (Reform 2) (revenue-equivalent to 5 percentage point capital tax cut):
  - K_τ (%) = 17.5
  - L_τ (%) = 15.08
  - C_τ (%) = 7
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.06
  - Change in Consumer Welfare (%) = 4.31
- Capital and Labor Tax Cut (Reform 3) (equal magnitude, revenue-equivalent):
  - K_τ (%) = 15.86
  - L_τ (%) = 15.86
  - C_τ (%) = 7
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 4.63
- Public Investment Reform (Reform 4):
  - K_τ (%) = 17.5
  - L_τ (%) = 17.5
  - C_τ (%) = 7
  - Public Investment (% of final output) = 5.6
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 3.23 (presented in table)

Additional fiscal facts reported:
- Following a 5 percentage point capital income tax cut (or revenue-equivalent labor tax cut), revenue is lower on the post-reform BGP by around 2 percentage point of final output. Unproductive government spending must be around 2 percentage points of final output lower on the new BGP compared with the benchmark BGP to keep government debt at its level on the original BGP.

Mechanics and economic channels highlighted (Reforms 1–4):
- Capital income tax cut (Reform 1) reduces distortions, raises post-tax return to capital, stimulates private physical capital accumulation; physical capital grows faster than human capital initially, raising the private capital to human capital ratio K̄/K_H̄; resources shift back to human capital as the new BGP is approached; welfare increases by around 4.8 percent.
- Labor income tax cut (Reform 2) raises post-tax wage, requires higher rental rate on private capital to avoid arbitrage; achieved via resource reallocation toward final output sector (higher share of human capital u_t to final output), leading to faster physical capital growth and ultimately higher aggregate K̄; welfare increases by around 4.3 percent.
- Combined cuts (Reform 3) produce growth effects similar to capital tax cut and welfare effect between Reforms 1 and 2.
- Public investment increase (Reform 4) raises public capital growth, increases G/K, boosts total factor productivity in both final output and human capital sectors; after initial crowding-out, physical and human capital growth rise and welfare increases by around 3¼ percent.

### Quantitative outcomes: Reform Packages 5–8 (compensated by consumption tax increases)
Baseline fiscal policy repeated:
- K_τ Rate (%) = 17.5
- L_τ Rate (%) = 17.5
- C_τ Rate (%) = 7
- Public Investment (% of final output) = 4.6
- Growth Rate of GDP per Capita (%) = 4.6

Reform outcomes (Tax Policy Reform Packages 5–7; consumption tax increases used to offset revenue loss):
- Capital Income Tax Cut with C_τ increase (Reform 5):
  - K_τ (%) = 12.5
  - L_τ (%) = 17.5
  - C_τ (%) = 12.2
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 0.14
- Labor Income Tax Cut with C_τ increase (Reform 6):
  - K_τ (%) = 17.5
  - L_τ (%) = 15.08
  - C_τ (%) = 13.6
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.06
  - Change in Consumer Welfare (%) = -0.48
- Capital and Labor Tax Cut with C_τ increase (Reform 7):
  - K_τ (%) = 15.86
  - L_τ (%) = 15.86
  - C_τ (%) = 12.2
  - Public Investment (% of final output) = 4.7
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = -0.08
- Public Investment and Consumption Tax Rise (Reform 8):
  - K_τ (%) = 17.5
  - L_τ (%) = 17.5
  - C_τ (%) = 10.33
  - Public Investment (% of final output) = 5.6
  - Change in Growth Rate of GDP per Capita (ppts) = 0.07
  - Change in Consumer Welfare (%) = 0.22

Mechanics and welfare implications (Reforms 5–8):
- Replacing lost revenue with higher consumption taxation causes an initial slowdown in consumption growth and imposes short-run welfare costs relative to offsetting revenue loss via cuts to unproductive spending.
- Reform 5 (capital tax cut financed by higher consumption tax) yields the same long-run growth effect as Reform 1 but a much smaller welfare gain (0.14% vs. 4.84%).
- Reform 6 (labor tax cut financed by higher consumption tax) shows a larger short-run consumption slowdown and an overall small welfare loss (-0.48%).
- Reform 7 (combined capital and labor cuts with consumption tax increase) yields a small overall welfare reduction (-0.08%).
- Reform 8 (public investment increase financed by higher consumption tax) still yields a positive welfare gain (0.22%) despite the consumption tax rise.

### Key quantitative takeaways and comparative statements
- Moderately sized distortionary tax cuts or public investment increases generate small permanent increases in annual growth of output per capita (typical reported change in growth rate of GDP per capita = 0.06–0.07 percentage points across reforms).
- Welfare effects differ markedly by financing:
  - Largest welfare gains occur when fiscal costs are offset by cuts to unproductive government spending (examples: 4.84%, 4.31%, 4.63%, ~3¼ percent).
  - Welfare gains are much smaller or negative when fiscal costs are offset by permanent consumption tax increases (examples: 0.14%, -0.48%, -0.08%, 0.22%).
- Revenue impact: a 5 percentage point capital income tax cut reduces revenue on the post-reform BGP by around 2 percentage point of final output, requiring unproductive spending cuts of around 2 percentage points of final output to maintain the pre-reform debt ratio.
- The interest rate on government bonds increases following capital tax cuts, expanding the interest-rate–growth differential (r_t^b − H̄) on the post-reform BGP under the calibration used, which can make sustaining the prior debt ratio infeasible without fiscal adjustment.

### Policy implications and conclusions (as stated in the source)
- Cuts to distortionary tax rates remove distortions to private investment, spurring faster output growth through endogenous investment choices and resource reallocation between final output and human capital sectors.
- Public capital increases (public investment) can raise total factor productivity and growth by increasing the ratio of public to private physical capital.
- The design of fiscal reform packages critically determines welfare outcomes: offsetting tax cuts or public investment increases with cuts to unproductive spending yields substantially larger welfare gains than financing them via higher consumption taxes.
- The quantitative results rely on a representative-agent framework; allowing for income and wealth inequality (heterogeneous agents) could change the growth and welfare effects of reforms and is left for future research.

*Italic: Source — content unit _wp16146 - 0.1 Depreciation rate: (PDF chapter/section provided).*

### APPENDIX I. THE COMPETITIVE EQUILIBRIUM

### APPENDIX I. THE COMPETITIVE EQUILIBRIUM

### A. Consumers’ Problem
- Setup:
  - Given initial conditions {B, H, K} (notation in source: 111,,KHB).
  - Consumers take as given infinite sequences of factor prices and bond prices {wt, rt, bt} and fiscal policy variables {τt^c, τt^K, τt^L, Gt}.
  - Choice variables: infinite sequences {ct, Kt, Ht, Bt, vt, ut} to maximize discounted utility.
- Objective (as in source):
  - Maximize ∑_{t=0}^∞ β^t (ct^{1-σ}-1)/(1-σ) subject to budget and human capital laws of motion.
- Constraints (period t):
  - Budget constraint (as in source):
    (1)(1)(1)(1)1
    cKLb
    tttK ttt tttt tttt   t
    cKK  BvrKuwHrB  
    
       
    (preserved exactly as in source).
  - Human capital law of motion (as in source):
    1
    111
    1
    H()g((1v)K,(1u)H)(1 )H
    t
    ttttttHt
    t
    G
    z
    K
    
    
    
    
    
- Lagrangian and multipliers:
  - Lagrangian written in full in source (equation (30)), with multipliers λ_t (budget constraint) and Ω_t (human capital law of motion).
- First-order conditions (as listed in source; equations preserved verbatim):
  - (31) '(   )(1)    0
    t
    c
    c t t t
    Luc
  - (32) 11111
    '
    111
    (1)(1) r
    () g   ( (1   v    ) K  , (1   u    ) H  )0
    t
    K
    K t t K  t    t t t
    t
    t K t t t t
    t
    L v
    G
    z
    K
         
    
    
    
    
    
  - (33) 11111
    '
    111
    (1)(1)
    (   )g ((1  v  )K,(1  u  )H)   0
    t
    L
    H t t  H t  t t t
    t
    t H t t t t
    t
    L w u
    G
    z
    K
    
    
    
    
            
    
  - (34) '
    1
    111
    1
    (1) r() g  ((1   v ) K    , (1   u  ) H    )    0
    t
    K
    t
    v t  t t t    t v t t t t
    t
    G
    L K z
    K
    
    
    
    
    
           
  - (35) '
    1
    111
    1
    (1)() g  ((1   v ) K    , (1   u  ) H   )    0
    t
    L
    t
    u t  t t   t u t t t t
    t
    G
    L w H z
    K
    
    
    
    
           
  - (36) 
    11
    10
    t
    b
    B t t  t
    L r   
    
          

### B. Firms’ Problem
- Firm maximization (period t):
  - Choose yt, v_{t-1}K_{t-1} and u_{t-1}H_{t-1} to maximize profits:
    max_{y, vK, uH} [ y r vK + w u H ] (source notation preserved).
  - Subject to production technology:
    1
    11
    1
    ()(vK,uH)
    t
    t t t t
    t
    G
    y q f K
    
    
    
    
    
- Reduced-form unconstrained problem (equation (37) in source):
  - max_{vK,uH} { π_t = q_t f((vK),(uH)) - r_t vK - w_t uH } (source expression preserved as in (37)).
- First-order conditions (as in source):
  - (38) '
    1
    11
    11
    ()(vK,uH)  0
    vK
    t t
    vK t t t t t
    t t
    G
    q f r
    K
    
    
    
    
    
    
    
    
  - (39) '
    1
    11
    11
    ()(vK,uH)    0
    t
    uH t t t t t
    t t
    G
    q f w
    u H K
    
    
    
    
    
    
    
    

### APPENDIX II. SOLVING FOR THE BALANCED GROWTH PATH

### Simplifying manipulations: factor price equalization
- Define ratio variables (as in source):
  - y-sector private capital ratio: 1 y_t ≡ (v_{t-1} K_{t-1})/(u_{t-1} H_{t-1}) (source notation preserved).
  - h-sector private capital ratio: 1 h_t ≡ (...) (source full expressions preserved).
- Combining consumer optimality (17),(18) and firm optimality (12),(13) yields solutions for 1_y t k_{t-1} and 1_h t k_{t-1} as functions of:
  - Relative price p_t, tax rates τ_t^K, τ_t^L, and productivity terms (G_{t-1}/K_{t-1}) in each sector.
- Proposition 1 (factor prices expressed only in terms of p_t, fiscal variables, and (G_{t-1}/K_{t-1})):
  - (40) r = r(1_{KL}, p_t, τ_t^K, τ_t^L, (G_{t-1}/K_{t-1})) — notation as in source.
  - (41) w = w(1_{KL}, p_t, τ_t^K, τ_t^L, (G_{t-1}/K_{t-1})) — notation as in source.
- Equilibrium conditions (equalization of marginal products across sectors, subject to taxes) given by (42) and (43) (preserved verbatim in source).

### A unique BGP
- Proposition 2: The model has a unique Balanced Growth Path (BGP).
- Key implicit difference equation in relative price p_t (equation (44) in source):
  - (44) (
    
    
    
    1111111
    1111
    KL
    t H  t    K t t t t t t
    p p r p p w p      
    
       )
- Implication:
  - There exists a unique p* such that p_{t+1} - p_t = 0; p must be constant on a BGP.
  - Given constant τ_t^K, τ_t^L and constant (G_{t-1}/K_{t-1}), there exist unique quantities (k*^y, k*^h, p*, etc.) and unique constant rental rate r and wage w.
- Normalized steady-state levels (equations (45) and (46) in source):
  - (45) Y^∘ = f(k^∘, (G/K)^{∘})q
  - (46) H^∘ = (1/(1-δ)) g(k^∘, (G/K)^{∘}) (sources preserved as in text).
- On the BGP:
  - Output per capita Y_t grows at same rate as human capital per capita H_t, with growth rate H^∘.
  - Consumption normalized c̃ grows at rate H^∘; government sets unproductive spending to grow at H^∘.
  - With constant τ^c, Euler equation for government bonds implies constant bond interest rate r^b; normalized government bond holdings B̃ grow at rate H^∘.

### APPENDIX III. THE GROWTH MECHANISM

- Proposition 3: The BGP growth rate H^∘ is given by (equation reproduced exactly as in source):
  - (47) 
    
    
    
    
    
    
    
    1
    1
    1
    (1)
    1
    1
    1
    1
    1
    11
    11
    111
    1
    KL
    K
    C
    G
    H
    A
    AK
    
    
    
    
    
    
    
    
    
    
    
    
       
    
    
    
    
    
    
    
    
    
    
    
    
    
    
       
    
    
    
    
    
    
    
    
    
    
    
- Proof sketch (as in source):
  - Using specific functional forms (6), (24), (25) and combining Euler equations (48) and (49).
  - Impose steady state with constant p, k^y, k^h, tax rates and G/K.
  - Under δ_K = δ_H = δ and additional manipulations (equations (50)-(53)), derive closed-form for H^∘ (equation (47)).

### APPENDIX IV. THE TRANSITION PATH

- Proposition 4:
  - Using functional forms (6),(24),(25), the share of human capital allocated to final goods production u_t is an increasing function of the share of private physical capital allocated to final goods production v_t:
    - (54) (u_t)'_{v_t} > 0
  - Proof uses consumer optimality condition (19) rewritten in (55); implies increase in v_t must be accompanied by increase in u_t when tax rates are constant.
- Proposition 5:
  - Relationship between u_t and the ratio of private physical capital to human capital _{t-1} K is given by (56) (preserved verbatim in source).
  - Proof: algebraic rearrangement using definitions of v and u and normalization by H_{t-1}.
- Dynamics after fiscal reform (numerical simulations, Section IV):
  - Relative price p_t and fiscal variables adjust quickly to new BGP values following reform (tax rates adjust immediately).
  - Suggests inverse relationship between long-run private physical-to-human capital ratio K^∘ and resource shares u and v.
- Proposition 6: Comparative statics on BGP physical-to-human capital ratio K^∘ (assuming functional forms (6),(24),(25), φ α > ? and h_y k_k > ? on BGP):
  1. An increase in physical capital income tax rate lowers BGP physical-to-human capital ratio:
     - ∂K^∘/∂τ_K^0 < 0 (notation in source: 0 K K     ).
  2. An increase in labor income tax rate has ambiguous effect; under parameter choices used in simulations the effect is negative:
     - ∂K^∘/∂τ_L^0 may be ambiguous, but is negative under simulation parameters (source preserved).
  3. An increase in ratio of public to private physical capital G^∘ = G/K raises K^∘ (provided γ = ε and ε sufficiently small):
     - ∂K^∘/∂G^∘ > 0 under stated sufficient conditions.
- Proof sketch:
  - Solve for k^y and k^h as functions of fiscal variables (equations (57)-(58) in source).
  - Use algebraic results to establish signs of derivatives and combine with human capital accumulation expression on BGP (59).

### APPENDIX V. A NUMERICAL EXAMPLE

### Welfare metric
- Consumer welfare after fiscal reform approximated by:
  - (60) W = ∑_{t=0}^∞ β^t (c_t^{1-σ}-1)/(1-σ) (as in source).
- Welfare effect of reform expressed as constant percentage consumption change making consumer indifferent between reform and pre-reform BGP.
- Two-step computation (as in source):
  1. Truncate transition at T and compute finite sum:
     - (61) W_1^* = ∑_{t=0}^T β^t (c_t^{1-σ}-1)/(1-σ).
  2. Add infinite geometric tail assuming new BGP reached and consumption grows at H^∘:
     - (62) W_2^* = ∑_{j=0}^∞ β^{T+j} (c_{T+j}^{1-σ}-1)/(1-σ) with growth at H^∘.
  - Total welfare W = W_1^* + W_2^* (source: 12 W W = +).
- Government budget constraint each period (as in source):
  - Full-period expression preserved in source text (includes terms with τ^c, τ^K, τ^L, G, r, B, etc.).
- Define primary balance pb_t as in source:
  - pb_t = (1) G
    c K L
    t t t t t t t t
    c r v K w u H G g τ τ τ δ (expression preserved as in source).
- Normalizing by H_{t-1} yields stationary budget constraint (63):
  - (63) r^1 B_{t-1} + B_t^{•} ≤ pb_t + B_t^{•} (source exact notation preserved).
- On steady state (BGP):
  - (64) r^b B^∘ + pb^∘ ≤ 0 (preserved as in source:   (b r H B pb )) — link between government debt ratio, primary balance and interest-growth differential on BGP.

### APPENDIX VI. ROBUSTNESS OF NUMERICAL SOLUTIONS

- Summary of numerical robustness findings (as reported in source):
  - Increasing pre-reform tax rates does not significantly alter long-run growth impact of a 5 percentage point cut to τ^K when offset by cut to unproductive government spending; welfare gain can be larger (5.29 percent vs 4.84 percent reported in Table 2).
  - If the capital tax cut is compensated by increase in consumption tax τ^C, welfare gain can be much smaller (as in Table 3).
  - Lower intertemporal elasticity of substitution (σ = 4 vs σ = 2) yields similar long-run growth impact for a 5 percentage point τ^K cut offset by spending cut, but welfare gain is smaller (3.29 percent vs 4.84 percent).
  - Changing exponent φ in human capital production function has relatively small effect on long-run growth impact of a 5 percentage point τ^K cut but larger effects on welfare.
  - Increasing public capital productivity exponents γ and ε from 0.05 to 0.15 can boost long-run growth impact of a 1 percentage point increase in public investment by ~0.2 percentage points and significantly increase welfare impact; values 0.15 lie within literature ranges.
- Table 4 (Robustness Tests) — selected rows preserved (numbers exactly as in source):
  - Baseline (Change of Initial Fiscal Policy):
    - Physical Capital Income Tax K_τ Rate (%) = 25
    - Human Capital Income Tax L_τ Rate (%) = 25
    - Cons. Tax C_τ Rate (%) = 15
    - Total government revenue and spending (% of final output) = 29.24 & 27.66
    - Growth Rate of GDP per Capita (%) = 1.42
    - Change in Consumer Welfare (%) = --
  - Reform (offset by unproductive spending cut):
    - K_τ = 20; L_τ = 25; C_τ = 15; Total gov rev & spend = 27.54 & 25.93; Growth Rate = 1.5; Change in Consumer Welfare = 5.29
  - Reform (offset by cons. tax rise):
    - K_τ = 20; L_τ = 25; C_τ = 21.25; Total gov rev & spend = 29.04 & 27.42; Growth Rate = 1.5; Change in Consumer Welfare = 0.05
  - Change of Coefficient of Relative Risk Aversion to σ = 4:
    - Baseline: K_τ = 17.5; L_τ = 17.5; C_τ = 7; Total gov rev & spend = 20.78 & 17.85; Growth Rate = 1.42; Change in Consumer Welfare = --
    - Reform (offset by unprod. spending cut): K_τ = 12.5; L_τ = 17.5; C_τ = 7; Total = 19.05 & 16.06; Growth Rate = 1.47; Change in Consumer Welfare = 3.29
  - Change of Parameter in Human Capital Production Function (φ = 0.45):
    - Baseline: K_τ = 17.5; L_τ = 17.5; C_τ = 7; Total = 19.58 & 18; Growth Rate = 1.42; --
    - Reform (offset by unprod. spending cut): K_τ = 12.5; L_τ = 17.5; C_τ = 7; Total = 17.84 & 16.21; Growth Rate = 1.51; Change in Consumer Welfare = 5.55
  - Change of Parameter in Human Capital Production Function (φ = 0.35):
    - Baseline: K_τ = 17.5; L_τ = 17.5; C_τ = 7; Total = 20.34 & 18.76; Growth Rate = 1.42; --
    - Reform (offset by unprod. spending cut): K_τ = 12.5; L_τ = 17.5; C_τ = 7; Total = 18.58 & 16.98; Growth Rate = 1.46; Change in Consumer Welfare = 3.75
  - Increase in Public Investment (from 4½ to 5½ % of Final Output) when γ, ε = 0.15:
    - Baseline: K_τ = 17.5; L_τ = 17.5; C_τ = 7; Total = 19.83 & 18.25; Growth Rate = 1.42; --
    - Reform (offset by unprod. spending cut): K_τ = 17.5; L_τ = 17.5; C_τ = 7; Total = 19.91 & 18.21; Growth Rate = 1.66; Change in Consumer Welfare = 10.7

*Italic source attribution: APPENDIX I. THE COMPETITIVE EQUILIBRIUM (source PDF _wp16146 - APPENDIX I. THE COMPETITIVE EQUILIBRIUM).*

### REFERENCES

### _wp16146 - REFERENCES

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### Government spending multipliers and macroeconomic dynamics
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### Human capital, education, migration, and growth
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### Theoretical foundations and models of growth and innovation
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*Source: _wp16146 - REFERENCES*

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