## wp18130

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### I. Introduction and main insights
- Progressivity: rising government share of net cash flows (government take); AETR defined as “the ratio of the present value of government receipts over the lifetime of a project to the present value of pre-tax cash flows, both calculated at some common discount rate.”
- Progressivity measured by plotting AETR against pre-tax IRR, NPV, or resource price; rising AETR profile = progressive regime.
- Key findings:
  - Regressive taxes (royalties, signature bonuses, land rental fees) exist to satisfy auxiliary objectives other than revenue maximization.
  - Auxiliary objectives include generating early revenues and ensuring revenues under weak economic conditions.
  - Given regressive elements, government’s revenue-maximizing design requires marginal tax rate progressivity in profit-sensitive instruments to capture residual rent.
  - Regressive taxes tend to be distortionary; in presence of distortions profit-sensitive taxes cease to be neutral, so optimal marginal progression must be set in a second-best environment.
  - Emphasis shifts from achieving progressivity in overall government take to setting an optimal degree of marginal tax rate progression in direct taxation of profit/rent.

### II. Purposes of progressivity — literature critique
- Practical observation: rent taxes typically combined with royalties and corporation tax; progressivity often achieved by full fiscal package rather than pure RRT.
- Equity arguments:
  - Analogy to progressive personal income tax is limited because investors often foreign and corporate profit tax may be shifted to consumers or workers.
  - Equity role is limited to government maximizing return as owner; depends on AETR height, not slope.
- Flexibility and political stability:
  - Flexibility = capacity of fiscal instruments to collect reasonable share of rent over time.
  - Political stability more tied to size (height) of government take, not progressivity.
  - Flexibility arguments often conflate progressivity with avoiding excessive use of distortionary/regressive taxes.

### III. Decomposing non-neutral taxes — model primitives and examples
- Model primitives:
  - Input γ produces F(γ), with F′>0, F′′<0.
  - Price p, input price c.
  - Economic rent V(γ) = pF(γ) − cγ.
- Neutral proportional rent tax at rate ρ:
  - After-tax profit π(γ**) = (1−ρ)V(γ**)
  - Government revenue T(γ**) = ρV(γ**)
  - AETR = ρ and dAETR/dp = 0.
- Factor tax at rate φ on input γ:
  - After-tax profit π(γ*) = V(γ*) − φcγ*
  - Government revenue T(γ*) = φcγ*
  - FOC: pF′(γ*) − (1+φ)c = 0; γ* < γ** and V(γ*) < V(γ**)
  - AETR = φcγ* / V(γ*)
  - For common F (quadratic, logarithmic) factor tax is regressive (d(AETR)/dp < 0); for exponential F(γ)=γ^α (0<α<1) AETR ∝ factor tax (d(AETR)/dp = 0).
- Royalties λ on value pF(γ) decompose as rent tax λ plus factor tax λcγ*; AETR = λ + λcγ*/V(γ*).
- Profit tax at rate τ with fraction 0<θ<1 of input deductible:
  - T = τ(pF(γ)−θcγ)
  - Decomposes to rent tax τ and implicit factor tax (1−θ)τ.
  - AETR = τ + (1−θ)τcγ*/V(γ*)

### IV. Progressive profit tax rates — framework and main analytical results
- Fiscal instruments parametrization:
  - Royalty 0≤λ<1
  - Progressive profit tax 0≤τ(p)≤1, τ increasing in p
  - Cost deductibility 0<θ≤1 (θ=1 → full deductibility → profit tax ≡ pure rent tax)
  - Signature bonus B≥0 (non-deductible)
- Firm FOC under taxes:
  - pF′(γ*) = (1−θ τ(p)) c / (1−τ(p)−λ)  (γ*>0 requires τ+λ<1)
- Observations:
  - Even with θ=1, λ>0 renders profit tax non-neutral.
  - With λ=0 and θ<1 the profit tax is distortionary.
  - Distortions imply ∂γ*/∂τ < 0, ∂γ*/∂λ < 0, ∂γ*/∂p > 0.
- Government objective: maximize T(p) subject to T(p) ≤ V(p), where
  - V(p) = pF(γ*) − cγ*
  - T(p) = τ(p)(pF(γ*) − θcγ*) + λpF(γ*) + B
- Binding constraint case (T(p) = V(p)):
  - Implicit condition: (1−τ−λ)pF(γ*) = (1−θ τ)cγ* + B
  - Comparative statics yield:
    - dτ/dp = (1−τ−λ) F(γ*) / (pF(γ*) − θcγ*) > 0
    - Hence optimal τ*(p) is increasing in p (marginal tax rate progressivity).
  - Effects of parameters:
    - Fixed payment B: tends to increase progressivity (d^2τ / dp dB ≥ 0 under conditions).
    - Increasing λ: ambiguous analytically; numerical simulations show increased progressivity when λ rises in illustrative cases.
  - Numerical examples (logarithmic F(γ)=ln γ, c=1, B=1, θ=.9):
    - With λ=.05:
      - p from 6 to 7: τ rises from τ=.618 to τ=.695 (∆τ = .077).
    - With λ=.08:
      - p from 6 to 7: τ rises from τ=.564 to τ=.646 (∆τ = .082).
- Non-binding constraint case (T(p) < V(p), Laffer peak before full rent capture):
  - Government FOC for revenue maximization yields conditions implying dτ/dp > 0 in many illustrative cases (e.g., quadratic F), so profit tax remains marginally progressive in typical cases.
- Implications for AETR progressivity:
  - Under binding constraint T=V, government take is 100 percent of realized rent by construction.
  - Considering observed rent ˆV = pF(γ*) − θcγ* (with θ<1), simulations with exponential F show AETR relative to ˆV rising with p when constraint binds; when non-binding, AETR can be constant with p (simulation-dependent).
  - Horizontal AETR in some simulations is a byproduct of optimal marginal tax progressivity rather than a design target.

### V. Practical implications and design recommendations
- Four general policy points:
  1. Regressive components must be justified by auxiliary objectives (early revenue, risk sharing).
  2. Political stability and resilience tied to overall AETR height, not slope.
  3. Profit-sensitive instruments should be designed progressively (tax rate rising with rent or correlates such as resource price); multiple tiers in RRT are an example.
  4. Rule-of-thumb: AETR should be broadly constant across profitability outcomes, with progressive elements inversely related to regressive elements.
- Diagnostic tools and recommendations:
  - Plot separate AETR curves for progressive and regressive instruments; more regressive distortionary elements imply profit-sensitive AETR should be more progressive.
  - Use tax buoyancy (elasticity of government revenue w.r.t. economic rent) as diagnostic: starting at breakeven price, elasticity should be close to one (e.g., 10 percent increase in project NPV → 10 percent increase in government revenue NPV).
  - Prefer a modest constant royalty with a progressive rent or corporate income tax, rather than progressive royalty schedules.
  - Make royalties creditable (with uplift for time value of money) against profit/rent taxes in post-payback periods to allow early revenues without compromising revenue maximization and to permit flatter profit tax schedules.
  - Dynamic implementation options: apply progressive schedule each period to present value of lifetime cumulative net cash flows with tax credits for prior-period taxes (Sumner (1978)-style), or use profit indicators (R-factor) when projects vary widely.

### VI. Conclusions and calibration guidance
- Core thesis: aim for a suitably high fixed proportion of rent (AETR height) while using progressive profit-sensitive instruments to complement regressive instruments in a second-best framework.
- Regressive elements reduce realized economic rent; progressive instruments should capture residual rent optimally given distortions.
- Calibration approach:
  - Determine tax rates at different prices (or profit indicators) so investors’ after-tax IRR is held at an acceptable level.
  - Target elasticity of government revenue with respect to rent equal to one.
  - Consider expressing tax schedule in terms of profit indicators (R-factor) for heterogeneous projects.
  - Use tax credits rather than deductions for royalties/signature bonuses to reduce distortions and lower need for progressivity.
- Policy implication: regressivity in some instruments can be justified by auxiliary goals, but should be offset by appropriately designed progressive profit-sensitive taxes to maximize rent capture subject to second-best constraints.

*Source — wp18130 (IMF working paper content provided).*

### References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### References

### I. INTRODUCTION
- The principle that fiscal regimes for petroleum and minerals should exhibit ‘progressivity’ is commonly advocated (see, e.g., Daniel, 2010: 190).
- Progressivity refers to a rising government share of the net cash flows of a project—the so-called government take.
- Boadway and Keen (2010: 38) define progressivity as subjecting “cumulative rentsVto some taxT(V)that is progressive in the sense that the average tax rateT(V)/Vincreases withV.”
- Keen et al. (2014: 20) define the Average Effective Tax Rate (AETR) as “the ratio of the present value of government receipts over the lifetime of a project to the present value of pre-tax cash flows, both calculated at some common discount rate.”
- The degree of progressivity can be gauged by plotting the AETR against different levels of the pre-tax internal rate of return (IRR) or the Net Present Value (NPV) of a project or against the price of the resource; a rising AETR profile is synonymous with a progressive tax regime.
- The paper provides a critical review of the literature on the progressive taxation of petroleum and minerals and offers a different perspective on its purpose and measurement.

### Main insights
- Regressive taxes (the opposite of progressive), such as royalties, signature bonuses, and land rental fees, exist to satisfy various government objectives other than revenue maximization.1
- Auxiliary objectives of fiscal regimes include generating tax revenues early in a project’s life cycle and ensuring revenues for the government even in the face of weakening economic conditions.
- Given the existence of regressive elements in the fiscal regime, the government’s primary objective of revenue maximization requires marginal tax rate progressivity in the design of its profit-sensitive fiscal instruments.
- Progressive tax instruments enable governments to capture the rent “left on the table” by the regressive instruments.5
- By their very nature, regressive taxes tend to be distortionary taxes, and vice versa.6
- In the presence of such distortions, profit-sensitive taxes themselves, even a direct tax on economic rent, cease to be neutral; therefore, the optimal degree of marginal tax rate progression of the profit-sensitive taxes must be considered in a second-best policy environment.
- Emphasis of tax policy evaluation shifts from achieving progressivity in the overall government take to setting an optimal degree of marginal tax rate progression in the direct taxation of profit or rent.

### Key analytical results and implications
- The higher the royalty rate, the more progressive the profit-sensitive tax rate schedule should be, although the general level of the tax rates on profit must be lowered to accommodate a high royalty rate.
- The overall effect of a royalty, together with an optimal progressive rate schedule, on the shape of the AETR graph is generally unclear and not necessarily expected to be progressive.
- It is useful to plot separately the AETR for the regressive and the progressive tax instruments to better visualize the performance of the profit-sensitive tax instruments for maximizing tax revenue, taken as a given the regressive instruments.
- A measure of the performance of the profit-sensitive tax rates is the ‘buoyancy’ or elasticity of total government take with respect to the changes in the economic rent generated by a project; if the elasticity is close to one, it means that, as the rent increases, say, due to an increase in the price of the resource, the progressivity of the profit-sensitive instruments fully offsets the regressive elements of the fiscal regime, and any windfall rent is captured as government revenue.
- Since royalties exist mainly to ensure early government revenues, the royalties should be creditable (with an uplift for the time value of money) against profit taxes (or rent taxes) in the post-payback period; this allows governments to achieve early revenues without compromising the objective of revenue maximization and permits the rate schedule for the profit taxes to be relatively flat, minimizing tax distortions.
- The central ideas are formalized and illustrated with a simple model in which a second-best optimal tax on rent is derived in the presence of other tax distortions; the theoretical model omits many real-world features of the extractive industries but clarifies and illustrates the central ideas precisely.

### Organization of the paper
- Section 2 reviews the literature on the purposes of progressivity.
- Section 3 critiques the literature and offers a different perspective on progressivity.

*Source: wp18130 - References (IMF working paper content provided).*

### Section 4 introduces a simple analytical model and uses it to establish the equivalence be-

### wp18130 - Section 4 introduces a simple analytical model and uses it to establish the equivalence be-

### Purposes of progressivity
- Literature rationale: progressive taxation proposed to achieve “equity” and “flexibility”/“stability.”
- Practical observation: in practice resource rent taxes are typically combined with royalties and corporation tax; progressivity is often achieved by the full package of fiscal instruments rather than by a pure RRT alone.
- Key claim: progressivity is most meaningful in a second-best environment with pre-existing tax distortions.

### Equity arguments (section II.A)
- Common analogy: progressive resource taxes likened to progressive personal income taxes (average tax rate increasing with income).
- Counterpoints:
  - Investors are often foreign shareholders, weakening domestic equity rationale.
  - “A claim to high rents is neither necessary nor sufficient for high income at a personal level.”
  - A corporate profit tax may be shifted to consumers or workers via prices or wages.
- Conclusion: equity role is limited to the government maximizing return as owner of the resource; this depends on the ‘height’ of the AETR curve, not its ‘slope.’

### Flexibility and political stability (section II.B)
- Definition: flexibility as “the capacity of fiscal instruments to collect a reasonable share of the resource rent over time under a range of future market outcomes.”
- Argument in literature: progressive systems can reduce populist pressures for expropriation and ad hoc tailoring of taxes.
- Critique in paper:
  - Political stability is more likely tied to the size (height) of government take, not progressivity per se.
  - The flexibility argument often conflates progressivity with avoidance of excessive use of distortionary/regressive taxes (e.g., royalties).

### A different perspective (section III)
- First-best policy: single proportional tax on economic rent approaching 100 percent (the trivial neutral solution).
- Practical impediments:
  - Multiple policy objectives (early revenue, revenue stability, risk aversion by government).
  - Lack of information to levy a pure economic rent tax (unobserved inputs, uncertain investor discount rates).
- Implication: regressive factor taxes (royalties, imperfect cost deductibility) are inevitable; progressive instruments should complement them to capture residual rent.

### Decomposing non-neutral taxes into a rent tax and a factor tax (section IV)
- Model primitives:
  - Input γ produces F(γ), with F′>0, F′′<0.
  - Price p, input price c.
  - Economic rent V(γ) = pF(γ) − cγ.
- Neutral proportional rent tax at rate ρ:
  - After-tax profit π(γ**) = (1−ρ)V(γ**)
  - Government revenue T(γ**) = ρV(γ**)
  - AETR = ρ and dAETR/dp = 0.
- Factor tax at rate φ on input γ:
  - After-tax profit π(γ*) = V(γ*) − φcγ*
  - Government revenue T(γ*) = φcγ*
  - First-order condition pF′(γ*) − (1+φ)c = 0; γ* < γ** and V(γ*) < V(γ**).
  - AETR = φcγ* / V(γ*)
  - For common production functions (quadratic, logarithmic) factor tax is regressive (d(AETR)/dp < 0); for exponential production F(γ)=γ^α (0<α<1) AETR is proportional to factor tax (d(AETR)/dp = 0).
- Royalties λ on value of sales pF(γ) decompose as:
  - Equivalent to rent tax λ plus factor tax λcγ*.
  - AETR = λ + λcγ*/V(γ*)
- Profit tax at rate τ with fraction 0<θ<1 of input cost deductible:
  - T = τ(pF(γ)−θcγ)
  - Decomposes to rent tax τ and implicit factor tax (1−θ)τ.
  - AETR = τ + (1−θ)τcγ*/V(γ*)

### Progressive profit tax rates — framework and main analytical results (section V)
- Fiscal instruments parametrization:
  - Royalty 0≤λ<1
  - Progressive profit tax 0≤τ(p)≤1, τ an increasing function of p
  - Cost deductibility 0<θ≤1 (θ=1 → full deductibility → profit tax equivalent to pure rent tax)
  - Signature bonus B≥0 (non-deductible)
- Firm first-order condition under taxes:
  - pF′(γ*) = (1−θ τ(p)) c / (1−τ(p)−λ)  (γ*>0 requires τ+λ<1)
- Key observations:
  - Even with θ=1, royalties λ>0 render the profit tax non-neutral.
  - With λ=0 and θ<1 the profit tax is distortionary.
  - Distortions imply ∂γ*/∂τ < 0, ∂γ*/∂λ < 0, ∂γ*/∂p > 0.
- Government objective: maximize T(p) subject to T(p) ≤ V(p), where
  - V(p) = pF(γ*) − cγ*
  - T(p) = τ(p)(pF(γ*) − θcγ*) + λpF(γ*) + B

- Binding constraint case (T(p) = V(p)):
  - Implicit condition: (1−τ−λ)pF(γ*) = (1−θ τ)cγ* + B
  - Comparative statics yield:
    - dτ/dp = (1−τ−λ) F(γ*) / (pF(γ*) − θcγ*) > 0
    - Hence optimal τ*(p) is increasing in p — marginal tax rate progressivity.
  - Effects of other parameters:
    - Fixed payment B: tends to increase progressivity (d^2τ / dp dB ≥ 0 under conditions).
    - Increasing royalty λ: ambiguous analytical sign, but numerical simulations with illustrative production functions show increased progressivity when λ rises.
  - Numerical examples (logarithmic F(γ)=ln γ, c=1, B=1, θ=.9):
    - With λ=.05:
      - p from 6 to 7: τ rises from τ=.618 to τ=.695 (∆τ = .077).
    - With λ=.08:
      - p from 6 to 7: τ rises from τ=.564 to τ=.646 (∆τ = .082).
- Non-binding constraint case (T(p) < V(p), Laffer peak before full rent capture):
  - Government FOC for revenue maximization leads to a condition whose comparative statics imply dτ/dp > 0 in many illustrative cases (e.g., quadratic production function), i.e., profit tax remains marginally progressive in typical cases.
- Implications for average tax rate progressivity:
  - Under binding constraint T=V, government take is 100 percent of realized rent by construction.
  - Considering observed rent ˆV = pF(γ*) − θcγ* (with θ<1), simulations with an exponential production function show AETR relative to ˆV rising with p when constraint binds; when non-binding, AETR can be constant with p (simulation-dependent).
  - The horizontal AETR in some simulations is a byproduct of optimal marginal tax progressivity rather than a target design feature.

### Practical implications (section VI)
- Four general points for policy evaluation:
  1. Regressive components must be justified by auxiliary objectives (early revenue, risk sharing).
  2. Political stability and resilience are determined by the size of overall AETR (height), not its progressivity (slope).
  3. Profit-sensitive instruments should be designed progressively (tax rate rising with rent or correlates such as resource price); multiple tiers in RRT are an example.
  4. A practical rule-of-thumb: AETR should be broadly constant across profitability outcomes, with progressive elements inversely related to regressive elements.
- Diagnostic tools and design recommendations:
  - Plot separate AETR curves for progressive and regressive fiscal instruments; more regressive distortionary elements imply the profit-sensitive AETR should be more progressive.
  - Use tax buoyancy (elasticity of government revenue with respect to economic rent) as a diagnostic: starting at breakeven price, elasticity should be close to one (e.g., 10 percent increase in project NPV → 10 percent increase in government revenue NPV).
  - Prefer a modest constant royalty with a progressive rent or corporate income tax, rather than progressive royalty schedules, which conflate early revenue and rent capture objectives and create large distortions.
  - Tax credit for royalties (with uplift for time value of money) would largely offset royalty-induced distortions and reduce need for marginal progressivity in rent tax.
  - Suggestion for dynamic implementation: apply progressive schedule each period to present value of lifetime cumulative net cash flows with tax credits for prior-period taxes (Sumner (1978)-style), or use profit indicators (R-factor) when projects vary widely.

### Conclusions (section VII)
- Main thesis: literature over-emphasizes achieving a progressive overall fiscal package; instead, government should aim for a suitably high fixed proportion of rent (height), using progressive profit-sensitive instruments to complement regressive instruments.
- Regressive elements (by design or due to unobserved/non-deductible costs) reduce realized economic rent; progressive instruments should capture the residual rent in a second-best framework.
- Calibration approach:
  - Determine tax rates at different prices (or profit indicators) so investors’ after-tax IRR is held constant at an acceptable level.
  - Target elasticity of government revenue with respect to rent equal to one.
  - Consider expressing tax schedule in terms of profit indicators (R-factor) when project heterogeneity is large.
  - Use tax credits rather than deductions for royalties/signature bonuses to reduce distortions and lower need for progressivity.
- Overall policy implication: regressivity in some instruments can be justified by auxiliary goals, but should be offset by appropriately designed progressive profit-sensitive taxes to maximize rent capture subject to second-best constraints.

*Italic: Source — wp18130 (PDF chapter/section) as supplied.*

### REFERENCES

### REFERENCES

### Cited works
- [1]  Boadway, Robin and Michael and Keen (2010) Theoretical Perspectives on Resource Tax Design. Chapter 2 in Daniel et al. (2010).
- [2]  Caldor, Jack (2010) Resource Tax Administration: the Implications of Alternative Pol- icy Choices. Chapter 11 in Daniel et al. (2010).
- [3]  Daniel, Philip, Brenton Goldsworthy, Wojciech Malizewnski, Diego Mesa Puyo, and Alistair Watson (2010) Evaluating Fiscal Regimes for Resource Projects: an Example from Oil Development. Chapter 7 in Daniel et al. (2010).
- [4]  Daniel, Philip, Michael Keen, and Charles McPherson (2010)The Taxation of Petro- leum and Minerals: Principles, Problems and Practice(New York: Routledge).
- [5]  Garnaut, Ross, and Ian Clunies Ross (1983)Taxation of Mineral Rents(Oxford: Clarendon Press).
- [6]  Hann, D. and C. Rowland (1986) UK Oil Taxation: Failings and Reform, Surrey En- ergy Economics Centre, University of Surrey, Discussion Paper no. 32.
- [7]  Keen, Michael, Peter Mullins, Oana Luca, and Roderick Eggert (2014) Israel: Review- ing the Fiscal Regime for Mining. International Monetary Fund, Fiscal Affairs Depart- ment.
- [8]  Kemp, Alexander G. (1975) Fiscal Policy and the Profitability of North Sea Oil Ex- ploitation,Scottish Journal of Political Economy22 (3): 237–257.
- [9]  Lad-Ojomo, Olatokunbo (2008/2009) What is the Role and Challenges of Progressive Taxation in Achieving Stability and Equitable Distribution of Oil Profits?CEPMLP Annual Review, Volume 12, Article 26 (Centre for Energy, Petroleum and Mineral Law and Policy, University of Dundee).
- [10]  Land, Bryan C. (2010) Resource Rent Taxes: a Reappraisal. Chapter 8 in Daniel et al. (2010).
- [11]  Luca, Oana, and Diego Mesa Puyo (2016) Fiscal Analysis of Resource Industries (FARI) Methodology, Technical Notes and Manuals, International Monetary Fund, Fiscal Affairs Department.
- [12]  Lund, Diderik (2009) Rent Taxation for Non-Renewable Resources,Annual Review of Resource Economics1: 287–308.
- [13]  Nakhle, Carole (2004)Petroleum Taxation: A Critical Evaluation with Special Appli- cation to the UK Continental Shelf, PhD dissertation, University of Surrey.
- [14]  Osmundsen, Petter (2005) Optimal Petroleum Taxation Subject to Mobility and In- formation Constraints. In S. Glomsrod and P. Osmundsen (eds.),Petroleum Industry Regulation within Stable States(New York: Ashgate).
- [15]  Osmundsen, Petter (2010) Time Inconsistency in Petroleum Taxation: Lessons from Norway. Chapter 15 in Daniel et al. (2010).
- 32
- [16]  Sumner, M.T. (1978) Progressive Taxation of Natural Resource Rents,The Manchester School: 1-16.

*Source: wp18130 - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18130.pdf_