## 1. Initial Conditions

## Source details

**Canonical URL:** [1. Initial Conditions](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09126.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09126.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09126.pdf.json)

---

### I. Introduction — purpose, gaps, and scope
- Purpose:
  - Systematically compare rules derived using various social welfare functions and common ad hoc rules.
  - Use Engel and Valdes (2000) theoretical framework and numerical simulations under uncertainty.
  - Consider three stylized country examples to represent a range of oil-producing countries (OPCs).
- Key gaps in literature identified:
  - Selection of an appropriate social welfare function for inter-temporal distribution of oil wealth rarely discussed.
  - Little research on appropriate or permissible level of debt for OPCs.
  - POIM recommendation to maintain financial and oil wealth at a constant level is typically unjustified.
- Scope limitations (model abstractions):
  - Abstracts from government capacity, quality of spending, government investment decisions.
  - Government savings held in foreign financial assets; expenditures restricted to public goods.
  - Channels through which fiscal policy affects non-oil GDP growth not modeled.
  - Considers oil-price volatility as single source of uncertainty; long-term non-oil GDP growth uncertainty not formally analyzed.
  - Results intended as input to policy design, not a complete framework.

### II. Fiscal Rules for OPCs — Optimizing rules (definitions and key equations)
- Framework assumptions:
  - Households live for one period, no bequest motive.
  - Government may tax non-oil GDP, fully capture oil rent, spend on public goods, save in foreign financial assets.
  - Government policy instruments set by maximizing a chosen social welfare function subject to constraints.
  - Maintained critical assumption: R/1 = β.
- Permanent income model (PIM):
  - Social welfare: per capita consumption (equation (1)).
  - Lifetime budget constraint and total wealth W defined (equations (2), (3), (4)).
  - Maximization yields maximum attainable per capita consumption c:
    - 0 ) 1 1( W R n c + − =  (equation (5))
  - Implication: may imply massive transfers between generations depending on per capita non-oil income growth.
- Permanent oil income model (POIM):
  - Government distributes only oil wealth; social welfare uses per capita government expenditures (equation (6)).
  - Oil wealth Woil and lifetime constraint (equation (7)).
  - Optimal constant per capita government expenditure g:
    - oil W R n g 0 ) 1 1( + − =  (equation (8))
  - POIM is a fiscal policy benchmark but may be overly restrictive by excluding non-oil tax intergenerational transfers.
- Modified permanent oil income model (MPOIM):
  - Government may tax non-oil GDP for transfers but limited to constant fraction τ of non-oil GDP.
  - Lifetime budget constraint includes SD (equation (9)) and SDW0 definition.
  - Optimal constant per capita government spending:
    - SD W 0 SD W R n g 0 ) 1 1( + − =  (equation (10))
  - Long-run properties and examples:
    - Government non-oil primary balance converges to τ under no oil revenues and growing per capita non-oil GDP (equation (11)).
    - Debt-to-non-oil-GDP ratio limit converges to expression in (12); example: τ = 1, nonoil_g = 0.04, and R = 1.05 produce limit debt ratio of 105 times non-oil GDP.
    - To achieve a “sustainable” debt ratio of 52.5 percent of non-oil GDP given other assumptions requires τ = 0.005 (a constant primary balance of ½ percent of non-oil GDP).
  - τ interpretation:
    - Share of non-oil GDP future generations willing to devote to intergenerational transfers; calibration should reflect sustainable debt limits.
  - All optimizing rules satisfy lifetime government budget constraints.

### Uncertainty — oil-price process and precautionary adjustments
- Oil price process (equation (13)):
  - t t t P P υ μ ψ μ + − = − )( log log 1 ,
  - υ ~ N(0, υ σ 2 ), μ has mean and variance; initial oil production has mean and variance.
- Engel and Valdez (2001) approximation for optimal POIM consumption under oil-price uncertainty (equation (14)):
  - 0 22 00 0, Q P σ σ Q )0,0( ]1[ ),( 00 22 00 00 gg IUBU Δ − Δ − ≈ ν σ σ ,
  - Correction factors diminish with initial financial wealth and remaining oil production.
- MPOIM uncertainty correction:
  - Analogous to POIM, adding present discounted value of non-oil tax revenues to initial financial assets under simplifying assumption that non-oil output and taxes are known without uncertainty and uncorrelated with oil revenues.

### Adjustment costs — smoothing costs and elicitation
- Augmented social welfare adds quadratic adjustment costs on per capita government consumption deviations from an optimal g*_t (equation (15)).
- Approximation for log of initial per capita government consumption (equation (16)):
  - )]log()[log()log()log( 1 * 10 − − ≈ − g g g g α , with α increasing with k and ρ.
- Elicitation of k via indifference condition (equation (17)):
  - 100 × a s × n a s 100 ρ − = 1 * 2 )( g s s k a na (expression presented in source).
- Used in numerical simulations to apply adjustment-cost correction to MPOIM.

### Ad hoc rules — definitions and fiscal implications
- Bird-in-hand rule:
  - Government limits consumption from oil wealth to returns from accumulated financial assets:
    - t t FRG )1( − =  (equation (18))
  - Modified to include present value of non-oil tax revenues to financial assets:
    - ∑ ≥ − n o n o i l t t t t Y R F R G τ 0 )1(  (equation (19))
  - Ensures long-term fiscal sustainability; less responsive to oil price shocks.
- Spending from current oil revenue:
  - Government fully spends current oil revenues:
    - oil t T t Y G = ≤  (equation (20))
  - After oil exhaustion, expenditures must be adjusted to satisfy lifetime constraint:
    - ∑ ≥ − n o n o i l t t t t T t Y R F R G τ 0 )1(  (equation (21))
  - Produces high volatility and abrupt adjustment upon oil depletion.
- POIM as percentage of non-oil GDP (POIM%):
  - Social welfare uses government consumption as share of non-oil GDP (equation (22)).
  - Optimal constant government consumption share:
    - oil W R g g 0 ) 1 1( + − = ˆ (equation (23))
  - Classified as ad hoc because it distributes oil wealth proportional to non-oil GDP, transferring resources from poorer to richer generations when per capita non-oil GDP grows.

### III. Numerical Comparisons — setup, calibration, and stylized country initial conditions
- Monte Carlo simulations:
  - 5,000 random realizations of oil prices over a 200-year horizon after estimating parameters of the oil price equation (13).
  - Random error in price equation is the only source of uncertainty; price-equation parameters known with certainty.
- Baseline price process (OLS on WEO averages, 1960-2012) (equation (24)):
  - t t t P P υ + − = − )67.3(log 93.0 67.3 log 1
  - υ σ 2  = 25.0
  - Implies stationary log oil prices with long-term mean price of $39 per barrel (in 2000 prices).
- Alternative specification:
  - Near-unit-root with ψ constrained to 0.99; constrained-sample estimation yields υ σ 2 = 2.0 and other calibrations to match long-term mean.
- Simulation details:
  - Initial uncertainty about initial oil price in equation (14) assumed equal to 0 2 σ .
  - Government consumption paths constructed sequentially using information available to authorities at decision times; optimizing rules re-optimize each period using latest price.
- Main evaluation criteria:
  - Mean social welfare functions over randomized sample for three social welfare functions: (1) overall consumption, (6) government consumption, (15) government consumption with adjustment costs.
  - Volatility measured by expected standard deviation of non-oil government primary balance as % of non-oil GDP.
- Stylized country examples — initial conditions (Table 1):
  - Parameters for Mature, Large, Medium producers:
    - Non-hydrocarbon GDP growth rate (%): Mature 4.0, Large 2.0, Medium 1.0
    - Non-hydrocarbon GDP (2000 US$ billions): Mature 10.0, Large 150.0, Medium 10.0
    - Non-hydrocarbon primary balance (2000 US$ billions): Mature -2.5, Large -75.0, Medium -2.5
    - Net foreign assets (2000 US$ billions): Mature 10.0, Large 150.0, Medium 5.0
    - Population growth rate (%): Mature 1.0, Large 2.0, Medium 2.0
    - Initial stock of oil (billions of barrels): Mature 1.0, Large 250.0, Medium 1.0
    - Annual extraction (billions of barrels): Mature 0.1, Large 5.0, Medium 0.1
    - Time to exhaust (years): Mature 10.0, Large 50.0, Medium 10.0
  - Memorandum items:
    - Oil wealth (NPV of oil revenue, 2000 US$ billions): Mature 31.7, Large 3744.6, Medium 31.7
    - Total wealth (NPV of non-oil GDP + NFA, 2000 US$ billions): Mature 1,133.7, Large 9,249.6, Medium 301.8
    - Oil wealth/Total wealth (%): Mature 2.8, Large 40.5, Medium 10.5
- Other model parameters (Table 2):
  - Initial oil price (2000 US$ per barrel): 39.1
  - Coeff. of relative risk aversion ρ: 3
  - Adjustment costs coefficients: s_na ×100 = 20 ; s_a ×100 = 10
  - Tax on non-oil GDP τ: 0.005
  - Gross real interest rate R: 1.05
  - Adjustment-cost elicitation: avoiding a 10 percent change in per capita government consumption (s_a ×100 = 10) is valued same as a 20 percent increase in absence of adjustment costs (s_na ×100 = 20).

### III. Numerical Comparisons — selected quantitative results (baseline)
- Mean social welfare functions normalized by POIM reported in Tables 3 and 4 (lower ratio indicates better performance since social welfare functions take negative values).
- Selected ratios to POIM (overall consumption, government consumption, government consumption with adjustment costs) — Mature economy (baseline):
  - Overall consumption (equation 1): PIM 0.18, POIM 1.00, MPOIM 0.98, MPOIM with precautionary savings 0.99, MPOIM with adjustment costs 0.97, POIM% 1.17, Bird-in-hand 1.01, Spending from current oil revenue 0.88.
  - Government consumption (equation 6): PIM 0.00, POIM 1.00, MPOIM 0.75, MPOIM with precautionary savings 0.75, MPOIM with adjustment costs 0.79, POIM% 6.05, Bird-in-hand 1.12, Spending from current oil revenue 3.29.
  - Government consumption with adjustment costs (equation 15): PIM 6.08, POIM 1.00, MPOIM 0.73, MPOIM with precautionary savings 0.79, MPOIM with adjustment costs 0.67, POIM% 7.37, Bird-in-hand 2.09, Spending from current oil revenue 4.11.
- Expected standard deviation of non-oil government primary balance as % of non-oil GDP (baseline):
  - Mature: PIM 90.57, POIM 2.84, MPOIM 2.46, MPOIM with precautionary savings 3.05, MPOIM with adjustment costs 0.78, POIM% 6.25, Bird-in-hand 5.81, Spending from current oil revenue 9.79.
  - Large: PIM 8.38, POIM 8.38, MPOIM 8.38, MPOIM with precautionary savings 6.10, MPOIM with adjustment costs 2.33, POIM% 8.38, Bird-in-hand 7.49, Spending from current oil revenue 31.40.
  - Medium: PIM 11.88, POIM 4.30, MPOIM 4.34, MPOIM with precautionary savings 4.97, MPOIM with adjustment costs 1.39, POIM% 3.40, Bird-in-hand 7.33, Spending from current oil revenue 11.08.

### III. Numerical Comparisons — main comparative findings (qualitative, with quantitative support)
- PIM vs POIM:
  - PIM maximizes social welfare function (1) by construction and gives highest government consumption under (6).
  - PIM produces implausibly high initial consumption for growing per capita non-oil GDP and implausibly low for falling per capita non-oil GDP; generates high volatility in non-oil government balance (e.g., std. dev. 90.57 for Mature in baseline).
  - POIM yields more plausible debt dynamics and lower volatility; consumption lower (higher) than PIM when per capita non-oil GDP growing (falling).
  - When per capita non-oil GDP constant, PIM and POIM equivalent under social welfare function (1).
- POIM vs MPOIM and MPOIM variants:
  - MPOIM offers significant welfare improvements over POIM when per capita non-oil GDP is growing or falling due to more optimal non-oil wealth distribution.
  - For the Large oil producer, differences between POIM and MPOIM are modest because τ = 0.005 transfers are small relative to oil wealth.
  - Precautionary savings (uncertainty correction) offers substantial improvement for Large producer under social welfare functions (6) and (15); smoother consumption path reduces adjustment costs and volatility.
  - Adjustment-cost correction produces much smoother government consumption and greatly reduces volatility of non-oil balance across economies (e.g., MPOIM with adjustment costs reduces std. dev. to 0.78, 2.33, 1.39 for Mature, Large, Medium respectively in baseline).
  - For Small/Medium producers, uncertainty adjustment can generate welfare losses under function (6) due to deeper initial consumption drops and higher adjustment costs.
- MPOIM vs ad hoc rules:
  - POIM% tends to reduce welfare compared to MPOIM when non-oil per capita GDP is nonconstant because it transfers resources from poorer to richer generations.
  - Bird-in-hand is conservative and yields lower welfare than MPOIM while building financial assets over time; lower responsiveness to oil prices and generally lower volatility of non-oil balance (not universally).
  - Spending current oil revenue generally reduces welfare (functions (6) and (15)) and causes high volatility and abrupt post-exhaustion adjustments; exceptions may occur (e.g., Mature producer under social welfare function (1) where front-loading raises welfare relative to many rules).

### Robustness and sensitivity
- Alternative near-unit-root price specification yields consistent results with baseline.
- Properly accounting for uncertainty becomes more important with higher persistence in oil prices, especially for Large oil producers.
- Under high persistence, MPOIM with uncertainty correction can outperform MPOIM with adjustment costs in social welfare function (15).

### IV. Conclusions — policy-relevant findings and recommendations
- Welfare implications of policy rules for OPCs are highly sensitive to:
  - Choice of social welfare function.
  - Initial conditions.
  - Non-oil growth prospects.
- Distribution of non-oil wealth matters especially for countries with relatively low oil reserves; elements of traditional debt sustainability analysis should inform fiscal rules.
- Policy guidance:
  - MPOIM (constraining transfers from non-oil revenues via τ) addresses POIM shortcomings by permitting limited transfers from richer to poorer generations; can generate welfare gains when calibrated appropriately.
  - Calibrate τ to be consistent with a sustainable debt limit; example calibration: τ = 0.005 yields a debt ratio of 52.5 percent of non-oil GDP under stated assumptions.
  - Apply corrections for oil-price uncertainty especially for Large oil producers and when oil prices are highly persistent.
  - Apply adjustment-cost considerations when initial government consumption is near or above unsustainable levels cautiously: smoothing is beneficial when initial position is overly restrictive, but not necessarily optimal when initial position is unsustainably high and uncertainty is large.
  - Ad hoc rules often perform poorly:
    - POIM% tends to transfer wealth from poorer to richer generations when non-oil per capita GDP grows.
    - Bird-in-hand is overly conservative and produces suboptimal consumption patterns.
    - Spending current oil revenue produces excessive volatility and sharp post-exhaustion adjustments; generally welfare-reducing.
- Practical caveats:
  - Analysis abstracts from government capacity, quality of public spending, government investment decisions, channels from fiscal policy to non-oil growth, macroeconomic stability considerations, and non-oil-related uncertainties.
  - Results should be used as inputs into fiscal-rule design, not as a complete framework.

*Source: _wp09126 - 1. Initial Conditions*

### 1. Initial Conditions ..................................................................................................

### _wp09126 - 1. Initial Conditions .................................................................................................

### Major sections (with page references)
- 1. Initial Conditions — 14
- 2. Model Parameters — 14
- 3. Comparison of Policy Rules (Baseline) — 15
- 4. Comparison of Policy Rules (Alternative Specification for the Oil Price Process) — 16

### Figures (with page references)
- Figure 1: PIM and POIM Rules for the Mature Oil Producer — 18
- Figure 2: PIM and POIM Rules for the Large Oil Producer — 18
- Figure 3: PIM and POIM Rules for the Medium Oil Producer — 19
- Figure 4: POIM and MPOIM Rules for the Mature Oil Producer — 20
- Figure 5: POIM and MPOIM Rules for the Large Oil Producer — 21
- Figure 6: POIM and MPOIM Rules for the Medium Oil Producer — 22
- Figure 7: MPOIM and ad hoc Rules for the Mature Oil Producer — 23
- Figure 8: MPOIM and ad hoc Rules for the Large Oil Producer — 24
- Figure 9: MPOIM and ad hoc Rules for the Medium Oil Producer — 24

### Structural overview (implicit from headings)
- The document begins with "Initial Conditions" and follows immediately with "Model Parameters" on the same page number, indicating initial conditions and parameter definitions are co-located.
- Sections 3 and 4 compare policy rules: a baseline comparison and an alternative specification focused on the oil price process.
- A set of nine figures compare policy-rule families (PIM, POIM, MPOIM, and ad hoc) across three producer categories (Mature, Large, Medium), with figures spanning pages 18 through 24.

*Source: _wp09126 - 1. Initial Conditions .................................................................................................*

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

### _wp09126 - References..............................................................................................................

### I. Introduction
- Literature on fiscal policy in oil producing countries (OPCs) is extensive but dominated by empirical country applications rather than analytical studies.
- Key gaps identified:
  - Selection of an appropriate social welfare function for inter-temporal distribution of oil wealth is rarely discussed.
  - Little research on appropriate or permissible level of debt for OPCs.
  - Permanent oil income model (POIM) recommendation to maintain financial and oil wealth at a constant level is typically unjustified.
- Paper objectives:
  - Systematically compare rules derived using various social welfare functions and common ad hoc rules.
  - Draw on Engel and Valdes (2000) for theoretical framework, and use numerical simulations for comparisons under uncertainty.
  - Consider three stylized country examples to represent a range of OPCs.
- Scope limitations:
  - Abstracts from government capacity, quality of spending, government investment decisions (government savings held in foreign financial assets; expenditures restricted to public goods), and channels through which fiscal policy affects non-oil GDP growth.
  - Considers oil-price volatility as single source of uncertainty; long-term non-oil GDP growth uncertainty not formally analyzed.
  - Results intended as an input to policy design, not a complete framework.

### II. Fiscal Rules for OPCs — Optimizing Rules
- Framework assumptions:
  - Households live for one period, no bequest motive; government may tax non-oil GDP, fully capture oil rent, spend on public goods, save in foreign financial assets.
  - Government policy instruments set by maximizing chosen social welfare function subject to constraints.
  - Critical maintained assumption: R/1 = β.
- Permanent income model (PIM)
  - Social welfare function (per capita consumption) given in equation (1).
  - Lifetime budget constraint and total wealth W defined (equations (2), (3), (4)).
  - Maximization yields maximum attainable per capita consumption c:
    - 0 ) 1 1( W R n c + − =  (equation (5))
  - Implication: may imply massive transfers between generations depending on per capita non-oil income growth.
- Permanent oil income model (POIM)
  - Government distributes only oil wealth; social welfare function uses per capita government expenditures (equation (6)).
  - Oil wealth Woil defined; lifetime constraint (equation (7)).
  - Optimal constant per capita government expenditure g financed by perpetual income from oil wealth:
    - oil W R n g 0 ) 1 1( + − =  (equation (8))
  - POIM is a fiscal policy benchmark but may be overly restrictive by excluding non-oil tax intergenerational transfers.
- Modified permanent oil income model (MPOIM)
  - Government may tax non-oil GDP for transfers but limited to constant fraction τ of non-oil GDP.
  - Lifetime budget constraint includes SD (equation (9)) and SDW0 definition.
  - Optimal constant per capita government spending:
    - SD W 0 SD W R n g 0 ) 1 1( + − =  (equation (10))
  - Long-run properties:
    - Government non-oil primary balance converges to τ under no oil revenues and growing per capita non-oil GDP (equation (11)).
    - Debt-to-non-oil-GDP ratio limit (with maintained assumption R/1=β and R/g + >1) converges to expression in (12); example: τ = 1, nonoil_g = 0.04, and R = 1.05 produce limit debt ratio of 105 times non-oil GDP.
    - To achieve a “sustainable” debt ratio of 52.5 percent of non-oil GDP given other assumptions requires τ = 0.005 (a constant primary balance of ½ percent of non-oil GDP).
  - τ interpretation: share of non-oil GDP future generations willing to devote to intergenerational transfers; calibration should reflect sustainable debt limits.
  - Constraining τ enhances sustainability; all optimizing rules considered satisfy lifetime government budget constraints.

### Uncertainty (Oil-price uncertainty)
- Oil prices modeled by (13):
  - t t t P P υ μ ψ μ + − = − )( log log 1 ,
  - υ is normally distributed shock with variance υ σ 2 , μ has mean and variance; initial oil production has mean and variance.
- Engel and Valdez (2001) derive optimal POIM consumption under oil-price uncertainty as approximation (equation (14)):
  - 0 22 00 0, Q P σ σ Q )0,0( ]1[ ),( 00 22 00 00 gg IUBU Δ − Δ − ≈ ν σ σ , with definitions for Δ BU and Δ IU as functions of parameters (see source).
  - Correction factors diminish with initial financial wealth and remaining oil production.
- MPOIM correction for uncertainty analogous, adding present discounted value of non-oil tax revenues to initial financial assets under simplifying assumption that non-oil output and taxes are known without uncertainty and uncorrelated with oil revenues.

### Adjustment costs
- Augmented social welfare function includes quadratic adjustment costs on per capita government consumption deviations from an optimal g*_t (equation (15)).
- Approximation for log of initial per capita government consumption (equation (16)):
  - )]log()[log()log()log( 1 * 10 − − ≈ − g g g g α , with α increasing with k and ρ.
- Elicitation of k via indifference condition (equation (17)):
  - 100 × a s × n a s 100 ρ − = 1 * 2 )( g s s k a na (as presented in source); used in numerical simulations to apply adjustment-cost correction to MPOIM.

### Ad hoc Rules
- “Bird-in-hand” rule:
  - Government limits consumption from oil wealth to returns from accumulated financial assets:
    - t t FRG )1( − =  (equation (18))
  - Modified to include present value of non-oil tax revenues to financial assets:
    - ∑ ≥ − n o n o i l t t t t Y R F R G τ 0 )1(  (equation (19))
  - Ensures long-term fiscal sustainability; less responsive to oil price shocks.
- Spending from current oil revenue:
  - Government fully spends current oil revenues:
    - oil t T t Y G = ≤  (equation (20))
  - After oil exhaustion, expenditures must be adjusted to satisfy lifetime constraint:
    - ∑ ≥ − n o n o i l t t t t T t Y R F R G τ 0 )1(  (equation (21))
  - Produces high volatility and abrupt adjustment upon oil depletion.
- POIM as percentage of non-oil GDP (POIM%):
  - Social welfare function uses government consumption as share of non-oil GDP (equation (22)).
  - Optimal constant government consumption share:
    - oil W R g g 0 ) 1 1( + − = ˆ (equation (23))
  - Classified as ad hoc because it distributes oil wealth proportional to non-oil GDP, transferring resources from poorer to richer generations when per capita non-oil GDP grows.

### III. Numerical Comparisons — Setup and Assumptions
- Monte Carlo simulations:
  - 5,000 random realizations of oil prices over a 200-year horizon after estimating parameters of the oil price equation (13).
  - Random error in price equation is the only source of uncertainty; price-equation parameters known with certainty.
- Baseline price process estimated by OLS using WEO average spot prices deflated by U.S. CPI over 1960-2012 (equation (24)):
  - t t t P P υ + − = − )67.3(log 93.0 67.3 log 1
  - υ σ 2  = 25.0
  - Implies stationary log oil prices with long-term mean price of $39 per barrel (in 2000 prices).
- Alternative specification: near-unit-root process with ψ constrained to 0.99; constrained-sample estimation yields υ σ 2 = 2.0 and other calibrations to match long-term mean.
- Initial uncertainty about initial oil price in equation (14) assumed equal to 0 2 σ .
- Simulation order: government consumption paths constructed sequentially using information available to authorities at decision times; optimizing rules re-optimize at each period start using latest price.
- Main evaluation criteria:
  - Mean social welfare functions over randomized sample for three social welfare functions: (1) overall consumption, (6) government consumption, (15) government consumption with adjustment costs.
  - Volatility measured by expected standard deviation of non-oil government primary balance as % of non-oil GDP.
- Stylized country examples — initial conditions (Table 1):
  - Mature, Large, Medium producers with parameters:
    - Non-hydrocarbon GDP growth rate (%) : Mature 4.0, Large 2.0, Medium 1.0
    - Non-hydrocarbon GDP (2000 US$ billions): Mature 10.0, Large 150.0, Medium 10.0
    - Non-hydrocarbon primary balance (2000 US$ billions): Mature -2.5, Large -75.0, Medium -2.5
    - Net foreign assets (2000 US$ billions): Mature 10.0, Large 150.0, Medium 5.0
    - Population growth rate (%): Mature 1.0, Large 2.0, Medium 2.0
    - Initial stock of oil (billions of barrels): Mature 1.0, Large 250.0, Medium 1.0
    - Annual extraction (billions of barrels): Mature 0.1, Large 5.0, Medium 0.1
    - Time to exhaust (years): Mature 10.0, Large 50.0, Medium 10.0
    - Memorandum items:
      - Oil wealth (NPV of oil revenue, 2000 US$ billions): Mature 31.7, Large 3744.6, Medium 31.7
      - Total wealth (NPV of non-oil GDP + NFA, 2000 US$ billions): Mature 1,133.7, Large 9,249.6, Medium 301.8
      - Oil wealth/Total wealth (%): Mature 2.8, Large 40.5, Medium 10.5
- Other model parameters (Table 2):
  - Initial oil price (2000 US$ per barrel) 39.1
  - Coeff. of relative risk aversion ρ 3
  - Adjustment costs coefficients: s_na ×100 20 ; s_a ×100 10
  - Tax on non-oil GDP τ 0.005
  - Gross real interest rate R 1.05
  - Adjustment-cost elicitation: avoiding a 10 percent change in per capita government consumption (s_a ×100 = 10) is valued same as a 20 percent increase in absence of adjustment costs (s_na ×100 = 20).

### III. Numerical Comparisons — Results (Baseline and Alternative Price Specs)
- Mean social welfare functions normalized by POIM reported in Table 3 (baseline) and Table 4 (alternative price process). Lower reported ratio indicates better performance (since social welfare functions take negative values).
- Selected numeric highlights from Tables 3 and 4 (ratios to POIM):
  - For overall consumption (equation 1), Mature: PIM 0.18, POIM 1.00, MPOIM 0.98, MPOIM with precautionary savings 0.99, MPOIM with adjustment costs 0.97, POIM% 1.17, Bird-in-hand 1.01, Spending from current oil revenue 0.88.
  - For government consumption (equation 6), Mature: PIM 0.00, POIM 1.00, MPOIM 0.75, MPOIM with precautionary savings 0.75, MPOIM with adjustment costs 0.79, POIM% 6.05, Bird-in-hand 1.12, Spending from current oil revenue 3.29.
  - For government consumption with adjustment costs (equation 15), Mature: PIM 6.08, POIM 1.00, MPOIM 0.73, MPOIM with precautionary savings 0.79, MPOIM with adjustment costs 0.67, POIM% 7.37, Bird-in-hand 2.09, Spending from current oil revenue 4.11.
  - Expected std. dev. of non-oil government primary balance as % of non-oil GDP (baseline):
    - Mature: PIM 90.57, POIM 2.84, MPOIM 2.46, MPOIM with precautionary savings 3.05, MPOIM with adjustment costs 0.78, POIM% 6.25, Bird-in-hand 5.81, Spending from current oil revenue 9.79.
    - Large: PIM 8.38, POIM 8.38, MPOIM 8.38, MPOIM with precautionary savings 6.10, MPOIM with adjustment costs 2.33, POIM% 8.38, Bird-in-hand 7.49, Spending from current oil revenue 31.40.
    - Medium: PIM 11.88, POIM 4.30, MPOIM 4.34, MPOIM with precautionary savings 4.97, MPOIM with adjustment costs 1.39, POIM% 3.40, Bird-in-hand 7.33, Spending from current oil revenue 11.08.
- Main comparative findings (qualitative, with quantitative support in tables and figures):
  - PIM vs POIM:
    - PIM maximizes social welfare function (1) by construction and gives highest government consumption under (6).
    - PIM produces implausibly high initial consumption for growing per capita non-oil GDP and implausibly low for falling per capita non-oil GDP; generates high volatility in non-oil government balance (e.g., std. dev. 90.57 for mature in baseline).
    - POIM yields more plausible debt dynamics and lower volatility; consumption lower (higher) than PIM when per capita non-oil GDP growing (falling).
    - When per capita non-oil GDP constant, PIM and POIM equivalent under social welfare function (1).
  - POIM vs MPOIM; MPOIM variants:
    - MPOIM offers significant welfare improvements over POIM when per capita non-oil GDP is growing or falling due to more optimal non-oil wealth distribution.
    - For large oil producer, difference between POIM and MPOIM modest because non-oil wealth transferred under MPOIM (τ = 0.005) is small relative to oil wealth.
    - Precautionary savings (uncertainty adjustment) offers substantial improvement for large producer under social welfare functions (6) and (15); smoother consumption path reduces adjustment costs and volatility.
    - Adjustment-cost correction produces much smoother government consumption and greatly reduces volatility of non-oil balance across economies (e.g., MPOIM with adjustment costs reduces std. dev. to 0.78, 2.33, 1.39 for Mature, Large, Medium respectively in baseline).
    - For small/medium producers, uncertainty adjustment can generate welfare losses under function (6) due to deeper initial consumption drops and higher adjustment costs.
  - MPOIM vs ad hoc rules:
    - POIM% (share-of-non-oil-GDP rule) reduces welfare compared to MPOIM when non-oil per capita GDP is nonconstant because it transfers resources from poorer to richer generations.
    - Bird-in-hand is conservative; yields lower welfare than MPOIM and builds financial assets over time, with lower responsiveness to oil prices and generally lower volatility of non-oil balance (not universally).
    - Spending current oil revenue generally reduces welfare (functions (6) and (15)) and causes high volatility and abrupt post-exhaustion adjustments; exceptions may occur (e.g., mature producer under social welfare function (1) where front-loading raises welfare relative to many rules).
- Robustness:
  - Alternative near-unit-root specification yields consistent results with baseline.
  - Properly accounting for uncertainty more important with higher persistence in oil prices, especially for large oil producers. Under high persistence, MPOIM with uncertainty correction can outperform MPOIM with adjustment costs in social welfare function (15).

### IV. Conclusions — Key Policy-relevant Findings and Recommendations
- Welfare implications of policy rules for OPCs are highly sensitive to:
  - Choice of social welfare function.
  - Initial conditions.
  - Non-oil growth prospects.
- Distribution of non-oil wealth matters especially for countries with relatively low oil reserves; elements of traditional debt sustainability analysis should inform fiscal rules for these countries.
- Policy guidance emerging from comparisons:
  - MPOIM (constraining transfers from non-oil revenues via τ) addresses shortcomings of POIM by permitting limited transfers from richer to poorer generations, and can generate welfare gains when calibrated appropriately.
  - Calibrate τ to be consistent with a sustainable debt limit; example calibration: τ = 0.005 yields a debt ratio of 52.5 percent of non-oil GDP under stated assumptions.
  - Apply corrections for oil-price uncertainty especially for large oil producers and when oil prices are highly persistent.
  - Apply adjustment-cost considerations when initial government consumption is near or above unsustainable levels cautiously: smoothing is beneficial when initial position is overly restrictive, but not necessarily optimal when initial position is unsustainably high and uncertainty is large.
  - Ad hoc rules often perform poorly:
    - POIM% tends to transfer wealth from poorer to richer generations when non-oil per capita GDP grows.
    - Bird-in-hand is overly conservative and produces suboptimal consumption patterns.
    - Spending current oil revenue produces excessive volatility and sharp post-exhaustion adjustments; generally welfare-reducing.
- Practical caveats:
  - Analysis abstracts from government capacity, quality of public spending, government investment decisions, channels from fiscal policy to non-oil growth, macroeconomic stability considerations, and non-oil-related uncertainties.
  - Results should be used as inputs into fiscal-rule design, not as a complete framework.

*Source: _wp09126 - References..............................................................................................................*

### References

### _wp09126 - References

### References

- Barnett, S. and R. Ossowski, 2003, “Operational Aspects of Fiscal Policy in Oil-Producing Countries,” in Fiscal Policy Formulation and Implementation in Oil-Producing Countries, ed. by J. Davis, R. Ossowski, and A. Fedelino (Washington: International Monetary Fund).

- Burnside, C., 2004, “Assessing New Approaches to Fiscal Sustainability Analysis.” World Bank, mimeo, September 2004.

- Carcillo, S., D. Leigh and M. Villafuerte, 2007, "Catch-Up Growth, Habits, Oil Depletion, and Fiscal Policy: Lessons from the Republic of Congo," IMF Working Papers 07/80, International Monetary Fund.

- Engel, E. and R. Valdes, 2000, “Optimal Fiscal Strategy for Oil Exporting Countries”, Working Paper No. 78, Center of Applied Economics (CEA), Dep. Ind. Engineering, U. of Chile, June 2000.

- Fouad, M., W. Maliszewski, M. Hommes, H. Morsy, M. Petri, and L. Soderling, 2007, "Public Debt and Fiscal Vulnerability in the Middle East" (January 2007). IMF Working Paper No. 07/12 (Washington: International Monetary Fund).

- Jafarov, E. and D. Leigh, 2007. "Alternative Fiscal Rules for Norway," IMF Working Papers 07/241, International Monetary Fund.

- Leigh, D. and J-P. Olters, 2006, Natural-Resource Depletion, Habit Formation, and Sustainable Fiscal Policy: Lessons from Gabon, IMF Working Paper 06/193, International Monetary Fund.

- Olters, J-P., 2007. "Old Curses, New Approaches? Fiscal Benchmarks for Oil-Producing Countries in Sub-Saharan Africa," IMF Working Papers 07/107, International Monetary Fund.

- Segura, A., 2006, "Management of Oil Wealth Under the Permanent Income Hypothesis: The Case of Sao Tome and Principe," IMF Working Papers 06/183, International Monetary Fund

- van der Ploeg, F. and A. Venables, 2008. "Harnessing Windfall Revenues in Developing Economies: Sovereign Wealth Funds and Optimal Tradeoffs Between Citizen Dividends, Public Infrastructure and Debt Reduction," CEPR Discussion Papers 6954, C.E.P.R. Discussion Papers.

*Source: _wp09126 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09126.pdf_