## Annex I: Summary Tables

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### I. Introduction — purpose and scope
- Objective:
  - quantify fiscal risks to hydrocarbon-exporting MENA countries from oil price volatility by estimating the probability that oil prices fall below each country’s fiscal break-even price.
- Key framing points:
  - Recent high commodity (hydrocarbon) prices improved headline fiscal aggregates and increased public finance buffers, but fiscal stances have been loosened by new spending pressures in many MENA countries.
  - Fiscal break-even oil prices have been trending upward in most countries and in some cases are near or exceed actual spot market oil prices.
  - Break-even prices measure the crude oil price that balances expenditures and total revenues in a given year; they do not account for past accumulation or depletion of net assets and thus are not a complete solvency measure.
  - The analysis does not attempt to forecast specific oil prices but to describe probabilistically the distribution of possible oil-price paths over the coming years.

### II. Data, price series, and modeling approach
- Sample and periods:
  - 11 hydrocarbon-exporting countries from the Middle East and North Africa region.
  - Historical data: 1980 to 2011, annual frequency.
  - Annual projections used in parts of the analysis: 2012–17.
- Price series and transformation:
  - Price used: Brent crude oil (London market price).
  - Deflation: Brent price deflated using U.S. CPI so the Brent series is in 2011 U.S. dollars per barrel.
- Modeling strategy:
  - Use historical oil price data (mean and standard deviation) to estimate the future distribution of oil prices.
  - Model the distribution of oil prices based on their historical behavior (in particular volatility) and generate stochastic simulations of possible future crude oil price paths.
  - Modeling intends to describe probabilistically likely distributions of future oil-price paths, not to forecast specific future prices.
- Break-even price definition:
  - The crude-oil price at which the overall fiscal deficit equals zero in a given year.
  - Break-even prices are presented in nominal and real terms in Tables 1 and 2.

### III. Measures of fiscal risk and simulation overview
- Two risk measures:
  - Measure I: Probability that Brent oil prices fall below the break-even price (Table 3; Figure 3); assumes break-even prices remain constant in real terms from 2011 onward (uses 2011 break-even prices).
  - Measure II: Probability that Brent oil prices fall below the break-even price (alternative measure) (Table 4; Figure 4); uses break-even prices estimated by IMF country teams for 2012–17.
- Stochastic simulation approach:
  - Historical behavior (mean and volatility) of Brent prices used to generate simulated future paths.
  - Simulations yield probabilities that Brent falls below each country’s break-even price over the horizon.
  - Historic and simulated real price of Brent (log) shown in Figure 5.

### IV. Key descriptive statistics and data points
- Countries analyzed: 11 hydrocarbon-exporting MENA countries.
- Historical estimation period: 1980 to 2011 (annual).
- Projection horizon used in parts of the analysis: 2012–17 (annual projections).
- Price unit: 2011 U.S. dollars per barrel (real Brent series).
- Nominal Brent oil prices averaged US$111.32 per barrel in 2011.

### V. Break-even prices (selected figures from Tables)
- Nominal break-even prices (U.S. dollars per barrel), selected countries:
  - 2011: ALG 104.7; BHR 113.7; IRQ 95.0; KWT 43.8; LBY 183.5; OMN 75.5; QAT 38.0; SAU 70.0; UAE 92.3; YMN 195.0.
  - 2017: ALG 112.1; BHR 128.6; IRQ 75.7; KWT 56.9; LBY 110.4; OMN 113.1; QAT 86.7; SAU 93.9; UAE 69.3; YMN (–).
- Real break-even prices (2011 U.S. dollars per barrel; U.S. CPI inflation assumed 2.0 percent annually over 2012–17), selected:
  - 2011: ALG 104.7; BHR 113.7; IRQ 95.0; KWT 43.8; LBY 183.5; OMN 75.5; QAT 38.0; SAU 70.0; UAE 92.3; YMN 195.0.
  - 2017: ALG 99.5; BHR 114.2; IRQ 67.2; KWT 50.5; LBY 98.0; OMN 100.4; QAT 77.0; SAU 83.4; UAE 61.5; YMN (–).

### VI. Model for oil-price simulations (Annex II) — specification and estimation
- Stochastic model:
  - The log-price of Brent, y_t, follows a geometric Brownian motion: dy_t = α dt + σ dW_t, where W_t is a standard Brownian motion.
- Discrete-time implications and likelihood:
  - y_t+1 − y_t ∼ N(α Δt, σ^2 Δt).
  - Log-likelihood and first-order conditions lead to closed-form MLEs.
- Closed-form MLE solutions:
  - α̂ = (1/N) ∑ (y_t+1 − y_t).
  - σ̂^2 = (1/N) ∑ (y_t+1 − y_t)^2 − (1/N) [∑ (y_t+1 − y_t)]^2.
- Estimated parameters used in simulations:
  - α̂ = 0.0342
  - σ̂ = 0.0617
- Simulation details:
  - Simulation horizon: 2012–17 (simulation start in 2012).
  - Confidence intervals based on one million repetitions.
  - Figure 5 shows historic and simulated real log-price of Brent with percentiles at 50%, 75%, 95%, and 99% over 1980–2025.

### VII. Main simulation results and cross-country comparisons
- General observations:
  - Fiscal risk probabilities differ considerably across countries and over time under both measures.
  - Uncertainty increases with time; the distribution of possible Brent price paths widens over the simulation horizon.
- Measure I (break-even prices constant in real terms from 2011) — selected probabilities:
  - Kuwait (KWT): 0.0 (2012) and 5.9 (2017).
  - Qatar (QAT): 0.0 (2012) and 3.6 (2017).
  - Yemen (YMN): 100.0 (2011); 98.8 (2012); 81.2 (2017).
  - Libya (LBY): 100.0 (2011); 97.7 (2012); 78.5 (2017).
  - Bahrain (BHR): 100.0 (2011); 52.8 (2012); 50.1 (2017).
  - Algeria (ALG): 0.0 (2011); 39.8 (2012); 44.7 (2017).
  - Countries with probability higher than 40 percent throughout 2012–17 under measure I: Yemen, Algeria, and Bahrain.
- Measure II (IMF country-team break-even prices for 2012–17) — selected probabilities:
  - Correlation between measures I and II for 2012 = 0.93.
  - Kuwait (KWT): 0.0 (2012); 9.2 (2017).
  - Qatar (QAT): 0.0 (2012); 26.2 (2017).
  - Saudi Arabia (SAU): 0.0 (2012); 26.2 (2017).
  - Libya (LBY): 100.0 (2011); 15.5 (2012); 40.4 (2017).
  - Iraq (IRQ): 0.0 (2011); 47.3 (2012); 19.4 (2017).
  - United Arab Emirates (UAE): 0.0 (2011); 4.1 (2012); 30.6 (2017).
- Notable dynamics and interpretations:
  - Libya’s nominal break-even price falls from US$183.5 per barrel in 2011 to US$88.5 per barrel in 2012 (IMF country-team estimate), driven by political situation and stabilization assumptions.
  - U.A.E. and Iraq: IMF-estimated break-even prices fall markedly between 2011 and 2017, reducing medium-term vulnerability relative to measure I.
  - Correlation between estimated break-even prices in 2011 and 2017 = 0.54.
  - Identical break-even prices can mask very different fiscal sustainability if accumulated wealth or proven oil reserves differ significantly (example: Oman vs. Saudi Arabia — Saudi Arabia has significantly larger net assets and proven oil reserves almost 50 times larger than Oman).
  - Break-even–based measures treat expenditures and non-oil revenues as exogenous; they do not capture likely policy adjustments in response to realized oil price shocks.

### VIII. Analytical conclusions emphasized
- Volatility in global oil prices poses significant medium-term risks to fiscal balances in oil-exporting MENA countries.
- Rising recurrent expenditures (for example, wages and salaries) increase fiscal vulnerability because such expenditures may be difficult to reverse if oil prices fall.
- Break-even prices have risen in most countries, reflecting loosened fiscal stances and increased spending.
- The break-even price is a simple, widely used fiscal yardstick but limited as a solvency indicator because it ignores past asset accumulation/depletion and access to global financial markets.

### IX. Policy implications and recommendations
- Countries identified as relatively more vulnerable to oil price volatility (examples: Yemen, Algeria, Bahrain) should:
  - Pay greater attention to the conduct of fiscal policy in the short- to medium-term.
  - Pursue fiscal consolidation chiefly by reducing expenditure pressures that might have arisen following temporary events.
  - Aim at building larger fiscal buffers to mitigate the impact if fiscal risks materialize.
- Considerations for policymakers and analysts:
  - Interpret break-even–based fiscal risk measures with caution because they do not account for asset/liability stocks, future fiscal dynamics, or endogenous budget adjustments to oil price realizations.

*Source: Annex I: Summary Tables from the provided IMF working paper content.*

### Annex I: Summary Tables ................................................................................................

### Annex I: Summary Tables

### I. Introduction — purpose and scope
- Objective: quantify fiscal risks to hydrocarbon-exporting MENA countries from oil price volatility by estimating the probability that oil prices fall below each country’s fiscal break-even price.
- Key framing points:
  - Recent high commodity (hydrocarbon) prices improved headline fiscal aggregates and increased public finance buffers, but fiscal stances have been loosened by new spending pressures in many MENA countries.
  - Fiscal break-even oil prices have been trending upward in most countries and in some cases are near or exceed actual spot market oil prices.
  - Break-even prices measure the crude oil price that balances expenditures and total revenues in a given year; they do not account for past accumulation or depletion of net assets and thus are not a complete solvency measure.
  - The analysis does not attempt to forecast specific oil prices but to describe probabilistically the distribution of possible oil-price paths over the coming years.
- Literature context:
  - Theoretical expectation under complete markets: optimal fiscal policy smooths spending and taxes over time (Riascos and Végh (2003)).
  - Political distortions can induce procyclical fiscal behavior (Tornell and Lane (1999); Talvi and Végh (2005); Alesina and Tabellini (2005); Ilzetzki (2008)).
  - Empirical literature has focused more on fiscal response to output cycles than directly on commodity-price cycles; only a few papers discuss fiscal risk from commodity-price shocks.
  - Commodity and oil price behavior is better characterized by variance than by trend; shocks are persistent and highly volatile (Cashin and McDermott (2002); Cashin, Liang and McDermott (2000)).

### II. Data and empirical methodology — data, price series, and modeling approach
- Sample and periods:
  - 11 hydrocarbon-exporting countries from the Middle East and North Africa region.
  - Historical data: 1980 to 2011, annual frequency.
  - Annual projections used in parts of the analysis: 2012–17.
- Price series and transformation:
  - Price used: Brent crude oil (London market price).
  - Deflation: Brent price deflated using U.S. CPI so the Brent series is in 2011 U.S. dollars per barrel.
  - Resulting series: real Brent price series presented in Figure 2 of the source.
- Modeling strategy:
  - Use historical oil price data (mean and standard deviation) to estimate the future distribution of oil prices.
  - Model the distribution of oil prices based on their historical behavior (in particular volatility) and generate stochastic simulations of possible future crude oil price paths.
  - Explicit statement: modeling intends to describe probabilistically likely distributions of future oil-price paths, not to forecast specific future prices.
- Break-even prices:
  - For each country, break-even price is defined as the crude-oil price at which the overall fiscal deficit equals zero in a given year.
  - Break-even prices for countries are presented in Tables 1 and 2 (nominal and real break-even prices).

### III. Measures of fiscal risk and simulation overview
- Two measures of fiscal risk are presented:
  - Measure I: Probability that Brent oil prices fall below the break-even price (Table 3; Figure 3).
  - Measure II: Probability that Brent oil prices fall below the break-even price (alternative measure) (Table 4; Figure 4).
- Stochastic simulation approach:
  - Historical behavior (mean and volatility) of Brent prices is used to generate simulated future paths.
  - Simulations yield probabilistic assessments such as the probability that Brent falls below each country’s break-even price over the horizon.
  - Historic and simulated real price of Brent (in logarithm) is shown in Figure 5.

### IV. Key descriptive statistics and facts from the source text
- Countries analyzed: 11 hydrocarbon-exporting MENA countries.
- Historical estimation period: 1980 to 2011 (annual).
- Projection horizon used in parts of the analysis: 2012–17 (annual projections).
- Price unit: 2011 U.S. dollars per barrel (real Brent series).
- Figures and tables referenced in the source:
  - Figures: 1, 2, 3, 4, 5.
  - Tables: 1, 2, 3, 4.
  - Annexes: Annex II (Modeling Oil Prices Using Geometric Brownian Motion), Annex III (Stochastic Simulations) are part of the full study structure.

### V. Analytical conclusions emphasized in the text
- Volatility in global oil prices poses significant medium-term risks to fiscal balances in oil-exporting MENA countries.
- Rising recurrent expenditures (for example, wages and salaries) increase fiscal vulnerability because such expenditures may be difficult to reverse if oil prices fall.
- Break-even prices have risen in most countries, reflecting loosened fiscal stances and increased spending.
- The break-even price is a simple, widely used fiscal yardstick but limited as a solvency indicator because it ignores past asset accumulation/depletion and access to global financial markets.

*Source: Annex I: Summary Tables from the provided IMF working paper content.*

### Annex I.

### Annex I.

### Methodology: oil price simulations and fiscal risk measures
- Oil price stochastic model:
  - The logarithm of Brent oil prices is modeled using a geometric Brownian motion: parameters ߙ (drift) and ߪ (volatility); ܤ denotes a standard Brownian motion (Wiener process).
  - Parameters ߙ and ߪ are estimated by maximum likelihood; Monte Carlo simulations generate future price paths from an initial log-price ݕ
଴ at time ݐ
଴.
  - Simulation horizon: 2012–17.
  - Annual data are used; risk measures relate to the probability that the annual average of crude oil prices in a given year falls below the break-even price.
- Break-even price definitions:
  - Break-even price: the price of crude oil that renders the fiscal balance equal to zero in a given year.
  - Two risk measures:
    - Measure I: assumes break-even prices remain constant in real terms from 2011 onwards (uses 2011 break-even prices).
    - Measure II: uses break-even prices estimated by IMF country teams for 2012–17.
  - Note: break-even prices here are single-year measures and do not account for past or future deficit dynamics or accumulated assets/liabilities (stocks), nor do they endogenize fiscal policy responses to realized oil prices.

### Key projected break-even prices (select figures from Tables)
- Nominal break-even prices (U.S. dollars per barrel), selected countries:
  - 2011: ALG 104.7; BHR 113.7; IRQ 95.0; KWT 43.8; LBY 183.5; OMN 75.5; QAT 38.0; SAU 70.0; UAE 92.3; YMN 195.0.
  - 2017: ALG 112.1; BHR 128.6; IRQ 75.7; KWT 56.9; LBY 110.4; OMN 113.1; QAT 86.7; SAU 93.9; UAE 69.3; YMN (–).
- Real break-even prices (in 2011 U.S. dollars per barrel; 2011 base year; U.S. CPI inflation assumed 2.0 percent annually over 2012–17), selected:
  - 2011: ALG 104.7; BHR 113.7; IRQ 95.0; KWT 43.8; LBY 183.5; OMN 75.5; QAT 38.0; SAU 70.0; UAE 92.3; YMN 195.0.
  - 2017: ALG 99.5; BHR 114.2; IRQ 67.2; KWT 50.5; LBY 98.0; OMN 100.4; QAT 77.0; SAU 83.4; UAE 61.5; YMN (–).
- Historical reference:
  - Nominal Brent oil prices averaged US$111.32 per barrel in 2011.

### Main simulation results and cross-country comparisons
- General observations:
  - Fiscal risk probabilities differ considerably across countries and over time under both risk measures.
  - Uncertainty increases with time in the model; the distribution of possible Brent price paths widens over the simulation horizon.
- Measure I (break-even prices constant in real terms from 2011):
  - Examples from Table 3:
    - Kuwait (KWT): probability of Brent falling below break-even = 0.0 (2012) and 5.9 (2017).
    - Qatar (QAT): 0.0 (2012) and 3.6 (2017) — medium-term probability in 2017 still lower than 6 percent in both Kuwait and Qatar.
    - Yemen (YMN): 100.0 (2011); 98.8 (2012); 81.2 (2017).
    - Libya (LBY): 100.0 (2011); 97.7 (2012); 78.5 (2017).
    - Bahrain (BHR): 100.0 (2011); 52.8 (2012); 50.1 (2017).
    - Algeria (ALG): 0.0 (2011); 39.8 (2012); 44.7 (2017).
  - Countries with probability higher than 40 percent throughout 2012–17 under measure I: Yemen, Algeria, and Bahrain.
- Measure II (break-even prices from IMF country teams for 2012–17):
  - Short-term (2012) results highly correlated with measure I: correlation between measures I and II for 2012 = 0.93.
  - Examples from Table 4:
    - Kuwait (KWT): 0.0 (2012); 9.2 (2017).
    - Qatar (QAT): 0.0 (2012); 26.2 (2017).
    - Saudi Arabia (SAU): 0.0 (2012); 26.2 (2017).
    - Libya (LBY): 100.0 (2011); 15.5 (2012); 40.4 (2017).
    - Iraq (IRQ): 0.0 (2011); 47.3 (2012); 19.4 (2017).
    - United Arab Emirates (UAE): 0.0 (2011); 4.1 (2012); 30.6 (2017).
  - Notable dynamics:
    - Libya’s break-even price falls sharply from US$183.5 per barrel in 2011 to US$88.5 per barrel in 2012 (nominal), driven by the political situation and stabilization assumptions.
    - In the U.A.E. and Iraq, IMF-estimated break-even prices fall markedly between 2011 and 2017, reducing medium-term vulnerability relative to measure I.
  - Correlation between estimated break-even prices in 2011 and 2017 = 0.54.
- Interpretation nuances:
  - Two countries with identical break-even prices in a year can have very different fiscal sustainability if one has significantly higher accumulated wealth or larger proven oil reserves (example: Oman vs. Saudi Arabia — Saudi Arabia has significantly larger net assets and proven oil reserves almost 50 times larger than Oman).
  - Break-even prices, as used here, treat fiscal expenditures and non-oil revenues as exogenous to oil prices; they do not capture likely policy adjustments in response to realized oil price shocks.

### Policy implications and recommendations
- Countries identified as relatively more vulnerable to oil price volatility (examples: Yemen, Algeria, Bahrain) should:
  - Pay greater attention to the conduct of fiscal policy in the short- to medium-term.
  - Pursue fiscal consolidation chiefly by reducing expenditure pressures that might have arisen following temporary events.
  - Aim at building larger fiscal buffers to mitigate the impact if fiscal risks materialize.
- Considerations for policymakers and analysts:
  - Interpret break-even–based fiscal risk measures with caution because they do not account for asset/liability stocks, future fiscal dynamics, or endogenous budget adjustments to oil price realizations.

*Source: IMF staff calculations; Annex I of the provided IMF working paper (tables and figures as presented in the source).*

### ANNEX II: MODELING OIL PRICES USING GEOMETRIC BROWNIAN MOTION

### ANNEX II: MODELING OIL PRICES USING GEOMETRIC BROWNIAN MOTION

### Model specification
- The log-price of Brent, y_t, is assumed to follow a geometric Brownian motion with stochastic differential equation:
  - dy_t = α dt + σ dW_t
- y_t denotes the log-price of Brent oil at time t.
- W_t is a standard Brownian motion (Wiener process).

### Likelihood and data transformation
- For a time series of log-prices y_t, …, y_T, the discrete-time transition implied by the continuous model is:
  - y_t+1 − y_t ∼ N(α Δt, σ^2 Δt)  (expressed in the source as equation [A2])
- The likelihood function L(y_t, …, y_T | σ, α; Δt) is defined as the product of conditional probabilities:
  - L = ∏ p(y_t+1 | y_t, σ, α; Δt)  (equation [A3])
- The conditional probability density for increments is given explicitly in equation [A4] with Gaussian kernel scaling by (σ√(2π Δt))^−1 and exponential of the squared deviation term divided by 2σ^2Δt.

### Log-likelihood and first-order conditions
- The log-likelihood ℓ(σ, α; Δt) is given in equation [A5] as:
  - ℓ(σ, α; Δt) = −(N/2) ∑ log(σ^2 π 2 Δt) + ... (full form retained in source as [A5])
- When Δt = 1, the log-likelihood simplifies to the form shown in equation [A6].
- Differentiating the log-likelihood yields the score equations:
  - ∂ℓ/∂α = (1/σ^2) ∑ (y_t+1 − y_t − α)  (equation [A7])
  - ∂ℓ/∂σ^2 = −(N/2σ^2) + (1/2σ^4) ∑ (y_t+1 − y_t − α)^2  (equation [A8])
- First-order conditions for maximum likelihood estimate (MLE) require:
  - ∂ℓ/∂α = 0 and ∂ℓ/∂σ^2 = 0  (equation [A9])

### Closed-form MLE solutions
- Solving the first-order conditions yields MLEs for α and σ^2:
  - α̂ = (1/N) ∑ (y_t+1 − y_t)  (equation [A10])
  - σ̂^2 = (1/N) ∑ (y_t+1 − y_t)^2 − (1/N) [∑ (y_t+1 − y_t)]^2  (equation [A11])
- These expressions depend only on the observed time series y_1, y_2, …, y_T and are straightforward to compute.

### Estimated parameters and simulations
- Based on the sample used in the source, the estimated parameter values are:
  - α̂ = 0.0342
  - σ̂ = 0.0617
- The estimated parameters were used in Monte Carlo stochastic simulations summarized in Annex III.
- Simulation details (from Annex III figure note):
  - The simulation starts in 2012.
  - Confidence intervals (percentiles) are based on one million repetitions.
- Figure 5 in Annex III presents historic and simulated real log-price of Brent oil with percentiles shown at 50%, 75%, 95%, and 99% over the 1980–2025 horizon.

*Source: ANNEX II: MODELING OIL PRICES USING GEOMETRIC BROWNIAN MOTION (IMF staff content from the supplied PDF).*

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