## 1. Stationarity Tests

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---

### I. Introduction — context and observed oil price dynamics
- Oil price movements have large effects on world economic growth, inflation, current account balances, and net foreign asset positions.
- Historical paths and recent observations:
  - Rose gradually to about US$75 per barrel in Q3 2007.
  - Spiked to more than US$140 per barrel in July 2008.
  - Fell to US$40 per barrel at end 2008.
  - Subsequently traded in a range between US$70 and US$85 per barrel (current trading range noted).
- Short-term forecasts and supply concerns:
  - EIA projection noted: oil prices to remain within the current trading range through end 2011.
  - IEA forecast: oil production in 2020 projected to be about 11 percent below the level projected three years earlier for 2020.
  - IEA projects an annual increase in oil supply of 1 million barrels per day through 2015, with production outside OPEC either declining or stagnant.
- Competing explanations for price movements:
  - Traditional supply and demand with extremely inelastic curves; Hamilton (2009) suggests price elasticity of demand may be as low as 0.06–0.1.
  - Kilian (2010) attributes unexpected demand growth after 2002 largely to non-OECD countries and links price declines to large negative growth shocks.
  - Financial flows and asset demand:
    - Two channels: looser global monetary conditions prompting yield search; and speculative bubble via commodity investments.
    - Barclays Capital Commodity Research: commodity assets under management rose from about US$70 billion in early 2005 to about US$270 billion in Q2 2008.
  - Evidence on speculation is mixed; inventory behavior and Granger-causality tests generally fail to support speculation as primary driver.

### II. Modeling oil prices — variables, data, and proxies used
- Data frequency: high frequency monthly data.
- Demand-side variables:
  - OECD consumption and OECD consumption/inventory ratio.
  - Emerging market real oil imports (oil imports deflated by oil price) — noted increase: oil demand by large emerging markets rose by about 24 percent per annum over 2002–08 (calculated for China, Chile, Brazil, Indonesia, Thailand, Malaysia, Turkey, Egypt, Poland, and India).
  - OECD inventories and consumption used for OECD demand; higher oil demand projected to raise prices.
- Asset-demand proxies:
  - Inflation expectations (breakeven rate: nominal U.S. government bond minus inflation-indexed bond).
  - VIX index (implied volatility of S&P 500 options) to measure risk aversion.
  - Global liquidity defined as sum of the U.S. monetary base and world international reserves.
- Supply-side variables:
  - OPEC production margin: ratio of OPEC production to production capacity (supply margin).
  - Non-OPEC production (absolute production).
  - Political risk: International Country Risk Guide index (ranges from a high of 100 (lowest risk) to a low of 0 (highest risk)); higher political risk expected to put upward pressure on prices.
- Speculation proxy:
  - NYMEX net long position of noncommercial investors (difference between long and short holdings by noncommercial investors); ICE change used as a check.
- Price measure:
  - Real oil price defined in terms of SDRs and deflated by a weighted average of the SDR basket deflators (real oil price in SDRs less volatile than real oil price in US$).

### III. Multivariate (reduced-form) model — stationarity tests, key estimates, and fit
- Stationarity / ADF test outcomes (selected entries preserved exactly):
  - nominal oil price: Test Statistic -1.44, P Value 0.56
  - Δ nominal oil price: Test Statistic -7.89, P Value 0.000***
  - real oil price: Test Statistic -1.55, P Value 0.51
  - Δ real oil price: Test Statistic -6.21, P Value 0.000***
  - OECD consumption: Test Statistic -2.62, P Value 0.09*
  - emerging markets oil imports: Test Statistic -1.40, P Value 0.58
  - Δ emerging markets oil imports: Test Statistic -9.90, P Value 0.000***
  - political risk: Test Statistic -2.33, P Value 0.16
  - Δ political risk: Test Statistic -9.84, P Value 0.000***
  - stock of non-commercial contracts: Test Statistic -4.74, P Value 0.000***
  - real global liquidity: Test Statistic 1.54, P Value 1.00
  - Δ real global liquidity: Test Statistic -8.77, P Value 0.000***
  - VIX index: Test Statistic -2.74, P Value 0.0667**
- Reduced-form equation (selected coefficient signs, t-statistics, and significance preserved exactly):
  - Long-run determinants (real oil price equation):
    - Emerging markets oil imports (t-1): coefficient 1.46, t-stat -8.00***
    - OECD consumption (t-1): coefficient 8.35, t-stat -3.85***
    - Non-OPEC oil supply (t-1): coefficient -8.78, t-stat 3.85***
  - Short-run determinants (real oil price equation):
    - Δ supply margin (t-1): coefficient 0.47, t-stat 1.04
    - Δ supply margin squared (t-1): coefficient -0.26, t-stat -2.74***
    - Δ polrisk (t-1): coefficient 0.90, t-stat 2.69***
    - Δ stock of non-commercial contracts (t-1): coefficient 0.25, t-stat 1.01
    - VIX index (t-1): coefficient 0.02, t-stat 1.25
    - Δ real global liquidity (t-1): coefficient -0.26, t-stat -0.43
    - error correction (t-1): coefficient -0.07, t-stat -1.98**
  - Model diagnostics:
    - Number of Observations 154
    - R-squared 0.24
    - LM-Stat- 2 lags (Null Hypothesis: No autocorrelation) 17.70
- Main empirical insights from reduced-form:
  - Long-run determinants have expected signs and are significant.
  - Error correction term significant but speed of adjustment slow (half life just over one year).
  - Short-run: supply margin positive and its square negative (large production relative to capacity changes not fully reflected in prices).
  - Change in political risk significant and positive; asset-demand variables (VIX and change in global liquidity) insignificant in reduced form; net noncommercial contracts have correct sign but not conventionally significant.
  - Model can replicate the 2007 pickup but fails to capture the full sharp decline since mid 2008.

### IV. Supply–demand (simultaneous) model — structural estimates and out-of-sample performance
- Estimation approach: simultaneous equations via 3SLS with lagged values; instruments include U.S. industrial production output gap, inflation expectations, and inflation forecasts.
- Demand equation (selected elasticities and coefficients preserved exactly):
  - Emerging markets oil imports: coefficient -0.14, t-stat -4.11 ***
  - Real global liquidity (t-1): coefficient 0.44, t-stat 6.00 ***
  - VIX index (t-1): coefficient -0.15, t-stat -5.10 ***
  - OECD inventory stock: coefficient -1.36, t-stat -4.64 ***
  - OECD consumption: coefficient -0.32, t-stat -1.30
  - Real oil price (t-1): coefficient 0.84, t-stat 21.99 ***
  - Stock of non-commercial contracts (t-1) (speculative behaviour): coefficient -0.10, t-stat -0.19 (insignificant)
  - R-squared 0.97; S.E. of Regression 3% (in percent of Mean of Dependent Variable); Durbin-Watson stat 1.44.
- Supply equation (non-OPEC supply) — key estimates preserved exactly:
  - Real oil price: coefficient 0.57, t-stat 4.37 ***
  - Real oil price (t-1): coefficient -0.49, t-stat -3.71 ***
  - OPEC supply margin: coefficient -0.02, t-stat -0.23 (insignificant)
  - R-squared -0.31; S.E. of Regression 1%; Durbin-Watson stat 1.20.
- Interpretation of structural estimates:
  - Price elasticity of OECD consumption about -0.32.
  - Price elasticity for emerging markets about -0.14 (more inelastic).
  - OECD inventories elasticity -1.36 (large negative relation with real oil price).
  - Real global liquidity and VIX are significant determinants in the structural demand equation (contrast with reduced form where they were insignificant).
  - Speculative proxy (stock of non-commercial contracts) is insignificant in the structural estimates.
  - Non-OPEC supply responds positively to real oil prices with elasticity 0.57.
- Out-of-sample dynamics:
  - Model estimated through 2006m12 and simulated forward to 2010m12.
  - Demand and supply curves partially pick up the 2007–08 rise and subsequent decline but cannot fully explain the magnitude of the run-up or the severity of the decline.
  - Supply locus is below actual outcome in 2007–08 but matches recent months (linked to rise in non-OPEC supply in second half of 2009).
  - Both demand and supply curves suggest the oil price is projected to rise somewhat further in 2010.

### V. Conclusion — synthesis of modelling results
- A rich model with simple dynamics can reasonably replicate out-of-sample developments except for the full amplitude of price swings between late 2007 through 2009.
- Reduced-form results: asset demand determinants provide little explanatory power; long-run movements mainly determined by non-OPEC supply and OECD and emerging market consumption demand.
- Structural simultaneous estimation: price elasticities of demand and supply comparable to literature; risk attitudes (VIX) and global liquidity contribute materially to the fit of the model.
- Evidence on speculation: measures of noncommercial contracts are generally insignificant in both reduced-form and structural results based on available data; inventories and fundamentals play important roles.

*Source: _wp10186 (IMF staff analysis as presented in the supplied content unit).*

### 1. Stationarity Tests ..................................................................................................

### 1. Stationarity Tests

### Listed Sections
- 1. Stationarity Tests .................................................................................................................10
- 2. Regression Estimates: Reduced Form .................................................................................11
- 3. Regression Estimates: Demand and Supply Determinants ..................................................13

### Figures
- 1. Commodity Investments ........................................................................................................4
- 2. Oil Prices: Role of Fundamentals and Speculation................................................................9
- 3. Oil Prices: Forecasts ............................................................................................................12
- 4. Oil Prices: Demand and Supply Determinants ....................................................................14

*Source: _wp10186 - 1. Stationarity Tests (PDF chapter/section)*

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

### _wp10186 - References .............................................................................................................

### I. INTRODUCTION — context and observed oil price dynamics
- Oil price movements have large effects on world economic growth, inflation, current account balances, and net foreign asset positions.
- Historical paths and recent observations:
  - Rose gradually to about US$75 per barrel in Q3 2007.
  - Spiked to more than US$140 per barrel in July 2008.
  - Fell to US$40 per barrel at end 2008.
  - Subsequently traded in a range between US$70 and US$85 per barrel (current trading range noted).
- Short-term forecasts and supply concerns:
  - EIA projection noted: oil prices to remain within the current trading range through end 2011.
  - IEA forecast: oil production in 2020 projected to be about 11 percent below the level projected three years earlier for 2020.
  - IEA projects an annual increase in oil supply of 1 million barrels per day through 2015, with production outside OPEC either declining or stagnant.
- Competing explanations for price movements:
  - Traditional supply and demand with extremely inelastic curves; Hamilton (2009) suggests price elasticity of demand may be as low as 0.06–0.1.
  - Kilian (2010) attributes unexpected demand growth after 2002 largely to non-OECD countries and links price declines to large negative growth shocks.
  - Financial flows and asset demand:
    - Two channels: looser global monetary conditions prompting yield search; and speculative bubble via commodity investments.
    - Barclays Capital Commodity Research: commodity assets under management rose from about US$70 billion in early 2005 to about US$270 billion in Q2 2008.
  - Evidence on speculation is mixed; inventory behavior and Granger-causality tests generally fail to support speculation as primary driver.

### II. MODELING OIL PRICES — variables, data, and proxies used
- Data frequency: high frequency monthly data.
- Demand-side variables:
  - OECD consumption and OECD consumption/inventory ratio.
  - Emerging market real oil imports (oil imports deflated by oil price) — noted increase: oil demand by large emerging markets rose by about 24 percent per annum over 2002–08 (calculated for China, Chile, Brazil, Indonesia, Thailand, Malaysia, Turkey, Egypt, Poland, and India).
  - OECD inventories and consumption used for OECD demand; higher oil demand projected to raise prices.
- Asset-demand proxies:
  - Inflation expectations (breakeven rate: nominal U.S. government bond minus inflation-indexed bond).
  - VIX index (implied volatility of S&P 500 options) to measure risk aversion.
  - Global liquidity defined as sum of the U.S. monetary base and world international reserves.
- Supply-side variables:
  - OPEC production margin: ratio of OPEC production to production capacity (supply margin).
  - Non-OPEC production (absolute production).
  - Political risk: International Country Risk Guide index (ranges from a high of 100 (lowest risk) to a low of 0 (highest risk)); higher political risk expected to put upward pressure on prices.
- Speculation proxy:
  - NYMEX net long position of noncommercial investors (difference between long and short holdings by noncommercial investors); ICE change used as a check.
- Price measure:
  - Real oil price defined in terms of SDRs and deflated by a weighted average of the SDR basket deflators (real oil price in SDRs less volatile than real oil price in US$).

### III. A multivariate (reduced-form) model — stationarity, key estimates, and fit
- Stationarity/ADF test outcomes (selected entries preserved exactly):
  - nominal oil price: Test Statistic -1.44, P Value 0.56
  - Δ nominal oil price: Test Statistic -7.89, P Value 0.000***
  - real oil price: Test Statistic -1.55, P Value 0.51
  - Δ real oil price: Test Statistic -6.21, P Value 0.000***
  - OECD consumption: Test Statistic -2.62, P Value 0.09*
  - emerging markets oil imports: Test Statistic -1.40, P Value 0.58
  - Δ emerging markets oil imports: Test Statistic -9.90, P Value 0.000***
  - political risk: Test Statistic -2.33, P Value 0.16
  - Δ political risk: Test Statistic -9.84, P Value 0.000***
  - stock of non-commercial contracts: Test Statistic -4.74, P Value 0.000***
  - real global liquidity: Test Statistic 1.54, P Value 1.00
  - Δ real global liquidity: Test Statistic -8.77, P Value 0.000***
  - VIX index: Test Statistic -2.74, P Value 0.0667**
- Reduced-form equation (selected coefficient signs, t-statistics, and significance):
  - Long-run determinants (real oil price equation):
    - Emerging markets oil imports (t-1): coefficient 1.46, t-stat -8.00***
    - OECD consumption (t-1): coefficient 8.35, t-stat -3.85***
    - Non-OPEC oil supply (t-1): coefficient -8.78, t-stat 3.85***
  - Short-run determinants (real oil price equation):
    - Δ supply margin (t-1): coefficient 0.47, t-stat 1.04
    - Δ supply margin squared (t-1): coefficient -0.26, t-stat -2.74***
    - Δ polrisk (t-1): coefficient 0.90, t-stat 2.69***
    - Δ stock of non-commercial contracts (t-1): coefficient 0.25, t-stat 1.01
    - VIX index (t-1): coefficient 0.02, t-stat 1.25
    - Δ real global liquidity (t-1): coefficient -0.26, t-stat -0.43
    - error correction (t-1): coefficient -0.07, t-stat -1.98**
  - Model diagnostics:
    - Number of Observations 154
    - R-squared 0.24
    - LM-Stat- 2 lags (Null Hypothesis: No autocorrelation) 17.70
- Main empirical insights from reduced-form:
  - Long-run determinants have expected signs and are significant.
  - Error correction term significant but speed of adjustment slow (half life just over one year).
  - Short-run: supply margin positive and its square negative (large production relative to capacity changes not fully reflected in prices).
  - Change in political risk significant and positive; asset-demand variables (VIX and change in global liquidity) insignificant in reduced form; net noncommercial contracts have correct sign but not conventionally significant.
  - Model can replicate the 2007 pickup but fails to capture the full sharp decline since mid 2008.

### IV. Estimating a supply–demand (simultaneous) model — structural estimates and out-of-sample performance
- Estimation approach: simultaneous equations via 3SLS with lagged values; instruments include U.S. industrial production output gap, inflation expectations, and inflation forecasts.
- Demand equation (selected elasticities and coefficients preserved exactly as reported):
  - Real Oil Price Analysis — Demand Determinants (t-statistics and significance):
    - Emerging markets oil imports: coefficient -0.14, t-stat -4.11 ***
    - Real global liquidity (t-1): coefficient 0.44, t-stat 6.00 ***
    - VIX index (t-1): coefficient -0.15, t-stat -5.10 ***
    - OECD inventory stock: coefficient -1.36, t-stat -4.64 ***
    - OECD consumption: coefficient -0.32, t-stat -1.30
    - Real oil price (t-1): coefficient 0.84, t-stat 21.99 ***
    - Stock of non-commercial contracts (t-1) (speculative behaviour): coefficient -0.10, t-stat -0.19 (insignificant)
  - R-squared reported as 0.97; S.E. of Regression 3% (in percent of Mean of Dependent Variable); Durbin-Watson stat 1.44.
- Supply equation (non-OPEC supply) — key estimates:
  - Real oil price: coefficient 0.57, t-stat 4.37 ***
  - Real oil price (t-1): coefficient -0.49, t-stat -3.71 ***
  - OPEC supply margin: coefficient -0.02, t-stat -0.23 (insignificant)
  - R-squared reported as -0.31; S.E. of Regression 1%; Durbin-Watson stat 1.20.
- Interpretation of structural estimates:
  - Price elasticity of OECD consumption about -0.32.
  - Price elasticity for emerging markets about -0.14 (more inelastic).
  - OECD inventories elasticity -1.36 (large negative relation with real oil price).
  - Real global liquidity and VIX are significant determinants in the structural demand equation (contrast with reduced form where they were insignificant).
  - Speculative proxy (stock of non-commercial contracts) is insignificant in the structural estimates.
  - Non-OPEC supply responds positively to real oil prices with elasticity 0.57 (noted as higher than some other aggregate estimates).
- Out-of-sample dynamics:
  - Model estimated through 2006m12 and simulated forward to 2010m12.
  - Demand and supply curves partially pick up the 2007–08 rise and subsequent decline but cannot fully explain the magnitude of the run-up or the severity of the decline.
  - Supply locus is below actual outcome in 2007–08 but matches recent months (linked to rise in non-OPEC supply in second half of 2009).
  - Both demand and supply curves suggest the oil price is projected to rise somewhat further in 2010 (projection phrasing preserved: "projected to rise somewhat further in 2010").

### V. CONCLUSION — synthesis of modelling results
- A rich model with simple dynamics can reasonably replicate out-of-sample developments except for the full amplitude of price swings between late 2007 through 2009.
- Reduced-form results: asset demand determinants provide little explanatory power; long-run movements mainly determined by non-OPEC supply and OECD and emerging market consumption demand.
- Structural simultaneous estimation: price elasticities of demand and supply comparable to literature; risk attitudes (VIX) and global liquidity contribute materially to the fit of the model.
- Evidence on speculation: measures of noncommercial contracts are generally insignificant in both reduced-form and structural results based on available data; inventories and fundamentals play important roles.

*Source: IMF staff analysis as presented in the supplied content unit.*

### References

### References

### Empirical studies on oil prices and shocks
- Chen, N., L. Graham, and A.J. Oswald
- Davidson, P., 2008, “Crude Oil Prices—Market Fundamentals or Speculation,” Challenge, Vol. 51, Vo. 4, pp. 110–8.
- Dees, S., Karadeloglou, P., Kaufmann, R., and M. Sanchez, 2007, “Modeling the World Oil Market: Assessment of a Quarterly Econometric Model,” Energy Policy, Vol. 35 (1) pp. 178–191.
- Hamilton, J., 2009, “Understanding Crude Oil Prices,” Energy Journal, Vol. 30, No. 2, pp. 179–206.
- Jimenez-Rodriguez, R., and M. Sanchez, 2004, “Oil Price Shocks and Real GDP Growth: Empirical Evidence from Some OECD Countries,” ECB Working Paper No. 362.
- Kilian, L., 2009, “Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market,” American Economic Review, Vol. 99, No. 3, pp. 1053–69.
- Kilian, L., 2010, “Oil Price Shocks, Monetary Policy, and Stagflation,” in: R. Fry, C. Jones, and C. Kent, eds., Inflation in an Era of Relative Price Shocks, RBA Annual Conference Volume, Reserve Bank of Australia.
- Krichene, N. 2002, “World Crude Oil and Natural Gas: A Demand and Supply Model,” Energy Economics, Vol. 24, pp. 557–76.
- Maugeri, L., 2009, “Understanding Oil Price Behavior through an Analysis of a Crisis,” Review of Environmental Economics and Policy, Vol. 3, No. 2, pp. 147–66.
- Ye, M., J. Zyren, and J. Shore, 2006, “Short-Run Crude Oil Price and Surplus Production Capacity,” International Advances in Economic Research, Vol. 12, No.3, pp. 390–4.

### Global liquidity, commodity prices, and financial conditions
- Belke, A., Bordon, I., and T. Hendricks, 2010, “Global Liquidity and Commodity Prices—A Co-integrated VAR Approach for OECD Countries,” Applied Financial Economics, Vol. 20, No. 3, pp. 227–42.
- Ciarlone, A., Piselli, P., and G. Trebeschi, 2009, “Emerging Markets’ Spreads and Global Financial Conditions,” International Financial Markets, Institutions, and Money, Vol. 19, No. 3, pp. 487–521.
- Ruffer, R., and L. Stracca, 2006, “What is Global Excess Liquidity, and Does it Matter?” ECB Working Paper No. 696.

### Price elasticity, demand estimates, and supply capacity
- Cooper, J., 2003, “Price Elasticity of Demand for Crude Oil: Estimates for 23 Countries,” OPEC Review, March 2003.
- Cooper, S., K. Norrish, and A. Sen, “Comodity Investment Flows: Q1 09 Update,” in: Commodity Research Barclays Bank, April 2009.
- Ye, M., J. Zyren, and J. Shore, 2006, “Short-Run Crude Oil Price and Surplus Production Capacity,” International Advances in Economic Research, Vol. 12, No.3, pp. 390–4.

### Discussion of speculation, market commentary, and official inquiries
- , 2008, “Oil Prices, Profits, and Recessions: An Inquiry Using Terrorism as an Instrumental Variable,” Centre for Economic Policy Research Discussion Paper No. DP6937.
- Soros, G., 2008, “George Soros: Rocketing Oil Price is a Bubble,” by Edmund Conway, The Telegraph (United Kingdom), May 26, 2008. Available via the Internet at http://www.telegraph.co.uk
- U.S. Senate, 2006, “The Role of Market Speculation in Rising Oil and Gas Prices: A Need To Put the Cop Back on the Beat,” Staff Report by the Permanent Subcommittee on Investigations of the Committee on Homeland Security and Governmental Affairs. Available via the Internet at http://hsgac.senate.gov

### Methodological and theoretical contributions
- Dees, S., Karadeloglou, P., Kaufmann, R., and M. Sanchez, 2007, “Modeling the World Oil Market: Assessment of a Quarterly Econometric Model,” Energy Policy, Vol. 35 (1) pp. 178–191.
- Kilian, L., 2009, “Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market,” American Economic Review, Vol. 99, No. 3, pp. 1053–69.
- Krichene, N. 2002, “World Crude Oil and Natural Gas: A Demand and Supply Model,” Energy Economics, Vol. 24, pp. 557–76.

*Source: _wp10186 - References*

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