## 1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities

## Source details

**Canonical URL:** [1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07135.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07135.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07135.pdf.json)

---

### Introduction and motivation
- Oil prices reached US$78 per barrel in July 2006 and then fell by about 25 percent toward the end of 2006.
- Nominal interest rates in most industrial countries fell to lowest post-war levels during 2003, resumed a slow upward move, and then paused in 2006; expansionary then accommodative monetary policy is linked to strong world economic growth during 2002–2006 and higher pressure on oil and gas markets.
- The paper builds a short-term world model for oil and gas prices with an explicit role for monetary policy and incorporates natural gas to capture cross-market linkages.

### Model structure, variables, and data
- Framework:
  - Simultaneous demand and supply (SEM) specified in structural form; recursive: natural gas equations are affected by oil, feedback from gas to oil omitted.
  - Demand functions driven by own price, world income, LIBOR, NEER; supply functions driven by own price, proven reserves, and price dummies.
- Endogenous and exogenous variables (logarithms except LIBOR):
  - Endogenous: LQ (Log crude oil output, millions of barrels per day), LP (Log crude oil nominal price, US$ per barrel), LG (Log natural gas output, billions of cubic meters per year), LPG (Log natural gas price, U.S. cents per thousand cubic feet).
  - Exogenous: LY (Log world real GDP), LIBOR (six–month U.S. dollar rate), LNEER (Log U.S. dollar nominal effective exchange rate), LORSV (Log crude oil proven reserves, billions of barrels), LGRSV (Log gas proven reserves, trillions of cubic meters), DUMO, DUMG.
- Data and samples:
  - Annual data for 1970–2006; alternative annual sample 1984–2006.
  - Quarterly data for 1984Q1–2006Q2 and 1996Q1–2006Q2.
  - Sources: International Energy Agency; Oil and Gas Journal; British Petroleum; U.S. DOE; IMF IFS.
- Estimation:
  - Two-stage least squares when simultaneity present; OLS if recursive.

### Key short-run elasticities (selected ranges and point estimates)
- Short-run demand elasticities:
  - Oil price elasticity: between -0.01 and -0.04.
  - Gas price elasticity: between -0.01 and -0.11.
- Short-run supply elasticities:
  - Oil supply price elasticity: between 0.01 and 0.02.
  - Gas supply price elasticity: between 0.03 and 0.05.
- Income elasticities:
  - Oil income elasticity: between 0.12 and 0.44.
  - Gas income elasticity: between 0.11 and 0.48.
- Monetary and exchange rate semi-elasticities:
  - Interest rate (LIBOR) semi-elasticity:
    - Oil: -0.006 for 1970–2006 (t-stat -2.55 reported in Table 1).
    - Oil: 0.003 for 1984–2006 (unexpected sign, insignificant).
    - Oil: 0.001 for 1984Q1–2006Q2 (unexpected sign, insignificant).
    - Oil: -0.002 for 1996Q1–2006Q2 (negative and insignificant).
    - Gas: -0.003 (significant) for 1970–2006; -0.005 (significant) for 1996Q1–2006Q2.
    - Example regression 1998Q1–2006Q2: interest rate semi-elasticity -0.004 (significant).
  - NEER elasticities:
    - Oil demand: -0.17 for 1984–2006 (annual); -0.03 for 1984Q1–2006Q2; -0.07 for 1996Q1–2006Q2.
    - Gas demand: -0.16 for 1984–2006; -0.05 for 84Q1–06Q2; -0.04 for 1996Q1–2006Q2 (insignificant in latter).

### Representative estimated coefficients and diagnostics (selected)
- Crude oil demand (1970–2006, Table 1):
  - Lagged dependent: Coeff. 0.54, T-Stat. 5.08
  - Crude oil price: Coeff. -0.01, T-Stat. -1.28
  - World GDP: Coeff. 0.12, T-Stat. 3.12
  - Interest rate: Coeff. -0.006, T-Stat. -2.55
  - NEER: Coeff. -0.023, T-Stat. -0.19
  - R^2 0.96; DW 1.93
- Natural gas demand (1970–2006, Table 1):
  - Lagged dependent: Coeff. 0.79; R^2 0.98–0.99 reported elsewhere.
  - Natural gas price: Coeff. -0.04, T-Stat. -3.29
  - Crude oil price effect on gas demand: Coeff. 0.01, T-Stat. 2.75
  - World GDP: Coeff. 0.11
  - NEER: Coeff. 0.10, T-Stat. 1.18
- Supply highlights (selected):
  - Oil supply lagged dependent ~ 0.72–0.79; oil price coefficients around 0.01–0.02; oil reserves coefficients 0.11–0.21.
  - Gas supply lagged dependent ~ 0.75–0.84; gas price coefficients 0.03–0.05; gas reserves coefficients 0.05–0.13.

### Model fits, sigmas, and forecasting performance
- Annual structural-form sigmas (standard errors of regression residuals):
  - Crude oil demand sigma = 0.0241663
  - Inverse crude oil supply sigma = 0.167612
  - Natural gas demand sigma = 0.0144985
  - Inverse natural gas supply sigma = 0.0864828
- Quarterly model (1984Q1─2006Q2) sigmas:
  - Oil demand: 0.0151522 (also reported 0.015 and 0.0150062 in variants)
  - Inverse oil supply: 0.0847762 (reported 0.085 in summary)
  - Gas demand: 0.0142549 (reported 0.014)
  - Inverse gas supply: 0.0745424 (reported 0.075)
- Fit and forecasting:
  - Model tracked quantities closely because outputs are low-volatility; residuals were white noise.
  - Prices exhibited larger residuals and higher volatility; in-sample forecasts may understate large price swings.
  - Examples of gas price volatility 2000–2006: rising suddenly by 68 percent in 2000; falling by 26 percent in 2002; rising by 69 percent in 2003; rising by 37 percent in 2005; falling by 9 percent in 2006.
  - Forecasting implication: allow wider error margins for price forecasts compared to quantity forecasts.

### Multiplier (long-run) results (selected values from Table 2)
- Crude Oil Output multipliers (effect of a 1 percent change in exogenous variable):
  - 1970–2006: World Income 0.246; Interest Rate -0.011; Exchange Rate -0.046; Oil Reserves 0.040
  - 1984–2006: World Income 0.330; Interest Rate 0.002; Exchange Rate -0.129; Oil Reserves 0.128
  - 84Q1–06Q2: World Income 0.548; Interest Rate 0.003; Exchange Rate -0.091
  - 96Q1–06Q2: World Income 0.462; Interest Rate -0.004; Exchange Rate -0.169
- Crude Oil Price multipliers:
  - 1970–2006: World Income 0.991; Interest Rate -0.045; Exchange Rate -0.185; Oil Reserves -1.654
  - 1984–2006: World Income 6.853; Interest Rate 0.043; Exchange Rate -2.690; Oil Reserves -6.940
  - 84Q1–06Q2: World Income 4.921; Interest Rate 0.030; Exchange Rate -0.820; Oil Reserves -3.882
  - 96Q1–06Q2: World Income 3.251; Interest Rate -0.031; Exchange Rate -1.192; Oil Reserves -0.487
- Natural Gas Output multipliers:
  - 1970–2006: World Income 0.593; Interest Rate -0.018; Exchange Rate 0.448; Oil Reserves -0.114
  - 84Q1–06Q2: World Income 0.917; Interest Rate 0.004; Exchange Rate -0.180
- Natural Gas Price multipliers:
  - 1970–2006: World Income 3.433; Interest Rate -0.108; Exchange Rate 2.239; Oil Reserves -1.211; Gas Reserves -1.809
  - 1984–2006: World Income 7.674; Interest Rate 0.045; Exchange Rate -3.005; Oil Reserves -6.882; Gas Reserves -0.423
- Key multiplier implications:
  - A one percent increase in world income could induce up to 0.5 percent increase in oil demand and up to 0.9 percent increase in gas demand in some samples.
  - Income-driven quantity increases can imply large percentage responses in prices (text examples: increases in oil prices by 7 percent and gas prices by 8 percent referenced).

### Structural VAR impulse-response insights
- SEM treated as near-VAR with four variables: oil output, oil price, gas output, gas price.
- Identified shocks and typical effects:
  - Oil demand shock: increases oil demand; gradual increase in oil prices; raises gas output and gas price.
  - Oil supply shock: abrupt increase in oil prices; depresses oil demand; increases gas output and gas prices via displacement.
  - Gas demand shock: raises gas demand and gas prices.
  - Gas supply shock: raises gas prices and depresses gas demand.
- Note: because model is recursive, shocks from gas sector are not transmitted back to oil sector in this formulation.

### Comparative dynamics and inertia
- Inertia (lagged dependent coefficients) highlights speed of adjustment:
  - Oil demand lagged coefficients: 0.54 (1970–2006); 0.04 (1984–2006); 0.63 (1984Q1–2006Q2); 0.54 (1996Q1–2006Q2).
  - Gas demand lagged coefficients: 0.79 (1970–2006); 0.33 (1984–2006); 0.65 (84Q1–06Q2); 0.25 (96Q1–06Q2).
  - Oil and gas supply lagged coefficients: oil ~0.72–0.79; gas ~0.75–0.84 across samples.
- Interpretation:
  - Gas demand exhibited higher stickiness historically than oil demand; oil demand became more flexible in some post-1984 samples.
  - Quantity adjustments are relatively slow but price adjustments can be large due to inelastic short-run responses.

### Policy implications and suggested model improvements
- Price inelasticities:
  - Short-term oil demand price elasticity ranged between -0.01 and -0.04; short-term oil supply-price elasticity also small; similar patterns in gas sector.
  - Small supply/demand imbalances can produce large price swings — a source of volatility.
- Monetary policy role:
  - LIBOR impacts oil and gas demand with lags; example implication: a one percent point increase in LIBOR (100 basis points) can reduce oil demand by -0.5 – -0.6 percent (interpretation from illustrative regressions).
  - NEER depreciation stimulates world hydrocarbon demand; appreciation depresses it.
  - Suggested that monetary policy rules should account for impacts of monetary instruments (e.g., interest rate, money base) on oil and gas prices.
- Practical implications:
  - Consumers: oil price increases raise budget share on oil and reduce non-oil consumption.
  - Fiscal: governments can levy high taxes on oil products without impairing tax yield in short run.
  - Trade: oil importers have limited room to cut imports, increasing import bills when prices rise.
  - Producers: inelastic demand may confer market power affecting prices.
- Model limitations and improvements:
  - Exogeneity of income, interest, and exchange rates should be addressed.
  - Incorporate expected inflation and use real interest rates in demand equations.
  - Long-run elasticities and long-term modeling are important but not addressed in this short-term focused paper.

### Representative structural equations (selected)
- Annual sample 1970–2006 (Crude Oil Demand):
  - LQ = 0.542*LQ(-1) - 0.0111*LP(-4) + 0.123*LY - 0.00561*LIBOR(-2) - 0.0231*LNEER + 1.52; sigma = 0.0241663
- Quarterly sample 1984Q1─2006Q2 (Crude Oil Demand):
  - LQ = 0.628*LQ(-1) - 0.0152*(LP-LP(-1)) + 0.204*LY + 0.00124*LIBOR(-2) - 0.034*LNEER + 0.774; sigma = 0.0151522
- Quarterly sample 1984Q1─2006Q2 (Natural Gas Demand):
  - LG = 0.649*LG(-1) - 0.107*(LPG-LPG(-1)) + 0.0132*LP + 0.257*LYW + 0.000989*LIBOR(-2) - 0.0524*LNEER + 1.24; sigma = 0.0142549
- Quarterly sample 1984Q1─2006Q2 (Inverse Natural Gas Supply):
  - LPG = 0.58*LPG(-1) + 0.687*LG(-1) + 0.138*LP - 0.311*LGRSV - 3.07; sigma = 0.0745424

*Source: _wp07135 - 1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities (selected excerpts).*

### 1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities..........................10

### 1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities

### Introduction and motivation
- Recent oil and gas markets experienced high price volatility, with oil prices hitting a record peak of US$78 per barrel in July 2006, then falling by about 25 percent toward the end of 2006.
- Nominal interest rates in most industrial countries fell to lowest post-war levels during 2003, resumed a slow upward move, and then paused in 2006; expansionary then accommodative monetary policy is linked to strong world economic growth during 2002–2006 and higher pressure on oil and gas markets.
- The paper builds a short-term world model for oil and gas prices with an explicit role for monetary policy and incorporates natural gas to capture cross-market linkages.

### Model structure and data
- The model is a simultaneous demand and supply framework specified in structural form, with:
  - Aggregate demand defined by demand-side variables (e.g., prices, world income).
  - Supply defined by supply-side variables (e.g., prices, world proven reserves).
- Special attention paid to cross-oil price elasticity linking natural gas to crude oil, motivated by substitution and historical shocks (e.g., 1973).
- Monetary variables included on the demand side:
  - LIBOR (London Inter-Bank Offered Rate, six–month U.S. dollar rate).
  - U.S. nominal effective exchange rate (NEER).
- Estimation performed on:
  - Annual data for 1970–2006.
  - Quarterly data for 1984Q1–2006Q2.

### Key empirical findings (elasticities and sensitivity)
- Short-run demand elasticities:
  - Oil price elasticity: between -0.01 and -0.04.
  - Gas price elasticity: between -0.01 and -0.11.
- Short-run supply elasticities:
  - Oil supply price elasticity: between 0.01 and 0.02.
  - Gas supply price elasticity: between 0.03 and 0.05.
- Income elasticities:
  - Oil income elasticity: between 0.12 and 0.44.
  - Gas income elasticity: between 0.11 and 0.48.
- Implications of elasticities:
  - Price inelasticity on both demand and supply implies that small excess demand or supply for oil or gas may require large movements in prices to clear markets.
  - Price inelasticity is a source of volatility in oil and gas prices.
- Monetary policy effects:
  - Demand for oil and gas was significantly influenced by the interest rate (LIBOR) and the exchange rate (NEER).
  - Interest rate semi–elasticity was estimated at -0.006 for oil and -

### Applications and uses of the model
- Short-term forecasting under scenarios for exogenous variables.
- Evaluating monetary policy implications for world oil and gas markets.
- Computing impulse responses to shocks (the paper includes annual and quarterly Structural VAR impulse responses and simulations).

### Robustness and scope limitations
- Robustness assessed by estimating the model on both annual (1970–2006) and quarterly (1984Q1–2006Q2) datasets.
- Long-run elasticities and long-term modeling are noted as important but are not addressed in this paper for reasons of space; long-term elasticities are typically higher than short-term elasticities.

*Source: _wp07135 - 1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities..........................10*

### 0.005 for gas, while NEER elasticity was estimated at -0.17 for oil and -0.16 for gas.

### _wp07135 - 0.005 for gas, while NEER elasticity was estimated at -0.17 for oil and -0.16 for gas.

### II. MODELING DEMAND AND SUPPLY OF CRUDE OIL AND NATURAL GAS
- SEM specified implicitly to describe demand and supply for oil and gas; identification through variables that shift demand or supply schedules.
- Crude oil demand (implicit): Qd = f(LQ, LP, LY, LIBOR, LNEER, εod)
- Crude oil supply (implicit): Qs = f(LQ, LP, LORSV, DUMO, εos)
- Natural gas demand (implicit): Gd = f(LG, LPG, LP, LY, LIBOR, LNEER, εgd)
- Natural gas supply (implicit): Gs = f(LG, LPG, LP, LGRSV, DUMG, εgs)
- Except for the interest rate, all variables are in logarithm form.

### Definitions of variables (as given)
- Endogenous:
  - Q = crude oil output, in millions of barrels per day, LQ = Log(Q)
  - P = crude oil nominal price, in U.S. dollars per barrel, LP = Log(P)
  - G = natural gas output, in billions of cubic meters per year (or quarter), LG = Log(G)
  - PG = natural gas price, in U.S. cents per thousand cubic feet, LPG = Log(PG)
- Exogenous:
  - Y = real GDP index for world economy, LY = Log(Y)
  - LIBOR = interest rate (London Inter─Bank Offered Rate, six–month U.S. dollar rate)
  - NEER = U.S. dollar nominal effective exchange rate, LNEER = Log (NEER)
  - ORSV = crude oil proven reserves, in billions of crude oil barrels, LORSV = Log (ORSV)
  - GRSV = natural gas proven reserves, in trillions of cubic meters, LGRSV = Log (GRSV)
  - DUMO = dummy variable for large changes in oil price
  - DUMG = dummy variable for large changes in natural gas price
- ε = disturbance term for oil demand (εod), oil supply (εos), natural gas demand (εgd), and natural gas supply (εgs).

### Theoretical and modeling choices
- Demand driven mainly by own price and income (Working (1927); Pindyck (1979); Pesaran, et al. (1998)).
- Gas demand includes own price, oil price, and world economic activity to examine oil→gas transmission.
- Interest rate and NEER included as explanatory variables:
  - Interest rate: instrument for monetary policy; affects aggregate demand and thus energy demand.
  - NEER: affects domestic prices of oil and gas (prices quoted in U.S. dollar) and real value of financial assets; operates via different transmission channels and lags than interest rates.
- Supply modeled following Fisher’s approach and standard production theory; oil supply is a function of own price and oil proven reserves; gas supply includes own price, oil price, and gas reserves.
- Model is recursive: natural gas equations are affected by oil; feedback from gas to oil omitted for simplicity.
- Model identification: no equation is a linear combination of others.

### Data, sample periods, and estimation methods
- Data frequencies and sample periods: annual data for 1970–2006, and 1984–2006; quarterly data for 1984Q1–2006Q2, and 1996Q1–2006Q2.
- Purpose of multiple frequencies and samples: to yield robust estimates.
- Data sources (as listed): International Energy Agency; Oil and Gas Journal; British Petroleum; U.S. Department of Energy (U.S. DOE); IMF International Financial Statistics (IFS).
- Estimation: two-stage least squares when demand and supply are simultaneously determined; ordinary least squares if recursive.

### III. SHORT-RUN DEMAND AND SUPPLY ANALYSIS — key points
- Short-run relations allow for lags and speed of adjustment toward equilibrium; error-correction formulation presented.
- Short-run oil demand–price elasticity findings:
  - Estimated at -0.01 (insignificant) for 1970–2006.
  - Estimated at -0.02 (significant) for 1984–2006.
  - Quarterly: -0.02 for 1984Q1–2006Q2, and -0.04 for 1996Q1–2006Q2 (often statistically insignificant).
  - General magnitude across specifications: between -0.01 and -0.04.
  - Price elasticities often insignificant contemporaneously; significance often achieved only with lags (lags could extend to six years).
  - Polynomial distributed lag (6 lags, degree 2) for 1970–2006: sum of lags = -0.05776 (t = -4.62), indicating significant cumulative effect.
- Income elasticity (short-run):
  - 0.12 for 1970–2006.
  - 0.44 for 1984–2006.
  - Quarterly: 0.20 for 1984Q1–2006Q2, and 0.19 for 1996Q1–2006Q2.
  - Income elasticity significant, sensitive to sample period, frequency, and specification; generally less than unity.
- Interest rate and NEER effects on oil demand (annual data):
  - LIBOR had a significant and negative effect with a lag of 2 periods; semi-elasticity of the order of -0.006 for 1970–2006.
  - NEER tended to depress oil and gas prices when appreciating; declining interest rates and depreciating NEER had the opposite effect.

### Table 1. Crude Oil and Natural Gas: Short-Term Demand and Supply Elasticities (selected coefficients and statistics preserved)
- Crude oil demand (1970–2006):
  - Lagged dependent: Coeff. 0.54, T-Stat. 5.08
  - Crude oil price: Coeff. -0.01, T-Stat. -1.28
  - World GDP: Coeff. 0.12, T-Stat. 3.12
  - Interest rate: Coeff. -0.006, T-Stat. -2.55
  - NEER: Coeff. -0.023, T-Stat. -0.19
  - R^2 0.96; DW 1.93
- Crude oil demand (1984–2006):
  - Lagged dependent: Coeff. 0.04, T-Stat. 0.32
  - Crude oil price: Coeff. -0.02, T-Stat. -2.17
  - World GDP: Coeff. 0.44, T-Stat. 6.48
  - Interest rate: Coeff. 0.003, T-Stat. 1.70
  - NEER: Coeff. -0.17, T-Stat. -3.12
  - R^2 0.99; DW 1.78
- Crude oil demand (84Q1–06Q2):
  - Lagged dependent: Coeff. 0.63, T-Stat. 7.43
  - Crude oil price: Coeff. -0.02, T-Stat. -1.30
  - World GDP: Coeff. 0.20, T-Stat. 3.98
  - Interest rate: Coeff. 0.001, T-Stat. 1.29
  - NEER: Coeff. -0.03, T-Stat. -2.29
  - R^2 0.97; DW 1.84
- Crude oil demand (96Q1–06Q2):
  - Lagged dependent: Coeff. 0.54, T-Stat. 5.23
  - Crude oil price: Coeff. -0.04, T-Stat. -1.15
  - World GDP: Coeff. 0.19, T-Stat. 2.13
  - Interest rate: Coeff. -0.002, T-Stat. -1.11
  - NEER: Coeff. -0.07, T-Stat. -2.17
  - R^2 0.96; DW 1.86
- Crude oil supply (selected):
  - Lagged dependent coefficients around 0.72–0.79 across samples; R^2 range 0.94–0.98.
  - Crude oil price coefficients around 0.01–0.02 (positive), t-stats variable.
  - Oil reserves coefficients 0.11–0.21.
- Natural gas demand (selected):
  - Lagged dependent coefficients 0.25–0.79; R^2 0.98–0.99.
  - Natural gas price coefficients -0.01 to -0.11 (negative), e.g., -0.04 (t = -3.29) for 1970–2006.
  - Crude oil price effect on gas demand: mixed signs and significance (e.g., 0.01 with t = 2.75 for 1970–2006).
  - World GDP coefficients 0.11–0.48.
  - NEER coefficients: 0.10 (t = 1.18) for 1970–2006; -0.16 (t = -2.21) for 1984–2006; -0.05 (t = -3.53) for 84Q1–06Q2.
- Natural gas supply (selected):
  - Lagged dependent coefficients 0.75–0.84; R^2 0.97–0.99.
  - Natural gas price coefficients positive: 0.03–0.05 (significant in many samples).
  - Crude oil price effect on gas supply: negative in several specifications (e.g., -0.05, t = -3.83 for 1970–2006).
  - Gas reserves coefficients 0.05–0.13.

### Empirical interpretation and implications (as stated)
- World demand for oil exhibits very low short-run price responsiveness; short-run demand price elasticities are consistently very low and often statistically insignificant.
- Short-run price-inelasticity contributes to high price volatility and has policy implications:
  - Consumers: oil price increases raise budget share on oil, reduce non-oil consumption.
  - Taxation: governments can levy high taxes on oil products without impairing tax yield.
  - Trade: oil importers have limited room to cut imports, leading to larger import bills.
  - Producers: inelastic demand may confer market power enabling influence on prices.
- Income elasticity is significant and drives business-cycle variation in oil markets; higher income elasticity increases sensitivity to business cycles.
- Monetary policy variables (LIBOR, NEER) jointly have significant impact on oil demand; LIBOR semi-elasticity ~ -0.006 for 1970–2006.

*Source: Excerpt from the IMF working paper text provided in the content unit.*

### 2006. For 1984–2006, the interest rate semi-elasticity, estimated at 0.003, had an unexpected

### _wp07135 - 2006. For 1984–2006, the interest rate semi-elasticity, estimated at 0.003, had an unexpected

### Interest rate semi-elasticity and monetary policy effects
- For 1984–2006, the interest rate semi-elasticity was estimated at 0.003, had an unexpected sign, and was statistically insignificant.
- For 1984Q1–2006Q2, the LIBOR coefficient was estimated at 0.001, had an unexpected sign, and was insignificant.
- For 1996Q1–2006Q2, the interest rate semi-elasticity was estimated at -0.002 (negative and insignificant).
- The parameter's significance and sign depended on:
  - Sample period (whether it corresponded to a period of active monetary policy).
  - Parsimony of the demand specification.
- Two illustrative regressions including episodes of highly active monetary policies:
  - Sample 1970–2006:
    - LQ = 0.877*LQ(-1) - 0.0107*LP - 0.00559*LIBOR(-2) + 0.601; R2 = 0.95; DW=2.22.
    - (t=9.67) (t=-0.873) (t=-2.40) (t=1.64)
  - Sample 1996Q1–2006Q2:
    - LQ = 0.812*LQ(-1) - 0.000104*(LP-LP(-1)) - 0.00463*LIBOR(-4) + 0.83; R2 = 0.94; DW=1.91.
    - (t=13) (t=-0.718) (t=-3.23) (t=3.06)
- Interpretation:
  - The interest rate semi–elasticity implies that a one percent point increase in LIBOR (100 basis points) can reduce oil demand by -0.5 – -0.6 percent.
  - Historical context:
    - Monetary tightening in 1980–1982 contributed to depress oil markets.
    - Expansionary monetary policies in 2000–2006 stimulated oil markets, pushing oil prices to unprecedented high levels.

### Exchange rate (NEER) elasticity on oil demand
- Estimated NEER elasticities for oil demand:
  - -0.17 for 1984–2006 (annual).
  - -0.03 for 1984Q1–2006Q2 (quarterly).
  - -0.07 for 1996Q1–2006Q2 (quarterly).
- Effect interpretation:
  - An appreciation of the NEER by one percent would cause a decline in oil demand by -0.17 percent (annual) and -0.03 to -0.07 percent (quarterly).
  - Depreciation would have the opposite effect.
- Sensitivity:
  - NEER elasticity could be significant or insignificant, with correct or incorrect sign, and was sensitive to specification.
- Illustrative regressions:
  - Sample 1984–2006:
    - LQ = -0.00562*LP(-1) + 0.43*LY - 0.129*LNEER + 2.6; R2 = 0.99; DW=1.89.
    - (t=-0.642) (t=32.5) (t=-2.35) (t=19.1)
  - Sample 1996Q1–2006Q2:
    - LQ = 0.547*LQ(-1) - 0.00028*(LP- LP(-1)) + 0.258*LY - 0.0914*LNEER + 1.13; R2 = 0.95; DW=1.81.
    - (t=4.95) (t=-1.88) (t=3.78) (t=-3.85) (t=4.08)
- Mechanism:
  - NEER depreciation causes an appreciation of non–dollar–dominated financial assets and makes imports, including oil imports, cheaper in non-dollar currencies, boosting world oil demand.
  - NEER appreciation causes depreciation of non–dollar–dominated financial assets and makes imports more expensive in non-dollar currencies, depressing world oil demand.

### Lagged dependent variable (inertia) in oil demand
- The coefficient on lagged dependent variable describes speed of adjustment toward full equilibrium after shocks.
- Annual data:
  - For 1970–2006, lagged demand coefficient estimated at 0.54 (considerable stickiness).
  - For 1984–2006, this inertia seemed to have disappeared; annual world demand close to long-run path.
- Quarterly data:
  - Lagged dependent variable estimates:
    - 0.63 for 1984Q1–2006Q2.
    - 0.54 for 1996Q1–2006Q2.
  - Quarterly world demand may take two to three quarters to return to equilibrium following a shock.

### Short-Run Natural Gas Demand Elasticities
- Own-price elasticities (natural gas demand):
  - -0.04 (significant) for 1970–2006.
  - -0.01 (insignificant) for 1984–2006.
  - Quarterly: -0.11 (significant) for 1984Q1–2006Q2; -0.04 (insignificant) for 1996Q1–2006Q2.
- Cross-price elasticity with oil price:
  - 0.01 for 1970–2006 (significant but low).
  - -0.02 for 1984–2006 (negative).
  - 0.01 to 0.02 for 1984Q1–2006Q2 and 1996Q1–2006Q2 (positive and significant).
  - Plausible interpretation: overall positive cross-oil price elasticity (substitution from oil to gas after oil shocks).
- Income elasticity (natural gas demand):
  - 0.11 for 1970–2006 (short-run).
  - 0.41 for 1984–2006.
  - 0.26 for 1984Q1–2006Q2.
  - 0.48 for 1996Q1–2006Q2.
- Monetary and exchange rate effects on gas demand:
  - Omission tests show LIBOR and NEER significant for gas demand.
  - Interest rate semi-elasticity estimates:
    - -0.003 (significant) for 1970–2006.
    - -0.005 (significant) for 1996Q1–2006Q2.
    - Example regression 1998Q1–2006Q2: interest rate semi-elasticity -0.004 (significant).
  - NEER elasticities:
    - -0.16 for 1984–2006 (significant).
    - -0.05 for 1984Q1–2006Q2 (significant).
    - -0.04 for 1996Q1–2006Q2 (insignificant).
  - Example regression 1998Q1–2006Q2:
    - LG = 0.327*LG(-1) - 0.0034*(LPG-LPG(-1)) + 0.0359*LP(-2) + 0.276*LY - 0.00468*LIBOR(-2) – 0.060*LNEER + 3.21; R2 = 0.98; DW=2.23.
    - (t=2.41) (t=-0.50) (t=3.78) (t=2.04) (t=-3.59) (t=-2.71) (t=5.06)
- Inertia in gas demand:
  - Lagged dependent variable coefficients:
    - 0.79 for 1970–2006 (high stickiness).
    - 0.33 for 1984–2006 (less displacement, faster return).
    - 0.65 for 1984Q1–2006Q2 (quarterly).
    - 0.25 for 1996Q1–2006Q2 (less inertia, structural change).

### Short-Run Crude Oil Supply Elasticities
- Relationship between gas/oil output and price ratios:
  - L(Q/G) = 0.34*L(P/PG) - 2.62; R2 = 0.67; DW = 0.92. (t=8.35) (t=-29.07)
- Oil supply price elasticity estimates:
  - 0.02 (insignificant) for 1970–2006 and 1984–2006.
  - 0.01 (significant) for 1984Q1–2006Q2.
  - 0.02 (significant) for 1996Q1–2006Q2 (response during 1999–2006).
- Oil reserves elasticity:
  - 0.14 (significant) for 1970–2006.
  - 0.21 (significant) for 1984–2006.
  - Quarterly: 0.14 (significant) for 1984Q1–2006Q2; 0.11 (insignificant) for 1996Q1–2006Q2.
- Inertia in oil supply:
  - Autoregressive coefficients:
    - 0.72 for 1970–2006.
    - High inertia continued for 1984–2006.
    - 0.79 for 1984Q1–2006Q2.
    - 0.71 for 1996Q1–2006Q2.

### Short-Run Natural Gas Supply Elasticities
- Gas supply own-price elasticity:
  - 0.05 (significant) for 1970–2006 and 1984–2006.
  - Quarterly: 0.04 (significant) for 1984Q1–2006Q2; 0.03 (insignificant) for 1996Q1–2006Q2.
- Cross-oil price elasticity on gas supply:
  - -0.05 (significant) for 1970–2006.
  - -0.03 (significant) for 1984–2006.
  - Quarterly: -0.01 (significant) for 1984Q1–2006Q2; -0.002 (insignificant) for 1996Q1–2006Q2.
- Gas reserves elasticity:
  - 0.05 (insignificant) for 1970–2006.
  - 0.08 (insignificant) for 1984–2006.
  - Quarterly: 0.12 (significant) for 1984Q1–2006Q2; 0.13 (significant) for 1996Q1–2006Q2.
- Inertia in gas supply:
  - Autoregressive coefficients:
    - 0.84 for 1970–2006.
    - 0.75 for 1984–2006.
    - 0.79 for 1984Q1–2006Q2.
    - 0.75 for 1996Q1–2006Q2.

### Comparison of oil and gas demand and supply relationships
- Both oil and gas demand:
  - Correct-signed and significant demand price elasticity, but extremely low magnitude.
  - Driven by level of economic activity with rising income elasticities.
  - Significantly responsive to changes in interest and exchange rates.
- Inertia:
  - Gas demand exhibited higher stickiness than oil demand.
  - Oil demand became more flexible and faster to converge toward steady-state equilibrium than gas demand.
- Supply similarities:
  - Both oil and gas supply influenced positively by own price and own reserves.
  - Cross-oil price elasticity on gas supply small and negative.

### Simulation of the Annual Model (1970–2006)
- Structural form (annual model) equations with reported standard errors (SE) and sigma:
  - Crude Oil Demand:
    - LQ = 0.542*LQ(-1) - 0.0111*LP(-4) + 0.123*LY - 0.00561*LIBOR(-2) - 0.0231*LNEER + 1.52;
    - (SE) (0.107) (0.00868) (0.0395) (0.0022) (0.118) (0.421)
    - sigma = 0.0241663
  - Inverse Crude Oil Supply:
    - LP = 0.713*LP(-1) + 1.16*LQ - 0.521*LORSV(-2) + 0.324*DUMO - 0.454;
    - (SE) (0.0625) (0.672) (0.313) (0.0506) (1.26)
    - sigma = 0.167612
  - Natural Gas Demand:
    - LG = 0.792*LG(-1) - 0.0396*(LPG(-1) - LPG(-2)) + 0.0143*LP(-4) + 0.11*LY - 0.00304*LIBOR(-2) + 0.0961*LNEER + 0.932;
    - (SE) (0.0762) (0.012) (0.0052) (0.0596) (0.00142) (0.0813) (0.421)
    - sigma = 0.0144985
  - Inverse Natural Gas Supply:
    - LPG = 0.9*LPG(-1) + 0.514*LG + 0.0378*LP - 0.18*LGRSV + 0.26*DUMG - 2.6;
    - (SE) (0.0654) (0.435) (0.0757) (0.327) (0.0301) (1.84)
    - sigma = 0.0864828
- Model performance:
  - The model tracked closely the data (Figure 2).
  - Residuals were white noise.
  - Reported sigma (standard error of regression residuals) values: 0.02 for oil demand (and other sigmas listed above).

*Source: _wp07135 - 2006 (excerpts provided).*

### 0.168 for inverse oil supply, 0.014 for gas demand, and 0.086 for inverse gas supply. Hence,

### _wp07135 - 0.168 for inverse oil supply, 0.014 for gas demand, and 0.086 for inverse gas supply. Hence,

### Model fit, residuals, and forecasting implications
- Reported standard errors of regression residuals (quarterly model, sample 1984Q1─2006Q2):
  - Oil demand: 0.015
  - Inverse oil supply: 0.085
  - Gas demand: 0.014
  - Inverse gas supply: 0.075
- Findings:
  - Oil and gas outputs have close fit with actual data because of their low volatility.
  - Oil and gas prices exhibited higher standard error for the residuals due to high volatility.
  - In-sample model replicated fluctuations in oil and gas prices but may underestimate large fluctuations.
  - Examples of gas price volatility during 2000–2006:
    - rising suddenly by 68 percent in 2000
    - falling by 26 percent in 2002
    - rising by 69 percent in 2003
    - rising by 37 percent in 2005
    - falling by 9 percent in 2006
  - In-sample forecast for oil prices during 2000–2006 was rather satisfactory due to persistence in rising trend.
- Forecasting implication:
  - Allow wider error margins for price forecasts compared to quantity forecasts in future short-term forecasting.

### Quarterly model: structural form and key parameter estimates (Sample 1984Q1─2006Q2)
- Crude Oil Demand (LQ):
  - LQ = 0.628*LQ(-1) - 0.0152*(LP-LP(-1)) + 0.204*LY + 0.00124*LIBOR(-2) - 0.034*LNEER + 0.774; sigma = 0.0151522
  - Reported standard errors (in order shown): (0.0866) (0.0131) (0.0518) (0.00109) (0.0159) (0.183)
- Inverse Crude Oil Supply (LP):
  - LP = 0.941*LP(-1) + 0.529*LQ(-2) - 0.229*LORSV + 0.181*DUMO - 0.448; sigma = 0.0847762
  - Reported standard errors (in order shown): (0.0286) (0.301) (0.239) (0.0141) (0.665)
- Natural Gas Demand (LG):
  - LG = 0.649*LG(-1) - 0.107*(LPG-LPG(-1)) + 0.0132*LP + 0.257*LYW + 0.000989*LIBOR(-2) - 0.0524*LNEER + 1.24; sigma = 0.0142549
  - Reported standard errors (in order shown): (0.0818) (0.0393) (0.0051) (0.0614) (0.000812) (0.0149) (0.278)
- Inverse Natural Gas Supply (LPG):
  - LPG = 0.58*LPG(-1) + 0.687*LG(-1) + 0.138*LP - 0.311*LGRSV - 3.07; sigma = 0.0745424
  - Reported standard errors (in order shown): (0.0768) (0.257) (0.0359) (0.175) (0.836)
- Additional diagnostic statements:
  - The quarterly model fitted closely the actual data (Figure 3).
  - The residuals were white noise.
  - Performance during 2000Q1─2006Q2: residuals tightly contained in a small error margin.

### Multiplier analysis: long-run multipliers across sample periods (selected values from Table 2)
- Interpretation: multipliers compute effect of a one percent change in exogenous variables on endogenous variables (derived from long-run reduced form).
- Selected multipliers by variable and sample period (as tabulated):
  - Crude Oil Output multipliers:
    - 1970–2006: World Income 0.246; Interest Rate -0.011; Exchange Rate -0.046; Oil Reserves 0.040; Gas Reserves 0.000
    - 1984–2006: World Income 0.330; Interest Rate 0.002; Exchange Rate -0.129; Oil Reserves 0.128; Gas Reserves 0.000
    - 84Q1–06Q2: World Income 0.548; Interest Rate 0.003; Exchange Rate -0.091; Oil Reserves 0.000; Gas Reserves 0.000
    - 96Q1–06Q2: World Income 0.462; Interest Rate -0.004; Exchange Rate -0.169; Oil Reserves -0.008; Gas Reserves 0.000
  - Crude Oil Price multipliers:
    - 1970–2006: World Income 0.991; Interest Rate -0.045; Exchange Rate -0.185; Oil Reserves -1.654; Gas Reserves 0.000
    - 1984–2006: World Income 6.853; Interest Rate 0.043; Exchange Rate -2.690; Oil Reserves -6.940; Gas Reserves 0.000
    - 84Q1–06Q2: World Income 4.921; Interest Rate 0.030; Exchange Rate -0.820; Oil Reserves -3.882; Gas Reserves 0.000
    - 96Q1–06Q2: World Income 3.251; Interest Rate -0.031; Exchange Rate -1.192; Oil Reserves -0.487; Gas Reserves 0.000
  - Natural Gas Output multipliers:
    - 1970–2006: World Income 0.593; Interest Rate -0.018; Exchange Rate 0.448; Oil Reserves -0.114; Gas Reserves 0.000
    - 1984–2006: World Income 0.428; Interest Rate 0.001; Exchange Rate -0.163; Oil Reserves 0.182; Gas Reserves 0.000
    - 84Q1–06Q2: World Income 0.917; Interest Rate 0.004; Exchange Rate -0.180; Oil Reserves -0.146; Gas Reserves 0.000
    - 96Q1–06Q2: World Income 0.714; Interest Rate -0.007; Exchange Rate -0.094; Oil Reserves -0.013; Gas Reserves 0.000
  - Natural Gas Price multipliers:
    - 1970–2006: World Income 3.433; Interest Rate -0.108; Exchange Rate 2.239; Oil Reserves -1.211; Gas Reserves -1.809
    - 1984–2006: World Income 7.674; Interest Rate 0.045; Exchange Rate -3.005; Oil Reserves -6.882; Gas Reserves -0.423
    - 84Q1–06Q2: World Income 3.122; Interest Rate 0.016; Exchange Rate -0.565; Oil Reserves -1.519; Gas Reserves -0.739
    - 96Q1–06Q2: World Income 1.957; Interest Rate -0.019; Exchange Rate -0.398; Oil Reserves -0.115; Gas Reserves -0.039
- Key multiplier insights:
  - A one percent increase in world income could induce 0.5 percent increase in oil demand and 0.9 percent increase in gas demand (statement in text referencing multipliers).
  - Consequent price effects cited in text: may cause an increase in oil prices by 7 percent and in gas prices by 8 percent.
  - Interest rate and exchange rate multipliers are generally negative: expansionary monetary policy (lower interest rates) and depreciating NEER stimulate oil and gas markets; tight monetary policy and appreciating NEER depress them.
  - Oil reserves multiplier tends to stimulate oil output and depress oil prices; ambiguous effect on gas output but tends to depress gas prices.
  - Gas reserves multiplier does not impact oil markets due to recursive model structure; it tends to stimulate gas output and depress gas prices.

### Structural VAR analysis and impulse responses
- SEM viewed as near-VAR with four variables: oil output, oil price, gas output, gas price.
- Four identified shocks:
  - Oil demand shock (through oil demand function)
  - Oil supply shock (through oil supply function)
  - Gas demand shock (through gas demand function)
  - Gas supply shock (through gas supply function)
- Impulse response patterns (text summary):
  - Oil demand shock:
    - Increases oil demand
    - Gradual increase in oil prices
    - Increases gas output and gas price
    - Example: experience during 2000─2006 where demand shock raised oil demand and progressively increased oil price, gas output, and gas price
  - Oil supply shock:
    - Acts abruptly, causing sharp increase in oil prices
    - Depresses oil demand
    - Increases gas output and gas prices via displacement from oil to gas
  - Gas demand shock:
    - Increases gas demand and gas prices
  - Gas supply shock:
    - Increases gas prices and depresses gas demand
    - Operates similarly to oil supply shock
  - Due to assumed recursiveness: shocks from gas sector are not transmitted to oil sector in this model formulation.

### Conclusions, policy implications, and suggested model improvements
- Elasticities and market sensitivity:
  - Short-term oil demand price elasticity ranged between -0.01 and -0.04 (often contemporaneously insignificant and significant only with lag) — highly price inelastic world demand for oil.
  - Short-term oil supply-price elasticity also small. Similar results for gas sector.
  - Cross-oil price elasticity: small, positive in gas demand equation, negative in gas supply equation.
  - Income elasticity significant, reported range in text: between 0.11 and 0.48 (text states: "It has been systematically less than unity.")
  - Implication: small imbalances in hydrocarbon demand or supply can lead to large price changes.
- Monetary policy role:
  - LIBOR (interest rate) has significant and negative semi-elasticity: active monetary policy influences oil and gas demand with some delay.
  - U.S. nominal effective exchange rate (NEER) shows significant and negative effect on oil and gas demands: depreciation of the U.S. dollar stimulates world hydrocarbon demand.
  - Policy suggestion: monetary policy should include impacts of monetary instruments (e.g., interest rate, money base) on oil and gas prices within the monetary policy rule.
  - Stable monetary conditions contribute to stable oil and gas markets.
- Model application and limitations:
  - Historical simulation: model fits closely and can retrace turning points in quantity and price data.
  - In-sample quantity forecasts have very small error margins; price forecasts deteriorate during wild price fluctuations — forecasting must assume wider error for prices.
  - SEM can be used as forecasting tool under hypothetical exogenous scenarios and to simulate impact of random shocks via impulse responses.
  - Deficiencies and suggested improvements:
    - Address exogeneity of income, interest, and exchange rates.
    - Bring in expected rate of inflation and use real interest rates in demand equations.

### Selected estimated regressions (representative equations and sigmas)
- Annual sample 1970─2006 (Crude Oil Demand):
  - LQ = 0.542*LQ(-1) - 0.0111*LP(-4) + 0.123*LY - 0.00561*LIBOR(-2) - 0.0231*LNEER + 1.52; sigma = 0.0241663
- Quarterly sample 1984Q1─2006Q2 (Crude Oil Demand):
  - LQ = 0.632*LQ(-1) - 0.0165*(LP-LP(-1)) + 0.204*LY + 0.00137*LIBOR(-2) - 0.0356*LNEER + 0.766; sigma = 0.0150062
- Quarterly sample 1984Q1─2006Q2 (Natural Gas Demand):
  - LG = 0.647*LG(-1) - 0.113*(LPG - LPG(-1)) + 0.0117*LP + 0.258*LY + 0.00096*LIBOR(-2) - 0.0521*LNEER + 1.25; sigma = 0.0144115
- Quarterly sample 1984Q1─2006Q2 (Natural Gas Supply):
  - LG = 0.79*LG(-1) + 0.0427*LPG(-1) - 0.0112*LP(-4) + 0.122*LGRSV + 0.75; sigma = 0.011

*Source: IMF Working Paper content (selected excerpts from the supplied PDF content)._*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07135.pdf_