## _wp0662

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---

### Main findings and thesis
- Oil prices are of overriding concern because runaway energy prices could become inflationary and cause an economic recession.
- The paper concludes that an oil demand shock, caused by record low interest rates, led to the exorbitant price increases noted in 2004–05.
- Monetary policy, conducted through changes in interest rates and monetary aggregates, has a significant and protracted effect on:
  - aggregate demand for goods and services,
  - asset prices such as exchange rates, housing prices, and stock prices.
- The sustained pressure on oil prices observed in 2004–05 is explained by an excessively expansionary monetary policy, with interest rates falling to record levels in an integrated international capital market.
- Stimulated by low interest rates and a depreciating U.S. dollar, demand for oil expanded faster than supply.
- Given the short-run price inelasticity of both oil demand and supply, equilibrium was obtained through a large increase in oil prices.

### Data, methods, and empirical focus
- Data: quarterly 1984Q1–2005Q2 and annual 1970–2005; monthly series for 1970M1–2005M7 used in several analyses.
- Methods and empirical elements:
  - Analysis of oil futures’ prices with estimates of implied volatility and GARCH volatility.
  - Simultaneous equations model (SEM) for world crude oil demand and supply emphasizing exchange and interest rates.
  - Two-stage least-squares for short-run estimates; error correction method (ECM) and cointegration analysis for long-run elasticities.
  - Vector autoregressive model (VAR) and impulse response analysis for crude oil price, NEER, and interest rates.
- Empirical tables and figures summarized:
  - Tables 1–4 (short-run and long-run elasticities; relationship between interest rates and oil prices; cointegrating relations).
  - Figures 1–8 (futures prices, volatility measures, price returns distribution, price vs. interest rates and NEER, VAR impulse responses, SEM actual/fitted values and residuals).

### SEM framework and estimation
- General dynamic SEM form: (AL)(BL)Zt = Xt + Ut, where Zt are endogenous variables, Xt exogenous variables, Ut error terms, and ()AL and ()BL are linear lag operators.
- Specific (log) equations:
  - Crude oil demand: d_t = c_d + γ_o p_t + γ_y y_t + γ_neer NEER_t + γ_i i_t + u_d,t
  - Crude oil supply: s_t = c_s + δ_o p_t + δ_ng ng_t + u_s,t
- Variable definitions:
  - q_o,t = crude oil output, in millions of barrels per day
  - p_o,t = crude oil nominal price, in U.S. dollars per bl
  - ng_t = natural gas output, in billions of cubic meters per year
  - y_t = real GDP index for the G7 countries
  - i_t = interest rate (federal funds rate, the three-month U.S. Treasury bill rate, or the U.S. government ten-year bond yield)
  - NEER = the U.S. dollar nominal effective exchange rate
- Assumptions: demand and supply disturbances uncorrelated (E(u_d u_s)=0); residuals serially uncorrelated, i.i.d. with standard errors σ_d and σ_s.
- Identification and lags: model identified; Akaike information criterion indicates optimal lag length of two periods.
- Four model specifications progressively include NEER and interest rates.

### Short-run demand findings (estimates and interpretation)
- Short-run price demand elasticity:
  - Ranges between –0.02 and –0.03 (both quarterly and annual), indicating very low short-run price elasticity.
- Short-run income elasticity:
  - Ranges between 0.12 and 0.19; statistically significant.
- NEER and interest rate short-run roles:
  - NEER elasticity ranges between –0.03 and –0.09; tends to be statistically significant at higher probability values.
  - Interest rate semi-elasticity is negative; statistically significant only for annual data. Quarterly semi-elasticity negative but not statistically significant (interpreted as working with a lag).
- Selected short-run elasticity estimates (t-statistics in parentheses) — Quarterly: 1984Q1–2005Q2; Annual: 1970–2005:
  - Model 1 (demand = f(crude price, GDP)):
    - Price elasticity: –0.02 (–1.59); –0.03 (–3.41)
    - Income elasticity: 0.19 (4.02); 0.12 (2.69)
  - Model 2 (demand = f(crude price, GDP, NEER)):
    - Price elasticity: –0.02 (–1.62); –0.02 (–2.55)
    - Income elasticity: 0.19 (3.98); 0.15 (2.66)
    - NEER elasticity: –0.03 (–1.87); –0.09 (–1.71)
  - Model 3 (demand = f(crude price, GDP, interest rate)):
    - Price elasticity: –0.02 (–1.34); –0.0003 (–0.20)
    - Income elasticity: 0.18 (3.28); 0.10 (2.37)
    - Interest rate semi-elasticity: –0.001 (–0.63); –0.004 (–2.50)
  - Model 4 (demand = f(crude price, GDP, NEER, interest rate)):
    - Price elasticity: –0.02 (–1.43); 0.005 (0.34)
    - Income elasticity: 0.18 (3.35); 0.11 (2.66)
    - NEER elasticity: –0.03 (–1.79); –0.09 (–1.85)
    - Interest rate semi-elasticity: -0.0008 (-0.39); –0.004 (–2.62)

### Long-run demand findings
- Long-run price elasticity:
  - Price inelastic, ranging between –0.03 and –0.08 depending on frequency and sample.
- Long-run income elasticity:
  - Ranges between 0.54 and 0.90; statistically significant but less than unity.
- Long-run NEER and interest rate effects:
  - NEER elasticity ranges between –0.26 and –0.29; statistically significant.
  - Interest rate semi-elasticity ranges between –0.01 and –0.06; significant and negative.
- Selected long-run elasticity estimates (t-statistics in parentheses) — Quarterly: 1984Q1–2005Q2; Annual: 1970–2005:
  - Model 1 (demand = f(crude price, GDP)):
    - Price elasticity: –0.03 (–0.98); –0.08 (–2.72)
    - Income elasticity: 0.75 (14.16); 0.64 (9.88)
  - Model 2 (demand = f(crude price, GDP, NEER)):
    - Price elasticity: –0.05 (–0.78); –0.06 (–3.02)
    - Income elasticity: 0.90 (7.71); 0.54 (11.41)
    - NEER elasticity: –0.29 (–2.05); –0.26 (–2.97)
  - Model 3 (demand = f(crude price, GDP, interest rate)):
    - Price elasticity: –0.06 (–1.18); –0.01 (–0.58)
    - Income elasticity: 0.25 (1.25); 0.26 (6.06)
    - Interest rate semi-elasticity: –0.06 (–3.77); –0.01 (–6.64)

### Short-run and long-run supply findings
- Short-run price supply elasticity:
  - Tends to be price inelastic and may respond negatively to price changes:
    - Price elasticity: 0.005 (0.91); –0.03 (–3.70)
  - Interpretation: limited supply response to price increases due to capacity constraints, quota fixation, or strategic preservation of price increases.
- Short-run natural gas effect on supply:
  - Natural gas elasticity: 0.26 (4.08); 0.11 (2.42)
- Long-run supply elasticities:
  - Long-run price elasticity: 0.007 (1.24); 0.08 (2.63)
  - Long-run natural gas elasticity: 0.73 (50.7); 0.30 (4.23)
- Additional supply facts:
  - Long-run own price elasticity of oil supply estimated at 0.08 for the annual data.
  - Natural gas and crude oil production are "perfectly correlated over 1970–2005."
  - World crude oil supply grew at an average rate of 1.7 percent a year during 1970–2005.
  - Implication: small excess demand would require a large change in prices to clear the market.

### Impulse response, VAR, and causality (monetary policy linkage)
- Directional findings by shock type:
  - Oil supply shock period (1974–1986): oil prices led interest rates; interest rates moved in same direction as crude oil prices.
  - Oil demand shock period (1998–2005): interest rates led oil prices; lower interest rates caused excess oil demand and rising oil prices.
- VAR and cointegration evidence:
  - Trivariate VAR: crude oil price, interest rates, NEER estimated on monthly and quarterly data.
  - For 1974–86: ordering interest rates, NEER, crude oil prices; positive shock to oil price → positive impulse response in interest rates; positive shock to NEER → negative response in oil price.
  - For 1998–2005: ordering crude oil, NEER, interest rates; negative innovation in interest rates → positive response in oil prices; negative innovation in NEER → positive effect on oil prices.
- Cointegration (vector error correction) selected coefficients (t-statistics in parentheses):
  - Oil supply shock period (1975M1–1987M12) normalized on Treasury Bill Rate: NEER 10.54 (3.80); Crude Oil Price –4.69 (–7.08); constant –43.57.
  - Oil supply shock period (1975Q1–1987Q4) normalized on Treasury Bill Rate: NEER 8.62 (2.96); Crude Oil Price –5.50 (–8.29); constant –32.15.
  - Oil demand shock period (2000M1–2005M7) normalized on Crude Oil Price: NEER 1.88 (2.14); Treasury Bill Rate 0.18 (4.0); constant –12.44.
  - Oil demand shock period (1998Q1–2005Q2) normalized on Crude Oil Price: NEER 0.82 (0.44); Treasury Bill Rate 0.34 (5.07); constant –8.02.

### Regression evidence on policy responses
- Supply shock regressions (rising phase 1974–81; declining phase 1982–86):
  - Rising phase: dependent = interest rate; estimated coefficient 6.04; implies interest rates increase by 6 percentage points for each 100 percent increase in oil prices.
  - Declining phase: coefficient 4.56; positive but smaller, indicating cautious relaxation of monetary policy.
- Selected reported regression statistics (Table 3 excerpts):
  - Tightening monetary policy (1975M1–1981M12): coefficient 6.04 (28.84), crude oil price 1.11 (10.6), Residual(-2) –0.38 (–3.60), R2 0.93, D–W 1.87.
  - Tightening monetary policy (1975Q1–1981Q4): coefficient 6.04 (12.20), crude oil price 0.76 (3.73), Residual(-2) –0.48 (0.23), R2 0.88, D–W 1.86.
  - Relaxing monetary policy (1982M1–1986M12): coefficient 4.56 (18.63), crude oil price 0.89 (8.09), Residual(-2) –0.10 (–0.96), R2 0.89, D–W 1.98.
  - Relaxing monetary policy (1982Q1–1986Q4): coefficient 4.83 (10.57), crude oil price 0.80 (4.94), Residual(-2) –0.52 (–4.94), R2 0.87, D–W 1.94.
- Oil demand shock regressions (1998M1–2005M7; 1998Q1–2005Q2):
  - Monthly 1998M1–2005M7: crude oil price coefficient –0.09 (–17.11); Treasury bill rate 1.14 (10.71); Residual(-2) –0.16 (–1.50); R2 0.95; D–W 2.01.
  - Quarterly 1998Q1–2005Q2: crude oil price coefficient –0.09 (–6.02); Treasury bill rate 1.33 (7.21); Residual(-2) –0.47 (–2.46); R2 0.86; D–W 2.13.
  - Interpretation: lower interest rates were causing excess demand for crude oil and causing oil prices to rise rapidly.

### Model estimates, multipliers, and fit
- Model fit:
  - The model predicts closely the quantities for crude oil; however, price prediction is less precise, particularly for the crude oil price, since the latter has shown large fluctuations in the period 1970–2005.
  - Residual standard error reported: 0.007 for crude oil output (residuals serially uncorrelated).
- Long-run multipliers (SEM):
  - A 1 percent increase in income leads to an increase in crude oil output by 0.49 percent and crude oil price by 2.8 percent.
  - A 1 percent increase in natural gas production leads to an increase by 0.30 percent in crude oil production and a decline in oil price by 1.47 percent.
  - An increase in the interest rate leads in the long-run to a decline in both crude oil demand and prices, with multipliers equal respectively to –0.004 and –0.02.
- Short-run properties reiterated:
  - Demand is price inelastic; significantly influenced by the level of economic activity.
  - Oil supply is highly price inelastic in the short run, but strongly correlated with natural gas production.
  - Combination of low price elasticities, high income elasticities, and rigid supply explains high and persistent volatility in the oil markets and the market power of producers.
- Endogenizing interest rates:
  - When interest rates are included endogenously in the SEM, impulse responses from shocks affecting interest rates are similar to those reported in the VAR analysis.

### Policy implications and recommendations
- Monetary policy as primary tool:
  - Stabilization of oil markets requires tightening of monetary policy and an increase in ex-ante real interest rates to contain oil price increases.
  - Monetary policy may have to be tightened to reduce oil prices to a stable path, consistent with overall price stability with an inflation rate not exceeding 2–3 percent a year.
  - The model can simulate the effect of interest rates on oil prices and determine an appropriate interest rate response for each desirable oil price path.
- Shock-specific policy differences:
  - During oil supply shocks: powerful increases in interest rates were required to choke off oil price increases, causing severe contraction in world economic growth; complementary measures included high taxes on petroleum consumption, energy substitution and conservation, and technological change toward higher energy efficiency.
  - During oil demand shocks: low interest rates contributed to rapid increases in oil prices; additional measures to contain oil demand, such as higher taxes, may be overshadowed by generalized inflation, making them less effective; appropriate tightening of monetary policy strong enough to uproot inflationary expectations will be required to achieve greater energy substitution and savings.
- Magnitude of response:
  - Regression evidence indicates that substantial increases in real interest rates—similar to those experienced during historical oil supply shocks—might be required to bring demand in line with supply and contain the inflationary effect of high oil prices.

### Model applications and alternatives
- Uses:
  - Policy analysis to simulate interest rate effects on oil prices and to determine appropriate interest rate responses for target oil price paths.
  - Forecasting endogenous variables given exogenous variables via reduced-form solution Ẑt = −B̂−1 Ĉ Xt.
- Alternative specifications:
  - Model can be rewritten in terms of percent price changes and in rational expectations form.
- Limitations:
  - Price prediction less precise due to large fluctuations in crude oil price over 1970–2005, though quantities are closely predicted.

### Selected data sources (from appendix)
- Arthur Andersen/Cambridge Energy Research Associates, Natural Gas Trends, 1985-2004.
- Arthur Andersen/Cambridge Energy Research Associates, World Oil Trends, 1985-2004.
- Cambridge Energy Research Associates: World Oil Watch, various reports, 1995-2004.
- International Energy Agency: Oil Market Report, various reports, 1995-2005.
- International Monetary Fund, International Financial Statistics, 1970-2005.
- Oil and Gas Journal, Worldwide Crude Oil and Gas Production, 2004.
- OPEC, Annual Statistical Bulletin, various publications, 1980-2005.
- U.S. Department of Energy, Twentieth Century Petroleum Statistics, 1990.

*Source: _wp0662 (IMF PDF excerpt).*

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

### _wp0662 - References

### Main findings and thesis
- Oil prices are of overriding concern because runaway energy prices could become inflationary and cause an economic recession.
- The paper concludes that an oil demand shock, caused by record low interest rates, led to the exorbitant price increases noted in 2004–05.
- Monetary policy, conducted through changes in interest rates and monetary aggregates, has a significant and protracted effect on:
  - aggregate demand for goods and services,
  - asset prices such as exchange rates, housing prices, and stock prices.
- The sustained pressure on oil prices observed in 2004–05 is explained by an excessively expansionary monetary policy, with interest rates falling to record levels in an integrated international capital market.
- Stimulated by low interest rates and a depreciating U.S. dollar, demand for oil expanded faster than supply.
- Given the short-run price inelasticity of both oil demand and supply, equilibrium was obtained through a large increase in oil prices.

### Data, methods, and empirical focus
- The analysis is based on time-series data for oil prices, exchange rates, and interest rates.
- Section II analyzes oil futures’ prices and presents estimates of:
  - implied volatility, and
  - GARCH volatility.
- The paper includes empirical exercises and model estimates summarized in tables and figures:
  - Tables: 1 through 4 (topics include short-run and long-run demand and supply elasticities; relationship between interest rates and oil prices; cointegrating relations between crude oil price, the NEER, and interest rates).
  - Figures: 1 through 8 (topics include crude oil daily futures prices; implied price volatility; GARCH volatility; price returns distribution; oil price, U.S. interest rates, and U.S. dollar NEER; impulse responses from a VAR; actual and fitted values and residuals of the SEM).

### Key empirical elements listed in the content
- Tables:
  - 1. World Crude Oil: Short-Run Demand and Supply Elasticities
  - 2. World Crude Oil: Long-Run Demand and Supply Elasticities
  - 3. World Crude Oil: Relationship Between Interest Rates and Oil Prices
  - 4. Cointegrating Relations Between Crude Oil Price, the NEER, and Interest Rates
- Figures:
  - 1. Crude Oil Daily Futures Prices
  - 2. Crude Oil Implied Price Volatility
  - 3. Crude Oil Futures Prices GARCH Volatility
  - 4. Crude Oil Price Returns Distribution, Daily
  - 5. Crude Oil Price, U.S. Interest Rates, and U.S. Dollar NEER
  - 6. Impulse Responses from a VAR for Crude Price, NEER, and Interest Rates
  - 7. Actual and Fitted Values and Residuals of the SEM
  - 8. Actual and Fitted Values and Residuals of the SEM (Interest Rate Endogenous)

*Source: _wp0662 - References*

### Section III analyzes a simultaneous equations model (SEM) for demand and supply of oil,

### _wp0662 - Section III analyzes a simultaneous equations model (SEM) for demand and supply of oil,

### SEM framework and purpose
- The SEM is a simultaneous equations model for world crude oil demand and supply emphasizing the role of the exchange and interest rates.
- General dynamic form: (AL)(BL)Zt = Xt + Ut, where Zt are endogenous variables, Xt exogenous variables, Ut error terms, and ()AL and ()BL are linear lag operators.
- Specific equations (variables in logarithms except interest rate):
  - Crude oil demand: d_t = c_d + γ_o p_t + γ_y y_t + γ_neer NEER_t + γ_i i_t + u_d,t
  - Crude oil supply: s_t = c_s + δ_o p_t + δ_ng ng_t + u_s,t
- Variable definitions:
  - q_o,t = crude oil output, in millions of barrels per day
  - p_o,t = crude oil nominal price, in U.S. dollars per bl
  - ng_t = natural gas output, in billions of cubic meters per year
  - y_t = real GDP index for the G7 countries
  - i_t = interest rate (federal funds rate, the three-month U.S. Treasury bill rate, or the U.S. government ten-year bond yield)
  - NEER = the U.S. dollar nominal effective exchange rate
- Assumptions: demand and supply disturbances are uncorrelated (E(u_d u_s) = 0), residuals serially uncorrelated, i.i.d. with standard errors σ_d and σ_s.
- Identification: the model is identified; optimal lag length indicated as two periods by Akaike information criterion.
- Estimation methods: two-stage least-squares for short-run estimates; error correction method (ECM) and cointegration analysis for long-run elasticities.
- Data: quarterly 1984Q1–2005Q2 and annual 1970–2005. Four model specifications progressively include NEER and interest rates.

### Short-run demand findings (estimates and interpretation)
- Short-run price demand elasticity:
  - Ranges between –0.02 and –0.03 (both quarterly and annual), indicating very low short-run price elasticity.
- Short-run income elasticity:
  - Ranges between 0.12 and 0.19; statistically significant.
- Role of NEER and interest rates in short-run demand:
  - NEER elasticity ranges between –0.03 and –0.09; tends to be statistically significant at higher probability values.
  - Interest rate semi-elasticity is negative; statistically significant only for annual data. Quarterly semi-elasticity negative but not statistically significant (interpreted as interest rates working with a lag).
- Policy implication highlighted: these results show oil markets can be significantly influenced in the short-run by monetary policy.

- Selected short-run elasticity estimates (t-statistics in parentheses) — Quarterly: 1984Q1–2005Q2; Annual: 1970–2005
  - Model 1 (demand = f(crude price, GDP)):
    - Price elasticity: –0.02 (–1.59); –0.03 (–3.41)
    - Income elasticity: 0.19 (4.02); 0.12 (2.69)
  - Model 2 (demand = f(crude price, GDP, NEER)):
    - Price elasticity: –0.02 (–1.62); –0.02 (–2.55)
    - Income elasticity: 0.19 (3.98); 0.15 (2.66)
    - NEER elasticity: –0.03 (–1.87); –0.09 (–1.71)
  - Model 3 (demand = f(crude price, GDP, interest rate)):
    - Price elasticity: –0.02 (–1.34); –0.0003 (–0.20)
    - Income elasticity: 0.18 (3.28); 0.10 (2.37)
    - Interest rate semi-elasticity: –0.001 (–0.63); –0.004 (–2.50)
  - Model 4 (demand = f(crude price, GDP, NEER, interest rate)):
    - Price elasticity: –0.02 (–1.43); 0.005 (0.34)
    - Income elasticity: 0.18 (3.35); 0.11 (2.66)
    - NEER elasticity: –0.03 (–1.79); –0.09 (–1.85)
    - Interest rate semi-elasticity: -0.0008 (-0.39); –0.004 (–2.62)

### Long-run demand findings
- Long-run price elasticity:
  - Price inelastic, ranging between –0.03 and –0.08 depending on frequency and sample.
- Long-run income elasticity:
  - Ranges between 0.54 and 0.90; statistically significant but less than unity.
- Long-run NEER and interest rate effects:
  - NEER elasticity ranges between –0.26 and –0.29; statistically significant.
  - Interest rate semi-elasticity ranges between –0.01 and –0.06; significant and negative.
- Selected long-run elasticity estimates (t-statistics in parentheses) — Quarterly: 1984Q1–2005Q2; Annual: 1970–2005
  - Model 1 (demand = f(crude price, GDP)):
    - Price elasticity: –0.03 (–0.98); –0.08 (–2.72)
    - Income elasticity: 0.75 (14.16); 0.64 (9.88)
  - Model 2 (demand = f(crude price, GDP, NEER)):
    - Price elasticity: –0.05 (–0.78); –0.06 (–3.02)
    - Income elasticity: 0.90 (7.71); 0.54 (11.41)
    - NEER elasticity: –0.29 (–2.05); –0.26 (–2.97)
  - Model 3 (demand = f(crude price, GDP, interest rate)):
    - Price elasticity: –0.06 (–1.18); –0.01 (–0.58)
    - Income elasticity: 0.25 (1.25); 0.26 (6.06)
    - Interest rate semi-elasticity: –0.06 (–3.77); –0.01 (–6.64)

### Short-run supply findings
- Short-run price supply elasticity:
  - Tends to be price inelastic and may respond negatively to price changes (quarterly estimates show 0.005; annual shows –0.03), indicating limited supply response to price increases due to capacity constraints, quota fixation, or strategic preservation of price increases.
- Natural gas effect on supply:
  - Short-run natural gas elasticity ranges between 0.11 and 0.26; natural gas production significantly influences crude oil supply.
- Selected short-run supply estimates (t-statistics in parentheses)
  - Price elasticity: 0.005 (0.91); –0.03 (–3.70)
  - Natural gas elasticity: 0.26 (4.08); 0.11 (2.42)

### Long-run supply findings
- Long-run price elasticity:
  - Positive but remains low (selected estimates in Table 2):
    - Price elasticity: 0.007 (1.24); 0.08 (2.63)
    - Natural gas elasticity: 0.73 (50.7); 0.30 (4.23)

### Impulse response, VAR, and monetary policy linkage (context from surrounding sections)
- Section IV (contextual summary): relationship between oil prices and interest rates is two-way and depends on the type of oil shock:
  - During an oil supply shock, oil prices led interest rates.
  - During an oil demand shock, interest rates led oil prices.
- A vector autoregressive model (VAR) is used to analyze the effect of an interest rate shock on oil prices (study referenced in surrounding sections).
- Main conclusion (from the paper): stabilization of oil markets requires tightening of monetary policy and an increase in ex-ante real interest rates.
  - Based on data for 1970–86: the degree of monetary tightening to rein in oil prices and their inflationary implications may be substantial and may involve a trade-off between inflation and output.
  - Based on data for 1986–2000: sustained noninflationary world economic growth would require a degree of stability in oil markets.

*Source: _wp0662 - Section III analyzes a simultaneous equations model (SEM) for demand and supply of oil, (PDF chapter/section).*

### 0.08 for the annual data. This result shows that long-run oil supply is determined by

### _wp0662 - 0.08 for the annual data. This result shows that long-run oil supply is determined by

### Key empirical findings on elasticities and market properties
- Long-run own price elasticity of oil supply estimated at 0.08 for the annual data.
- Long-run natural gas elasticity is statistically significant and ranges between 0.30 and 0.73.
- Natural gas and crude oil production are "perfectly correlated over 1970–2005."
- Oil markets are characterized by price inelastic demand and supply.
- World crude oil supply grew at an average rate of 1.7 percent a year during 1970–2005.
- Implication: small excess demand would require a large change in prices to clear the market.
- Demand is responsive to income level; supply is influenced by natural gas production.
- Oil markets are vulnerable to macroeconomic policies, particularly monetary policy transmitted via exchange and interest rate channels.

### Role of monetary policy: Model and mechanism
- Standard monetary policy model components (McCallum and Nelson, 2000):
  - IS curve: yiEpEyσν
  - Aggregate supply (AS) (Augmented-Phillips curve): pyyEpλβε
  - Interest rate policy equation (Taylor’s rule): ipyyiμμμη
- Definitions:
  - t y is aggregate output; t y is potential/full employment output.
  - t p is price level; t p∆ is inflation rate.
  - t i is nominal interest rate.
  - t ν, t ε, and t η are shocks to aggregate demand, aggregate supply, and monetary policy, respectively.
  - t E is an expectation operator.
- In the model, monetary aggregates are omitted; monetary policy is essentially based on Taylor’s rule adjusting the interest rate in response to inflation or the output gap.
- Aggregate demand responds negatively to ex-ante real interest rate and positively to expected output; lower ex-ante real interest rate stimulates aggregate demand and energy demand.

### Technical chart evidence (1970M1–2005M7)
- Three epochs identified in monthly series for crude oil prices, interest rates, and NEER:
  - Epoch 1: 1970–1986 — characterized by oil supply shocks; oil prices peaked at US$41/bl in 1980M11.
    - World inflation peaked at 13.5 percent in 1974 and 13.2 percent in 1980; averaged 10.1 percent during 1974–81.
    - Federal funds rate peaked at 19.08 percent in 1981M1.
    - U.S. Treasury bill rate peaked at 16.29 percent in 1981M5.
    - Ten-year government bond yield peaked at 15.32 percent in 1981M9.
    - World economic growth contracted to an average growth rate of 0.8 percent during 1980–82.
  - Epoch 2: 1986–1999 — period of relative stability for oil prices; unit root test shows oil prices were stationary.
  - Epoch 3: 1999–2005 — historically record low interest rates and depreciating NEER; federal funds rate maintained at 1 percent during 2003M7–2004M6; crude oil prices exceeded US$70/bl in September 2005.

### Regression analysis: supply shock and demand shock periods
- Supply shock period divided into rising phase (1974–81) and declining phase (1982–86).
  - Rising phase: dependent variable = interest rate; interest rates respond to oil prices.
    - Estimated regression coefficient: 6.04.
    - Interpretation: interest rates would increase by 6 percentages points (600 basis points) for each 100 percent increase in oil prices.
    - Data example: crude oil prices rose from US$11.17/bl to US$40.97/bl; federal funds rate rose from 4.61 percent to 19.1 percent; U.S. Treasury bill rate rose from 4.35 percent to 16.29 percent.
  - Declining phase: regression coefficient estimated at 4.56, significant and positive but smaller than in upward phase, indicating cautious relaxation of monetary policy.
- Table 3 (selected reported estimates; t-statistics in parentheses; samples indicated):
  - Tightening monetary policy (1975M1–1981M12): coefficient 6.04 (28.84), crude oil price 1.11 (10.6), Residual(-2) –0.38 (–3.60), R2 0.93, D–W 1.87.
  - Tightening monetary policy (1975Q1–1981Q4): coefficient 6.04 (12.20), crude oil price 0.76 (3.73), Residual(-2) –0.48 (0.23), R2 0.88, D–W 1.86.
  - Relaxing monetary policy (1982M1–1986M12): coefficient 4.56 (18.63), crude oil price 0.89 (8.09), Residual(-2) –0.10 (–0.96), R2 0.89, D–W 1.98.
  - Relaxing monetary policy (1982Q1–1986Q4): coefficient 4.83 (10.57), crude oil price 0.80 (4.94), Residual(-2) –0.52 (–4.94), R2 0.87, D–W 1.94.
- Oil demand shock period (1998M1–2005M7; 1998Q1–2005Q2):
  - Dependent variable = crude oil price; forcing variable = interest rate.
  - Estimated regression coefficient: –0.09 (–17.11) for monthly sample 1998M1–2005M7 with Treasury bill rate 1.14 (10.71), Residual(-2) –0.16 (–1.50), R2 0.95, D–W 2.01.
  - Quarterly sample 1998Q1–2005Q2: Crude oil price coefficient –0.09 (–6.02), Treasury bill rate 1.33 (7.21), Residual(-2) –0.47 (–2.46), R2 0.86, D–W 2.13.
  - Interpretation: lower interest rates were causing excess demand for crude oil and causing oil prices to rise rapidly.

### VAR and cointegration analysis
- Trivariate VAR: crude oil price, interest rates, NEER estimated on monthly and quarterly data.
- For 1974–86 (oil supply shock period): ordering interest rates, NEER, crude oil prices.
  - A positive shock to oil price has a positive impulse response on interest rates.
  - A positive shock to NEER has a negative impulse response on oil price.
- For 1998–2005 (oil demand shock period): ordering crude oil, NEER, interest rates.
  - A negative innovation in interest rates has a positive response in oil prices.
  - A negative innovation in NEER has a positive effect on oil prices.
- Impulse response figures summarized:
  - Oil supply shock period: responses shown for 1974M1–1986M12 (monthly) and 1974Q1–1986Q4 (quarterly).
  - Oil demand shock period: responses shown for 1999M1–2005M7 (monthly) and 1998Q1–2005Q2 (quarterly).
- Vector error correction (cointegration) results (Table 4; t-statistics in parentheses):
  - Oil supply shock period (sample 1975M1–1987M12): normalized on Treasury Bill Rate: coefficients 1, 10.54 (3.80) for NEER, –4.69 (–7.08) for Crude Oil Price, constant –43.57.
  - Oil supply shock period (1975Q1–1987Q4): normalized on Treasury Bill Rate: coefficients 1, 8.62 (2.96) for NEER, –5.50 (–8.29) for Crude Oil Price, constant –32.15.
  - Oil demand shock period (2000M1–2005M7): normalized on Crude Oil Price: coefficients 1, 1.88 (2.14) for NEER, 0.18 (4.0) for Treasury Bill Rate, constant –12.44.
  - Oil demand shock period (1998Q1–2005Q2): normalized on Crude Oil Price: coefficients 1, 0.82 (0.44) for NEER, 0.34 (5.07) for Treasury Bill Rate, constant –8.02.
- Interpretation:
  - During oil supply shock period, interest rates moved in the same direction as crude oil prices.
  - During oil demand shock period, crude oil prices moved inversely with interest rates.

### Policy implications and historical evidence
- During oil supply shocks, powerful increases in interest rates were required to choke off oil price increases, causing severe contraction in world economic growth.
- Other simultaneous measures during supply shock episodes included high taxes on petroleum consumption, energy substitution and conservation, and technological change oriented toward higher energy efficiency.
- During oil demand shock period, historically low interest rates contributed to rapid increases in oil prices; given rigid short-run oil supply and low price elasticities, small excess demand (for consumption or speculation) can generate large changes in oil prices.
- Monetary policy, as a policy variable, can be used to contain oil price increases but may cause temporary contraction in world economic growth.

### Solution of the SEM and model fit
- Structural equation model (SEM) written as t BZ C X U= , where Z is vector of endogenous variables, X vector of exogenous and predetermined variables, and U vector of error terms satisfying E(Ut)=()0 and E(Xj Ut)=()0.
- Reduced-form solution: 1ˆˆˆ t t t Z B C X
−
=−.
- Knowledge of exogenous variables enables forecasting of endogenous variables, particularly oil demand.
- The SEM closely fits the data.
- Residual standard errors reported: 0.007 for crude oil output (residuals serially uncorrelated).

*Italic: Content based solely on the provided IMF PDF excerpt.*

### 0.103 for crude oil price. The model predicts closely the quantities for crude oil; however, price

### _wp0662 - 0.103 for crude oil price. The model predicts closely the quantities for crude oil; however, price

### Model estimates and multipliers
- Model fits:
  - The model predicts closely the quantities for crude oil; however, price prediction is less precise, particularly for the crude oil price, since the latter has shown large fluctuations in the period 1970–2005.
- Long-run multipliers (SEM):
  - A 1 percent increase in income leads to an increase in crude oil output by 0.49 percent and crude oil price by 2.8 percent.
  - For natural gas production, a 1 percent increase leads to an increase by 0.30 percent in the crude oil production and a decline in oil price by 1.47 percent.
  - An increase in the interest rate leads in the long-run to a decline in both crude oil demand and prices, with multipliers equal respectively to –0.004 and –0.02.
- Short-run properties:
  - Demand is price inelastic; it is, however, significantly influenced by the level of economic activity.
  - Oil supply is highly price inelastic in the short run, but strongly correlated with natural gas production.
  - The combination of low price elasticities, high income elasticities, and rigid supply explains high and persistent volatility in the oil markets and the market power of producers.

### Interest rates, impulse responses, and causality
- Endogenizing interest rates:
  - The model can be re-specified to include interest rates as endogenous variables; when specified this way, the effect of interest rate innovations is apprehended via impulse responses.
  - Computations show that impulse responses from shocks affecting interest rates in the SEM are similar to those reported in the VAR analysis.
- Directional dynamics:
  - During an oil supply shock—characterized by perturbations in oil supply, under stable oil demand conditions—oil prices led interest rates. Monetary policy was deployed to compel oil prices down by forcing a downward adjustment in the demand for oil commensurate with the supply disturbances, achieved by substantial increases in real interest rates through targeting nonborrowed reserves.
  - During a demand shock—characterized by major shifts in oil demand, under stable oil supply conditions—interest rates led oil prices.
- Impulse response patterns:
  - A positive shock to interest rates tends, on impact, to depress both crude oil demand and prices.
  - A positive shock to oil prices tends, on impact, to increase interest rates.

### Policy implications and recommendations
- Monetary policy and inflation targets:
  - Monetary policy may have to be tightened to reduce oil prices to a stable path, consistent with overall price stability with an inflation rate not exceeding 2–3 percent a year.
  - The model can simulate the effect of interest rates on oil prices and determine an appropriate interest rate response for each desirable oil price path.
- Supply vs. demand shocks—policy differences:
  - In a supply shock, the change in oil prices results in a relative price change that encourages stronger energy substitution and savings.
  - In a demand shock, most asset prices move upward with a general increase in the price level; the relative change in oil prices becomes less noticeable, so energy substitution and energy savings effects are reduced.
  - Additional measures to contain oil demand, such us higher taxes, may be overshadowed by the general price increase and will have a limited effect on oil demand during a demand shock.
  - If greater energy substitution and savings are to be achieved during a demand shock, an appropriate tightening of monetary policy, strong enough to uproot inflationary expectations, will be required.
- Magnitude of policy response:
  - The regression coefficients indicate that the response of one variable to the other was significantly high during major shocks; consequently, an important increase in real interest rates, similar to those experienced during the oil supply shock, might be required to bring demand in line with supply and contain the inflationary effect of high oil prices.

### Model performance and applications
- Model tracking:
  - The model was shown to track closely oil output and prices as well as interest rates, though large deviations in quantities and prices remain in some periods.
- Uses:
  - The model can be used in policy analysis to simulate interest rate effects on oil prices and to determine appropriate interest rate responses for target oil price paths.
- Alternative specifications:
  - The model can also be rewritten in terms of percent price changes and in rational expectations form.

### Data sources (selected from appendix)
- Arthur Andersen/Cambridge Energy Research Associates, Natural Gas Trends, 1985-2004.
- Arthur Andersen/Cambridge Energy Research Associates, World Oil Trends, 1985-2004.
- Cambridge Energy Research Associates: World Oil Watch, various reports, 1995-2004.
- International Energy Agency: Oil Market Report, various reports, 1995-2005.
- International Monetary Fund, International Financial Statistics, 1970-2005.
- Oil and Gas Journal, Worldwide Crude Oil and Gas Production, 2004.
- OPEC, Annual Statistical Bulletin, various publications, 1980-2005.
- U.S. Department of Energy, Twentieth Century Petroleum Statistics, 1990.

*Source: _wp0662 - 0.103 for crude oil price. The model predicts closely the quantities for crude oil; however, price (IMF PDF content).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp0662.pdf_