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The Relationship between Crude Oil and Natural Gas Prices

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**1. **The Relationship between Crude Oil and Natural Gas Prices Peter Hartley Kenneth Medlock III Jennifer Rosthal

**2. **Outline Motivation
Methodology
OLS Engle-Granger
VECM
Data
Results
Cointegrating Relationships
OLS
VECM
Error Correction Model
OLS
3SLS
Conclusions

**3. **Why focus on natural gas and oil prices? Historically, a 10:1 ratio between $/barrel of crude oil and $/mmbtu of natural gas
The “rule of thumb” has recently changed to 6:1 or 7:1, with some debate about what is appropriate
Some question whether there is a stable relationship at all
Is such a relationship reliable, for example, for guiding futures or options trading or planning investments?
What could lead to such relationship?
Substitution in end-use
Energy content relationship

**4. **Real values of natural gas and oil products Natural gas prices appear to related to residual fuel oil prices
They also have brief periods where they spike above even the WTI price in energy-equivalent terms

**5. **Error correction model Basic idea: there is a long run equilibrium stable functional relationship between a small number of variables
Example: two variables tend to a particular ratio
Arbitrage is often the source of stable equilibrium price ratios
Shocks lead to short run departures from this equilibrium relationship but adjustments tend to re-establish the relationship in the long run
Research strategy:
Identify a stable long run relationship
OLS
VECM – Johansen MLE
Identify shocks that cause departures from that relationship
Estimate the adjustment process
OLS/IV
3SLS

**6. **Electricity sector role Energy input is a very important cost
Investments have been made to limit differences between fuels with respect to pollution and other non-energy characteristics
Some NERC regions have plants with switching capability
In more regions, substitution is possible by running plants for different periods of time
Plants move up and down the supply stack as fuel prices change
Leads us to a focus on:
Residual fuel oil rather than WTI
Technical change affecting heat rates of CCGT as an explanation for the apparent changed equilibrium relative price ratio
Cost of generation:
$/MWh = ($/Btu)*(Btu/MWh) = fuel price*heat rate

**7. **Data Monthly prices of natural gas (HH) from Natural Gas Weekly, wholesale price of fuel oil and WTI crude from the EIA
Convert prices to real values using industrial electricity retail price as the deflator
Logarithmic transformations re-scale fluctuations by the levels of the variables
Heat rate data were constructed from the EPA NEEDS data and the Annual Electric Generator Report (Form-860)
A capacity-weighted heat rate was calculated for each plant type in each NERC region
The heat rate data forces us to the monthly frequency
Other variables used to model the short run adjustment process:
Beginning of month storage levels (EIA)
Heating (HDD) and cooling (CDD) degree days
Deviations from the 1990-2005 average to measure unusual weather
Extreme HDD variable measures the top decile of the HDD distribution
A constructed variable to reflect Gulf Coast hurricanes
Chicago February 1996 incident
Monthly fixed effects

**8. **Heat Rates Capacity weighted heat rates calculated:
Heat Rate ratios have a nonlinear time trend over the time period due to the adoption of CCGT plants
Lower heat rates for gas plants decrease the cost of electricity generation using gas ceteris paribus

**9. **Stationarity and cointegration When variables have trends, there is a danger that standard statistical methods can lead to spurious relationships
A variable with a stochastic trend -- a random walk -- is said to be integrated, which is one type of non-stationarity
Two integrated variables are cointegrated if they are functionally related in way that leaves a stationary residual error term
Because the function eliminates the trending components of the variables, it represents a long run equilibrium tendency
The residual error measures departures from that long run equilibrium tendency
If the system is dynamically stable, departures should lead to self-correcting movements over time
The short run adjustment process is called an error correcting mechanism
Testing revealed the logarithms of prices and relative heat rates were non-stationary but rates of change were in all cases stationary

**10. **Estimated long run relationships - OLS

**11. **Resulting Oil-Gas Price Relationship

**12. **Estimated long run relationships - VECM Johansen VECM uses a maximum likelihood approach to simultaneously solve the cointegrating equations
Again, we find a cointegrating relationship between NG and RFO and a second cointegrating relationship between RFO and WTI
The NG-RFO relationship is dependent on relative heat rates with the expected sign

**13. **Estimated dynamic adjustment equations

**14. **Error Correction Model OLS cointegrating equation
IV ECM – due to the potential endogeneity of the change in residual fuel oil price, we use a set of instruments (lagged residual price change, current and lagged WTI price change, weather, and storage)
Hausman test shows that we can treat a change in the price of residual fuel oil as exogenous in the natural gas price adjustment equation
VECM
The error correction model is obtained using three stage least squares
The VECM approach allows us to impulse response functions
Results using the OLS and VECM approach are similar

**15. **Impulse Response Functions IRFs measure the effect of a one standard deviation change in the impulse variable on the response variable

**16. **Some observations on the dynamic equations All variables have the expected signs
The adjustment process in response to deviations is stable
Both HDD and CDD deviations have significant, but short-lived, effects on short run NG price movements
Extreme HDD deviations affect RFO prices and the Feb 1996 extreme weather in Chicago had a strong but temporary effect on NG prices
Hurricanes are another significant factor for NG prices
1 bcf shut-in from hurricanes ? approximately $1.03/mmbtu NG increase
Higher storage levels at the beginning of a month lead to lower prices over the month
Seasonal patterns in price movements appear reasonable
Changes in the residual fuel oil price affect natural gas prices more than vice versa
Changes in WTI have a large effect on residual fuel oil prices but not directly on natural gas prices
We find evidence of a chain of causation WTI ? RFO ? NG

**17. **Thanks! P.S. I am currently on the job market
in case anyone is looking ?