The Relationship between Crude Oil and Natural Gas Prices

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The Relationship between Crude Oil and Natural
Gas Prices

• Peter HartleyKenneth Medlock IIIJennifer Rosthal

James A. Baker III Institute of Public
PolicyRICE UNIVERSITY
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Outline

• Motivation
• Methodology
• OLS Engle-Granger
• VECM
• Data
• Results
• Cointegrating Relationships
• OLS
• VECM
• Error Correction Model
• OLS
• 3SLS
• Conclusions

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Why focus on natural gas and oil prices?

• Historically, a 101 ratio between /barrel of
  crude oil and /mmbtu of natural gas
• The rule of thumb has recently changed to 61
  or 71, 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

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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

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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 priceheat rate

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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

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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

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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

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Estimated long run relationships - OLS

• Both residuals are stationary, but if the first
  equation
• omits the relative heat rate, or
• uses WTI instead of residual fuel oil
• the residual from that equation becomes
  non-stationary

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Resulting Oil-Gas Price Relationship
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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

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Estimated dynamic adjustment equations
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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

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Impulse Response Functions

• IRFs measure the effect of a one standard
  deviation change in the impulse variable on the
  response variable

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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

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Thanks!

• P.S. I am currently on the job market
• in case anyone is looking ?