The Switching Relationship between Natural Gas and Oil Prices. Matthew Brigida*

Transcription

1 The Switching Relationship between Natural Gas and Oil Prices Matthew Brigida* Abstract: Herein we more accurately capture the cointegrating relationship between natural gas and crude oil prices by controlling for nonstationarity induced by endogenous changes in regime. Specifically, we allow the cointegrating equation to switch between m states, according to a firstorder Markov process. First, we find evidence that regime-switching exists in the relative pricing relationship, and that two is the optimal number of states. Once we control for this type of nonstationarity natural gas and crude oil prices are cointegrated, and in an error correction model the state-weighted residuals contain unique information and allow for faster recovery toward equilibrium in response to exogenous shocks. Further, our analysis finds evidence that natural gas and crude oil prices did not permanently decouple in the early 2000s, but rather experienced a temporary shift in regimes. We find that forecasts of the relative pricing of natural gas and crude oil should be conditioned on state probability. [This version: December 14, 2012] *Associate Professor of Finance, Clarion University of Pennsylvania. Mailing address: Department of Finance, 840 Wood St., Clarion, PA mbrigida@clarion.edu 1

2 1. Introduction This analysis captures the relative pricing relationship between natural gas and crude oil prices by controlling for nonstationarity in the cointegrating relationship specifically induced by endogenous changes in regime. Once such regime changes are controlled for the relative pricing relationship recovers from exogenous shocks much more quickly. This allows better measures of present energy market integration, better forecasts of relative prices, and a more thorough understanding of how technological changes affect the natural gas and crude oil pricing relationship. That the regime-switching is endogenous is an important point. In our model, changes in regime are determined solely by the underlying data generating process. This obviates any biases the econometrician may have in determining whether regime changes exist, and the timing of such changes. This analysis contributes to the prior literature by allowing for a type of nonstationarity which was disallowed in earlier models. Specifically, I allow for endogenous changes in parameter estimates driven by a switch in regime. Such a process may be stationary in each regime, but nonstationary as a whole, because the parameter changes cause a change in the mean and variance of the process. 2

3 Previous analyses have found mixed results with respect to the relative pricing of natural gas and crude oil 1. Serletis and Herbert (1999), Villar and Joutz (2006), Bachmeier and Griffin (2006), Brown and Yucel (2008) Hartley, Medlock and Rosenthal (2008), and Ramberg and Parsons (2012) have broadly found evidence that natural gas and oil prices are cointegrated. However, noted in many of these analyses is the presence of structural breaks in the relative pricing relationship. Ramberg and Parsons (2012) point to a relative outperformance of oil in the interval , with natural gas dominating thereafter. They further note that the relationship may have abruptly changed again in 2009, though their data set ended too soon to be able to tell. Our present analysis, using the regime-switching model and data through 2012, shows that Ramberg and Parson s conjecture was correct. In 2009 relationship switched to a regime marked by outperformance by crude oil. That is, consistent with Ramberg and Parson s (2012) observation, during a period spanning there were two main switches in states in the early and late 2000s respectively. In addition, we show within each state the cointegrating relationship between natural gas and oil is stable. That is, once you control for changes in regime, there is a stable relationship between natural gas and oil prices. Including such structural breaks into any model of the relationship is important because, as Villar and Joutz (2006) note, structural changes in the cointegrating equation can cause forecast failure. This renders the relationship useless for policy decisions. The present analysis 1 For more on the methodology of these cointegration analyses see: Hendry and Juselius (2000) and (2001); Engle and Granger (1987). 3

4 incorporates such structural changes into the cointegrating equation, and thereby the error correction model (ECM). In this analysis we offer an answer to the idea that the relative pricing relationship between natural gas and oil permanently decoupled in the early 2000s. Using the regimeswitching model, and data though 2012, I will show that the parameters governing the relationship between natural gas and crude oil did indeed change from , however the parameters have since reverted to their pre-2000 values. That is, the decoupling was a temporary shift in regimes. Throughout this paper we use a standard error correction model (ECM) analysis similar to prior literature, but with our regime-switching cointegrating equation. However we do not compare our results to earlier analyses. This would not be fruitful given different data sets and observation periods. We instead also estimate the ECM with a control (the standard nonswitching cointegrating equation) and compare our results to this control. This way, our analysis compliments prior analyses by motivating the use of a regime-switching cointegrating equation in others ECM. Lastly, understanding the relative pricing of natural gas and oil is important for both corporate managers and policymakers. Models of the pricing relationship are necessary to estimate cash flows in the long-term capital budgeting plans of both energy producers and consumers. For instance dynamics of the relationship may dictate whether an energy producer should drill wells to target natural gas or oil. Alternatively, the relative pricing may determine the type of fuel to use when building a power plant. For policymakers the relative pricing may affect decisions from permitting energy transportation infrastructure to setting royalty payments. 4

5 The paper is as follows: section 2 presents the Markov-switching cointegration equation, the determination of the number of states, and results; section 3 describes the ECM and results; section 4 concludes. 1.1 A priori, why would we expect changes in regimes? Some events which may induce regime switches in the relationship between natural gas and oil are technological changes and legislation, among others. For example, Hartley et al (2008) found evidence that the marked increase in the use of the combined-cycle combustion turbines for electricity generation in the late 1990s made natural gas electricity generation more cost effective, thereby substantially increasing demand for natural gas and thereby increasing prices. More recently, an increase in the supply of shale gas because of the introduction of hydrofracking has driven North American natural gas prices lower. 2. Markov-Switching Cointegrating Equation The cointegrating equation with first-order, M-state, endogenous Markov-switching parameters may be written as:, (1) and (2) (3) 5

6 (4) (5) where for, if then, and otherwise. Construction of the likelihood function for the above Markov Switching cointegrating equation was done by prediction error decomposition using the Hamilton filter (see Hamilton (1994) or Kim and Nelson (1999)). Minimization of the negative log-likelihood was done using the optim function in the R programming language. The minimization was unconstrained. The residuals of the m-state model are weighted by filtered state probability, which is the probability that the relationship is in state S t given information only through time t-1. This means probabilities in the residual are not biased by using information through time T, as would be the case if we used smoothed state probabilities 2. The time t weighted residual in the m-state case is: (6) where denotes the information available at time t-1, and denotes the time t residual of the state m model. The data used to estimate the model are monthly and weekly logged prices for rolling front month NYMEX full-size natural gas and oil futures. The crude oil contract is for west Texas intermediate deliverable in Cushing Oklahoma, and the natural gas contract is for delivery 2 Smoothed probabilities are, which are the probabilities that the model is in state m at time t given information through time T. 6

7 at the Henry Hub in Louisiana. The data are available from the Energy Information Agency of the U.S. Department of Energy. 2.1 Determining the number of states To determine the appropriate number of states, the cointegrating equation was estimated allowing for the number of states to range from one to three. Note, a one-state equation is the standard, non-switching, cointegrating equation. The results of each model were compared using Akaike s Information Criterion (AIC), and a two-state process was found to best describe the process. Specifically, using monthly prices, the negative log-likelihood values were , -8.36, and for the one, two, and three-state models respectively. This implies AIC values of , , and for the three states respectively. Similarly, using weekly prices the negative log-likelihood values were , , and , implying AIC values of , , and for the one, two, and three state models respectively. Note that the two-state model is best regardless of whether the sampling frequency is weekly or monthly. The filtered state probabilities of the two-state model are in figures 1 and 2. Filtered state probabilities for the three-state model are in figures 3 and 4. First note that the state probabilities in the two-state model are stable in that once they are in a given state they remain in that state for some time. If fact, using the estimated transition probabilities, we may calculate the expected duration of a given state m as: (7) 7

8 where E(D m ) is the expected duration of state m, and p mm is the probability of being in state m at time t given the process was in state m at time t-1. For the two-state model, using monthly prices, the expected duration is 6.94 years and 4.66 years for state 1 and 2 respectively. Using weekly prices, the expected duration is 3.10 years and 2.13 years for state 1 and 2 respectively 3. Furthermore, the two-state model exhibits distinct regime switching. That is, at each time point the model is confident of either being in state 1 or 2. Lastly, both the model estimated using weekly and monthly data agree regarding the state at each point in time. This is evidence that the two-state model fits the underlying data-generation process well. Conversely, figure 3 shows that the three-state model using monthly prices is usually unclear about which state the process is in at each point in time. In addition, the state probabilities are unstable using monthly prices. Figure 4 shows that using weekly prices the state probabilities show distinct regime switching with stable state probabilities. However this highlights that the state probabilities do not agree at each point in time when we compare the probabilities estimated from weekly and monthly data. This is further evidence against a threestate model. [INSERT FIGURES 1, 2, 3, AND 4 HERE] 2.2 Results: Two state model For comparison, we estimated the cointegrating equation for both a two-state Markovswitching process and the standard one-state regression. We then tested for stationary residuals 3 We expect the expected state duration to be shorter for weekly prices given the increased number of opportunities to transition in a fixed time period. 8

9 in the cointegrating equation using both the Augmented Dickey-Fuller and the Phillips-Perron tests. Using monthly prices, similar to Hartely et al (2008), we find non-stationary residuals in the one-state cointegrating equation. We also find the residuals of the regression on weekly prices are also nonstationary. We conclude the logs of natural gas and oil prices are not cointegrated in the one-state model. Alternatively, using the two-state model we reject the null of nonstationarity in the residuals of the cointegrating equation at the 1% level for both the Augmented Dickey-Fuller and the Phillips-Perron tests, and for both weekly and monthly prices. This is evidence that the two series are cointegrated in the two-state model. That is, the series are cointegrated once we control for nonstationarity in the residuals induced by changes in regimes. Further regarding the appropriateness of the two-state model, using t-tests on the parameters estimated in the two-state model, we find the, and coefficients are all significantly different at the 1% level depending on the state. That is, is significantly different from, etc. Also, the probability of remaining in state 1 at time t given you are in state 1 at time t-1 is 98.80% for the monthly series and 99.38% for the weekly series. Similarly, the probability of remaining in state 2 at time t given you are in state 2 at time t-1 is 98.21% for the monthly series, and 99.10% for the weekly series. As noted earlier, the effect is that the model is stable within each state, and experiences few and distinct changes in state. 9

10 We conclude, by every measure, the two-state model is more appropriate for modeling the cointegrating equation of natural gas and oil prices. The results of the one and two-state cointegrating regressions are in Tables 1 and 2 below. [INSERT TABLES 1 and 2 HERE] 3. Error Correction Model with Regime Dependent Residuals In this section we use the state-weighted residuals from the switching cointegration regression to estimate an ECM of natural gas and crude oil prices. We then compare these results to the same ECM estimated using a standard non-switching cointegrating term. Similar to earlier analyses, the price of crude oil is determined exogenously in the ECM. Our error correction model (ECM) is: (8) where X is a matrix of exogenous control variables. The variables are: cooling degree days (CDD); heating degree days (HDD); deviations from the average number of CDDs and HDDs; the natural gas storage differential from the 5-year average; Baker Hughes North American rotary rig count. All of the control variables are standard except for the rig count. We included the variable because there is anecdotal evidence that, because natural gas prices have dropped below marginal production costs, rig count has become more sensitive to natural gas prices. As the 10

11 natural gas price increases toward marginal costs, more rigs are brought online, and conversely when prices decline rigs are idled. From a recent article 4 in Bloomberg news, Gas producers in North America including Chesapeake Energy Corp. (CHK) are killing their commodity s biggest rally in 10 months by opening more wells, putting the U.S. on track to have record gas supplies this year. Given this reasoning, we expect changes in the rig count to be positively related to contemporaneous changes in the price of natural gas. 3.1 Data Natural gas and oil prices are, as earlier mentioned, rolling front-month logged futures prices from the NYMEX and available from the EIA. The natural gas storage data are also from the EIA. CDD and HDD are population-weighted national averages and are available from the U.S. National Weather Service s Climate Prediction Center. Rig count data are available from Baker Hughes. 3.2 Results 5 The main result of the ECM is that the coefficient of the cointegrating term is about for the two-state model, and for the one-state model. This means that if natural gas and crude oil are out of their long-term equilibrium, then in the next month natural gas adjusts toward equilibrium at over twice the rate using the two-state as compared to the one-state model. Further, a 90% adjustment to equilibrium takes approximately 14 months using the two-state Following are results of the ECM on monthly prices. Estimates of the ECM on weekly data are similar and available on request. 11

12 model, and 37 months using the one-state model. This shows the marked improvement in forecasting ability of the two-state cointegrating equation. Additionally, in table 3 we see the coefficient of the cointegrating term in the one-state model is significant if only four lagged changes in natural gas are included, but is insignificant if twelve lagged changes are included. This is evidence that the cointegrating term in the one-state model contains information which is already in the lagged changes in natural gas prices. That is, the one-state cointegrating term contains redundant information. Alternatively, the coefficient of the cointegrating term from the two-state model is significant regardless of the number of lagged changes in natural gas included in the ECM. Thus, the two-state cointegrating term contains unique information. This, also, is evidence in favor of the two-state model of the cointegrating equation. Regarding the rig count explanatory variable, the change in rig count is positively and significantly related to changes in natural gas prices in the full ECM (12 natural gas price lags). The coefficient of implies an increase in the rig count of 100 rigs coincides with a 2.02% increase in natural gas prices. The average monthly variation in the rig count is 94. In model specifications with fewer lags of the change in natural gas the rig count variable is still positive, though insignificant. We also tested for a threshold effect where the change in rig count became more important once the natural gas price fell below $5 per mmbtu. We found the rig count coefficient is positive and larger when natural gas prices are below the $5 threshold, but not significantly larger. [INSERT TABLE 3 HERE] 12

13 3.3 Results including residual fuel oil For robustness we estimated an ECM with contemporaneous and once lagged changes in logged residual fuel oil 6. Hartley et al. (2008) found evidence that crude oil does not affect natural gas prices directly, but rather that crude oil affects residual fuel oil which in turn affects natural gas prices. The results of this model are in Table 4 below. Consistent with Hartley et al. (2008), using switching residuals, when we include residual fuel oil and four lagged changes in natural gas, then the coefficient of the contemporaneous change in logged crude oil is no longer significant. When using non-switching residuals, the coefficient of crude oil remains significant. Importantly, when including residual fuel oil the coefficients of the cointegrating terms still imply much faster reversion to the long-term price equilibrium using switching residuals rather than non-switching. This shows the preference for the switching cointegrating equation is robust to whether crude oil prices act on natural gas prices directly, or rather through residual fuel oil as an intermediary. [INSERT TABLE 4 HERE] 4. Conclusions Herein we have found evidence for a regime-switching relationship between natural gas and oil prices. This evidence is, firstly, that the cointegrating equation is well-suited to a regimeswitching model with two states. The cointegrating equation s residuals are stationary when 6 U.S. Residual Fuel Oil Retail Sales by Refiners (Dollars per Gallon) available from the EIA. 13

14 using the switching model, and nonstationary when the relationship is constrained to one state. The filtered probabilities also exhibit stable states with distinct regime-switching. Additional evidence for the superiority of the regime-switching model is found by comparing the results of an ECM of natural gas and crude oil prices with two-state residuals, to the results of the same ECM using one-state residuals. We found that the ECM with two-state residuals recovers from an exogenous shock at over twice the rate of the ECM with one-state residuals. Further, we found that in the ECM, the two-state cointegrating term contains unique information whereas the one-state term contains redundant information. These results have many practical implications. Firstly, this analysis shows there is a stronger relationship between natural gas and crude oil once one controls for switches in regimes. That is, when controlling for endogenous regime switching there is faster reversion of natural gas and crude oil prices to their long-term equilibrium, which implies these energy markets are more integrated that one would otherwise estimate. The results also imply that natural gas and crude oil prices did not permanently decouple in the early 2000s, but rather exhibited a temporary shift in August of 2000 to a regime wherein natural gas prices performed relatively better than crude oil prices. This regime lasted, with one interruption, until approximately May of 2009, after which the relationship has reverted to its original state with oil price increases outpacing natural gas prices. The evidence in this analysis is that there is unique information gained through allowing endogenous regime switching when considering the long-term relative prices of natural gas and crude oil. This information allows a more thorough and accurate understanding of the 14

15 relationship. In sum, forecasts of the relative pricing of natural gas and oil should be conditioned on state probability. 15

16 References Bachmeier, L.J. and J.M. Griffin, (2006) Testing for Market Integration: Crude Oil, Coal, and Natural Gas The Energy Journal 27(2): Brown, S.P.A., and M.K. Yucel, (2008) What drives natural gas prices? The Energy Journal 29(2): Engle, R. F., and C.W.J. Granger (1987). Cointegration and Error Correction: Representation, Estimation, and Testing. Econometrica 50: Kim, C.J., and C.R. Nelson, (1999) State-Space Models with Regime Switching, The MIT Press. Hamilton, J.D. (1994). Time Series Analysis. Princeton: Princeton University Press. Hartley, P.R., K.B. Medlock III, and J.E. Rosthal (2008). The relationship of natural gas to oil prices. The Energy Journal 29(3): Hendry, D.F. and K. Juselius (2000). Explaining Cointegration Analysis: Part I. The Energy Journal, 21(1): Hendry, D.F., and K. Juselius. (2001). Explaining Cointegration Analysis: Part II. The Energy Journal, 22(1): Ramberg, D.J., and J.E. Parsons (2012). The weak tie between natural gas and oil prices The Energy Journal 33(2): Serletis, A., and J. Herbert, (1999). The message in North American energy prices. Energy Economics 21:

17 Tables Table 1. Results of Estimating Cointegrating Equation Regressions (equations 1-5) with Monthly Prices There are 225 monthly observations for natural gas and oil prices. The one-state model has 222 degreesof-freedom, and the two-state model has 217. The alternative hypothesis in the augmented Dickey-Fuller and Phillips-Perron tests is to conclude the residual series is stationary. Residuals in the two-state model are weighted by the filtered state probability. p-values are below the coefficient in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels respectively. One-State Model Two-State Model State (5e-6)*** (0.7518) (0.2068) ln(likelihood) AIC Augmented Dickey Fuller Test (0.6109) Phillips-Perron Test (0.5434) (0.01)*** (<0.01)*** (1.4e-8)*** Table 2. Results of Estimating Cointegrating Equation Regressions (equations 1-5) with Weekly Prices There are 978 weekly observations for natural gas and oil prices. The one-state model has 975 degrees-offreedom, and the two-state model has 970. The alternative hypothesis in the augmented Dickey-Fuller and Phillips-Perron tests is to conclude the residual series is stationary. Residuals in the two-state model are weighted by the filtered state probability. p-values are below the coefficient in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels respectively. One-State Model Two-State Model State (0.0050)*** (0.0043)*** ln(likelihood) AIC Augmented Dickey Fuller Test (0.4312) Phillips-Perron Test (0.2849) (0.0100)*** (<0.01)***

18 Table 3. Error-Correction Model Results: Below are estimates of the error correction model on monthly data from June 1997 to September There are 184 observations. The response variable is the change in the log Henry Hub natural gas price from time t-1 to time t. *, **, *** denote significance at the 10%, 5%, and 1% levels respectively. Variable Switching Residuals Non-Switching Residuals Intercept (0.0028)*** (0.0103)** (0.0014)*** (0.0051)*** (0.0182)** (0.0054)*** (0.1670) (0.0120)** (0.0004)*** (0.0003)*** (0.0002)*** (7.2e-5)*** (0.0820)* (0.0119)** (0.2954) (0.0798)* (0.4773) (0.9925) (0.1645) (0.4100) (0.2845) (0.8562) (0.0995)* (0.3959) (0.4498) (0.2070) (0.8012) (0.5000) (0.1330) (0.0618)* (0.9274) (0.8054) (0.7677) (0.6646) (0.0851)* (0.0837)* (0.0002)*** (0.0004)*** (0.8746) (0.9613) (0.4070) (0.4656)*** (0.0721)* (0.0960)* CDD t (0.0001)*** (0.0002)*** (0.0002)*** (0.0004)*** CDDDEV t (5e-7)*** (2e-05)*** (3.6e-6)*** (0.0001)*** HDD t (0.0998)* -6.9e-05 (0.1621) (0.0780)* -7.1e-5 (0.1528) HDDDEV t (3e-5)*** (5e-06)*** (4.7e-5)*** (1.4e-5)*** STORAGE DIFF t (0.0233)** -2.2e-05 (0.5597) (0.004)*** -7.8e-5 (0.0722)* RIG COUNT DIFF t (0.0446)** 6.2e-05 (0.4234) (0.0765)* 4.3e-5 (0.5792) F-statistic (5e-12)*** (1e-09)*** (2.3e-11)*** (2.3e-9)*** adj. R

19 Table 4. Error-Correction Model Results: Including Residual Fuel Oil Below are estimates of the error correction model on monthly data from June 1997 to August There are 183 observations. The response variable is the change in the log Henry Hub natural gas price from time t-1 to time t. *, **, *** denote significance at the 10%, 5%, and 1% levels respectively. Variable Switching No switching Intercept (0.0033)*** (0.0012)*** (0.0014)*** (0.0002)*** (0.0049)*** (0.0046)*** (0.0089)*** (0.0024)** (0.1063) (0.0517)* (0.0575)* (0.0295)** (0.0863)* (0.1034) (0.0826)* (0.0957)* (0.0595)* (0.0639)* (0.0467)** (0.0234)** (0.0163)** (0.0205)** (0.0931)* (0.0759)* (0.6217) (0.8126) (0.9340) (0.4512) (0.1088) (0.2989) CDD t (7.3e-5)*** (0.0001)*** (0.0001)*** (6e-5)*** CDDDEV t (2.3e-5)*** (0.0001)*** (0.0002)*** (0.0006)*** HDD t -9.7e-5 (0.0612)* (0.0397)** (0.0534)* (0.0176)** HDDDEV t (6.4e-6)*** (1e-5)*** (1.6e-5) (2e-5)*** STORAGE DIFF t -1.4e-5 (0.7012) -4e-5 (0.2239) -7.3e-5 (0.0918)* -8e-5 (0.0252)** RIG COUNT DIFF t 6.9e-5 (0.3742) 7e-5 (0.3119) 5e-5 (0.5120) 4e-5 (0.5669) F-statistic (1.2e-9)*** (2e-10)*** (1.9e-9)*** (1e-10)*** adj. R

20 Figures Figure 1. Monthly Data: Both the natural gas and crude oil price series below are in logs and less the mean of the logged series. Below the price series is the probability that the relative pricing relationship is in state 2. 20

21 Figure 2. Weekly Data: Both the natural gas and crude oil price series below are in logs and less the mean of the logged series. Below the price series is the probability that the relative pricing relationship is in state 2. 21

22 Figure 3. 3 states, monthly series: Below is the probability that the relative pricing relationship between natural gas and crude oil is in each state in the 3-state cointegrating equation. 22

23 Figure 4. 3 state, weekly series: Below is the probability that the relative pricing relationship between natural gas and crude oil is in each state in the 3-state cointegrating equation. 23