# North American Natural Gas Supply Forecast: The Hubbert Method Including the Effects of Institutions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Role of Geology

## 3. The Role of Institutions

## 4. The Role of Technology

The method Hubbert employs in projecting ultimate domestic crude oil discoveries (and production) is purely a statistical exercise and is not the result of geological or engineering analysis. … One looks in vain in Hubbert’s paper for an analysis of causes which would be sufficient to determine the ultimate level of cumulative discoveries. … Economic and technological factors which determine how much oil ultimately can be produced have changed dramatically with time and undoubtedly will continue to so do in the future.

(URR refers to) the proportion of the total (resources) which is recoverable. It is logical that this should increase over time as technological advances raise the proportion of a field which can be recovered economically and as other changes lower costs and thus make it economical to produce … less productive wells.

We thus do not have to worry about how much oil may be contained in known oil fields (with the Hubbert curve) over and above the American Petroleum Institute’s estimates of proved reserves, or how much improvement may be effected in the future in both exploration and productivity techniques, for those will all be added in the future as they have been in the past (emphasis added) by revision and extension in addition to new discoveries. And there is as yet no evidence of an impending departure in the future from the orderly progress which has characterized the evolution of the petroleum industry during the last hundred years.

## 5. The Role of Markets

## 6. The Multi-Cycle Hubbert Model

_{o}is the year of peak production and "a" is a parameter that determines the initial rate of increase in production.

_{1}=a, and b

_{2}can be estimated econometrically to obtain URR by solving $URR=-\frac{{b}_{1}}{{b}_{2}}$.

_{0}+ β

_{1}* CQD + β

_{2}* CQD

^{2}+ β

_{3}* IND

_{1}+ β

_{4}* IND

_{1}* CQD + ε

_{1}is a single dummy or indicator variable. The reason the single indicator variable is used in two terms is because in order for a second cycle to occur, both the intercept and the slope must change at the same point in time. However, since there may be more than one institutional change, more than one indicator variable can be added. For example with two indicator variables for two different institutional change events, we have as follows:

_{0}+ β

_{1}* CQD + β

_{2}* CQD

^{2}+ β

_{3}* IND

_{1}+ β

_{4}* IND

_{1}* CQD + β

_{5}* IND

_{2}+ β

_{6}* IND

_{2}* CQD + ε

_{0}+ ε

_{1}PCPR

## 7. Unit Roots and Stationarity

## 8. Data and Statistical Analysis to 2003

Number of indicator variables | OLS equation results | Log Likelihood | F-test results for significance of last two terms |
---|---|---|---|

0 | QD = 26 – 0.03*CQD + 2.7E-05*CQD^2 (0.00) (0.01) (0.00) numbers in parentheses are p values | -160 | Not Applicable. The OLS results show a convex curve, which does not fit theory. |

Number of indicator variables | OLS equation results | Log Likelihood | F-test results for significance of last two terms |
---|---|---|---|

1 | QD = 21 – 0.01*CQD + 3E-06*CQD^2 (0.00) (0.68) (0.91) -20*IND74 + 0.028*IND74*CQD (0.32) (0.32) numbers in parentheses are p values | -159 | F = 0.52 p value (0.6) However, indicator variables make the relationship concave. |

Number of indicator variables | OLS equation results | Log Likelihood | F-test results for significance of last two terms |
---|---|---|---|

2 | QD = -17 + 0.16*CQD + 2E-04*CQD^2 (0.14) (0.002) (0.001) -86*IND74 + 0.13*IND74*CQD (0.001) (0.000) -141*IND88 + 0.15*IND88*CQD (0.000) (0.000) numbers in parentheses are p values | -151 | F = 7.85 p value (0.001) The indicator variable at 1988 is significant |

Number of indicator variables | OLS equation results | Log Likelihood | F-test results for significance of last two terms |
---|---|---|---|

3 | QD = -45 + 0.29*CQD + 3E-04*CQD^2 (0.000) (0.000) (0.000) -143*IND74 + 0.22*IND74*CQD (0.000) (0.000) -142*IND88 + 0.15*IND88*CQD (0.000) (0.000) -198*IND98 + 0.45*IND98*CQD (0.000) (0.000) numbers in parentheses are p values | -140 | F = 11 p value (0.000) The indicator variable at 1998 is significant |

Number of indicator variables | OLS equation results | Log Likelihood | F-test results for significance of last two terms |
---|---|---|---|

4 | QD = -43 + 0.28*CQD - 3E-04*CQD^2 (0.000) (0.000) (0.000) -140*IND74 + 0.21*IND74*CQD (0.000) (0.000) -140*IND88 + 0.15*IND88*CQD (0.000) (0.000) -376*IND98 + 0.32*IND98*CQD (0.000) (0.000) +165*IND01 - 0.14*IND01*CQD (0.23) (0.203) numbers in parentheses are p values | -138 | F = 2.25 p value (0.12) The indicator variable at 2001 is not significant, nor are any additional indicator variables above three. |

Dependent Variable: QD (rate of Discovery, TCF/year) | Method: Least Squares | Sample (adjusted): 1950 2003 | Included observations: 54 after adjustments | |
---|---|---|---|---|

Variable | Coefficient | Std. Error | t-Statistic | Prob. |

C | -44.49650 | 11.12255 | -4.000565 | 0.0002 |

CQD | 0.288214 | 0.049082 | 5.872076 | 0.0000 |

CQD^2 | -0.000310 | 5.11E-05 | -6.067955 | 0.0000 |

DUM74 | -142.5313 | 24.29129 | -5.867589 | 0.0000 |

DUM74*CQD | 0.218415 | 0.036063 | 6.056481 | 0.0000 |

DUM88 | -142.1555 | 31.36988 | -4.531592 | 0.0000 |

DUM88*CQD | 0.154212 | 0.032936 | 4.682121 | 0.0000 |

DUM98 | -198.4099 | 44.74262 | -4.434472 | 0.0001 |

DUM98*CQD | 0.173554 | 0.038161 | 4.547991 | 0.0000 |

R-squared | 0.712710 | Mean dependent var | 19.64048 | |

Adjusted R-squared | 0.661637 | S.D. dependent var | 6.144504 | |

S.E. of regression | 3.574198 | Akaike info criterion | 5.536370 | |

Sum squared resid | 574.8700 | Schwarz criterion | 5.867868 | |

Log likelihood | -140.4820 | F-statistic | 13.95454 | |

Durbin-Watson stat | 1.898074 | Prob(F-statistic) | 0.000000 |

Null Hypothesis: RESIDUAL has a unit root | |||

Lag Length: 0 (Automatic based on SIC, MAXLAG=10) | |||

Exogenous: Constant | |||

t-Statistic | Prob.* | ||

Augmented Dickey-Fuller test statistic | -6.786332 | 0.0000 | |

Test critical values: | 1% level | -5.416 | |

5% level | -4.7 | ||

10% level | -4.348 | ||

*MacKinnon (1996) one-sided p-values. |

## 9. Price Effects on the Hubbert Multi-Cycle

Dependent Variable: Detrended Discovery | |||||||

Method: Least Squares | |||||||

Sample (adjusted): 1951 2003 | |||||||

Included observations: 53 after adjustments | |||||||

Variable | Coefficient | Std. Error | t-Statistic | Prob. | |||

C | -0.040188 | 0.042086 | -0.954904 | 0.3441 | |||

Per Cent Change in Price | 0.000296 | 0.002290 | 0.129388 | 0.8976 | |||

R-squared | 0.000328 | Mean dependent var | -0.038431 | ||||

Adjusted R-squared | -0.019273 | S.D. dependent var | 0.287248 | ||||

S.E. of regression | 0.290003 | Akaike info criterion | 0.399157 | ||||

Sum squared resid | 4.289199 | Schwarz criterion | 0.473507 | ||||

Log likelihood | -8.577655 | F-statistic | 0.016741 | ||||

Durbin-Watson stat | 2.858432 | Prob(F-statistic) | 0.897560 |

Dependent Variable: Detrended Discovery | |||||||

Method: Least Squares | |||||||

Sample (adjusted): 1951 2003 | |||||||

Included observations: 51 after adjustments | |||||||

Variable | Coefficient | Std. Error | t-Statistic | Prob. | |||

C | -0.032290 | 0.044585 | -0.724231 | 0.4724 | |||

Average per cent change in price, lags 1 and 2 | -0.001293 | 0.003289 | -0.393277 | 0.6958 | |||

R-squared | 0.003147 | Mean dependent var | -0.039084 | ||||

Adjusted R-squared | -0.017197 | S.D. dependent var | 0.291033 | ||||

S.E. of regression | 0.293525 | Akaike info criterion | 0.424717 | ||||

Sum squared resid | 4.221683 | Schwarz criterion | 0.500475 | ||||

Log likelihood | -8.830278 | F-statistic | 0.154667 | ||||

Durbin-Watson stat | 2.822783 | Prob(F-statistic) | 0.695821 |

Dependent Variable: Discovery | |||||||

Method: Least Squares | |||||||

Sample (adjusted): 1951 2003 | |||||||

Included observations: 54 after adjustments | |||||||

Variable | Coefficient | Std. Error | t-Statistic | Prob. | |||

C | 1.709939 | 7.106074 | 0.240631 | 0.8109 | |||

CQD | 0.063999 | 0.026211 | 2.441643 | 0.0185 | |||

CQD^2 | -7.40E-05 | 2.46E-05 | -3.013717 | 0.0042 | |||

PRICE | 5.079707 | 1.186377 | 4.281698 | 0.0001 | |||

DUM88 | -82.44584 | 30.89720 | -2.668392 | 0.0105 | |||

DUM88*CQD | 0.101482 | 0.033427 | 3.035962 | 0.0039 | |||

DUM98 | -15.60761 | 46.20748 | -0.337772 | 0.7371 | |||

DUM98*CQD | 0.015013 | 0.039134 | 0.383638 | 0.7030 | |||

R-squared | 0.614061 | Mean dependent var | 19.64048 | ||||

Adjusted R-squared | 0.555332 | S.D. dependent var | 6.144504 | ||||

S.E. of regression | 4.097368 | Akaike info criterion | 5.794520 | ||||

Sum squared resid | 772.2676 | Schwarz criterion | 6.089185 | ||||

Log likelihood | -148.4521 | F-statistic | 10.45570 | ||||

Durbin-Watson stat | 1.631885 | Prob(F-statistic) | 0.000000 |

^{2}and the log likelihood of Table 10 are lower than that of Table 6. See Table 11.

Model: | R^{2} | Log Likelihood |
---|---|---|

Price plus two indicator Variables (1988, 1998) | 0.614 | -148 |

Three indicator Variables (1974, 1988, 1998) | 0.713 | -141 |

## 10. Discussion of Indicator Variables and Institutions

#### 10.1. Indicator Variable #1, 1974

#### 10.2. Indicator Variable #2, 1988

#### 10.3. Indicator Variable #3, 1998

#### 10.4. 2005 Expected Price Change

#### 10.5. Further Variables

## 11. The North American Natural Gas Production Forecast—Peak Gas

Dependent Variable: QD (rate of Discovery, TCF/year) | Method: Least Squares | Sample (adjusted): 1950 2008 | Included observations: 59 after adjustments | |
---|---|---|---|---|

Variable | Coefficient | Std. Error | t-Statistic | Prob. |

C | -45.4603 | 11.94264 | -3.80655 | 0.0004 |

CQD | 0.292579 | 0.052688 | 5.553024 | 0.0000 |

CQD^2 | -0.00031 | 5.48E-05 | -5.7364 | 0.0000 |

DUM74 | -144.505 | 26.09661 | -5.53733 | 0.0000 |

DUM74*CQD | 0.221414 | 0.038736 | 5.716007 | 0.0000 |

DUM88 | -144.198 | 33.74944 | -4.27261 | 0.0001 |

DUM88*CQD | 0.156407 | 0.03543 | 4.414479 | 0.0001 |

DUM98 | -155.192 | 44.94822 | -3.45267 | 0.0012 |

DUM98*CQD | 0.138126 | 0.038546 | 3.583422 | 0.0008 |

DUM05 | -373.362 | 66.67524 | -5.59972 | 0.0000 |

DUM05*CQD | 0.269746 | 0.048294 | 5.585535 | 0.0000 |

R-squared | 0.801235 | Mean dependent var | 20.92674 | |

Adjusted R-squared | 0.759825 | S.D. dependent var | 7.866405 | |

S.E. of regression | 3.855137 | Akaike info criterion | 5.703235 | |

Sum squared resid | 713.3798 | Schwarz criterion | 6.090572 | |

Log likelihood | -157.245 | F-statistic | 19.34911 | |

Durbin-Watson stat | 2.02837 | Prob(F-statistic) | 0.000000 |

^{th}century when oil and gas production increased by at most 10% per year, but rather a production curve where reserves are well known. When reserves are well known such as when the trans-Alaska oil pipeline opened in 1977, 8 years following the discovery of the great Prudhoe Bay oil field and thus where explorers had had a full 8 years to delineate and develop the field before actual production could commence, production can increase fast. In fact, in the Prudhoe case, oil production increased by an average of 100% per year for four years until it reached the maximum output and plateaued.

^{2}

## 12. The Strategic Natural Gas Market

## 13. Conclusions

## Glossary of Terms

AR | autoregressive |

ADF | augmented Dickey Fuller |

BCF | billion cubic feet |

CBM | coal bed methane |

CQD | cumulative gas discovery to date |

CQP | cumulative production |

Downstream | pipelines, refineries and retail sales |

E&P | exploration and production |

EROI | energy return on investment |

I(0) | non-integrated, stationary term |

I(1) | integrated of order one |

I(2) | integrated of order two |

LNG | liquefied natural gas |

OCS | outer continental shelf |

OLS | ordinary least squares |

PCDD | percent change in detrended discovery |

PCPR | percent change in Price |

QP | current rate of production |

QD | current rate of gas discovery |

RATS | a statistical software package |

SAS | statistical package for estimating |

TCF | trillion cubic feet |

URR | ultimately recoverable resource |

Upstream | where oil and gas wells are |

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**MDPI and ACS Style**

Reynolds, D.B.; Kolodziej, M.
North American Natural Gas Supply Forecast: The Hubbert Method Including the Effects of Institutions. *Energies* **2009**, *2*, 269-306.
https://doi.org/10.3390/en20200269

**AMA Style**

Reynolds DB, Kolodziej M.
North American Natural Gas Supply Forecast: The Hubbert Method Including the Effects of Institutions. *Energies*. 2009; 2(2):269-306.
https://doi.org/10.3390/en20200269

**Chicago/Turabian Style**

Reynolds, Douglas B., and Marek Kolodziej.
2009. "North American Natural Gas Supply Forecast: The Hubbert Method Including the Effects of Institutions" *Energies* 2, no. 2: 269-306.
https://doi.org/10.3390/en20200269