World Oil Depletion: Diffusion Models, Price Effects, Strategic and Technological Interventions

Renato Guseo ASPO-5 San Rossore 18-19 July 2006, Italy

Department of Statistical Sciences

Renato Guseo

University of Padova, Italy

5-th International ASPO Conference,San Rossore, 18-19 July 2006, Italy

World Crude Oil Production

1900 10 20 30 40 50 60 70 80 90 2000

Thousand barrels daily

Global

USA (NGL)

World Production and Prices

Crude Oil Production and Prices per Barrel

VariablesProduction (barrel x 1000)Price (dollars, 2002)

1900 1920 1940 1960 1980 2000 20200

8(X 10000)

Fonte: BP Statistical Review of World Energy, 2004

Growth and Development after World War II -1-

• Cohen, J.E. (2003) Human Population: The next Half Century, Science, 203, 1172-1175;

• Exceptional demographic expansion;• Rural population peak in rich countries: 1950;• Increse of world average life: 30 years in 1900

and 65 years in 2000;• Population: 6.3 billion in 2004; United Nations

Population Division: 8.9 billion in 2050 (ex medium variant scenario forecasting);

• Regional population contraction in 2050: Japan -24%; Italy -22%; FSU -29%;

• USA dominance in oil estraction and refining: shock 1918 (positive with local memory);

• Decisive military advantage. Competitive advantage after World War II;

• American way of life;• Energetic Surplus based on cheap crude oil;• Structural change in sustainable economic

evolution based on non-renewable resources;

• Today risk: physical restrictions towards expansion in oil production due to emergent demand by China and India;

• Risk of a late migration towards renewable energetic resources;

• Emerging technologies are not completely sustainable and efficient (fuel-cells, hydrogen, photovoltaic systems, solar thermal systems, eolic systems, etc.).

Recent strategic researches

1. Morse, E.L. e Jaffe, A.M. (2001). “Strategic Energy Policy Challenges for the 21st Century”; (2000 - aprile 2001); James A. Baker III Institute for Public Policy of Rice University, Texas; Council of Foreign Relations of USA

2. National Energy Policy Development Group, (2001, Task Force supervised by D. Cheney).

• USA energetic policy since 1940 – security -;• Global Economic growth based on a production surplus

with cheap prices;• New emerging world oil demand; • Supply dependence (Midle East).

Non-Renewable Resources Depletion: Hubbert and recent

developtments• Hubbert, M.K. (1949). Energy from fossil fuels, Science, 4,

103-109.

• In 1956 Hubbert forecasts the peak of annual production within 48-lower states in USA by year 1970;

• Campbell, C. e Laherrère, J. (1998). The End of Cheap Oil, Scientific American, March 1998.

• Laherrère, J. (2003). Modelling future oil production, population and the economy, ASPO 2nd international workshop on oil and gas, Paris, 26-27.

• ASPO (Association for the Study of Peak Oil and Gas);

Economic and financial “estimation” of oil reserves: inflated figures

• Warranties on international long-term loans;

• Investments on production plants;

• OPEC restrictions overcoming: export is proportional to the “declared” reserves.

BP - Statistical Review of World Energy

Source: BP Statistical Review of World Energy

Ultimate Recoverable Resouce: URR• URR: total amount of a finite resource obtainable at the end of

extraction process;

• Geologic estimates of Oil URR during the life- cycle of resource extraction:

1. Production to date. Oil heterogeneity. (weight 100%);2. Proven reserves. Ex-post recovery factor 35% is a median and

today’s variability is very large. Revision principles and “reserves growth” (USGS) enlarge uncertainties;

3. Probable and possible reserves: undiscoverd petroleum based on subjective assessments (probability, e.g. 5%).

•Could we do a simple weighted sum of such components? Probably not

Recent statistical modeling • Guseo, R. (2004) Interventi strategici e aspetti competitivi nel

ciclo di vita di innovazioni, Working Paper Series, 11, Department of Statistical Sciences, University of Padua.

• Guidolin, M. (2004) Cicli energetici e diffusione delle innovazioni. Il ruolo dei modelli di Marchetti e di Bass, Thesis, University of Padua.

• Guseo, R and Dalla Valle, A. (2005) Oil and Gas Depletion: Diffusion Models and Forecasting under Strategic Intervention, Statistical Methods and Applications, 14(3), 375-387;

• Guseo, R., Dalla Valle, A. and Guidolin, M. (2006) World Oil Depletion Models: Price effects compared with strategic or technological interventions, Technological Forecasting and Social Change (in press);

• Guseo, R. (2006) Bass-let Detection of Automobile Successive Generations: Evidence from the Italian Case (submitted).

Crude Oil Production: Diffusion of an Innovation

• Oil production is modulated by the dynamics of international demand;

• Oil demand is a function of the diffusion processes related to basical technologies (transport, chemical industries, heating, etc.);

• Diffusion of technological innovations is conditioned by social communication structure: innovators and imitators (word-of-mouth)

Bass Equation: BM• z’(t) = mf(t) = m[p+qF(t)][1-F(t)] or• z’(t) = pm+(q-p)z(t) - (q/m) z(t)2 (Riccati)

• z’(t)=mf(t) (instantaneous adoptions); • f(t)=F’(t) • z(t)=m F(t) (cumulative adoptions);

F(t)=z(t)/m• f(t)/[1-F(t)]=p+qF(t) Bass Hazard rate • m=potential market; carrying capacity; URR• p=innovation coefficient, p>=0• q=imitation coefficient, q>=0

Normalized Bass models: BM and GBM

BM: f(t)/[1-F(t)]=[p+qF(t)] “Standard”

GBM: f(t)/[1-F(t)]=[p+qF(t)] x(t) “GBM”

x(t) is a quite general intervention function: integrable, positive and “centered” around unitary “neutral pole”: 1.

Representation of temporal price variations, of advertising pressure, of political, strategic, legal, environmental interventions.

Equation Solution: GBM

IIII btatbtatcctx

)()(2)()(12211

Exp. shocks

Rect. shocks

Mixed shocks

IecIec aab

IIcIec baaabtx

)()(2)(

)())(()('

Plot of Fitted Model

0 20 40 60 800

3(X 1000)

Great Britain: GBM, 2 mixed sh.Estimation method: MarquardtEstimation stopped after maximum iterations reached.Number of iterations: 31Number of function calls: 330Estimation Results Asymptotic 95,0% Asymptotic Confidence IntervalParameter Estimate Standard Error Lower Upper----------------------------------------------------------------------------m 4513,39 154,806 4196,77 4830,0p 0,0000708436 0,0000324773 0,00000441993 0,000137267q 0,111872 0,00516425 0,10131 0,122434c1 8,54019 1,02935 6,43493 10,6454b1 -0,250721 0,0114596 -0,274159 -0,227284a1 10,7677 0,458356 9,83028 11,7052c2 -0,331417 0,0175489 -0,367309 -0,295526a2 23,4341 0,190843 23,0438 23,8245b2 28,6819 0,164258 28,3459 29,0178----------------------------------------------------------------------------Analysis of VarianceSource Sum of Squares Df Mean Square Model 6,52091E7 9 7,24545E6Residual 657,546 29 22,674-----------------------------------------------------Total 6,52097E7 38Total (Corr.) 3,31712E7 37R-Squared = 99,998 percentR-Squared (adjusted for d.f.) = 99,9975 percentStandard Error of Est. = 4,76172Mean absolute error = 3,10566Durbin-Watson statistic = 0,889298

Positive Shock with local memory

Great Britain: analysis• The “saddle” 1987-

1991-1999 is perfectly absorbed by a rectangular shock:

• a) Petroleum Reven Tax modification;

• b) pipelines restructuring 1986-1991; symmetric behaviour confirms ordinary regime;

• c) partial production stall due to the reduction of new discoveries.

Multiple X-Y Plot

Variables GBbp DIFF(PRED) DIFF(FOR)

0 20 40 60 80 0

USA: 48 lower States and Alaska,one exponential shock

Estimation Results---------------------------------------------------------------------------- Asymptotic 95,0% Asymptotic Confidence IntervalParameter Estimate Standard Error Lower Upper----------------------------------------------------------------------------m 224,885 0,784401 223,328 226,442p 0,000445866 0,0000177788 0,000410571 0,000481162q 0,0571941 0,000403937 0,0563922 0,057996c1 0,682617 0,0735348 0,536632 0,828602b1 -0,0852885 0,00948373 -0,104116 -0,0664609a1 18,0477 0,981086 16,1 19,9954---------------------------------------------------------------------------- Analysis of Variance-----------------------------------------------------Source Sum of Squares Df Mean Square -----------------------------------------------------Model 735809,0 6 122635,0Residual 7,39124 95 0,0778026-----------------------------------------------------Total 735817,0 101Total (Corr.) 352880,0 100 R-Squared = 99,9979 percentR-Squared (adjusted for d.f.) = 99,9978 percentStandard Error of Est. = 0,278931Mean absolute error = 0,207909Durbin-Watson statistic = 0,173839

Plot of Fitted Model

0 20 40 60 80 100 1200

Multiple X-Y Plot

VariablesbariliDIFF(PREDb1)DIFF(PREDbe1)

0 20 40 60 80 100 1200

Positive shock with local memory

USA: 48 lower States and Alaska, ARMAX(4,0,2) sharpening

Forecasting - bariliAnalysis SummaryData variable: bariliNumber of observations = 101Start index = 1,0Sampling interval = 1,0 Forecast Summary----------------Forecast model selected: ARIMA(4,0,2) + 1 regressorNumber of forecasts generated: 40Number of periods withheld for validation: 0 ARIMA Model SummaryParameter Estimate Stnd. Error t P-value----------------------------------------------------------------------------AR(1) 1,21416 0,691695 1,75534 0,082426AR(2) -0,140994 1,11031 -0,126986 0,899220AR(3) -0,146337 0,49692 -0,294488 0,769028AR(4) -0,132467 0,0891259 -1,48629 0,140514MA(1) 0,591549 0,68527 0,863235 0,390183MA(2) 0,299352 0,650254 0,460362 0,646308DIFF(PREDbe1) 0,20426 0,0890786 2,29303 0,024052----------------------------------------------------------------------------Backforecasting: yesEstimated white noise variance = 0,00495321 with 95 degrees of freedomEstimated white noise standard deviation = 0,0703791Number of iterations: 17

Time Sequence Plot for bariliARIMA(4,0,2) + 1 regressor

actualforecast95,0% limits

0 30 60 90 120 150-1

Shock: 1918

Alaska: ARMAX(2,0,1) sharpening

Multiple X-Y Plot

Variables alaskap DIFF(FORar2ma1)

0 20 40 60 80 0

2,4 Residual Autocorrelations for alaskac

ARIMA(2,0,1) with constant + 1 regressor

0 3 6 9 12 15-1

ARIMA Model SummaryParameter Estimate Stnd. Error t P-value----------------------------------------------------------------------------AR(1) 0,323713 0,100318 3,22686 0,002667AR(2) -0,172177 0,054492 -3,15967 0,003195MA(1) -0,818595 0,102552 -7,98224 0,000000PREDbme1 0,847508 0,0501864 16,8872 0,000000Mean -0,0143829 0,0282678 -0,508809 0,613990Constant -0,0122034 ----------------------------------------------------------------------------Backforecasting: yesEstimated white noise variance = 0,00281514 with 36 degrees of freedomEstimated white noise standard deviation = 0,0530579Number of iterations: 20

World Oil data:Daily Production

Sources:

• Industriedatenbank 2001 (1900 – 1986)

• BP Statistical Review of World Energy (1987- 2002)

GBM: x(t) pure prices control

GBM exp shocks + price effect

Guidolin (2004): GBM, 2 exp shocks

World Oil Depletion Models

VariablesProduction datagbm2e+for

8(X 10000)

GBM: 3 exp shocks (memory persistence)

World Oil Depletion Models

VariablesProduction datagbm3e+for

8(X 10000)

GBM 3 exp shocks: estimates(memory persistence)

q/p = 608 Qp=1%;

999994708,02 R

06,17)1951/.( parzmF

World Oil Depletion: GBM with three shocks vs Hubbert-Bass

Oil Peak: 2007

Depletion time 90% : 2019 Depletion time 95% : 2023

URR=1524 Gbo

Oil market Operators: prices growth

• Demand and supply self-control similar to 1973 and 1979-’83 behaviour. Extension of crude oil economic life cycle;

• Limited techonological efficiency margins due to the improvementes of 70’s , 80’s and 90’s;

• Savings through “life styles” modification: this is the central dilemma in industrialized countries;

• Sluggishness of middle class whose life style is based on an expected irreversible and indefinite growth and development.

New Emergent Economies

• Increase in crude oil requirements by recent emergent economies: China, India, and other Asiatic countries;

• US EIA (Energy Information Administration) “forecasts” a world oil demand of 40 Gbo/year (or 109.6 milion daily barrels) in 2020;

• Guseo, Dalla Valle, Guidolin (2006) and Bakhtiari (2004) forecast, in 2019-20, only 55 milion daily barrels.

Crude Oil: Area consumption

Consumi medi giornalieri (in barrel X 1000)

Variables

North Ame

Europe Eurasia

Asia Pacific

South Central Ame

Middle East

Africa

1960 1970 1980 1990 2000 20100

3(X 10000)

Outlook• Nuclear fission perspective is probably a tardy

strategy with known collateral externalities. A new plant in Italy can be launched after 13-15 years;

• Technological, political and economic efforts must be distributed in different areas: photovoltaic, solar thermal, bio-fuel, biomass, eolic, hydrogen, etc.;

• Electric sector: distributed investments (photovoltaic, micro-cogeneration, etc.).

• Individual and collective mobility.

World Oil Depletion: GBM with three shocks vs Hubbert-Bass vs five shocks scenario

World Oil Depletion: GBM with three shocks vs five shocks vs four shocks scenarios

Shock 2008 (sim. 1951)

Depletion time 90% : 2017

World Oil Depletion: Diffusion Models, Price Effects, Strategic and Technological Interventions

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