Econometric modelling of world oil supplies: terminal price and the time to depletion

• DOI: http://doi.org/10.1111/opec.12012
• Date: 01 June 2013
• Author: Kamiar Mohaddes
• Published date: 01 June 2013

Econometric modelling of world oil

supplies: terminal price and the time

to depletion

Kamiar Mohaddes

Lecturer and Fellow in Economics, Faculty of Economics and Girton College, University of Cambridge,

Cambridge CB3 0JG, UK. Email: km418@cam.ac.uk

Abstract

This paper develops a novel approach bywhich to identify the price of oil at the time of depletion;

the so-called ‘terminal price’ of oil. It is shown that while the terminal price is independent of

both gross domestic product growth and the price elasticity of energy demand, it is dependent on

the world real interest rate and the total lifetime stock of oil resources, as well as on the marginal

extraction and scarcity cost parameters. The theoretical predictions of this model are evaluated

using data on the cost of extraction, cumulative production and provenreser ves.The predicted ter-

minal prices seem sensible for a range of parameters and variables, as illustrated by the sensitivity

analysis. Using the terminal price of oil, we calculate the time to depletion and determine the

extraction and price profiles over the lifetime of the resource. The extraction profiles generated

seem to be in line with the actual production and the predicted prices are generally in line with

those currently observed.

1. Introduction

There are two main strands to the literature on exhaustibleresources, and on the modelling

of oil prices and supplies in particular. In one of these strands, a number of models seek to

explain particular developments in oil prices mainly relying on tools from the industrial

organisation literature to do so. In the other, the focus has been on the application of the

Hotelling model to the oil market. While the former strand aims to model the price and

extraction of oil overtime, its models generally only explain individual events, such as the

first oil shock, and not the evolutionof oil prices over time (for an extensive survey of these

models see Crémer and Salehi-Isfahani, 1991). On the other hand,the Hotelling model and

its extensions develop theoretical models that yield predictions governing the rate of

change of oil prices, but on their own they are not able to determine the level of oil prices

JEL Classifications: C23, Q31, Q47

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and/or the profile of oil production in the world economy. Neither of these two modelling

approaches helps in determining the optimal price of oil at the time of resource exhaustion.

Rather, such terminal prices are assumed a priori, independent of the modelling strategy

under consideration. In addition, most of these models from both strands typically abstract

from the single most important factor determining energy demand, namely the real gross

domestic product (GDP), in their demand specifications.This is an impor tant shortcoming

in a growing world economy where real output is expected to rise over the foreseeable

future.

In this paper, instead of looking at the growthrate of oil prices, see for instance Lin and

Wagner (2007), or assuming what the price level will be at the time of depletion, as in

Khanna (2001), we use a new approach to identify the price of oil at the time of depletion;

referred to as the ‘terminal price’ of oil, P

tT

t

,

∗. We show that the terminal price of oil does

not depend on any of the demand function parameters. Thus the particular demand func-

tion chosen is not relevantfor estimation of P

tT

t

,

∗. In fact it is illustrated that P

tT

t

,

∗net of mar-

ginal extraction cost (a) is only determined by the real interest rate (r) and the estimates of

the total amount of the resource available (TRt) scaled by d, the scarcity coefficient. As

such our framework allows for the possibility of new discoveries or revisions to the total

amount of the resource available,which in turn will lead to an update in the estimate of the

terminal price.

Furthermore, we specify a demand function for total energy and model the demand for

oil as a fraction of this. Our setting allows the share of oil in total energy to decrease as

other energy products increasingly take on more of the share of oil (as has been happening

over the past three decades).Thus, a substitution effect of oil for other energy products is

implicitly present in the model. We also include real output in our demand specification to

capture the outward-shifting energy demand curve.

We use annual data on extraction costs and production from 1975 to 2008 for a

panel of 57 major oil producers to estimate the parameters of the cost function. Using

these estimates and data on cumulative extraction and proven reserves, we estimate

the terminal price of oil. The predicted terminal price seems sensible for a range of

parameters and variables as illustrated by the sensitivity analysis.The terminal price and

estimates of the demand function, obtained using annual data from 1965 to 2009 for a

panel of the 65 largest oil-consuming countries, are used to determine the price and

extraction profiles, as well as the time to depletion (Tt). The predicted prices of the

model are close to the ones recently observed and the extraction profiles generated seem

to be in line with the actual production: they are increasing over time and are in the right

magnitude.

The rest of the paper is set out as follows: Section 2 givesa brief review of the relevant

literature while Section 3 sets up and develops our theoretical model. Section 4 describes

the data and the methodology used to estimate the cost and demand functions, and presents

Econometric modelling of world oil supplies 163

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the estimation results that are used to determine the terminal price. In Section 5 we

describe the methodology used to calculate the time to depletion as well as the predicted

extraction and price profiles of our theoretical model. Finally, Section 6 offers some con-

cluding remarks.

2. Literature review

The two oil shocks in the 1970s generated a great deal of interest in the oil market. In order

to understand and explain the way in whichoil markets behave, a number of models were

developed, mainly using tools from the industrial organisation literature. Some of these

models emphasised the oil market as being non-competitive and the role of the Organisa-

tion of Petroleum Exporting Countries (OPEC) as a price maker.Others assumed OPEC to

have no market power and therefore emphasised the role of perfect competition in the oil

markets.

Within this literature three different types of non-competitive models can be identi-

fied: the first stressed the role of OPEC as a monolithic cartel (Gilbert, 1978; Pindyck,

1978b), the second group only considered a subset of OPEC to be a cartel (Eckbo, 1976;

Hnyilicza and Pindyck, 1976), while the third group perceived there to be a dominant pro-

ducer that held market power (Mabro, 1975; Erickson, 1980; Adelman, 1985).

On the other hand, the competitivemodels can be broken down into four different cat-

egories. These focused on either property rights (Mead, 1979; Johany, 1980; Mabro,

1986), supply shocks (MacAvoy, 1982; Verleger, 1982), exhaustibility and expectations

(Griffin, 1985; Salehi-Isfahani, 1995), and target revenues (Bénard, 1980; Crémer and

Salehi-Isfahani, 1980; Teece, 1982) as reasons for the development of oil prices since the

first oil shock.

However, none of these models can explain the evolution of oil prices or production in

the past (or the future), although they are usually very good at explaining individualevents

such as the first or second oil shock. For instance, while the property rights model does a

fairly good job at explaining the price increases during the first oil shock (1973/74), it does

not explain the price increases in the two subsequent oil shocks (1978/79 and 1990/91).

Similarly, while the target revenue model can partly explain the evolution of oil prices in

certain periods, one can argue that governments do not set production of oil solely on the

basis of balancing their budgets. Moreover,empirical tests of the non-competitive models

show that OPEC can at best be described as a weak cartel with loose coordination among

the member countries, see for instance Gulen (1996) and Salehi-Isfahani (1987). This

result is also more recently supported by Marcel and Mitchell (2006) and Lin (2008)

among others, who argue that while OPEC was a successful cartel in the first fewdecades

after its establishment, the organisation has not been successfully colluding overthe past

two decades.1More importantly, the competitive and non-competitive models do not

Kamiar Mohaddes164

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