OXFORD INSnTUTE

E N E R G Y ST U D I ES

= FOR-

Uncertainty and Irreversible Investment :

An Empirical Analysis of Development of Oilfields

on the UKCS

Carlo A. Favero M. Hashem Pesaran Sunil Sharma

Oxford Institute for Energy Studies

€E17

1992

UNCERTAINTY AND IRREVERSIBLE INVESTMENT. AN EMPIRICAL ANALYSIS OF DEVELOPMENT

OF OILFIELDS ON THE UKCS'

CARLO A FAVERO Queen Mary College University of London

M. HASHEM PESARAN Cambridge University and University of California, Los Angeles

SUNK SHARMA University of California, h s Angeles

EE 17 OXFORD INSTITUTE FOR ENERGY STUDIES

* This paper is part of a research project sponsored by the Oxford Institute for Energy Studies. We are indebted to Marcus Miller and Robert Bacon for helpful comments and suggestions. Partial financial support from the Isaac Newton Trust of Trinity College is gratefully acknowledged.

The contents of this paper are the author’s sole responsibility.

They do not necessarily represent the views of the Oxford Institute for

Energy Studies or any of its Members.

Copyright 0 1992

Oxford Institute for Energy Studies Registered Charity, No: 286084

All rights mewed. No part of this publication may be reproduced, stored in a retrieval syslem, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, wiihou prior permission of the Oxford Institute for Energy Studies.

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ISBN 0 948061 71 5

CONTENTS

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 . Oil Investment in the North Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

The Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 .

4 . Applying The Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.1 TheData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Concluding Remarks 19

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

TABLES

1. North Sea Oilfields with Annex B Approved 1989. . . . . . . . . . . . . . . . 23

2. Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3. Maximum Likelihood Estimates of Models for Appraisal Duration Under 26 Adaptive Price Expectations with Parameter 8 . . . . . . . . . . . . . . . . . .

4. Maximum Likelihood Estimates of Models for Appraisal Duration Under Rational Price Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

FIGURFS

1. Plot of Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

ABSTRACT

The aim of this paper is to analyse the implications of the theory of irreversible

investment under uncertainty for investment in oilfields on the United Kingdom

Continental Shelf (UKCS). We model the decision to proceed with the

development investment as an optimal stopping problem and apply the established

theory to derive the determinants ofthe optimal policy. Data OH the length of the

time period between discovery and development are available for individual

oiIfields on the UKCS. The theory is empirically examined by exploring the

significance of the determinants of the optimal policy in explaining the variation

in the development lag of individual oilfields. Applying statis ticaI duration

analysis to the North Sea data, we find a strong effect of expected price and

associated price uncertainty on the length of the appraisal stage of the investment

projects.

1 INTRODUCTION

Irreversible investment under uncertainty has recently received a considerable

amount of attention in the theoretical literature [McDonald and Siege1 (19861,

Dixit (1989, 1991), Pindyck (1988, 1989), Ingersoll and Ross (1990)’ Bertola

(1990)]. When an investment decision is costly to reverse and the payoffs are

uncertain, the investment decision involves comparing the value of investing today

with the present value of investing at all possible times in the future. The

investment expenditure involves the cost of ‘exercising the option’ t o invest at any

time in the future and a project is adopted only when the expected payoff exceeds

the cost by an amount equal t o the value of the option. Option pricing techniques

have been used to examine the determinants of irreversible investment under

uncertainty, and show that even risk-neutral firms may be reluctant to invest

when the future is uncertain. Oil investment in the North Sea is an example of

irreversible investment. It involves three separate but highly interrelated

activities: exploration, development of the oilfield, and extraction, We claim that

on the United Kingdom Continental Shelf (IJKCS) the irreversible decision is

made when development is undertaken. In other words, the exploration activity

provides the firm with the option t o invest, whose value is affected by the

uncertainty that surrounds future oil prices.

Theoretical results from the theory of irreversible investment under

uncertainty have already been applied to investment in natural resources

[Brennan and Schwartz (1985)j and also specifically to oil investment Dkern

(19881, Paddock et al. (1988)l. However, despite the great number of theoretical

papers, very little has been done in terms of empirically evaluating this type of

0.I.E .S. 1

investment model. In fact, it is very difficult to derive closed fo rm solutions, even

for extremely simple problems, and the theoretical section of the various papers

is typicalIy completed by simulations rather than by econometric analysis of actual

data [Berg (1991), Bertola (1990), Brennan and Schwartz (1985)l.

The aim of this paper is to bridge this gap by applying the theory of

irreversible investment under uncertainty to explain empirically the lags in the

development of oilfields on the UKCS. We interpret the decision to proceed with

the development investment as determined by an optimal stopping rule.and apply

the established theory to derive the determinants of the optimal policy. Data on

the length of the time period between discovery and development are available for

individual oilfields on the UKCS. The theory is examined by exploring the

significance of the determinants of the optimal stopping rule in explaining the

variation in the development lags of individual oilfields. The application is

implemented by using statis tical duration analysis.

The paper is organized into three sections. The first section provides a brief

description of the process of oil investment in the North Sea, and shows the

applicability of the theory of irreversible iiivestment under uncertainty to this

process. The second section develops a theoretical model and derives the

determinants of the decision to develop an oilfield. In the third section duration

analysis is used to evaluate the importance of the variables suggested by the

theory to explain the lengths of development lags on the UKCS.

2 O.I.E.S.

2 OIL INVESTMENT IN THE NORTH SEA

Consider the case of a firm operating in the North Sea. The investment project

consists of three stages: exploration, development and extraction. Previous work

[Favero and fesaran (1992)] has highlighted the importance of the dynamics of

these processes for explaining the sensitivity of a firm’s decision to economic

factors. I t is argued that once the exploration stage is completed, economic factors

are the main determinants of the development decision. The extraction decision

depends on economic and engineering considerations mainly determined by the

amount of reserves in the ground. These factors generate a typical hump-shaped

profile for extraction that can be detected both at the aggregate level and at the

individual field level (see relevant figures in Favero and Pesaran (1992)).

Development of an oilfield starts after exploration has been successfully

completed and the uncertainty regarding the amount of oil in a particular field has

been resolved. This stage can be divided into an appraisal stage and a technical

development stage. The appraisal stage covers the time span between discovery

and the date of government approval (Annex B), which is needed before a field can

be developed. The technical development stage starts when the Annex B is

granted and ends once the extraction gets under way. During the appraisal stage

the firm does not commit itself to any substantial irreversible investment but

continues drilling in order to evaluate the potential of the discovered field and,

after the appraisal drilling is found to be satisfactory, prepares a project plan in

collaboration with the Department of Energy. When the project plan is formalized

and the Annex B approval is obtained, the firm is committed to an irreversible

investment. In the technical development stage, the optimal development effort

O.I.E.S. 3

and extraction rate are mainly determined by available technology and the

characteristics of the oilfield. Moreover, the Annex B has t o specify the type of

development envisaged, the off-shore loading system, the location of platform, sub-

sea wells, pipelines and terminals, and the maximum and minimum quantity of

oil and gas that will be produced each year. Therefore, the primary contribution

of economic analysis in the examination (of the timing) of the investment process

lies in explaining the duration of the appraisal development lag. In the next

section we use the theory of optimal stopping (of Wiener processes) to model this

lag.

4 O.I.E.S.

3 THE THEORETICAL MODEL

Consider the investment decision of a representative firm that has already

discovered an oilfield: the economic environment is described by a state variable

R, the level of known reserves available for extraction, and the control variable

x, the development effort. At the level of an individual oilfield it is reasonable to

assume that the rate of extraction is not a control variable, due to the presence of

technical constraints and the pressure dynamics of the oilfield, and is a [possibly

nonlinear] function of reserves,

In what follows we assume that the reserve process evolves stochastically

according to the following equation

Equation (1) is a continuous time representation of the stock-flow dynamics of

available reserves, and states that the change in reserves available for extraction

depends on the extraction rate, on the new additions to reserves and on

revisionslextensions of existing reserves.' Extraction is a nonlinear function of

reserves qt = q(R,), new additions t o reserves are functions of the development

effort. The revisions t o the existing level of reserves are a hnction of the real oil

price and make the differential equation stochastic. We model the real oil price

The discrete time analogue of equation 11) is:

where A, the additions to reserves available for production are functions of development effort on past discoveries, extraction q is a nonlinear function of available reserves and U are the revisionslextensions of reserves.

O.I.E.S. 5

p as a standard Wiener process,2 so that E(dp) = 0, and E(dp2) = dt. The noise

parameter 0 is assumed to be uniformly bounded away from zero. The time

horizon of the firm is H. At any T < €3, the firm can go ahead with the

development plan and colIect a payoff G(&,T) given by:

Once the firm has taken the decision to develop a field and has therefore obtained

the Annex B, a lengthy process of technical development is necessary before the

field comes on stream. We assume that this process lasts k periods [see Favero

and Pesaran (199211 and that the discount rate is r. The payoff is the stream of

discounted profits from the oil investment. They are obtained by subtracting from

the gross revenue ps+kq(Rstk), t.he operating cost C(R& the development costs,

w,x,, and the ‘sunk’ exploration costs Co. All the prices and costs are computed

at post-tax values [Favero (1992)l. The operating costs are related t o the Ievel of

available reserves because the cost of extraction depends inversely on the pressure

in the oilfield, which in turn is directly related t o the level of reserves.

Define the value function, starting at time t with an initial state

& = R by V(R,t) = Max E[ G(R,,T) e-r(T-t)] X

(3)

The oil price relevant to the firm’s decision is the real oil price. In empirical work on the North Sea [Pesaran (19901, Favero (19921, Favero and Pesaran (199211, the real oil price is computed by deflating the price of Brent crude with the average quarterly index of export prices of industrial countries compiled by the IMF. The assumption o f a Wiener process for nominal oil prices may not be appropriate because it is possible t o argue that the existence of the OPEC cartel should be reflected in some mean reversion of the series. However, this argument does not have the same force as far as real oil prices are concerned. In fact using the augmented Dickey-Fuller tests we could not reject the hypothesis that there exists a unit root in real oil prices.

6 O.I.E.S.

where E[..] stands for the conditional expectations with respect to the information

at time t. To derive the nature of the optimal stopping rule we compare the two

alternatives: (i) stopping a t once, and (ii) continuing for a small interval of time

dt with the control at level x, and behaving optimally in the future. Stopping

at once delivers a payoff G(R,t). The value of continuing can be approximated by

E[ V(R+dR,t+dt) (1 -r dt)] (4)

where we have ignored terms of higher order than dt. Assuming differentiability

of V at R, and using Ito’s Lemma we get

where Vt(.),VR(.) refer to the partial derivatives of V with respect to t and R,

and V, is the second-order partial derivative of V with respect to R. Note, by

taking the expectations in (4) up to terms in dt, we are implicitly assuming that

the firm is risk-neutral; nevertheless, because of the stochastic nature of the

problem, the payoff of the continuation policy is affected by the variance of the real

oil price. The policy of continuing yields

Using Bellman’s Principle of Optimality we get

where the maximization is performed with respect to the control variable x. The

necessary conditions for optimaiity are:

O.I.E.S. 7

(i) In the interior of any set of values of (R,t) where continuation is optimal, we

(ii) In the interior of any set of values of (R,t) where stopping is optimal, we have

Th se necessary conditions are completed by the 'smooth-pa tin$ requirem nts:

(10)

Such conditions ensure that, for a given critical R*(t) such that stopping is

optimal for R I R* and continuation for R I R", V is differentiable at R* and

tangential to G (see, Malliaris and Brock (1988), Dixit (1990)).

For the value function in (7) we can rewrite equation (8) as

The above expression makes clear that under our assumptions, the theory of

irreversible investment under uncertainty yields three economic determinants of

oil prices, the variance of the

n the oilfield, If the firm starts

the duration of the appraisal lag: expected rea

expected real oil prices and the level of reserves

8 O.I.E.S.

developing a field at time t, the relevant oil prices are the expected oil prices for

time onwards, because we assume that it takes k periods before the

development of the oilfield is completed. The impact of the path of expected oil

prices depends o n the derivative of the extraction function with respect to the level

of reserves and on the variance of the increments of the oil price process. The

effect of the variance of real oil prices on the duration of the appraisal lag is

determined by the form of the operating cost function and the extraction cost

function. Also, the level of reserves in a field plays a role because it affects

operating costs. The next section of the paper is devoted to the investigation of

the empirical relevance of these factors in determining the length of the appraisal

lag.

t+k

O.I.E.S. 9

10 O.I.E.S.

4 APPLYING THE THEORY

In order to empirically evaluate the theory developed in the previous section we

use econometric methods €or analysing the duration of events. Let L denote the

length of the appraisal lag for an oilfield (i.e. the time span between discovery and

Annex B approval), F(t) the distribution of L, S(t)=l-F(t) the survival function, and

fit) the associated density. In sequential decision models it is easier t o think in

terms of the hazard function, h(t)=f(t)/[l-S(t)] (see, Kiefer (1990), Lancaster

(1990)). For small At, h(t).At can be interpreted as the conditional probability that

the event under consideration occurs in the interval [t,t+At) given it has not

occurred till t . We introduce covariates using the Cox (1972) formulation,

factorizing the hazard as

where hJt,a) is the ‘baseline’ hazard function with parameter a, and X is a row-

vector of covariates with associated coefficients p. If the regressors are time-

invariant, pk can be interpreted as the proportional effect of the kth covariate on

the hazard rate of completing the appraisal stage. We estimate p by two different

approaches. First we use the partial likelihood method advocated by Cox (1972)

to estimate p without specifying the form of h&t). Next we consider a Weibull

specification, h(t)=ata-l, for the baseline hazard.

The alternative models are estimated using maximum likelihood procedures

available in SAS, For Cox’s partial likelihood method the p is interpreted as above

while the coefficients for the Weibull regression model can be interpreted as

derivatives of the logarithm of duration with respect to explanatory variables. To

illustrate this further, note that the specification in (12) can be written in the

O.I.E.S. 11

form:

where A represents the integrated hazard and E is an error term with a specified,

though possibly non-normal distribution. For the Weibull specification E has an

extreme value distribution and A,(t)=ta. This leads to the log-linear model

Since the coefficients are estimated in SAS by considering the logarithm of the

duration as the dependent variable, we can interpret the coefficients as (-a) times

the derivative of log duration with respect to the explanatory variables. For

comparing the coefficients from the two methods, those reported for the Weibull

regression model should be multiplied by (-d.

4.1 The Data

The data used in the duration analysis is composed of 53 oilfields under

production on the United Kingdom Continental Shelf in 1989. (Table 1) The main

features of the data are summarized in Table 2. The dependent variable is the

duration of the appraisal lag, defined as the number of months between the

discovery of the oilfield and the granting of the Annex B approval. In our data

there is no right-censoring of this variable and all observations are complete. The

covariates used fall into two categories: (a) economic variables, derived from the

theoretical model developed in the previous section, (b) other variables, mainly

geological variables, included in the analysis to eliminate potential heterogeneity

12 O.I.E.S.

between different fields.3 The economic variables are the size of the fields, two

different measures of expectations (conditional on information available at the

time of Annex B approval) for the real post-tax oil prices' a t the time of

production start-up, and two corresponding measures of the variance of real oil

prices. The size of the oilfields, SIZE, is measured as recoverable reserves in

millions of barrels, estimated by the operators at Annex 8 approval. The first

measure of price expectations, P, is the level of real post-tax oil price at the time

Annex B is obtained. This price is computed under the rational expectations

hypothesis and the assumption that the real post-tax oil price follows a random

walk. The associated measure of variance VARDP, is obtained by considering the

recursive estimates of the standard errors of the regression of (P,-P,.J on a

constant. The regression is performed on quarterly data from 1960:l to the

quarter in which Annex B is obtained. The starting period was chosen to match

the beginning of licensing for exploratory activity on the UKCS. As an alternative

to rational expectations we also considered the adaptive expectations hypothesis.

In fact the results obtained in previous work on the subject Pesaran (1990),

Favero (1992), Favero and Pesaran (1992)l favour the adaptive scheme for the real

oil price expectations formation process. The alternative price expectations

variabIe, Pt(e> is constructed recursively according to the formula

The data sources are severa1 issues ofDeuelopment of Gas and Oil Resources of the United Kingdom published yearly by the Department of Energy. IMF Financial Statistics, Petroleum Economist and the 1991 Companies Book, published by the London Stock Exchange. The derivation of the real oil price series is extensively described in Pesaran (1990).

Favero (1992) provides a discussion of how the post-tax prices are computed.

O.I.E.S. 13

These price expectations are computed using quarterly post-tax real oil prices with

an initial value set equal to the actual value in 1960:l. The value for 8 is chosen

by a grid search procedure and the results are reported in the next section. The

measure for the variance of oil prices associated with Pt(9>, which we denote by

VARPB, is obtained by considering the recursive estimates of the standard errors

of the regression of P, on P,(Q). Again, the regression is based o n quarterly data

from 1960:l to the quarter in which the Annex B is approved. A possible

alternative to o u r historical measure of variance could be an implicit volatility

measure, derived from the theoretical model in Section 3, Given o u r data the

latter measure could not be calculated because it involves the specification and

estimation of the operating cost function and the extraction function for the 53

oilfields in our sample.

The variables that we include in our analysis t o account for potential

heterogeneity across oilfields are WATERD, the depth of the sea expressed in

meters, GASRES, the recoverable gas reserves in billions of cubic feet,

OPERATOR, the equity market value (in 1991 million of pounds) of the operator

of the oilfields. The first two variables were introduced to take account of

geological differences between fields, the third variable is meant to capture

differences in the diversification, and therefore in the cost of waiting, between

small and large oil companies.

4.2 Empirical Results

The estimation results are reported in Tables 3 and 4. We fit proportional hazard

models when the baseline hazard is treated as a nuisance function and left

14 0.I.E .S.

unspecified as in Cox (1972, 19751, and also models in which the baseline is

parameterized as a Weibull. The former approach can be interpreted as a

marginal likelihood of ranks in which only the ranking or ordering of the different

durations is used to estimate the p coefficients (see Cox and Oakes (19841,

Kalbfleisch and Prentice (1980)). The parametric approach utilizes both the

ranking as well as the time differences between durations to jointly estimate the

baseline hazard parameters and the covariate coefficients. The parametric model

will clearly be more efficient if the assumed parametric form of the baseline

hazard is correctly specified. However, under misspecification the estimated

parameters will not be consistent. The advantage of Cox’s (1975) partial likelihood

method is that we obtain consistent estimates of p without having t o commit to

a particular parametric baseline hazard.

Each of the models is estimated under both the adaptive expectations and

the rational expectations hypothesis. The grid search on the adaptive expectations

parameter delivered a value of 0.98, remarkably close t o the 0.96 obtained by

Pesaran (1990) and Favero (1992) using aggregate time-series data. Also in line

with previous research, the adaptive mechanism yields better statistical results

than the rational expectations hypothesis.

Under adaptive expectations the impact of expected prices (with 0=0.98) and

associated uncertainty (measured by the historical measures) on the hazard rate

of appraisal duration is non-linear. The expected prices, P98, increase the hazard

if r2.57 - 1.48 VARP981 is positive. This implies that expected prices have a

positive effect if the associated variance is low [i.e. less than 1.74 (=2.57/1.48)] and

a negative effect if the variance is high. Similarly, VARP98 has a positive impact

O.I.E.S. 15

on the hazard if the expected prices are low [i.e. less than 1.09 (=1.62/1.48)1 and

a negative impact if they are relativeIy high. Such nonlinear effects are

compatible with the economic model discussed in the previous section. In fact the

decision criterion derived in equation (11) includes a term representing the

interaction between the first and second moments of the distribution of prices.6

The variables not suggested by the theoretical model, but included in the

analysis to take care of the possible heterogeneity between oilfields, do not play

an important role in explaining the duration of the appraisal lag. The t-ratios for

GASRES, WATERD and OPERATOR are below one and the hypothesis of their

joint significance is clearly rejected by the likelihood ratio test [which yields a

value 2.74 in the Cox model and 2.28 in the Weibull model, for a chi-square

statistic with 3 degrees of freedom]. Also, note that the scale parameter a for the

Weibull model is approximately 2 and significantly different from 1 [ a = l gives the

exponential distribution]. This implies positive duration dependence for the

hazard, i.e. the conditional probability of starting the irreversible investment in

an oilfield in the small interval [t,t+At), given that this has not occurred before t,

increases in t.

Specification checking is done by graphing ‘generalized residuals’ in the sense

of Cox and Snell (1968). For each oilfield, we define this residual to be the

estimated probability of surviving till time t, where tis the observed appraisal lag.

The PHGLM procedure in SAS tha t was used for estimation reports a statistic, similar to the multiple correlation coeficient in the linear regression model, measuring the predictive ability o f the model. I t is based on Akaike’s information criterion and i s related t o Mallow’s C,. Individual statistics for each covariate akin to partial correlation coefcients are also calculated. For the Cox model (with all covariates) in Table 2 this statistic was 0.353; the individual statistics for P98, VAFtP98 and P98*Vf#P98 were 0.09, 0.11, -0.17 respectively, and those for the other covariates were zero.

16 O.I.E.S.

By the probability integral transformation, the distribution of these generalized

errors is a unit exponential. A plot of the residuals against their empirical

distribution, if the model fits, should approximately give a 45-degree line through

the origin. Figure 1 displays the residual plot for the Cox model (with all

covariates) reported in Table 2. Although such graphical checks are not definitive,

the figure is suggestive that the model fits reasonably well.

O.I.E.S. 17

18 O.I.E.S.

5 CONCLUDING REMARKS

The objective of this paper was t o show that the theory of irreversible investment

under uncertainty can be applied to explain the duration of the appraisal lag in

oil investment. Our results suggest that expected prices and associated

uncertainty are crucial determinants of the decision to go ahead with an

irreversible investment. More specifically, under the adaptive expectations

hypothesis, expected prices increase the hazard rate of undertaking the project

provided that price uncertainty is low. Further, the effect of uncertainty is a

function of the expected price level, and the volatility of prices has a positive

impact on the duration of investment appraisal when prices are low and a

negative impact when prices are high.

O.I.E.S. 19

I

20 O.I.E.S.

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Berg, C. (19911, ‘The Value of Waiting to Invest in Swedish Manufacturing‘, mimeo, University of Stockholm.

BertoIa, G. (19891, ‘Irreversible Investment’, mimeo, Princeton University.

Brennan, M. J. and Schwartz, E. S. (1985), ‘Evaluating natural resources investment’, Journal of Business, 58, 135-57.

Cox, D.R. (1972), ‘Regression models and life tables’, Journul of the Royal Statistical Society, B, 34, 187-220.

Cox, D.R. and Oakes, D. (19841, Analysis of Survival Data, Chapman and Hall, London.

Cox, D.R. and Snell, E.J. (1968), ‘A general definition of residuals’, Journal ofthe Royal Statistical Society, B, 30, 248-275.

Dixit, A. (19891, ‘Entry and exit decisions under uncertainty’, Journal of Political E C O ~ O ~ Y , 97,620-38.

(1990), ‘A Heuristic Derivation of the Conditions for Optimal Stopping of Brownian Motion’, mimeo, Princeton University.

(199 11, ‘Irreversible investment with price ceilings’, Journal of Political Economy, 99,54 1-57.

Ekern, S. (19881, ‘An optioii pricing approach to evaluating petroleum projects’, Energy Economics, 91-99.

Favero, C.A. (1992), ‘Taxation and optimization of oil exploration and production: the U.K. Continental Shelf, Oxford Economic Pupers, forthcoming.

and Pesaran, M.H. (19921, ‘Oil Investment in the North Sea’, mimeo, Cambridge University .

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O.I.E.S. 21

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22 O.I.E.S.

Table I:

North Sea Oilfields with Annex B Approved in 1989’

Recoverable Annex B Production Oil

Oilfields Discovery2 Approval2 Start-up Reserves2

Alwyn North Arbroath Argyll Auk Balmoral Beatrice Beryl Brae South Brae North Brae Cent. Brent Buchan Chanter (Sep) Claymore Clyde Cormorant South Cormorant North Crawford

Deveron Don Duncan Dunlin Eider Emerald Forties Fulmar Gannet Glamis Heather High1 ander Hutton

Cyrus

Aug. 75 Jan. 69 Sep. 71 Feb. 71 Aug. 75 Sep. 76 Sep. 72 Jul. 77 Jun. 75 Mar. 76 Jul. 71 Aug. 74 Sep. 85 May. 74 Jun. 78 Sep. 72 Aug. 74 Jan. 75 Oct. 79 Sep. 72 Jan. 76 Jan. 81 Jul. 73 May 76 Jan. 78 Oct. 70 Nov. 75 Jan. 79 Sep. 82 Dec. 73 Apr. 76 Dec. 73

Oct. 82 Dec. 87 Feb. 73 Feb. 72 Nov. 83 Aug. 78 Jul. 73 Jan. 80 Dec. 83 Mar. 88 Aug. 72 Mar-. 78 Dec. 87 Aug. 75 Dec. 82 May.74 Apr. 79 Sep. 88 Nov. 84 Sep. 84 Mar. 88 Oct. 83 May.74 Oct. 85 Jan. 89 Dec. 71 Jun. 78 Sep. 89 Dec. 87 Aug. 74 Nov. 83 Aug. 80

Nov. 87 Jan. 90 Jun. 75 Dec. 75 Nov. 86 Sep. 81 Jun. 76 Jul. 83 Apr. 88 Dec. 89 Nov. 76 May. 81 Jan. 92 Nov. 77 Mar. 87 Dec. 79 Feb. 82 Apr. 89 Jan. 90 Sep. 84 Oct. 89 Nov. 83 Aug. 78 Nov. 88 Jan. 90 Sep. 75 Feb. 82 Jan. 92 Jul. 89 Oct. 78 Feb. 85 Aug. 84

25.0 13.7 9.7

14.3 10.2 20.7 69.0 40.0 21.0

9.0 241.1

13.0 1.1

70.3 17.7 28.9 54.5

0.5 1.7 2.7 4.2 2.5

50.0 11.5 5.4

332.8 76.0 22.0

2.3 13.6 8.6

27.4

Source: Brown Book. 1

The second, third and fourth colwnns report respectively the discovery date, the annex B date and the production start-up date. The last column reports the size of each field, measured by the operator’s estimate o f initially recoverable reserves (in million of tonnes),

O.I.E.S. 23

Table 1 continued

North Sea Oilfields with Annex B Approved in 1989

Oilfields

Recoverable Annex B Production Oil

Discovery Approval Start-up Reserves

North West Hutton Innes Ivanhor/Rob Roy Kittiwake L M e Magnus Maureen Miller Moira Montrose Ninian Murchison Ness Osprey Petronella Piper Scapa Statfjord Tartan Tern Thistle

Apr. 75 Mar. 83 Jan. 75 Sep. 81

Jul. 74 Feb. 73 Mar. 83 May 88 Nov. 71 Apr. 74 Sep. 75 May 86 Feb. 74 Feb. 75 Jan. 73 Jul. 75 Feb. 74 Dec. 74 Apr. 75 Jul. 72

Aug. aa

Jul. 79 Nov. 84 Jan. 86 Sep. 87 Sep. 89 Dec. 78 Jan. 78 Oct. 88 Sep. 89 Mar. 74 Jun. 74 Sep. 76 May 87 Nov. 88 May 86 Apr. 73 Sep. 85 Sep. 74 Aug. 77 Jan. 85 Jul. 74

Apr. 83 Jan. 85 Jul. 89 Nov. 90 Oct. 89 Aug. 83 Sep. 83 Jan. 92 Jun. 90 Jul. 76 Dec. 78 Sep. 80 Aug. 87 Jan. 91 Dec. 86 Dec. 76 Sep. 85 Nov. 79 Jan. 81 Jun. 89 Feb. 78

16.0 0.8 8.0 9.3 0.1

102.1 28.0 32.0

0.8 13.1

157.0 45.6 6.7 8.3 3.1

126.9 8.6

445.7 14.3 23.8 60.3

24 O.I.E.S.

Table 2:

Summary Statis tics

STD DEV MAX 11 VARIABLES 1 MEAN MIN

DUR

SIZE

WATERD

GASRES

OPERATOR

63.01

328

126.5

178.79

11522

1.54

590

28.06

485.31

7250

3030 0.004

186 76

2500 0

17930 1

1.70

II vARDp I VARP97 I II p97 I

2.97 1.42

0.50

1.52 3 VARP98

5.04

2.28

5.24 I

DUR:

SIZE: WATERD : GASRES: OPERATOR:

55.22 227 1

0.78 I 3.36 0.92

0.76 2.42 0.007

0.45 2.16 0.89

I

0.15

0.89

0.16

duration of the appraisal lag in months (time span between discovery of an oilfield and beginning of development i.e. approval of Annex B) size of recoverable reserves in millions of barrels depth of the sea in meters size of recoverable gas reserves in billions of cubic feet equity market value in 1991 million of pounds of the company operating the oilfield real after-tax oil price measured a t time of Annex B approval historical measures of the variance of the real oil price process adaptive expectations {with parameter 8) for the real after-tax oil prices formed at the time of Annex B approval historical measures of the variance of the adaptive expectations (with parameter 8) for real oil prices

O.I.E.S. 25

Table 3:

Variables

Note:

Cox Models Weibull models

Maximum Likelihood Estimates of Models €or Appraisal Duration Under Adaptive Price Expectations with Parameter 8

SIZE

P98

VARP98

P98*VARP98

0.49 0.42 -0.26 -0.22 (0.36) (0.31) (0.17) (0.14)

(1.18) (1.12) (0.49) (0.47) 2.57 1.90 -0.85 -0.58

1.62 1.25 -0.71 -0.56 (0.67) (0.65) (0.30) (0.30)

-1.48 -1.23 0.64 0.55

a-’

(0.44)

-0.54 (0.56)

CONSTANT

(0,42. ) (0.18) (0.18)

0.23 (0.26)

GASRES

OPERATOR

WATERD

0.17 -0.05 (0.35) (0.17)

-0.22 0.11 (0.23) (0.11)

LOG-LIKELI -133.70 -135.07 -50.76 -51.90

Standard errors are reported in parentheses. Also, to compare the p estimates in the Cox and Weibull models, the estimates in the Weibull model should be mult,iplied by -a, which in the above models is approximately equal t o -2.

26 O.I.E.S.

Table 3 continued:

9

0.3

0.5

LOG- 0 LOG- LIKELIHOOD LIKELIHOOD

- 142.62 0.95 -152.03

-141.93 0.96 -134.24

0.7

0.9

0.93

O.I.E.S.

-142.02 0.97 -133.95

-140.80 0.98 -133.70

-139.15 0.99 -135.62

27

I

Note:

Variables

a-'

CONSTANT

Table 4

Cox Models Weibull models

0.50 0.51 (0.06) (0.06)

(0.85) (0.84) -0.36 -0.07

Maximum Likelihood Estimates of Models for Appraisal Duration Under Rational Price Expectations

SIZE

P

VARDP

P*VARDP

WATERD

GASRES

OPERATOR

LOG-LIKELI

0.52 0.44 -0.30 -0.25 (0.36) (0.31) (0.17) (0.15)

-1.18 -1.19 0.74 0.77 (0.41) (0.40) (0.18) (0.18)

0.03 -0.36 0.30 0.49 (0.901 (0.89) (0.42) (0.41)

(0.16) (0.16) (0.07) (0.07)

-0.53 0.26 (0.57) (0.27)

0.11 -0.02 (0.35) (0.18)

-0.20 0.11 (0.23) (0.11)

-134.75 -135.07 -51.38 -52.55

0.13 0.17 -0.14 -0.16

Standard errors are reported in parentheses. Also, to compare the p estimates in the Cox and Weibull models, the estimates in the Weibull model should be multiplied by -a, which in the above models is approximately equal to -2.

28 O.I.E.S.

FIGURE - 1 PLOT OF RESIDUALS

0.9-

0.8,

0.7,

0.6

0.5

0.4

I .

0 0: 1 0.2 0.3 Re si duals

O.I.E.S. 29

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