J.P. Boone r Energy Economics 23 2001 211᎐226 218
might explain the migration of exploration capital abroad. The following section describes the empirical model used to help answer this question.
3. Empirical model used to estimate the present value of exploration investment
3.1. Methodology Since exploration expenditures are made to yield future cash flows, the value of
the exploration investment is the present value of the future cash flows that exploration yields. This value can be estimated by associating exploration expendi-
tures of a given period with the present value of the future cash flows of reserves discovered in a subsequent year. In particular, I specify the present value of oil and
gas reserves discovered in year t as a function of current and lagged exploration expenditures:
L L
Ž . SM PROD s ␣ q
␣ USEXPL
q ␣
FEXPL q
2
Ý Ý
ᎏ i t
1,k i tyk
2,k i tyk
i t
ks ks
USEXPL is defined as the sum of USDRL and USACQ, while FEXPL is defined as WWDRL q WWACQ-USEXPL. The slope coefficient ␣
measures
1, k
the dollar value of reserves discovered in year t from 1 invested in US exploration during year t y k, and ␣
measures the dollar value of reserves discovered in
2, k
year t from 1 invested in non-US exploration during year t y k. The length of the lag, L, indicates the period of time necessary to complete an exploration project.
The present value of the return earned from the exploration investment is calculated by discounting the slope coefficients at a rate of interest, r, that reflects
the risk of the firm’s exploration activity. So, the present value of 1 invested in US exploration is calculated as
L
␣
1,k
Ž . PVUSEXPL s
3
Ý
k
Ž .
1 q r
ks
and the present value of 1 invested in non-US exploration is calculated as
L
␣
2,k
Ž . PVFEXPL s
. 4
Ý
k
Ž .
1 q r
ks
To help mitigate the multicollinearity problem inherent in estimating the model Ž .
Ž . as specified in 2 , I estimate model 2 as a degree 2 polynomial distributed lag.
This approach, based on the assumption that the distribution of lag coefficients can be approximated as: ␣
s  q  k q  k
2
; and ␣ s ␦ q ␦ k q ␦ k
2
, re-
1, k 1
2 2,k
1 2
U
Ž .
Ž duces the number of parameters that must be estimated from 2
L q 1 to six  ,
. 
,  , ␦ , ␦ ␦ . Thus, I estimate the parameters  ,  ,  , ␦ , ␦ , ␦ and then
1 2
1, 2
1 2
1 2
use these estimated parameters to calculate the value of the lag coefficients ␣ ,
1, k
J.P. Boone r Energy Economics 23 2001 211᎐226 219
␣ . Similarly, the covariance matrix of ␣
, ␣ is obtained from the covariance
2, k 1,k
2,k
Ž .
Ž .
matrix of  ,  ,  , ␦ , ␦ ␦
. See Almon 1965 and Greene 1997 for further
1 2
1, 2
details. Ž .
Since the variables in 2 are undeflated, I control for size-related coefficient bias by including SMOG BOY as a regressor and base statistical inferences on
ᎏ
Ž .
White 1980 heteroskedasticity-consistent covariance matrix. I also control for firm-specific and time-specific fixed-effects by including firm and time dummies.
Thus, the empirical model that I estimate is:
SM PROD s q q SMOG BOY
ᎏ i t
0 i 1t
2 ᎏ
i t
L
2
Ž .
q  q  k q  k
USEXPL
Ý
1 2
i tyk
ks L
2
Ž .
Ž . q
␦ q ␦ k q ␦ k FEXPL
q 5
Ý
1 2
i tyk i t
ks
Ž . Model 5 is estimated by pooling firm-specific cross-sectional observations taken
from the Arthur Andersen Reserve Disclosures Database across the period 1981᎐1996. The length of the lag, L, is based on the lag yielding the best ‘fit’ as
assessed by the model R
2
and the standard errors of the coefficients. The slope coefficients  and ␦ are retained and used to calculate the lag coefficients ␣
,
1, k
␣ , which are then discounted at a 10 rate of interest to yield point estimates of
2, k
PVUSEXPL and PVFEXPL. The discount rate of 10 is chosen to retain consistency with the calculation of SM PROD.
ᎏ
Ž . Ž .
Two additional aspects about model 5 warrant elaboration. First, model 5 constrains dollars invested outside the US to generate identical returns. For
example, 1 invested in Country A is assumed to generate the same return as 1 invested in Country B. This simplifying assumption was necessary because firms
generally do not report to shareholders country-specific information on exploration investment and reserve disclosures. To the extent this assumption is materially
Ž . inaccurate, model 5 is misspecified. Second, exploration technology undoubtedly
has changed across the past 15 years, and this change in technology may well have Ž .
impacted returns on exploration investment. Model 5 attempts to control for the effects of any intertemporal change in technology on returns to exploration
investment by including year dummy variables.
3.2. Results Ž .
Empirical estimates of model 5 and related tests of coefficients are presented in Panels A and B of Table 2, while the lag coefficients calculated from the
estimates in Panel A and related tests of coefficients are summarized in Panels C Ž .
and D. Turning first to Panels A and B, we see that model 5 exhibits generally good fit, with the null hypothesis that  s  s  s ␦ s ␦ s ␦ s 0 strongly
1 2
1 2
Ž
2
. rejected
s 20.71, p s 0.01 , the null hypothesis that  s  s  s 0 re-
1 2
J.P. Boone
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220 Table 2
a
Regression analysis Coefficient
Estimated value Asymptotic t-statistic
Ž .
H :  s 0 or ␦ s 0
i i
Ž . Panel A᎐Estimates of parameters in model 5
UUU
 1.40
2.44
U
 y
0.47 y
1.80
1
 0.04
1.18
2 UUU
␦ 2.08
2.93 ␦
y 0.14
0.46
1
␦ 0.01
0.14
2
Ž . Panel B᎐Linear restriction test of parameters in model 5
Restriction Test statistic
2 UUU
Ž . Restriction 1:  s  s  s ␦ s ␦ s ␦ s 0
6 s 20.71
1 2
1 2
2 U
Ž . Restriction 2:  s  s  s 0
3 s 6.09
1 2
2 UU
Ž . Restriction 3: ␦ s ␦ s ␦ s 0
3 s 9.88
1 2
Coefficient Estimated value
Asymptotic t-statistic Ž
. H :  s 0 or ␦ s 0
i i
Ž . Ž .
Panel C᎐Parameters in model 2 calculated from model 5 estimates
UUU
␣ 1.40
2.44
1,0 UUU
␣ 0.97
2.43
1,1 UU
␣ 0.60
2.02
1,2
␣ 0.31
1.24
1,3
␣ 0.09
0.42
1,4
␣ y
0.06 y
0.36
1,5
␣ y
0.13 y
1.18
1,6
␣ y
0.13 y
0.66
1,7 UUU
␣ 2.08
2.93
2,0 UUU
␣ 1.94
3.14
2,1 UUU
␣ 1.83
3.02
2,2 UUU
␣ 1.72
2.83
2,3 UUU
␣ 1.63
2.71
2,4 UUU
␣ 1.54
2.60
2,5
J.P. Boone
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221 Ž
. Table 2
Continued Restriction
Hypothesis tested Test Statistic
Ž . Panel D᎐Linear restriction tests of parameters in model 2
L
␣
1, k 2
UU
Restriction 4: PVUSEXPL s s
H : 2.89 s 0 s
5.19
Ý
k
Ž . .
1 q 0.10
ks
H : 2.89 0
a
L
␣
2, k 2
UUU
Restriction 5: PVFEXPL s s
H : 10.27 s 0 s
8.92
Ý
k
Ž .
1 q 0.10
ks
H : 10.27 0
a
L
␣
1, k 2
Restriction 6: PVUSEXPL s y
1 s 0 H : 2.89 y 1 s 0
s 2.22
Ý
k
Ž .
1 q 0.01
ks
H : 2.89 y 1 0
a
L
␣
2, k 2
UUU
Restriction 7: PVFEXPL s y
1 s 0 H : 10.27 y 1 s 0
s 7.27
Ý
a k
Ž .
1 q 0.10
ks
H : 10.27 y 1 0
a 2
UUU
Restriction 8: PVUSEXPL s PVFEXPL H : 2.89 s 10.27
s 9.08
H : 2.89 10.27
a a U UU UUU
Ž .
, , ,
denotes significance at the 0.10, 0.05 and 0.01 levels, respectively. All statistical tests based on White’s 1980 heteroskedasticity-consistent covariance matrix.
J.P. Boone r Energy Economics 23 2001 211᎐226 222
Fig. 5. Lag coefficient for US exploration investment.
Ž
2
. jected
s 6.09, P s 0.10 , and the null hypothesis that ␦ s ␦ s ␦ s 0 re-
1 2
Ž
2
. jected s 9.88, P s 0.05 .
Panel C shows that the lag coefficients ␣ are statistically significant for lags 0
1, k
through 2, while the lag coefficients a are statistically significant for lags 0
2, k
through 7. Figs. 5 and 6 graphically depict the estimated slope coefficients ␣ and
1, k
␣ , revealing that both ␣
and ␣ decline monotonically through lag 7. The
2, k 1,k
2,k
slope coefficients ␣ when discounted at 10 yields an estimated value of
1, k
PVUSEXPl of 2.89, which is statistically distinguishable from zero at the 0.05 Ž
. level of significance Panel D, restriction 4 . Similarly, the slope coefficients ␣
2, k
when discounted at 10 yield an estimated value of PVFEXPL of 10.27 which is Ž
statistically distinguishable from zero at the 0.01 level of significance Panel D, .
Restriction 5 . Restriction tests 6 and 7 evaluate whether exploration is a positive net present
Ž .
value project that is, whether PVUSEXPL y 1 0 and PVFEXPL y 1 0 . Restriction 6 is unable to reject the null hypothesis that PVUSEXPL y 1 s 0
while, in contrast, restriction 7 is able to reject the null hypothesis that PVFEXPL y
1 s 0. Thus, restriction 7 indicates that investment in non-US exploration is a positive net present value project, but restriction 6 is unable to reject the null
hypothesis that US exploration investment is not a positive net present value project.
Restriction 8, a test of the null hypothesis that a dollar invested in US ex-
J.P. Boone r Energy Economics 23 2001 211᎐226 223
Fig. 6. Lag coefficient for non-US exploration investment.
ploration yields the same present value return as a dollar invested in non-US exploration, is rejected, thus indicating that non-US exploration investment yields a
greater present value return than investment in US exploration. Overall, the results reported in Table 2 provide evidence suggesting that non-US
exploration is a higher positive net present value project than is US exploration, implying the possibility that exploration capital has migrated abroad in search of
higher returns on investment. An alternative explanation, however, is that the higher net present value of non-US exploration investment represents a risk
premium to compensate firms for accepting the additional risk associated with non-US exploration, and thus, risk-adjusted returns to non-US exploration are the
Ž .
same as or perhaps even less than US exploration. To probe the plausibility of this alternative explanation, I compare the mean lag for US exploration investment
to the mean lag for non-US exploration. The mean lag is an approximate measure of the number of years that it takes for one-half of the benefits from the
investment to be realized. Under the assumption that investments that pay off
Ž sooner rather than later are in some sense less risky, the exploration province US
. or non-US with the greater mean lag will be interpreted as ‘riskier.’ The mean lag
of the jth exploration province is defined as
L
Ž . mean lag s
kw 6
Ý
j jk
ks
J.P. Boone r Energy Economics 23 2001 211᎐226 224
where ␣
jk
Ž . w s
7
jk
L
␣
Ý
jk
ks
The mean lag for US exploration investment is 0.48 years, while the mean lag for non-US exploration investment is 3.2 years. Fig. 7, which plots the cumulative
proportion of benefits received from exploration investment as a function of time, provides an intuitive interpretation of these mean lags. As Fig. 7 shows, approxi-
mately 50 of the reserves yielded by a 1 investment in US exploration have been discovered within approximately 1 year after the investment, while it takes between
3 and 4 years to discover 50 of the reserves yielded by a 1 investment in non-US exploration. Thus, the mean lag as a measure of exploration risk indicates that
non-US exploration investment is riskier than US exploration investment. In turn, this suggests that at least some of the excess net present value earned on non-US
exploration investment represents a premium to compensate for the heightened risk associated with non-US exploration. Unfortunately, the research design does
not permit one unambiguously to infer whether all of the excess net present value
Ž earned on non-US investment represents risk premium implying that the risk-
adjusted returns to US exploration investment and non-US exploration investment .
are the same , or whether only a portion of the excess net present value earned on Ž
non-US investment represents risk premium implying that the risk-adjusted re- turns to non-US exploration investment exceed those earned on US exploration
. investment .
Fig. 7. Cumulative reserve discoveries as proportion of total reserves discovered.
J.P. Boone r Energy Economics 23 2001 211᎐226 225
4. Concluding comments
