Boynton et al. Journal of Energy Finance and Development 4 1999 1–27 9
Table 2 Test of Coefficient Restrictions
F statistic p value
Test SCALE8992: Joint test that the coefficients on LNEXP, LNDEV, LNOUT, LAGEXP and LAGDEV sum to 1; that the coefficients on LNEXP91,
LNDEV91, LNOUT91, LAGEXP91 and LAGDEV91 sum to 0; that the coefficients on LNEXP90, LNDEV90, LNOUT90, LAGEXP90 and
LAGDEV90 sum to 0; and that the coefficients on LNEXP89, LNDEV89, LNOUT89, LAGEXP89 and LAGDEV89 sum to 0.
1.09 .36
Test EXP: Joint test that the coefficients on LNEXP89, LNEXP90, LNEXP91 are all 0.
3.03 .03
Test DEV: Joint test that the coefficients on LNDEV89, LNDEV90, LNDEV91 are all 0.
1.15 .33
Test OUT: Joint test that the coefficients on LNOUT89, LNOUT90, LNOUT91 are all 0.
1.72 .16
tions for the 119-firm sample for the regression. The R
2
value of .91 adjusted R
2
value of .87 suggests that the model captures much of the complexity of the exploration process. The model explains approximately 91 of the variation in LNADD, the
natural logarithm of the additions and extension to proved reserves. Table 2 presents tests of various restrictions on the estimation of the Cobb-Douglas
regression. One cannot reject at normal levels of statistical significance the restriction that the sum of the beta slope coefficients for each year equals 1, suggesting that
there are constant returns to scale Kmenta, 1986, pp. 412–422. Test SCALE8992 has a p 5 .36 . .10. One can reject the restriction that the coefficients on LNEXP
in each year, 1989–1992, are equal, suggesting that in one year a significant difference occurs in the coefficient on LNEXP and is allowed in the model by the use of year-
specific bs slopes. Test EXP has a p 5 .03 , .05. However, one cannot reject at normal levels of statistical significance the restriction that the estimated coefficients
on LNDEV in each year are equal. Test DEV has a p 5 .33 . .10. The same is true for the estimated coefficients on LNOUT. Test OUT has a p 5 .16 . .10.
Table 3 presents the Cobb-Douglas regression derived index of exploration effi- ciency EFF for each of the 119 firms in our sample ranked on EFF. The measure
EFF for each firm is the estimate of the firm-specific multiplier for each firm divided by the largest such estimated multiplier.
11
The measure EFF for a firm is a single value for 1989–1992 and represents the average efficiency of a firm during the 4-year
estimation period compared to the average efficiency of the firm that was most efficient. By construction, higher rank on EFF is a sign of exploration efficiency relative to
lower rank on EFF. In section 3, we compare rank on EFF with rank on each of four finding costs ratios and rank on each of two operating profit ratios.
3. Descriptive statistics for sample of 119 publicly owned oil and gas firms for 1990–1992
Table 4 A presents descriptive statistics for 18 data items for our sample of 119 oil and gas firms for the three years, 1990–1992. Table 4, B and C, presents the descriptive
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Boynton et
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1–27 Table 3
Exploration Efficiency Index EFF for 119 Oil and Gas Firms for 1989–1992 Rank Name
Symbol EFF
Rank Name Symbol
EFF 1
Alexander Energy Corp AEOK
1.00000 31
Barnwell Industries BRN
0.42459 2
Washington Energy Co. WEG
0.92696 32
Phillips Petroleum Co. P
0.41382 3
Barrett Resources Corp. BARC
0.89308 33
National Fuel Gas Co. NFG
0.40788 4
The Phoenix Resource Companies, Inc. PHNI 0.87786
34 Kerr-McGee Corp.
KMG 0.40097
5 Brown Tom, Inc.
TMBR 0.85837
35 Maxus Energy Corp.
MXS 0.37695
6 Garnet Resources Corp.
GARN 0.83043
36 Union Pacific Corp.
UNP 0.37253
7 Sage Energy Co.
6041C 0.83031
37 Unit Corp.
UNT 0.37222
8 Southwestern Energy Co.
SWN 0.82081
38 Edisto Resources Corp.
EDS 0.35675
9 Burlington Resources, Inc.
BR 0.81865
39 Noble Affiliates, Inc.
NBL 0.35392
10 Swift Energy Co.
SFY 0.81599
40 Columbia Gas System
CG 0.35330
11 Energen Corp.
EGN 0.76212
41 Consolidated Natural Gas Co.
CNG 0.35111
12 Cabot Corp.
CBT 0.75797
42 Apache Corp.
APA 0.34999
13 American National Petroleum
ANPC 0.68602
43 Nicor, Inc.
GAS 0.34841
14 Nahama Weagant Energy Co.
NAWE 0.68435
44 Sonat, Inc.
SNT 0.34648
15 Tesoro Petroleum Corp.
TSO 0.64229
45 Societe National Elf Aquitaine
ELF 0.34209
16 Hallwood Energy Corp.
HEP 0.62813
46 Primeenergy Corp.
PNRG 0.33986
17 KCS Energy, Inc.
KCSE 0.59825
47 North Canadian Oils, Ltd.
NCD 0.33873
18 Mitchell Energy Development
MND 0.56897
48 Helmerich Payne
HP 0.32884
19 CMS Energy Corp.
CMS 0.56859
49 Oneok, Inc.
OKE 0.32434
20 Presidio Oil Company
PRS.B 0.56369
50 Prairie Oil Royalties Co., Ltd.
POY 0.32210
21 Unocal Corp.
UCL 0.55532
51 American Exploration Co.
AX 0.32169
22 Questar Corp.
STR 0.55394
52 Canadian Occidental Petroleum
CXY 0.32090
23 New London, Inc.
NLON 0.49489
53 Wiser Oil Co.
WISE 0.31890
24 Oryx Energy Co.
ORX 0.46870
54 Snyder Oil Corp.
SNY 0.31853
25 Montana Power Co.
MTP 0.45498
55 Mesa, Inc.
MXP 0.31793
26 Triton Energy Corp.
OIL 0.45251
56 Ashland Oil, Inc.
ASH 0.31407
27 Coastal Corp.
CGP 0.43367
57 Bellwether Exploration Co.
BELW 0.30875
28 Basic Earth Science Systems
3BSIC 0.43242
58 Royal DutchShell GRP Comb.
RDSC.CM 0.29707
29 Enron Oil Gas Co.
EOG 0.42855
59 Equitable Resources, Inc.
EQT 0.29583
30 Pogo Producing Co.
PPP 0.42508
60 Norcen Energy Resources
NCN 0.29375
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11 Table 3 continued
Rank Name Symbol
EFF Rank Name
Symbol EFF
61 USX Corporation
MROX.CM 0.29095
91 Ranger Oil, Ltd.
RGO 0.19019
62 Atlantic Richfield Co.
ARC 0.28984
92 Amoco Corp.
AN 0.18496
63 Bow Valley Industries, Ltd.
OBVI 0.27717
93 Numac Oil Gas, Ltd.
NMC 0.18303
64 Anadarko Petroleum Corp.
APC 0.27217
94 Devon Energy Corp.
DVN 0.18143
65 Enserch Corp.
ENS 0.26874
95 Convest Energy Partners-LP
COV 0.17948
66 Wainoco Oil Corp.
WOL 0.26385
96 Patrick Petroleum Co.
PPC 0.17302
67 Box Energy Corp.
BOXXA 0.26177
97 Mobil Corp.
MOB 0.17030
68 Seagull Energy Corp.
SGO 0.25807
98 Exxon Corp.
XON 0.16911
69 Murphy Oil Corp.
MUR 0.25759
99 Maynard Oil Co.
MOIL 0.16332
70 BHP Broken Kill Proprietary
BHP 0.25632
100 Du Pont E.I.-Conoco, Ltd.
DD 0.16139
71 Fina, Inc.
FI 0.25276
101 Gulf Canada Resources, Ltd.-ORD
GOU 0.15659
72 Dekalb Energy Co., -CL B
ENRGB 0.25008
102 Chevron Corp.
CHV 0.15193
73 British Petroleum PLC-ADR
BP 0.24863
103 Howell Corp.
HWL 0.14846
74 Wilshire Oil of Texas
WOC 0.24604
104 Plains Resources, Inc.
PLX 0.14026
75 Home Oil Company, Ltd.
HO 0.24085
105 British Gas
BRG 0.13826
76 Penn Virginia Corp.
PVIR 0.23664
106 Repsol, S.A.
REP 0.13396
77 Total
TOT 0.23192
107 Equity Oil Co.
EQTY 0.13218
78 Sceptre Resources, Ltd.
SRL 0.23123
108 Sun Co., Inc.
SUN 0.12979
79 MDU Resources Group, Inc.
MDU 0.22787
109 Amerada Hess Corp.
AHC 0.12931
80 Crystal Oil Co.
COR 0.22422
110 Brock Exploration Corp.
BKE 0.12758
81 Global Natural Resources
GNR 0.22204
111 Santa Fe Energy Resources
SFR 0.12055
82 McFarland Energy, Inc.
MCFE 0.22124
112 Allegheny Western Energy
ALGH 0.10401
83 Louisiana Land Exploration
LLX 0.22002
113 Vintage Petroleum, Inc.
VPI 0.07687
84 Pennzoil Co.
PZL 0.21823
114 Hondo Oil Gas Co.
HOG 0.07574
85 Canadian Pacific, Ltd.
CP 0.21755
115 Hadson Energy Resources Corp.
HERC 0.07085
86 Occidental Petroleum Corp.
OXY 0.21479
116 Forest Oil Corp.
FOIL 0.06588
87 Texaco, Inc.
TX 0.21024
117 Resource America, Inc.
REXID 0.04697
88 Plains Petroleum Corp.
PLP 0.19496
118 Union Texas Petroleum Holdings, Inc. UTH
0.02497 89
Coho Resources, Inc. COHO
0.19178 119
Beard Oil Co. BOC
0.01570 90
Exploration Company of Louisiana XCL 0.19102
12 Boynton et al. Journal of Energy Finance and Development 4 1999 1–27
statistics for the 53 full cost firms and the 65 successful efforts firms, respectively.
12
The 18 data items are: 1. ADD 5 SFAS 69 additions and extensions to proved reserves in thousands of
BOE converting 6 mcf of natural gas to 1 BOE. 2. EXP 5 SFAS 69 exploration expenditures in thousands of dollars.
3. DEV 5 SFAS 69 development expenditures in thousands of dollars. 4. OUT 5 SFAS 69 oil and gas production in thousand of dollars.
5. EFF 5 the Cobb-Douglas regression derived index of exploration efficiency. 6. FC1 5 exploration expenditures worldwide for year t thousands of dollars
divided by oil and gas additions and extensions to proved reserves worldwide for year t thousands of BOE.
7. FC3 5 total exploration expenditures worldwide for three years, years t, t 2 1, and t 2 2 thousands of dollars divided by total oil and gas additions and
extensions to proved reserves worldwide for years t, t 2 1, and t 2 2 thousands of BOE.
8. FC1D 5 total of exploration expenditures and development expenditures world- wide for year t thousands of dollars divided by oil and gas additions and
extensions to proved reserves worldwide for year t thousands of BOE. 9. FC3D 5 total of exploration expenditures and development expenditures world-
wide for three years, years t, t 2 1, t 2 2 thousands of dollars divided by total oil and gas additions and extensions to proved reserves worldwide for years t,
t 2 1, t 2 2 thousands of BOE.
10. ROS 5 total net income from oil and gas operations worldwide for year t thousands of dollars divided by total oil and gas revenues worldwide for year
t thousands of dollars.
11. ROA 5 total net income from oil and gas operations worldwide for year t thousands of dollars divided by total oil and gas assets “capitalized costs”
worldwide for year t thousands of dollars. 12. SDDA1 5 total of oil and gas DDA depreciation, depletion, and amortization
and exploration expense worldwide for year t thousands of dollars divided by total oil and gas revenues worldwide for year t thousands of dollars.
13
13. SDDA2 5 total oil and gas DDA and exploration expense worldwide for year t
thousands of dollars divided by total oil and gas assets “capitalized costs” worldwide for year t thousands of dollars.
13
14. WWTOTREV 5 total oil and gas revenues worldwide for year t thousands of dollars.
15. WWNETCST 5 total oil and gas assets “capitalized costs” worldwide for year t thousands of dollars.
16. WWRESPFT 5 total net income from oil and gas operations worldwide for year t thousands of dollars.
17. WWDEPDEP 5 total of oil and gas DDA depreciation, depletion, and amorti- zation worldwide for year t thousands of dollars.
18. WWEXPEXP 5 total oil and gas exploration expense worldwide for year t thousands of dollars.
Boynton et al. Journal of Energy Finance and Development 4 1999 1–27 13
Table 4 A indicates that the mean median oil and gas annual revenues WWTO- TREV for the 119 firms for the three years 1990–1992 was 989.9 million 77.4
million. Table 4, B and C, indicates that the mean median for the 53 full-costs firms was 93.5 million 43.4 million and for the 65 successful efforts firms was 1.705
billion 306.1 million. The largest 1-year revenues for a full cost firm was 690.2 million and 18.9 billion for a successful efforts firm. Mean median oil and gas assets
capitalized costs WWNETCST for the 119 firms was 2.0 billion 256.9 million, 390.1 million 136.5 million for the 53 full cost firms, and 3.3 billion 766.6
million for the 65 successful efforts firms. Mean median exploration expenditures EXP for the 119 firms was 110.5 million 11.0 million, 18.2 million 6.6 million
for the 53 full cost firms, and 184.6 million 31.8 million for the 65 successful efforts firms. Mean median development expenditures DEV for the 119 firms was 230.4
million 22.7 million, 25.9 million 10.2 million for the 53 full cost firms, and 392.7 million 56.4 million for the 65 successful efforts firms.
Turning to performance measures, the mean median EFF for the 119 firms was .35 .29, .40 .34 for the 53 full cost firms, and .30 .26 for the 65 successful efforts
firms. The mean median ROS for the 119 firms was 12.8 16.7, 12.4 21.8 for the 53 full cost firms, and 13.0 13.9 for the 65 successful efforts firms. The
mean median ROA for the 119 firms was 7.3 6.1, 5.7 5.8 for the 53 full cost firms, and 8.7 6.5 for the 65 successful efforts firms.
3.1. Spearman rank correlations between the four finding costs ratios and EFF Table 5 A presents Spearman rank correlation coefficients between each of the 9
ratios EFF, FC1, FC3, FC1D, FC3D, ROS, ROA, SDDA1, SDDA2, and Table 5, B and C, presents the correlations for the 53 full cost firms and the 65 successful
efforts firms, respectively. As expected, rank on each of the finding costs ratios, FC1, FC3, FC1D, and FC3D,
is negatively correlated with rank on EFF. The rank correlations for the sample of 119 oil and gas firms are 2.61, 2.66, 2.66, and 2.81, respectively see Table 5 A,
row 1, columns 2, 3, 4, and 5. The rank correlations for the 53 full cost firms are 2
.48, 2.53, 2.57, and 2.78 Table 5 B. The rank correlations for the 65 successful efforts firms are 2.70, 2.74, 2.70, and 2.83 Table 5 C. All of the rank correlations
are significantly different from zero p 5 .0001. By construction, higher rank on EFF is a sign of exploration efficiency relative to lower rank on EFF. The strong negative
rank correlations that we find suggest that firms that rank low on finding costs ratios rank high on EFF, and firms that rank high on finding costs ratios rank low on EFF.
The observed correlations between finding costs ratios and EFF are consistent with finding costs ratios functioning as a measure of exploration efficiency. In section 3.4,
we will use rank regression to test if the four estimated rank correlation for the 119 firms are in fact different from each other in a statistically significant sense.
3.2. Spearman rank correlations between the four finding costs ratios and ROS and ROA As expected, rank on each of the finding costs ratios, FC1, FC3, FC1D, and FC3D,
is negatively correlated with rank on the operating profit ratio ROS. The rank correla-
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Boynton et
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1–27 Table 4
Descriptive Statistics for SFAS 69 Data Variable
N Mean
Std. Dev. Median
Minimum Maximum
A. 119 oil and gas firms for 1990–1992 ADD
357 39303
94305 4885.000000
1.666667 864833
EXP 357
110524 251307
11000 5.000000
1559370 DEV
357 230385
581401 22737
102.000000 4023210
OUT 357
62351 159966
6147.833333 80.333333
1134833 EFF
357 0.345377
0.219230 0.293752
0.015700 1.000000
FC1 357
9.241122 66.880183
2.769773 0.034414
1227.272727 FC3
357 3.388785
4.576513 2.518210
0.209560 68.238806
FC1D 357
32.026693 269.064689
7.908745 0.612497
5030.303030 FC3D
357 9.344196
13.783221 6.699927
1.374082 223.714286
ROS 356
0.127645 0.270596
0.167005 2
2.074211 0.634936
ROA 357
0.073463 0.169093
0.061326 2
0.750000 1.638618
SDDA1 356
0.461091 0.305978
0.394080 0.044624
2.704104 SDDA2
357 0.274128
1.927235 0.148421
36.536437 WWOTREV
357 989881
2644562 77363
18908910 WWNETCST
357 2005365
4931287 256903
494.000000 31619000
WWRESPFT 357
151524 437926
13569 2
363000 3127000
WWDEPDEP 357
241060 557769
36334 3610000
WWEXPEXP 357
85387 211191
1289.000000 1392990
B. 53 full cost oil and gas firms for 1990–1992 ADD
159 6909.665618
9557.865634 3084.333333
12.166667 61592
EXP 159
18159 28850
6605.000000 5.000000
182700 DEV
159 25931
35573 100226
102.000000 185600
OUT 159
7636.363732 10287
3050.333333 80.333333
56185 EFF
159 0.397588
0.235002 0.338734
0.065882 1.000000
FC1 159
3.837322 4.390481
2.303009 0.034414
28.916767 FC3
159 2.803540
2.141749 2.239956
0.209560 11.668363
FC1D 159
15.418123 34.589801
6.286123 0.876200
264.532110 FC3D
159 7.593945
7.220574 5.893351
1.692939 61.560582
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15 Table 4 continued
Variable N
Mean Std. Dev.
Median Minimum
Maximum ROS
158 0.123728
0.349298 0.217909
2 2.074211
0.434148 ROA
159 0.056923
0.122187 0.057511
2 0.339920
0.742964 SDDA1
158 0.491089
0.398573 0.388859
0.044624 2.704104
SDDA2 159
0.133280 0.089729
0.108068 0.549147
WWOTREV 159
93455 124433
43392 690200
WWNETCST 159
390076 560956
136500 1807.000000
2883800 WWRESPFT
159 12953
39627 7663.000000
2 218900
234300 WWDEPDEP
159 45072
62413 18160
382100 WWEXPEXP
159 214.465409
1557.214182 12200
C. 65 Successful efforts oil and gas firms for 1990–1992
ADD 195
64499 120661
10968 1.666667
864833 EXP
195 184575
320304 31800
48.000000 1559370
DEV 195
392694 746417
56437 128.000000
4023210 OUT
195 106015
206016 20685
196.666667 1134833
EFF 195
0.304175 0.197875
0.258065 0.015700
0.877856 FC1
195 13.755537
90.261925 3.080717
0.070606 1227.272727
FC3 195
3.882917 5.843175
2.790990 0.333482
68.238806 FC1D
195 45.935088
362.555014 8.990383
0.612497 5030.303030
FC3D 195
10.784560 17.360293
7.906503 1.374082
223.714286 ROS
195 0.130122
0.187587 0.138893
2 0.821050
0.634936 ROA
195 0.086658
0.199735 0.064756
2 0.750000
1.638618 SDDA1
195 0.439605
0.202527 0.406644
0.071078 1.628491
SDDA2 195
0.390977 2.603652
0.180544 0.064443
36.536437 WWOTREV
195 1704649
3410120 306053
3182.000000 18908910
WWNETCST 195
3292641 6364926
766633 494.000000
31619000 WWRESPFT
195 261446
567464 39891
2 363000
3127000 WWDEPDEP
195 397934
714796 103300
766.000000 3160000
WWEXPEXP 195
154317 266600
22000 9.000000
1392990
16 Boynton et al. Journal of Energy Finance and Development 4 1999 1–27
Table 5 Spearman Rank-Order Correlation Analysis for EFF with Finding Costs and Profitability 1990–1992
EFF FC1
FC3 FC1D
FC3D ROS
ROA SDDA1 SDDA2
A. All 119 firms EFF
1.00 2.61 2.66 2.66 2.81 .24
.10 2.06 2.21 FC1
1.00 .77
.81 .65 2.32 2.20
.18 .24
FC3 1.00
.54 .78 2.38 2.22
.19 .30
FC1D 1.00
.73 2.23 2.13 .11
.18 FC3D
1.00 2.27 2.10 .09
.27 ROS
1.00 .78 2.63 2.51
ROA 1.00 2.75 2.04 NS
SDDA1 1.00
.35 SDDA2
1.00 B. Full cost firms only
53 firms EFF
1.00 2.48 2.53 2.57 2.78 .21
.17 2.20 2.18 FC1
1.00 .73
.77 .59 2.27 2.28
.25 .08 NS
FC3 1.00
.43 .72 2.36 2.35
.36 .13
FC1D 1.00
.66 2.16 2
.15 .13 NS
.05 NS FC3D
1.00 2.26 2.21 .25
.20 ROS
1.00 .90 2.74 2.41
ROA 1.00 2.77 2.17
SDDA1 1.00
.51 SDDA2
1.00 C. Successful efforts firms only
65 firms EFF
1.00 2.70 2.74 2.70 2.83 .19
.09 NS .06 NS 2.03 NS
FC1 1.00
.80 .85
.70 2.29 2.15 .11 NS
.27 FC3
1.00 .61
.83 2.35 2.15 .05 NS
.34 FC1D
1.00 .76 2.29 2.14
.08 NS .10 NS
FC3D 1.00 2.21 2.08 NS 2.05 NS
.13 ROS
1.00 .82 2.57 2.29
ROA 1.00 2.74
.08 NS SDDA1
1.00 .20
SDDA2 1.00
, , denote the significance levels of .10, .05, and .01, respectively, obtained in a 2-tailed test of the null hypothesis that the estimated parameter equals zero. NS denotes not significant.
tions for the sample of 119 oil and gas firms are 2.32, 2.38, 2.23, and 2.27, respectively Table 5 A, column 6, rows 2, 3, 4, and 5. The rank correlations for the 53 full cost
firms are 2.27, 2.36, 2.16, and 2.26 Table 5 B. The rank correlations for the 65 successful efforts firms are 2.29, 2.35, 2.19, and 2.21 Table 5 C. All of the rank
correlations are significantly different from zero generally p 5 .01 or better except for FC1D for full cost firms at p 5 .05. By inspection, the negative rank correlations
with ROS are only about one half the magnitude of the negative rank correlations with EFF. The observed correlations between finding costs ratios and ROS are consis-
tent with finding costs ratios functioning as an indicator of potential profitability. In
Boynton et al. Journal of Energy Finance and Development 4 1999 1–27 17
section 3.5, we will use rank regression to test if the four estimated rank correlations for the 119 firms are in fact different from each other in a statistically significant sense.
As expected, rank on each of the finding costs ratios, FC1, FC3, FC1D, and FC3D, is negatively correlated with rank on the operating profit ratio ROA. The rank correla-
tions for the sample of 119 oil and gas firms are 2.20, 2.22, 2.13, and 2.10, respectively Table 5 A, column 6, rows 2, 3, 4, and 5. The rank correlations for the 53 full cost
firms are 2.28, 2.35, 2.15, and 2.21 Table 5 B. The rank correlations for the 65 successful efforts firms are 2.15, 2.15, 2.14, and 2.08 Table 5 C. For the 53 full
cost firms, the rank correlations for ROS and for ROA are similar, but for the 65 successful efforts firms, and therefore for the full 119 firms, the negative rank correla-
tion on ROA is weaker than for ROS. The observed correlations between finding costs ratios and ROA are consistent with finding costs ratios functioning as an indicator
of potential profitability. In section 3.5, we will use rank regression to test if the four estimated rank correlations for the 119 firms are in fact different from each other in
a statistically significant sense.
3.3. Spearman rank correlations between each of ROS and ROA and EFF As expected, rank on each of the operating profit ratios, ROS and ROA, is positively
correlated with rank on EFF. The rank correlations for the sample of 119 oil and gas firms are .24 and .10, respectively Table 5 A, row 1, columns 6 and 7. The rank
correlations for the 53 full cost firms are .21 and .17 Table 5 B. The rank correlations for the 65 successful efforts firms are .19 and .09 Table 5 C. All of the rank correlations
for ROS are significantly different from zero at p 5 .01 or better. The rank correlation for ROA is significantly different from zero for the 53 full cost firms p 5 .04 but
not for the successful efforts firms p 5 .20 and only marginally significant for the 119 firm sample p 5 .07. The result for ROS and for ROA for full cost firms is
consistent with profitability depending, in part, on exploration efficiency.
3.4. Rank regression results comparing finding costs ratios FC1, FC3, FC1D, and FC3D to EFF
We wish to compare the association between finding costs ratios FC1, FC3, FC1D, and FC3D and EFF in such a way as to determine if the association is stronger or
weaker for any of the four finding costs ratios in a statistically significant sense. The four estimated rank correlations between finding costs ratios FC1, FC3, FC1D, and
FC3D and EFF presented in section 3.1 Table 5 A, row 1, columns 2, 3, 4, and 5 do appear to differ some 2.61 for FC1, 2.66 for FC3, 2.66 for FC1D, and 2.81 for
FC3D. A test of statistical difference between any two correlations is possible using a transformation of the paired correlations to a z score followed by a t test.
14
We wish to compare all four correlations jointly. Use of multiple t tests to test the four correla-
tions two at a time may lead to an error in estimating the statistical significance level of the tests and may lead to finding a difference in the correlations when none exists
at the level desired. In regression it is possible to construct tests that impose restrictions on two or more variables at once and to test the restriction with an F test Kmenta,
18 Boynton et al. Journal of Energy Finance and Development 4 1999 1–27
Table 6 Rank Regression Analysis of Association between EFF, Profitability, and Finding Costs
Dependent variable
Intercept FC1
FC3 FC1D
FC3D R
2
EFF .808
2 .615
33.505 214.695
.379 EFF
.831 2
.662 36.173
216.577 .437
EFF .833
2 .665
36.458 216.769
.443 EFF
.908 2
.816 51.245
226.500 .665
ROS .649
2 .298
22.222 25.871
.089 ROS
.687 2
.374 24.191
27.577 .140
ROS .601
2 .202
20.070 23.890
.041 ROS
.632 2
.264 21.424
25.155 .070
ROA .592
2 .181
19.695 23.473
.033 ROA
.606 2
.210 20.285
24.051 .044
ROA .553
2 .103
18.191 21.960
.011 ROA
.547 2
.092 17.980
21.736 .008
, , denote the significance levels of .10, .05, and .01, respectively, obtained in a 2-tailed test of the null hypothesis that the estimated parameter equals zero; t statistics in parentheses.
1986, pp. 412–422. We use regression to test the restriction that the estimated associa- tion with EFF is the same for all four finding costs ratios.
The regressions are rank regressions. The original value of the variables in an observa- tion has been replaced by the rank of that value in the sample divided by n 1 1 for a
sample of size n. The transformed values for each variable range from 1n 1 1 to n
n 1 1. Each variable after transformation has a uniform distribution on the zero- one interval with mean 12 and variance 112 for large n and subject to rounding
errors. The fact that the transformed variables in the rank regressions have equal means and equal variances is important. In a simple regression of one variable, Y,
on another, X, if the two variables have equal variances then the b slope coefficient on X will be equal to the correlation coefficient between X and Y.
15
If the two variables have the same mean, the regression intercept will be that mean time 1 minus the
estimated b. Finally, for any regression of Y on one X, the regression R
2
will be the square of the correlation of X and Y.
Table 6 presents the regression of three dependent variables, EFF, ROS, and ROA,
Boynton et al. Journal of Energy Finance and Development 4 1999 1–27 19
on each of four independent variables, FC1, FC3, FC1D, and FC3D, taken one at a time for a total of 12 regressions for the purpose of developing our analysis. Table 7
presents three stacked regressions one for of each EFF, ROS, and ROA as dependent variables on all four finding costs ratios. Each stacked regression is used to test an
equality restriction on the estimated bs slopes on the finding costs ratios. Table 8 reports the rejection or non-rejection of the equality restriction.
Row 1 of Table 6 presents the results of regressing rank on EFF on rank on FC1. The estimated b slope coefficient is 2.615, which is also the estimated correlation
and which is within rounding error of the earlier estimated rank correlation of 2.61. The intercept is .808, which is approximately .5[1 2 2.615]. The R
2
is .379, which is approximately the square of 2.615. In row 2 of Table 6, the estimated b slope
coefficient on FC3 is 2.662, which is also the estimated correlation and is within rounding error of the prior estimate of 2.66. The intercept is .831, which is approxi-
mately .5[1 2 2.662]. The R
2
is .437, which is approximately the square of 2.662. In row 3 of Table 6, the estimated b slope coefficient on FC1D is 2.665, which is
also the estimated correlation and is within rounding error of the prior estimate of 2
.66. The intercept is .833, which is approximately .5[1 2 2.665]. The R
2
is .443, which is approximately the square of 2.665. In row 4 of Table 6 the estimated b slope
coefficient for FC3D is 2.816, which is also the estimated correlation and is within rounding error of the prior estimate of 2.81. The intercept is .908, which is approxi-
mately .5[1 2 2.816]. The R
2
is .665, which is approximately the square of 2.816. Row 1 of Table 7 presents a stacked regression of EFF on all four finding costs
ratios in a single regression for the purpose of testing an equality restriction on the estimated bs slopes on each finding costs ratios Kmenta, 1986, pp. 412–422. The
stacked regression in row 1 of Table 7 has four times as many observations as any of the regressions in rows 1–4 of Table 6. Each observation in the stacked regression is
one of the original observations from the regressions in rows 1–4 of Table 6 expanded, so that it includes, in addition to the original dependent variable and the original
independent variable, the other three independent variables but with zero values for those additional variables. Arbitrarily, the intercept is assigned to the FC1 observa-
tions, and zero-one dummy variables are assigned to each of the three other sets of observations: RIFC3 for FC3 observation, RIFC1D for FC1D observations, and
RIFC3D for FC3D observations.
The b slope coefficients for FC1, FC3, FC1D, and FC3D in row 1 of Table 7 are the same as in rows 1–4 of Table 6, respectively. The intercept is the same as the
intercept for FC1 in row 1 of Table 6. The sum of the intercept and the coefficient on RIFC3 is the same as the intercept for FC3 in row 2 of Table 6. The sum of the
intercept and the coefficient on RIFC1D is the same as the intercept for FC1D in row 3 of Table 6. The sum of the intercept and the coefficient on RIFC3D is the
same as the intercept for FC3D in row 4 of Table 6. The R
2
for row 1 of Table 7 is the average of the R
2
s in rows 1–4 on Table 6. Table 8 reports the rejection or non-rejection of the equality restriction on the
stacked regression presented in Table 7. The restriction requires that the four bs slopes be estimated as if equal and that the four intercepts also be estimated as if
→
Boynton et
al. Journal
of Energy
Finance and
Development
4 1999
1–27 Table 7
Stacked Rank Regression Analysis for the Purpose of Testing an Equality Restriction on the Estimated Coefficients on the Finding costs Ratios—Estimated Regression Coefficients
Intercept RIFC3
RIFC1D RIFC3D
RFC1 RFC3
RFC1D RFC3D
R
2
EFF .808
.023 .025
.100 2
.615 2
.662 2
.665 2
.816 36.648
.737 .800
3.202 216.074
217.263 217.375
221.292 .481
ROS .649
.038 2
.048 2
.017 2
.298 2
.374 2
.202 2
.264 22.174
.916 21.150
2.406 25.859
27.346 23.982
25.197 .085
ROA .592
.015 2
.039 2
.045 2
.181 2
.210 2
.103 2
.092 19.605
.340 2.910
21.047 23.458
24.009 21.973
21.750 .024
, , denote the significance levels of .10, .05, and .01, respectively, obtained in a 2-tailed test of the null hypothesis that the estimated parameter equals zero; t statistic in parentheses.
Boynton et al. Journal of Energy Finance and Development 4 1999 1–27 21
Table 8 Test of Equality Restrictions
F Test statistic for dependent variable
Restriction tested EFF
ROS ROA Joint test that 1 the coefficients on RFC1, RFC3, RFC1D, and RFC3D are equal
and 2 that the coefficients on RIFC3, RIFC1D, and RIFC3D are all zero 2.58 .99
.62 denotes the significance level of .05, obtained in a 2-tailed test of the null hypothesis that the
estimated parameter equals zero.
equal, the latter by specifying that the coefficients on RIFC3, RIFC1D, and RIFC3D be estimated as if equal to zero. The restriction is rejected for EFF at the .05 level
see column 2 in Table 8. If the restriction is imposed, the R
2
will be reduced from .481 to.475,
16
and the estimated common correlation will be 2.689.
17
By inspection, the bs slopes of FC1, FC3, and FC1D are “close” at 2.62, 2.66, and 2.66 to the estimated common correlation of 2.69 under the restriction. However,
based on the F test, the b of 2.82 for FC3D is significantly different from higher than that estimated common correlation of 2.69 under the restriction and from the
b s for the other three finding costs ratios. For the 119-firm sample, FC1, FC3, FC1D,
and FC3D are all negatively rank correlated with EFF and useful as measures of exploration efficiency, but rank on FC3D is significantly more useful than rank on
the others.
3.5. Rank regression results comparing finding costs ratios FC1, FC3, FC1D, and FC3D to operating profit ratios ROS and ROA
Table 6 presents see rows 5, 6, 7, and 8 the regression of ROS on each of the finding costs ratios taken one at a time for the purpose of developing our analysis.
Row 2 of Table 7 presents a stacked regression including all four finding costs ratios in a single regression for the purpose of testing an equality restriction on the estimated
b s slopes on each finding costs ratios. Table 8 reports the rejection or non-rejection
of the equality restriction. The restriction requires that the four bs slopes be estimated as if equal and that the four intercepts also be estimated as if equal, the latter by
specifying that the coefficients on RIFC3, RIFC1D, and RIFC3D be estimated as if equal to zero. The restriction is not rejected at normal levels of statistical significance
for ROS see column 3 in Table 8. If the restriction is imposed, the R
2
will be reduced from .085 to.081,
18
and the estimated common correlation will be 2.285.
19
For the 119-firm sample, FC1, FC3, FC1D, and FC3D are all negatively correlated with ROS, but no finding costs measure has a higher significance. Each of the finding
costs ratios is useful as an indicator of potential profitability. Table 6 presents see rows 9, 10, 11, and 12 the regression of ROA on each of
the finding costs ratios taken one at a time for the purpose of developing our analysis. Row 3 of Table 7 presents a stacked regression, including all four finding costs ratios
22 Boynton et al. Journal of Energy Finance and Development 4 1999 1–27
in a single regression for the purpose of testing an equality restriction on the estimated b
s slopes on each finding costs ratios. Table 8 reports the rejection or non-rejection of the equality restriction. The restriction requires that the four bs slopes be estimated
as if equal and that the four intercepts also be estimated as if equal, the latter by specifying that the coefficients on RIFC3, RIFC1D, and RIFC3D be estimated as if
equal to zero. The restriction is not rejected at normal levels of statistical significance for ROA see column 3 in Table 8. If the restriction is imposed, the R
2
will be reduced from .024 to .022,
20
and the estimated common correlation will be 2.147.
21
For the 119-firm sample, FC1, FC3, FC1D, and FC3D are all negatively correlated with ROA, but no finding costs measure has a higher significance. Each of the finding
costs ratios is useful as an indicator of potential profitability.
4. Summary of findings
