wildcats Activities
The Statement of the Problem:
Recently, oil becomes more influence to almost every economics
sector as a key material. As can be seen from news, when there are
some changes in an oil price or OPEC announces a new strategy, its
effect spreads to every part of economy directly and indirectly.
Thats a reason why people always observe the oil price and try to
forecast the changes of it. The most important factor affecting to
the price is its supply that is determined by the number of
wildcats drilled. Therefore, study in relation between the number
of wellheads and other economic variables may give us some
understanding of the mechanism indicated the amount of oil
supplies. In this paper, we will consider a relation between the
number of wellheads and three key factors: price of the wellhead,
domestic output and GNP constant dollars. We also add trend
variable in the models due to the consumption of oil varies from
time to time. Moreover, this paper will use an econometrics method
to estimate parameters in the model, apply some tests to verify the
result we acquire and then conclude the model Formulation of a
General Model
Practically, the number of wildcats drilled depends on many
factors such as demand for oil, 0`,ner energy's price and OPEC
policy etc. If demand for oil is high, the oil production and its
supply Increase. In the paper, we will focus on four main factors:
price at the wellhead, domestic output, GNP, time trend and vices
versa. The simple single-equation model is:
Y = the number of wildcats drilled XZ = price at the wellhead in
the previous period (In constant dollar, 1972 = 100) X3 = domestic
output X4 = GNP constant dollars (1972 = 100) XS = trend variable,
1948 = 1, 1949 = 2,..., 1978 = 31
9
wildcats Activities
According to the model, there are four exogenous variables in
the equation: oil price, domestic output. GNP and trend variable..
thus we can predict directions of the results before estimating the
model. Firstly, if the oil price rise, it can be inferred that
there is an increase in demand for oil. As a result, manufactures
have to adapt their oil production to response rising demand, that
is, coefficient of X2 is expected to be positive since change in Y
moves in the same direction as X2 change. Secondly, in the case of
domestic output, which demonstrates a condition of production? The
more domestic outputs are, the more amount of oil is used to
produce those outputs. Thus, coefficient of X3 should be positive
as well.Thirdly, when national income or GNP increases, it is a
sign that people have more purchasing power. Hence, demand for oil
will grow directly via consumption of oil and indirectly via
consumption of other goods which use oil as a raw material. The
relation is predicted to be positive as well. Finally, in the term
of time variables showing the change in oil production over the
time. The expected coefficient of this trend variable is positive
because from time to time, there are new machine created everyday
so the usage of oil as a source of energy is more and more Data
Source and Description
Data and model are obtained from Damodar N. Gujaeati, Basic
Econometrics, MaGraw-Hill, fourth edition, 2003. The data is annual
time-series of oil production from 1948 to 1978. There are five
variables ~ our model: Y, X1 , X2 , X3 , X4 and X5. Here is the
table of the definitions of variables. Variables Y XZ X3 X4
Definitions The number of wildcats drilled Price at the wellhead in
the previous period Domestic output GNP constant dollars Units of
measurement Thousands of wildcats Per barrel price, constantof
barrels per Millions S day Constant $ billion
9
wildcats Activities
X5
Trend variable Table 1 Definitions of variables
-
Descriptive statistics of each variable:
9
wildcats Activities
9
wildcats Activities
Model Estimation and Hypothesis Testing
9
wildcats Activities 1. Parameter Estimation
we apply the ordinary least square method and the output is show
below: Dependent Variable: Y Method: Least Squares Date: 10/18/09
Time: 18:30 Sample: 1 31 Included observations: 31 Variable C X2 X3
X4 X5 Coefficien t -9.798930 2.700179 3.045134 -0.015994 -0.023347
Std. Error 8.931248 0.698589 0.941113 0.008212 0.273410 t-Statistic
-1.097151 3.865190 3.235673 -1.947619 -0.085394 Prob. 0.2826 0.0007
0.0033 0.0623 0.9326 10.63742 2.355480 3.977479 4.208767 8.917142
0.000113
R-squared 0.578391 Adjusted R-squared 0.513529 S.E. of
regression 1.642889 Sum squared resid 70.17616 Log likelihood
-56.65093 Durbin-Watson stat 0.938545
Mean dependent var S.D. dependent var Akaike info criterion
Schwarz criterion F-statistic Prob(F-statistic)
Table 2 Parameter estimated by ordinary least square
methodEstimated equation with t statistic in the parentheses: Yt =
- 9.798930+2.700179X2t+ 3,456X3t -0.015994X4t - 0.0237Xu (-1.11)
R2=058 (3.88)(3.26) (-1.96) (-0.08)
SE =1.636
2. Hypothesis Testing Three of five. coefficients are
insignificant at the 5 percent level (accept H 0: i= 0) because
their t statistics are less than 2.052 (from t distribution table,
df = 27) in absolute value and the rest are significant. In
addition, it is obvious that R 2 value is only 0.58, which means
that the explanatory variables in the right hand
9
wildcats Activities
side can explain 58% of the movement in Y. Therefore,
verification, and adjustment will be needed to improve the
equation. 3. Multicollinearity3.1) Test for Multicollinearity
From table 2, it is obvious that although R2 value is quite
moderate, there are only two significant t ratios. Thus, it may
have a relationship among explanatory variables in this model. To
ensure the existence of multicollinearity, we will use a
correlation matrix to consider the pair-wise
Y
X2
X3
X4
X5
Y X2 X3
1.000000 0.135193 0.426595 -0.557392 0.529881
0.13519 3 1.00000 0 0.30542 4 0.18201 8 0.16088 2
0.42659 5 0.30542 4 1.00000 0 0.82714 7 0.84805 0
0.55739 2 0.18201 8 0.82714 7 1.00000 0 0.99058 9
-0.529881 0.160882 0.848050 0.990589 1.000000
X4X5
Table 3 Correlation matrix
As can be seen from the table 3, several of these pair-wise
correlations are quite high. For instance, correlation between X,
and X5 is 0.990589, between X3 and X, is 0.827147 and between X3
and XS is 0.848050, respectively. It indicates that there is a
collinearity problem in our model. 3.2) Correction for
Multicollinearity According to table 3, there is a strong
relationship among X 3 ,X4
and XS leading to the
multicollinearity in our equation. To correct the model, we will
drop a variable owing to we can't find more information to add or
poll in the model. We decide to drop X4 because of two reasons: 1.
X3(domesic output) and X4(GNP) are quite similar. Hence, using only
one of them would be better for the model 2. From the correlation
matrix in table 3, it manifests a strong relationship among
9
wildcats Activities X3,X4 and X5. So if we drop one of them, it
may improve out model. especially, correlation between X4 and X5 is
close to one so it may be good to drop X4 or X5 instead of X3 After
drop X4 and Conduct the OLS Method over the model again, the
regression results are as follow:
Dependent Variable: Y Method: Least Squares Date: 10/19/09 Time:
10:40 Sample: 1 31 Included observations: 31 Variable C X2 X3 X5
R-squared Adjusted R-squared S.E. of regression Sum squared resid
Log likelihood Durbin-Watson stat Coefficient -16.90701 2.655855
3.172020 -0.508888 0.516882 0.463202 1.725778 80.41438 -58.76178
0.659223 Std. Error 8.562803 0.733446 0.986224 0.117925 t-Statistic
-1.974471 3.621066 3.216328 -4.315345 Prob. 0.0586 0.0012 0.0034
0.0002 10.63742 2.355480 4.049147 4.234178 9.628973 0.000171
Mean dependent var S.D. dependent var Akaike info criterion
Schwarz criterion F-statistic Prob(F-statistic)
Table 4 Parameter estimated by OLS method.
Estimated equation with t statistic in the parentheses: Y t =
-16.9922 + 2.6565X, + 3.1870X, - 0.5103X, (-1.99) (3.63) (3.24)
(-4.34) (2)
R2 = 0.52 SE = 1.721 Almost coefficients are significant at the
5 percent level (reject Ho: Rt=0 because their t are greater than
or equal to 2.048 in absolute value). Except only coefficient of
constant term but its t statistic is close to 2 so we will ignore
its insignification. This equation is considerably better than
uncorrected equation and the multicollinearity is already
eliminated from our model. 4_A.uiocorrelation
9
wildcats Activities
4_1) Test for autocorrelation
From Fig. 1, residual line has a pattern indicating that there
is a positive autocorrelation. To ensure that this problem exists,
we will exert Durbin-Watson test According to table 4,
Durbin-Watson statistic is equal to 0.653 and from Durbin-Watson d
statistic table at 5 percent level : dL= 1.229 and dU =
1.650Positive Autocorrelation 0 d L = 1.229 d U = 1.650 0 653 4- d
L 4- d U No autocorrelation Negative autocorrelation 4
We will find that Durbin-Watson statistic falls in positive
autocorrelation region. As a result, we reject null hypothesis (H.
: P= 0), that is, there is autocorrelation in our model surely.
4.2. Correction on for Autocorrelaion
9
wildcats Activities
We Reestimate the equation by using Corchrane-Orcutt procedure
and a serial correlation is eliminated. The regression results are:
Dependent Variable: Y Method: Least Squares Date: 06/02/02 Time -.
10:28 Sample(adjusted): 2 31 Included observations: 30 after
adjusting endpoints Convergence achieved after 9 iterationsVariable
C X2 X3 X5 AR(1) R-squared Adjusted R-squared S.E. of regression
Sum squared resid Log likelihood Durbin-Watson stat Inverted AR
Roots Coefficien t 5.095206 1.137359 0.942234 -0.351872 0.710037
0.878218 0.858733 0.879268 19.32782 -35.97337 1.832106 71 Std.
Error 5.260470 0.442307 0.608573 0.092804 0.093735 Mean dependent
var S.D. dependent var Akaike info criterion Schwarz criterion
F-statistic Prob(F-statistic) t-Statistic 0.968584 2.571423
1.548268 -3.791557 7.574928 Prob. 0.3420 0.0165 0.1341 0.0008
0.0000 10.73400 2.339377 2.731558 2.965091 45.07108 0000000
Table5.Parameter estimated by OLS Method. Y. = 50952 - 1' 373x,
Y 3.1870X3t - 0.5103X 5t R 2- =0.88 DW = 1.823 Now Durbin-Watson
statistic is equal to 1.823, so it falls into no autocorrelation
region. Therefore, we accept null hypothesis, in the other word,
there is no statistically significant evidence of autocorrelation,
positive or negative. Besides, the equation is greately better than
the prior one because R2 value rises from 0.52 to 0.88. SE=0.879
(3)
5. Heteroscedasticity Test for Heteroscedasticity
9
wildcats Activities
White test with no cross term,
White Heteroskedasticity Test: -statistic Obs`R-squaredF
1.257117 7.408680
Probability Probability
0.315129 0.284699
Table 6 no cross term white test 2) White test with cross
term,
White Heteroskedasticity Test: F-statistic Obs'R-squared
0.955024 9.017470
Probability Probability
0.502733 0.435663
Table 7 white test with cross term Value of nR2 from both tests
are less than critical chi-square value at 5 percent level of
significant (df = 3): )2 = 9.815 . Thus, we can accept null
hypothesis (Ho : (XI = 0 where OC is a coefficient in auxiliary
equation) . We can conclude that there is no heteroscedasticity in
our model.
Interpretation of the Results and Conclusions
The final results of the regression (equation 3) show that the
explanatory variables on the rtght hand side can explain 88% of
movement in change of the number of wildcats drilled. The remained
variables which substantially influence to the dependent variable
is 3 variables, we drop X4 in the correcting process. As we
predicted the direction of the results before estimation, we
expected the coefficient of X4 should be positive. But after
estimated original data, we found that it is negative. Therefore,
it is possible that XQ or GNP may not a proper variable for this
model. At last, we obtain the final results: Yt = 5.0952 + 1.1373X,
+ 3.1870X3t - 0.5103X,
9
wildcats Activities
It shows that domestic output (X) has a strong and positive
effect on the number of wildcats as we predicted earlier. The price
at the wellhead (X) also has the expected positive impact whereas
time trend has negative effect on the number of wildcats.
Limitation of the Study and Possible Extensions
There are some drawbacks in the paper, especially in the part of
review of literature that is -o; cited at all. Moreover, our model
is based on only 31 observations and data-collecting time is
outof-date which is from time period 1948 to 1978. Therefore, if
apply their results to a current situation, it may not absolutely
correct. It is recommended that larger and more update observation
should be considered. In addition, to improve the model, we ought
to observe other variables having effects to the number of wildcats
drills such as the decision of OPEC committees about the quantity
of world oil. Either added or omitted variables may increase Rz
value of the model as well
(VII). References
1).Gujarati, Damodar N., Basic Econometrics, Mcgrawhill, 2003
2).Pindyck, Robert S., and Daniel L. Rubinfeld, Econometric Models
And Economic Forecasts, Mcgrawhill, 1998 3.).Cobham, David,
Macroeconomic Analysis an intermediate text, Longman, 1998
AppendixThousand s of wildcats, (Y) Per barrel price constan t$
(X2) Domesti c output (millions of barrels GNP, Constant $
billions, (X4) TIME (X5)
9
wildcats Activitiesper day), (X3) 5.52 5.05 5.41 6.16 6.26 6.34
6.81 7.15 7.17 6.71 7.05 7.04 7.18 7.33 7.54 7.61 7.80 8.30 8.81
8.66 8.78 9.18 9.03 9.00 8.78 8.38 8.01 7.78 7.88 7.88 8.67
8.01 9.06 10.31 11.76 12.43 13.31 13.10 14.94 16.17 14.71 13.20
13.19 11.70 10.99 10.80 10.66 10.75 9.47 10.31 8.88 8.88 9.70 7.69
6.92 7.54 7.47 8.63 9.21 9.23 9.96 10.78
4.89 4.83 4.68 4.42 4.36 4.55 4.66 4.54 4.44 4.75 4.56 4.29 4.19
4.17 4.11 4.04 3.96 3.85 3.75 3.69 3.56 3.56 3.48 3.53 3.39 3.68
5.92 6.03 6.12 6.05 5.89
487.67 490.59 533.55 576.57 598.62 621.77 613.67 654.80 668.84
681.02 679.53 720.53 736.86 755.34 799.15 830.70 874.29 925.86
980.98 1,007.72 1,051.83 1,078.76 1,075.31 1,107.48 1,171.10
1,234.97 1,217.81 1,202.36 1,271.01 1,332.67 1,385.10
1948 = 1 1949 = 2 1950 = 3 1951 = 4 1952 = 5 1953 = 6 1954 = 7
1955 = 8 1956 = 9 1957 = 10 1958 = 11 1959 = 12 1960 = 13 1961 = 14
1962 = 15 1963 = 16 1964 = 17 1965 = 18 1966 = 19 1967 = 20 1968 =
21 1969 = 22 1970 = 23 1971 = 24 1972 = 25 1973 = 26 1974 = 27 1975
= 28 1976 = 29 1977 = 30 1978 = 31
Source: Energy Information Administration, 1978 Report to
Congress.
9
