Paper#1 2940605: Quantitative Methods in Economic Analysis
Application of Regression models and Estimation problems
A Paper On A relation between the number of wilsdcats drilled and three key factors: price at the wellhead, domestic output and GNP constant dollars.
BY SK. ASHIQUER RAHMAN ID#4585974929 A Thesis Submitted In Partial Fulfillment of the Requirement for the Degree of Masters in International Economics and Finance
TO, ASSISTANT PROFESSOR
Masters in International Economics and Finance Faculty of Economics, Chulalongkorn Chulalongkorn University, Phayathai Road, Bangkok-10330,Thailand.Tel: (662) 218 6295, (662) 218 6218,Fax:(662) 218 6295, E-mail:
[email protected] [email protected],, http:// www.econ.chula.ac.th/prog www.econ .chula.ac.th/programme/ma_inte ramme/ma_inter.html r.html
Wilsdcats Activities
2002
June 1, 2002
Letter of Transmittal.
Here is my paper on A relation between the number of wilsdcats drilled and three key factors: price at the wellhead, domestic output and GNP constant dollars.” that I was assigned. It was a great opportunity for me to acquire practical knowledge of the Quantitative Methods in Economic Analysis and forecasting
I have concentrated my best effort to achieve the objectives of the report and hope that my endeavor will serve the purpose.
I believe that the knowledge and experience I have gathered during my paper preparation will immensely help me in my professional life. I will be obliged if you kindly approve this effort.
Sincerely yours
Sk. Ashiquer Rahman Id#4585974929
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Any institutional education would not be completed if it were confined within theoretical aspects. Every branch of education has become more competed by their practical application and accomplishment of full knowledge. We shall be benefited by our education if we can effectively apply the institutional education in practical fields. Hence, we all need practical education to apply theoretical knowledge in real world. By considering this importance “faculty of economics” arranges the Quantitative Methods in Economic Analysis courses for the students of Masters in International Economics and Finance. As a part of this program my topic was selected as “A relation between the number of wilsdcats drilled and three key factors: price at the wellhead, domestic output and GNP constant dollars.”)”
I tried my best to conduct an effective study by arrange and analysis data. There may be some mistakes, which are truly unintentional. unintentional. So, I would request to look at the matter with merciful mind.
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First, all praises go to almighty Allah, the most gracious, the most merciful to give me the ability for all these I have done.
Then I would like to thank Ms. Wanwadee Wongmongkol. Now I would like to thank Dr.Bangorn Tubtimtong Assistant Professor, Chulalongkorn Chulalongkorn University, University,
Phayathai Road,
Bangkok,Thailand Bangkok,Thailand to give me the opportunity opportunity to do this project. project.
I would also like to thank Professor. Paitoon Wiboonchutikula, Ph.D ,Associate professor and Chairperson of Faculty of Economics, Chulalongkorn University & Professor Salinee. Secretatery international economics and finance. My striking thanks go to honorable sir Dr. MN.Sirker who has helped me in all aspect to prepare the report.
I would like to thank lab incharge incharge Ms. Mink Mink . Last but but not the least I wish wis h t o t hank ha nk my friends, William Lloyed ,Nakarin and Athipat, for their very helpful discus discussio sions. ns.
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Title
2002
Page
Letter of Transmittal
ii
Preface
iii
Acknowledgement
iv
Table Of Content
v
Statement Of The Problem
1-1
Literature Review
1-1
Formulation Of General Model
1-2
Data Sources &Description
2-5
Model Estimation And Hypothesis Testing
6-10
Interpretation Of The Results And Conclusions
11-11
Limitations Of The Study And Possible Extensions
11-12
References
11-12
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The Statement Statement of of the 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. That’s 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 of a a General General Model Model
Practically, the number of wildcats drilled depends on many factors such as demand deman d for f or oil, 0`, 0`,ner 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
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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 results before before estimating the model. Firstly, if the oil price rise, it can be inferred 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 and Description 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 f ive variables variabl es ~ our model: model: Y, Y, X1 , X 2 , X 3 , X 4 and X5. Here is the table of the definitions of variables. Variables
Definitions
Units of measurement
Y
The number of wildcats drilled
Thousands of wildcats
XZ
Price at the wellhead in the
Per barrel price,
X
Domestic output
Millions of barrels per
GNP constant dollars
Constant $ billion
X5
Trend variable Table 1 Definitions of variables
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Descriptive statistics of of each each variable:
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Model Estimation Model Estimation and and Hypothesis Hypothesis Testing
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
R-squared Adjusted R-squared S.E. of regression
Coefficient -9.798930 2.700179 3.045134 -0.015994 -0.023347
Std. Error 8.931248 0.698589 0.941113 0.008212 0.273410
-1.097151 3.865190 3.235673 -1.947619 -0.085394
0.578391 Mean dependent var 0.513529 S.D. dependent var 1.642889 Akaike info criterion
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t-Statistic
Prob. 0.2826 0.0007 0.0033 0.0623 0.9326
10.63742 2.355480 3.977479
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Sum squared resid Log likelihood Durbin-Watson stat
70.17616 -56.65093 0.938545
Schwarz criterion F-statistic Prob(F-statistic) Prob(F-statistic)
4.208767 8.917142 0.000113
Table 2 Parameter estimated by ordinary least square method
Estimated equation with t statistic in the parentheses: Yt = - 9.798930+2.700179X2t+ 3,456X3t -0.015994X4t - 0.0237X u (-1.11)
(3.88)
R2=058
(3.26)
(-1.96)
(-0.08)
SE =1.636
2. Hypothesis Testing Three Three of five. five. coefficients are insignificant at the 5 percent level (accept ( accept H0: βi= 0) because their t statistics are less than 2.052 (from t distribution table, df = 27) in absolute value value and the rest are significant. In addition, it is obvious that R2 value is only 0.58, which means that the explanatory variables in the right hand side can explain 58% of the movement in Y. Therefore, verification, and adjustment will be needed to improve the equation. 3. Multicollinearity 3.1) 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
1.000000
0.135193
0.426595
0.557392
-0.529881
X2
0.135193
1.000000
0.305424
0.182018
0.160882
X3
0.426595
0.305424
1.000000
0.827147
0.848050
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X4 X5
-0.557392
0.182018 0 .182018
0.827147
1.000000
0.990589
0.529881
0.160882
0.848050
0.990589
1.000000
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 X3 ,
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 bett er for the model model 2. From the correlation matrix in table 3, it manifests a strong relationship among 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 X 4 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
Coefficient
Std. Error
t-Statistic
Prob.
C X2 X3 X5
-16.90701 2.655855 3.172020 -0.508888
8.562803 0.733446 0.986224 0.117925
-1.974471 3.621066 3.216328 -4.315345
0.0586 0.0012 0.0034 0.0002
R-squared Adjusted R-squared
0.516882 0.463202
Mean dependent var S.D. dependent var
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10.63742 2.355480
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S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
1.725778 80.41438 -58.76178 0.659223
Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) Prob(F-statistic)
4.049147 4.234178 9.628973 0.000171
Table 4 Parameter estimated by OLS method.
Estimated equation with t statistic in the parentheses: Yt = -16.9922 -16.9922 + 2.6565X, 2.6565X, + 3.1870X, - 0.5103X, (2) (-1.99)
(3.63)
(3.24)
(-4.34)
R2 = 0.52 SE = 1.721 Almost coefficients are significant at the 5 percent level (reject H o: Rt=0 because their t are greater than or equal to 2.048 in absolute value). Except only coefficie c oefficie nt of constant term but but its t statistic statistic is close close to 2 so we we will ignore its insignification. This equation is considerably better than uncorrected equation and the multicollinear ity is already already eliminat eliminated ed from our model. 4_A.uiocorrelation 4_1) Test for autocorrelation
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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-Wats on d statistic table table at 5 percent percent level : dL = 1.229 and dU = 1.650 Positive
No autocorrelati on
Autocorrelati on
Negative autocorrelati on
0
4 dL = 1.229 dU = 1.650
4- dL
4- d U
0 653
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 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 iterations Variable
Coefficien
C X2 X3 X5 AR(1)
5.095206 1.137359 0.942234 -0.351872 0.710037
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.878218 0.858733 0.879268 19.32782 -35.97337 1.832106
Inverted AR Roots
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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)
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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
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Table5.Parameter estimated by OLS Method. Y. = 50952 - 1' 373x, 373x, Y 3.1870X3t - 0.5103X5t (3) R 2- =0.88
SE=0.879 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 R 2 value rises from 0.52 to 0.88.
5. Heteroscedasticity Test for Heteroscedasticity White test with no cross term,
White Heteroskeda sticity Test: 1.257117 7.408680
-statistic Obs`R-squared F
Probability Probability
0.315129 0.284699
Table 6 no cross term white test 2) White test with cross term,
White Heteroskedasticity Test: F-statistic
0.955024
Probability
0.5027 33
Obs'R-squared Obs'R-squared
9.01747 0
Probability
0.43566 3
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.
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Interpretation of the Results and and Conclusions 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
4 in
X
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 X Q 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, It shows that domestic output (X) has a strong and positive effect on the number of wildcats 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 of the the Study Study and and Possible 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
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(VII). References
1).Gujarati, Damodar N., Basic Econometrics, Mcgrawhill, 2003 Economic Forecasts, Mcgrawhill, 2).Pindyck, Robert S., and Daniel L. Rubinfeld, Econometric Models And Economic
1998 3.).Cobham, David, Macroeconomic Analysis an intermediate text, Longman, 1998
Appendix Thousands of wildcats, (Y )
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
Source: Energy
Per barrel price constant $ (X 2) 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
Domestic output (millions of barrels per day), (X 3) 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
Information Administration, 1978 Report to Congress.
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GNP, Constant $ billions, (X 4)
TIME (X 5)
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
