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The Determinants of Crude Oil Prices
Osama M. Badr 1 and Ahmed F. El-khadrawi2
Abstract
Understanding the factors driving crude oil price fluctuations is essential for assessing their
effects. For this purpose, the study based on the price equation presented by Kaufmann et al (2004)
and expand the model to include another set of potential determinants that may reflect the
fluctuations in crude oil prices. These determinants classified in to three types of factors: Supply
and demand factors and factor associated with the behavior of financial market participants. The
study employed quarterly data from 2008Q1 to 2015Q4. Engel and Granger econometric
techniques allow us to estimate the short and long-run effects of the previous determinants on the
crude oil prices. The results of our analysis indicate a robust effects of GDP growth for both China
an OECD countries to crude oil prices fluctuations. Changes in the refining capacity also appear
robustly related to oil prices changes. On the other hand, indicate little-to-no evidence that
increased role of speculators drives prices.
1. Introduction:
After four years of stability at around $105 per barrel, oil prices have declined sharply since
June 2014. It is expected that Middle East and oil exporting countries will face slowdown and
weakness in economic environment due to sharp drop in oil prices. After four years of stability at
around $105 per barrel, oil prices have declined sharply since June 2014. It is expected that Middle
East and oil exporting countries will face slowdown and weakness in economic environment due
to this sharp drop in oil prices. Especially, the last oil price decline is due to factors related to
global economic conditions like changes in oil supply caused by technology Aasim et al (2015).
Whereas last changes can reflect a symptom of unexpected shocks in global economic activity.
There is a belief that the current decline in oil prices driven by supply factors will have positive
effects on global economic growth over the medium term. In spite of that, the severe economic
pressures on oil exports countries as well as the uncertainty associated with the occurrence of
crisis, may limit the optimistic expectations of the global economy in the short term.
There is no doubt that oil price drop lowering consumers cost of living which leads to
increased consumer's real income if only price decline have been passed to them. At the same time
price drop means decline in firm's marginal costs using oil in their production which implies more
benefits. But the flipside to these gains is income losses of oil producers.
The effects of these factors not depend on demand and supply factors only but also on the
decline type, whether a temporary or permanent. If the oil prices drop on a temporary basis, the
1
Osama M. Badr, Faculty of Commerce, Tanta University, Egypt, College of Business, Umm Al-Qura University,
KSA, Email: [email protected]
2
Ahmed F. El-khadrawi, Faculty of Commerce, Damietta University, Egypt,Faculty of Islamic Economic and
Finance, Umm Al-Qura University, KSA, Email: [email protected]
1
gains will be in oil importing countries which they will be mostly winner. While the oil exporting
countries will lose their expected income which put a pressure on the national budget and lead to
increase borrowing and public debt. But if the oil prices drop on a permanent basis especially in
case of economy reliance on revenues from oil exports to fund other activities in the economy.
Such countries experience a terms-of-trade loss, governments will need to adjust and reconstruct
the public spending.
From all the above, Identifying the determinants for the oil price decline is critically important
for assessing its likely global economic impact. According to that, our aim is to examine which
factors are significant in determining crude oil prices between 2008 -2015. Our study organized as
follows; Section II. Review the causes behind oil prices fluctuations. Section III presents the
economic and financial consequences associated with oil prices fluctuation. Section IV presents
the empirical model used, the estimation technique and discusses the empirical results. Section V.
brief summary and the important conclusion derived from the study.
2. The causes behind fluctuations in oil prices plunge
As per any storable commodity, oil demand and supply conditions determine long-run trends
in oil price, however, there are other factors and expectations can play a critical role in driving
price fluctuations (e.g. geopolitical conflicts in some oil producing regions and producers decisions
specially OPEC’s decisions and finally with appreciation of U.S dollar).
Theoretically, there are four groups of explanatory factors can be identified as possible
contributors to the development of crude oil prices. First, change in demand due to change in global
economic growth. Second, changing in supply or anticipating supply. Third, change in objectives
and decisions of crude oil producers. Fourth, the factors associated with the behavior of financial
market participants and speculation.
According to Hamilton (2008) and Dees et al. (2008), the above determinants are not
necessarily mutually exclusive, but can complement each other. Kilian (2009) Argue that during
the period 1975-2007, oil price shocks have been driven mainly by demand shocks rather than
supply shocks. This essentially stems from precautionary demand driven by uncertainty about
future supplies. Peersman (2011) discriminate between oil demand shocks and oil supply shocks
to study the macroeconomic effects across 11 industrialized countries. The results indicate that for
oil demand shocks driven by global economic activity, almost all countries experience inflationary
pressure and a temporary increase of economic activity. But when arise in oil prices is caused by
oil-specific demand shocks there will be a transitory decline of output.
Similarly, Cashin et al (2014) compare between supply-driven and demand-driven oil-price
shocks to study the macroeconomic consequences for 38 countries and regions using quarterly
data covering the period 1979-2011. The results were similar pretty much to Peersman (2011), in
the fact that oil importing countries became more susceptible to oil supply shocks compared to oil
exporting countries, while oil demand shocks can't explain cross-country differences.
2
From literature review, we can note that the most important variables that affect the oil price
are supply and demand quantity. World economic activity represented by world GDP and
advanced economies GDP. Temperature and its influence on oil price. Which we can describe it
over the time in the following figures.
Fig (1b ) show that Advanced economies represent more than 60% from World GDP and Fig
(1b ) show that World GDP and Advanced economies GDP declined from year 2008 to 2009 and
start to rose from 2009 to 2014 but re-declined from 2014 to 2015 due to slowdown in advanced
economies especially Chinese Economy.
100000
80000
80000
60000
60000
40000
40000
20000
20000
World
Advanced economies
World
2013
2010
2007
2004
2001
1998
1995
1992
1989
1986
0
1983
2013
2010
2007
2004
2001
1998
1995
1992
1989
1986
1983
1980
0
Fig (1b) World and Advanced
Economies GDP
1980
Fig (1a) World and Advanced
Economies GDP
100000
Advanced economies
Fig (2) show the world economy growth rate fluctuation from year 2008 to 2015 especially
the declined in world economy growth year 2009 and 2015.
Fig (2) World Economy Growth Rate
0.3
0.2
0.1
0
-0.1
198119831985198719891991199319951997199920012003200520072009201120132015
Fig (3) show the reflect of global climate changing with increasing the global temperature
which will lead to increase the oil demand
3
Fig (3) Global Temperature
1
0.8
0.6
0.4
0.2
0
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Fig (4a) show the fluctuation of oil demand & supply but since the first quarter2013 where
the world supply increase over the world demand and Fig (4b) show that Non OPEC supply
quantity is bigger than OPEC supply quantity which indicate and explain the OPEC weakness to
control Oil market over the time
100
Fig (4b) OPEC & Non- OPEC Supply
Fig (4a) World Oil Demand & Supply
70
95
60
90
50
40
85
30
20
80
world Demand
world supply
10
non-opec supply
opec supply
1Q08
3Q08
1Q09
3Q09
1Q10
3Q10
1Q11
3Q11
1Q12
3Q12
1Q13
3Q13
1Q14
3Q14
1Q15
3Q15
1Q08
3Q08
1Q09
3Q09
1Q10
3Q10
1Q11
3Q11
1Q12
3Q12
1Q13
3Q13
1Q14
3Q14
1Q15
3Q15
0
75
Fig (5) shows the crude oil price which reflects the change in above variables. and represent
wide price swings in times of shortage or oversupply during the period 1982-2015.
160
140
120
100
80
60
40
20
0
Fig (5) OPEC Oil Basket Price U$/Bbl
4
4. Methodology
4.1The Model
To determine the most important factors which influencing crude oil prices, the study based
on the price equation presented by Kaufmann et al (2004) and expand the model to include another
set of variables that may reflect the decline in crude oil prices based on the quarterly data covering
the period 2008-2015. So our model can be expressed as following:
πΏπ‘œπ‘”(𝑃)𝑑 = π‘Ž0 + π‘Ž1 πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘β„Ž)𝑑 + π‘Ž2 πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘œπ‘’)𝑑 + π‘Ž3 πΏπ‘œπ‘”(π·π‘Žπ‘¦π‘ )𝑑 + π‘Ž4 πΏπ‘œπ‘”(𝑅𝑒𝑓𝑖𝑛𝑒)𝑑
+ π‘Ž5 πΏπ‘œπ‘”(πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™)𝑑 + π‘Ž6 πΏπ‘œπ‘”(π‘‡π‘’π‘šπ‘)𝑑 + π‘Ž7 πΏπ‘œπ‘”(𝑂𝑖𝑙. 𝑠𝑑)𝑑
+ π‘Ž8 πΏπ‘œπ‘”(𝑂𝑖𝑙. π‘Ÿπ‘’)𝑑 + π‘Ž9 πΏπ‘œπ‘”(π‘π‘’π‘’π‘Ÿ)𝑑
+ πœ€π‘‘
(1)
Where (P) is the crude oil prices. (πΊπ·π‘ƒπ‘β„Ž), (πΊπ·π‘ƒπ‘’π‘œ) is the gross domestic product growth
of China and OECD respectively. (π·π‘Žπ‘¦π‘ ) is days of forward consumption of the OECD and China
crude oil stocks, which is calculated by dividing the sum of OECD and China Stocks of crude oil
by China and OECD demands for crude oil. (𝑅𝑒𝑓𝑖𝑛𝑒) is the total refining capacity worldwide.
(πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™)is the capacity utilization by OPEC, which denote the rate at which the processing
capacities of the available refineries are utilized, and can calculated by divided OPEC production
by OPEC capacity. (π‘‡π‘’π‘šπ‘) is the average world temperature. (𝑂𝑖𝑙. 𝑠𝑑) is worldwide oil stocks.
(𝑂𝑖𝑙. π‘Ÿπ‘’) is the worldwide oil reserves. (π‘π‘’π‘’π‘Ÿ ) is the Nominal effective exchange rate of the U.S.
dollar. (Ξ΅t ) is the error term. All the variables are expressed in natural logarithms in order to
estimate their elasticities.
4.2 Data Description and Sources
From equation (1), we expect the regression coefficient associated with (πΊπ·π‘ƒπ‘β„Ž) and
(πΊπ·π‘ƒπ‘’π‘œ) to be positive – an increase in gross domestic product of china and OECD raises oil
prices. The coefficient of (π·π‘Žπ‘¦π‘ ) is expected to be negative, as an increase in oil stocks reduce oil
price by reducing reliance on current production and thereby lowering the lowering the risk
premium that associated with a supply disruption. We also expect a negative relationship between
Refining capacity (𝑅𝑒𝑓𝑖𝑛𝑒) and oil prices. If there is a general expansion of refining capacities,
bottlenecks caused by growing demand can be countered more quickly. Following this logic, a
negative impact on crude oil prices would be the result. On the other hand, if the rate of actual
utilization (πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™) gets closer the total refining capacity limit (which means a shortage in the
market), the crude oil prices will raise. We expect a positive relationship between (π‘‡π‘’π‘šπ‘) and
crude oil prices. We expect a negative effect of (𝑂𝑖𝑙. 𝑠𝑑) and (𝑂𝑖𝑙. π‘Ÿπ‘’) on prices. Finally, the
coefficient of (π‘π‘’π‘’π‘Ÿ) is expected to be negative.
The data used in this study obtained from U.S Energy Information Administration (EIA) and
IMF website.
4.3 The Estimations Procedure
5
In order to estimate equation (1), we use Engle and Granger’s (1987) procedure to estimate
our model. This method seems appropriate for our study in the sense that it allows us to estimate
the long-run and short-run relationship between the crude oil prices and the considered explanatory
variables.
According to Engel and Granger if the variables in the model is not stationary in level I(0),
we will get spurious regression. In spite of that, Engle - Granger believes that there is a possibility
to generate a linear combination from non-stationary time series data, and if this linear combination
is stationary, the time series is integrated of the same order. Thus, the variables can be used in their
level. The focus of the cointegration test is to find out whether this combination generated from
the model is Stationary or integrated I(0) by applying the Augmented Dickey Fuller (ADF) test
(Dickey and Fuller, 1979) on the residuals. if we reject the null, it means that there is a
cointegration between variables, which indicates an existence of long-term equilibrium
relationship between the variables of the model.
Since the error correction model (ECMs) depends on its first step to carry out the verification
process of a long-run equilibrium relationship between the variables (through regression of the cointegration represented by equation (1)) using the application of ordinary squares (OLS), the
second step of this test is to estimate the ECMs which reflect the short-term relationship by entering
the residual lagged for one period . Accordingly the equation will be as follow:
𝑛
𝑛
𝑛
π›₯πΏπ‘œπ‘”(𝑃)𝑑 = π‘˜0 + βˆ‘ πœ†1𝑖 π›₯πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘β„Ž)π‘‘βˆ’π‘– + βˆ‘ πœ†2𝑖 π›₯πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘œπ‘’)π‘‘βˆ’π‘– + + βˆ‘ πœ†3𝑖 π›₯πΏπ‘œπ‘”(π·π‘Žπ‘¦π‘ )π‘‘βˆ’π‘–
𝑖=1
𝑛
𝑖=1
𝑖=1
𝑛
𝑛
+ βˆ‘ πœ†4𝑖 π›₯πΏπ‘œπ‘”(𝑅𝑒𝑓𝑖𝑛𝑒)π‘‘βˆ’π‘– + βˆ‘ πœ†5𝑖 π›₯πΏπ‘œπ‘”(πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™)π‘‘βˆ’π‘– + βˆ‘ πœ†6𝑖 π›₯πΏπ‘œπ‘”(π‘‡π‘’π‘šπ‘)π‘‘βˆ’π‘–
𝑖=1
𝑛
𝑖=1
𝑛
𝑛
𝑖=1
+ βˆ‘ πœ†7𝑖 π›₯πΏπ‘œπ‘”(𝑂𝑖𝑙. 𝑠𝑑)π‘‘βˆ’π‘– + βˆ‘ πœ†8𝑖 π›₯πΏπ‘œπ‘”(𝑂𝑖𝑙. π‘Ÿπ‘’)π‘‘βˆ’π‘– + βˆ‘ πœ†8𝑖 π›₯πΏπ‘œπ‘”(π‘π‘’π‘’π‘Ÿ)π‘‘βˆ’π‘–
𝑖=1
𝑖=1
𝑖=1
+ πœŒπœ‚π‘‘βˆ’1 + πœπ‘‘
(2)
In which π›₯ is the first difference, and πœ‚π‘‘βˆ’1 is the one period lagged discrepancy (or
disequilibrium) term, which estimated from the cointegration equation (1). The number of lags (n)
for the right-hand side variables is chosen using the Akaike information criteria.
The coefficient ρ in the ECM model measures the adjustment force which should be
significant and negative. The negative value for ρ indicates that disequilibrium between crude oil
prices and its determinants moves prices toward its long-run equilibrium value.
5. Empirical Results and Discussion
Before turning to the estimation results, it is important to make preliminary test which assess
whether the variables used in equation (1) are stationary or integrated of the same order I(1) by
applying the ADF test. The results in table (1) in the appendix show that all the variables in model
6
(1) are not stationary in levels but stationary in their first difference, which mean that all the
variables are integrated in same order I(1), and therefore can be used in their levels.
Table (2) in the appendix, shows the results of cointegration equation (1). All the variables
have signs consistent with what was expected and, except for Temperature, are significant. The
coefficients of πΊπ·π‘ƒπ‘β„Ž, πΊπ·π‘ƒπ‘œπ‘’ are positive and highly significant. The estimates imply that a one
percent additional increase in gross domestic product for China or OECD countries is associated
with around 0.110 and 0.382 per cent increase in crude oil prices. The effect of π·π‘Žπ‘¦π‘  is negative.
An increase in stocks reduces reliance on current production, which tends to lower the risk
premium that is associated with a supply disruption. One percent point additional increase in days
of forward consumption results a reduction in crude oil prices by about 0.225. Refining capacity
has a negative effect on the long-run level of oil prices. As we expected, Capacity utilization has
a positive impact on oil prices. The signs of the regression coefficients are consistent with a priori
expectations that prices drop rapidly at low levels of capacity utilization and rise rapidly at high
levels of capacity utilization.
As expected, the coefficients associated with the worldwide oil stocks and worldwide oil
reserves are negative. One per cent additional increase in oil stocks and oil reserves is associated
with of about 0.042 and 0.072 percent in oil prices. Finally, the coefficient associated with
exchange rate is negative. The estimates imply that a one percent appreciation in U.S. dollar is
associated with a decline of about 0.009.
Let us now move to the ECM (equation (2)), Table (3) in the appendix shows the short-run
dynamics of oil prices. The regression results indicate that the cointegrating relationship given by
equation (1) can be interpreted as an equation for the long-term determinants of oil price. The
coefficient of the error correction term, which Known as the adjustment force (𝜌) is negative, and
around 0.53, implying that 53 percent of the disequilibrium of the period t –1 is revised in period
t.
6. Conclusion
Understanding the factors driving crude oil price fluctuations is essential for assessing their
effects. For this purpose, the study based on the price equation presented by Kaufmann et al (2004)
and expand the model to include another set of potential determinants that may reflect the
fluctuations in crude oil prices. These determinants classified in to three types of factors: Supply
and demand factors and factor associated with the behavior of financial market participants. The
study employed quarterly data from 2008Q1 to 2015Q4. Engel and Granger econometric
techniques allow us to estimate the short and long-run effects of the previous determinants on the
crude oil prices. The results of our analysis indicate a robust effects of GDP growth for both China
an OECD countries to crude oil prices fluctuations. Changes in the refining capacity also appear
robustly related to oil prices changes. On the other hand, the speculation factors indicate little-tono evidence that increased role of speculators drives prices.
References:
7
1. Kaufmann, R.K, S. Dees, P. Karadeloglou, and M. Sanchez. (2004), β€œDoes OPEC matter?
An econometric analysis of oil prices”, The Energy Journal, 25(4), 67-90.
2. Aasim, M. H., Rabah, A., Peter, B., Vikram, H., Thomas, H., Paulo, M., Martin, S., (2015),
β€œGlobal Implications of Lower Oil Prices”, IMF staff discussion note, SDN/15/15.
3. Hamilton, J. (2009), β€œCauses and Consequences of the Oil Shock of 2007–08”, Brookings
Papers on Economic Activity (Spring), 215-283
4. Dées, S. Gasteuil, A. Kaufmann, R. and Mann, M. (2008), β€œAssessing the factors behind
oil price changes”, European Central Bank, Working paper NO. 855.
5. Hamilton, J. (2008), β€œUnderstanding Crude Oil Prices”, NBER, Working Paper 14492
6. Kilian, L. (2009), β€œNot all Oil Price Shocks are Alike: Disentangling Demand and Supply
Shocks in the Crude Oil Market”, American Economic Review 99(3), Pp 1053–1069
7. Cashin, P., K. Mohaddes, and M. Raissi. (2014), β€œThe differential effects of oil demand
and supply shocks on the global economy”, Energy Economics 44, 113-134.
8. Peersman, G. and I. Van Robays. (2012). β€œCross-country differences in the effects of oil
shocks.” Energy Economics, 34(5), 1532-1547.
9. Benes, J., M. Chauvet, O. Kamenik, M. Kumhof, D. Laxton, S. Mursula and J. Selody.
(2012), β€œThe Future of Oil: Geology versus Technology”, IMF Working Paper No. 12/109.
10. U.S. Energy Information Administration (EIA),www.eia.gov
8
Appendix
Table 1: Unit root test for the variables used in the study
Variables
πΏπ‘œπ‘”(𝑃)
πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘β„Ž )
πΏπ‘œπ‘”(𝐺𝐷𝑃0𝑒 )
πΏπ‘œπ‘”(π·π‘Žπ‘¦π‘ )
πΏπ‘œπ‘”(𝑅𝑒𝑓𝑖𝑛𝑒)
πΏπ‘œπ‘”(πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™)
πΏπ‘œπ‘”(π‘‡π‘’π‘šπ‘)
πΏπ‘œπ‘”(𝑂𝑖𝑙. 𝑠𝑑)
πΏπ‘œπ‘”(𝑂𝑖𝑙. π‘Ÿπ‘’)
π‘π‘’π‘’π‘Ÿ
Augmented Dickey-Fuller test
Level
Trend
First difference
-1.30
No
-4.42*
(---)
(-2.63)
-0.80
No
-6.42*
(---)
(-2.63)
-2.10
No
-5.45*
(---)
(-2.63)
-2.31
No
-4.29*
(---)
(-2.63)
-1.33
No
-5.81*
(---)
(-2.63)
-2.11
No
-6.10*
(---)
(-2.63)
-1.18
No
-4.92*
(---)
(-2.63)
-2.02
No
-6.94*
(---)
(-2.63)
-1.95
No
-4.88*
(---)
(-2.63)
-1.11
No
-4.27*
(---)
(-2.63)
Trend
No
No
No
No
No
No
No
No
No
No
Table (2): Estimates for long-run Price Equation (1)
Cointegrating equation: Dependent variable : 𝐋𝐨𝐠(𝑷)𝐭
C
πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘β„Ž)𝑑
πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘œπ‘’)𝑑
Log(π·π‘Žπ‘¦)𝑑
Log(𝑅𝑒𝑓𝑖𝑛𝑒)𝑑
Log(πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™)𝑑
Log(π‘‡π‘’π‘šπ‘)𝑑
Log(𝑂𝑖𝑙. 𝑠𝑑)𝑑
Log(𝑂𝑖𝑙. π‘Ÿπ‘’)𝑑
Log(π‘π‘’π‘’π‘Ÿ)𝑑
Coefficient
22.84
0.110
0.382
-0.225
-0.824
0.021
0.034
-0.042
-0.072
-0.009
𝑅2
t-Statistic
(-5.92)*
(6.61)*
)5.27)*
(-3.28)*
(-2.97)**
(2.93)**
(-1.37)
(-2.96)**
(-2.72)**
(-6.22)*
0.73
2.19
-4.22 (>-2.63 (1%))
0.614
D.W
ADF
Breusch-p
ο‚· The numbers in parentheses are t-ratio. *, **, *** denote statistical significance
at 1%, 5%, and 10% respectively.
ο‚· D.W refers to Durbin-Watson test for serial correlation.
9
ο‚· ADF refers to Augmented Dickey Fuller test for stationarity of the residuals.
ο‚· Breusch‐P indicates the Breusch–Pagan test for heteroscedasticity.
Table (3): Estimates for short-run Price Equation (2)
ECM : Dependent variable : 𝐋𝐨𝐠(𝑷)𝐭
Ξ”log(𝑃)π‘‘βˆ’1
Ξ”πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘β„Ž)𝑑
Ξ”πΏπ‘œπ‘”(πΊπ·π‘ƒπ‘œπ‘’)𝑑
Ξ”Log(π·π‘Žπ‘¦)𝑑
Ξ”Log(𝑅𝑒𝑓𝑖𝑛𝑒)𝑑
Ξ”Log(πΆπ‘Žπ‘π‘’π‘‘π‘–π‘™)𝑑
Ξ”Log(π‘‡π‘’π‘šπ‘)𝑑
Ξ”Log(𝑂𝑖𝑙. 𝑠𝑑)𝑑
Ξ”Log(𝑂𝑖𝑙. π‘Ÿπ‘’)𝑑
Ξ”Log(π‘π‘’π‘’π‘Ÿ)𝑑
(𝜌)
𝑅2
Coefficient
0.007
0.097
0.237
-0.102
-0.372
0.009
0.010
-0.012
-0.044
-0.002
-0.53
t-Statistic
(1.88)***
(2.63)**
)3.14)*
(-2.46)**
(-2.61)**
(2.22)**
(-1.12)
(-2.34)**
(-2.51)**
(-2.38)**
(-4.10)*
0.68
1.72
-6.24 (>-2.63 (1%))
(-37.524)
0.336
0.273
D.W
ADF
AIC (1)
Breusch-p
Normality
ο‚· The number in parentheses are t-ratio. *, **, *** denote statistical significance
at 1%, 5%, and 10% respectively.
ο‚· D.W refers to Durbin-Watson test for serial correlation.
ο‚· Breusch‐P indicates the Breusch–Pagan test for heteroscedasticity.
ο‚· Normality refers to the normality test for the residuals
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