The Asymmetric
Impact of Oil Prices on Gasoline Prices
Dale Bremmer*
Department of Humanities and Social Sciences, Rose-Hulman Institute of Technology
Kevin Christ**
Department of
Humanities and Social Sciences, Rose-Hulman Institute of Technology
June
2002
To be presented at the “Applied Econometrics and Computational Methods”
Session
Of the 77th Annual Conference of the Western Economic
Association International
The Westin Seattle,
JEL CLASSIFICATION: C1, D4, Q4
KEY WORDS: Gasoline Prices, Crude Oil Prices, Asymmetric
Impact
______________________
* Department of Humanities and Social
Sciences, Rose-Hulman Institute of Technology, 5500 Wabash Avenue, Terre Haute,
IN 47803. Tel. 812-877-8456. Fax:
812-877-8909. E-mail:
** Department
of Humanities and Social Sciences, Rose-Hulman Institute of Technology, 5500
Wabash Avenue, Terre Haute, IN
47803. Tel. 812-872-6226. Fax:
812-877-8909. E-mail:
I. Introduction
After a
lengthy period of fairly stable gasoline prices, recent volatility has renewed
an old debate over the nature of retail gasoline price adjustment to shocks in
the cost of crude oil. It is not
uncommon to hear people claim that retail gasoline prices rise faster than they
fall in response to changes in the world price of crude oil, or even that
increases in crude oil prices are passed on in the form of higher gasoline
prices while decreases in crude oil are not.
This commonly held view that gasoline price adjustment is asymmetric
thus typically has two dimensions -- speed and magnitude. Taken literally, the second of these claims
is clearly implausible, as it would lead to ever-widening cost-price
margins. That cost-price margins have
not exhibited a long-term secular increase does not, however, negate the
possibility of a meaningful magnitude effect for consumers. If cost increases are passed on more quickly
than cost decreases, then a contemporaneous magnitude effect will arise. In this paper, we investigate whether the
magnitude of price adjustment is indeed asymmetric, and if so, whether there
are notable differences in the effect for different regions of the country and
different frequency of the data - - monthly, weekly, or daily.
The period
from mid-summer to late fall 2001 illustrates why so many people believe that
gasoline price adjustments are asymmetric.
For the week of July 16, crude oil was 54.1 cents per gallon and the
average retail price of regular gasoline was $1.33.[1] Over the next eight weeks, the prices of both
rose, so that by the week of September 10, crude oil was 60.5 cents per gallon
and the retail price of gasoline peaked at $1.51. Thus, a 12% increase in crude oil prices was
associated with an almost 14% increase in the price of gasoline. From this retail price peak, the price of
both crude oil and gasoline fell over the following eight weeks, so that by the
week of November 5, crude oil was 41.4 cents per gallon and the retail price of
gasoline was $1.17. Thus, a 32% decrease
in the price of crude oil was associated with only a 23% fall in the price of
gasoline. Thus, while the magnitude of
the retail price increase closely mirrored the late-summer increase in the
price of crude oil, the autumn decline in crude oil prices was only partially
reflected in falling retail gasoline prices.
Such episodes provide anecdotal evidence of asymmetric responses that
are unfavorable for consumers, and typically give rise to charges of market
power abuse.
The
difficulty with such analysis is that it is easy to find historical episodes
that illustrate different relationships.
In the five weeks from early December 1998 to mid January 1999, the
price of crude oil rose 19%. In the
ensuing four weeks up to early February, the price of crude oil fell almost
13%. During this time, gasoline prices
barely move from a range of $0.91 to $0.94.
In another episode, from mid-June to the end of July in 1998, the price
of crude oil rose by 19%, but retail gasoline prices actually fell by about
1.4%.
Asymmetric
output price adjustment to changes in input costs has been called a “stylized
fact” for many markets (Peltzman, 2000), one that poses significant challenges
to prevailing theories of price determination.
Most models of price determination allow no distinction for different
kinds of input price shocks on output prices -- equal magnitude increases and
decreases in input prices should result in symmetric changes in output
prices. It is often assumed that
asymmetric price responses of the type investigated here are the result of
market power being exercised at different points in the supply chain. Speculation about the causes of asymmetries
is not limited to monopoly power, however, and includes focal point pricing,
inventory and menu costs, and signal extraction problems brought on by
uncertainty (Borenstien, et al, 1997).
While of continuing theoretical interest, such speculation is not the
focus of this paper. Instead, we simply
investigate the temporal and regional nature of asymmetric responses, if they
exist at all.
Gasoline
markets would seem to offer a classic opportunity for this phenomenon to
emerge, as there is such a clear relationship between the input and the
output. Previous studies seem to concur that retail gasoline prices respond more quickly to
input cost increases than to input cost decreases, although the timing and
significance of the effect is open to question.
While the hypothesis of symmetry in the overall response of retail
prices to increases or decreases in the price of crude oil seems supportable,
the pattern of the adjustment does seem to be different, thus giving rise to
short-term magnitude effects (Karrenbrock, 1991). These different magnitude
effects seems to prevail for about six to eight weeks (Borenstein, et
al, 1997), after which the distinction between an input price increase and
decrease seems to fade.
Table 1
presents simple evidence of this time structure to the adjustment process. The contemporaneous (week-on-week) correlation
between changes in the price of crude oil and regular gasoline is positive but
weak. As the time horizon lengthens, the
correlation between changes in crude oil prices and retail gasoline prices
becomes stronger.
Attention to the potentially asymmetric price adjustment seems to
increase with the volatility of crude oil prices. During periods of relatively stable crude oil
prices, retail gasoline prices also exhibit relative stability. But crude oil price spikes heighten
consumers’ awareness of the sensitivity of travel costs to the vagaries of
crude oil prices. Recent years have seen
highly volatile crude and gasoline prices.
Table 2 provides a very broad summary of gasoline and crude oil price
behavior over recent years. Two features
stand out regarding gasoline prices.
First is the changing nature of the medium-term trends in prices. A period of relative price stability for most
of the early 90s was followed by a 2-year period of declining prices, which in
turn has been followed by the most recent period of rising prices. The second feature is the relative volatility
of these price changes. Compared to the
early 1990s, prices have been more volatile since 1997, and much more so since
1999. This volatility has introduced new
levels of uncertainty into gasoline prices.
To
investigate fully the existence and nature of pricing asymmetry, we use price
data from the Energy Information Administration, which maintains rich sets of
daily, weekly and monthly time series for gasoline and crude oil prices. In this paper, we are interested mainly in
furthering our understanding of the dimensions of any asymmetry over time and
across regional markets. While these
data do not account for differences in sales and excise taxes across states, we
don’t feel these effects are significant to our results, or severely limit the
usefulness of our regional analysis.
II. The regression model and its data
The specification of the general regression model
We employ
a simple regression model to test for a contemporaneous, asymmetric response of
retail gasoline prices to changes in the price of crude. Let 
denote the retail price of regular gasoline in time t, while
is the price of crude in time t. The price of gasoline is affected by
supply-side factors such as the price of crude and demand-side factors such as
household income and whether it’s the summer vacation season. The supply of gasoline and its price is also
influenced by the price of alternative fuels derived from crude oil such as jet
fuel and heating oil. Let all the other
relevant determinants of the price of gasoline, other than the price of crude,
be denoted by xt, a k x 1 column vector of the other
explanatory variables at time t. Let Xit
be the ith element of xt, or in other words, Xit
is one of the other k explanatory variables, other than the price of crude,
that affects the price of regular gasoline at time t. To identify times when the price of crude
increased, let Dt be a dummy variable such that Dt equals
1 if - 
> 0, or Dt equals 0 if 
.
The general specification of the regression model is
(1)
where β0, β1, β2, and vector α are the unknown regression parameters to be estimated, while ut is the error term of white noise. If crude oil prices increase from time t-1 to time t, then Dt equals 1 and equation (1) becomes
. (2)
Conversely, if the price of crude remains constant between periods t-1 and t, or if the price of crude declines between times t-1 and t, then equation (1) becomes
. (3)
From equation (2), it follows that if the price of oil increases between periods t-1 and t then
; (4)
however, according to equation (3), if the price of oil remains constant or falls between periods t-1 and t, then
. (5)
Thus, the
statistical test to determine the presence of a contemporaneous, asymmetric
price response simplifies to a simple t-test on whether β2 is
statistically different from zero. If
the estimated coefficient of β2 is statistically significant,
then there is statistical evidence of an asymmetric response of the price of
gasoline to the price of crude oil. Rejection of the null hypothesis that 
would imply that the price of gasoline responds
disproportionately with increases in the price of crude compared to decreases
in the price of crude.
In this paper, we test variations of
this general specification using data sets with different frequency and
different cross-sections. The regression
is estimated separately using monthly, weekly, and daily spot prices. The different cross-sections include
Monthly data: The regression specification and data
To test for asymmetry with monthly data, we estimate the following model:
(6)
where , , and Dt are as defined above, Yt
denotes monthly disposable nominal income, and Mit, i = 2, . . . ,
12, are monthly dummy variables used to control for seasonal price
effects. The price of gasoline should be
directly related to the price of crude; therefore, β1 is
expected to be positive. Gasoline should
be a normal good implying increases in monthly income
results in increased demand for gasoline and higher gas prices. Thus, α1 is also expected to
be positive. Finally, if the price
response of gasoline prices is asymmetric to changes in the price of crude, the
popular assumption is that β2 is positive, implying that the
absolute value of the change in gasoline prices is greater when the price of
crude increases compared to a decrease in the price of crude.
In the monthly data set, the price
of regular gasoline (in cents/gallon) is the
Weekly data: The regression specification and data
With weekly data, choosing a proxy
variable to capture changes in demand becomes problematic. For monthly
(7)
With
the weekly data set, 
is the weekly retail price of regular gasoline measured in
cents per gallon, while 
is the weekly import weighted price per barrel of crude oil
(measured in dollars$ per barrel).[4] Again, as with the monthly data, positive
values for β1 and β2 are expected.
The Department of Energy has several
different data sets of weekly time series for the price of regular gas. There are national data consisting of retail
prices for the entire country, as well as data for five multi-state regions:
the East region, the
Daily data: The regression specification and data
Finally, daily spot prices are used
to determined whether increases in gasoline prices,
caused by an increase in the price of crude, are greater than decreases in
gasoline prices when the price of oil falls.
Daily spot prices of regular gas and crude oil are obtained from the web
pages of the Department of Energy. Due
to the lack of good proxies to capture daily demand, the regression model
focuses solely on the effect of crude oil prices on the price of gasoline. In a regression identical in structure to
equation (7), is set equal to the New York spot price of conventional
regular gasoline (in cents per gallon), while , the price of crude, is measured by the spot price of West
Texas Intermediate crude oil (in dollars per barrel).[6]
Econometric issues
When analyzing time series such as gasoline prices, crude oil prices, and monthly income, the problems associated with autocorrelation arise when using time series data. The presence of first-order autocorrelation in the regression specifications listed in equations (6) and (7) is tested using the Bruesch and Godfrey test for serial correlation. If autocorrelation is present, then the regression parameters and ρ, the first-order autocorrelation coefficient are estimated using nonlinear least squares - - an approach which gives estimates that are both asymptotically equivalent to maximum likelihood estimates and asymptotically efficient.[7]
The problems associated with spurious regression results are another econometric problem that may be encountered with time-series data. Studies using macroeconomic time series have shown when a nonstationary independent variable is regressed on a nonstationary explanatory variable, spurious regression results may occur.[8] In this case, the regression is characterized by high a R2 and simple, independent t-tests incorrectly reject the hypothesis that the estimated parameters are equal to zero while there is no true underlying relationship between the explanatory variable and the dependent variable. Augmented Dickey-Fuller tests are used to determine whether each data series exhibits a unit root and is, consequently, nonstationary. If the price of regular gas and one of its independent variables are nonstationary, then equations (6) and (7) are estimated using first differences of the variables instead of the variables in level form.
III. Empirical Results
Tables 3 through 11 list the results of the unit root tests and the estimated parameters of equations (6) and (7). In general, the statistical evidence indicates that the prices of regular gas and crude oil are nonstationary, and the absolute change in gas prices is greater with increases, rather than decreases, in the price of crude oil.
Monthly data
Using monthly data, Table 3 reports the unit root tests for monthly income and the prices of regular gasoline and crude oil. In this and all other augmented Dickey-Fuller tests performed in the paper, lags of the first-differences of the data were added until serial correlation was removed. Using level data, the hypothesis that the regular gas price series has a unit root can only be rejected at the ten percent level. The level data of crude oil prices is nonstationary as the hypothesis of a unit root is never rejected. Using first-differenced data, the augmented Dickey-Fuller tests indicate all these series are stationary. Given the weak statistical evidence that the level data of regular gas prices is stationary, the null hypothesis of a unit root is only rejected at the 10% percent level - - the weakest level of statistical significance, these variables were used to estimate equation (6) both in level and first-differenced forms. The regression results are listed in Table 4.
The first two columns of regression results in Table 4 pertain to level data, while the third and fourth columns in Table 4 refer to the results obtained from data that was first-differenced. Examining the level data results first, the low Durbin-Watson statistic of 0.404 agrees with the results of the Bruesch-Godfrey tests that indicate first-order autocorrelation is present. Correcting for autocorrelation, the results in the second column indicate that the price of regular gas is directly related both to the price of crude and monthly income. The coefficients for both of these variables (2.416 and 7.059, respectively) are both positive and statistically different from zero at the one percent level. Dummy variables for the months of April through November are positive and statistically significant at either the one- or five-percent level. The most surprising result is that the estimated parameter β2 is negative and significant. The interpretation here is that a $1 decrease in price of a barrel of crude causes gasoline prices to fall by 2.416 cents per gallon, but a $1 increase in the price of crude per barrel causes the price of regular gas to increase only by 2.354 cents per gallon. The results indicate that the response of gasoline prices to changes in crude prices is asymmetric, but the result is opposite the one heard in the press. Here gasoline prices are more responsive to a fall, not an increase, of crude oil prices.
However, not much confidence should be placed on this result because both the price of regular gas and crude oil were shown to be nonstationary. Consequently, the regression results may be spurious and inferences based on standard t-test and F-tests are misleading.[9]
Given the problems of unit roots and spurious regressions, the third and fourth columns of Table 4 refer to results obtained from using first-differenced data. Similar to the results obtained from using level data, the results in the third column indicate autocorrelation is present (the Durbin-Watson statistic was 1.620, and the Bruesch-Godfrey confirmed the presence of AR(1) errors). The results in the fourth column of Table 1 indicate that changes in crude oil are directly related to changes in the price of regular gas (the coefficient of 1.900 is statistically significant at the one-percent level). The positive and statistically significant estimates for the dummy variables on the months of March, April, May, and June indicate that these months have significantly higher priced gasoline than the other months. In a surprising result, the estimated coefficient associated with changes in income, while positive as expected, is statistically insignificant (the t-value is less than 0.05).
Just as surprising is the result
that the estimated parameter for β2 is statistically
insignificant. The estimated parameter
of 0.151 is positive, but the associated t-statistic is less than 0.5,
indicating that the parameter estimate of 0.151 is not statistically different
from zero. Consequently, using monthly
data, after taking first differences and correcting for autocorrelation, the
results of the fourth column in Table 4 indicate there is no contemporaneous
asymmetry between the price of regular gasoline and the price of crude. The estimated value for β1
indicates that a 
$1 change in the price of a barrel of crude implies a 1.9 cent change in price of a gallon of regular gas.
The
results using weekly data of
Using the various samples of weekly data, the results of the unit root test are listed in Table 5, while the estimation results of equation (7) are listed in Tables 6 and 7. The regression results from using data in levels is shown in Table 6, while the results in Table 7 come from data that has been first-differenced.
The Dickey-Fuller test results in
Table 5 indicate that most of the weekly data series exhibit units
roots and are nonstationary. Using level
data, only in the sample composed of
The results of the levels data in
Table 6 mimic the results found for level data in Table 4. Using weekly data and either
Unlike the results obtained from
monthly data, once first differences of the data are taken and the regressions
are corrected for autocorrelation, Table 7 does contain statistical evidence of
contemporaneous price asymmetry of regular gas prices with crude oil
prices. This is the “expected” outcome
where larger increases in regular gas prices with occur with increases in the
price of crude oil increases and smaller decreases in gas prices occur with a
decrease in oil prices. The estimate for
β2, the regression parameter which indicates evidence of an
asymmetric response is positive and statistically significant for samples that
include U.S. data, East Coast data, both Central and Lower Atlantic data, and
the Gulf Coast data. The coefficients for
β2 in the
The
Weekly prices: The state and city samples
Tables 8 and 9 list the results of the weekly data pertaining to cross-sections of selected states and cities. The regression results reported in Table 8 deal with both data in level form and in first differences, but there is no correction for autocorrelation. Table 9 lists the regression results after correcting for first-order serial correlation for both data samples - - data in levels and data in first differences.
Again, the results in Tables 8 and 9 mimic those of Table 4. When using levels data, the estimated value of β2 is consistently negative, and generally statistically significant. Once again, this leads to the conclusion that gasoline prices increase less given an increase in the price of oil compared to the decline in gasoline prices that occurs when crude prices fall. All the regressions using data in level form in Table 8 exhibit autocorrelation as the Durbin-Watson statistic ranges from 0.10 to 0.21. The data in levels form in Table 8 also tend to give spurious results as indicated by the relatively high R2s and the low Durbin-Watson statistics.
The right-hand column of Table 9
lists the regression results after taking first differences and correcting for
autocorrelation. The results are mixed
and not as strong as previous samples with larger geographic areas. The estimated values of β1
are generally positive, as only the estimate for
It is interesting that the state and
city data do not exhibit any statistically stronger evidence of price
asymmetry. If the ability to raise
prices disproportionately higher because of an input shock is a characteristic
of market power, one would intuitively suspect strong evidence of market power
in smaller geographic markets. The data
for
Results using daily spot prices
The unit root tests for the spot price for regular gas prices and crude oil prices are listed in Table 10. In a result that is counter to both the monthly and weekly data, the null hypothesis of a unit root is rejected at the one-percent level for each of these data series. Both of these data series are stationary in level form.
Despite both the dependent and independent variables appear to be stationary, the regression results using data in levels form appear to suffer from the problems caused by spurious regression results. In an outcome that is consistent with previous results, the estimation results in the first regression reported in Table 9 are characterized by a high R2 of 0.86, but a low Durbin-Watson of 0.058. Once again, the estimated value of the coefficient that captures an asymmetric price response, β2, is negative, but it is not statistically different from zero. However, when the model is estimated with data in first-differenced form and corrected for serial correlation, the estimated for β2 is 0.192, both positive and statistically significant at the five-percent level. These results indicate the presence of an asymmetric response of the product’s price to a supply shock. A one dollar increase in the price of a barrel of crude leads to a 2.014 cent increase in the price of regular gas. Since there are 42 gallons of crude in a barrel, a one dollar increase in the price of crude implies a 2.38 cent increase in the price of crude per gallon. These estimates imply an increase in the price of a gallon of crude of 2.38 cents leads to a 2.014 cent price increase in a gallon of gasoline. This almost one-for-one price increase exceeds the estimates of previous studies and it is higher than the estimates from the weekly data reported in Table 7.
The estimates in Table 11 also indicate that when crude prices fall by one dollar per barrel, the price of a gallon of regular gasoline falls by 1.829 cents per gallon. While the difference between 2.014 and 1.829 is statistically significant, one has to wonder whether the difference is economically significant to consumers and firms.
IV. Conclusions
The attempt to determine whether
there is a contemporaneous, asymmetric response of regular gas prices to
increases and decreases in the price of crude brought mixed results. Regressions using weekly and daily
Weekly data of multi-state
Several thrusts for future research come from the paper. Frequency of the data and whether asymmetric price responses occur in annual, quarterly, monthly, weekly, or daily data needs to be explained. The effect of the market size - - city, state, regional, or national - - on the detection of asymmetric price behavior needs explanation. Model dynamics needs to be explored and maybe additional lagged price changes needs to be introduced. Nonetheless, the results of this paper are interesting and important. Studies using both weekly and daily data indicate that there is an contemporaneous, asymmetric response of gas prices to changes in the price of crude. If the price of a barrel of crude oil increases by $1 per barrel - - an increase in the price of almost 2.38 cents per gallon of crude, the price of regular gas increases between 1.343 and 2.004 cents per gallon. One the other hand, if the price of crude falls by $1 per barrel, or equivalently, 2.38 cents per gallon, the price of crude will fall between 0.611 and 1.812 cents per gallon. Future research will have answer why these responses vary in magnitude across smaller regions.
Table 1
Correlation Between Crude Oil and Gasoline Price Changes
Weekly Percentage Price
Changes
|
Contemporaneous (One-Week
Change) |
Two-Week Trend |
Three-Week Trend |
Four-Week Trend |
Five-Week Trend |
|
0.2876 |
0.4500 |
0.5440 |
0.5822 |
0.6202 |
Table 2
Average Weekly Price Changes
in Retail Gasoline and Crude Oil
Cents per Gallon
|
|
Jan. ’91 to Dec. ‘96 |
Jan. ’97 to May ‘02 |
Jan. ’97 to Dec. ‘98 |
Jan. ’99 to May ‘02 |
|
Gasoline: |
|
|
|
|
|
DP |
0.01 |
0.04 |
-0.30 |
0.25 |
|
Std. Dev. |
1.01 |
2.48 |
0.88 |
3.03 |
|
|
|
|
|
|
|
Crude
Oil: |
|
|
|
|
|
DP |
|
-0.04 |
-0.33 |
0.13 |
|
Std. Dev. |
|
2.32 |
1.45 |
2.69 |
Table
3
Augmented
Dickey-Fuller Tests for Unit Roots - - Monthly Data
|
Variable |
Type |
Test Statistic† |
Lags |
|
Regular Gas Price |
Levels |
2.828*** |
3 |
|
Regular Gas Price |
first differences |
8.053* |
2 |
|
Crude Price |
Levels |
2.313 |
4 |
|
Crude Price |
first differences |
9.267* |
3 |
|
Monthly Income |
Levels |
4.120* |
4 |
|
Monthly Income |
first differences |
12.521* |
2 |
*, and *** indicate the null hypothesis of a unit root can be rejected at the 1%, and 10%
level of significance, respectively. Lags indicate number of lagged first differences included as explanatory variables in the Augmented Dickey-Fuller (ADF) regression. All specifications include a constant, but no trend. †1% critical value = 3.454, 5% critical value = 2.871, 10% critical value = 2.572. Sample consists of 307 monthly observations between July 1976 and December 2001.
Table 4
The Effect of
Changes in the Price of Crude Oil on the Price of Regular Gas: Monthly
|
|
Dependent Variable and Sample |
|||
|
|
Gas Pricet |
Gas Pricet |
Change in Gas Pricet |
Change in Gas Pricet |
Independent Variables |
(76:2-01:12) |
(76:3-01:12) |
(76:3-01:12) |
(76:4-01:12) |
|
Intercept |
22.866* |
31.074* |
-1.014 |
-1.104*** |
|
|
(1.461) |
(3.853) |
(0.648) |
(0.655) |
|
Crude Pricet |
2.753* |
2.416* |
|
|
|
|
(0.042) |
(0.114) |
|
|
|
Dt (Crude Pricet) |
-0.086* |
-0.062* |
|
|
|
|
(0.027) |
(0.015) |
|
|
|
Incomet |
7.538* |
7.059* |
|
|
|
|
(0.156) |
(0.619) |
|
|
|
|
|
|
|
|
|
Change in Crude Pricet |
|
|
1.922* |
1.900* |
|
|
|
|
(0.228) |
(0.251) |
|
Dt (Change in Crude Pricet) |
|
|
0.137 |
0.151 |
|
|
|
|
(0.361) |
(0.390) |
|
Change in Incomet |
|
|
0.506 |
1.030 |
|
|
|
|
(5.794) |
(5.509) |
|
February |
0.215 |
0.228 |
1.036 |
1.090 |
|
|
(1.381) |
(0.605) |
(0.881) |
(0.802) |
|
March |
0.830 |
0.752 |
1.418 |
1.515*** |
|
|
(1.382) |
(0.802) |
(0.873) |
(0.871) |
|
April |
2.955** |
2.979* |
3.402* |
3.485* |
|
|
(1.380) |
(0.919) |
(0.869) |
(0.870) |
|
May |
5.234* |
5.265* |
3.259* |
3.335* |
|
|
(1.388) |
(0.997) |
(0.881) |
(0.884) |
|
June |
5.893* |
6.081* |
2.234** |
2.310* |
|
|
(1.380) |
(1.034) |
(0.870) |
(0.873) |
July |
4.723* |
4.935* |
-0.001 |
0.071 |
|
|
(1.380) |
(1.048) |
(0.878) |
(0.881) |
|
August |
3.604* |
3.925* |
0.162 |
0.241 |
|
|
(1.380) |
(1.035) |
(0.872) |
(0.878) |
|
September |
3.183** |
3.647* |
0.879 |
0.964 |
|
|
(1.381) |
(0.995) |
(0.872) |
(0.876) |
|
October |
1.693 |
2.194** |
-0.378 |
-0.300 |
|
|
(1.382) |
(0.922) |
(0.872) |
(0.874) |
|
November |
1.330 |
1.798** |
0.686 |
0.758 |
|
|
(1.380) |
(0.800) |
(0.874) |
(0.865) |
|
December |
0.553 |
0.943 |
0.248 |
0.304 |
|
|
(1.380) |
(0.603) |
(0.883) |
(0.809) |
|
ρ |
|
0.849* |
|
0.177* |
|
|
|
(0.032) |
|
(0.062) |
|
R2 |
0.956 |
0.984 |
0.471 |
0.487 |
|
F |
461.660* |
1219.137* |
18.774* |
18.542* |
|
DW |
0.404 |
1.535 |
1.620 |
1.855 |
|
N |
311 |
310 |
310 |
309 |
Standard errors in parentheses. *, **, and *** indicate the estimated coefficient is statistically different from zero at the 1%, 5%, or 10% level of significance, respectively. All t-tests are two-tail tests. Dt equals 1 if the price of crude increased since the last period, 0 otherwise. The ρ is the first-order autocorrelation coefficient in a AR(1) model.
Table 5
Augmented Dickey-Fuller Tests for Unit Roots - - Weekly Data
|
Variable |
Type |
Test Statistic |
|
|
levels |
2.121 |
|
|
first differences |
6.70* |
|
Crude Price |
levels |
1.573 |
|
Crude Price |
first differences |
9.755* |
|
Regular Gas Price– East Region |
levels |
1.929 |
|
Regular Gas Price– East Region† |
first differences |
6.298* |
|
Regular Gas Price – |
levels |
2.001 |
|
Regular Gas Price – |
first differences |
5.107* |
|
Regular Gas Price– |
levels |
1.974 |
|
Regular Gas Price– |
first differences |
5.121* |
|
Regular Gas Price– |
levels |
1.959 |
|
Regular Gas Price– |
first differences |
6.713* |
|
Regular Gas Price– Midwest Region† |
levels |
2.892** |
|
Regular Gas Price– Midwest Region |
first differences |
7.628* |
|
|
levels |
1.915 |
|
|
first differences |
6.558* |
|
Regular Gas Price– |
levels |
2.148 |
|
Regular Gas Price– |
first differences |
6.784* |
|
Regular Gas Price– West Region† |
levels |
2.380 |
|
Regular Gas Price– West Region |
first differences |
6.782* |
|
Regular Gas |
levels |
1.975 |
|
Regular Gas |
first differences |
3.804* |
|
Regular Gas |
levels |
2.322 |
|
Regular Gas |
first differences |
4.375* |
|
Regular Gas |
levels |
2.855*** |
|
Regular Gas |
first differences |
5.302* |
|
|
levels |
2.739*** |
|
|
first differences |
2.982** |
|
Regular Gas |
levels |
2.127 |
|
Regular Gas |
first differences |
3.877* |
|
Regular Gas Price– Chicago |
levels |
4.237* |
|
Regular Gas Price– Chicago |
first differences |
4.096* |
|
Regular Gas Price– Denver |
levels |
2.244 |
|
Regular Gas Price– Denver |
first differences |
4.430* |
|
Regular Gas Price– Houston |
levels |
1.973 |
|
Regular Gas Price– Houston |
first differences |
3.674* |
|
Regular Gas Price– |
levels |
1.869 |
|
Regular Gas Price– |
first differences |
3.937* |
|
Regular Gas |
levels |
2.545 |
|
Regular Gas |
first differences |
2.922** |
|
Regular Gas Price– |
levels |
1.764 |
|
Regular Gas Price– |
first differences |
3.468** |
*,**,*** indicate the null hypothesis of a unit root can be rejected at the 1%, 5%, and 10%
level of significance,
respectively. † indicates the ADF
regression contained two lags, while all others only contained one lag. All specifications include a constant, but no
trend. The
Table 6
National and
Regional Effects of Crude Oil Price on Regular Gas Price: Weekly
|
Gas Prices in: |
|
|
|
|
R2 |
DW |
|
64.337* |
3.000* |
-0.125* |
|
0.87 |
0.12 |
|
|
(1.467) |
(0.075) |
(0.041) |
|
|
|
|
90.579* |
1.726* |
-0.028* |
0.980* |
0.99 |
1.13 |
|
|
(6.881) |
(0.146) |
(0.012) |
(0.012) |
|
|
East
|
63.051* |
3.071* |
-0.182* |
|
0.87 |
0.14 |
|
|
(1.432) |
(0.073) |
(0.040) |
|
|
|
East
|
102.399* |
1.229* |
-0.027* |
0.993* |
0.99 |
0.84 |
|
|
(14.247) |
(0.110) |
(0.007) |
(0.007) |
|
|
|
67.824* |
3.220* |
-0.236* |
|
0.86 |
0.17 |
|
|
(1.602) |
(0.082) |
(0.045) |
|
|
|
|
112.409* |
0.958* |
-0.028* |
0.995* |
0.99 |
0.64 |
|
|
(18.733) |
(0.113) |
(0.007) |
(0.006) |
|
|
|
66.502* |
3.170* |
-0.209* |
|
0.86 |
0.15 |
|
|
(1.563) |
(0.008) |
(0.044) |
|
|
|
|
110.339* |
1.023* |
-0.0245* |
0.995* |
0.99 |
0.67 |
|
|
(17.845) |
(0.110) |
(0.007) |
(0.006) |
|
|
|
60.291* |
2.967* |
-0.154* |
|
0.88 |
0.13 |
|
|
(1.380) |
(0.071) |
(0.039) |
|
|
|
|
92.945* |
1.428* |
-0.029* |
0.988* |
0.99 |
1.04 |
|
|
(9.734) |
(0.125) |
(0.008) |
(0.009) |
|
|
|
61.150* |
3.143* |
-0.048 |
|
0.79 |
0.13 |
|
|
(2.033) |
(0.104) |
(0.057) |
|
|
|
|
73.597* |
2.551* |
-0.031*** |
0.943* |
0.97 |
1.29 |
|
|
(5.958) |
(0.237) |
(0.017) |
(0.020) |
|
|
Gulf
|
62.993* |
2.879* |
-0.154* |
|
0.86 |
0.14 |
|
|
(1.408) |
(0.072) |
(0.040) |
|
|
|
Gulf
|
95.201* |
1.320* |
-0.024* |
0.988* |
0.99 |
1.05 |
|
|
(9.597) |
(0.126) |
(0.008) |
(0.009) |
|
|
|
73.982* |
2.894* |
-0.219* |
|
0.82 |
0.18 |
|
|
(1.659) |
(0.085) |
(0.047) |
|
|
|
|
111.873* |
1.019* |
-0.035* |
0.984* |
0.98 |
1.31 |
|
|
(9.851) |
(0.169) |
(0.011) |
(0.011) |
|
|
West
|
80.986* |
3.049* |
-0.187* |
|
0.74 |
0.10 |
|
|
(2.203) |
(0.113) |
(0.062) |
|
|
|
West
|
124.496* |
1.88* |
-0.038* |
0.984* |
0.99 |
0.67 |
|
|
(0.1125) |
(0.0018) |
(0.0001) |
(0.0099) |
|
|
Standard errors in parentheses. * and *** indicate the estimated coefficient is statistically
different from zero at the 1% or 10% level of significance, respectively. All t-tests are two-tail tests. Dt equals
1 if the price of crude increased since the last period, 0 otherwise. The sample size of the regressions without
the ρ associated with the AR(1) error term
consists of 273 weekly observation between
Table 7
National and
Regional Effects of Crude Oil Price on Regular Gas Price:
Weekly
|
Δ Gas Prices in: |
|
|
|
|
R2 |
DW
|
|
-0.225 |
1.186* |
0.744*** |
|
0.34 |
1.09 |
|
|
(0.184) |
(0.211) |
(0.387) |
|
|
|
|
-0.215 |
0.611* |
0.732** |
0.570* |
0.52 |
2.19 |
|
|
(0.269) |
(0.175) |
(0.303) |
(0.051) |
|
|
East
|
-0.244*** |
0.697* |
0.777* |
|
0.30 |
0.79 |
|
|
(0.140) |
(0.168) |
(0.295) |
|
|
|
East
|
-0.151 |
0.233** |
0.589* |
0.738* |
0.64 |
2.03 |
|
|
(0.268) |
(0.105) |
(0.181) |
(0.042) |
|
|
|
-0.186 |
0.523* |
0.552*** |
|
0.18 |
0.60 |
|
|
(0.144) |
(0.165) |
(0.303) |
|
|
|
|
-0.050 |
0.175*** |
0.283*** |
0.789* |
0.66 |
2.08 |
|
|
(0.303) |
(0.095) |
(0.163) |
(0.038) |
|
|
|
-0.212 |
0.569* |
0.646** |
|
0.23 |
0.61 |
|
|
(0.140) |
(0.160) |
(0.294) |
|
|
|
|
-0.090 |
0.189** |
0.437* |
0.791* |
0.68 |
2.06 |
|
|
(0.298) |
(0.092) |
(0.159) |
(0.038) |
|
|
|
-0.271*** |
0.836* |
0.877* |
|
0.32 |
1.00 |
|
|
(0.158) |
(0.182) |
(0.333) |
|
|
|
|
-0.200 |
0.334** |
0.711* |
0.637* |
0.55 |
2.09 |
|
|
(0.254) |
(0.139) |
(0.242) |
(0.048) |
|
|
|
-0.247 |
1.875* |
0.833 |
|
0.28 |
1.29 |
|
|
(0.314) |
(0.360) |
(0.662) |
|
|
|
|
-0.290 |
1.259* |
0.948 |
0.408* |
0.38 |
2.12 |
|
|
(0.392) |
(0.340) |
(0.592) |
(0.057) |
|
|
Gulf
|
-0.313** |
0.723* |
0.971* |
|
0.29 |
1.00 |
|
|
(0.158) |
(0.181) |
(0.333) |
|
|
|
Gulf
|
-0.286 |
0.245*** |
0.901* |
0.6119* |
0.53 |
2.15 |
|
|
(0.242) |
(0.142) |
(0.247) |
(0.049) |
|
|
|
-0.123 |
0.559** |
0.453 |
|
0.09 |
1.25 |
|
|
(0.217) |
(0.248) |
(0.456) |
|
|
|
|
-0.028 |
0.239 |
0.240 |
0.432* |
0.23 |
2.14 |
|
|
(0.275) |
(0.228) |
(0.401) |
(0.432) |
|
|
West
|
-0.086 |
0.574** |
0.507 |
|
0.08 |
0.65 |
|
|
(0.235) |
(0.270) |
(0.495) |
|
|
|
West
|
0.132 |
0.295*** |
-0.081 |
0.729* |
0.55 |
1.82 |
|
|
(0.425) |
(0.172) |
(0.298) |
(0.042) |
|
|
Standard errors
in parentheses. *, **, and *** indicate the estimated coefficient is
statistically different from zero at the 1%, 5%, or 10% level of significance,
respectively. All t-tests are two-tail
tests. Dt
equals 1 if the price of crude increased since the last period, 0
otherwise. The sample size of the
regressions without the ρ associated with the AR(1)
error term consists of 272 weekly observation between
