Anticipated and unanticipated effects of crude oil prices and gasoline inventory changes on gasoline prices Stanislav Radchenko ∗ University of North Carolina at Charlotte revised April, 2005 Abstract This paper examines the effect of anticipated and unanticipated changes in oil prices and gasoline inventory on US gasoline prices. I show that gasoline price adjustments are faster and stronger for anticipated changes in oil prices and inventory levels than for unanticipated changes. In all versions of the adjustment model, the response of gasoline prices to unantici- pated oil price changes is lagged and incomplete. In versions of the model where anticipated and unanticipated oil price changes are not restricted to have the same effect, the response of gasoline prices to anticipated changes in oil prices is immediate and large. As anticipated oil price changes become more restricted to have the same effect as unanticipated changes, the response of gasoline prices to anticipated oil price changes becomes muted and delayed. Keywords: gasoline price response, anticipated price changes, gasoline inventory, lags in gasoline adjustment, unanticipated price changes * Radchenko is with the Department of Economics, University of North Carolina at Charlotte, Charlotte, NC 28223. Direct editorial correspondence at e-mail: [email protected], (704) 687-6157. I would like to thank participants of 2005 IAEE meeting in Philadelphia, January 2005 for their helpful comments. Special thanks are to five anonymous referees for many constructive suggestions.
Transcript
Anticipated and unanticipated effects of crudeoil prices and gasoline inventory changes on
gasoline prices
Stanislav Radchenko∗
University of North Carolina at Charlotte
revised April, 2005
Abstract
This paper examines the effect of anticipated and unanticipated changes in oil prices and
gasoline inventory on US gasoline prices. I show that gasoline price adjustments are faster
and stronger for anticipated changes in oil prices and inventory levels than for unanticipated
changes. In all versions of the adjustment model, the response of gasoline prices to unantici-
pated oil price changes is lagged and incomplete. In versions of the model where anticipated
and unanticipated oil price changes are not restricted to have the same effect, the response
of gasoline prices to anticipated changes in oil prices is immediate and large. As anticipated
oil price changes become more restricted to have the same effect as unanticipated changes,
the response of gasoline prices to anticipated oil price changes becomes muted and delayed.
∗Radchenko is with the Department of Economics, University of North Carolina at Charlotte, Charlotte,NC 28223. Direct editorial correspondence at e-mail: [email protected], (704) 687-6157. I wouldlike to thank participants of 2005 IAEE meeting in Philadelphia, January 2005 for their helpful comments.Special thanks are to five anonymous referees for many constructive suggestions.
1 Introduction
The question of lags in the response of gasoline prices to oil price changes has received con-
siderable attention from researchers. Since the study by Borenstein, Cameron, and Gilbert
(1997) which illustrates that gasoline prices adjust slowly to changes in crude oil prices,
several explanations of the observed phenomena have been suggested and tested. Borenstein
and Shepard (2002) argue that the slow response of gasoline prices is attributed to the high
cost of adjustment of production and inventory.1 Johnson (2002) argues that a search cost
may lead to long lags in the response of gasoline prices. Godby, Lintner, Stengos, and Wand-
schneider (2000) empirically explore the behavior of gasoline and oil prices and suggest that
only oil price changes that are bigger than some threshold level lead to revision of gasoline
prices. Similar results were obtained by Radchenko (2005) who points to possible nonlinear-
ities in retail gasoline prices and the role that different kinds of oil price fluctuations play
in the gasoline price response. In this paper, I add new evidence to the literature on lags in
the adjustment of gasoline prices to changes in crude oil prices by analyzing the response of
gasoline prices to anticipated and unanticipated oil price fluctuations.
I apply a methodology originally developed by Cochrane (1998) to distinguish between the
effect of anticipated and unanticipated oil price changes on the adjustment of retail gasoline
prices and use it to analyze the lags in the response of gasoline prices. Instead of developing
a structural model that embodies gasoline prices and anticipated and unanticipated oil price
changes, I use a reduced form approach in the analysis. The obtained results demonstrate
that empirical responses of gasoline prices to changes in oil market conditions (oil prices and
gasoline inventory) depend crucially on whether one assumes that changes in oil prices and
inventory are anticipated or unanticipated. I estimate models with different restrictions on
anticipated/unanticipated oil price movements to demonstrate how the measures of gasoline
price adjustment vary as one makes the restriction on the equal effect of anticipated and
1Consideration of the inventory adjustment cost along with the production adjustment cost is importantbecause it is known that many commodities do not exhibit statistically significant cost of adjusting produc-tion. See Pindyck (1994) who presents evidence of insignificant cost of adjustment for copper, heating oil,and lumber.
1
unanticipated changes more or less binding. The reported evidence is used to support the
cost of adjustment explanation of gasoline price lags advocated by Borenstein and Shepard
(2002).
In addition, anticipated and unanticipated gasoline inventory changes are added to the
model to examine the asymmetric response of gasoline prices to anticipated and unantici-
pated changes in inventory. The model allows to analyze interactions among gasoline inven-
tory, oil prices, and gasoline prices. It is generally agreed that producers must determine
output prices, production levels, and inventory levels jointly with expected inventory draw-
downs and buildups. Borenstein and Shepard (2002) argue that inventory dynamics are
important in understanding gasoline price dynamics. Pindyck (1994, 2001) presents models
that explain how prices, rates of production, and inventory are determined.
The findings of the paper may be summarized as follows. Gasoline prices respond much
faster to anticipated changes in oil prices than to unanticipated oil price changes, lending
further support to the cost of adjustment explanation of the gasoline price lags. While there
is a lag in the response of gasoline prices to unanticipated oil price changes, there is no lag in
the gasoline price adjustment to anticipated oil price changes. The gasoline price response
depends on the assumed restriction about the effect of anticipated and unanticipated changes
in the model. As the restriction becomes more binding, the adjustment of gasoline prices
to anticipated oil price changes becomes weaker and looks more similar to the response of
gasoline prices to unanticipated oil price changes. It is shown that both anticipated and
unanticipated changes of gasoline inventory have an asymmetric effect on gasoline prices.
Gasoline price adjustment is large and significant in the long-run after a positive shock to
gasoline inventories. However, the gasoline adjustment is insignificant in the long-run after
a negative shock to gasoline inventories. I also find evidence of asymmetry in the effect of
gasoline inventory changes on oil prices. A positive shock the gasoline inventory series leads
to a statistically significant adjustment of oil prices, while a decline in gasoline inventory has
insignificant effect on oil prices.
The structure of the paper is as follows. I present motivation for the anticipated/unanticipated
2
model of oil price changes in Section 2. In Section 3, I explain the details of the econometric
approach that I use to construct gasoline price responses to anticipated and unanticipated
movements in oil prices and gasoline inventory. In Section 4, I describe the data and results.
Concluding remarks are in Section 5.
2 Motivation of the anticipated/unanticipated oil price
changes
The basis for the analysis of anticipated and unanticipated oil price changes is found in
papers by Tang and Hammoudeh (2002) and Hammoudeh (1996) who develop an oil-price
target zone model. These authors explicitly model predicted and unpredicted (stochastic)
components in oil demand and supply. As a result, the oil price includes an unpredicted term
and a predicted term representing market participants’ anticipation of OPEC intervention.2
Tang and Hammoudeh (2002) present empirical support for the oil-price target zone model.
I follow the literature on the oil-price target zone model and assume that some changes
in oil prices may be anticipated correctly by refineries because of a systematic predictable
component attributed to OPEC policy, to seasonal fluctuations, or to both.3 For example,
refineries may anticipate correctly changes in the oil price when the crude oil price approaches
the bounds of the announced price band or when OPEC has its regular meetings to decide on
the current state of the market and production quotas. Based on the expectations of OPEC
meeting outcomes,4 refineries may start the necessary production and inventory adjustment
earlier5 so that by the time OPEC makes its announcement on production quotas refineries
2Hammoudeh and Madan (1995) argue that under ”normal conditions” the oil market participants formexpectations that may even cause a turnaround in the market in anticipation of OPEC’s intervention.
3OPEC officially announced its goal to keep oil prices in the price band of $22-28 a barrel for OPEC’sReference Basket. The official Press releases can be found at http://www.opec.org.
4There is uncertainty in the link between OPEC policy and oil prices because of cheating on quotas, devi-ations from the official policy. Wirl and Kujundzic (2004) analyze the possible impact of OPEC Conferenceoutcomes and suggest that sufficient information about the possible OPEC Conference outcome is leakedprior to a meeting.
5Borenstein and Shepard (2002) note that refineries optimize their production using a complex algorithmand it is costly for them to make supply adjustments immediately.
3
are better positioned to implement gasoline price adjustments immediately and fully.
In addition, oil price shocks can be caused by an unanticipated variation in demand
and/or non-OPEC related supply shocks. When a change in the oil price is unanticipated,
refineries may not be able to undertake an immediate and full price adjustment because
of high production and inventory costs of adjustment. Therefore, one may expect that
anticipated and unanticipated oil price changes lead to different gasoline price adjustments.
I conjecture that gasoline prices respond faster to anticipated oil price changes than to
unanticipated oil price changes, and I test this conjecture in the paper.
Another reason for separating the impact of anticipated and unanticipated oil price shocks
is that a clarification of the effects may help the interpretation of empirical evidence on the
source of lags in the response of gasoline prices. The common aspect of many papers,
including one of my papers, empirically exploring the relationship between oil prices and
gasoline prices is that the authors compute the measures of adjustment of gasoline prices
to changes in oil prices without explaining whether this measure is the response of gasoline
prices to anticipated oil price changes, to unanticipated oil price changes, or to a combination
of anticipated and unanticipated price changes. This leads to differences in the reported
results from various empirical models.
The proposed anticipated/unanticipated model explains the difference in results from the
partial adjustment model (PAM) and the vector autoregressive model (VAR). I demonstrate
that the measures of the gasoline price adjustment from the VAR and PAM gasoline models
describe different phenomena. The measure of adjustment of gasoline prices from a VAR
model captures the response of gasoline prices only to unanticipated oil price changes;6 the
measure of gasoline price adjustment from a PAM type model captures the response of
gasoline prices to a combination of both anticipated and unanticipated oil price changes by
implicitly assuming that both types of price changes have the same effect on gasoline prices.
6Christiano, Eichenbaum, and Evans (1998) point out that the VAR methodology is asymptoticallyequivalent to the following two step procedure. In the first step, realized shocks are estimated by the fittedresiduals in the ordinary least squares regression of the variable of interest on the variables in the informationset. In the second step, a researcher estimates the dynamic response of a variable to shocks by regressingthe variable on the current and lagged values of the estimated shocks (residuals).
4
Both models are unrealistic; it is unlikely that anticipated and unanticipated oil price
changes have the same effect on the gasoline price, as in PAM, or that only unanticipated oil
price changes influence the gasoline price, as in VAR. I apply a model that allows both kinds
of oil price changes to have a different impact on gasoline prices and show how one may
recover the measures of gasoline price adjustment to different kinds of oil price movements.
The last reason for the analysis of anticipated/unanticipated oil price changes is that it
supports evidence on the validity of the cost of adjustment explanation of gasoline price lags
advocated by Borenstein and Shepard (2002). This hypothesis is supported by empirical
evidence if it is shown that unanticipated changes in oil prices lead to lags in the response of
gasoline prices and gasoline prices respond without substantial lags to anticipated changes
in oil prices and gasoline inventory.7 This is one of the findings presented in this paper.
3 The model of the anticipated/unanticipated oil price
changes
This section describes the approach underlying the estimation. I modify the approach of
Cochrane (1998) to investigate the response of gasoline prices to oil price and gasoline in-
ventory changes when refineries react to both anticipated and unanticipated fluctuations in
the variables.8
The reason for the inclusion of inventory is my conjecture that when oil prices rise or
decline, they affect not only gasoline prices but also the level of gasoline inventory which has
a feedback effect on oil and gasoline prices. For example, an oil price increase should lead to
an increase in the gasoline price, but it may also lead to an increase in gasoline inventory in
the long run if, responding to higher oil prices, gasoline production does not decline as much
as the quantity of gasoline demanded. The production surplus then leads to an increase in
7A referee pointed out that depending on the timing and cost structure, it could still be that anticipatedchanges had substantial lags.
8Cochrane (1998) investigates how the VAR-based measures of the effect of money on output change asone varies the relative effects of anticipated/unanticipated money.
5
gasoline inventory, but, because of inventory capacity constraints, the increase in gasoline
inventory may decrease the oil demand and force oil producers to decrease oil prices which,
in turn, causes gasoline prices to decline as well.
It is generally agreed that retail gasoline prices respond to oil price movements asymmet-
rically, that is gasoline prices adjust faster to oil price increases than to oil price decreases.9
Less attention has been paid to whether changes in gasoline inventory have asymmetric ef-
fect on gasoline prices. I add inventory increases and decreases in the model to address this
question.10
3.1 The econometric model
The basis for the analysis of the relation between oil and gasoline prices is the following
model:
△gt = a∗(L)[λ△o+
t + (1 − λ)(△o+
t − Et−1△o+
t−1)] + d∗(L)[λ△o−t
+(1 − λ)(△o−t − Et−1△o−t−1)] + b∗(L)△gt−1 + et, (1)
where △gt = gt − gt−1 and gt is the retail gasoline price, △o+t = max{△ot, 0}, △o−t =
min{△ot, 0}, △ot = ot − ot−1 and ot is the crude oil price, a∗(L), b∗(L) and d∗(L) are lag
polynomials, in particular a∗(L) = a∗
0 +∑q
i=1 a∗
i Li, b∗(L) and d∗(L) are defined in a similar
way, the term Et−1△o+t denotes the expectation of oil price increase at period t given the
information up to the period t − 1, the term (△o+t − Et−1△o+
t−1) captures the effect of
unanticipated oil price increases. The terms △o+t and △o−t do not discriminate whether a
change in oil price is anticipated or unanticipated implying the same effect of anticipated
and unanticipated oil price fluctuations on gasoline price.
In this model, λ is a prespecified parameter that determines the restriction on the effect
9See Borenstein et al. (1997), Godby et al. (2000) or Brown and Yucel (2000) for the analysis ofasymmetry in the gasoline price adjustment and for more references on this literature.
10I would like to thank referees for this suggestion.
6
of anticipated and unanticipated oil price changes and varies between 0 and 1. As λ → 1,
the anticipated and unanticipated shocks are restricted to have the same effect on gasoline
prices and model (1) reduces to the partial adjustment model (PAM):
△gt = a∗(L)△o+
t + d∗(L)△o−t + b∗(L)△gt−1 + et. (2)
The response function of gasoline prices to a combination of anticipated and unanticipated
changes in crude oil prices is measured by the structural parameters in a∗(L) and d∗(L). As
λ → 0, there is no binding restriction that anticipated and unanticipated oil prices have the
same effect and the model specifies that gasoline prices respond only to unanticipated oil
The parameters of the polynomial a∗(L) and d∗(L) can be used to construct the response
of gasoline prices to unanticipated changes in crude oil prices. Empirically, the analysis of
model (3) is conducted using the VAR framework because an autoregressive polynomial may
be represented as a moving average (MA) polynomial which allows a researcher to estimate
the response of the variable of interest to the unanticipated changes in other variables.
Model (2) has proved to be a popular choice for the analysis of gasoline markets. Boren-
stein et al. (1997) employ the partial adjustment framework to analyze the fluctuations in
gasoline and oil prices. Johnson (2002) use a variant of the PAM to examine the search
cost explanation for the long lags in the response of gasoline prices to oil prices. The same
approach was followed by Radchenko (2005) who introduced Markov switching in polynomi-
als a∗(L) and d∗(L). Godby et al. (2000) use the error correction threshold autoregressive
model, which is similar to the PAM, to investigate the Canadian retail gasoline market.
Galeotti, Lanza, and Manera (2003) employ an error-correction model to analyze the Euro-
7
pean gasoline markets. The structural parameters a∗(L) and d∗(L) are used to construct the
cumulative response function of gasoline prices to changes in crude oil prices.11 The analysis
of gasoline markets in the VAR framework (3) was conducted by Borenstein and Shepard
(2002) and Radchenko (2004).
I estimate model (1) because it nests the VAR model and the PAM model as special
cases for λ = {0, 1} and allows a researcher a more flexible approach for the analysis of
gasoline responses in the presence of anticipated/unanticipated price changes by varying the
values of λ between zero and one. I consider how the estimated gasoline responses shift for
λ = {0, 0.25, 0.50, 0.75, 1}. As λ increases from 0 to 1, it is interpreted that the restriction
on the equal effect of anticipated and unanticipated oil price changes becomes more binding.
When λ = 1, the restriction is binding and anticipated and unanticipated changes have the
same effect.
To examine the effect of inventory increases and decreases, I add these variables together
with oil increases and decreases in model (1). I adopt Cochrane’s (1998) identification
scheme to recover the structural parameters of a∗(L) polynomial based on the estimates of
the reduced VAR model. I order variables as follows [△J+t ,△J−
t ,△o+t ,△o−t ,△gt], where
△Jt denotes a change in gasoline inventory, △J+t and △J−
t are defined similarly to △o+t and
△o−t . I assume that gasoline inventory dynamics have a contemporaneous effect on both oil
and gasoline prices, while oil prices have a contemporaneous effect on gasoline prices, and
gasoline prices effect oil prices and gasoline inventory with a lag. The ordering of the variables
may be an important issue in the VAR methodology. There is no theoretical guidance as to
the ordering of variables in the model, but I check the sensitivity of results for alternative
orderings and find that results are not substantially affected when other variable orderings
are used.
To construct orthogonalized impulse responses using the Cholesky decomposition, I es-
timate the VAR model with oil and gasoline prices and gasoline inventory and obtain the
following MA representation:
11See Borenstein et al. (1997) and Johnson (2002) for the details of how to recover the gasoline responseto oil prices based on the parameters a∗(L).
8
△J+t
△J−
t
△o+t
△o−t
△gt
=
cj+j+(L) cj+j−(L) cj+o+(L) cj+o−(L) cj+g(L)
cj−j+(L) cj−j−(L) cj−o+(L) cj−o−(L) cj−g(L)
co+j+(L) co+j−(L) co+o+(L) co+o−(L) co+g(L)
co−j+(L) co−j−(L) co−o+(L) co−o−(L) co−g(L)
cgj+(L) cgj−(L) cgo+(L) cgo−(L) cgg(L)
ej+t
ej−t
eo+t
eo−t
egt
, (4)
where E(ete′
t) = I, et = [ ej+t ej−t eo+t eo−t egt ]′. The polynomial cgo+(L) represents
the adjustment of gasoline prices to the normalized shock in oil price increase series, cgo+(L) =
cgo+,0 + cgo+,1L + cgo+,2L2 + ..., and other polynomials are defined similarly.
3.2 The response to unanticipated oil price or gasoline inventory
changes
In order to identify the parameters of the polynomial a∗(L) and d∗(L) for an unanticipated
shock, one needs to substitute the moving average representation for △gt from model (4)
into model (1) and equate the coefficients on the error term. For example, for the response
of gasoline prices to an unanticipated shock in oil price increase series, I obtain
cgo+(L) = a∗(L)(λco+o+(L) + (1 − λ)co+o+(0)). (5)
To obtain equation (5), note that the VAR response of △gt to the unanticipated oil price
change is △gt = cgo+(L)eo+t, the VAR response of △o+t to the unanticipated oil price change
is △o+t = co+o+(L)eo+t and △o+
t − Et−1o+t−1 = co+o+(L)eo+t − Et−1[co+o+(L)eo+t] = co+o+(0).
One may match powers of L in equation (5) to recover the {a∗
j} from {cgo+,j} and {co+o+,j}:
a∗
0 =cgo+,0
co+o+,0
; a∗
j =cgo+,j − λ
∑j−1
k=0 a∗
kco+o+,j−k
co+o+,0
, j > 0. (6)
This formula can be applied to find the adjustment of gasoline prices to unanticipated
increases and decreases in gasoline inventory.
9
3.3 The response to anticipated oil price or gasoline inventory
changes
One interesting question is how gasoline prices respond to changes in crude oil prices and
gasoline inventory that are anticipated in the model in which both anticipated and unantic-
ipated oil price changes matter and are not restricted to have the same effect on gasoline
prices. For illustration, I show how to recover the parameters of a∗(L) and d∗(L) polynomials
for an anticipated change in oil price increase, but the formulas can be easily used for an-
ticipated changes in gasoline inventory. If a change in oil price increase series is anticipated,
then equation (5) becomes
cgo+(L) = a∗(L)λco+o+(L). (7)
One may match powers of L in equation (7) to recover the {a∗
j} from {cgo+,j} and {co+o+,j}:
a∗
0 =cgo+,0
λco+o+,0
; a∗
j =cgo+,j − λ
∑j−1
k=0 a∗
kco+o+,j−k
λco+o+,0
, j > 0. (8)
Note from equation (8) that the response of gasoline prices to anticipated oil price changes
is not defined for the model λ = 0, the model with only unanticipated oil price changes.
3.4 The difference in VAR and PAM gasoline responses
It has been reported that the PAM and VAR models produce different responses of gasoline
prices. Borenstein and Shepard (2002) use both the PAM and the VAR models to estimate
the adjustment of gasoline prices to crude oil prices. They show that estimated gasoline
price responses from the VAR model indicate a faster adjustment to oil price changes than
those responses from the PAM. Balke, Brown, and Yucel (1998) consider several alternative
model specifications (PAM and error correction specification) for the asymmetry analysis of
gasoline prices. The authors find that results are puzzling because different models produce
10
different evidence on asymmetry.12
To understand the difference in the PAM and VAR results, notice that for the model
in which the effect of anticipated and unanticipated oil prices changes is the same (λ = 1),
equation (5) simplifies to
a∗(L) =cgo+(L)
co+o+(L), (9)
which is the response of gasoline prices to crude oil price changes recovered from estimation
of the PAM. If one estimates the VAR model (λ = 0), one recovers the adjustment of gasoline
prices to an oil price innovation eo+t
a∗(L) =cgo+(L)
co+o+(0). (10)
Notice that gasoline responses in (9) and (10) are different. Therefore, the PAM models and
VAR models produce different results because of the implicit assumption that these models
estimate the response of gasoline prices to different kinds of oil price changes. While the
VAR model measures the responses of gasoline prices only to unanticipated oil price changes
(the so-called oil price shocks) the PAM measures the responses of gasoline prices to some
kind of weighted average of both anticipated and unanticipated oil price changes restricting
both kinds of oil price movements to have the same effect on gasoline prices.
12To analyze the relationship between oil price volatility and the gasoline price asymmetry, Radchenko(2004) constructs several proxies for asymmetry in the gasoline response and finds that the the constructedproxies are different for the PAM and VAR models.
11
4 Data and Results
Weekly data on gasoline inventories, retail gasoline prices and crude oil prices have been
obtained from US Department of Energy for the period from March 1991 to February 2003.13
The Department’s US average weekly retail gasoline price is for Monday of each week, while
the average weekly gasoline inventory level is for Thursday of each week. Data have been
deseasonalized by running a regression on weekly dummy variables.14
Retail prices include taxes which may raise a problem if there were any significant gasoline
tax fluctuations over the time period considered. While there were no significant movements
in state average taxes, federal tax rates on gasoline increased from 14.1 cents per gallon
to 18.4 cents per gallon on October 1, 1993.15 To check for the effect of this increase on
the parameter estimates, I have included a dummy variable into the regression model. The
dummy variable takes on a value zero before October 1, 1993 and a value one otherwise.
The empirical results are robust to the inclusion of this tax dummy variable. Given that it
is insignificant, I omit it from the model estimation that is presented.
Another potential concern is inflation. The time period in estimation is relatively short,
March 1991 - August 2002, and the inflation rate for the period was quite low, ranging from
1.54 % to 3.58 % on an annual basis. The analysis is restricted to differences in the log levels
of oil and gasoline prices and gasoline inventory rather than the log levels of prices so that
inflation biases do not accumulate and the biases should not be severe.
The model estimation was performed using log-differenced data in the VAR model esti-
mation, implying a simple percent mark-up rule for margins.16 This, in turn, implies that
crude-gasoline margins increase with the price of crude oil. To test the robustness of the
estimates to a change in a functional form of the data,17 I have estimated the model with
13The data can be accessed at http://www.eia.doe.gov/neic/historic/hpetroleum2.htm#Gasoline.14Results are similar if no deseasonalization is applied.15One may check federal tax rates on motor fuels at http://www.fhwa.dot.gov/ohim/hs00/fe101a.htm and
state motor-fuel tax rates at the following webpage: http://www.fhwa.dot.gov/ohim/hs00/mf205.htm.16One may check Borenstein et al. (1997) for more details.17Borenstein, Cameron and Gilbert (1997) and Johnson (2002) argue that a use of data in levels in
estimation of the long-run equilibrium relationship between crude oil and gasoline price is more appropriate.
12
differenced data without log transformation and I have found the results to be similar across
the two specifications. Therefore, I report the empirical results only for the log-differenced
specification of the model. Log-differencing of the data also makes all variables in the model
stationary.
The lag length for VAR model is chosen based on the AIC. When models, with the
number of lags set to five and λ set to 0 and 1, are estimated over the full sample period,
results imply the pattern of gasoline price responses displayed in Figure 1. The two solid lines
on the top four graphs in Figure 1 are the estimated cumulative responses of gasoline prices
to oil price increases and decreases with the upper solid line always representing the gasoline
price response to an oil price increase. The two solid lines on the bottom four graphs are
the estimated cumulative gasoline price responses to inventory increases and decreases with
the upper solid line always representing the gasoline price response to an inventory decrease.
The dashed lines define a 90 percent confidence interval for the responses.18 Graphs labeled
with anticipated shock show the response of gasoline prices to an anticipated change in oil
prices and gasoline inventory. Likewise, graphs labeled with unanticipated shock show the
adjustment to a unanticipated shock in the variables.
For λ = 1, the response of gasoline prices to anticipated and unanticipated oil price
and inventory fluctuations, presented in Figure 1, are identical. This is because in this
model there is no difference between the effect of those price changes and they are assumed
(restricted) to have the same effect by construction. The response of gasoline prices seems to
have a slight hump-shaped form, where the initial increase in gasoline prices is followed by a
decline in the price level.19 For a positive shock in the oil price, gasoline prices adjust almost
completely to the estimated long-run equilibrium during the first four weeks.20 The long-run
equilibrium passthrough rate for these data (φ1) is estimated to be 0.42 and the gasoline
18The confidence intervals for the impulse response functions were constructed using the approach ofKillian (1998).
19The hump-shaped response of gasoline prices depends on a model specifications. In one of the earlierversions of this paper, I have estimated a three variable VAR model with gasoline inventory, oil prices, andgasoline prices and I have found a more pronounced hump-shaped response of gasoline prices.
20Because I construct cumulative responses, they do not have to converge to zero in the long-run.
13
response function to oil price increase shocks converges approximately to this value (0.36)
in four weeks.21 This is a faster speed of adjustment than the one reported by Borenstein et
al. (1997) who report the adjustment in ten weeks.
The response of gasoline prices to a shock in oil price decrease series seems to be smaller
and incomplete. The cumulative decline of gasoline prices in the long-run to a negative shock
in oil prices is 0.2. Having compared this value with the long-run response of gasoline prices
to a positive shock, I conclude that the evidence supports the asymmetry in the adjustment
of gasoline prices to shocks in oil prices.
The dynamics of gasoline prices in the model with λ = 0 are slightly different. For the
model with λ = 0, the gasoline prices, presented in Figure 1, react only to unanticipated
oil price and inventory changes and remain unchanged if an oil price change is anticipated.
Similar to the model with λ = 1, the response of gasoline prices to shocks in oil price increases
and decreases is asymmetric. The gasoline prices adjust to the long-run equilibrium after the
oil price increase during the first four weeks after the oil price change, but the adjustment
to an oil price decrease is incomplete. Also, notice that the response of gasoline prices to
unanticipated changes is very similar for the values λ = 0 and λ = 1.
Figure 1 presents the response of gasoline prices to changes in gasoline inventories. Results
on gasoline price and inventory dynamics are interesting because they show evidence on
asymmetry in the response of gasoline prices to changes in gasoline inventories. The effect
of a shock that decreases inventories is almost three times smaller than the effect of a shock
that increases gasoline inventories in the short-run. Moreover, the response of gasoline price
to a negative shock in gasoline inventories is weakly significant only in the short run (for the
weeks 3-4) and becomes insignificant in the long-run. The adjustment of gasoline prices to a
21When the long-run equilibrium relation is estimated using levels of oil and gasoline prices instead of logs,the estimated passthrough rate is 1.04 which is close to the previously reported estimates. To estimate thepassthrough rate, I run the following regression model:
ln gt = φ0 + φ1ln ot + φ2TIME + ǫt (11)
where the variable TIME represents the time trend and ǫt is a white noise process. The long-run relation ofthis form is standard in the literature and was used, for example, by Borenstein et al. (1997) and Johnson(2002).
14
positive shock in inventories is large and significant in the long-run. To my knowledge, this
result has not been reported in the literature before.
By looking at Figure 1, one may conclude that changes in gasoline inventories have a
larger effect on gasoline prices than changes in oil prices. However, changes in oil prices have
a larger variation than changes in gasoline inventories. Standard deviations are 4.88 and
1.24 for oil price changes and gasoline inventory changes respectively.
Because there is not much difference between anticipated and unanticipated changes for
λ = 0 and λ = 1, a researcher would miss the effect of anticipated shocks without looking
at the models with intermediate levels of λ. Therefore, I vary the values of λ between 0 and
1. That is, I look at models in which both anticipated and unanticipated oil price changes
influence the gasoline price and they are permitted to have different effects on gasoline prices
depending on the value of λ. Therefore, the restriction on the equal effect of anticipated and
unanticipated shocks is not binding.
For the model with λ = 0.25, one may observe a fast and big response of gasoline prices
to anticipated oil price changes during the first month in Figure 2. Notice that the response
of gasoline prices to anticipated oil price changes is much stronger than to unanticipated
variation in oil prices. Gasoline prices change by 1-1.5%, depending on whether oil prices
increase or decrease, in response to an anticipated 1% change in oil prices during the first
four weeks and by 0.4-1% during the first week only. That is, the complete adjustment to
the long-run equilibrium (0.42) is achieved within the first week (no lags) when an oil price
change is anticipated. In contrast, the response of gasoline price to 1% unanticipated oil
price change is slower and is equal to 0.3-0.36% in four weeks. The complete adjustment for
unanticipated changes occurs only for oil price increases and with a lag of five weeks.
The dynamics of gasoline price adjustments in this model confirms the prior expectation
that the response of gasoline prices to anticipated oil price changes is without substantial
lags, while the response of gasoline prices to unanticipated oil price changes is delayed.
As reported for the models with λ = {0, 1}, gasoline prices have a slightly hump-shaped
response and tend to decline during the next 6-8 weeks after reaching their peak in week 5.
15
The response of gasoline prices to shocks in oil prices stabilizes around weeks 12-13.
For models with λ = 0.50 and λ = 0.75, the restriction on the effect of anticipated and
unanticipated changes is more binding compared to the model with λ = 0.25. One may
observe a considerable shift in the dynamics of gasoline prices when oil price movements are
anticipated. As I increase λ and make the restriction more binding, the response of gasoline
prices to anticipated oil price changes starts to look more like the adjustment of gasoline
prices to unanticipated oil price changes. Gasoline prices respond only 0.5-0.7% (compared
to 1-1.5% for the model with λ = 0.25) to a 1% anticipated shock in oil price increases and
decreases for the model with λ = 0.50. The response is even smaller, 0.35-0.5%, for the
model with λ = 0.75.
The gasoline price response to unanticipated oil price changes seems to be only slightly
affected by the restriction on the effect of anticipated and unanticipated price changes in
the model. The response of gasoline prices to a unanticipated oil price change is almost the
same for the model with different values of λ during the first four weeks and differs slightly
only in the long run.
Because the empirical results confirm prior expectations about the effect of anticipated
and unanticipated oil price changes on gasoline prices, I conclude that an assumption of both
anticipated and unanticipated changes in oil prices is empirically plausible and it may be an
explanation for the reported evidence of long lags in the response of gasoline prices. Lags
in the response of gasoline price occur if the oil price changes are unanticipated and there
are no lags in the response of gasoline prices for anticipated oil price changes supporting the
cost of production and inventory explanation for lags in the adjustment of gasoline price.
Thus, the observed lags in the response of gasoline prices may be attributed to the fact that
most changes in oil prices are not anticipated.
Figure 3 depicts the response of gasoline prices to anticipated and unanticipated positive
and negative shocks in gasoline inventories for λ = {0.25, 0.5, 0.75}. One may notice that
the adjustment to anticipated shocks is much stronger than to unanticipated shocks. Unlike
the response of gasoline prices to anticipated shocks, the adjustment of gasoline prices to
16
unanticipated shocks in inventories is not very sensitive to changes in λ. The response of
gasoline prices to anticipated shocks is the strongest for λ = 0.25. As the value of λ increases
and the restriction on the effect of anticipated and unanticipated gasoline inventory shocks
becomes more binding, the adjustment of gasoline prices to anticipated and unanticipated
changes becomes similar. Just like for the case λ = 1.0 in Figure 1, one may observe an
asymmetry in the response of gasoline prices to positive and negative shocks in gasoline
inventoreis.
One potential explanation for the asymmetric response is inventory capacity constraints.
Refineries keep the optimal level of inventory to satisfy sudden increases in gasoline demand
or unanticipated supply disruptions (stock-out avoidance motive). Therefore, when there
is an increase in demand or a market shock that leads to a decline in gasoline inventories,
refineries gradually increase production to cope with a realized shock and replenish gasoline
inventory without adjusting the gasoline price much. When there is an unexpected increase
in gasoline inventories, refineries may be forced to decrease gasoline prices fast because of
lack of spare inventory capacity and the high cost of production decrease.
Having established that changes in gasoline inventory have a significant negative effect
on gasoline prices, I look at the interactions between gasoline inventory and oil prices. In the
model, there are two series for oil prices (oil price increase series and oil price decrease series)
and two series for gasoline inventory. One may look at how all these variables influence each
other, but I present results for only selected impulse responses. I focus on the effect of oil
price increases on gasoline inventory increases and on the impact of oil price decreases on
inventory declines.
I also examine how shocks to inventory declines effect oil increases and how gasoline
inventory increases influence oil price declines. The effect of gasoline inventory declines on
oil price decreases is found to be insignificant as is the effect of gasoline inventory decreases
on oil price increases.
Figures 4 - 5 present the response of gasoline inventory variables to changes in oil prices.
One may notice that there is statistically significant change in gasoline inventories in the
17
long-run after a shock that causes an increase in oil prices even though the lower bound of
confidence interval is close to zero. The adjustment of gasoline inventories is insignificant
for shocks that cause a decrease the oil price in the long-run. Therefore, one may interpret
this finding as evidence of asymmetry in the effect of oil price changes on gasoline inventory
levels. Overall, I conclude that when one looks at oil price increases and decreases and
inventory increases and decreases, the effect of changes in oil prices on gasoline inventories
is small.22
Figures 6 - 7 present evidence of asymmetry in the adjustment of oil prices to shocks in
gasoline inventory variables. Both anticipated and unanticipated negative shocks to gasoline
inventories do not have a statistically significant effect on oil prices. This result holds for
all values of λ considered and can be seen in Figure 6. However, a shock that increases oil
inventories leads to a statistically significant decline in oil prices. The effect of inventory
shock is particularly high when λ = 0.25 and the shock is anticipated. This can be seen
in Figure 7. The result is reminiscent of the effect of gasoline inventory shocks on gasoline
prices. While shocks that increase inventories have a significant effect on gasoline prices, the
effect of shocks that decrease inventories on gasoline price is insignificant. Thus, I think the
finding that oil prices do not respond to declines in gasoline inventories is attributed to the
lack of response in gasoline prices.
5 Conclusions
I apply an adjustment model that allows anticipated and unanticipated oil price movements
have different effects on gasoline prices. In this framework, the gasoline price response
depends on the assumed restriction about the effect of anticipated/unanticipated oil price
fluctuations. The paper illustrates that gasoline prices respond differently to anticipated and
unanticipated changes in oil prices and gasoline inventories. The response of gasoline prices
to an anticipated change in oil prices is fast and completed within a week after the oil price
22The effect of oil price on gasoline inventory is stronger and more significant if one looks at a three-variableVAR model in which oil prices and gasoline inventories are not split into increases and decreases.
18
change; the gasoline price response to unanticipated oil price changes is slow and incomplete.
The response of gasoline prices to anticipated changes in oil prices is the strongest and fastest
for the versions of the model where the restriction on the equal effect of anticipated and
unanticipated shocks is not binding. As the restriction becomes more binding, the response
of gasoline prices to anticipated oil price changes becomes muted and delayed.
The obtained results support evidence in the literature that the cost of adjustment of
production and inventory are responsible for the long lags observed in the response of gasoline
prices. The observed lags in the adjustment of gasoline prices may occur if most changes in
oil prices are unanticipated.
New findings of the paper also include the strongly asymmetric effect of changes in
gasoline inventories on gasoline prices. An increase in gasoline inventory has a statistically
significant effect on gasoline prices, while a decline in gasoline inventory has insignificant
effect. This leads to an asymmetric effect of gasoline inventory changes on oil prices. Oil
prices respond to increases in gasoline inventories, while they are insensitive to declines in
gasoline inventories. I also present weak evidence of the asymmetric effect of changes in oil
prices on gasoline inventories. Increases in oil prices seem to lead to statistically significant
increases in gasoline inventories in the long-run, while declines in oil prices do not have a
significant effect on gasoline inventory declines in either the short-run or long-run.
In sum, the obtained results present new evidence about the role of anticipated and unan-
ticipated oil price and gasoline inventory changes on gasoline prices. The explicit restriction
about the effect of anticipated oil price and gasoline inventory changes determines the ad-
justment of gasoline prices. Future work should use a structural approach to analyze this
question further. The structural approach should allow a researcher to estimate the value of
λ rather than vary it for different models. This will allow for a more precise evaluation of
the effect of anticipated price changes.
19
References
Adelman, M. A., 2002. World oil production & prices 1947-2000. The Quarterly Review ofEconomics and Finance 42, 169-191.
Bacon, R. W., 1991. Rockets and feathers: the asymmetric speed of adjustment of UK retailgasoline prices to cost changes. Energy Economics 13, 211-218.
Balke, N. S., Brown, S. P. A., and M. K. Yucel, 2002. Oil price shocks and the U.S. economy:where does the asymmetry originate? The Energy Journal 23(3), 27 - 52.
Brown, S. P. A., and M. K. Yucel, 2000. Gasoline and crude oil prices: why asymmetry?Federal Reserve Bank of Dallas Economic and Financial Review, Third Quarter, 23-29.
Balke, N. S., Brown, S. P. A., and M. K. Yucel, 1998. Crude oil and gasoline prices: anasymmetric relationship? Federal Reserve Bank of Dallas Economic Review, First Quarter,2-11.
Blinder, A. S., Canetti E. R., Lebow D. E., and J. B. Ruud, 1998. Asking about prices: anew approach to understanding price stickiness. New York, Sage Foundation.
Borenstein, S., and A. Shepard, 2002. Sticky prices, inventories, and market power in whole-sale gasoline markets. Rand Journal of Economics 33, 116-139.
Borenstein, S., Cameron A. C., and R. Gilbert, 1997. Do gasoline prices respond asymmet-rically to crude oil price changes? The Quarterly Journal of Economics 112, 305-339.
Christiano, L. J., Eichenbaum, M., and C. L. Evans, 1998. Monetary policy shocks: whathave we learned and to what end? NBER working paper 6400.Clements, M. P., and H. M. Krolzig, 2002. Can oil shocks explain asymmetries in the USbusiness cycle? Empirical Economics 27, 185-204.
Cochrane, J. H., 1998. What Do the VARs Mean? Measuring the Output Effects of MonetaryPolicy. Journal of Monetary Economics 41(2), 277-300.
Galeotti, M., Lanza A., and M. Manera, 2003. Rockets and feathers revisited: an interna-tional comparison on European gasoline markets. Energy Economics 25, 175 - 190.
Godby, R., Lintner A. M., Stengos T., and B. Wandschneider, 2000. Testing for asymmetricpricing in the Canadian retail gasoline market. Energy Economics 22, 349-368.
Hamilton, J. D., 2003. What is an oil shock? Journal of Econometrics 113, 201-339.
Hamilton, J. D., 1994. Time Series Analysis. Princeton University Press.
Hammoudeh, S., 1996. Oil price, mean reversion and zone readjustments. Southern Eco-nomic Journal 62(4), 916-929.
Hammoudeh, S., and V. Madan, 1995. Expectations, target zones, and oil price dynamics.Journal of Policy Modeling 17(6), 597 - 613.
Johnson, R. N., 2002. Search Costs, Lags and Prices at the Pump. Review of IndustrialOrganization 20, 33-50.
Kilian, L., 1998. Small-sample confidence intervals for impulse response functions. TheReview of Economics and Statistics 80, 218-230.
Kim, C.-J., and C. R. Nelson, 1998. State-space models with regime switching: classical andGibbs-sampling approaches with applications. The MIT press.
20
Kohl, W. L., 2002. OPEC behavior, 1998-2001. The Quarterly Review of Economics andFinance 42, 209-233.
Peltzman, S., 2000. Prices rise faster than they fall. Journal of Political Economy 108, 466- 502.
Pindyck, R. S., 1994. Inventories and the short-term dynamics of commodity prices. RandJournal of Economics 25, 141-159.
Pindyck, R. S., 2001. The dynamics of commodity spot and futures market: a primer. TheEnergy Journal 22(3), 1-29.
Radchenko, S., 2005. Lags in the response of gasoline prices to changes in crude oil prices:the role of short-term and long-term shocks. Energy Economics, forthcoming.
Radchenko, S., 2004. Oil Price Volatility and the Asymmetric Response of Gasoline Pricesto Oil Price Increases and Decreases. UNCC mimeo.
Raymond, J. E., Rich R. W., 1997. Oil and the macroeconomy: a Markov state-switchingapproach. Journal of Money, Credit, and Banking 29, 193-213.
Shin, D., 1994. Do product prices respond symmetrically to changes in crude prices? OPECReview, 137-157.
Reilly B., and R. Witt, 1998. Petrol price asymmetries revisited. Energy Economics 20,297-308.
Tang, L., and S. Hammoudeh, 2002. An empirical exploration of the world oil price underthe target zone model. Energy Economics 24, 577 - 596.
Wirl F., and A. Kujundzic, 2004. The impact of OPEC Conference outcomes on world oilprices 1984-2001. The Energy Journal 25, 45 - 62.
Figure 1: The response of gasoline prices to shocks in oil price increase, oil price decrease series, inventoryincrease and inventory decrease series. The two solid lines on top four graphs are the estimated responses ofgasoline prices to oil price increases and decreases with the upper solid line always representing the gasolineprice response to an oil price increase. The two solid lines on bottom four graphs are the estimated gasolineprice responses to inventory increases and decreases with the upper solid line always representing the gasolineprice response to an inventory decrease. The dashed lines represent 90% confidence intervals.
22
0 5 10 15−0.4
−0.2
0
0.2
0.4
Oil −> Gasoline, Unanticipated shock, λ =0.25
0 5 10 15
−1
0
1
2
Oil −> Gasoline, Anticipated shock, λ =0.25
0 5 10 15−0.4
−0.2
0
0.2
0.4
Oil −> Gasoline, Unanticipated shock, λ =0.50
0 5 10 15
−0.5
0
0.5
1
Oil −> Gasoline, Anticipated shock, λ =0.50
0 5 10 15−0.4
−0.2
0
0.2
0.4
Oil −> Gasoline, Unanticipated shock, λ =0.75
0 5 10 15−0.5
0
0.5
Oil −> Gasoline, Anticipated shock, λ =0.75
Figure 2: The response of gasoline prices to shocks in oil price increase and oil price decrease series. Thetwo solid lines are the estimated responses of gasoline prices to oil price increases and decreases with theupper solid line always representing the gasoline price response to an oil price increase. The dashed linesrepresent 90% confidence intervals.
Figure 3: The response of gasoline prices to shocks in inventory increase and inventory decrease series.The two solid lines are the estimated responses of gasoline prices to oil price increases and decreases withthe upper solid line always representing the gasoline price response to an inventory decrease. The dashedlines represent 90% confidence intervals.
