Anticipated and unanticipated effects of crude oil prices and gasoline inventory changes on gasoline prices

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1 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, 25 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 unanticipated 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 Direct editorial correspondence at sradchen@ .uncc.edu, (74) I would like to thank participants of 25 IAEE meeting in Philadelphia, January 25 for their helpful comments. Special thanks are to five anonymous referees for many constructive suggestions.

2 1 Introduction The question of lags in the response of gasoline prices to oil price changes has received considerable 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 (22) argue that the slow response of gasoline prices is attributed to the high cost of adjustment of production and inventory. 1 Johnson (22) argues that a search cost may lead to long lags in the response of gasoline prices. Godby, Lintner, Stengos, and Wandschneider (2) 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 (25) who points to possible nonlinearities 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 1 Consideration of the inventory adjustment cost along with the production adjustment cost is important because it is known that many commodities do not exhibit statistically significant cost of adjusting production. See Pindyck (1994) who presents evidence of insignificant cost of adjustment for copper, heating oil, and lumber. 1

3 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 (22). In addition, anticipated and unanticipated gasoline inventory changes are added to the model to examine the asymmetric response of gasoline prices to anticipated and unanticipated changes in inventory. The model allows to analyze interactions among gasoline inventory, oil prices, and gasoline prices. It is generally agreed that producers must determine output prices, production levels, and inventory levels jointly with expected inventory drawdowns and buildups. Borenstein and Shepard (22) argue that inventory dynamics are important in understanding gasoline price dynamics. Pindyck (1994, 21) 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

4 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 (22) 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 (22) 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 earlier 5 so that by the time OPEC makes its announcement on production quotas refineries 2 Hammoudeh and Madan (1995) argue that under normal conditions the oil market participants form expectations that may even cause a turnaround in the market in anticipation of OPEC s intervention. 3 OPEC officially announced its goal to keep oil prices in the price band of $22-28 a barrel for OPEC s Reference Basket. The official Press releases can be found at 4 There is uncertainty in the link between OPEC policy and oil prices because of cheating on quotas, deviations from the official policy. Wirl and Kujundzic (24) analyze the possible impact of OPEC Conference outcomes and suggest that sufficient information about the possible OPEC Conference outcome is leaked prior to a meeting. 5 Borenstein and Shepard (22) note that refineries optimize their production using a complex algorithm and it is costly for them to make supply adjustments immediately. 3

5 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. 6 Christiano, Eichenbaum, and Evans (1998) point out that the VAR methodology is asymptotically equivalent to the following two step procedure. In the first step, realized shocks are estimated by the fitted residuals in the ordinary least squares regression of the variable of interest on the variables in the information set. In the second step, a researcher estimates the dynamic response of a variable to shocks by regressing the variable on the current and lagged values of the estimated shocks (residuals). 4

6 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 (22). 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 inventory 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 7 A referee pointed out that depending on the timing and cost structure, it could still be that anticipated changes had substantial lags. 8 Cochrane (1998) investigates how the VAR-based measures of the effect of money on output change as one varies the relative effects of anticipated/unanticipated money. 5

7 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 asymmetrically, 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 effect on gasoline prices. I add inventory increases and decreases in the model to address this question The econometric model The basis for the analysis of the relation between oil and gasoline prices is the following model: g t = a (L)[λ o + t + (1 λ)( o + t E t o + t)] + d (L)[λ o t +(1 λ)( o t E t o t)] + b (L) g t + e t, (1) where g t = g t g t and g t is the retail gasoline price, o + t = max{ o t, }, o t = min{ o t, }, o t = o t o t and o t is the crude oil price, a (L), b (L) and d (L) are lag polynomials, in particular a (L) = a + q i=1 a il i, b (L) and d (L) are defined in a similar way, the term E t 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 E t o + t) 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 9 See Borenstein et al. (1997), Godby et al. (2) or Brown and Yucel (2) for the analysis of asymmetry in the gasoline price adjustment and for more references on this literature. 1 I would like to thank referees for this suggestion. 6

8 of anticipated and unanticipated oil price changes and varies between 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): g t = a (L) o + t + d (L) o t + b (L) g t + e t. (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, 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 price changes: g t = a (L)( o + t E t o + t) + d (L)( o t E t o t) + b (L) g t + e t. (3) 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. Borenstein et al. (1997) employ the partial adjustment framework to analyze the fluctuations in gasoline and oil prices. Johnson (22) 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 (25) who introduced Markov switching in polynomials a (L) and d (L). Godby et al. (2) use the error correction threshold autoregressive model, which is similar to the PAM, to investigate the Canadian retail gasoline market. Galeotti, Lanza, and Manera (23) employ an error-correction model to analyze the Euro- 7

9 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 (22) and Radchenko (24). I estimate model (1) because it nests the VAR model and the PAM model as special cases for λ = {, 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 = {,.25,.5,.75, 1}. As λ increases from 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 +, Jt, o + t, o t, g t ], where J t denotes a change in gasoline inventory, J t + and Jt 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 estimate the VAR model with oil and gasoline prices and gasoline inventory and obtain the following MA representation: 11 See Borenstein et al. (1997) and Johnson (22) for the details of how to recover the gasoline response to oil prices based on the parameters a (L). 8

10 J t + Jt o + t o t g t c j + j +(L) c j + j (L) c j + o +(L) c j + o (L) c j + g(l) e j + t c j j +(L) c j j (L) c j o +(L) c j o (L) c j g(l) e j t = c o + j +(L) c o + j (L) c o + o +(L) c o + o (L) c o + g(l) e o + t, (4) c o j +(L) c o j (L) c o o +(L) c o o (L) c o g(l) e o t c gj +(L) c gj (L) c go +(L) c go (L) c gg (L) e gt where E(e t e t) = I, e t = [e j + t e j t e o + t e o t e gt ]. The polynomial c go +(L) represents the adjustment of gasoline prices to the normalized shock in oil price increase series, c go +(L) = c go +, + c go +,1L + c go +,2L , 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 g t 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 c go +(L) = a (L)(λc o + o +(L) + (1 λ)c o + o +()). (5) To obtain equation (5), note that the VAR response of g t to the unanticipated oil price change is g t = c go +(L)e o + t, the VAR response of o + t to the unanticipated oil price change is o + t = c o + o +(L)e o + t and o + t E t o + t = c o + o +(L)e o + t E t [c o + o +(L)e o + t] = c o + o +(). One may match powers of L in equation (5) to recover the {a j} from {c go +,j} and {c o + o +,j}: a = c go +, ; a j = c go +,j λ j c o + o +, k= a kc o + o +,j k c o + o +,, j >. (6) This formula can be applied to find the adjustment of gasoline prices to unanticipated increases and decreases in gasoline inventory. 9

11 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 unanticipated 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 anticipated changes in gasoline inventory. If a change in oil price increase series is anticipated, then equation (5) becomes c go +(L) = ã (L)λc o + o +(L). (7) One may match powers of L in equation (7) to recover the {ã j} from {c go +,j} and {c o + o +,j}: ã = c go +, ; ã j = c go +,j λ j λc o + o +, k= ã kc o + o +,j k λc o + o +,, j >. (8) Note from equation (8) that the response of gasoline prices to anticipated oil price changes is not defined for the model λ =, 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 (22) 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 Yücel (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 1

12 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) = c go +(L) (9) c o + o +(L), 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 = ), one recovers the adjustment of gasoline prices to an oil price innovation e o + t a (L) = c go +(L) (1) c o + o +(). Notice that gasoline responses in (9) and (1) 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. 12 To analyze the relationship between oil price volatility and the gasoline price asymmetry, Radchenko (24) constructs several proxies for asymmetry in the gasoline response and finds that the the constructed proxies are different for the PAM and VAR models. 11

13 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 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, 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 August 22, 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 estimation, 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 13 The data can be accessed at 14 Results are similar if no deseasonalization is applied. 15 One may check federal tax rates on motor fuels at and state motor-fuel tax rates at the following webpage: 16 One may check Borenstein et al. (1997) for more details. 17 Borenstein, Cameron and Gilbert (1997) and Johnson (22) 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

14 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 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 9 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. 2 The long-run equilibrium passthrough rate for these data (φ 1 ) is estimated to be.42 and the gasoline 18 The confidence intervals for the impulse response functions were constructed using the approach of Killian (1998). 19 The hump-shaped response of gasoline prices depends on a model specifications. In one of the earlier versions of this paper, I have estimated a three variable VAR model with gasoline inventory, oil prices, and gasoline prices and I have found a more pronounced hump-shaped response of gasoline prices. 2 Because I construct cumulative responses, they do not have to converge to zero in the long-run. 13

15 response function to oil price increase shocks converges approximately to this value (.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.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 = are slightly different. For the model with λ =, 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 = 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 21 When the long-run equilibrium relation is estimated using levels of oil and gasoline prices instead of logs, the estimated passthrough rate is 1.4 which is close to the previously reported estimates. To estimate the passthrough rate, I run the following regression model: ln g t = φ + φ 1 ln o t + φ 2 TIME + ǫ t (11) where the variable TIME represents the time trend and ǫ t is a white noise process. The long-run relation of this form is standard in the literature and was used, for example, by Borenstein et al. (1997) and Johnson (22). 14

16 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 = 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 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 =.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.4-1% during the first week only. That is, the complete adjustment to the long-run equilibrium (.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.3-.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 = {, 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

17 The response of gasoline prices to shocks in oil prices stabilizes around weeks For models with λ =.5 and λ =.75, the restriction on the effect of anticipated and unanticipated changes is more binding compared to the model with λ =.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.5-.7% (compared to 1-1.5% for the model with λ =.25) to a 1% anticipated shock in oil price increases and decreases for the model with λ =.5. The response is even smaller,.35-.5%, for the model with λ =.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 = {.25,.5,.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

18 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 =.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. 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

19 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 =.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 22 The effect of oil price on gasoline inventory is stronger and more significant if one looks at a three-variable VAR model in which oil prices and gasoline inventories are not split into increases and decreases. 18

20 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 unanticipated 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 adjustment 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

21 References Adelman, M. A., 22. World oil production & prices The Quarterly Review of Economics and Finance 42, Bacon, R. W., Rockets and feathers: the asymmetric speed of adjustment of UK retail gasoline prices to cost changes. Energy Economics 13, Balke, N. S., Brown, S. P. A., and M. K. Yücel, 22. Oil price shocks and the U.S. economy: where does the asymmetry originate? The Energy Journal 23(3), Brown, S. P. A., and M. K. Yücel, 2. Gasoline and crude oil prices: why asymmetry? Federal Reserve Bank of Dallas Economic and Financial Review, Third Quarter, Balke, N. S., Brown, S. P. A., and M. K. Yücel, Crude oil and gasoline prices: an asymmetric relationship? Federal Reserve Bank of Dallas Economic Review, First Quarter, Blinder, A. S., Canetti E. R., Lebow D. E., and J. B. Ruud, Asking about prices: a new approach to understanding price stickiness. New York, Sage Foundation. Borenstein, S., and A. Shepard, 22. Sticky prices, inventories, and market power in wholesale gasoline markets. Rand Journal of Economics 33, Borenstein, S., Cameron A. C., and R. Gilbert, Do gasoline prices respond asymmetrically to crude oil price changes? The Quarterly Journal of Economics 112, Christiano, L. J., Eichenbaum, M., and C. L. Evans, Monetary policy shocks: what have we learned and to what end? NBER working paper 64. Clements, M. P., and H. M. Krolzig, 22. Can oil shocks explain asymmetries in the US business cycle? Empirical Economics 27, Cochrane, J. H., What Do the VARs Mean? Measuring the Output Effects of Monetary Policy. Journal of Monetary Economics 41(2), Galeotti, M., Lanza A., and M. Manera, 23. Rockets and feathers revisited: an international comparison on European gasoline markets. Energy Economics 25, Godby, R., Lintner A. M., Stengos T., and B. Wandschneider, 2. Testing for asymmetric pricing in the Canadian retail gasoline market. Energy Economics 22, Hamilton, J. D., 23. What is an oil shock? Journal of Econometrics 113, Hamilton, J. D., Time Series Analysis. Princeton University Press. Hammoudeh, S., Oil price, mean reversion and zone readjustments. Southern Economic Journal 62(4), Hammoudeh, S., and V. Madan, Expectations, target zones, and oil price dynamics. Journal of Policy Modeling 17(6), Johnson, R. N., 22. Search Costs, Lags and Prices at the Pump. Review of Industrial Organization 2, Kilian, L., Small-sample confidence intervals for impulse response functions. The Review of Economics and Statistics 8, Kim, C.-J., and C. R. Nelson, State-space models with regime switching: classical and Gibbs-sampling approaches with applications. The MIT press. 2

22 Kohl, W. L., 22. OPEC behavior, The Quarterly Review of Economics and Finance 42, Peltzman, S., 2. Prices rise faster than they fall. Journal of Political Economy 18, Pindyck, R. S., Inventories and the short-term dynamics of commodity prices. Rand Journal of Economics 25, Pindyck, R. S., 21. The dynamics of commodity spot and futures market: a primer. The Energy Journal 22(3), Radchenko, S., 25. 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., 24. Oil Price Volatility and the Asymmetric Response of Gasoline Prices to Oil Price Increases and Decreases. UNCC mimeo. Raymond, J. E., Rich R. W., Oil and the macroeconomy: a Markov state-switching approach. Journal of Money, Credit, and Banking 29, Shin, D., Do product prices respond symmetrically to changes in crude prices? OPEC Review, Reilly B., and R. Witt, Petrol price asymmetries revisited. Energy Economics 2, Tang, L., and S. Hammoudeh, 22. An empirical exploration of the world oil price under the target zone model. Energy Economics 24, Wirl F., and A. Kujundzic, 24. The impact of OPEC Conference outcomes on world oil prices The Energy Journal 25,

23 Oil > Gasoline, Unanticipated shock, λ = Oil > Gasoline, Unanticipated shock, λ = Inventory > Gasoline, Unanticipated shock, λ = Inventory > Gasoline, Unanticipated shock, λ = Oil > Gasoline, Anticipated shock, λ = Oil > Gasoline, Anticipated shock, λ = Inventory > Gasoline, Anticipated shock, λ = Inventory > Gasoline, Anticipated shock, λ = Figure 1: The response of gasoline prices to shocks in oil price increase, oil price decrease series, inventory increase and inventory decrease series. The two solid lines on top four graphs are the estimated 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 bottom four graphs are the estimated 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 represent 9% confidence intervals. 22

24 Oil > Gasoline, Unanticipated shock, λ = Oil > Gasoline, Unanticipated shock, λ = Oil > Gasoline, Unanticipated shock, λ =.75 Oil > Gasoline, Anticipated shock, λ = Oil > Gasoline, Anticipated shock, λ = Oil > Gasoline, Anticipated shock, λ = Figure 2: The response of gasoline prices to shocks in oil price increase and oil price decrease series. The two solid lines are the estimated 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 dashed lines represent 9% confidence intervals. 23