A threshold cointegration analysis of asymmetric price transmission from crude oil to gasoline prices

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Economics Letters 89 (2005) 233 239 www.elsevier.

Lai Department of Economics, California State University, Los Angeles, CA 90032, USA Received 3 June 2003; received in revised form 14 April 2005; accepted 11 May 2005 Available online 8 August 2005

1 Economics Letters 89 (2005) A threshold cointegration analysis of asymmetric price transmission from crude oil to gasoline prices Li-Hsueh Chen, Miles FinneyT, Kon S. Lai Department of Economics, California State University, Los Angeles, CA 90032, USA Received 3 June 2003; received in revised form 14 April 2005; accepted 11 May 2005 Available online 8 August 2005 Abstract This study provides new supportive evidence for asymmetric adjustment in U.S. retail gasoline prices. The asymmetric transmission is found to occur not just through the spot markets of crude oil and refinery gasoline but also through their future markets. Further evidence also shows that the observed asymmetry in price transmission primarily occurs downstream not upstream of the transmission process. D 2005 Elsevier B.V. All rights reserved. Keywords: Spot gasoline price; Crude oil; Threshold cointegration; Asymmetric adjustment JEL classification: C32; Q40 1. Introduction Often construed as an abuse of market power, many consumers complain that gasoline prices at the pump respond faster to a crude oil price increase than to a decrease. The perceived asymmetry points to a potential gap in price theory (Peltzman, 2000). Despite this perception, recent empirical findings on price asymmetry have been mixed for North American markets (Shin, 1994; Duffy-Deno, 1996; Balke et al., 1998; Borenstein et al., 1997; EIA, 1999; Godby et al., 2000). This study follows T Corresponding author. Tel.: ; fax: address: mfinney@calstatela.edu (M. Finney) /$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi: /j.econlet

2 234 L.-H. Chen et al. / Economics Letters 89 (2005) Borenstein et al. (1997) which analyzes price transmission at various stages in the production and distribution chain. We depart from previous research in identifying the potential role future markets may play in asymmetric price transmission. Futures prices rapidly disseminate information on current and future cost conditions to gasoline retailers. Moreover, most crude oil and refinery gasoline transactions are conducted through contract arrangements with pricing terms tied to either spot or future prices. This study analyzes asymmetric gasoline price adjustment using threshold cointegration analysis. The threshold determining the switch in model equations is defined by whether the downstream price (in or close to retail markets) is above or below its equilibrium level relative to the upstream price (in or close to crude oil markets). This differs from the modeling approach of previous studies, which defines alternate regimes as periods of either rising or falling upstream prices. The standard approach does not fully account for the idea that movement in downstream gasoline prices is toward equilibrium, which, in a given period, may not be in the same direction as the upstream price change. Given an upstream shock such as a large increase in crude oil prices, the move re-establishing market equilibrium would entail an increase in downstream (retail) gasoline prices that could continue even after crude oil prices have begun to fall. In our analysis, it is the change in the disequilibrium deviation between downstream and upstream prices not a reversal in the upstream price movement that determines the switch in model equations. We do find empirical evidence of asymmetric price response but, in contrast to Borenstein et al. (1997), we identify its source to be at the stage closer to the retail market (downstream) as opposed to the upstream level. Retail gasoline prices are also found to respond asymmetrically to both gasoline spot and future prices at the refinery stage. 2. Threshold cointegration analysis We examine weekly data on crude oil spot and future prices, gasoline spot and future prices, and U.S. retail gasoline prices. All the weekly data are based on prices on the first business day of each week. The crude oil prices are for West Texas Intermediate, the U.S. benchmark grade. The spot prices of crude oil and refinery gasoline are closing prices on the New York Mercantile Exchange (NYMEX). The future prices of crude oil and refinery gasoline are NYMEX settlement prices for the nearby contract expiring in the third nearest delivery month. Data from overlapping future contracts are compiled, with rollover to the next contract in the first week of each month. The retail prices are national averages for self-serve regular unleaded gasoline reported from the Energy Information Administration s (EIA) weekly Motor Gasoline Price Survey. The sample data cover the period January 1991 through March The start date of the sample is dictated by the availability of the EIA survey data on retail prices. Before performing cointegration analysis, we used the efficient DF-GLS unit root test (Elliott et al., 1996; Cheung and Lai, 1995) to check for nonstationarity in individual price series. While the unitroot hypothesis could not be rejected for all level series, the first-differenced price series were always found to be stationary. The test results support the hypothesis that crude oil and gasoline price series are each integrated of order one. This integration property readily lends itself to cointegration analysis. In our analysis of price asymmetry, we employ Enders and Siklo s (2001) test for threshold cointegration, which extends Engle and Granger s procedure to encompass possible asymmetric

3 L.-H. Chen et al. / Economics Letters 89 (2005) adjustment to disequilibrium. Consider X t the downstream price variable and Y t the upstream price variable, both of which are integrated of order one. Let the cointegrating relationship be X t ¼ f 0 þ f 1 Y t þ e t ; ð1þ where e t measures the deviation from the equilibrium relationship between X t and Y t. Consistent estimates of the equilibrium error, e t, can be obtained using the simple least squares method. For the two variables to be cointegrated, e t should be stationary. To allow for asymmetric adjustment dynamics, deviations from equilibrium are modeled to follow a threshold autoregressive process: De t ¼ I t q 1 e t 1 þ ð1 I t Þq 2 e t 1 þ Xp / k De t k þ u t ; ð2þ where D is the difference operator and I t =1 if X t 1 bf 0 +f 1 Y t 1 and 0 otherwise. By allowing q 1 and q 2 to take different values, the model recognizes that positive and negative deviations from equilibrium can be corrected for at different speeds. If cointegration exists, q 1 b0 and q 2 b0. Testing for cointegration can be performed based on the t Max and U tests proposed by Enders and Siklos (2001). The t Max statistic is given by the larger t-statistic of q 1 and q 2. A significantly negative t Max statistic would imply that q 1 and q 2 are both negative. The U test is an F-test examining the joint hypothesis of q 1 =0 and q 2 =0. Table 1 contains the results of the t Max and U tests for cointegration. To gain extra insight into possible channels of price transmission, we explore not only the cointegrating relationship between crude oil and retail gasoline prices but also relationships within the intermediate markets: from crude oil to refinery gasoline prices, and from refinery gasoline to retail prices. The t Max and U test results strongly support the existence of long-run equilibrium relationships between crude oil (spot or future) prices, refinery gasoline (spot or future) prices, and retail gasoline prices. Table 1 Results from the Enders Siklos test for threshold cointegration Price variables in the cointegrating relationship Cointegration test statistics Y t X t t Max U Crude oil prices vs. retail gasoline prices: Crude oil spot Gasoline retail 3.676** ** Crude oil futures Gasoline retail 3.376** ** Crude oil prices vs. refinery gasoline prices: Crude oil spot Gasoline spot 5.183** ** Crude oil futures Gasoline spot 4.163** ** Crude oil spot Gasoline futures 3.976** ** Crude oil futures Gasoline futures 3.242** ** Refinery gasoline prices vs. retail gasoline prices: Gasoline spot Gasoline retail 2.944** 8.894** Gasoline futures Gasoline retail 3.915** ** The lag used for each test is determined using the general-to-specific method (Ng and Perron, 1995) with a maximum lag order of 8 allowed. The null hypothesis under test is no cointegration. Approximate critical values for the t Max and U tests are tabulated by Enders and Siklos (2001). For the t Max test statistic, critical values are 1.69 for the 10% significance level and 1.89 for the 5% significance level. For the U test statistic, critical values are approximately 5.21 for the 10% significance level and 6.33 for the 5% significance level. Statistical significance is indicated by double asterisks (**) for the 5% level.

4 236 L.-H. Chen et al. / Economics Letters 89 (2005) A threshold error-correction model The threshold cointegration results further suggest the underlying adjustment dynamics of X t in response to changes in Y t can be captured using an error-correction model: DX t ¼ l þ I t q 1 EC t 1 þ ð1 I t Þq 2 EC t 1 þ Xp a k DY t k þ Xp b k DX t k þ v t : ð3þ where EC t 1 =X t 1 f 0 f 1 Y t 1, the one-period lagged error term for the cointegrating Eq. (1). As noted by Enders and Siklos (2001), a more general specification may incorporate threshold effects of lagged DY t and DX t with a k and b k depending on whether EC t 1 is positive or negative. To evaluate the potential asymmetry in price transmission to X t from Y t, we consider the following threshold model: 8 k þ EC t 1 þ Xp a þ k DY t k þ Xp >< b þ k DX t k þ v t if X t 1 bf 0 þ f 1 Y t 1 DX t ¼ l þ ð4þ >: k EC t 1 þ Xp a k DY t k þ Xp b k DX t k þ v t otherwise: This permits different adjustment processes for X t in response to positive and negative deviations from equilibrium. A positive shock to Y t can lead to X t bf 0 +f 1 Y t, with X t being below its equilibrium level relative to Y t.. X t will adjust upward to track Y t to correct the price deviation from equilibrium. A negative shock to Y t, on the other hand, can lead to X t Nf 0 +f 1 Y t. When X t is above its equilibrium level relative to Y t, X t will move downward, thereby gradually eliminating the price discrepancy. It should be noted that the threshold here is defined with respect to X t being above or below its equilibrium level relative to Y t. This departs from previous studies, in which the explanatory variables are typically split into two regimes based on the sign of DY t in individual periods. To the extent that market price adjustments are not instantaneous, defining the regimes based on whether Y t is increasing or decreasing in specific periods may lead to misleading inferences on the actual response of X t because it ignores the information reflected by the relative equilibrium level of X t and Y t. Suppose that X t is the retail gasoline price and Y t represents the crude oil price. Consider two alternative situations: (1) The crude oil price jumped 5 dollars in the first period and then fell 10 cents in the second period, and (2) the crude oil price jumped 4 dollars in the first period, followed by another 90 cents increase during the second period. Both led to a net increase of 4.9 dollars for the crude oil price. Because of lagged responses to the higher crude oil price, the retail price would rise over time in both situations. Under the conventional approach, the first scenario would trigger a regime switch but the second scenario would not. Under our approach, in contrast, no regime change would take place in either case so long as the retail gasoline price remained below equilibrium and was adjusting upward to catch up with the higher crude oil price. In short, the key feature of our threshold model is that the retail price of gasoline rises (falls) not simply because the crude oil price change is positive (negative) during a given period, but because the retail price is below (above) its equilibrium level relative to the crude oil price. The above specification also distinguishes between long- and short-run adjustments. The long-run adjustment of X t is determined by the parameters, k + and k. The short-run adjustment of X t, which is governed by the parameters, a k +, a k, b k +, and b k (for k =1, 2,..., p), may come either from its own

5 L.-H. Chen et al. / Economics Letters 89 (2005) history of lagged dynamics or from the lagged effects of Y t.ifk + p k, X t exhibits asymmetry in longrun adjustment. If either a k + p a k or b k + p b k or both, X t displays asymmetry in short-run adjustment. Table 2 presents the results from tests for adjustment symmetry. The test for long-run symmetry examines the null hypothesis H 0 : k + =k, whereas the test for short-run symmetry entertains the null hypothesis H 0 : a k + =a k and b k + =b k for all k. A rejection in either case will indicate asymmetry in price adjustment. As Table 2 shows, significant evidence indicating the presence of asymmetric transmission from crude oil prices in both spot and future markets to retail gasoline prices can be found. The asymmetric price transmission seems to apply to short- and long-run adjustments alike. To better understand where the asymmetric transmission occurs, possible market linkages are broken down into two stages: Stage I is from crude oil to spot gasoline markets at the refinery level, and Stage II is from refinery gasoline to retail markets. For Stage I, we find no significant evidence of price asymmetry (except for some possibly weak evidence from the future market). For Stage II, in contrast, there is strong evidence of asymmetric price transmission through both spot and future markets. Our findings form an interesting comparison to those reported by Borenstein et al. (1997), who further include an intermediate spot to wholesale gasoline stage in their breakdown of price transmission not captured in our two-stage setup. These researchers uncover evidence of asymmetric price response emanating, in contrast to our results, at both the crude oil to spot gasoline stage and the wholesale to retail gasoline stage. Their study finds no persistent price asymmetry at the modeled intermediate stage. Indeed, wholesale prices closely track spot prices. The finding is supportive of our model of price transmission, which excludes this intermediate stage. To analyze more fully the asymmetric price adjustment at the distribution stage, we examine the cumulative response of retail prices to a 10-cent per gallon change in either spot prices or future prices of refinery gasoline. Fig. 1 shows the cumulative response estimates at different adjustment horizons measured in weeks. Confirming the presence of long adjustment lags, the thick solid line gives the retail price response estimates for the case of a positive shock in the refinery price, and the thin solid line Table 2 Testing for asymmetry in gasoline price adjustment From Y t To X t Short-run adjustment Long-run adjustment Short- and long-run adjustment H 0 : All a + k =a k and b + k =b k H 0 : k + =k H 0 : k + =k, a + k =a k and b + k =b k From crude oil to retail gasoline prices: Crude oil spot Gasoline retail 2.061** [0.008] [0.053] 2.073** [0.007] Crude oil futures Gasoline retail 3.180** [0.001] 4.544** [0.033] 3.319** [0.000] Stage I transmission to refinery gasoline prices: Crude oil spot Gasoline spot [0.538] [0.876] [0.648] Crude oil futures Gasoline spot [0.085] [0.649] [0.130] Crude oil spot Gasoline futures [0.467] [0.287] [0.511] Crude oil futures Gasoline futures [0.082] [0.056] [0.055] Stage II transmission to retail gasoline prices: Gasoline spot Gasoline retail 1.785** [0.030] ** [0.000] 2.222** [0.003] Gasoline futures Gasoline retail 2.527** [0.001] 5.147** [0.024] 2.684** [0.000] H 0 describes the respective null hypotheses under test. For short-run adjustment, both a + k =a k and b + k =b k are restrictions applying to all individual lags (k =1, 2,..., p) of the estimated threshold error-correction model. Corresponding p-values for F- tests are given in brackets. Statistical significance is indicated by double asterisks (**) for the 5% level.

6 238 L.-H. Chen et al. / Economics Letters 89 (2005) Retail price response (in cents) Cumulative response to a 10-cent change in the spot price of refinery gasoline Time elapsed (in weeks) Retail price response (in cents) Cumulative response to a 10-cent change in the futures price of refinery gasoline Time elapsed (in weeks) Fig. 1. Asymmetric transmission from refinery to retail gasoline prices. The thick and thin solid lines with markers show the cumulative price response estimates after different weeks of adjustment, with the dotted lines displaying the corresponding 95% confidence bands for these estimates. The thick solid line applies to the case of a positive price shock, whereas the thin solid line is for a negative price shock. indicates the corresponding estimates for the case of a negative price shock. The 95% confidence bounds for these response estimates are presented as dotted lines. The estimation results indicate that retail prices tend to respond faster to an increase than to a decrease in refinery prices. In particular, the difference in response is statistically significant for the retail price adjustment during the first 3 weeks subsequent to a refinery price shock. The response difference becomes statistically insignificant as the retail price adjustment goes into the fourth week and beyond. Similar asymmetric adjustment behavior of retail prices can be observed under changes in both spot and future prices of refinery gasoline. 4. Conclusion This study takes a different approach in defining the switching thresholds in a cointegration model of price adjustment and finds retail gasoline prices respond asymmetrically to crude oil price changes. We

7 L.-H. Chen et al. / Economics Letters 89 (2005) find evidence of asymmetry not only in short- and long-run adjustment but also across the spot and future markets. Moreover, the study provides new evidence that the observed asymmetry in retail gasoline price adjustment occurs primarily at the downstream stage involving gasoline distribution, not at the upstream stage between refinery and crude oil markets. The source of the estimated asymmetry warrants further investigation. Borenstein et al. (1997) points out that both inventory adjustment and consumer search behavior may cause price asymmetry. Our findings of asymmetry at the downstream but not upstream level is consistent with the consumer search hypothesis. Lewis (2004) proposes a reference price model in which consumer search behavior responds differently to falling versus rising retail prices as a source of downstream price asymmetry. Johnson (2002) also suggests that search costs play a significant role in generating asymmetric adjustment in retail gasoline prices. Acknowledgement The authors are grateful to an anonymous referee for useful comments and suggestions. References Balke, N.S., Brown, S.P.A., Yücel, M.K., Gasoline and crude oil prices: an asymmetric relationship? Federal Reserve Bank of Dallas Economic Review, First Quarter, Borenstein, S., Cameron, A.C., Gilbert, R., Do gasoline prices respond asymmetrically to crude oil price changes? Quarterly Journal of Economics 112, Cheung, Y.W., Lai, K.S., Lag order and critical values of a modified Dickey Fuller test. Oxford Bulletin of Economics and Statistics 57, Duffy-Deno, K.T., Retail price asymmetries in local gasoline markets. Energy Economics 18, Elliott, G., Rothenberg, T.J., Stock, J.H., Efficient tests for an autoregressive unit root. Econometrica 64, Enders, W., Siklos, P.L., Cointegration and threshold adjustment. Journal of Business and Economic Statistics 19, Energy Information Administration (EIA), Prices Changes in the Gasoline Market: Are Midwestern Gasoline Prices Downward Sticky? U.S. Department of Energy, Washington, DC. Godby, R., Lintner, A.M., Stengos, T., Wandschneider, B., Testing for asymmetric pricing in the Canadian retail gasoline market. Energy Economics 22, Johnson, R.N., Search costs, lags and prices at the pump. Review of Industrial Organization 20, Lewis, M., 2004, Asymmetric price adjustment and consumer search: an examination of the retail gasoline industry, Discussion Paper, Department of Economics, Ohio State University. Ng, S., Perron, P., Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90, Peltzman, S., Prices rise faster than they fall. Journal of Political Economy 108, Shin, D., Do product prices respond symmetrically to changes in crude oil prices? OPEC Review 18,

COINTEGRATION AND MARKET EFFICIENCY: AN APPLICATION TO THE CANADIAN TREASURY BILL MARKET. Soo-Bin Park* Carleton University, Ottawa, Canada K1S 5B6

1 COINTEGRATION AND MARKET EFFICIENCY: AN APPLICATION TO THE CANADIAN TREASURY BILL MARKET Soo-Bin Park* Carleton University, Ottawa, Canada K1S 5B6 Abstract: In this study we examine if the spot and forward