Airfares and oil prices: 'Feathers and Rockets ...

Download PDF
3 downloads 0 Views 573KB Size Report
Comment
Oct 18, 2017 - adjustment indicate that the large reduction in oil prices has been passed .... (Util), (4) the wholesale price of jet fuel (JetW), (5) the retail price of.
Energy Economics 68 (2017) 515–521

Contents lists available at ScienceDirect

Energy Economics journal homepage: www.elsevier.com/locate/eneeco

Airfares and oil prices: ‘Feathers and Rockets’ adjustments Robert K. Kaufmann Department of Earth and Environment, Boston University, Boston, MA 02215, USA

a r t i c l e

i n f o

Article history: Received 30 August 2016 Received in revised form 8 May 2017 Accepted 13 October 2017 Available online 18 October 2017 JEL classification: L4 Q40 N7 R40 R48 K21 Keywords: Airfares Oil markets Asymmetric adjustments

a b s t r a c t One reason that the US Department of Justice is examining collusion within the airline industry may be the small (12%) decline in airfares that follows a large (57%) drop in crude oil prices. This relatively small response could be caused by three mechanisms related to the oil market; (1) slow rates of adjustment, (2) airfares adjust asymmetrically to changes in the oil market, or (3) asymmetric adjustments within the oil market that are communicated symmetrically to airfares. I evaluate these hypotheses by estimating a cointegrating vector autoregression model from monthly data and testing the error correction mechanism for asymmetry. Although small, estimated rates of adjustment indicate that the large reduction in oil prices has been passed to airfares. Tests of the error correction model do not provide evidence for asymmetric adjustments between airfares and oil market. Contrary to the relation between crude oil and motor gasoline prices, prices for jet fuel adjust faster to reductions in crude oil prices and so cannot be responsible for the relatively small decline in airfares. Although the CVAR model does not identify an oil-related mechanism that can generate the small decline in airfares relative to the large decline in the price for crude oil, this absence does not imply the converse, that airlines collude to set airfares. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The price of crude oil declines by about 57%, from $102.51 to $43.58 between June 2014 and May 2016. During that period, the CPI for airfare declines by about 12%. This small decline is somewhat surprising; jet fuel accounts for about 33% of average operating costs incurred by the airline industry (Berghofer and Lucey, 2014). Consistent with this large percentage, industry analysts estimate that the reduction in oil prices will save US airlines about $20 billion in 2015 (New York Times, January 20, 2015). The juxtaposition of a large cost saving and a relatively small price reduction is a topic for both academic researchers and policy enforcement. From an academic perspective, airlines respond to changes in oil prices three ways; (1) changing the energy efficiency of their operations (i.e. changing the fleet), (2) passing the cost increases (decreases) to passengers, and (3) hedging fuel costs (Morrell and Swan, 2006). Of these, Berghofer and Lucey (2014) find that hedging behavior and changes in fleet diversity do not reduce exposure to the risk that is associated with changes in oil prices. Furthermore, hedging may increase the risk premium and increase costs (Aabo and Simkins, 2005), perhaps by 1% of fuel costs (Rao, 1999). Despite these costs, the accounting losses of hedging will be more than offset by lower fuel prices, such that US airlines will save $15 billion (New York Times, 2015). Academic research suggests that the degree to which cost increases (decreases) are passed on to passengers may be influenced competition E-mail address: [email protected].

https://doi.org/10.1016/j.eneco.2017.10.011 0140-9883/© 2017 Elsevier B.V. All rights reserved.

in the airline industry. High levels of competition make it difficult to raise ticket prices in response to rising prices for jet fuel (Carter and Simkins, 2004). Consistent with this hypothesis, the Portuguese airline industry could not recover the full cost of higher fuel prices (Button et al., 2011). Recent research indicates that the intensity of competition among airlines is decreasing. Concentration in the US airline industry increases between 2007 and 2009 (Johnston and Ozment, 2011). The resultant reduction in competition may slow additions to capacity. Robert Mann, a former airline executive states; “The industry is full at these prices. You can't stimulate additional revenue by cutting prices.” Based on these concerns, in June 1015, the US Department of Justice opened an inquiry into whether the airline industry is colluding to limit seating. Beyond a reduction in competition, the small effect (to date) of lower oil prices on airfares could be caused by asymmetric rates of adjustments in the relation among the price of crude oil, the price of jet fuel, and airfares. If the price of jet fuel and/or airfares respond asymmetrically to changes in crude oil prices (or other components of the oil market), such that increases in crude oil prices are translated into higher prices for jet fuel and air travel faster than reductions in crude oil prices are translated into lower prices for jet fuel and air travel, the small decline in airfares as of June 2016 (the last month for which data are available) may be caused by an asymmetric rate of adjustment to lower prices for crude oil. This hypothesis echoes an extensive literature on the relation between prices for crude oil and motor gasoline, which suggests that increases in crude oil prices translate into higher

516

R.K. Kaufmann / Energy Economics 68 (2017) 515–521

motor gasoline prices faster than lower crude oil prices translate into lower motor gasoline prices (e.g. Perdiguero-Garcia, 2013; Frey and Manera, 2007). This pattern of asymmetric adjustment is termed a ‘rockets and feathers’ effect (Bacon, 1991). To test for an asymmetric relation between the price of jet fuel and air travel, Wadud (2015) uses a method developed by Gately (1992), which decomposes jet fuel prices into three components; price rises to a new all-time high, price declines, and price rises back towards a previous high. Each of these price changes has a different effect on airfares such that a one dollar rise in the price of jet fuel to a new all-time high generates a larger increase in airfares than a one dollar rise in the price of jet fuel that leaves prices below the previous all-time high (Wadud, 2015). These results suggest that the price of jet fuel does not define a unique price level for airfares. That is, the relation between the price of jet fuel and air travel is ‘path dependent.’ Although path dependency could explain the small effect of large reductions in crude oil prices (if the equilibrium response to price reductions is smaller than the equilibrium response to price increases), path dependency or regime change (e.g. Holmes and Panagiotidis, 2009) are different from the asymmetric rates of adjustment that are described by the ‘rockets and feathers’ relation between the price for crude oil and motor gasoline. Here, I test three hypotheses about how the oil market may cause airfares to fall by a small percentage relative to a large decline in the price for crude oil: 1) Airfares adjust very slowly to changes in airfares. 2) Airfares adjust asymmetrically to changes in the oil market. 3) The oil market adjusts asymmetrically to changes in the price of crude oil, and these asymmetric adjustments are communicated symmetrically to airfares. These hypotheses are tested by estimating a cointegrated vector autoregression (CVAR) model from monthly data. The cointegrating relations identify long-run relations for wholesale and retail prices for jet fuel, inventories of jet fuel, and airfares. The results indicate that slow or asymmetric rates of adjustment cannot account for the small decline in airfares relative to the large drop in crude oil prices. Surprisingly, the retail price for jet fuel adjusts faster to reductions in the price for crude oil, which is opposite the asymmetric rate of adjustment between prices for crude oil and motor gasoline in many markets. I hypothesize that this ‘feathers and rockets’ effect is generated by the relative rigidity of refinery yields for jet fuel, which generates a trade-of between the rate at which price changes are passed through to jet fuel and the refiner's cost of holding inventories of jet fuel. Together these results indicate that the small decline in airfares cannot be attributed to relations within the oil market or the relation between the oil market and airfares. The failure to identify an oil-related mechanism for the relatively small decline in airfares does not imply the converse, that airlines collude to set airfares; nor does it rule out collusion. These results and the methods used to obtain them are described in five sections. The second section describes the data and the statistical methodology. The statistical results are described in the third section. Section 4 describes the long-and short-run relations among components of the oil market and their relation with airfares. Section 5 concludes with a short discussion about what these results imply about possible causes for the small decline in airfares relative to crude oil prices. 2. Methodology

asymmetries at a weekly or daily frequency, but high frequency asymmetries could not generate the longer adjustments that are discussed in the introduction. I include components of the oil market beyond the price of jet fuel because previous research suggests that omitted variables can bias statistical tests for symmetric rates of adjustment. Including time series for the inventories of crude oil, inventories of motor gasoline, and refinery utilization rates in the cointegrating relations and the error correction models for motor gasoline prices reduces the likelihood of rejecting the null hypothesis of symmetric rates of adjustment (Kaufmann and Laskowski, 2005). Data on the U.S. city average for airline fares (CUSR0000SETG01) are obtained from the Bureau of Labor Statistics. These data are deflated by monthly values of the U.S. city average for all items (CUUR0000SA0) to generate real airfares (Fare). Monthly data are compiled for six components of the US oil market; (1) the average price of crude oil purchased by refiners (PCrude), (2) inventories of crude oil (CStock), (3) refinery utilization rates (Util), (4) the wholesale price of jet fuel ( JetW), (5) the retail price of jet fuel ( JetR), and (6) inventories of jet fuel ( JStock). Observations for the nominal monthly price of crude oil (dollars per barrel) purchased by refiners (R0000____3) are obtained from the Energy Information Administration. The same source is used to compile time series for the U.S. kerosene-type jet fuel nominal wholesale/resale price (EMA_EPJK_PWG_NUS_DPG) by refiners (dollars per gallon), U.S. kerosene-type jet fuel nominal retail sale prices by refiners (EMA_EPJK_PTG_NUS_DPG; dollars per gallon), U.S. ending stocks excluding SPR of crude oil (MCESTUS1 thousand barrels), U.S. Ending Stocks of Kerosene-Type Jet Fuel (MKJSTUS1 –thousand barrels), and the US percent utilization of refinery operable capacity (MOPUEUS2). Prices for crude oil and jet fuel are deflated using the U.S. city average for all items that is described above.1 The availability of observations differs among variables. Observations for some of the oil-related variables start in the 1970′s, but January 1989 is the first observation for airfares. Conversely, the data for airfares extend through June 2016, whereas May 2016 is the most recent observation for some of the oil market variables. As such, the sample period includes 329 monthly observations from January 1989 through May 2016. To eliminate the effects on inverting matrices with elements that differ greatly in size (due to different units of measurement), the time series for each variable is standardized as follows: ðyt −yÞ xt ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi Var ðyÞ

ð1Þ

In which yt is the value (in original units), y is the average value over the sample period, and Var(y) is the variance over the sample period. 2.2. Statistical methodology The statistical methodology consists of two general stages.2 In the first stage, I estimate a CVAR model to quantify the long- and short-run relations among the six components of the oil market and their relation with airfares. In the second stage, the long-run relations are used to calculate the disequilibria in each cointegrating relation, these disequilibria are decomposed based on the change in the price of crude oil, and these decomposed disequilibria are used in an error correction model to test the null hypothesis that variables adjust symmetrically.

2.1. Data 1

I compile monthly data on airfares and six components of the oil market that may affect airfares. Monthly data likely would fail to detect

As such, all prices refer to real prices. Two steps are needed because the CATS software used to estimate the CVAR does not allow for asymmetric rates of adjustment. 2

R.K. Kaufmann / Energy Economics 68 (2017) 515–521

In the first step, I estimate a CVAR model, for which the general form is given by: Δxt ¼ A0 Δwt þ A1 Δwt−1 þ Φ1 Δxt−1 þ Πðxt−1 wt−1 Þ0 þ k0 þ ΘM þ ε t ð2Þ in which xt is a vector of (p) endogenous variables whose behavior is being modeled (CStock, Util, JetW, JetR, JStock, and Fare), wt is a vector of exogenous variables (PCrude), k0 is a vector of constant terms, M is a vector of eleven dummy variables, one for each month Jan-Nov, A0,A1, Φ1, Θ, and Π are matrices of regression coefficients, Δ is the first difference operator (Δ xt =xt − xt−1), and ε is Niid(0, Ω). When the time series are nonstationary, the long-run matrix Π can be formulated as: Π ¼ αβ0

ð3Þ

in which α is a p × r matrix of adjustment coefficients (also known as loadings), β′ is an r × p matrix of cointegration coefficients that define stationary deviations from long-run equilibrium relationships, and r is the number of long-run cointegrating relations. The number of cointegrating relations present is given by the rank (r) of the Π matrix. The cointegration rank r is determined by solving an eigenvalue problem in which the eigenvectors are estimates of β and α = f(β) can be found for a given β. The eigenvectors, β, are determined by an orthogonality condition and are ordered according to their degree of stationarity (Juselius, 2006). For a more detailed description of the CVAR model see Juselius (2006). Several diagnostic tools are available to determine the rank of Π; the most common is the likelihood based trace test (Johansen, 1996), which tests the null hypothesis of (p-r) unit roots against the alternative hypothesis of (p − r + 1) unit roots. The test procedure is based on a sequence of tests, starting from r = 0 (no stationary relations among the endogenous and/or exogenous variables), r = 1 (p-1 stochastic trends, one stationary cointegration relation) and ending with (r = p) (all cointegration relations are stationary). The test is based on the null hypothesis of a unit root and, therefore, often has low power to reject a unit root when the true root is close to the unit circle. The second stage tests the null hypothesis that the endogenous variables adjust symmetrically to disequilibria in each of the cointegrating relations. This stage uses a four-step procedure (Granger and Lee, 1989); (1) using estimates for β to calculate disequilibria in each cointegrating relation, (2) decomposing these disequilibria based on changes in the price of crude oil, (3) using these decomposed disequilibria to estimate an error correction model, and (4) testing restrictions that impose symmetric rates of adjustment. The disequilibria (μ) for each cointegrating relation (r) are calculated as follows:   ^ xt−1; wt−1; μ r;t ¼ β r

ð4Þ

^ is the cointegrating vector for cointegrating relation (r) in which β that is estimated from Eq. (2). In the second step, changes in the price of crude oil are used to decompose the disequilibria from each cointegrating relation as follows: þ

ε r;t ¼ ðΔPCrudet N 0Þ  μ r;t

−

εr;t ¼ ðΔPCrudet ≤ 0Þ  μ r;t

ð5Þ ð6Þ

This decomposition is chosen to test the null hypothesis that changes in the price of crude oil affect the rate at which the oil market and/or airfares adjust towards equilibrium. As such, it is similar to the decomposition used to analyze the relation between the prices for crude oil and motor gasoline (e.g. Kaufmann and Laskowski, 2005). But this decomposition differs from previous models of asymmetric

517

price responses, which decompose the residual based on the sign of the residual (Granger and Lee, 1989) or changes in the residual (Escribano and Pfann, 1997). Such specifications test a different set of hypotheses, such as whether the rate at which airfares adjust to conditions in the oil market depends on whether airfares are greater than or less than the equilibrium value. In the third step, the decomposed residuals + εr, t and − εr, t are specified in an unrestricted error correction model that is given by: Δxt ¼ k0 þ

r X

þ

γi þ εr;t−1 þ

i¼1

þ Γ 1 Δxt−t þ

11 X

r X

−

γ i − εr;t−1 þ A0 Δwt þ A1 Δwt−t

i¼1

θi M i þ τi

ð7Þ

i¼1

in which τ is a normally distributed random error term. Eq. (7) is estimated using OLS and the standard errors are calculated using the procedure developed by Newey and West (1987). In the final step, the null hypothesis that endogenous variable (x) adjusts symmetrically to disequilibrium in each cointegrating relation is tested by imposing individual restrictions + γi = − γi. This null hypothesis is tested using the F-form of the Wald test, which can be evaluated against a χ2 distribution with one degree of freedom. Cook et al. (1999) find that this test has a low power to reject the null hypothesis. This suggests that statistics which reject the null hypothesis at p b 0.10 may represent cases in which the null hypothesis should be rejected. Rejecting the null hypothesis + γi = − γi. indicates that changes in the price of crude oil affect the rate at which the dependent variable adjusts to disequilibrium in cointegrating relation i. The nature of this asymmetry is given by the absolute size of + γi relative to − γi. If ( − 1 b + γi, − γi b 0) and (|+ γi, | N |− γi, |) would indicate that the dependent variable (x) adjusts faster towards equilibrium when the price of crude oil rises (Fig. 1). Such a result would be consistent with the ‘rockets and feathers’ effect. 3. Results The rank of the Π matrix is determined using the the trace test. This statistic strongly rejects (p b 0.0001) the null that there are 0, 1, 2, or 3 cointegrating relations, but fails to reject (p N 0.068) the null hypothesis that there are four cointegrating relations. The Π matrix is assigned a rank of four based on the large increase in the p value from the first four tests (p b 0.0001) to the test of four cointegrating relations (p N 0.068) along with the failure to reject four cointergating relations at the usual p = 0.05 significance level. Identifying the long run structure of the CVAR requires several types of restrictions (Pesaran and Shin, 1994). Greenslade et al., (2002) suggest that the efficiency of identifying the long-run structure can be improved by first attempting to reduce the number of endogenous variables. I evaluate whether variables can be excluded from the x vector in Eq. (2) by testing a restriction that makes all elements of α equal to zero in the equation for a given endogenous variable. Results fail to reject the null hypothesis that the real price of crude oil (PCrude) is weakly exogenous (Table 1). For all other variables, the test statistic rejects the null hypothesis (p b 0.01). Furthermore, for the equation for crude oil prices, I fail to reject a set of restrictions that makes the elements of the Γ1 matrix associated with the lagged first difference of the six endogenous variable equal to zero (χ2(6) = 7.45, p N 0.28). Based on these results, the real price of crude oil is made weakly exogenous by transferring this variable from the x vector to the w vector in Eq. (2). Using this specification, I impose overidentifying restrictions on the CVAR. I fail to reject (χ2(9) = 6.85, p N 0.65) an overidentified structure that imposes nine overidentifying restrictions (Table 2). Each variable is present in one more or cointegrating relations, which is consistent with exclusion tests (Table 1).

518

R.K. Kaufmann / Energy Economics 68 (2017) 515–521

Fig. 1. Asymmetric rates of adjustment. Symmetric adjustment (γ= −0.08) (black lines) creates the same period of adjustment. Prices do not adjust along the same path because the initial rates of adjustment are greatest (because disequilibrium is greatest). Conversely, a ‘rockets and feathers’ effect implies that the price of jet fuel adjusts faster (+ γ= −0.15) and has a shorter adjustment period in response to an increase in the price of crude oil price (red line) than adjustment (− γ= −0.05) to a reduction in the price of crude oil (blue line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The elements of α indicate that each cointegrating relation loads into the equation for one or more of the variables in the cointegrating relation in a way that moves that endogenous variable towards the equilibrium value that is implied by the cointegrating relation (Table 2). This allows me to interpret each cointegrating relation as a long-run relationship for one or more endogenous variables. As described in the next section, these interpretations clarify the linkages among components of the oil market and their relation with airfares. Tests of + γi = − γi. indicate that the assumption of symmetric rates of adjustment varies across endogenous variables and cointegrating relations (Table 3). The null hypothesis of symmetry is rejected (p b 0.05) for cointegrating relations that load into the equations for refinery utilization rates, wholesale and retail prices for jet fuel, and inventories of jet fuel. Conversely, I cannot reject restrictions that make the equations for inventories of crude oil and airfares adjust symmetrically to disequilibrium in each cointegrating relation. Table 1 Tests on the time series properties of the data and the specification of the CVAR. Variable

Exclusion

Weakly exogenous

Stationarity

ADF

CStock Util JetW JetR JStock Fare PCrude

χ2(4) = 10.61⁎ χ2(4) = 36.41⁎⁎ χ2(4) = 46.71⁎⁎ χ2(4) = 47.43⁎⁎ χ2(4) = 27.25⁎⁎ χ2(4) = 30.31⁎⁎ χ2(4) = 33.21⁎⁎

χ2(4) = 35.55⁎⁎ χ2(4) = 27.20⁎⁎ χ2(4) = 17.00⁎⁎ χ2(4) = 16.77⁎⁎ χ2(4) = 26.42⁎⁎ χ2(4) = 16.21⁎⁎

χ2(3) = 9.73⁎ χ2(3) = 14.26⁎⁎ χ2(3) = 9.69⁎ χ2(3) = 9.63⁎ χ2(3) = 1.94 χ2(3) = 9.48⁎ χ2(3) = 9.89⁎

−3.12+ −1.32 −2.75 −2.77 −2.04 −3.66⁎ −3.72⁎

χ2(4) = 4.78

Test statistics reject at the null hypothesis at the **1%, *5%, +10% level. The Exclusion test evaluates the null hypothesis that the series can be eliminated from all four cointegrating relations (excluded from cointegration space). The test of weak exogeneity evaluates the null hypothesis that disequilibrium in each of the four cointegrating relations does not affect the variable. The test of stationarity evaluates the null hypothesis that the time series is stationary. The ADF statistic evaluates the null hypothesis that the variable contains a stochastic trend. For more information on these tests, see Dennis (2006).

4. Discussion 4.1. Interpreting long-run relations The first cointegrating relation (CR #1) in Table 2 includes the price of crude oil, the wholesale price for jet fuel, and inventories of jet fuel. Signs associated with the elements of β indicate a positive relation between the price of crude oil and the wholesale price for jet fuel and a negative relation between the wholesale price for jet fuel and inventories of jet fuel. This negative relation is consistent with cost smoothing by refineries. Restrictions on the elements of β do not reject the null hypothesis that the price of crude oil and the wholesale price for jet fuel change on a onefor-one basis (χ2(1)=0.31,pN 0.86). Disequilibrium in CR #1 moves the

Table 2 Statistical estimate for CVAR model. CR #1

CR #2

CR #3

CR #4

−1.000⁎⁎ − − 1.000⁎⁎

− −0.004⁎ − −1.000⁎⁎ 1.000⁎⁎

− − − − −1.224⁎⁎ −17.040⁎⁎ 1.000 −72.476⁎⁎ −0.023⁎ 0.122⁎⁎ −0.013⁎⁎ −0.012⁎⁎ 0.103⁎⁎ −0.056⁎⁎

Elements of β Pcrude Cstock Util JetW JetR JStock Fare Constant

0.580⁎⁎ − −

− − −

− − 1.000⁎ − − −10.136⁎⁎ − 46.593⁎⁎

Elements of α ΔCstock ΔUtil ΔJetW ΔJetR ΔJStock ΔFare

0.046 0.324+ −0.223⁎⁎ −0.214⁎⁎ 0.348 −0.233+

−0.201 3.138 −0.574 −1.050⁎ 1.012 −0.481

0.040⁎ −0.197⁎⁎ 0.023⁎⁎ 0.021⁎⁎ −0.158⁎⁎ 0.089⁎⁎

Coefficients are statistically significantly different from zero at the: **1%, *5%, +10% level.

R.K. Kaufmann / Energy Economics 68 (2017) 515–521 Table 3 Rates of adjustment in the unrestricted model (Eq. (7)) and tests of symmetry. +

γi

−

γi

Ho: + γi =− γi

CStock CR #1 CR #2 CR #3 CR #4

0.25⁎ −0.05 0.01 0.00

0.13⁎ 0.11 0.01 0.00

0.83 0.02 0.01 0.02

Util CR #1 CR #2 CR #3 CR #4

−1.18⁎⁎ −1.38 0.28⁎⁎ −0.17⁎⁎

−0.68⁎⁎ 6.02 0.26⁎⁎ −0.16⁎⁎

2.17 9.49⁎⁎ 0.25 0.15

JetW CR #1 CR #2 CR #3 CR #4

0.19⁎ 0.23 −0.02⁎ 0.01⁎

0.19⁎ −1.80⁎ −0.02+ 0.01+

0.00 8.44⁎⁎ 0.11 0.12

JetR CR #1 CR #2 CR #3 CR #4

0.19⁎⁎ 0.88⁎ −0.02⁎ 0.01⁎

0.19⁎⁎ −1.19⁎ −0.01+ 0.01+

0.00 9.47⁎⁎ 0.16 0.17

JStock CR #1 CR #2 CR #3 CR #4

1.02⁎ 0.60 0.21⁎ −0.14⁎

0.35 7.72⁎ 0.23⁎

−0.15⁎⁎

5.27⁎ 2.17 0.11 0.05

Fare CR #1 CR #2 CR #3 CR #4

0.18 −1.38 −0.04 0.02

−0.05 −1.06 −0.02 0.01

1.38 0.03 0.22 0.20

Coefficients and test statistics are statistically significantly different from zero at the: **1%, *5%, +10% level. The test of the null hypothesis is distributed as a χ2 with one degree of freedom.

519

wholesale price for jet fuel towards the equilibrium level that is implied by CR #1, but does not move inventories of jet fuel towards the longrun value that is implied by CR #1 (Table 2). As such, CR #1 is interpreted as a long-run relation for the wholesale price for jet fuel. The second cointegrating relation (CR #2) includes inventories of crude oil, the wholesale price of jet fuel and the retail prices for jet fuel. Elements of β indicate that retail and wholesale prices are positively related and restrictions on these elements of β fail to reject (χ2(1) = 0.81, p N 0.36) the null hypothesis that these prices change on a onefor-one basis. The value of α3, 2 is not statistically different from zero, which indicates that disequilibrium in CR #2 does not affect wholesale jet prices. Conversely α4, 2 indicates that disequilibrium in CR #2 moves the retail price for jet fuel towards the long-run value implied ^ 4;2 ¼ −1:05 is not by CR #2. Furthermore, the point-estimate for α statistically different from −1.0 (t = 0.13, p N 0.91). This implies that the retail price for jet fuel adjusts fully to disequilibrium in CR #2 within a single month. As such, CR #2 can be interpreted as a long-relation for the retail price of jet fuel. The third cointegrating relation includes refinery utilization rates and inventories of jet fuel, and a constant (Fig. 2). The elements of β indicate a positive relation between refinery utilization rates and inventories of jet fuel. The elements of α indicate that refinery utilization rates adjust to disequilibrium in CR #3 in a way that moves it towards the long-run value that is implied by CR #3. As such, CR #3 can be interpreted as a long-run relation for refinery utilization rates. The fourth cointegrating relation includes the retail price for jet fuel, inventories of jet fuel, and airfares (and a constant). Disequilibrium in CR #4 moves airfares (and inventories of jet fuel) towards a long-run value that is implied by CR #4. As such, CR #4 can be interpreted as a long-run relation for airfares and inventories of jet fuel. Signs on the elements of β indicate that higher prices for airfares are associated with higher prices for jet fuel while inventories of jet fuel are negatively related to the retail price for jet fuel.

Fig. 2. A cointegrating relation for airfares includes the (transformed—Eq. (1)) retail price for jet fuel (green line), (transformed—Eq. (1)) inventories of jet fuel (black line), and (transformed—Eq. (1)) and airfares (red line). Given the one-to-one relation between crude oil and wholesale prices for jet fuel (CR #1) and the one-to-one relation between the wholesale and retail price for jet fuel, the retail price for jet fuel follows the (transformed—Eq. (1)) price for crude oil (blue line). (For interpretation of the references to colour in this figure legend, the reader is referred to the online version of this chapter.)

520

R.K. Kaufmann / Energy Economics 68 (2017) 515–521

Based on these interpretations of the four cointegrating relations, the following sections evaluate the three hypotheses for the relatively small reduction in airfares relative to the large reduction in the price for crude oil. Hypothesis #1. Airfares adjust slowly to change in the oil market. The rate at which airfares adjust to disequilibrium with the oil market ^ 6;4 ¼ −0:056 (Table 2), which indicates about 6% of the disis given by α equilibrium is eliminated each month. At this rate, it takes about 12 months (ln(2)/0.056) for the recent reduction in jet fuel prices to be fully incorporated into airfares. It has been almost two years since crude oil prices started to drop in the fall of 2014. This would imply that slow rates of adjustment are not responsible for the small drop in airfares relative to oil prices. Hypothesis #2. Asymmetries in the relation between airfares and the oil market. For the disequilibrium in each of the four cointegrating relations, the test statistic fails to reject the restrictions that make airfares adjust symmetrically (Table 2). Furthermore, the significance levels for all tests (p N 0.25) are well below critical values. There is some evidence that the failure to reject symmetric rates of adjustment depends on the variable that is used to decompose the residual from the cointegrating relations (Eqs. (5)–(6)). If the residual is decomposed using changes in the retail price of jet fuel,3 the test statistic rejects the null hypothesis that airfares adjust symmetrically to disequilibrium in CR #2. If present, this asymmetry probably is unimportant. The retail price of jet fuel adjusts completely within one month to disequilibria in CR #2, so disequilibrium, and asymmetric adjustments to it, are short-lived. Furthermore, CR #2 does not contain Fare, therefore this asymmetry does not affect the rate at which airfares adjust towards their long-run equilibrium value. Together, these results suggest that airfares adjust symmetrically to changes in the oil market. Hypothesis #3. Asymmetries in the oil market. Within the oil market, there is evidence for asymmetric rates of adjustment. The test statistic rejects the null hypothesis of symmetric rates of adjustment for four components of the oil market; (1) refinery utilization rates, (2) wholesale prices for jet fuel, (3) retail prices for jet fuel, and (4) inventories of jet fuel. For these variables, there are two types of asymmetric adjustments; direct and indirect. Indirect asymmetries occur when a variable adjusts asymmetrically to disequilibrium in a cointegrating relation that does not include that variable. For example, refinery utilization rates adjust asymmetrically to disequilibrium in CR #2, but CR #2 does not contain refinery utilization rates. As such, indirect asymmetries do not directly affect the rate at which a variable adjust towards its long-run equilibrium and so are largely ignored in the discussion that follows. Direct asymmetries occur when an endogenous variable adjusts asymmetrically to disequilibrium in a cointegrating relation that includes the endogenous variable. Table 3 identifies one direct asymmetry; retail prices for jet fuel adjust asymmetrically to disequilibrium in CR #2. For this direct asymmetry, the values of + γi and − γi are inconsistent with the ‘rockets and feathers’ effect. Disequilibrium in CR#2 loads into the equation for the retail price for jet fuel more rapidly when crude oil prices fall (− γi = −1.19) than when they rise (+ γi = 0.88). This implies that retail prices for jet fuel adjust faster to disequilibrium with wholesale prices for jet fuel when prices for crude oil decline. Despite the large difference between − γi and + γi, the effect of this asymmetry on observed prices for jet fuel probably is relatively small because the short-run effects of crude oil prices on the wholesale and retail prices for jet fuel are large. The elements of A0 associated with wholesale 3 There is no asymmetry if the cointegrating relations are decomposed based on changes in the wholesale price of jet fuel.

and retail prices for jet fuel are 0.769 (t = 23.8, p b 0.001) and 0.757 (t = 23.2, p b 0.001) respectively. These values indicate that about three quarters of a change in the price for crude oil appears immediately in the wholesale and retail price for jet fuel. Another 0.141 (t = 2.40, p b 0.05) and 0.147 (2.48, p b 0.05) appear in wholesale and retail prices for jet fuel respectively after one month, as indicated by the elements of A1. Together, these short-run effects translate about 90% of the change in crude oil prices to jet fuel prices within a month. As such, the asymmetric rates of adjustment to CR#2 apply to a relatively small disequilibrium. This small effect, coupled with values that imply retail prices for jet fuel adjust faster towards equilibrium when crude oil prices drop suggest that asymmetric rates of adjustment are not responsible for the relatively small decline in airfares relative to the large decline in oil prices. Results that indicate the retail price of jet fuel adjusts faster rate when the price of crude oil falls are opposite the ‘rockets and feathers’ effect that is observed in some motor gasoline markets. This implies a ‘feathers and rockets’ effect for the jet fuel market, in which prices drop faster than they rise. To explain this ‘feathers and rockets’ effect, I postulate that the rigidity of refinery yields of jet fuel creates a tradeoff between the rate at which refiners pass price changes to the retail price of jet fuel and refiner's cost of holding inventories of jet fuel. Refinery yields of jet fuel are relatively fixed, which implies that refining a barrel of crude oil creates a relatively fixed quantity of jet fuel. In the US, refinery yields for kerosene jet fuel average 9.7% (±0.36%) between 1993 and 2014 (US Energy Information Administration). As such, the yield of jet fuel is a distant third to the yields of motor gasoline (45.9% ± 0.74) and distillates (25% ± .76). Under these conditions, refinery runs probably are not scheduled to match demand for jet fuel. Consistent with this notion, the production-to-sales variance ratio for jet fuel is b1 (Considine, 1997). For periods when the quantity of jet fuel produced is greater than (less than) sales, refiners put the difference into (out of) their inventories of jet fuel.4 For refineries, the marginal benefit of storing refined petroleum products (i.e. their convenience yield) is associated with smoothing production and lowering the cost of production (Considine, 1997). But once these benefits are realized, refiners gain little by holding physical stocks of jet fuel. The costs to a refinery (as opposed to an airline or a retailer) of a stock-out of jet fuel are relatively small. Once refiners produce jet fuel, refineries probably will seek to minimize their inventories of jet fuel. The costs of holding these post-production inventories of jet fuel create an incentive for refineries to adjust the rate at which they pass changes in the price of crude oil on to the price of jet fuel. Although there is a negative relation between the retail price for jet fuel and inventories of jet fuel (CR #4), consumers may continue to purchase jet fuel if refiners slowly transmit price increases for crude oil to jet fuel because anticipation of additional price increases for jet fuel will move purchases forward. These purchases will slow the total draw on jet fuel inventories that are held by consumers. Higher purchases and slower inventory draws will dampen any increase in refinery inventories of jet fuel. Conversely, consumers would slow purchases and accelerate their inventory draw if price increases for crude oil are passed rapidly to the price of jet fuel. Following this strategy would cause refinery inventories of jet fuel to build. Of these two strategies, refiners may prefer to slow the rate at which prices of crude oil are passed through to the price of jet fuel because this option may avoid the added cost to refiners of storing additional quantities of jet fuel. Conversely, a reduction in the price of crude oil lowers the price for jet fuel and raises total inventories of jet fuel. If changes in the price of jet fuel lag reductions in the price of crude oil, the anticipation of additional price reductions for jet fuel will discourage consumer purchases of jet fuel and will slow their inventory build. As such, the strategy of 4 Refineries hold about 36% of jet fuel inventories. Between 1993 and 2014 (the entire period for which observations are available), US refiners hold an average of 14.78 million barrels of kerosene and light oils (which includes products beyond jet fuel). During the same period, total stocks of jet fuel average 40.98 million barrels. Data from US EIA.

R.K. Kaufmann / Energy Economics 68 (2017) 515–521

slowly reducing prices for jet fuel when crude oil price decline would cause refinery inventories of jet fuel to build. The cost associated with this build could be lowered if reductions in the price of crude oil are passed rapidly to the price of jet fuel because this would accelerate purchases and build consumer inventories of jet fuel. Of these two strategies for passing price increases for crude oil to jet fuel, refiners may prefer to speed the rate at which reductions in the price of crude oil are passed through to jet fuel because this may allow refiners to minimize their inventories of jet fuel, which reduces costs to refineries. Similarly, slowing the rate at which increases in the price of crude oil are passed to the price of jet fuel allows refiners to minimize their inventories of jet fuel. These efforts to minimize the refiner's cost of holding physical barrels of jet fuel may generate a ‘feathers and rockets’ effect, in which the price of jet fuel rises slowly (and inventories are drawn slowly) when the price of crude oil rises whereas, the price of jet fuel declines rapidly (and inventories of jet fuel build rapidly) when the price of crude oil declines. These asymmetric rates at which refineries build and draw inventories of jet fuel are consistent with an asymmetry that is implied by CR #4, which also is a long-run relation for jet fuel inventories. To illustrate, suppose the oil market starts at equilibrium. If crude oil prices rise by one unit, there is an immediate one-to-one increase in the wholesale price for jet fuel (via CR #1). But this rise translates to a relatively small increase in the retail price of jet fuel due to its asymmetric adjustments to CR #2. This small increase makes the disequilibrium in CR #4 slightly negative. This small negative value generates a relatively small draw on inventories of jet fuel. Now consider the same (absolute) sized one-unit reduction in crude oil prices. Again, the reduction is translated immediately (on a one-toone basis) to the wholesale price of jet fuel. This reduction translates to a relatively large reduction in the retail price of jet fuel due to its asymmetric adjustment to CR #2. This makes the disequilibrium in CR #4 positive and larger (in an absolute sense) than the disequilibrium associated with the one unit rise in crude oil prices described above. And this larger positive value generates a relatively large build in inventories of jet fuel (compared to the small draw described above). Together, these effects are consistent with the trade-off between inventory changes and the rates at which changes in crude oil prices are passed to jet fuel prices that may generate the ‘feathers and rockets’ effect, in which the retail price of jet fuel adjusts at a faster rate when the price of crude oil falls. 5. Conclusion In summary, the statistical results reported above do not support hypotheses that the small drop in airfares relative to the large drop in crude oil prices is associated with incomplete adjustment to the oil market (Hypothesis #1) or asymmetric rates of adjustment to changes in the oil market (Hypothesis #2). Similarly, the ‘feathers and rockets’ asymmetric rate of adjustment by retail prices for jet fuel implies that a large decline in crude oil prices would be passed on to airfares faster than a corresponding increase in crude oil prices. As such, this analysis provides little evidence that relations within the oil market are responsible for the small decline in airfares relative to the large drop in oil prices. Although the statistical results do not identify a mechanism in the oil market that could generate the small decline in airfares relative to the large decline in the price for crude oil, this absence does not does not support an alternative hypothesis, that airlines collude to set airfares. First, the CVAR accounts for a small portion of the monthly variation in airfares (R2 = 0.14) relative to the other variables, such as the wholesale price for jet fuel (e.g. R2 = 0.78). This implies that (1) the CVAR does not include the most important determinants of airfares or (2) monthly changes in airfares are largely random. Second, the CVAR model that is estimated here contains six endogenous variables and one exogenous variable, the price of crude oil. Persistent movements in the price for crude oil would account for all persistent movements in the six endogenous variables (including

521

airfares) if the Π matrix were full rank (i.e. if there were six cointegrating relations). But this is not the case; there are only four cointegrating relations. This implies that there are two endogenous stochastic trends. These trends could represent the supply of air travel, the demand for air travel, and/or collusion among airlines. Identifying the causes for these persistent movements are beyond the focus on the oil market proscribed by this analysis. As such, the causes for the small decline in airfares relative to the large decline in the price for crude oil hopefully will be elucidated by the Department of Justice, which will focus on the airline industry, per se. Acknowledgements I thank comments from two anonymous reviewers, Renan Silverio, and participants in the Fall 2015 meeting of Project LINK. All mistakes that remain are solely my responsibility. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.eneco.2017.10.011. References Aabo, T., Simkins, B.J., 2005. Interaction between real options and financial heeding: fact or fiction in managerial decision-making. Rev. Financ. Econ. 14 (3/4), 353–369. Bacon, R.W., 1991. Rockets and feathers: the asymmetric speed of adjustment of UK retail gasoline prices to cost changes. Energy Econ. 13 (3), 211–218. Berghofer, B., Lucey, B., 2014. Fuel hedging, operational hedging, and risk exposure— evidence from the global airline industry. Int. Rev. Financ. Anal. 34, 124–139. Button, K., Costa, A., Costa, F., Cruz, C., 2011. Problems of cost recovery by European airlines since market liberalization. Transp. Plan. Technol. 34 (2), 125–138. Carter, D.A., Simkins, B.J., 2004. The markets reaction to unexpected, catastrophic, events: the case of airline stock returns and the September 11th attacks. Q. Rev. Econ. Finance 44 (4), 539–558. Considine, T.J., 1997. Inventories under joint production: an empirical analysis of petroleum refining. Rev. Econ. Stat. 79 (3), 493–502. Cook, S., Holly, S., Turner, P., 1999. The power of tests for non-linearity: the case of granger-lee asymmetry. Econ. Lett. 62, 155–159. Dennis, J.G., 2006. CATS in RATS Cointegration Analysis of Time Series, Version 2. Estima, Evanston, IL. Escribano, A., Pfann, G., 1997. Nonlinear error correction, asymmetric adjustment, and cointegration. Econ. Model. 15 (2), 197–206. Frey, G., Manera, M., 2007. Econometric models of asymmetric price transmission. J. Econ. Surv. 21 (2), 349–4915. Gately, D., 1992. Imperfect price-reversibility of oil demand: asymmetric responses of US gasoline consumption to price increases and declines. Energy J. 13 (4), 179–207. Granger, C.W.J., Lee, T.H., 1989. Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. J. Appl. Econ. 4, S145–S159. Greenslade, J.V., Hall, S.G., Henry, S.G.B., 2002. On the identification of cointegrated systems in small samples: a modelling strategy with an application to UK wages and prices. J. Econ. Dyn. Control. 26 (9-10), 1517–1537. Holmes, M., Panagiotidis, T., 2009. Cointegration and asymmetric adjustment: some new evidence concerning the behavior of the U.S. current account. B.E. J. Macroecon 9 (1), 1–25. Johansen, S., 1996. Likelihood-based Inference in Cointegrated Vector Autoregressive Models. Advanced Texts in Econometrics. Oxford University Press, Oxford. Johnston, A., Ozment, J., 2011. Concentration in the airline industry: evidence of economies of scale? J. Transp. Manag. 59–74. Juselius, K., 2006. The Cointegrated VAR Model: Methodology and Applications. Advanced Texts in Econometrics. Oxford University Press, Oxford. Kaufmann, R.K., Laskowski, C., 2005. Causes for an asymmetric relation between the price of crude oil and refined petroleum products. Energ Policy 33, 1587–1596. Morrell, P., Swan, W., 2006. Airline jet fuel hedging: theory and practice. Transp. Rev. 26 (6), 713–730. Newey, W.K., West, K.D., 1987. A simple positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Perdiguero-Garcia, J., 2013. Symmetric or asymmetric oil prices? A meta-analysis. Energ Policy 57, 389–397. Pesaran, M.H., Shin, Y., 1994. Long run structural modeling. University of Cambridge, Mimeo. Rao, V.K., 1999. Fuel price management using futures. J. Air Transp. Manag. 5 (1), 39–44. US Energy Information Administration, d. http://www.eia.gov/dnav/pet/pet_pnp_pct_dc_ nus_pct_m.htm. Wadud, Z., 2015. Imperfect reversibility of air transport demand; effects of air fare, fuel prices, and price transmission. Transp. Res. A 72, 16–26.