WORKING 

 PAPERS

Asymmetric Pass-Through 

in U.S. Gasoline Prices

Matthew Chesnes

WORKING PAPER NO. 302

June 2010

___________________________________________________________________________

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______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
Asymmetric Pass-Through in U.S.

Gasoline Prices∗

Matthew Chesnes†

Bureau of Economics

Federal Trade Commission

June 18, 2010

∗The opinions expressed here are those of the author and not necessarily those of the Federal Trade

Commission or any of its Commissioners. I thank Michael Noel, Matthew Lewis, Chris Taylor, Louis

Silvia, David Meyer, Doug Herman, and participants at the 2010 International Industrial Organization Conference for their suggestions and comments. Elisabeth Murphy provided excellent research

assistance. All remaining errors are my own.

†Email: mchesnes@ftc.gov.

1
Abstract

This paper presents new evidence of asymmetric pass-through, the notion that

upward cost shocks are passed through faster than downward cost shocks, in U.S.

gasoline prices. Much of the extant literature comes to seemingly contradictory

conclusions about the existence of an asymmetry, though the differences may be

due to different aggregation (both over time and geographic markets) and the use

of different price series including crude oil, wholesale, and retail gasoline prices. I

utilize a large and detailed dataset to determine where evidence of a pass-through

asymmetry exists, and how it depends on the aggregation and price series chosen

by the researcher.

Using the standard error correction model, I find evidence of pass-through

asymmetry in the response of daily and weekly retail prices to wholesale rack price

changes, though the magnitude varies by geographic market. On average, retail

prices rise more than four times as fast as they fall. Branded gasoline features

significantly more asymmetry with respect to rack prices compared with unbranded

gasoline. Over time, nation-wide asymmetry varies significantly from year to year

peaking in 2005. Midwest cities, like Louisville and Minneapolis, feature more

asymmetry compared with other parts of the country. F-tests broadly confirm

the results and illustrate that data selection and aggregation, as well as model

specification, can have important implications on the findings of asymmetric passthrough.

2
1 Introduction

There is a large literature analyzing the cost to price pass-through in industries ranging

from automobiles (Gron and Swenson (1982)), to cheese products (Kim and Cotterill

(2008)), to the beef industry (Goodwin and Holt (1999)). The literature has not only

focused on the ability of firms to successfully capture rents when input costs change,

but also on how the rate of pass-through varies when the costs increase versus decrease.

In the gasoline industry, this asymmetric phenomenon is known as rockets and feathers,

reflecting the fact that retail prices tend to increase quickly when costs (say, wholesale

gasoline prices) rise, but drift down slowly when they fall.1 Much of the extant literature

comes to seemingly contradictory conclusions about the existence of this phenomenon,

though the differences may be due to different data sources, price series, aggregation

over time and across geographic areas, as well as misspecified models. In this paper,

I re-examine the pass-through in gasoline prices using a detailed dataset available at a

high frequency, across many cities, and at several price levels in the vertical distribution

process for gasoline.

The gasoline industry has been the focus of a particularly large amount of research

on pass-through for several reasons. Gasoline is a fairly homogeneous product and both

retail and intermediate wholesale prices are relatively transparent compared with other

industries.2 Much of the variation in gasoline prices is driven by the price of crude

oil, the key input into gasoline.3 This crude oil is traded on a world market and the

price is also transparent to market players and to consumers. In spite of this, there are

1The production and distribution of gasoline is just one part of the petroleum industry, which produces a whole range of refined products. The rockets and feathers literature has focused primarily on

gasoline prices.

2Rack prices for wholesale gasoline are observable and in 2009, refiner rack sales accounted for 60% of

the total gasoline supplied in the US. See http://tonto.eia.doe.gov/dnav/pet/pet_cons_refmg_c_

nus_epm0_mgalpd_a.htm and http://tonto.eia.doe.gov/dnav/pet/pet_cons_psup_dc_nus_mbbl_

m.htm. The rest is sold to lessee-dealer stations at (unobserved) dealer-tank-wagon (DTW) prices and

via transfer prices to refiner-operated stations.

3See The Federal Trade Commission, “Gasoline Price Changes: The Dynamics of Supply, Demand

and Competition,” 2005.

3
dynamics present in the gasoline industry which are difficult to explain with competitive

or oligopolistic economic models.

The literature on rockets and feathers dates back to at least 1991 when Robert

Bacon found evidence of an asymmetric response in gasoline prices in the UK. Since that

time, others have found evidence of the phenomenon including Borenstein, Cameron,

and Gilbert (1997, hereafter BCG), Lewis (forthcoming), Ye et. al. (2005), and most

recently, Deltas (2008). These studies all utilize some form of an error correction model

(outlined below) and consider some combination of crude oil prices, wholesale prices (rack

or spot), and retail gasoline prices. They also vary by the geography they consider and

how the data are aggregated over time (i.e., daily, weekly, or monthly). There are also

several papers that, due to either a different data source or model, find no evidence of an

asymmetric price response including Bachmeier and Griffin (2003) and Godby (2000).

The former paper also tests BCG results using daily data; however they only focus on

the transmission of crude oil to spot gasoline prices.

This paper is similar to BCG in that I analyze several different prices (crude oil, spot

gasoline, rack, and retail prices) over a long period of time. However, unlike BCG who

use weekly and bi-weekly data from the Lundberg Survey, I have access to daily data

on all prices. I also avoid a modeling assumption by BCG (discussed below) which was

questioned by Bachmeier and Griffin (2003) and instead use a more standard approach.

If it exists, there is little consensus on what causes the asymmetric response, though

explanations range from consumer search costs, to explicit or implicit collusion, to inventory management by consumers. Deltas, for example, looks at how the asymmetric

response varies with the level of retail market power and finds more asymmetry in markets with relatively more retail market power.4 Lewis (forthcoming) and others posit

4Market power is proxied by the average markup observed in the market over his sample period. It is

tempting to assume that markets in which firms face less competition will feature firms quickly passing

on cost increases to consumers, and only slowly (or possibly never) passing on cost savings. Markets

with many competing firms should feature perfect pass-through. For industry-wide cost changes, this is

generally true, however the opposite results when the cost change is firm-specific. Bulow and Pfleiderer

(1983) show that firm-specific cost changes are more completely passed through the less competitive is

4
that consumer search behavior could be causing the asymmetric response. If consumers

are more likely to search for a low price when prices are expected to rise, then competition will be fierce when costs are rising and margins tight. However, if prices are falling,

consumers may search less and this provides retailers with short-term market power and

allows them to slowly lower prices and increase their margins. If this is the case, it

still does not explain why asymmetric adjustment varies across time or across different

geographic areas.

Asymmetric adjustment of downstream prices to changes in an upstream cost (such

as a wholesale price) is generally divided into two forms: amount asymmetry and pattern

asymmetry. Amount asymmetry occurs when the aggregate change over a period of time

is different when costs are rising versus when they are falling. This asymmetry is not the

focus of most studies because it would imply that the upstream and downstream prices

would diverge over time, which is not the case with gasoline prices. Pattern asymmetry

involves differences in the relative speed of pass-through. As an example, one may find

evidence of pattern asymmetry if a 10% increase in wholesale prices leads to a 10%

increase in retail prices after one week, but an equivalent decrease in wholesale prices

leads to only a 5% decline in retail prices after one week. Consistent with the literature,

I will focus my analysis on pattern asymmetry.

In this study, I look for pattern asymmetry in pass-through, and I vary the geography,

the time aggregation, and products considered. I find the strongest evidence of pattern

asymmetry in the rack to retail prices at both the city and national level. On average,

retail prices rise more than four times as fast as they fall. Branded gasoline features

significantly more asymmetry compared with unbranded gasoline.

Asymmetry varies significantly from year to year and across cities. For example,

while in Los Angeles, the asymmetry of branded rack to retail price changes is fairly

the market. (See also, Ten Kate and Niels (2005).) The reason is that when faced with a cost decrease,

say, firms with a greater market share will benefit relatively more from the increase in quantity demanded

which more than offsets the lower revenue from passing on the cost decrease in the form of lower prices.

5
constant over time, in Phoenix, it is over four times as high in 2005 versus in 2007.

Using weekly instead of daily data, tends to attenuate the evidence of asymmetry in

some cases, though increases it in others.

The paper proceeds as follows. In section 2, I outline the model that I employ and

specification tests that need to be run to justify its use. I discuss the data and provide

basic descriptive statistics in section 3 and present the results of my model in section

4, including asymmetric pass-through results for different geographic areas, at different

levels of time aggregation, and for different products. In section 5, I conclude and provide

a brief outline of a complementary paper which seeks to explain why pass-through rates

and asymmetry vary by city and over time.

2 Model

I estimate an error correction model (ECM) frequently used in the literature, though in

various forms (e.g., Bachmeier and Griffin (2003)). I estimate two versions of the model:

one which is run individually for each city (metro area)5 and the other is a national-level

model with fixed effects included for each city, which allows for different markups in

each city.6 The latter regression measures the average pass-through rate across all cities,

while allowing the long-term relationship to vary by city. I allow for a difference in the

pass-through of positive and negative upstream price changes.

While I estimate the model for several pairs of upstream and downstream prices, for

simplicity, the following is the rack to retail pass-through model for a given city:

5Most of the metro areas in my sample are major cities. Some cities near state borders are split

across state lines, so for example, Louisville, KY and Louisville, IN are separate metro areas. See figure

A.1 for an example. This is important because often different types of gasoline (e.g., conventional, RFG,

and California Air Resources Board (CARB) gasoline) are sold in different states.

6

I use the term “national-level,” though prices are not aggregated, but instead the specification

includes prices from all major cities in my dataset.

6
∆Retailt =

L

+

X1

i=0

β

+

1i∆

+Rackt−i +

L

−X1

i=0

β

−

1i∆

−Rackt−i (1)

+

L

+

X2

i=1

β

+

2i∆

+Retailt−i +

L

−X2

i=1

β

−

2i∆

−Retailt−i

+ β

+

3

(Retailt−1 − γ0 − γ1Rackt−1)

| {z }

z

+

t−1

+ β

−

3

(Retailt−1 − γ0 − γ1Rackt−1)

| {z }

z

−

t−1

+t.

Note ∆Retailt−i = Retailt−i −Retailt−(i−1). Lag lengths are determined by minimizing the Bayesian Information Criterion (BIC):

BIC = K ∗ log(N) + N ∗ [Log(RSS/N)], (2)

where K is the number of parameters to be estimated, N is the number of observations,

and RSS = ˆ

0

ˆ from equation 1. I could allow the lag lengths to vary separately for

positive and negative changes as well as for rack and retail prices. However, since determining the optimal lag lengths for each price series, versus using a fixed (and equal) lag

length for all, does not affect the qualitative results, in the analysis below I fix the lag

length at 21 days in all regressions. This also allows me to compare regressions across

cities and over time since I will utilize the same specification in each.

The expression zt−1 = Retailt−1 − γ0 − γ1Rackt−1 is the error correction term, and

it captures the long-run relationship between the upstream and downstream prices. β

+

3

and β

−

3

should both be negative: if retail prices are above their equilibrium level (zt−1 >

0), retail prices should fall and if they are below the level predicted by the rack price

(zt−1 < 0), retail prices should rise.

Following the two-step method proposed by Engle and Granger (1987), I estimate γ0

7
and γ1 by running OLS on the following equation:

Retailt−1 = γ0 + γ1Rackt−1 + zt−1. (3)

The residuals, zt−1, are then inserted directly into the model.7 BGC estimate the longterm relationship in the same step as the rest of the parameters and instrument for

the upstream prices to control for possible endogeneity. As outlined in Bachmeier and

Griffin (2003), this may lead to problems with the resulting estimates.8 Once I obtain

the residuals, I can estimate equation 1 by OLS.

The national-level regression is similar, though it includes city-level fixed effects in

the error correction term:

Retailt−1 = γ0 + γ1Rackt−1 +

X

27

i=2

φiCityi + zt−1. (4)

As mentioned in the introduction, there are two potential types of asymmetry:

amount and pattern. In terms of the model parameters, amount asymmetry would

be of the form:

L

+

X1

i=0

β

+

1i

6=

L

−X1

i=0

β

−

1i

, (5)

however, this cannot exist over the long-term since upstream and downstream prices do

not tend to drift apart. Pattern asymmetry could be found if any one of the following

7Since the two series are cointegrated, the OLS regression yields super-consistent estimates of the γ

parameters. The estimates can then be inserted into the model as if they were known parameters.

8BCG run a two-stage least squares regression and instrument for the upstream price with the crude

oil price in England and a forward prices of crude in the US. However, while they reject the null that

there is no endogeneity in the prices, their 2SLS and OLS estimates are very similar.

8
three conditions are met:

β

+

1i

6= β

−

1i

for some i (6)

|β

+

3

| 6= |β

−

3

| (7)

L

+

1 6= L

−

1

or L

+

2 6= L

−

2

. (8)

The asymmetry in equation 6 is the one commonly analyzed in the literature. While

the aggregate pass-through should be the same for positive and negative rack price

changes, the pattern of the pass-through may be different. If any of the coefficients on

the same lag are different, this is evidence of pattern asymmetry. The coefficients on the

first lag, β

+

1,1

and β

−

1,1

are particularly important because they measure the contemporaneous speed of pass-through, assuming the model could be approximated as a first-order

difference equation.

The second pattern asymmetry (noting again that β3 should be negative reflecting

mean-reversion) involves the speed at which relative prices return to their long-term

equilibrium levels. We have evidence of the rockets and feathers type of asymmetry if

this mean reversion is slower (closer to zero) when retail prices are above their long-term

levels and faster (closer to one) when retail prices should be adjusting upwards toward

their long-term levels.

Finally, if I allowed the BIC-optimum lag lengths to vary for positive and negative

changes, further evidence of pattern asymmetry is obtained if the optimal lag lengths

are different. Though this is often the case, I fix the lag lengths and focus most of my

attention on asymmetries in contemporaneous pass-through and mean reversion via the

error correction term.

9
3 Data and Descriptive Statistics

I combine two datasets to perform the analysis. Spot prices are available from Reuters

via the Energy Information Administration (EIA) and rack and retail price data are

from the Oil Price Information Service (OPIS). All data are available daily (I will discuss weekends and missing values below) from January 1999 through December 2009.

Summary statistics are provided in tables 1, 2, and 3. All prices are reported in cents

per gallon (cpg).

Spot prices include the price of West Texas Intermediate (WTI) crude oil at Cushing,

Oklahoma. I also obtain the conventional regular and reformulated regular gasoline prices

along with the RBOB9spot for New York harbor, the Gulf Coast, and Los Angeles. Spot

prices are reported as of the close of day, Monday through Friday.

Average Margin

Spot Price N Min Mean Max Std Dev Date Range Over WTI

Conventional - NY 2,726 29.03 131.33 341.55 66.86 Jan 1999 - Dec 2009 16.93

Conventional - Gulf 2,726 27.00 130.69 487.25 68.43 Jan 1999 - Dec 2009 16.29

Conventional - LA 2,726 38.00 143.91 382.51 69.69 Jan 1999 - Dec 2009 29.51

RFG - NY 1,859 30.43 101.61 282.95 41.19 Jan 1999 - June 2006 18.24

RFG - Gulf 1,834 28.65 99.87 344.50 41.52 Jan 1999 - May 2006 17.66

RFG - LA 1,222 40.00 91.04 167.00 22.09 Jan 1999 - Nov 2003 28.04

RBOB - NY 1,340 75.33 188.64 357.60 56.37 July 2004 - Dec 2009 23.90

RBOB - Gulf 889 82.30 207.06 487.25 63.87 May 2006 - Dec 2009 26.09

RBOB - LA 1,679 78.00 188.54 389.60 62.30 Mar 2003 - Dec 2009 41.21

WTI 2,726 27.10 114.41 345.98 62.71 Jan 1999 - Dec 2009 -

Table 1: Daily Spot Prices (Cents per Gallon)

I use rack prices from OPIS for 20 U.S. cities. These rack prices are for the type of

gasoline used in each city since many cities utilize different types of gasoline (conventional, RFG, etc.). In some cases, rack prices for different types of gasoline are reported

in the same city. In these cases, I use the rack price that corresponds to the type of

gasoline that is used in each retail market area. For example, the Fairfax, VA rack

reports both conventional and RFG prices. Since I observe retail data for stations in

9Reformulated Blendstock for Oxygenate Blending.

10
Washington, DC, as well as the Virginia, Maryland, and West Virginia suburbs of DC,

I match the RFG rack price to DC, VA, and MD since each uses primarily RFG, while

the WV retail prices are matched to the conventional rack since that area primarily uses

conventional gasoline. Rack prices are reported as of 9AM, Monday through Saturday,

and are available for both branded and unbranded products.

Border Average Margin

States N Min Mean Max Std Dev Date Range Over WTI

Atlanta (Conventional) 4,014 33.09 126.90 354.29 72.11 Jan 1997 - Dec 2009 25.17

Boston (RFG) 4,065 36.05 131.09 362.22 70.51 Jan 1997 - Dec 2009 29.05

Chicago (RFG) 4,066 38.94 135.05 363.34 70.77 Jan 1997 - Dec 2009 33.21

Cleveland (Conventional) 4,066 32.33 128.70 359.30 70.68 Jan 1997 - Dec 2009 26.97

Dallas (RFG) 4,066 34.65 129.35 356.63 71.14 Jan 1997 - Dec 2009 27.73

Denver (Conventional) 4,066 33.37 129.55 364.76 70.82 Jan 1997 - Dec 2009 27.64

Detroit (Conventional) 4,066 31.10 128.73 361.20 71.17 Jan 1997 - Dec 2009 27.04

Fairfax (Conventional) WV 4,066 34.46 125.95 351.70 70.12 Jan 1997 - Dec 2009 23.76

Fairfax (RFG) DC, MD, VA 4,066 37.11 130.35 356.28 71.52 Jan 1997 - Dec 2009 28.49

Houston (RFG) 4,065 33.77 127.19 355.03 70.71 Jan 1997 - Dec 2009 25.37

Los Angeles (CARB) 2,825 59.28 174.35 392.91 66.58 Dec 2000 - Dec 2009 47.56

Louisville (Conventional) IN 4,049 32.66 128.32 355.70 70.66 Jan 1997 - Dec 2009 26.29

Louisville (RFG) KY 2,857 39.65 160.73 376.64 77.56 Feb 1998 - Dec 2009 40.54

Miami (Conventional) 4,066 34.84 126.63 353.51 70.97 Jan 1997 - Dec 2009 24.64

Minneapolis (Conventional) 4,064 35.18 130.67 357.47 70.81 Jan 1997 - Dec 2009 28.90

New Orleans (Conventional) 4,066 32.81 124.01 350.88 69.96 Jan 1997 - Dec 2009 21.86

Newark (RFG) 3,803 38.82 134.25 355.16 69.20 Mar 1997 - Dec 2009 27.17

Phoenix (Conventional) 4,066 43.60 140.32 366.58 71.25 Jan 1997 - Dec 2009 39.44

Salt Lake City (Conventional) 4,065 37.05 134.35 367.52 69.56 Jan 1997 - Dec 2009 32.22

San Francisco (CARB) 2,809 59.23 171.41 375.37 65.27 Jan 2001 - Dec 2009 44.24

Seattle (Conventional) 4,066 41.66 135.62 364.57 70.37 Jan 1997 - Dec 2009 34.19

St Louis (Conventional) IL 4,065 31.94 128.38 355.41 71.62 Jan 1997 - Dec 2009 26.62

St Louis (RFG) MO 3,337 57.92 149.81 359.20 66.52 May 1999 - Dec 2009 32.47

Racks that service multiple states with different types of wholesale gasoline are indicated in the "Boarder States" column. For example, the Fairfax, 

VA rack sells RFG to stations in Washington DC and its nearby suburbs, while it sells conventional gasoline to stations in West Virginia.

Table 2: Daily Rack Prices (Cents per Gallon)

Finally, I utilize pre-tax retail price data from OPIS for the 27 retail metro areas all

within the 20 cities for which I have rack prices. Retail prices are (usually) end of the

day prices as they are recorded from the last swipe of a consumer’s “fleet-card” on a

given day.10 OPIS averages all the prices they receive each day (at most one from each

station) to determine the price for the metro area. After 2001, the prices are reported

every day of the week. OPIS samples over 100,000 stations each day and covers branded

and unbranded stations. The three most expensive cities for retail gasoline in 2008 were

10See http://www.opisretail.com/methodology.html for more information on OPIS’s retail data. More

than one-half of the stations in the OPIS sample report a price each day, though the sample of stations

may change from day to day.

11
Miami, San Francisco, and Washington DC. These three cities also featured the highest

retail markups over the wholesale price.

Average Margin

N Min Mean Max Std Dev Date Range Over Rack

Atlanta 3,817 49.35 152.19 346.67 69.64 Jan 1999 - Dec 2009 9.35

Boston 3,817 58.16 163.20 366.50 68.77 Jan 1999 - Dec 2009 16.58

Chicago 3,817 55.82 163.88 365.56 70.41 Jan 1999 - Dec 2009 13.25

Cleveland 3,817 45.37 156.72 358.05 68.93 Jan 1999 - Dec 2009 12.30

Dallas 3,817 50.31 156.40 359.55 70.41 Jan 1999 - Dec 2009 11.14

Denver 3,816 49.03 158.37 360.39 70.36 Jan 1999 - Dec 2009 13.39

Detroit 3,817 46.10 155.22 360.01 69.34 Jan 1999 - Dec 2009 10.71

Houston 3,817 51.19 154.57 357.81 70.11 Jan 1999 - Dec 2009 11.64

Los Angeles 3,816 56.39 175.32 392.76 71.13 Jan 1999 - Dec 2009 13.46

Louisville IN 3,815 42.28 153.94 364.86 69.26 Jan 1999 - Dec 2009 10.20

Louisville KY 3,816 47.53 163.66 389.74 72.31 Jan 1999 - Dec 2009 7.51

Miami 3,817 68.21 177.18 383.47 73.14 Jan 1999 - Dec 2009 34.61

Minneapolis MN 3,817 54.06 158.88 360.77 68.43 Jan 1999 - Dec 2009 12.58

Minneapolis WI 3,815 51.50 158.18 353.03 68.37 Jan 1999 - Dec 2009 11.78

New Orleans 3,815 56.13 157.52 362.36 70.84 Jan 1999 - Dec 2009 18.00

Newark 3,816 57.82 163.97 367.73 69.48 Jan 1999 - Dec 2009 19.41

New York City 3,817 60.55 166.93 365.48 68.54 Jan 1999 - Dec 2009 22.32

Pheonix 3,816 54.55 167.61 376.72 69.38 Jan 1999 - Dec 2009 10.50

Salt Lake City 3,816 46.67 158.08 373.46 70.96 Jan 1999 - Dec 2009 8.48

San Francisco 3,815 80.72 188.67 390.37 67.09 Jan 1999 - Dec 2009 28.24

Seattle 3,816 63.10 171.78 384.57 69.82 Jan 1999 - Dec 2009 20.03

St Louis IL 3,817 43.00 150.40 351.03 68.03 Jan 1999 - Dec 2009 6.27

St Louis MO 3,816 42.16 155.76 362.64 70.02 Jan 1999 - Dec 2009 6.56

Washington DC 3,756 58.14 174.30 380.73 73.39 Jan 1999 - Dec 2009 26.97

Washington MD 3,817 54.27 165.07 368.13 71.50 Jan 1999 - Dec 2009 18.97

Washington VA 3,817 50.87 160.03 363.64 70.84 Jan 1999 - Dec 2009 13.97

Washington WV 3,815 43.27 156.50 360.02 71.32 Jan 1999 - Dec 2009 14.95

This table shows statistics by "retail market area" as reported by OPIS. Prices are generated using Fleet Card purchases 

from all stations in the area.

Table 3: Daily Retail Prices (Cents per Gallon)

Given the different reporting times of day for each price series, when running regressions using daily data, it is important that lags are used where appropriate. For

example, when considering the speed of pass-through from rack to retail, I can consider

the effect for the same time stamp since end of day retail prices have a chance to adjust

to a change in the rack price observed at the beginning of the day. However, in the

spot to rack pass-through regressions, I use the lagged spot price because these two price

series are reported at the same time of day.

12
Border Proportion

States N Mean N Mean Unbranded > Branded

Atlanta (Conventional) 4,014 126.90 4,002 123.81 0.049

Boston (RFG) 4,065 131.09 4,066 126.20 0.039

Chicago (RFG) 4,066 135.05 4,066 131.75 0.042

Cleveland (Conventional) 4,066 128.70 4,062 125.90 0.072

Dallas (RFG) 4,066 129.35 4,066 126.67 0.083

Denver (Conventional) 4,066 129.55 4,066 127.07 0.066

Detroit (Conventional) 4,066 128.73 4,016 125.44 0.069

Fairfax (Conventional) WV 4,066 125.95 4,004 123.60 0.065

Fairfax (RFG) DC, MD, VA 4,066 130.35 4,066 126.69 0.050

Houston (RFG) 4,065 127.19 4,065 124.38 0.071

Los Angeles (CARB) 2,825 174.35 2,582 176.58 0.282

Louisville (Conventional) IN 4,049 128.32 4,062 124.78 0.051

Louisville (RFG) KY 2,857 160.73 3,723 144.23 0.128

Miami (Conventional) 4,066 126.63 4,066 123.64 0.041

Minneapolis (Conventional) 4,064 130.67 4,066 127.65 0.039

New Orleans (Conventional) 4,066 124.01 4,066 120.77 0.035

Newark (RFG) 3,803 134.25 3,809 129.57 0.052

Phoenix (Conventional) 4,066 140.32 4,066 134.14 0.142

Salt Lake City (Conventional) 4,065 134.35 4,065 131.96 0.090

San Francisco (CARB) 2,809 171.41 2,412 178.16 0.287

Seattle (Conventional) 4,066 135.62 4,066 130.89 0.164

St Louis (Conventional) IL 4,065 128.38 4,025 124.99 0.066

St Louis (RFG) MO 3,337 149.81 3,323 150.13 0.270

Branded Unbranded

Table 4: Branded versus Unbranded Rack Prices (Cents per Gallon)

In table 4, I report statistics on branded versus unbranded rack prices. Generally,

unbranded gasoline is more homogeneous across refiners because it includes only a generic

package of additives and lacks a brand name premium. Therefore, in most cases, branded

gasoline is about 5 cents more expensive than unbranded. However, as evidence in the

right-hand column shows, at times the unbranded price actually exceeds the branded

price and this happens quite often in Los Angeles, San Francisco, and St. Louis. Many

of these inversions follow supply shocks (e.g., hurricanes and refinery outages) as refiners

may be giving priority to their branded customers to maintain the brand image, resulting

in a more severe supply reduction for unbranded gasoline. Whatever the cause, below I

investigate the asymmetric response for branded and unbranded fuel separately.

13
3.1 Data Issues

Before focusing on the results, there are a few issues with the data that need to be

addressed. I run my regressions at both a daily and a weekly frequency. Weekly data

was generated as the simple average of the daily series. This means that sometimes the

average is over five days, other times six days, four days, etc. Early in the sample, the

data suffer from many missing values, though starting in 2002, the data are much more

complete. Therefore, I restrict the regressions to dates from January 2002 - December

2009.

Due to holidays, etc, there are still some missing values in the daily data. Instead of

interpolating on each of these days, I do the following:

1. Include any day that has data on both the upstream and downstream price.

2. Do not include any date that is missing both the upstream and downstream price.

3. Include a partial observation if it occurs on Monday - Friday, leaving the missing

value in the data.11

This means that the duration between observations is usually one day (adjacent days)

or three days (for weekends) though at times may be longer if both prices are missing for

a period of time. I have analyzed the distribution of changes in all the prices as it varies

by the number of days between adjacent non-missing observations. I find that there is

almost no “weekend effect” in that the changes in price from Friday to Monday have

the same distribution as the changes on adjacent days. However, there are a few longer

periods in the data with missing values and the distribution of changes is much wider.

Therefore, I control for these large jumps by including a dummy variable which equals

one if any of the changes on the upstream or downstream price are for a period of five

11The reason I include the partial observation instead of dropping it is to eliminate situations where

two lagged differences are included in an observation, one over adjacent days, and the other over a much

longer number of days. In effect, this method results in dropping several observations when I estimate

the model, but reduces the number of long gaps between consequative observations.

14
days or more. With this set of observations, lags are formed and if missing values are

present in any observation, it is removed from the analysis.12

Finally, at one time the spot price for RFG was for reformulated gasoline blended

with MTBE, which has now been banned in most states.13 It has been replaced by the

RBOB spot price, which is RFG that will eventually get blended with an oxygenate

(typically ethanol). In New York and LA, there is some overlap in the two series so I

create my complete spot price for RFG as the old RFG spot for the early part of the

sample, and as soon as the RBOB spot is available, I switch to that price. The two

prices are similar to each other during the overlap period.14 For the Gulf Coast, there is

no overlap (the RFG spot ends on one day and the RBOB spot begins being reported

on the very next day) so I concatenate the two series to form my complete RFG spot

price. However, the RBOB price on its first day being reported is 38 cents higher than

the RFG spot on the previous day.15 I have done robustness checks by only running

the regression using dates where I observe the RFG spot price and the results are very

similar.

4 Results

Before analyzing the results, it is important to test for stationarity of the regressors. I

run Augmented Dickey Fuller (ADF) tests which show that all price series do indeed

have a unit root so first differencing is necessary. I then run another ADF test on each

set of price series together and confirm that the upstream and downstream price series

are cointegrated (i.e., the residuals from the long-run regression equations 3 and 4 are

12Removing observations only after lags are formed guarantees that the lagged differences in a given

observation are all over approximately the same (small) duration of time.

13In others, the liability protection has been removed so refiners are reluctant to use it.

14A simple regression of the RFG spot on the RBOB spot during the overlap yields a slope coefficient

of 0.94 for NY and 0.95 for LA.

15Compared with mean absolute day to day changes for RFG and RBOB of 2.6 and 5.1 cents respectively.

15
stationary).16 Therefore, estimating the long-term relationship in the first stage provides

super-consistent estimates which can be entered into the model directly. Durbin Watson

tests for autocorrelation correlation are also run and fail to reject the hypothesis that

there is no autocorrelation in the residuals for each model.

I divide the results into several sections which consider the differences in pattern

asymmetry among different price relationships, across cities and in the national regression, by the time aggregation of the data, for branded versus unbranded wholesale gasoline, and over time. Finally, I show formal F-tests of pattern asymmetry for each type

of model.

4.1 Price Relationships

I investigate pass-through asymmetry for combinations of the crude oil price, the gasoline

spot price, the branded and unbranded rack prices, and the retail price series. The

following tables and figures summarize the results of equation 4, which incorporate data

from all cities and includes city-level fixed effects in the long-term first-stage regression.

The relationships include the following:

1. Crude oil price to the gasoline spot price, the rack prices, and the retail price.17

2. Closest gasoline spot price to the rack prices and the retail price.18

3. Rack prices to the retail price.

Complete results for one of these regressions (rack to retail) is shown in table A.1

in the appendix. However, following the literature on asymmetric pass-through, it is

much easier to present the results graphically. The reason is that a one-time change

in the upstream price will have an immediate effect on the downstream price, but the

16ADF test statistics on the rack to retail price relationship are all greater than six compared with a

5% critical value of 3.33 from MacKinnon (2010).

17I estimate the crude to spot relationship for each of the six spot prices available on EIA’s website:

conventional gasoline and RFG in NY, Houston, and LA.

18I use the NY spot price for Boston and Newark. I use the LA spot price for LA, San Francisco,

Phoenix, Salt Lake City and Seattle. For the rest, I use the Gulf Coast spot price.

16
total effect may be drawn out over a period of days and include both the short-term

speed of adjustment (the β1 terms in equation 1), the own-lag effects (the β2 terms), and

the long-term error correction effects (the β3 terms). For this reason, I present impulse

response functions which trace out the effects of a ten cent per gallon change (positive

or negative) in the upstream price on the downstream price over a period of several days

following the shock. The 95% confidence bands are also shown in each graph.19

Figures 1 and 2 below, along with figures A.2, A.3, A.4, and A.5 in the appendix

display the impulse response function tracing out the effect on the downstream price of

a 10 cpg change in the upstream price. While each of the figures shows some kind of

asymmetric response, the rockets and feathers type (where the response time of positive

shocks exceeds negative shocks) is strongest in the rack to retail and spot to retail

relationships. However, while the asymmetry in both of these relationships becomes

statistically insignificant after about seven to ten days, the asymmetry in spot to retail

prices is significantly smaller than rack to retail. A weaker (and sometimes reverse)

asymmetry is shown in the crude to gasoline spot, rack, and retail price regressions.

Bacon (1991) found a similar asymmetry in rack to retail prices, while Bachmeier and

Griffin (2003) find no evidence of asymmetry in the crude oil to gasoline spot price transmission, consistent with my results. BCG (1997) do not find any significant asymmetry

in the spot to retail relationship, though their study relies on bi-weekly data.

4.2 Individual City Results

The evidence of asymmetries found in the previous section is mostly confirmed by regressions run at the individual city level. In table 5, I present results on the difference in

the first coefficients on the upstream price for positive and negative changes. Though a

complete picture of pass-through asymmetry can only be seen from an impulse response

19To account for possible nonlinearities in the relationships between the upstream and downstream

prices, I consider an upstream price increase from 200 cpg to 210 cpg and a corresponding decrease from

210 cpg to 200 cpg.

17
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

Branded Rack to Retail, National

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure 1: Impulse Response Function: Rack to Retail Prices, All Cities Included

graph, this first coefficient embodies the speed of pass-through if we think of the model

as approximating a first-order difference equation.

I include the difference by city and for each of the city-specific price relationships. The

difference in the β1 coefficients in the crude oil to rack and retail price relationships are

mostly insignificant or have a reverse asymmetry as measured by the speed coefficient.

The spot to rack regressions reveal asymmetry in several cities, including Detroit, Miami,

and St. Louis. The final two columns on rack to retail prices again confirm the strong

asymmetry in all cities as was found in the previous section. The asymmetry is the

strongest in Cleveland, Detroit, Louisville, and Minneapolis, while it is weakest in San

Francisco and the West Virginia suburbs of Washington DC.

18
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

Spot to Retail, National

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure 2: Impulse Response Function: Gasoline Spot to Retail Prices, All Cities Included

In table 6, I present the results on the form of asymmetry shown in equation 7: the

difference between the positive and negative coefficients on the error correction term.

The results for the rack to retail relationships are similar to above, and the long-term

correction asymmetry appears more in the crude to rack and retail price relationships,

while it has the opposite sign in spot to rack price regressions.

The type of fuel utilized in each city is also related to the degree of pass-through

asymmetry. For example, St. Louis IL, Louisville IN, and Washington WV all utilize

conventional gasoline and all have lower asymmetry than their neighboring retail metro

areas which utilize RFG.

While the differences in the speed of adjustment and error correction terms provides

19
Atlanta -0.20*** -0.09 -0.02 0.01 0.03 0.23*** 0.14***

Boston -0.10*** -0.12* -0.05*** 0.03 0.12*** 0.14*** 0.07***

Chicago -0.04 -0.04 -0.06** 0.06** -0.02 0.13*** 0.09***

Cleveland -0.09* 0.10 -0.21*** 0.05* -0.06 0.31*** 0.21***

Dallas -0.21*** -0.11* -0.05*** 0.03 0.02 0.12*** 0.07***

Denver -0.09** -0.11** -0.02 0.02 0.03 0.11*** 0.08***

Detroit -0.01 0.16** -0.09** 0.08*** 0.09** 0.32*** 0.20***

Washington DC -0.14*** -0.05 -0.08*** -0.01 -0.10*** 0.15*** 0.08***

Washington MD -0.14*** -0.05 -0.03 -0.01 -0.10*** 0.13*** 0.06***

Washington VA -0.14*** -0.05 -0.03* -0.01 -0.10*** 0.12*** 0.08***

Washington WV -0.14*** 0.06 -0.10*** 0.05*** -0.04 0.07*** 0.01

Houston -0.14*** -0.02 -0.06*** 0.00 0.13*** 0.14*** 0.06***

Los Angeles -0.03 -0.13 -0.01 0.02 0.07 0.16*** 0.01**

Louisville IN -0.20*** -0.10 -0.15*** 0.00 -0.01 0.27*** 0.16***

Louisville KY -0.19*** -0.08 -0.19** -0.04 -0.10*** 0.37*** 0.27***

Miami -0.16*** -0.15** -0.07*** 0.04** 0.20*** 0.15*** 0.07***

Minneapolis St Paul MN -0.08 -0.16** -0.17*** 0.07*** -0.17*** 0.38*** 0.31***

Minneapolis St Paul WI -0.08 -0.16** -0.13*** 0.07*** -0.17*** 0.08*** 0.07***

New Orleans -0.23*** -0.08 -0.04** 0.01 0.06** 0.13*** 0.05***

Newark -0.10*** -0.14** -0.07*** 0.02 -0.08*** 0.19*** 0.10***

New York -0.10*** -0.14** -0.06*** 0.02 -0.08*** 0.11*** 0.05***

Phoenix 0.05* -0.12* -0.03* 0.02 0.01 0.11*** 0.04***

Salt Lake City 0.02 -0.01 -0.01 0.02** 0.01 0.16*** 0.11***

San Francisco -0.02 -0.23*** 0.02 0.04** 0.01 0.08*** 0.00

Seattle -0.04* -0.16*** -0.02* 0.01 0.07** 0.15*** 0.04***

St Louis IL -0.03 0.04 -0.06 0.10*** 0.13*** 0.20*** 0.15***

St Louis MO 0.04 0.21** -0.10* 0.06** 0.17*** 0.32*** 0.16***

WTI to 

Retail

WTI to 

Unbranded 

Rack

Spot to 

Branded 

Rack

Spot to 

Unbranded 

Rack

Branded 

Rack to 

Retail

Unbranded 

Rack to 

Retail

1

+ - 1-

Difference in positive and negative speed coefficients. Positive and significant differences are evidence of rockets and feathers. ***, **, * significant at the 1%, 5% and 

10% levels respectively.

WTI to 

Branded 

Rack

Table 5: Asymmetry in Difference in First Coefficients on Lagged Upstream Price

a first approximation of the asymmetric adjustment, a better measure would account

for the overall price path resulting from prices rocketing up following cost increases and

feathering down following cost decreases. Therefore, I first calculate the impulse response

function for negative and positive shocks and then calculate the retail price under two

regimes:

1. Following a downward cost shock, retail prices feather down at the rate seen in the

data.

2. Following a downward cost shock, retail prices rocket down at the same rate they

rocket up following cost increases.

20
Atlanta 0.03*** 0.05*** -0.01 -0.22*** -0.14*** -0.01 0.02**

Boston 0.01 0.01 0.00 -0.06*** -0.03 0.02*** 0.01***

Chicago 0.00 0.02 0.01*** -0.09*** -0.04* 0.09*** 0.08***

Cleveland 0.03** 0.06*** 0.06*** -0.09*** -0.12*** 0.32*** 0.05***

Dallas 0.02* 0.05*** 0.00 -0.26*** -0.22*** 0.03*** 0.04***

Denver 0.01 0.03** 0.00 -0.04*** -0.03 0.05*** 0.04***

Detroit 0.02* 0.01 0.03*** -0.10*** -0.06*** 0.11*** 0.03

Washington DC 0.03*** 0.06*** -0.01 -0.20*** -0.20*** 0.00 0.01

Washington MD 0.03*** 0.06*** 0.00 -0.20*** -0.20*** 0.01 0.01***

Washington VA 0.03*** 0.06*** 0.00 -0.20*** -0.20*** 0.01* 0.01***

Washington WV 0.02* 0.03 0.01 -0.29*** -0.13*** 0.04*** 0.02*

Houston 0.02** 0.04** 0.00 -0.29*** -0.28*** 0.02*** 0.02***

Los Angeles 0.01** 0.00 0.00* -0.01 0.06 0.00 0.01***

Louisville IN 0.02 0.05*** 0.04*** -0.12*** -0.07** 0.14*** 0.13***

Louisville KY 0.02* 0.03* 0.04** -0.14*** -0.03 0.19*** 0.20***

Miami 0.03*** 0.05*** 0.00 -0.38*** -0.31*** 0.02*** 0.02***

Minneapolis St Paul MN 0.03*** 0.04** 0.04*** -0.04** -0.05** 0.24*** 0.23***

Minneapolis St Paul WI 0.03*** 0.04** 0.01 -0.04** -0.05** 0.04*** 0.04***

New Orleans 0.03*** 0.05*** 0.01 -0.39*** -0.41*** 0.03*** 0.03***

Newark 0.01 0.03** 0.00 -0.08*** -0.08** 0.02*** 0.01***

New York 0.01 0.03** 0.00 -0.08*** -0.08** 0.02*** 0.01***

Phoenix 0.01* 0.04*** 0.00 -0.02** -0.17*** 0.00 0.01***

Salt Lake City 0.00 0.01 0.00 -0.02*** -0.02*** 0.02*** 0.03***

San Francisco 0.02** -0.01 0.01** -0.03** -0.01 0.00 0.01***

Seattle 0.00 0.00 0.00 -0.02*** -0.06*** 0.00 0.01***

St Louis IL 0.02 0.04** 0.03** -0.06*** 0.04 0.06*** 0.05***

St Louis MO 0.01 -0.03* 0.04*** -0.05** -0.08*** 0.14*** 0.04**

Unbranded 

Rack to 

Retail

WTI to 

Branded 

Rack

WTI to 

Unbranded 

Rack

WTI to 

Retail

Spot to 

Branded 

Rack

Spot to 

Unbranded 

Rack

Branded 

Rack to 

Retail

Difference in positive and error correction coefficients. Positive and significant differences are evidence of rockets and feathers. ***, **, * significant at the 1%, 5% and 

10% levels respectively.

3

+ - 3-

Table 6: Asymmetry in the Difference in Coefficients on the Error Correction Term

Calculating the average price in each regime and computing the difference between

the two yields the total cost to the consumer of the asymmetric adjustment. I do this

analysis for each city and the resulting asymmetry is reported in figure 3.

Louisville, IN features the largest asymmetry with prices almost 5 cpg higher when

they feather down instead of rocket down (even though its speed of adjustment estimate was lower than neighboring Louisville, KY). Other cities, such as, Newark, Cleveland, Salt Lake City, and Washington DC also show relatively more asymmetry, while

Washington WV and Minneapolis WI (both conventional gasoline users) have the least

asymmetry. The loss in the unbranded rack to retail asymmetry is smaller in all cities

21
0

1

2

3

4

5

6

Louisville IN 

Newark 

Cleveland 

Salt Lake City 

Washington DC 

Minneapolis St Paul MN

St Louis MO 

Louisville KY 

Los Angeles Phoenix 

Denver 

Washington VA 

Washington MD 

New York 

Boston 

Atlanta 

Houston 

Detroit 

Miami 

New Orleans 

Seattle 

Dallas 

Chicago 

St Louis IL 

San Francisco 

Washington WV 

Minneapolis St Paul WI

Consumer Loss from Asymmetry (Cents per Gallon)

Avg Price Feather Down − Avg Price Rocket Down

Branded

Unbranded

Figure 3: Consumer Loss from Asymmetric Adjustment

averaging around 2 cpg.

4.3 Time Aggregation

One of the major differences between the various studies in the extant literature is the

frequency of the data used. Many rely on less frequent, bi-weekly or monthly data simply

because it it more widely available. In this section, I consider the effect of using daily

versus weekly data on the likelihood of finding evidence of pass-through asymmetry.

Figure 4 shows the same impulse response function for crude to rack prices, but the

top panel uses daily data while the bottom panel uses average weekly prices. While, in

general, both show a lack of asymmetry, the time required to reach complete pass-through

is about a week in the daily regression and over two weeks in the weekly regression. Important day-to-day variation is being smoothed, which masks the pass-through dynamics

22
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

WTI to Branded Rack, National, Daily

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

0 0.5 1 1.5 2 2.5 3

0

5

10

15

Weeks Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

WTI to Branded Rack, National, Weekly

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure 4: Frequency Analysis: Daily vs Weekly, Crude to Rack

23
between the two prices.

The results are similar when considering rack to retail prices in figure 5. Both impulse

response functions show evidence of asymmetry though the pattern of the asymmetry is

different. While the asymmetry disappears in ten days in the daily regression, it continues

in the weekly regression for about three weeks when pass-through of the negative shock

is finally completed.

4.4 Branded versus Unbranded

Branded wholesale gasoline is generally a few cents more expensive than unbranded gasoline given the former has proprietary additives (and a brand-name premium) included.

However, at times, the unbranded price will exceed the branded price, and this occurs

especially following negative supply shocks. As shown in figure 6, the (first lag) asymmetry for branded gasoline is significantly higher than for unbranded gasoline in almost

every city.

Therefore, while the unbranded price may “rocket up” more quickly than the branded

price following a supply shock, the speed at which it retreats back to equilibrium levels

is slower for the branded price. In some cities, such as, Seattle and Los Angeles, the

difference in asymmetry is very large with branded prices being more than twice as

asymmetric compared with unbranded prices.20 In future work, I will investigate these

relationships further, specifically considering how the asymmetric response varies for dayto-day price movements compared with the dynamics following major supply disruptions.

20The result that unbranded gasoline prices exhibit less asymmetry may be consistent with the literature that claim heterogeneous consumer search costs are the cause of asymmetric adjustment. Consumers

who buy branded gasoline are likely more loyal to a single brand, while unbranded buyers are more likely

to shop around for the best price. A negative cost shock would be passed on more quickly to unbranded

prices than to branded prices, reducing the asymmetry in the unbranded price relationship.

24
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

Branded Rack to Retail, National, Daily

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

0 0.5 1 1.5 2 2.5 3

0

5

10

15

Weeks Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

Branded Rack to Retail, National, Weekly

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure 5: Frequency Analysis: Daily vs Weekly, Rack to Retail

25
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Louisville KY 

Minneapolis St Paul MN

Detroit 

Cleveland 

St Louis MO 

Louisville IN 

St Louis IL 

Atlanta 

Newark 

Salt Lake City 

Chicago 

Seattle 

Los Angeles Boston 

Houston 

Dallas Miami 

New Orleans 

Washington MD 

Washington DC 

Phoenix 

Washington VA 

San Francisco 

Washington WV 

Minneapolis St Paul WI

Denver 

New York 

Speed of Pass−Through (Positive less Negative)

β

+1 − 

β

−1

Branded

Unbranded

Figure 6: Branded vs Unbranded Analysis, Rack to Retail (95% confidence bands shown)

4.5 Differences Over Time

Finally, in figure 7 below and figure A.6 in the appendix, I investigate how pass-through

asymmetry has changed over time. For this analysis, I estimate my model at a daily

frequency for both branded and unbranded gasoline, but I run 80 separate overlapping

regressions on a 12-month window of data centered on each month in the data. I then

calculate the total loss due to asymmetry under the two regimes laid out above.

The asymmetry in pass-through from rack prices to retail prices varies significantly

from year to year and peaks in 2005, possibly because 2005 was the most active hurricane

season in history. In 2009, pass-through asymmetry cost consumers about 2 cpg on

branded gasoline and between 1 and 1.5 cpg on unbranded gasoline. This assumes that

consumers purchase their gas uniformly across all days no matter if prices are rising or

falling.

26
Jan02 Jan04 Jan06 Jan08 Jan10

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Date

Asymmetry (CPG)

Asymmetry Over Time, Rolling 12−Month Regressions

All City Specification

Rack to Retail

Branded

Unbranded

Figure 7: Time Analysis: Pass-Through Asymmetry by Year, National

4.6 Formal Tests of Asymmetry

In order to formally test for asymmetry, I report F-statistics for the pattern asymmetry

in equation 6. I test the following hypothesis:

H0 : β

+

1i = β

−

1i ∀ i

H1 : β

+

1i

6= β

−

1i

for some i.

Note this is a two-sided test, so includes the possibility that the asymmetry is both the

rockets and feather type and the opposite. To implement the test, I save the residual sum

of squares, RSSu, from the full (unrestricted) model where the coefficients are allowed to

vary separately for positive and negative shocks. I then estimate a symmetric (restricted)

27
model, with only one set of β1i coefficients and save RSSr. Note that minimizing the

BIC separately for each model would mean that a different number of lags is included in

each.21 Therefore, I again restrict the number of lags to be 14 days in both regressions

so the only difference between the models is the restriction on the parameters. Formally,

the test statistic is of the usual form:

F ̃ =

(RSSr − RSSu)/(Ku − Kr)

RSSu/(N − Ku)

, (9)

where Ku and Kr are the number of parameters to be estimated in the unrestricted and

restricted models respectively. Results are reported in tables 7, 8, and 9 below.

The statistics reported in the tables largely confirm what has been shown in the impulse response functions in the previous sections. There is strong evidence of asymmetry,

both in each city separately and in the all-city specification, in rack to retail prices and

spot to rack prices. The evidence is less strong when the upstream price is the crude

oil price. The branded rack to retail price relationship again show stronger evidence of

asymmetry compared with unbranded rack to retail prices.

The year-by-year regressions reveal some interesting patterns. Though the completeyear regressions show pattern asymmetry in San Francisco for branded rack to retail

prices, the F-statistics for the individual year regressions are almost never significant.

The branded rack to retail regressions for 2009 alone only show evidence of asymmetry in

17 of the 27 metro areas, though the complete-year regressions show strong asymmetry

in 26 of the 27 metro areas. Thus, one implication is that studies which rely on shorter

samples may not find evidence of asymmetry, when it does exist. Further investigation is

required to determine what types of shocks (day-to-day movements versus large changes)

are driving the asymmetric results over the entire sample.

21See Ye, et. al. (2005) for a discussion of this issue.

28
Atlanta 3.33*** 4.45*** 2.00*** 2.67*** 12.53*** 21.35*** 17.74***

Boston 3.63*** 3.69*** 2.18*** 5.34*** 4.45*** 16.08*** 12.45***

Chicago 2.78*** 2.66*** 1.82** 16.83*** 14.20*** 8.47*** 6.52***

Cleveland 3.36*** 4.05*** 1.58** 2.43*** 3.84*** 7.63*** 6.72***

Dallas 5.39*** 3.68*** 3.10*** 16.79*** 18.73*** 15.54*** 12.05***

Denver 2.52*** 3.01*** 1.16 10.18*** 6.44*** 8.33*** 6.29***

Detroit 3.36*** 1.83** 1.77** 4.37*** 4.46*** 24.57*** 15.28***

Washington DC 4.22*** 4.63*** 1.78** 16.43*** 21.34*** 15.49*** 13.21***

Washington MD 4.22*** 4.63*** 3.26*** 16.43*** 21.34*** 18.71*** 15.42***

Washington VA 4.22*** 4.63*** 1.55* 16.43*** 21.34*** 21.98*** 20.22***

Washington WV 4.10*** 4.50*** 1.58** 3.49*** 3.77*** 3.32*** 5.54***

Houston 4.89*** 5.23*** 2.53*** 17.31*** 10.04*** 24.12*** 12.32***

Los Angeles 3.87*** 2.35*** 1.05 0.76 2.76*** 9.34*** 1.81**

Louisville IN 4.52*** 4.09*** 1.35 4.21*** 1.86** 7.60*** 6.69***

Louisville KY 3.73*** 4.24*** 2.08*** 19.47*** 20.61*** 5.64*** 6.92***

Miami 3.91*** 3.28*** 2.07*** 1.81** 11.96*** 19.75*** 10.55***

Minneapolis St Paul MN 2.76*** 3.67*** 1.41 10.02*** 3.88*** 9.91*** 9.18***

Minneapolis St Paul WI 2.76*** 3.67*** 4.80*** 10.02*** 3.88*** 7.54*** 6.38***

New Orleans 5.88*** 4.25*** 2.19*** 3.48*** 7.59*** 11.35*** 4.77***

Newark 3.32*** 3.04*** 3.14*** 4.71*** 2.93*** 24.87*** 14.91***

New York 3.32*** 3.04*** 2.60*** 4.71*** 2.93*** 13.13*** 7.70***

Phoenix 1.53* 3.79*** 1.43* 2.21*** 1.78** 3.84*** 3.67***

Salt Lake City 3.56*** 3.88*** 1.35 1.68** 1.11 11.81*** 7.20***

San Francisco 2.72*** 2.11*** 0.81 1.19 2.07*** 3.75*** 0.99

Seattle 3.70*** 3.10*** 1.06 2.65*** 3.06*** 10.25*** 4.07***

St Louis IL 3.97*** 2.33*** 1.49* 4.86*** 4.32*** 6.36*** 6.47***

St Louis MO 3.05*** 6.33*** 1.43* 16.08*** 14.56*** 7.41*** 5.73***

All City Regression 69.58*** 54.68*** 240.65*** 193.75*** 192.97*** 155.39*** 86.97***

Branded Rack 

to Retail

Unbranded 

Rack to Retail

WTI to 

Branded Rack

WTI to 

Unbranded 

Rack

WTI to Retail Spot to 

Branded Rack

Spot to 

Unbranded 

Rack

Significance at the 1% (***), 5% (**), and 10% (**) levels.

Table 7: F-Statistics On the Existence of Pattern Asymmetry (All Years)

5 Conclusion and Future Work

The purpose of this study was to understand why so many researchers have studied

asymmetric pass-through in the gasoline industry and have come to varying conclusions.

Many of the discrepancies can be explained by variations in the data and the model

specification. I found that pass-through asymmetries do exist in wholesale rack to retail

prices as well as in spot to retail prices, but the asymmetry is weak to non-existent in

other price relationships.22 Pass-through asymmetry in the branded wholesale to retail

price relationship was shown to be larger than its unbranded counterpart. Averaging

22In some cases, I find evidence of prices rising slower than they fall, however the magnitude of this

asymmetry is relatively small.

29
Atlanta 1.50* 1.96*** 1.70** 7.17*** 1.33 2.14*** 4.22*** 2.02***

Boston 1.80** 5.07*** 0.88 4.80*** 1.55* 3.31*** 1.55* 2.15***

Chicago 1.10 1.60** 1.56* 2.06*** 1.41 3.13*** 2.01*** 2.11***

Cleveland 1.05 2.05*** 2.56*** 1.50* 1.17 1.92*** 1.97*** 1.80**

Dallas 2.72*** 1.48* 2.08*** 4.34*** 1.70** 3.49*** 2.53*** 2.15***

Denver 1.28 1.30 1.06 3.83*** 1.51* 1.42 0.95 1.83**

Detroit 0.82 1.04 3.39*** 4.97*** 3.43*** 3.22*** 4.49*** 2.27***

Washington DC 0.49 1.11 1.08 5.47*** 1.32 1.83** 2.65*** 1.39

Washington MD 2.40*** 1.73** 1.72** 5.29*** 2.65*** 2.20*** 3.69*** 2.01***

Washington VA 1.62** 1.64** 2.25*** 6.16*** 2.83*** 2.97*** 3.28*** 2.25***

Washington WV 1.13 1.50* 1.27 2.74*** 0.69 1.70** 1.30 1.82**

Houston 2.02*** 2.21*** 2.31*** 7.18*** 2.65*** 5.54*** 4.74*** 3.79***

Los Angeles 1.40 2.30*** 2.55*** 1.69** 1.24 2.36*** 2.34*** 1.37

Louisville IN 1.69** 0.80 1.67** 3.32*** 1.35 1.96*** 2.01*** 0.68

Louisville KY 0.82 0.76 1.33 3.03*** 1.56* 1.47* 1.11 1.26

Miami 2.04*** 2.31*** 0.67 3.13*** 4.76*** 4.63*** 2.38*** 5.76***

Minneapolis St Paul MN 1.75** 0.71 2.53*** 1.99*** 2.92*** 3.61*** 2.08*** 1.36

Minneapolis St Paul WI 2.06*** 1.59** 2.50*** 4.23*** 2.14*** 1.83** 1.19 1.13

New Orleans 1.49* 1.32 3.56*** 2.06*** 3.05*** 3.07*** 1.75** 2.70***

Newark 1.06 4.74*** 1.09 6.33*** 2.90*** 2.16*** 2.48*** 2.28***

New York 0.85 3.70*** 1.41 3.44*** 1.68** 2.35*** 1.44* 1.30

Phoenix 1.91*** 1.67** 2.32*** 2.46*** 1.48* 1.05 0.96 0.82

Salt Lake City 1.79** 1.73** 1.70** 3.61*** 4.18*** 1.71** 2.68*** 1.21

San Francisco 0.95 1.03 1.85** 1.05 1.54* 0.58 0.87 1.03

Seattle 2.27*** 2.86*** 2.83*** 1.48* 0.79 3.95*** 4.30*** 2.10***

St Louis IL 1.78** 0.93 1.00 2.77*** 1.10 1.47* 2.07*** 1.20

St Louis MO 1.86** 1.51* 0.68 2.66*** 1.69** 1.33 1.69** 1.93***

All City Regression 4.77*** 7.71*** 13.81*** 47.00*** 14.25*** 16.00*** 27.08*** 10.57***

2009

Significance at the 1% (***), 5% (**), and 10% (**) levels.

2002 2003 2004 2005 2006 2007 2008

Table 8: F-Statistics, Branded Rack to Retail Prices (By Year)

daily data to obtain a weekly price series attenuates the findings of asymmetry as it

masks important day-to-day variation in prices.

Still, this leaves several open questions including why there are differences in the

pass-through asymmetry across cities and between branded and unbranded wholesale

gasoline. Research that has attempted to explain the asymmetry has focused on the

demand side, with consumer search cost and inventory management by drivers being the

leading explanations. Unless consumers vary across cities, supply-side factors could help

explain the geographic variation.

In future work, I will focus on which supply-side characteristics are associated with

30
Atlanta 0.96 1.68** 1.07 3.06*** 1.04 1.93*** 2.71*** 1.80**

Boston 0.89 4.03*** 0.83 3.27*** 1.45* 1.63** 1.48* 1.99***

Chicago 1.13 1.56* 1.32 2.43*** 0.85 3.16*** 2.01*** 1.53*

Cleveland 0.84 1.78** 2.91*** 2.18*** 1.52* 1.42* 1.92*** 1.31

Dallas 2.41*** 1.12 1.67** 3.72*** 1.65** 2.36*** 1.54* 2.14***

Denver 1.30 0.60 1.36 4.14*** 1.14 1.65** 1.57** 1.31

Detroit 0.72 1.55* 2.18*** 3.94*** 2.84*** 1.67** 3.05*** 0.80

Washington DC 0.67 1.14 1.15 6.08*** 0.66 1.64** 0.87 1.50*

Washington MD 1.55* 0.95 1.44* 5.59*** 1.58** 1.42 1.63** 1.80**

Washington VA 1.14 0.83 2.09*** 11.14*** 2.40*** 1.74** 1.83** 1.67**

Washington WV 1.28 1.20 1.85** 4.14*** 1.00 0.73 1.02 1.51*

Houston 2.74*** 0.91 1.97*** 3.89*** 2.02*** 1.94*** 3.35*** 2.16***

Los Angeles 1.08 1.27 1.42* 1.43* 1.11 1.08 2.07*** 1.31

Louisville IN 1.25 0.98 2.54*** 5.51*** 1.31 1.19 1.27 1.08

Louisville KY 1.78** 0.63 1.44* 4.13*** 1.57** 1.38 1.20 2.14***

Miami 2.29*** 1.84** 0.50 1.74** 3.61*** 2.52*** 0.94 3.77***

Minneapolis St Paul MN 1.58** 0.45 1.90*** 1.78** 2.47*** 3.24*** 2.12*** 1.00

Minneapolis St Paul WI 1.61** 1.99*** 1.85** 1.78** 1.70** 1.09 1.15 1.18

New Orleans 1.28 1.13 2.98*** 1.32 2.41*** 2.18*** 0.88 1.36

Newark 0.85 3.83*** 0.70 3.39*** 0.67 1.82** 2.60*** 1.61**

New York 0.52 2.49*** 1.00 3.70*** 0.86 2.19*** 1.00 1.21

Phoenix 1.64** 1.23 0.64 4.10*** 1.76** 2.66*** 1.26 1.73**

Salt Lake City 3.30*** 1.03 0.86 4.10*** 2.72*** 2.06*** 1.76** 0.92

San Francisco 0.89 1.33 0.99 0.52 0.78 0.42 0.81 0.53

Seattle 1.67** 2.01*** 1.70** 0.83 1.54* 1.88*** 1.38 1.11

St Louis IL 1.16 0.84 0.94 1.97*** 1.32 1.72** 4.36*** 1.33

St Louis MO 0.86 0.84 0.77 2.17*** 2.20*** 0.90 1.87** 2.28***

All City Regression 3.19*** 4.66*** 11.33*** 33.01*** 7.06*** 8.48*** 15.08*** 5.30***

2002 2003 2004 2005 2006 2007 2008 2009

Significance at the 1% (***), 5% (**), and 10% (**) levels.

Table 9: F-Statistics, Unbranded Rack to Retail Prices (By Year)

more or less asymmetric pass-through. These may include differences in the retail ownership structure (e.g., a larger percentage of lessee-dealer owned stations versus independents) similar to the study by Lewis (2009) and retail concentration similar to the

study by Deltas (2008). In addition, the results in this paper indicate that, at least

in some cities, pass-through asymmetry varies over time. Supply-side shocks caused by

hurricanes, pipeline disruptions, and refinery maintenance or outages, which only affect

certain geographic areas and vary from year to year, may provide an explanation.

31
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35
A Appendix

!

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!!!

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!

!!

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!

!

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!

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!

!

!

!

!

"

Belle

DECATUR

Cahokia

Hartford

St. Louis

St. Peters Wood River Refinery

Jefferson City

CAPE GIRARDEAU

" Refinery

! Refined Products Terminal

St. Louis MSA

Illinois

Missouri

St. Louis MSA

Illinois

Missouri

Figure A.1: St. Louis Retail Market Areas.

36
Parameter Estimate Standard Error

Constant -0.087*** 0.011

+ (Rack(t) - Rack(t-1)) 0.274*** 0.004

+ (Rack(t-1) - Rack(t-2)) 0.101*** 0.004

+ (Rack(t-2) - Rack(t-3)) 0.059*** 0.004

+ (Rack(t-3) - Rack(t-4)) 0.036*** 0.004

+ (Rack(t-4) - Rack(t-5)) 0.052*** 0.004

+ (Rack(t-5) - Rack(t-6)) 0.044*** 0.004

- (Rack(t) - Rack(t-1)) 0.068*** 0.004

- (Rack(t-1) - Rack(t-2)) 0.085*** 0.004

- (Rack(t-2) - Rack(t-3)) 0.056*** 0.004

- (Rack(t-3) - Rack(t-4)) 0.075*** 0.004

+ (Retail(t-1) - Retail(t-2)) 0.335*** 0.005

+ (Retail(t-2) - Retail(t-3)) -0.244*** 0.005

- (Retail(t-1) - Retail(t-2)) 0.328*** 0.012

- (Retail(t-2) - Retail(t-3)) 0.101*** 0.013

- (Retail(t-3) - Retail(t-4)) -0.025** 0.012

- (Retail(t-4) - Retail(t-5)) 0.011 0.012

- (Retail(t-5) - Retail(t-6)) 0.132*** 0.011

+ EC Term -0.021*** 0.001

- EC Term -0.059*** 0.002

N

R2

Durbin-Watson Statistic

54,530

2.020

0.45

Dependent Variable: Retail(t) - Retail(t-1). City-level fixed effects included 

in the first-stage regression. ***, **, * significant at the 1%, 5% and 10% 

levels respectively.

Table A.1: Regression Results: Branded Rack to Retail Prices, All Cities Included

37
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

WTI to Gasoline Spot, National

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure A.2: Impulse Response Function: Crude Oil to Gasoline Spot Prices, All Cities

Included

38
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

WTI to Branded Rack, National

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure A.3: Impulse Response Function: Crude Oil to Rack Prices, All Cities Included

39
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

WTI to Retail, National

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure A.4: Impulse Response Function: Crude Oil to Retail Prices, All Cities Included

40
0 2 4 6 8 10 12 14 16 18 20

0

5

10

15

Days Since Upstream Price Shock

Change in Downstream Price (Cents/Gallon)

Impulse Response:

Spot to Branded Rack, National

10 Cent/Gallon Upstream Shock

Positive Shock

+95 CI

−95 CI

Negative Shock

+95 CI

−95 CI

Figure A.5: Impulse Response Function: Gasoline Spot to Rack, All Cities Included

41
2002 2005 2007

0

5

10

15

Date

Asymmetry (CPG)

Louisville IN

2002 2005 2007

0

5

10

15

Date

Asymmetry (CPG)

Cleveland

2002 2005 2007

0

5

10

15

Date

Asymmetry (CPG)

Washington DC

2002 2005 2007

0

5

10

15

Date

Asymmetry (CPG)

Minneapolis St Paul WI

Branded

Unbranded

Figure A.6: Time Analysis: Pass-Through Asymmetry over Time and by City

42