WORKING 

 PAPERS

Retail Gasoline Pricing: 

What Do We Know?

Daniel Hosken

Robert McMillan

Christopher Taylor

WORKING PAPER NO. 290

Original Release: May 2007

Revised: February 2008

___________________________________________________________________________

FTC Bureau of Economics working papers are preliminary materials circulated to stimulate discussion

and critical comment. The analyses and conclusions set forth are those of the authors and do not

necessarily reflect the views of other members of the Bureau of Economics, other Commission staff, or

the Commission itself. Upon request, single copies of the paper will be provided. References in

publications to FTC Bureau of Economics working papers by FTC economists (other than

acknowledgment by a writer that he has access to such unpublished materials) should be cleared with the

author to protect the tentative character of these papers.

______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
Retail Gasoline Pricing: What Do We Know? 

Daniel S. Hosken 

Robert S. McMillan 

Christopher T. Taylor1

Federal Trade Commission 

Revised: February 2008 

Abstract 

We use a data set consisting of a three year panel of prices from a sample of gasoline 

stations located in suburban Washington D.C. and a corresponding census of the region’s 

stations to develop three new empirical findings about retail gasoline pricing. First, while 

average retail margins vary substantially over time (by more than 50% over the three 

years we analyze), the shape of the margin distribution remains relatively constant. 

Second, there is substantial heterogeneity in pricing behavior: stations charging very low 

or very high prices are more likely to maintain their pricing position than stations 

charging prices near the mean. Third, retail gasoline pricing is dynamic. Despite the 

heterogeneity in station pricing behavior, stations frequently change their relative pricing 

position in this distribution, sometimes dramatically. We then relate these three findings 

to relevant theories of retail pricing. While many models of retail pricing are consistent 

with some of our findings, we find that all have serious shortcomings. 

JEL Codes: D4, L44, L81 

Key Words: Retailing, Petroleum Industry, Pricing, Gasoline 

 

1

 Corresponding author, Christopher Taylor, Bureau of Economics, Federal Trade 

Commission, 600 Pennsylvania Ave, NW, Washington, DC 20580, ctaylor@ftc.gov, 202-

326-2997. Views and opinions expressed in this paper are solely those of the authors and 

should not be interpreted as reflecting the views of the Federal Trade Commission, any of its 

individual Commissioners, or other members of the staff. Comments by Emek Basker, 

Matthew Lewis, Michael Noel, David Meyer, David Reiffen and Steven Tenn and excellent 

research assistance by Van Brantner and Elisabeth Murphy are appreciated. 
2

1.0 Introduction 

The recent increases in the price of gasoline have focused attention on all levels of 

the gasoline supply chain, from refining to retail. Following Hurricane Katrina retail prices 

jumped more than 50 cents per gallon over several days in some cities, leading to claims of 

‘gouging’. In response to these price spikes the U.S. Congress considered legislation 

providing civil and criminal sanctions for price gouging.1 In contrast, states have expressed 

concern about new retail formats (primarily supermarkets and mass merchandisers) selling 

gasoline at too low a price. In response to these concerns, some states have modified or 

increased enforcement of “sales below cost” or minimum markups laws.2 

The increased concern about gasoline pricing has led to increased interest in how 

retail gasoline prices are determined and how they change. Previously, large panel data sets 

of station specific gasoline prices have generally not been available. Recently, credit card (i.e., 

“fleet card”) transaction data has enabled researchers to examine the pricing behavior of a 

large number of gasoline stations over an extended period of time. 

 We use a three year panel data set of weekly gasoline prices based on fleet card 

transactions from 272 gasoline stations located in the Northern Virginia suburbs of 

Washington, DC, along with a census of the stations in the area (consisting of station 

locations and a wealth of station characteristics), to establish a number of new empirical 

findings about retail gasoline pricing and relate these findings to the existing theoretical 

literature on pricing behavior. Our analysis suggests deficiencies in existing theories in 

explaining retail gasoline pricing. 

 Our first finding is that the retail markup (defined as retail price less a measure of 

wholesale price and taxes) for gasoline shows sizeable changes over time and these changes 

are persistent. In other words, there are sizeable regime changes in average margins. For 

 

1

 Many states have gouging statutes. Following Hurricane Katrina more than 100 gasoline 

stations were investigated by states for gouging. See: Federal Trade Commission (2006).

2

 At least six states (Alabama, Kansas, New York, Michigan, Virginia, and Wisconsin) have 

considered legislation that would have introduced or modified minimum markup or sales 

below costs laws on gasoline. See FTC staff letter to The Honorable Gene DeRossett, 

Michigan House of Representatives, June 2004. 

http://www.ftc.gov/os/2004/06/040618staffcommentsmichiganpetrol.pdf
3

instance, in our sample, the weekly median margin is more than 17 cents per gallon for 26 

consecutive weeks (the mean of the median is 19.4 cents) in 1997 and 1998 before falling to 

less than 14 cents a week (the mean of the median is 10.7 cents) for 12 weeks. While the 

changing margins may be partially explained by asymmetric price adjustment, our empirical 

work suggests that equilibrium margins are changing as well. 

Second, we find that stations do not appear to use simple static pricing rules: stations 

do not charge a fixed mark-up over their wholesale costs, nor do they maintain their relative 

position in the pricing distribution over time. Instead, a particular gasoline station frequently 

changes its relative position in the pricing distribution, sometimes dramatically. From one 

week to the next, stations are more likely than not to change their relative position measured 

in either dollars (above or below the regional mean) or rank (price relative to closest 

stations). 3 There is, however, heterogeneity in station’s pricing decisions. Stations that charge 

very high or very low prices in one period are much more likely to charge high or low prices 

in subsequent periods. Interestingly, there appears to be an asymmetry in this behavior. 

Stations charging low prices appear to remain low priced stations for much longer periods 

than high priced stations. Surprisingly, while some stations consistently charge relatively high 

or low prices, the only station characteristic that is a good predictor of this heterogeneity is a 

station’s brand affiliation. Other stations characteristics, e.g., offering repair services or full 

service gasoline, and measures of localized competition are not consistently associated with a 

station’s retail mark-up. 

 Third, while there is heterogeneity in gasoline station pricing, with some stations 

charging, on average, high or low prices, a subset of gasoline stations change their average 

pricing strategy over time. Roughly 30% of stations significantly change their “typical price” 

(defined as a station’s mean price in a year relative to the mean price in Northern Virginia in 

that year) from one year to the next. Between 1997 and 1998 nearly 25% of gasoline stations 

changed their relative position in the pricing distribution by more than 20 percentile points, 

e.g., moving from the 70th percentile to the 50th percentile. The observed changes in pricing 

strategy are economically important. During our sample period, the mean station earned a 

margin of roughly 14 cents a gallon. Between 1997 and 1998, 33% of stations changed their 

relative margin by roughly 4 cents. This corresponds to a change in retail mark-up roughly 

 

3

 Lach (2002) finds very similar results in a sample of retail prices of consumer goods in 

Israel; i.e., the relative position of a retailer in the pricing distribution changes frequently. 
4

28% of the region’s average markup. A substantial number of gasoline stations make large 

changes in their pricing decisions over relatively short time periods. 

 We then relate our findings to five types of retail pricing models that appear relevant 

to explaining retail gasoline pricing. The first two types of models consist of static models. 

The pure strategy models (e.g., Thomadsen (2005)) predict that in each period retailers will 

charge the single-period profit-maximizing prices which vary with localized demand, 

competition, and marginal costs. An important implication of these models is they predict 

no inter-temporal price variation when costs and market structure remain constant. A 

second type of static model allows for mixed strategies in prices (e.g., Varian (1980)) that 

generate equilibria in which prices and margins vary even when costs and market structure 

remain constant. We then describe three types of dynamic models and formulate 

competition as a repeated (history-dependent) game and are thus also able to generate 

equilibriums in which prices and margins vary even when costs and market structure remain 

constant. There are three types of dynamic models: models of collusive behavior (e.g., Green 

and Porter (1984) and Haltiwanger and Harrington(1991)), models with history-dependent 

demand curves that lead to asymmetric price adjustment (e.g., Lewis (2005a)), and models of 

Edgeworth cycles (e.g., Maskin and Tirole (1988)). 

 While each of these models is consistent with some elements of the retail gasoline 

pricing we observe, none fit all the stylized facts. For example, while there is heterogeneity 

in gasoline station pricing (consistent with a model predicting constant margins), stations 

frequently change their margins (both absolutely and relatively). Static models predicting 

mixed strategies in prices fail to predict the persistence in pricing we observe. Our findings 

clearly show that a station’s pricing is dynamic: pricing in week t depends on pricing week t1. The existing dynamic models also do not comport well with our findings. While margins 

change dramatically during our sample period, there is no evidence of price wars. The shape 

of the retail margin distribution stays constant. Similarly, models of asymmetric price 

adjustment or Edgeworth cycles are also not supported by our data. 

 The remainder of paper is organized as follows. The next section provides a brief 

review of the empirical gasoline pricing literature, a summary of relevant institutional detail 

about gasoline retailing and describes our data. Section three presents our empirical findings. 

Section four discusses the various models of pricing behavior most likely to be applicable to 
5

retail gasoline. Section five relates these theoretical models to our empirical findings. Section 

six concludes and presents possible avenues for further work. 

2.0 Literature Review, Background, and Data 

Constrained by available data, researchers have historically examined either intertemporal or inter-station price variation. The research on inter-temporal variation, often 

referred to as the “rockets and feathers” literature, uses pricing data at various levels of the 

industry (i.e., spot, rack and retail) usually aggregated over large geographic areas to examine 

the price response of gasoline at one level, e.g. retail, to a change in price at another level, 

e.g. wholesale. Some papers in this literature find that retail prices increase more quickly 

following increases to wholesale prices than decreases, (see, e.g., Borenstein et al (1997)), 

while others (e.g. Galeotti et al. (2003)) find the opposite result. The results of this literature 

are mixed and seem to depend on the time aggregation of the data (daily, weekly, or 

monthly), the level of the industry examined (refining, distribution, or retail), and the 

estimation technique. Although we find some statistical evidence of asymmetric adjustment, 

we find that this modeling approach leaves important features of the data unexplained. 

The research on inter-station price variation uses station-level data either as a singleperiod cross-sectional or a short panel.4

 These papers have found that much of the interstation variation retail price can be explained by brand affiliation, some measures of localized 

competition (typically a measure of localized station density and/or distance to the closest 

rival), and a handful of station attributes (e.g., if the station also performs repairs, has a 

convenience store, or offers full service gasoline). Our results suggest that these findings may 

not be robust across different time periods or geographic locales. 

Our paper belongs to a relatively nascent (but rapidly growing) group of papers 

which lies at the convergence of these two branches of the empirical gasoline pricing 

literature and uses relatively long panels of weekly (or daily) station-level pricing data to 

examine the dynamics of station-level pricing behavior. Eckert and West (2003, 2004a, 

2004b) and Noel (2005, 2007a, 2007b) analyze station-level dynamics, and find evidence of 

 

4

 Examples of papers examining retail gasoline pricing in a cross section or short panel see, 

Slade (1992), Shepard (1990, 1991, 1993), Barron et al. (2000, 2004), and Hastings (2004). 
6

Edgeworth cycles in station-level retail pricing. Lewis (2007) also finds evidence of 

Edgeworth cycles using a panel of aggregated (to the city) retail gasoline pricing. Lewis 

(2005a) verifies that the “rockets and feathers” pattern is present in station-level data in 

Southern California. Lewis (2005b) is the study most similar to ours. It examines retail price 

dispersion using a sample of station-level pricing data from southern California. In contrast 

to our paper, however, Lewis (2005b) focuses directly on relating price dispersion to models 

of consumer search while we focus on models of retailer pricing. 

2.1 Institutional Detail 

Gasoline stations are retailers. They receive gasoline from a distributor (sometimes 

vertically integrated) and resell it to consumers. Like other retailers, gasoline stations 

compete on prices, quality (location, cleanliness, speed of pumps), and bundles of services 

(convenience store, repair services). There are, however, a number of important 

characteristics of gasoline retailing that differentiate it from other types of retailing. First, the 

issue of consumers purchasing “bundles” of products is less important to gas stations than 

to other types of retailers, such as food or clothing. Virtually every consumer entering a gas 

station purchases gasoline, while only a subset will purchase other goods (beer, cigarettes, or 

repair services).5 Because a low price on gasoline is attractive to every potential consumer, the 

price of gasoline is more strategic than the pricing of other products sold by the gas station.6

Second, relative to many other products, gasoline is fairly homogeneous. These factors 

suggest consumer search for gasoline is easier than many other retail goods. Third, neither 

the station nor the consumer can hold meaningful inventories of the product. A tanker truck 

 

5

 For example, convenience stores, which represent the largest retail channel of gasoline sales 

(approximately 75%) report that gasoline sales represent roughly 69.5% of convenience store 

revenues in 2003. National Association of Convenience Stores web page, visited 1/31/07. 

6

 Lal and Matutes (1994) develop a model of retailers selling bundles of products with low 

prices on a subset of products to attract consumers. Hosken and Reiffen (2004) extend Lal 

and Matutes model showing that the low priced items are in most consumers’ bundles. 
7

holds 7,500 to 9,000 gallons of gasoline. A typically station sells more than 90,000 gallons a 

month which means over 10 deliveries a month.7 

 One advantage of studying gasoline retailing is that some measures of marginal cost, 

wholesale or “rack” prices for branded and unbranded gasoline, are observable to 

researchers.8 The gas stations that purchase branded gas at the rack are owned and operated 

by individuals who, in essence, operate franchises. Other firms (sometimes the same firms 

selling branded gasoline, sometimes firms acting purely as distributors) will post unbranded 

prices for gasoline that will be sold at stations unaffiliated with a brand. 

 There are, however, two other channels of retail gasoline distribution for which 

marginal cost are unobserved. Stations that are owned and operated by a refiner (i.e., 

completely vertically integrated) “pay” an unobserved transfer price for gasoline. There are 

also a significant number of “lessee dealer” stations in Northern Virginia. These stations are 

owned by the refiner but operated by separate entities.9

 These stations pay an unobserved 

wholesale price for gasoline that is determined by the refiner. In addition, the wholesale price 

paid by different lessee dealers operating in the same metropolitan area may vary.10 Thus, at 

any time, there may be a number of different marginal costs across stations within the same 

region. We follow the literature in viewing the posted rack prices as the opportunity cost of 

gasoline, since refiners and distributors choose to sell at that price. 

We examine stations located in the Northern Virginia suburbs of Washington DC. 

This region likely contains all of the important retail gasoline competitors in Northern 

Virginia. While Northern Virginia is in the same metropolitan area as both Washington DC 

and Suburban Maryland, commuting patterns and the relative prices of gasoline in these 

 

7 For a discussion of the average level of gasoline sales by station and tanker delivery see, 

Federal Trade Commission, 2004, pp. 218 and 241.

8

 The wholesale distribution point of gasoline is refereed to as the “rack”, the point where 

trucks obtain the gasoline for the retail stations. The terms rack and terminal are used 

synonymously. 

9

 In Virginia refiners can not build new company owned and operated gasoline stations but 

the 1979 divorcement law allowed refiners to continue to operate the stations they owned. 

10 See Meyer and Fischer (2004) for an extensive description of lessee dealer pricing and zone 

pricing. 
8

areas likely negates the impact of pricing in Maryland and DC on stations in Virginia. The 

regions in Virginia beyond our sample area likely do not contain many important 

competitors because there are very few stations in these regions with very little population. 

2.2 Data 

Our data come from three sources. We have a three year panel of average weekly 

retail prices for 272 stations in Northern Virginia. These data come from the Oil Price 

Information Service (“OPIS”), and are generated from fleet card11 transaction data. We also 

have data from OPIS on the wholesale prices of both branded and unbranded gasoline at the 

closest rack to our stations, Fairfax, Virginia. 

We have a census of all of the roughly 600 stations in Northern Virginia for 1997, 

1998, and 1999 from New Image Marketing. The census consists of annual surveys of 

stations’ addresses, attributes (e.g., whether the station has service bays, a convenience store, 

and the number of pumps), and a description of the station’s vertical relationship with its 

supplier. While we do not observe the pricing of all stations, we are able to construct 

variables measuring the competitive environment each of the stations in our sample faces. 

Specifically, we calculate measures of station density (the number of stations located within 

different mileage bands of our sampled station) and the distance to the closest station. 

 Finally, we obtained information on neighborhood characteristics (measured at the 

zip-code level) from the U.S. Census. These variables, which include median household 

income, population, population density, and commuting time, are from the 2000 census and 

correspond to conditions in 1999. 

 

11 Fleet cards are often used by firms whose employees drive a lot for business purposes, e.g., 

salesman or insurance claims adjusters. Fleet cards are used to monitor what items 

employees charge to the firm. A station reports a price in a given week if one the fleet cards 

that OPIS observes was used at that station during the week. Most, but not all, stations in 

the sample are observed every week. Hence, the panel is unbalanced. We have dropped 

stations from the analysis that are observed very infrequently: a station is excluded if it is not 

observed for at least 10 weeks in a calendar year. 
9

We examine three different measures of price. The retail price of gasoline is the price 

recorded at the pump (including taxes) for the most commonly sold variation of gasoline (87 

octane). We use the average “branded rack” as our measure of wholesale price. This is 

defined as the average price of all of the “branded” gasoline’s offered at the rack in a week. 

We have chosen the branded rack as our benchmark measure of wholesale price because the 

majority of stations sell a branded product. Our results, however, are robust to the choice of 

rack price.12 Finally, we define a station’s mark-up (margin) to be the retail price less the 

branded rack price and taxes. Thus, a station’s margin corresponds to its incremental profit. 

Descriptive statistics for the data on OPIS sample of stations used in the pricing analysis as 

well as the descriptive statistics on the population of stations in Northern Virginia are 

presented in Table 1. On average there are almost 8.6 stations within 1.5 miles of the stations 

in both the OPIS sample the population. The other variables, station attributes and 

demographics, have similar means and standard deviations in both the OPIS sample and the 

population with two exceptions. First, the OPIS sample has a higher fraction of stations that 

sell only self service gasoline (84% vs. 74%). Second, the distribution of station 

management also differs between the two samples, e.g., 58% of stations in the OPIS sample 

are lessee dealers vs. 46% of stations in Northern Virginia. 

The break down of station affiliations in our sample is presented in Table 2. The 

OPIS data set omits some major brands (specifically, Exxon and Amoco) as well as some 

minor brands and independents.13 Due to the lack of Exxon and Amoco stations in our 

price data, there is proportional over sampling of the remaining brands such as Shell and 

Texaco. 

 

12 Branded rack prices are the wholesale prices for the refiner providing the gasoline, (such as 

Texaco, Exxon, or Mobil). Unbranded rack prices are the prices charged by a distributor 

(often, but not always a refiner) for gasoline that will ultimately be sold to consumers under 

the name of an independent gasoline retailer. During our sample the branded gasoline price 

is a few cents per gallon higher than unbranded gasoline price. 

13 Some brands (ordinarily) disallow OPIS from reporting their fleet card purchases, and 

some brands do not accept fleet cards (e.g., ARCO). The decision to accept a fleet card is not 

made by each station but by brand. 
10

3.0 Results

 In this section we describe empirical findings about retail gasoline pricing. First, we 

find that the distribution of retail margins within a region shifts dramatically over time. 

While our data is consistent with a pattern of asymmetric price adjustment (price increases 

being passed through more quickly than price decreases), our findings suggest this 

explanation is incomplete. Second, we find that stations do not appear to follow simple 

pricing rules: both their margins and their prices relative to other stations fluctuate over time. 

While there is systematic heterogeneity in some stations’ pricing, e.g., stations consistently 

charging relatively high or low prices, station characteristics (other than brand affiliation) and 

measures of localized competition are not good predictors of this heterogeneity. Third, we 

find that the systematic component of a station’s pricing decision (the station’s average 

relative price) changes, often substantially, from year to year. 

3.1 Finding 1: Retail Margins Vary Substantially Over Time 

 Retail margins vary dramatically over time. Figure 1 shows the branded rack price of 

gasoline and the plot of the 25th, 50th, and 75th percentiles of the distribution of gasoline 

stations’ retail margins (retail price less wholesale prices and taxes) by week from 1997 

through 1999. During this time period the average retail margin was 14.4 cents per gallon, as 

high as 20.9 cents per gallon (in 1999), and as low as 5.7 cents (also in 1999). The figure also 

shows that the entire pricing distribution tends to shift over time; i.e., the spread between 

the 25th and 75th percentile is fairly stable, roughly 4 cents per gallon in 1997, and 5 cents in 

1998 and 1999. 

 Although the margins in our dataset vary over time, they also exhibit a high degree of 

persistence. For example, the median margin is more than 17 cents per gallon for 26 

consecutive weeks (averaging 19.4 cents) in 1997 and 1998 before falling to less than 14 

cents per gallon (averaging 10.7 cents) for 12 weeks. Obviously, the change in retail profits 

associated with this change in margin is sizeable. While we do not observe output, it is 
11

reasonable to assume that changes in quantity are relatively small (gasoline demand is very 

inelastic), while the retail margin fell by 50%.14

3.2 Finding 2: Stations Do Not Follow Simple Pricing Rules 

 

 The wholesale price of gasoline is volatile. At the beginning of our sample the 

wholesale price of gasoline is approximately 75 cents per gallon. In early 1999 it fell to 35 

cents before rising back to 75 cents per gallon in late 1999. The primary source of retail 

price variation in our data results from a gasoline station changing its price in response to a 

change in the wholesale price, or when the station changes its price relative to other stations. 

This can be seen most clearly by a simple decomposition of price; that is, decomposing 

overall price variation into between station and within station price variation. Figure 2 plots 

the percentage of within price variation for each year in our data set, and separately by 

station ownership type for each year. In 1997 and 1998 roughly 2/3 of retail price variation 

is generated by a station changing its prices over time, 1/3 of price variation is the result of 

differences in a station’s mean pricing. In 1999 (when wholesale gasoline prices more than 

doubled) within price variation rose to 90%. There are some slight differences in the 

proportion of price variation by ownership type, however, the changes do not appear to be 

systematic. Company owned and operated stations, for example, have disproportionately 

low within price variation in 1997, but not in 1998 or 1999. A station’s ownership type does 

not appear to be important source of either the within or between price variation in our data. 

Because changes in wholesale costs are such an important component of retail price 

variation and are not the focus of our study, we define retail price variation as the deviations 

 

14 Our finding of dramatic changes in retail margins is potentially consistent with recent 

empirical research on asymmetric price adjustment in retail gasoline markets sometimes 

referred to as the “rockets and feathers” literature (see, e.g., Borenstein et al. (1997) and 

Lewis (2005a)). These studies find that increases in wholesale gasoline prices are passed 

through more quickly than wholesale price decreases. While there is some statistical evidence 

of asymmetric pass through of wholesale costs in our data, the coefficients of estimated 

asymmetric price adjustment model were not economically plausible and differed 

substantially from those found in the existing literature (see section 5.4). 
12

about the region’s mean price at a point in time. We analyze retail price dispersion by 

examining the residuals from the following regression: 

(1) ( ) it t it it

t

p = + ∑ γ Week Indicator e

where pi,t is station i’s gasoline price in week t, and the t γ are the coefficients corresponding 

to weekly indicators. We estimate equation (1) using data for each station and time period. 

The frequency distribution of the estimated error terms (eit) is presented in Figure 3. Most 

prices are very close to the mean: 56% and 71% of prices are within 2.5 cents and 3.5 cents 

of the mean, respectively. The tails of the distribution are quite thick. Roughly 3.5% of prices 

are more than 10 cents from the mean. To illustrate further, we plot a normal frequency 

distribution with the same mean and standard deviation as the observed residuals (mean 

zero, standard deviation of 3.99 cents). If the residuals were normal, we would expect to see 

47% and 62% of prices within 2.5 and 3.5 cents of the mean, and 1.2% of prices more than 

10 cents from the mean. We can easily reject the null that the residuals have a normal 

distribution.15 

 The general pattern seen for the pooled data also holds when looking at the residuals 

separately by year.16 While the shape of the distribution differs somewhat across years (prices 

appear less disperse in 1997 than either 1998 or 1999), most gasoline prices are very close to 

the mean: 75%, 69% and 66% are within 3.5 cents of the mean in 1997, 1998 and 1999. 

Further, the tails are thick: roughly 2% of prices are more than ten cents from the mean in 

1997 and 4% of prices are more than ten cents from the mean in 1998 and 1999.17 An 

implication of this result is that models estimated using maximum likelihood and an 

 

15 The kurtosis of the residual distribution is 6.07, the p-value for the test of normality is 

essentially zero. A normal random variable has a kurtosis of 3, variables with a kurtosis 

greater than 3 are said to be leptokurtic. 

16 See Appendix Figures 1-3. 

17 If the residuals were normally distributed, the expected proportion of prices within 3.5 

cents of the mean would be: 68%, 60% and 59% and the proportion of prices more than 10 

cents from the mean would be 0.5%, 1.6%, and 1.9% in 1997, 1998 and 1999. The residual 

distributions in 1997, 1998, and 1999 have kurtosis of 9.21, 5.45, and 4.55. In each year, we 

reject the null of normality of the residual distribution with a p-value of zero. 
13

assumption that errors are normally distributed may yield inefficient parameter estimates, 

see, e.g., White (1982). 

 While retail gasoline prices are tightly distributed about the mean, some stations 

charge prices very different than the mean. Further, average retail markups change 

substantially during the sample period (by 50%), and these different regimes are persistent. 

Despite significant changes in retail margins and gasoline prices over time, the shape of the 

distribution of prices about the median margin does not change very much – during our 

sample period the inter-quartile range is typically between 3 and 6 cents. This leads to a 

question: is the gasoline pricing distribution stable over time? Do individual stations pick a 

price relative to their rivals and maintain that price, or do stations change their relative 

position in the pricing distribution? 

 We find that gasoline stations change their relative prices frequently. While some 

stations charge systematically higher or lower prices, relative prices change frequently. 

Finally, in contrast to many previous papers, station characteristics, other than brand 

affiliation, do not explain much of a station’s average relative pricing. 

We analyze a firm’s price changes by defining the firm’s relative price in week t to be 

the residual from equation (1); i.e., the difference between station i’s price in week t and the 

mean price of all stations in our sample in week t. We round the residual to the nearest cent 

and construct a Markov transition matrix where the elements of the matrix show the 

probability of being y cents above (below) the mean in period t conditional on being x cents 

above (below) the mean in period t-1. The matrix is presented in Appendix Table 1, 

however, a more intuitive understanding of the matrix can be seen from graphing the 

conditional probability distributions in Figure 4.18 For example, Figure 4.J plots the 

probability distribution of a gasoline station’s price in period t conditional on the station 

charging the region’s mean price in period t-1; i.e., the residual from equation (1) in period t-

 

18 To facilitate presentation we have omitted large deviations from the region’s mean price in 

constructing Figure 4 and appendix Table 1. We plot the Markov transition matrices if the 

previous period’s relative price (the residual from eq. (1)) is between -9 and 9. This limits the 

number of frequency distributions presented in Figure 4 to 19. Similarly, we also truncated 

the distribution of the current period’s relative price to be between -15 and 15. Together, 

these restrictions omit roughly 10% of the pricing observations from the figure. 
14

1 rounds to zero. Figure 4.J shows that the probability that a station will continue to charge 

the mean price in the region in period t is 0.47, and the probability the station will be 

charging a price within a penny of the region’s mean in period t is 0.84. 

 There are two key observations from Figure 4. First, there is persistence in gasoline 

stations’ relative prices. The modal choice of a station is to maintain its relative pricing from 

week to week; i.e., if a station is 4 cents below the mean in period t-1, it is most likely to be 4 

cents below the mean in period t. Second, despite this persistence, for all of the conditional 

probability distributions, the mode is less than 50%. Thus, more than 50% of the time a 

station’s relative price will change by at least one cent each week. The shape of the 

probability distributions of stations charging low prices in period t looks very different than 

stations charging high prices in period t. Stations charging relatively low prices have more 

mass at or near the mode than those stations charging relatively high prices (compare 

Figures 4.A-4.D to 4.O-4.S). This suggests that stations charging high prices converge to the 

mean more quickly than stations charging low prices. The transition matrices show that 

while gas stations periodically charge high prices, they do not maintain abnormally high 

prices for very long. Low prices, however, appear to be more persistent. 

 To examine the importance of this heterogeneity in characterizing retail gasoline 

pricing, we control for both time effects and time invariant-station effects in equation (2) 

below, 

(2) ( ) ( ) it i it t it it

i t

p = ++ ∑ ∑ θ γ Station Indicator Week Indicator u

where the θ i are gasoline station specific fixed-effects; that is, θ i is station i’s mean relative 

price where 0 θ i = corresponds to the station whose average relative price is the mean price. 

Equation (2) models stations pursuing a static pricing strategy with the markup a function of 

(time-invariant) observed and unobserved attributes (as measured by the θ i ’s). The 

interpretation of the residuals from equation (2) is very different than equation (1). For 

example, uit is now the deviation from station i’s pricing in period t after controlling for 

station i’s time-invariant effects. If we observe persistence in a station’s residual, uit , then it 

means that the station is systematically charging higher or lower prices than its typical relative 

price. Not surprisingly, equation (2) explains more of the variation in retail pricing than (1). 

The R-squared increases from 0.88 to 0.95 and we are able to explain most of the large 

deviations in stations’ prices. Figure 5 plots the residuals from regression 2 and shows that 
15

only 0.9% of residuals are more than 10 cents from the mean (compared to 3.4% from the 

regression in equation (1)). 

 Figure 6, constructed analogously to Figure 4, presents the Markov transition matrix 

with the residuals from equation (2).19 The interpretation of Figure 6, however, differs from 

Figure 4, because it shows the probabilities of transitions between consecutive weeks where 

prices are measured relative to a specific station’s average relative price (rather than relative to 

the average price in Northern Virginia). For example, in Figure 6.O, we see a station 

charging a price 5 cents more than its mean price in week t-1 is predicted to be charging a 

price 5 cents more than its mean in week t with probability 0.31. There are two notable 

differences between Figures 4 and 6. First, controlling for a station’s mean relative pricing 

(θ i ) explains a great deal of the persistence in pricing. This can most clearly be seen by the 

decrease in the modal prices in moving from Figure 4 to Figure 6 when a station is not 

charging a price close to its mean price; that is, excluding Figures 6.I, 6.J, and 6.K. While the 

modal price charged in week t is the price charged in t-1 in both figures, this mode is lower in 

Figure 6 than Figure 4. Second, there is quicker convergence to the mean in Figure 6. A 

station charging a price above its own mean is predicted to return to its own mean price more 

quickly than a station charging a higher price than the region’s mean is predicted to return to 

the region’s mean price. It is interesting to note, however, that even controlling for a station’s 

average pricing, the predicted pricing distribution at time t depends on t-1; that is, pricing 

decisions are inherently dynamic. 

 While this analysis is informative, it has compared prices over a large region and so 

potentially misses some important aspects of localized competition. In densely populated 

Northern Virginia, it is unlikely that a gas station considers the prices of stations 10 miles 

away when setting its prices. It is easy to imagine that stations develop simple pricing rules, 

such as maintaining the second lowest price among the ten closest stations, or being 3 cents 

lower than a store with a prime location. 

 

19 Appendix Table 2 contains the matrix corresponding to Figure 6. As in constructing 

Figure 4, we have omitted observations if the previous period’s relative price is between -9 

and 9, and if the current period’s relative price to be between -15 and 15. Together, these 

restrictions omit roughly 8% of the pricing observations from Figure 6. 
16

We examine localized pricing by determining each station’s price position relative to 

its 9 closest rivals each week (where a rank of 1 corresponds to the lowest price and 10 to 

the highest).20 To illustrate a station’s rank over time, we plotted the weekly price ranks of a 

Crown station and a Mobil station in our data set (see Figure 7). The relative pricing patterns 

for the two stations are noticeably different. The Crown station charges very low relative 

prices each period, and is most often the lowest. This pattern is not unique to this Crown 

station: all Crown stations in our sample persistently charge relatively low prices. In 

contrast, the Mobil station changes its relative position in the pricing distribution frequently, 

sometimes being the highest and sometimes the lowest priced station. While this particular 

Mobil station is an outlier in changing its relative price very frequently, similar patterns are 

seen for many other stations in our data. 

Because it is not feasible to report the relative rank series for every station, we create 

an analogous aggregate measure. We construct a Markov transition matrix and graphically 

present it in Figure 8. This figure has the same interpretation as Figures 4 and 6. Figure 8 

shows a very similar pattern to the week to week price changes of the relative prices from all 

of Northern Virginia. The modal strategy for a station is to maintain its relative pricing 

position from week to week. Stations charging prices close to the median of the distribution 

(a rank of 4, 5, 6, or 7) are much more likely to change relative position from week to week 

than stations at the high and low end of the distribution. The same pattern emerges when 

viewing stations prices relative to a narrower group of stations consisting of its four closest 

rivals (see Figure 9). Stations charging low or high prices in one week (rank 1 or 5) are more 

likely to charge low/high prices in the subsequent week than stations prices near the median 

(ranks 2, 3, and 4). 

 

20 Our price data is a sample of stations. We analyze station prices relative to the 9 closest 

stations in our sample. This set of stations differs from the 9 closest in the population. While 

this distinction could be important, we think it is not. As is discussed below, the pattern in 

relative ranks is very similar to the pattern in relative prices seen in Figures 4 and 6. 
17

3.2.1 Estimating a Station’s Idiosyncratic Pricing Function 

Many prior studies which examine localized gasoline pricing have been limited to 

either cross-sectional or a short panel of data.21 These data limitations have forced 

researchers both to use observable characteristics rather than station fixed effects, and to 

assume that the relationship between stations’ prices and their measurable characteristics are 

relatively constant over time.22 The richness of our dataset allows us to evaluate the 

robustness of these assumptions. In general, we find that observable station characteristics 

(other than a station’s brand affiliation) are poor predictors of station-specific pricing. 

 We begin by estimating a specification including the key control variables from the 

literature. Specifically we estimate a station’s retail margin in each week (markup over the 

wholesale price of branded gas) as a function of station attributes,23 demographics 

corresponding to the station’s zip code,24 indicators for the brand of gasoline sold, localized 

competition, and the vertical relationship between the station and its gasoline supplier as in 

equation (3) below where i is the store index and t is the week index.25

(3) arg ( )

 ( ) ( )

 ( Re ) ( ) ( ) 

it k l it

l

m it n it

m n

o it p it q it it

o pq

M in Localized Competition Variables

Demographics Station Characteristics

Vertical lationship Brand Indicator Year

α γ

δ β

π θ λμ

= + +

+ +

+ ++

∑

∑ ∑

∑ ∑∑ 

 

21 Eckert and West (2004a, 2004b), Lewis (2005a, 2005b) and Noel (2007a) are exceptions. 

22 The goal of these studies is not to measure the returns to different station characteristics 

or brand. In most cases, the authors are trying to control for other factors that affect 

gasoline prices and include these characteristics as control variables. In some of the short 

panel studies, (such as, Hastings (2004)), authors use station level fixed-effects as controls. 

23 A subset of station characteristics were missing for 8 of the stations in our data set. For 

this reason, regression (3) was estimated using data for the 264 rather than 272 stations.

24 Because gasoline stations likely draw customers from a region larger than a census block, 

we use zip code level measures of the demographic variables. 

25 Because individual stations appear many times in the data set, we estimate clustered 

standard errors (at the station level). 
18

We construct two types of variables to measure localized competition similar to 

those used in the literature. The first set of variables measure the density of localized 

competition: the number of stations located with 1.5 miles of station i and the distance 

between station i and the next closest station.26 Presumably, other things equal, a greater 

density of localized competition should result in lower retail margins. The next set of 

variables measures the type of nearby competitors. Hastings (2004), for example, finds that a 

given gas station charges lower prices when facing an unbranded competitor, and higher 

prices when facing only branded competitors. In our sample, there are four station brands 

that charge systematically low gasoline prices: Coastal, Crown, RaceTrac, and Sheetz. Each 

of these stations can be viewed as unbranded in the sense defined by Hastings (2004).27 We 

define a variable that measures the proportion of the ten closest stations that are one of 

these four brands. We construct an analogous variable to measure which stations face 

disproportionately high priced competitors: the fraction of the ten closest competitors that 

are Exxon or Mobil stations (the two market leaders). If vertically integrated gasoline 

stations charge different retail prices than other stations, then a gas station competing with 

many vertically integrated gasoline stations may charge different prices than a firm 

competing with independent stations. To allow for this possibility, we construct two 

variables that measure the level of vertical integration of nearby stations. The fraction of the 

ten closest stations that are either 1) owned an operated by a refiner, or 2) are owned by a 

refiner but leased to an operator. 

The results from estimating this equation are shown in the first column of Table 3. 

Consistent with the literature, we find that brand effects are very important predictors of 

retail margins. Company owned and operated stations also earn higher margins, roughly 1.5 

cents. This finding does not, however, imply that vertically integration causes retailers to 

charge higher prices. Because of Virginia’s divorcement law, refiners can only own and 

operate stations that were in operation before 1979. In northern Virginia, older stations are, 

 

26 These measures of localized competition are identical to those used in Barron et al. (2004). 

27 While Crown stations were technically branded (owned and operated by a small refiner), 

Crown operated its stations like an unbranded retailer. That is, Crown did not engage in 

extensive advertising to develop a gasoline brand like the major U.S. gasoline refiners, e.g., 

Exxon, Mobil, or Shell. 
19

on average, located in more densely populated areas with higher land costs. Thus, this 

increased margin may result because older stations are located in more valuable locations. 

Interestingly, we find that although the station’s demographic environment (median 

household income, population, population density, and median commuting time) are 

important predictors of margins, none of the stations’ physical attributes (e.g., having a 

convenience store) appear to be important predictors. The estimated coefficients on the 

stations’ physical attributes are both statistically and economically (all less than a penny) 

insignificant. 

The remaining columns of Table 3 report the estimates when we allow the 

coefficients to vary across years. A few findings are worth noting. First, the estimated 

coefficients on the demographic variables change significantly across years. Whether this is 

the result of measurement error (these variables come from the 2000 census and correspond 

to conditions in 1999), or a change in the pricing function is unclear. Second, the estimated 

brand coefficients for those stations which make up a large share of our sample, Mobil, 

Crown, Shell and Texaco, vary from year to year. Third, two of the estimated localized 

competition variables are somewhat significant, however only in one year. In the 1997 

regression, an increase in the fraction of nearby low priced stations is predicted to lower 

retail margins, as is a decrease in the distance to the next closest station. However, the size 

of the economic effect in both cases is small. The maximum value of the low priced 

competition variable is .3, implying that retail margins drop by 1.2 cents relative to facing no

low priced competition. Similarly, decreasing the distance to the closest gas station by on 

standard deviation (.34 miles) is predicted to lower prices by about 0.33 cents. 

In sum, we do not find an important consistent relationship between a station’s 

margin and either station characteristics or localized competition. This finding is likely not an 

artifact of the specific functional form used to measure competition or station 

characteristics. Alternative measures of localized competition; e.g., including the number of 

stores within 1/2 mile, 1 mile, 3 miles, and interactions of these measures, are not consistent 

predictors of retail margins (results available on request). Similarly, we have examined many 
20

other station attributes (including measures of nearby traffic conditions) and do not find a 

relationship between these attributes and retail gasoline markups.28 

 As noted above, Crown stations followed a different pricing strategy during our 

sample period than other stations in Northern Virginia.29 In particular, Crown stations 

charge relatively low prices independent of the localized competitive environment. For this 

reason, we fully interact a Crown indicator variable with all of the other variables in the 

pricing equation – effectively dropping the Crown stations from the sample. The results for 

the non-Crown coefficients appear in Table 4. 

 The key difference we see in estimating the model for the non-Crown stations is the 

importance of one of the variables measuring the density of local competition is statistically 

significant in the pooled model and in the models estimated separately for 1997 and 1998. 

However, the estimated effect is still fairly small. Having the closest station one standard 

deviation closer (0.34 miles) is predicted to lower prices about 0.5 cents. While this finding 

causes our results to look more similar to the literature, it also suggests that the pricing 

function implied by equation (3) is not uniform across stations. 

3.3 Finding 3: Many Stations Change Their Pricing Strategy Over Time 

 The pricing pattern we see in Figure 6, after controlling for both time and station 

fixed-effects, suggests that stations change relative prices over time. To examine this we 

estimate a slightly modified version of equation (2) where we allow the station effects to vary 

by calendar year (q=1997, 1998, 1999): 

 

28While the change in retail gasoline markups over time could theoretically be the result of 

collusive behavior among gasoline wholesalers supplying Northern Virginia, recent evidence 

suggests this is not the explanation. Taylor and Hosken (2007) examined the wholesale (rack) 

price of gasoline at Fairfax, the supply point for Northern Virginia and found that the 

average wholesale price in Fairfax during this time period reflected the product price in the 

Gulf, the source of marginal supply, and the cost of transport. 

29 All but one of the Crown gasoline stations in our sample are owned and operated by the 

refiner. These stations are vertically integrated and the refiner controls retail pricing. 
21

,

(4) p = (Week Indicators ) (Station Indicators )(Year ) q

it t it i it it it

t iq

∑ ∑ γ θ + + w

If a station’s idiosyncratic relative pricing changes from year to year ( ) 1997 1998 1999 , θθθ iii ≠ ≠

we conclude the station is pursuing a different pricing strategy. We use two different 

approaches to measure a station’s pricing changes year to year. 

 First, we record the percentile corresponding to a station’s estimated fixed-effect in 

the store-effect distribution in year k; i.e., we rank all q θ i from smallest to largest and record 

the percentile corresponding to each q θ i . We then calculate the difference in a station’s 

percentile between each pair of years in our data set (1997 vs. 1998, 1998 vs. 1999, and 1997 

vs. 1999).30 These results are shown in the first section of Table 5. The table shows that 

small changes in a station’s relative pricing are fairly common. For example, between 1997 

and 1998 more than half of gasoline stations change their relative position in the pricing 

distribution by at least 10 percentile points. Further, some stations dramatically change their 

position in the pricing distribution, e.g., between 1997 and 1998 4% of gasoline stations 

estimated store-effects changed by more than 50 percentile points in the pricing distribution. 

 Second, we measure the absolute change (in cents) in the station effects from year to 

year. In Table 5, we see that many of the changes in station effects are statistically significant. 

In comparing stores observed in 1997 and 1998, 1998 and 1999, and 1997 and 1999, we find 

that 33%, 27%, and 45% (respectively) of changes in estimated store effects are statistically 

significant with a (conditional) mean change in price of between 3 and 4 cents per period. 

The observed changes in pricing strategy are economically important. For example, in our 

data, the mean margin is roughly 14 cents per gallon. 

4.0 Existing Models of Retail Pricing 

 Because of the richness of these data, the results described in Section III can shed 

light on the ability of various retail pricing models to explain behavior. In this regard, we 

 

30 In estimating equation 4 we require at least 10 observations per year. With this restriction 

we had 170, 163, and 193 comparisons between 1997 and 1998, 1997 and 1999, and 1998 

and 1999 respectively. 
22

suffer from an embarrassment of riches -- many pricing models appear relevant to retail 

gasoline. Because there are so many, we use this section to first relate these models and their 

empirical predictions to one another. The next section relates those predictions to our 

findings. 

We are aware of five different types of models of pricing behavior that may be 

applied to retail gasoline. The first two types of models assume that each retailer’s actions in 

each period are independent of prior play. The first set limits stations to play pure strategies. 

These models predict that in each period retailers will charge the single-period profitmaximizing prices which will vary with localized demand, competition, and marginal costs. 

An important implication is these models predict no inter-temporal price variation when 

costs and market structure remain constant. Manuszak (2002) and Thomadsen (2005) are 

typical examples of this modeling approach. Although his model’s complexity prohibits one 

from making definitive statements about its predictions for margins, in practice, Manuszak 

finds that his model generates roughly constant markups over time when demand follows a 

mixed logit.31

The second type of model allows for mixed strategies, and thus generates equilibria 

in which prices and margins vary even when costs and market structure remain constant. 

Varian (1980) provides an explanation of why a retailer would vary retail prices, independent 

of changes in wholesale prices that appears appropriate for gasoline retailing.32 In Varian’s 

 

31 See, for example, Manuszak’s (2002) Figure 4. 

32 There are models of retailing which generate retail price changes independent of costs, but 

the features that drive these price changes are not present in retail gasoline. Conlisk et al. 

(1984), Sobel (1984) and Pesendorfer (2002) examine how changes in retail prices can be 

used as a means of price discrimination. These models include purchases that can be shifted 

over time (consumers either wait to purchase or carrying inventory). Pashigian (1988) and 

Pashigian and Bowen (1991) develop models for goods with a “fashion” element where 

prices systematically decline over a fashion season independent of wholesale costs. Hoch et 

al. (1994) examines how every day low priced firms and high-low price firms can both exist 

in the same market at the same time. Hoch et al. examines retailers selling a bundle of goods 

to consumers (such as food retailers) where the retailers offer differential markups on 

products in the bundle. As discussed earlier, this modeling approach is less appropriate for 
23

model, consumers are heterogeneous in their willingness to search for low prices; some buy 

only at the first retailer they encounter, others compare prices and buy from the retailer 

offering the lowest price. Consequently, each retailer faces a tradeoff between charging a 

high price and selling only to consumers who do not search, versus charging a low price and 

potentially also selling to consumers who do search. Varian shows that the only symmetric 

equilibrium features mixed strategies, where all retailers choose their price from a continuous 

distribution with no mass points. In this equilibrium each retailer changes his price each 

period. Baye et al. (1992) show that asymmetric equilibria also exist when using Varian’s 

modeling approach. Specifically, a subset of retailers can always charge a high price (equal to 

a consumer’s willingness to pay) and only sell to customers who do not search, while the 

remainder of retailers play a mixed strategy identical to the strategy examined by Varian.33 

Other models formulate competition as a repeated (history-dependent) game and are 

thus generate equilibria in which prices and margins vary even when costs and market 

structure remain constant. These dynamic models can be grouped into three categories: 

models of collusive behavior, models with history-dependent demand curves that lead to 

asymmetric price adjustment, and models of Edgeworth cycles. 

 A number of papers use collusive equilibria with price wars to explain changes in 

margins over time. Green and Porter (1984) provide a model of collusive behavior that relies 

on imperfect monitoring to generate periodic price wars in equilibrium. Although they 

explicitly model competition in industries characterized by quantity competition, commonly 

known cost functions, and imperfect monitoring, their model can be extended to cover 

industries with price competition where the uncertainty is over the cost functions rather than 

the price. For example, Athey and Bagwell (2001) and Athey et al. (2004) model an infinitely 

repeated Bertrand game with publicly observed prices and private i.i.d. cost shocks, which 

closely matches many of the features of retail gasoline competition. Applying a semiparametric approach to examine stations’ pricing behavior directly, Slade (1987, 1992) finds 

 

gasoline stations which are more like single product retailers. 

33 Hong et al. (2002) examines a dynamic version of Varian’s model where the consumers 

who search can also store the good for future consumption. Because gasoline cannot 

effectively be stored for future consumption by consumers (in contrast to grocery products), 

this model is not relevant for retail gasoline pricing. 
24

evidence of a price war in Vancouver, Canada in 1983. She finds that stations’ pricing 

behavior – in particular, stations’ responses to their competitors’ prices – varies over time. 

Rotemberg and Saloner (1986) also offer a model of collusion that predicts 

fluctuating margins. In their model collusion breaks down during periods of relatively high 

demand, due to the fact that during those periods the gains from cheating are more likely to 

outweigh the subsequent punishments during lower demand periods. In an extension of this 

model, Haltiwanger and Harrington (1991) show that an increase in expected costs should 

lower the likelihood of collusion in the current period. Borenstein and Shepard (1996) test 

this theory using data on retail gasoline margins. Using a panel of city level data, they find 

that current retail margins increase in response to higher anticipated demand and fall in 

response to an anticipated increase in wholesale prices. 

 A second group of dynamic models stem from the recent empirical gasoline pricing 

literature focused on the asymmetric adjustment of the retail price of gasoline to changes in 

wholesale price. Lewis (2005a) provides theoretical underpinnings for these findings by 

formulating a “reference price” model that leads consumers to search less when prices are 

falling. In his model, consumers are slow to update their expectations about the distribution 

of prices and search less when prices are falling. This generates a kinked residual demand 

curve which in turn leads to asymmetric effects of marginal cost shocks on retail prices. 

A third group of dynamic models stem from a model proposed by Maskin and Tirole 

(1988). In these models, stations play an alternating-move game choosing prices from a 

discrete grid. In equilibrium, stations undercut one another on price until it becomes 

unprofitable, at which point stations begin a new cycle by charging a high price. Although 

the original theoretical model relies on a number of assumptions inconsistent with retail 

gasoline competition, Noel (2005) has shown that cycling equilibria are still possible under 

considerably weaker conditions. Eckert (2002, 2003) and Eckert and West (2003, 2004a, 

2004b) find evidence consistent with Edgeworth cycles in several Canadian cities, as does 

Noel (2007a, 2007b). One shortcoming of these models is that it can be difficult to 

determine when and whether stations are in a cycling equilibrium. Eckert (2002) and Noel 

(2005) use a Markov switching regression to determine this. 
25

5.0 Evaluating theories of retail pricing for gasoline markets 

 The models described in the previous section have general predictions about the 

distribution of retail prices. In this section of the paper we describe how well each model 

matches our empirical findings. While no one theory can be expected to fully characterize 

the market place, we find substantial shortcomings in each approach. 

5.1 Static Games with Pure Strategies 

 Modeling gasoline stations as charging a fixed markup over cost; i.e., modeling a 

station’s decision using pure strategies as in Manuszak (2002) and Thomadsen (2005), has 

some empirical support. Our findings suggest that a large fraction of the retail gasoline price 

variation can be explained by including time effects, which control for common wholesale 

price changes, and station effects, which non-parametrically control for station specific 

localized demand, competition, and costs. In particular, the use of time-invariant store 

effects explains most of the large differences between a station’s price and the market price. 

This can be seen by comparing the residual plots from Figures 3 (which only controls for 

time effects) and Figure 5 (which also controls for station effects). The evidence strongly 

suggests that gasoline stations have systematically different mean prices. 

We see two important inconsistencies between these models and our findings. First, 

prices change substantially from period to period, suggesting that a fixed markup model is 

potentially missing important aspects of a gasoline station’s pricing behavior. This can most 

clearly be seen by examining the plot of the Markov Transition Matrix in Figure 6. This 

figure shows us that even controlling for the systematic component of a station’s pricing, 

there is still a substantial probability that the station will be charging a different relative price 

in subsequent periods. Further, the matrix shows that the movement back to mean pricing 

takes many periods. For example, if a station is charging a price at least 5 cents less than its 

mean price (an event that occurs about 3% of the time) the probability it will charge a price 

within a penny of its mean price in the next period is less than 10%. Clearly, there are 

dynamic components to pricing. Second, while there is a systematic aspect of a station’s 

pricing, a significant fraction of stations appear to change where they are in the pricing 

distribution from year to year. The fraction changing relative price is large, nearly 30%, and 

the changes in a station’s position in the price distribution can be substantial. Together 
26

these two inconsistencies reject a static modeling approach that predicts that gasoline 

stations have either constant margins or maintain a constant relative position in the pricing 

distribution. 

Finally, even though there are systematic differences in mean price across stations, 

implementation of the modeling approach may be difficult because of data limitations. In 

our data, only a station’s brand affiliation and measures of localized demand (zip-code level 

demographics) explain a sizeable fraction of a station’s systematic mark up. The failure of 

either station amenities or measures of localized competition to explain station markups is 

disappointing. To credibly identify these types of models, the econometrician must observe 

characteristics of stations that both vary across stations and are associated with price. 

Equally troubling is that some brands behave very differently than others for unknown 

reasons. Crown gas stations were low price leaders in the Northern Virginia suburbs. As 

Figure 7 demonstrates, Crown systematically was the lowest priced gas station. To our 

knowledge there is no set of variables that would allow us to a priori predict this behavior. 

5.2 Static Games with Mixed Strategies

 Some aspects of gasoline pricing are consistent with prices being generated by mixed 

strategy similar to Varian (1980). We find that the modal choice for a gasoline station is to 

change its price each week. This is consistent with Varian’s model, which has no masspoints. Strictly speaking, all firms in Varian’s model should have the same mean price 

(retailers in Varian’s model are identical and thus draw prices from the same distribution). 

However, it would not be difficult to extend the model to incorporate firm heterogeneity 

into the model (e.g., allow station’s to face either different numbers of competitors or 

different fractions of consumers who search) which would generate different pricing 

distributions for different gas stations. 

 The more important inconsistency between Varian’s model and our results is that 

while prices change every period, the model implies that each price draw should come from 

the same pricing distribution. Empirically, this implication is clearly violated. Figure 6, for 

example, shows that the price distribution for time t+1 depends importantly on the price at 

time t. The modal price at time t+1 is the price at time t, and the pricing distribution at time 

t+1 is tightly centered around the price at time t. While this result could be explained by 
27

assuming that gasoline stations experience idiosyncratic autoregressive cost shocks, we find 

this explanation unlikely. Instead, it appears that a model of true dynamics; in which recent 

history matters, is required to explain changes in a gasoline’s relative margin over time. 

 There is evidence that some retailers play very different pricing strategies; that is, 

some firms may play a mixed-price strategy while other firms maintain a relative position in 

the pricing distribution. However, in contrast to the prediction in Baye et al. (1992), the 

stations that maintain their position in the pricing distribution charge a systematically low

rather than a high price. Thus asymmetric equilibria generated by Varian’s modeling 

approach do not explain the asymmetric pricing behavior seen in our sample of retail 

gasoline stations. 

5.3 Repeated Games with Collusion 

 A prediction of tacit collusion models (especially Green and Porter) is that average 

margins should vary over time (price wars). In an environment in which sellers are 

differentiated, this would translate into shifts in the price distribution, in which the shape of 

the distribution remains more or less constant, but the mean changes. As noted the price 

distribution does have this property. If the characteristics of firms do not change, this 

model would imply that a firm’s price (relative to the mean) would remain fixed in all 

collusive periods. We find, however, that in every time period, including periods of high and 

low margins, firms change their relative position in the pricing distribution.34 That is, the 

mechanism that supports collusion in these models is that decreases in prices by one firm are 

met by subsequent decreases in price for all firms. Hence, if a significant fraction of firms are 

changing their relative price every period, the model would suggest that the market would 

always be in the penalty phase. 

 While our finding that gasoline stations frequently change their position in the 

pricing distribution suggests collusion is unlikely, Borenstein and Sheppard (1996) (B&S) 

found empirical evidence consistent with model of collusion developed by Rotemberg and 

 

34 We have recalculated the transition matrix shown in Figure 6 separately by year and find 

the same pattern. Gasoline stations are more likely than not to change their prices every 

period in each year. 
28

Saloner (1986) and extended by Haltiwanger and Harrington (1991). We conduct a test 

similar to B&S to determine if the pattern they found in retail margins exists in our data. 

The logic underlying B&S’s test is that retailers anticipate future wholesale gasoline prices 

because there is a lag in the pass thru of crude price changes to wholesale price changes. An 

anticipated increase in wholesale costs is predicted to lower future retailer profits which leads 

to cheating on the collusive agreement in the current period. In other words, an anticipated 

increase in costs should lower the likelihood of retail collusion today. Thus, we should 

expect (and B&S found) that an increase in expected rack prices will lower current period 

margins. 

B&S used a panel of prices (measured at the city level) from 43 cities over 72 months 

for their test. In conducting our test, we use the aggregate rack and retail prices from our 

sample. The first step is to forecast wholesale prices. Then we estimated a retail markup 

equation that was a function of anticipated wholesale price. We follow B&S’s modeling 

approach as closely as possible. However, there are two important differences in our 

approach due to differences in our data sets. First, our study examines weekly data rather 

than monthly data. For this reason, our coefficient estimates are not directly comparable to 

B&S. Second, we do not have access to quantity data for Northern Virginia. Thus, our 

estimated margin equations do not include current or anticipated future demand as in B&S.35

Future rack prices are estimated to be a function of the lagged rack and crude price, 

and two lags of the change in crude and rack prices. In addition, the forecasting equation 

allows for asymmetric price adjustment; that is increases in lagged crude or rack prices can 

have different effects on expected rack prices than decreases. The forecasting equation, (4) 

below, also includes an error correction term; i.e., the lags of the rack and crude price. 

01 12 23 14 2

5 16 27 18 2

4

9 1 10 1

(4) 

 

 

t tttt

tt tt

t t j jt

 RACK a a RACK a RACK a RACK a RACK

a CRUDE a CRUDE a CRUDE a CRUDE

a RACK a CRUDE D M

++ −−

−− −−

++ −−

− − −−

− −

= +Δ +Δ +Δ +Δ

+Δ +Δ +Δ +Δ

++ +

11

4

1

t

j

e =

∑ +

RACKt is the average wholesale price for branded gasoline at the Fairfax rack in week t, 

CRUDEt is the spot price (per gallon) of West Texas Intermediate crude oil at Cushing, OK 

in week t (the most commonly quoted U.S. crude price), 1 , ΔRACK RACK RACK t tt = − −

 

35 The equations we estimate closely parallel B&S’s equations 1, 2, and 4 (See pages 439-441). 
29

1 , Δ= − CRUDE CRUDE CRUDE t tt− RACK RACK t t

+ Δ =Δ if 0, ΔRACKt > otherwise 

0, RACKt

+ Δ = RACK RACK t t− Δ =Δ if 0, ΔRACKt < 0, ΔRACKt > otherwise 

0, RACKt

− Δ = and CRUDE CRUDE t t+ − Δ Δ are defined similarly, the Mjt are month 

indicators (included to control for seasonality), and the coefficients corresponding to the 

month indicators and the disturbance have a superscript that corresponds to the equation 

number. 

Given the expected future rack price, we then estimate two versions of the margin 

equation which closely parallel those in B&S. The first, equation (5) below, specifies a simple 

lag structure.

11

5 5

01 2 13

1

(5) t t t t j jt t

j

 MARGIN b b RACK b EXPECTED RACK b RACK D M e +

=

=+ + +Δ + + ∑

MARGINt = RET t

 - RACKt, RETt is the average retail price in our sample in week t, and 

EXPECTED RACKt+1 is the expected rack price in week t+1 which is estimated by equation 

(4) above. The second margin equation, (6) below, uses a more general lag structure that 

allows the current margin to be a function of multiple lags and includes an error correction 

term. In addition, like equation (4), this specification allows for asymmetric adjustment. 

0 1 12 13 14

5 16 27 8 19 2

8 19 2

(6) 

 

 

t t t t t

t t tt t

t t

 MARGIN c c EXPECTED RACK c RACK c RET c RACK

c RACK c RACK c RACK c RACK c RACK

c RET c RET

+

+ −−

+ + −− −

−− −−

+

− −

= + + + +Δ

+Δ +Δ +Δ +Δ +Δ

+Δ +Δ 10 1 11 2

11

6 6

1

 

t t

j jt t

j

c RET c RET

DM e

+ −−

− −

=

+Δ +Δ

+ + ∑

 The variables in equation (6) are defined analogously to those in (4) and (5). 

 In estimating equations (4), (5), and (6), we assume that the wholesale price of 

gasoline at the Fairfax rack and the retail price are not jointly determined; i.e., RACKt

 is 

uncorrelated with the disturbance term in equations (4), (5), and (6).36 One additional 

 

36 In contrast to B&S, we do not instrument for rack prices. In our data, the rack price is the 

price of wholesale gasoline at the Fairfax , VA rack. Refiners supplying wholesale gasoline in 

Fairfax use pipelines connecting the major U.S. refining region in the Gulf to the major 

population centers on the eastern seaboard of the U.S. Refiners supplying Fairfax have the 

option of selling gasoline anywhere along the pipelines. Because gasoline demand in 
30

complication in estimating equation (5) is that the error term appears to be non-stationary 

(the estimated autocorrelation coefficient is .99). Thus, we estimate equation (5) as a first 

difference to generate a stationary error, as shown in equation (5a) below. We can reject the 

null hypothesis of a unit root in equation (5a).37 

1 1

2 1

3 1

(5 ) ( )

 ( )

 ( )

t t-1 tt

t t

t t

a MARGIN MARGIN b RACK RACK

b EXPECTED RACK EXPECTED RACK

b RACK RACK D

−

+

−

− =−

+ −

+ Δ −Δ +

11

1 1

1

( ) j jt jt t t

j

M M ee − −

=

∑ − +−

Table 7 presents the coefficient estimates for equations (5a) and (6). In contrast to 

B&S, the estimated impact of expected prices on current retail margins is sensitive to the 

specification of the lag process. The estimate from Model (5a) is similar to what B&S found: 

an increase in expected rack prices leads to a modest decrease in current retail margins. In 

contrast, the estimate from equation (6), which allows for a much more general lag process, 

finds essentially no effect of expected future rack prices on current retail margins. We 

interpret these findings as evidence that there are important dynamics in retail margins. 

However, because the test is very sensitive to model specification and because retail gasoline 

stations frequently change relative position in the price distribution, we conclude that 

conventional collusion models are unlikely to explain the observed changes in retail margins 

in our data. 

5.4 History Dependent Demand/Asymmetric Price Adjustment 

 In order to examine asymmetric price adjustment as an explanation for changes in 

retail margins in our data, we follow Borenstein et al. (1997) and Bachmeier and Griffin 

(2003), in estimating the following equation: 

 

Northern Virginia is a small fraction of U.S. gasoline demand, we treat the rack price as 

unaffected by demand in Northern Virginia. 

37 The Dickey-Fuller test statistic is 6.18 which implies the p-value corresponding to the 

rejecting the null hypothesis of a non-stationary disturbance is essentially zero. While 

equation (5a) does not include an intercept, we estimate it with an intercept that is effectively 

zero. 
31

2 2 + - +-

t-k t-k t-k t-k

0 1

0 0 1 -1 2 -1

(7) RET ΔRACK + ΔRACK + ΔRET RET

 + (Time Trend ) [ RET RACK ]

( ) (+) t k i kk

k k

t t tt

β β θθ

α δ δδ ε

+ − +−

= =

Δ = Δ

++ + +

∑ ∑ 

where the variables in equation (7) have the same definitions as those described in the 

previous subsection (i.e., equations (4), (5), and (6)). The motivation behind this specification 

is to allow retail prices to adjust asymmetrically in response to both changes in wholesale 

(rack) and previous retail prices changes. The term in brackets is defined as the error 

correction component of the estimating equation, which implicitly defines the long run 

relationship between retail and rack prices; that is, 2

1

δ

δ corresponds to the long-run pass thru 

rate between wholesale and retail prices. 

 There is some controversy about correctly estimating equation (7). Borenstein et al. 

estimate all of the parameters from equation (7) in one step. Bachmeier and Griffin (B&G) 

argue that a two step procedure is superior. In B&G’s preferred approach, the error 

correction term is estimated in a first stage. The estimated coefficients from the error 

correction term are then imposed (as if they were estimated without error) and the remaining 

parameters are estimated in the second stage. We estimate models of asymmetric price 

adjustment using an estimation strategy very similar to both Borenstein et al. and B&G,38

shown in columns 1 and 2, respectively, of Table 7.39 Because the Borenstein et al. and B&G 

 

38 Following B&G’s suggestion, we estimate their model by first estimating the cointegrating 

relationship (corresponding to the error correction term) using OLS. We use these parameter 

estimates to construct the error correction term. The error correction term is than imposed 

on the model (as if estimated without error) in estimating the remaining parameters in 

equation (6) by OLS and calculate Newey-West standard errors. 

39 Because we only have 3 years of weekly data for one city, it is not possible to include time 

dummies in our model as B&G and Borenstein et al. do. We have, however, included month 

of year dummies to control for seasonality in estimating equation (6). These coefficient 

estimates are not included for brevity, but are available on request. 
32

estimation methods are very different, only the coefficients corresponding to the price 

adjustment terms shown in Table 7 are directly comparable.40 

The parameter estimates corresponding to the price adjustment terms (the ΔRackt-k

and ΔRett-k terms) for the Borenstein et al. and B&G approaches are remarkably similar 

both in terms of the magnitudes and degrees of statistical precision. The estimated 

coefficients, however, are not economically plausible, or similar to the empirical results in 

either Borenstein et al. or B&G. For example, our estimates imply that wholesale price 

increases, but not price decreases, are passed through to retail. The estimated coefficient on the 

contemporaneous increase in wholesale price ( + ΔRACKt ) is estimated to be between .25 and 

.27, and is statistically significant. The estimated effect on a contemporaneous wholesale 

price decrease is never economically or statistically significant (less than .03 in absolute 

value). In contrast, Borenstein et al. and B&G find much larger effects of changes in 

wholesale prices on retail prices for both wholesale price increases and price decreases.41 For 

this reason, we do not think a model of asymmetric price adjustment provides a good 

explanation for the changes in retail price we find in our data.42 

 

40 While both Borenstein et al. and B&G techniques are used to estimate essentially the same 

model (B&G do not include a time trend), a non-linear transformation is required to directly 

compare the parameter estimates corresponding to the intercept and the error correction 

terms of the two models. 

41 In all of the specifications B&G estimate, the contemporaneous effect of a change in 

upstream price on the downstream price is at least .75 (see Table 1, page 774). Borenstein et 

al., find large differences in the effect of contemporaneous wholesale price increases than 

decreases on retail prices, e.g., .62 vs. .2 in their Table 1, page 320, column 4. However, both 

papers find economically and statistically significant effects of decreases in wholesale price 

on retail price not seen in our data. 

42 Al-Gudhea et al. (2007) find sizeable asymmetry at the retail level. The asymmetry is most 

pronounced in the downstream portion of the distribution chain, the response of retail price 

to crude oil or wholesale gasoline price shocks. This asymmetry however lasts a matter of 

days and therefore does not explain the changes in retail margin we see in our data. 
33

 The last two columns of Table 7 include indicator variables corresponding to the 

years 1997 and 1998. For the B&G model we include these variables in the estimation of the 

cointegrating relationship, in Borenstein et al. we simply add them to equation (7). If these 

variables are economically significant, the implication is that the long-run margin is shifting 

between years. The estimates of B&G model suggest that the margins have changed. Here 

we see that long-run margins appear to shift down in both 1998 and 1999 relative to 1997. 

We interpret this evidence as suggesting that city-level margins appear to change by 

economically significant amounts over time. 

5.5 Edgeworth Cycles 

 The most widely used test for Edgeworth cycles to date is the “eyeball test”. The 

theoretical model predicts that retail stations’ margins should have rapid increases followed 

by slower decreases. This leads to a pronounced saw-tooth pattern over time, which is 

particularly noticeable when wholesale prices are roughly constant; most empirical tests of 

cycle behavior are constructed largely with the goal of quantifying this test. Eckert and West 

(2003) suggests several possibilities, including: looking for asymmetry in the distribution of 

the length of “price runs”43 and looking at the number of periods with little or no change in 

retail price (or margin). Lewis (2007) uses a threshold for the median daily price change. 

Eckert (2002) and Noel (2005, 2007b) offer more complex models of regime-switching to 

identify cycling, but this approach necessitates additional modeling assumptions regarding 

the behavior of prices under each regime. Thus, a finding of regime switching cannot be 

distinguished from a failure to correctly model the within-regime pricing behavior of the 

stations. 

 We employ several tests and find that our data are largely inconsistent with cycling 

behavior. First, as can be seen in Figure 1, the characteristic saw-tooth pattern indicative of 

cycling is not readily apparent. While there are some short-term fluctuations in margins, 

these are all on the order of one to three cents and do not explain the larger fluctuations. 

The larger fluctuations are too long-lived to be consistent with cycling. The existing literature 

has typically found cycles measured in hours or weeks, not months. Second, the Markov 

 

43 A “price run” is defined as a set of weeks with consecutive same-sign price changes. 
34

transition matrices in Figure 6 are not consistent with cycling behavior. The theory of cycling 

behavior (both symmetric and asymmetric) predicts that while stations might be relenting or 

undercutting, they do not leave their margins unchanged. Thus, there should be very little 

mass on the diagonal. This is not consistent with what we observe: that stations residuals are 

most likely to remain where they were in the previous week, and that there is very little mass 

in the upper left and lower right corners. 

6.0 Discussion and Conclusion 

 We examined weekly pricing for three years in the late 1990s of 272 stations in 

Northern Virginia. Our main finding is that gasoline stations do not appear to follow simple 

static pricing rules. Gasoline stations do not charge constant margins, nor do they simply 

maintain the same relative position in the pricing distribution. We find from week-to-week, 

gas stations are more likely than not to change their relative position in the pricing 

distribution (measured relative to a regional price or rank among nearby stations). There is 

also heterogeneity in stations’ pricing behavior over time. Stations that charge very high 

prices or very low prices in one week are much more likely to charge high or low prices in 

subsequent weeks than stations charging prices near the mean. There is also an interesting 

asymmetry in this behavior: low priced stations are much more likely to remain low priced 

than high priced stations are to remain high. While most week-to-week changes in pricing 

position are small, a significant number of stations make large changes in their pricing. For 

example, 24% of stations change their relative position in the pricing distribution by more 

than 25 percentage points between 1998 and 1999. 

 We believe our most interesting finding is that retail margins change sizably over 

time. For example, for a six month period the implied retail mark-up (retail price less taxes 

and wholesale prices) is roughly 19 cents for 6 months and then falls to about 10 cents for 3 

months. The evidence suggests the entire distribution is shifting over time, not just the 

median or mean. In a market with little entry or exit, little non-geographic differentiation, 

where wholesale prices are observable with little brand variation in rack prices and inelastic 

demand, one would expect more constant retail margins. The explanation that prices reflect 

coordinated behavior (e.g., tacit collusion followed by periodic price wars), is also difficult to 

accept. In both high and low margin periods, gasoline stations continuously change their 
35

relative positions in the pricing distribution. Hence, these models predict that the market 

would always be in the penalty phase. Further, tacit collusion would appear unlikely in 

Northern Virginia given the low level of concentration at the retail level – there are roughly 

25 different brands of retail gasoline in Northern Virginia.44 This finding is worthy of further 

investigation. More generally, many of our results can be interpreted as adding to mounting 

evidence, e.g., Eckert and West (2003, 2004a, 2004b), Noel (2007a, 2007b) and Slade (1992), 

that localized retail gasoline competition appears to be characterized by regime shifts in 

pricing. 

 We have also examined how our empirical findings relate to existing theories of 

pricing that appear most relevant for retail gasoline. While each of these theories explains 

some aspects of gasoline pricing, none provide explanations for the pricing dynamics we 

observe. Given the explosion in the quantity of data available for studying retail gasoline 

markets, we view retail gasoline markets as a promising area for future research. We hope 

that our empirical findings can provide useful guidance for future work on modeling retail 

gasoline pricing behavior. 

 

 

44 Because most branded stations are operated independent of the refiner, this understates 

the number of independent price-setting agents. Most stations in our data are operated by a 

lessee dealer (an individual who leases the station from the refiner) or a jobber (a franchisee 

that owns the station.) The lessee dealer or jobber sets the retail price, not the refiner. 
36

References 

Al-Gudhea, S., Kenc, T. and S. Dibooglu, 2007, “Do Retail Gasoline Prices Rise 

More Readily Than They Fall? A Threshold Cointegration Approach.,” Journal of Economics 

and Business, v. 59, pp. 560-574. 

Athey, S. and K. Bagwell, 2001, “Optimal Collusion with Private Information,” The 

RAND Journal of Economics, v. 32, pp.428-465. 

Athey, S., K. Bagwell, and C. Sanchirico, 2004, “Collusion and Price Rigidity,” Review 

of Economic Studies, v. 71, pp. 317-349. 

Bachmeier, L. and J. Griffin, 2003, “New Evidence on Asymmetric Gasoline Price 

Responses,” The Review of Economics and Statistics, v. 85, pp.772-776. 

Barron, J., B. Taylor, and Umbeck, J., 2000, “A Theory of Quality-Related 

Differences in Retail Margins: Why There is a Premium on Premium Gasoline,” Economic 

Inquiry, 38 (4), 550-569. 

Barron, J., B. Taylor, and Umbeck, J., 2004, “Number of Sellers, Average Prices and 

Price Dispersion,” International Journal of Industrial Organization, v. 22 pp. 1041-66. 

 Baye, M, D. Kovenock and C. G. DeVries, 1992, “It Takes Two to Tango: 

Equilibrium in a Model of Sales,” Games and Economic Behavior; 4, pp. 493-510. 

Borenstein, S., A. Cameron, and R. Gilbert, 1997, “Do Gasoline Prices Respond 

Asymmetrically to Crude Oil Price Changes,” Quarterly Journal of Economics, v. 112, pp. 305- 

339. 

Borenstein, S., A. Shepard, 1986, “Dynamic Pricing in Retail Gasoline Markets,” The 

RAND Journal of Economics, v. 27, pp. 429-251. 

 Conlisk, J., Gerstner, E., and Sobel, J., 1984, “Cyclic Pricing by a Durable Goods 

Monopolist,” Quarterly Journal of Economics v. 99, pp. 489-505. 

 Eckert, A, 2002, “Retail Price Cycles and Response Asymmetry,” The Canadian Journal 

of Economics, v. 35, pp. 52-77. 

 Eckert, A. and D. West, 2003, “Retail Price Cycles and the Presence of Small Firms,” 

International Journal of Industrial Organization, v. 21, pp. 151-170. 

 Eckert, A. and D. West, 2004a, “Retail Gasoline Price Cycles across Spatially 

Dispersed Gasoline Stations,” Journal of Law and Economics, v. 47, pp. 245-73. 

 Eckert, A. and D. West, 2004b, “A Tale of Two Cities: Price Uniformity and Price 
37

Volatility in Gasoline Retailing,” Annals of Regional Science, v. 38, pp. 25-46. 

 Federal Trade Commission, 2004, The Petroleum Industry: Mergers, Structural Change, and 

Antitrust Enforcement. 

 Federal Trade Commission, 2006. Investigation of Gasoline Price Manipulation and PostKatrina Gasoline Price Increases. 

 Galeotti, M., A. Lanza and M. Manera, 2003, “Rockets and Feathers Revisited: An 

International Comparison on European Gasoline Markets,” Energy Economics V. 25 pp. 175-

190. 

 Green, E. and R. Porter, 1984, “Noncooperative Collusion Under Imperfect Price 

Competition,” Econometrica v. 52 pp.87-100. 

 Haltiwanger, J, J. Harrington, 1991, “The Impact of Cyclical Demand Movements on 

Collusive Behavior”, RAND Journal of Economics, v. 22, pp. 89-106. 

 Hastings, J., 2004, “Vertical Relationships and Competition in Retail Gasoline 

Markets: Empirical Evidence from Contract Changes in Southern California,” American 

Economic Review, 94(1), pp. 317-328. 

 Hoch S., X. Dreze, and M. Purk, 1994., “The EDLP, High Low and Margin 

Arithmetic”, Journal of Marketing, 58: 16-27. 

 Hong, P, R. P. McAfee, and A. Nayyar, 2002, “Equilibrium Price Dispersion with 

Consumer Inventories” Journal of Economic Theory; 105, pp. 503-517. 

 Hosken, D. and D. Reiffen, 2004, “How do Retailers Determine Sale Products: 

Evidence from Store-Level Data,” Journal of Consumer Policy; 27, pp.141-177. 

 Lal, R. and C. Matutes, 1994, “Retail Pricing and Advertising Strategies,” Journal of 

Business; 67, pp. 345-70. 

 Lach, S., 2002, “Existence and Persistence of Price Dispersion: An Empirical 

Analysis,” Review of Economics and Statistics, 84(3), pp. 433–444

 Lewis, M., 2005a, “Asymmetric Price Adjustment and Consumer Search: An 

Examination of the Retail Gas Market,” working paper. 

 Lewis, M., 2005b, “Is Price Dispersion a Sign of Competition,” working paper. 

 Lewis, M, 2007, “Temporary Wholesale Gasoline Price Spikes Have Long-lasting 

Retail Effects: The Aftermath of Hurricane Rita,” working paper. 

 Manuszak, M., 2002, “The Impact of Upstream Mergers on Retail Gasoline Prices,” 

working paper. 
38

 Maskin, E. and J. Tirole, 1988, “A Theory of Dynamic Oligopoly, II: Price 

Competition, Kinked Demand Curves, and Edgeworth Cycles,” Econometrica, v. 56, pp. 571-

99. 

 Meyer, D. and J. Fischer, 2004, “The Economics of Price Zones and Territorial 

Restrictions in Gasoline Marketing,” Federal Trade Commission Bureau of Economics Working 

Paper #271. 

Noel, M., 2007a, “Edgeworth Price Cycles, Cost-Based Pricing and Sticky Pricing in 

Retail Gasoline Markets,” Review of Economics and Statistics, forthcoming. 

Noel, M., 2007b, “Edgeworth Price Cycles: Evidence from the Toronto Retail 

Gasoline Market,” Journal of Industrial Economics, forthcoming. 

Noel, M., 2005, “Edgeworth Price Cycles and Focal Prices: Computational Dynamic 

Markov Equilibria,” working paper. 

Pashigian, B, 1988, “Demand Uncertainty and Sales: A Study of Fashion and 

Markdown Pricing,” American Economic Review, 78, pp. 936-53. 

Pashigian, B. and B. Bowen, 1991, “Why are Products Sold on Sales?: Explanations 

of Pricing Regularities,” Quarterly Journal of Economics v. 106, pp.1014-1038. 

 Pesendorfer, M., 2002, “Retail Sales: A Study of Pricing Behavior in Super Markets,” 

Journal of Business, v. 75, pp.33-66. 

 Porter, R., 1985, “On the Incidence and Duration of Price Wars,” Journal of Industrial 

Economics, v 33, pp. 415-426. 

 Rotemberg, J. and G. Saloner, 1986, “A Supergame-Theoretic Model of Price Wars 

During Booms,” American Economic Review, v. 76, pp.390-407. 

Shepard, A., 1990, “Pricing Behavior and Vertical Contracts in Retail Markets,” 

American Economics Association Papers and Proceedings, 80(2), 427-431. 

Shepard, A., 1991, “Price Discrimination and Retail Configuration,” Journal of Political 

Economy, 99(11), 30-53. 

Shepard, A., 1993, “Contractual Form, Retail Price, and Asset Characteristics in 

Gasoline Retailing,” RAND Journal of Economics, 24(1), 58-77. 

Slade, M., 1987, “Interfirm Rivalry in a Repeated Game: An Empirical Test of Tacit 

Collusion,” The Journal of Industrial Economics, v. 35, pp.499-515. 

Slade, M., 1992, “Vancouver’s Gasoline-Price Wars: An Empirical Exercise in 

Uncovering Supergame Strategies,” Review of Economic Studies, 59, 257-276. 
39

 Thomadsen, R., 2005, “The Effect of Ownership Structure on Prices in 

Geographically Differentiated Industries,” The RAND Journal of Economics, v. 36, pp.908-929. 

 White, H. (1982) “Maximum Likelihood Estimation of Misspecified Models” 

Econometrica, v. 50 1-25. 

 Varian, H.R. (1980) “A Model of Sales,” American Economic Review; 70, pp. 

651-9. 
Table 1: Descriptive Statistics for OPIS Sample and Census

Minimum Maximum

Mean 

(StdDev) 

OPIS Sample

Mean 

(StdDev) 

Census

Continuous Variables:

Retail Price (cents) 71.9 145.9 111.45 n/a

 Std Dev 11.35

Number of Gas Stations within 1.5 miles 0 10 8.62 8.30

 Std Dev 2.66 2.83

Distance to Closest Gas Station (miles) 0.002 3.08 0.21 0.20

 Std Dev 0.34 0.42

Fraction of Mobil and Exxon Stations 

Nearby 0 1 0.36 0.35

 Std Dev 0.16 0.18

Fraction of Low-Priced Stations Nearby 0 0.4 0.04 0.05

 Std Dev 0.07 0.08

Fraction of Lessee Dealer Stations Nearby 0 0.9 0.51 0.46

 Std Dev 0.18 0.20

Fraction of Company Owned and Operated 

Stations Nearby 0 0.6 0.11 0.13

 Std Dev 0.11 0.13

Number of Pumps 1 16 7.69 7.28

 Std Dev 2.85 3.31

Population in Zip Code 1377 62132 30393.73 29658.97

 Std Dev 12467.93 12389.33

Population Density in Zip Code 131.4 12305.9 4423.13 4271.787

 Std Dev 2793.66 2888.824

Median Family Income in Zip Code 37304 154817 72002.68 73284.14

 Std Dev 18195.71 20082.67

Median Household Commuting Time in 

Zip Code (minutes) 22 42 30.70 30.36

 Std Dev 3.91 4.28

Indicator Variables:

Convenience Store 0.05 0.07

Provides Repair Service 0.62 0.56

Outdated Format 0.24 0.29

Self Serve Only 0.84 0.74

Ownership Type:

Lessee Dealer 0.58 0.46

Jobber Owned 0.08 0.09

Company Owned and Operated 0.14 0.13

Open Dealer 0.21 0.27

Year=1997 36.19

Year=1998 31.74

Year=1999 32.07

Number of Observations (station-weeks) 27,853 570
Table 2: Comparison of Brand Distribution In New Image Marketing Census and OPIS Sample

New Image 

Census 

Brand Percent of 

Station-Weeks

Percent of 

Stations

Percent of 

Stations

Amoco 0.00 0.00 9.3

Blue Max 0.00 0.00 0.18

BP 0.4 1.14 1.05

Chevron 0.66 2.27 1.75

Citgo 10.31 15.91 11.58

Coastal 0.05 0.38 0.7

Crown 7.19 5.68 3.16

Dixie 0.00 0.00 0.35

Eagle 0.00 0.00 0.18

Exxon 0.00 0.00 22.11

Gas King 0.00 0.00 0.18

Getty 0.71 0.76 0.7

Global 0.00 0.00 0.18

Hess 0.75 1.52 1.93

JAC 0.00 0.00 0.18

Merit 0.42 0.76 0.35

Mobil 27.62 23.86 14.39

Quarles 0.00 0.00 0.53

Racetrac 0.00 0.00 0.18

Sheetz 0.27 0.38 0.53

Shell 23.71 21.21 11.23

Sunoco 5.31 6.06 3.33

Texaco 22.27 19.32 10

Wawa 0.00 0.00 0.18

Xtra Fuels 0.33 0.75 0.7

Unbranded 0.00 0.00 5.09

OPIS Sample
Table 3: Regressions of Retail Margin on Station Characteristics And Time Indicators

(All Stations)

Coefficient T-Statistic Coefficient T-Statistic Coefficient T-Statistic Coefficient 

Company Owned and Operated 1.52 2.13 1.02 1.72 1.72 1.80 1.50 

Lessee Dealer 0.53 1.40 0.46 1.08 0.41 0.91 0.76 Fraction of Lessee Dealer Stations Nearby -0.49 -0.59 -0.28 -0.35 -0.15 -0.13 -0.97 

-0.31 -0.21 0.10 0.07 -0.76 -0.37 -0.19 

Fraction of Mobil and Exxon Stations Nearby 0.11 0.11 1.22 1.41 -0.35 -0.24 -1.20 

Fraction of Low-Priced Stations Nearby 1.48 0.65 -2.98 -1.66 2.75 0.80 4.22 Number of Gas Stations within 1.5 miles -0.04 -0.60 -0.03 -0.40 -0.04 -0.46 -0.08 Distance to Closest Gas Station (miles) 0.43 0.65 0.97 1.98 0.20 0.24 -0.16 Convenience Store -0.81 -1.28 -0.29 -0.39 -0.14 -0.17 -0.46 Provides Repair Service 0.92 2.63 0.68 2.30 1.40 3.04 1.00 Outdated Format 0.63 1.89 0.28 0.60 0.67 1.72 0.79 Self Serve Only -0.05 -0.71 -0.05 -0.99 -0.06 -0.68 -0.01 Number of Pumps 0.40 1.09 -0.04 -0.08 1.32 2.74 0.32 Log of Population in Zip Code -1.50 -3.81 -0.72 -2.75 -1.68 -3.54 -2.00 Log of Population Density in Zip Code 0.75 3.65 -0.20 -1.03 1.18 4.08 1.58 Log of Median Income in Zip Code 1.57 2.56 0.08 0.13 2.13 2.48 3.19 Log of Median Travel Time -5.17 -4.85 -0.28 -0.35 -8.73 -5.43 -7.85 Station Fixed Effects (Citgo Omitted)

BP 2.37 1.65 3.53 2.64 -1.65 -2.35 n/aChevron -2.94 -2.68 -2.46 -2.04 -6.58 -9.19 -0.65 Coastal -9.79 -12.05 -11.58 -13.20 n/a n/a

Crown -4.54 -5.58 -4.22 -5.15 -5.39 -4.97 -3.66 Getty -0.34 -0.36 0.47 0.23 -1.65 -1.88 -1.00 Hess -4.39 -4.60 -1.93 -1.32 -5.74 -4.81 -4.77 Kenyon -0.53 -0.90 n/a -2.00 -2.72 n/a

Merit -2.78 -2.37 n/a -5.45 -5.26 -2.75 

Mobil 0.14 0.25 1.62 2.27 -1.09 -1.56 -0.40 Sheetz -5.81 -5.56 n/a -5.83 -4.23 -4.32 

Shell 0.87 1.68 1.37 2.05 -0.05 -0.07 1.10 Sunoco -2.88 -4.12 -1.61 -2.16 -4.22 -5.19 -3.43 Texaco 2.01 4.08 2.57 3.84 0.96 1.48 2.20 Xtra Fuels -1.30 -1.76 -1.74 -2.26 -0.51 -0.54 n/a

Constant 59.74 6.34 58.97 6.49 71.28 5.27 47.37 Number of Observations (station-weeks)R-squaredFraction of Company Owned and Operated Stations Nearby

Pooled 1997 1998 199

Notes: The Retail Margin is defined as the retail price less the branded rack, the omitted station brand is Citgo, the omitted ownership types are open dealers, standard errors clustered by station, and each specification includes week dummies (not shown).

8835

0.68

892

0.6

27853

0.66

10073

0.67
Table 4: Regressions of Retail Margin on Station Characteristics and Time Indicators

(Non-Crown Stations)

Coefficient T-Statistic Coefficient T-Statistic Coefficient T-Statistic Coefficient 

Company Owned and Operated 1.63 2.15 1.05 1.65 1.87 1.84 1.61 Lessee Dealer 0.55 1.44 0.50 1.15 0.40 0.88 0.77 Fraction of Lessee Dealer Stations Nearby -0.91 -1.06 -0.54 -0.66 -0.56 -0.49 -1.52 

-0.11 -0.07 0.15 0.09 -0.44 -0.21 0.11 

Fraction of Mobil and Exxon Stations Nearby -0.14 -0.13 1.26 1.37 -0.78 -0.52 -1.67 Fraction of Low-Priced Stations Nearby 0.59 0.25 -3.52 -1.78 1.63 0.45 3.17 Number of Gas Stations within 1.5 miles -0.04 -0.54 -0.02 -0.39 -0.03 -0.34 -0.08 Distance to Closest Gas Station (miles) 1.47 2.72 1.55 2.73 1.56 2.02 1.02 Convenience Store -1.03 -1.68 -0.38 -0.52 -0.44 -0.56 -0.71 Provides Repair Service 0.93 2.65 0.70 2.36 1.38 3.01 1.00 Outdated Format 0.48 1.50 0.21 0.45 0.47 1.27 0.60 Self Serve Only -0.08 -1.21 -0.05 -1.13 -0.12 -1.35 -0.06 Number of Pumps 0.55 1.52 0.00 0.01 1.60 3.30 0.50 Log of Population in Zip Code -1.50 -3.72 -0.74 -2.69 -1.71 -3.47 -1.96 Log of Population Density in Zip Code 0.74 3.49 -0.19 -0.94 1.15 3.79 1.54 Log of Median Income in Zip Code 1.68 2.52 -0.02 -0.02 2.43 2.59 3.37 Log of Median Travel Time -4.79 -4.50 -0.08 -0.10 -8.29 -5.22 -7.43 Station Fixed Effects (Citgo Omitted)

BP 2.25 1.61 3.47 2.43 -1.48 -2.11 n/aChevron -2.85 -2.48 -2.32 -1.80 -6.65 -9.64 -0.50 Coastal -10.06 -12.14 -11.59 -12.96 n/a n/aCrown n/a n/a n/a n/aGetty -0.06 -0.06 0.65 0.32 -1.26 -1.47 -0.60 Hess -4.30 -4.30 -1.80 -1.16 -5.63 -4.53 -4.70 Kenyon -0.57 -0.94 n/a -2.12 -2.83 n/a

Merit -2.70 -2.40 n/a -5.31 -5.00 -2.68 

Mobil 0.17 0.28 1.62 2.25 -1.00 -1.43 -0.38 Sheetz -5.30 -5.15 n/a -5.03 -3.78 -3.72 

Shell 0.95 1.80 1.37 2.04 0.11 0.18 1.22 Sunoco -2.67 -3.86 -1.52 -2.02 -3.90 -4.97 -3.16 Texaco 2.05 4.06 2.56 3.81 1.06 1.63 2.26 Xtra Fuels -0.74 -1.01 -1.52 -1.90 0.33 0.35 n/a

Constant 57.59 5.84 59.38 6.09 67.24 4.74 47.31 Number of Observations (station-weeks)R-squaredFraction of Company Owned and Operated Stations Nearby

Pooled 1997 1998 199

Notes: The Retail Margin is defined as the retail price less the branded rack, the omitted station brand is Citgo, the omitted ownership types are joopen dealers, standard errors clustered by station, and each specification includes week dummies (not shown).

8,194

0.67

8,1

0.6

25,883

0.65

9,298

0.63
1997 to 1998 1998 to 1999 1997 to 1999

Change in Relative Distribution of:

10+ Percentage Points 52% 35% 67%

15+ Percentage Points 37% 21% 52%

20+ Percentage Points 25% 13% 40%

25+ Percentage Points 16% 10% 27%

50+ Percentage Points 4% 2% 6%

75+ Percentage Points 1% 1% 1%

1997 to 1998 1998 to 1999 1997 to 1999

33% 27% 45%

3.82 2.76 3.84

Number of Comparisons 170 193 163

Notes: This table presents the magnitude of changes in a station's relative margin between years conditional on the change 

in a station's margin being statistically significant. For example, between 1997 and 1998 33% of station's changed their 

average margin (measured relative to the average margin in northern Virginia) by a statistically significant amount. 

Conditional on the change being statistically significant, the mean change in relative margin was 3.82 cents.

Mean Size of Change

(in cents, conditional on being significant)

Percent of Statistically Significant Changes (zIn Cents

Table 5: Change In Relative Position of Gas Station Fixed Effects 

in Frequency Distribution Between Years

Notes: This table analyzes the changes over time in the estimated station-level fixed effects from regressions of margins 

on weeks and station fixed effects estimated separtately by year. This table examines how station-level fixed effects 

change between years by examining where in the frequency distribution a station's fixed effect falls between two years. 

For example, 4% of gasoline stations experienced a dramatic change in their relative price between 1997 and 1998, 

changing by 50 percentage points, e.g., moving from the 25th percentile to the 75th percentile.

Table 6: Change In Relative Size of Gas Station Fixed Effects Between Years
Table 7: Test of Borenstein and Shepard (1996)

Estimation of Margin Equation

Variable Coefficient T-Statistic Coefficient T-Statistic

EXPECTED RACKt+1 -0.397 -2.500 -0.002 -0.030

RACKt -0.194 -2.620 n/a n/a

ΔRACKt -0.490 -3.890 n/a n/a

RACKt-1 n/a n/a -0.918 -13.230

RETt-1 n/a n/a 0.923 52.910

ΔRACK+

t n/a n/a -0.759 -11.030

ΔRACK+

t-1 n/a n/a 0.165 1.730

ΔRACK+

t-2 n/a n/a -0.028 -0.560

ΔRACKt n/a n/a -1.007 -25.950

ΔRACKt-1 n/a n/a 0.027 0.480

ΔRACKt-2 n/a n/a -0.066 -1.890

ΔRET+

t-1 n/a n/a 0.438 2.390

ΔRET+

t-2 n/a n/a 0.097 0.810

ΔRETt-1 n/a n/a 0.404 2.680

ΔRETt-2 n/a n/a 0.042 0.320

Constant 0.006 0.060 0.651 1.910

Observations

Estimation Method

Note: Dependent Variable is the average retail margin in our sample in week t (RETt - RACKt

). 

RACKt is the Fairfax branded rack price in week t, RETt is the average retail price of gasoline in 

Northern Virginia in week t, ΔRackt=Rackt-Rackt-1, ΔRETt=RETt-RETt-1., ΔRET+

t=ΔRETt if 

ΔRET>0, ΔRETt-1=ΔRETt-1 if ΔRETt-1<0. ΔRACK+t-1 and ΔRACK-t-1 are defined analagously. 

Equation (5a) is estimated as a first difference. The estimating equations also include 11 monthly 

indicator variables.

Equation (6)

150 150

Equation (5a)

OLS, Newey-West Standard 

Errors

OLS, Newey-West Standard 

Errors
Table 8: Estimation of Asymmetric Price Adjustment Models

Coefficient T-statistic Coefficient T-statistic Coefficient T-statistic Co

Primary Equation

Constant 3.898 3.670 -0.702 -1.780 5.022 2.370 ΔRACK+

t 0.256 3.530 0.268 3.810 0.246 3.250 

ΔRACK+t-1 0.165 1.900 0.248 2.700 0.157 1.870 ΔRACK+t-2 -0.022 -0.470 0.031 0.620 -0.023 -0.500 

ΔRACKt -0.001 -0.020 -0.031 -0.750 -0.005 -0.120 

ΔRACK-t-1 0.023 0.460 0.073 1.450 0.019 0.370 

ΔRACK-t-2 -0.066 -1.880 -0.016 -0.430 -0.072 -2.110 

ΔRET+t-1 0.432 2.340 0.416 2.260 0.426 2.230 

ΔRET+t-2 0.104 0.940 0.122 0.900 0.096 0.880 ΔRET-t-1 0.409 2.700 0.525 3.700 0.384 2.580 ΔRET-t-2 0.063 0.470 0.209 1.510 0.046 0.340 RACKt-1 0.084 5.050 n/a n/a 0.087 5.160 

RETt-1 -0.081 -4.680 n/a n/a -0.088 -4.800 

Time -0.001 -0.860 n/a n/a -0.010 -0.300 

Year=1998 n/a n/a n/a n/a 0.317 0.180 

Year=1999 n/a n/a n/a n/a 0.927 0.270 

Error Correction Term n/a n/a 0.003 0.810 n/a n/a 

Cointegrating Relationship

Constant n/a n/a 56.00 32.24 n/a n/a 

Rackt-1 n/a n/a 0.93 32.16 n/a n/a 

Year=1998 n/a n/a n/a n/a 

Year=1999 n/a n/a n/a n/a 

ObservationsEstimation Method

151 151 151 

Borenstein et al. Bachmeier and Griffin Borenstein et al. 

OLS, Newey West Standard 

Errors

OLS, Newey West Standard 

Errors OLS

Note: Rackt is the Fairfax branded rack price in week t, Rett is the average retail price of gasoline in Northern Virginia in week t, 

ΔRackt=Rackt-R

specifications include month indicator variables (not shown).

OLS, Newey West Standard 

Errors
Figure 1: Weekly Retail Gasoline Margins and Branded Rack Prices 

1997-1999

05

1015202530

1/1/1997

3/1/1997

5/1/1997

7/1/1997

9/1/1997

11/1/1997

1/1/1998

3/1/1998

5/1/1998

7/1/1998

9/1/1998

11/1/1998

1/1/1999

3/1/1999

5/1/1999

7/1/1999

Week

Cents Per Gallon (Margin)

25th Percentile 75th Percentile 50th Percentile Branded Rack Price
Figure 2: Percentage of Retail Price Variation Generated by Time Series Varia

Overall and By Station Ownership Type

(Within Variation)

0%

10%20%30%40%50%60%70%80%90%

100%

Overall, 1997

Lessee Dealer, 1997

Company Operated, 1997

Open Dealer, 1997

Jobber Station, 1997

Overall, 1998

Lessee Dealer, 1998

Company Operated, 1998

Open Dealer, 1998

Jobber Station, 1998

Overall, 1999

Lessee Dealer, 1999

Company Operated, 199

Op

Ownership Type and Year

Percentage
0 .05 .1 .15 .2

Density

-30 -20 -10 0 10 

Residuals

Figure 3: Frequency Distribution of Residuals

from Regression of Weekly Station Prices on Weekly Indicat

1997-1999
0 10 20 30 40 50

0 10 20 30 40 500 10 20 30 40 500 10 20 30 40 50

-15 -10 

-15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15

Figure 4.A: P = -9 in Period t-1 Figure 4.B: P = -8 in Period t-1 Figure 4.C: P = -7 in Period t-1 Figure 4.D: P = -6 in Period t-1 Figure 4.E

Figure 4.F: P = -4 in Period t-1 Figure 4.G: P = -3 in Period t-1 Figure 4.H: P = -2 in Period t-1 Figure 4.I: P = -1 in Period t-1 Figure 4.

Figure 4.K: P = 1 in Period t-1 Figure 4.L: P = 2 in Period t-1 Figure 4.M: P = 3 in Period t-1 Figure 4.N: P = 4 in Period t-1 Figure 4.O

Figure 4.P: P = 6 in Period t-1 Figure 4.Q: P = 7 in Period t-1 Figure 4.R: P = 8 in Period t-1 Figure 4.S: P = 9 in Period t-1

Percent

Price In Current Period (t)

Figure 4: Single-Period Empirical Markov Transition Matrix

Relative Price in Current Week Conditional on Relative Price In Previo

Residuals from Regression of Price on Week Indicators
0 .05 .1 .15 .2 .25

Density

-30 -20 -10 0 10 

Residuals

Figure 5: Frequency Distribution of Residuals

from Regression of Weekly Station Prices on Store and Weekly In

1997-1999
0 10 20 30 40 50

0 10 20 30 40 500 10 20 30 40 500 10 20 30 40 50

-15 -10 

-15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15

Figure 6.A: P = -9 in Period t-1 Figure 6.B: P = -8 in Period t-1 Figure 6.C: P = -7 in Period t-1 Figure 6.D: P = -6 in Period t-1 Figure 6.E

Figure 6.F: P = -4 in Period t-1 Figure 6.G: P = -3 in Period t-1 Figure 6.H: P = -2 in Period t-1 Figure 6.I: P = -1 in Period t-1 Figure 6.

Figure 6.K: P = 1 in Period t-1 Figure 6.L: P = 2 in Period t-1 Figure 6.M: P = 3 in Period t-1 Figure 6.N: P = 4 in Period t-1 Figure 6.O

Figure 6.P: P = 6 in Period t-1 Figure 6.Q: P = 7 in Period t-1 Figure 6.R: P = 8 in Period t-1 Figure 6.S: P = 9 in Period t-1

Percent

Price In Current Period (t)

Figure 6: Single-Period Empirical Markov Transition Matrix

Relative Price in Current Week Conditional on Relative Price In Previo

Residuals from Regression of Price on Store and Week Indicato
1 10

01 Jan 97

01 Jan 98

01 Jan 99

01 Jan 00

01 Jan 97

01 Jan 98

01 Jan 99

CROWN MOBIL

Rank

Week

Figure 7: Rank of a Crown and a Mobil Station's Prices

Relative to Nine Closest Stations

• • • 

• • • • •• 

• . 

-

. •• • • 

- • ••• • •••••• 

•• • ••• • • • •• 

•••• . ..... 

-

.

• ••• . . _ ....

•• • • • • •••• • • •• •• 

_ 

.. _. ••• • • • •• • • 

-

... 

.- .- -- • 
0 20 40 60 80

0 20 40 60 800 20 40 60 80

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10

Figure 8.A: Rank=1 in t-1 Figure 8.B: Rank=2 in t-1 Figure 8.C: Rank=3 in t-1 Figure 8.D: 

Figure 8.E: Rank=5 in t-1 Figure 8.F: Rank=6 in t-1 Figure 8.G: Rank=7 in t-1 Figure 8.H: 

Figure 8.I: Rank=9 in t-1 Figure 8.J: Rank=10 in t-1

Percent

Rank In Current Period (t)

Figure 8: Markov Probabilities for Ten Closest Stations: 

 Rank in Pricing Distribution at t conditional on Rank at t-1

1 Lowest, 10 Highest
0 20 40 60 80

0 20 40 60 80

0 1 2 3 

0 1 2 3 4 5 0 1 2 3 4 5

Figure 9.A: Rank=1 in t-1 Figure 9.B: Rank=2 in t-1 Figure 9.C: RanFigure 9.D: Rank=4 in t-1 Figure 9.E: Rank=5 in t-1

Percent

Rank In Current Period (t)

Figure 9: Markov Probabilities for Five Closest Stations: 

 Rank in Pricing Distribution at t conditional on Rank at t-1

1 Lowest, 5 Highest
Appendix Table 1: Single-Period Empirical Markov Transition Matrix

Residuals from Regression of Price on Week Indicators

(Elements of Table are Percentages) Relative Price at t

Relative 

Price at t-1 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 

-9 1 0 2 2 5 17 32 18 9 5 3 3 1 1 1 0 1 1 1 0 0 0 0 0 0 0 -8 2 0 2 1 1 4 16 32 22 9 5 3 3 1 0 0 0 1 0 0 0 0 0 0 0 1 -7 1 0 0 0 1 1 5 11 37 25 8 3 3 2 2 1 0 0 0 0 0 0 0 0 0 0 -6 1 0 0 0 0 0 1 3 11 47 23 6 3 1 1 1 0 0 0 0 0 0 0 0 0 0 -5 0 0 0 0 0 0 1 1 3 15 44 23 7 2 2 1 0 0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 0 0 1 1 4 15 44 24 5 2 1 1 1 0 0 0 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 1 1 4 16 45 21 5 3 1 1 1 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 1 1 4 14 42 26 6 3 1 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 2 4 14 42 24 6 3 1 1 1 0 0 0 0 0 

0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 13 47 24 4 2 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 4 17 49 19 4 2 1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 7 18 44 18 4 2 1 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 4 7 18 46 13 4 1 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 7 10 19 37 13 4 1 1 1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 4 4 9 11 17 34 11 2 1 1 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 6 9 12 11 16 25 10 4 1 0 7 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 6 9 12 8 11 10 25 7 2 1 8 0 0 0 0 0 0 0 0 0 0 0 1 1 3 1 4 6 5 8 6 8 14 7 17 12 5 9 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 11 6 5 10 7 8 10 3 19 9 
Appendix Table 2: Single-Period Empirical Markov Transition Matrix

Residuals from Regression of Price on Store and Week Indicators

(Elements of Table Are Percentages) Relative Price at t

Relative 

Price at t-1 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 

-9 2 0 0 0 2 4 18 22 16 14 6 8 0 4 0 0 6 0 0 0 0 0 0 0 0 0 -8 0 2 0 0 2 5 8 12 18 15 12 7 10 2 2 3 2 0 0 0 0 2 0 0 0 0 -7 0 0 0 2 0 2 2 9 25 19 20 10 2 6 2 1 0 0 0 2 0 0 0 0 0 0 -6 0 0 0 0 1 1 2 5 15 21 20 10 6 6 6 3 2 2 1 0 0 0 0 0 0 0 -5 0 0 0 0 0 0 1 2 3 8 29 26 10 8 5 2 3 2 1 1 0 0 0 0 0 0 -4 0 0 0 0 0 0 0 0 1 4 11 29 26 8 7 3 5 2 1 1 1 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 1 2 9 35 29 9 6 3 2 1 1 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 0 1 2 11 40 29 8 4 2 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 3 13 46 25 5 2 1 1 0 0 0 0 0 0 

0 0 0 0 0 0 0 0 0 0 0 0 1 2 5 18 48 20 4 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 3 7 21 45 16 3 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 1 3 6 10 23 38 13 3 1 1 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 1 3 4 6 11 19 38 12 2 1 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 7 8 11 17 27 13 3 1 0 0 0 5 0 0 0 0 0 0 0 1 0 0 1 1 3 4 8 6 6 8 16 31 10 2 1 0 1 1 6 0 0 0 0 0 0 0 0 0 0 0 2 1 7 3 4 7 6 7 12 12 27 9 0 0 0 7 0 0 0 0 0 0 0 0 1 0 0 2 1 4 8 8 6 9 8 10 6 12 19 2 3 0 8 0 0 0 0 0 0 0 0 0 3 0 0 6 3 6 3 3 3 9 6 12 12 3 9 6 9 9 0 0 0 0 0 3 0 0 0 0 0 3 10 6 10 13 6 13 3 6 0 3 6 0 0 6 
0 .05 .1 .15 .2

Density

-30 -20 -10 0 10 

Residuals

Appendix Figure 1: Frequency Distribution of Residua

from Regression of Weekly Station Prices on Weekly Indic

1997
0 .05 .1 .15 .2

Density

-30 -20 -10 0 10 

Residuals

Appendix Figure 2: Frequency Distribution of Residua

from Regression of Weekly Station Prices on Weekly Indic

1998
0 .05 .1 .15 .2

Density

-30 -20 -10 0 10 

Residuals

Appendix Figure 3: Frequency Distribution of Residua

from Regression of Weekly Station Prices on Weekly Indic

1999