WORKING 

 PAPERS

Edgeworth Price Cycles in Gasoline: 

Evidence from the U.S.

Paul R. Zimmerman

John M. Yun

Christopher T. Taylor

WORKING PAPER NO. 303

June 2010

___________________________________________________________________________

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author to protect the tentative character of these papers.

______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
1

Edgeworth Price Cycles in Gasoline: Evidence from the U.S.* 

 Paul R. Zimmerman† 

U.S. Federal Trade Commission 

John M. Yun 

U.S. Federal Trade Commission 

 Christopher T. Taylor 

U.S. Federal Trade Commission 

Abstract 

Studies of gasoline prices in multiple countries have found a repeated sequence of asymmetric 

cycles where a sharp price increase is followed by gradual decreases. This price pattern is linked 

to Maskin & Tirole’s (1988) theoretical duopoly pricing game that produces a similar pattern, 

Edgeworth price cycles. We examine data on average daily city-level retail gasoline and diesel 

prices for 355 cities in the U.S. from 2001-2007 using multiple methods to identify price cycles. 

We show that a relatively small number of U.S. cities concentrated in a number of contiguous 

upper Midwestern states evidence Edgeworth cycle-like pricing behavior. Within our data set 

cities tend to either cycle in all years or they do not cycle at all. We examine prices in cycling and 

non-cycling cites controlling for other factors and find consumers are no worse off, and likely 

better off, on average, in cycling than non-cycling cities. Finally, unlike previous studies, we find 

that some vertically integrated (branded) retail gasoline stations are themselves potentially 

important drivers of the scale and scope of cycling in retail gasoline prices. 

JEL Codes: D4, L44, L81 

Key Words: Retailing, Petroleum industry, Pricing, Gasoline, Dynamic oligopoly, Edgeworth 

price cycles 

June 24, 2010 

* The views expressed in this article are those of the authors and do not necessarily reflect those of the 

Federal Trade Commission. Comments by Matthew Chesnes, Steven Tenn, participants at the 2008 

International Industrial Organization Conference, and excellent research assistance by Elisabeth Murphy 

and Anne Miles are appreciated. 

† Contact author, 600 Pennsylvania Avenue NW, M-8059, Washington DC, 20580. Phone: (202) 326-3159. 

E-mail: pzimmerman@ftc.gov. 
2

1 Introduction

A number of recent studies have found a repeating asymmetric, cyclical pattern in retail 

gasoline prices which can be described as a sharp and relatively large price increase followed by 

smaller and more gradual price decreases.1

 This type of pricing pattern corresponds with that 

predicted by Maskin & Tirole (1988) in their theoretical Edgeworth (price) cycle model. Their 

model examines a sequential pricing game between two firms selling a homogenous good. A 

large price increase, or “restoration,” by one firm is followed by the other firm with subsequent 

decreases, or “cheating,” until the price is close to marginal cost and there is another restoration. 

This model implicitly suggests some form of price leadership and tacit collusion. 

 In the recent literature, Edgeworth cycles are typically identified in one of two ways: 

either through (1) “casual empiricism,” i.e., eyeballing the data; or (2) a replicable statistical 

measure. Many of these statistical measures essentially parameterize some portion of the eyeball 

test, e.g., a description of the median price change or the number of consecutive periods with 

price decreases relative to consecutive increases. A few papers, including Noel (2007a, 2007b) 

and Eckert (2002), use a Markov switching model to examine the probability of regime changes, 

e.g., whether the probability of staying in the price decrease regime is greater or less than the 

probability of staying in the price increase regime. 

One issue in the literature is the competing methods for identifying price cycles and 

whether the methods lead to the same conclusions. We use multiple parameterizations of the 

eyeball test as well as a Markov switching model to identify price cycling. These methods 

generally lead to the same results. 

 A second issue in the cycling literature is how widespread and persistent price cycling is 

in the U.S.1

 We examine retail pricing data for 355 cities in the U.S. using daily prices for over a 

six year period from 2001-2007. Recent studies examining cycling in U.S. cities use significantly 

 

1

 For studies of Edgeworth cycles in gasoline using Canadian data see Eckert (2002), Eckert (2003), Eckert 

& West (2004a, 2004b), Noel (2007a, 2007b), Atkinson (2009), for studies using Australian data see Wang 

(2007, 2009). 
3

less data.2

 We show that a relatively small number of U.S. cities evidence Edgeworth cycle-like 

pricing behavior. Our results confirm that cycling cities are concentrated in a number of 

contiguous upper Midwestern states: Michigan, Ohio, Indiana, Illinois, Kentucky, and Missouri. 

We also find that cities tend to either be cycling or not. In other words, within our data set cities 

tend to either cycle in all years or they do not cycle at all. 

 The third and largest issue in the cycling literature is what causes cycling. The causes of 

cycling are generally examined indirectly by examining attributes of cycling cities either on their 

own or in relation to attributes of non-cycling cities. Recent research on U.S. cities has examined 

factors such as the concentration of independents (Lewis, 2009a), concentration of independents 

with convenience stores and number of major brands (Doyle et al., 2010), and possible price 

leadership by independents (Speedway and QuikTrip) in the Midwest (Lewis, 2009b). Using data 

on ownership concentration, our results suggest that higher concentration of company-ownedand-operated cites is correlated with more cycling. 

 A related issue that has only been touched upon in recent work is whether cycling is 

ultimately harmful to consumers. In the research concerning Australia and Canada, cycling has 

been in a number of cases the outcome of explicit collusion.3

 In papers examining cycling in the 

U.S., there have been suggestions that cycling is the outcome of price leadership (Lewis, 2009b), 

which would suggest a lack of competition. Doyle et al. (2010) find that cycling tends to occur in 

markets with mid-level concentration and that cycling cities may have no different prices than 

non-cycling cities. We examine prices in cycling and non-cycling cites controlling for other 

factors and find consumers are no worse off, and likely better off, on average, in cycling than 

non-cycling cities. This is a unique finding and is inconsistent with cycles in the U.S. arising from 

 

2

 Doyle et al. (2010) examine one year of data for 115 metropolitan areas. Lewis (2009a) examines 85 

cities over 18 months and Lewis (2009b) examines data for 280 cities for somewhat less than 4 years but 

uses a 3 day moving average of retail prices. 3

 For papers finding Edgeworth cycles resulting from explicit collusion, see Wang (2008, 2009), and 

Erutku & Hildebrand (2010). 
4

tacit collusion unless non-cycling cities are either less competitive or have significantly different 

costs. 

 The next section of the paper describes previous papers examining Edgeworth cycles in 

gasoline. The third section of the paper reviews the data used in this study. The fourth section 

details our price cycling identification strategies and discusses the results. The fifth section 

examines possible causes of cycling and possible consumer effects. The sixth section of the paper 

presents conclusions and recommendations. 

2 Literature review 

Most prior studies examining Edgeworth cycles in retail gasoline prices have looked at 

Canadian or Australian data, and in a number of cases cycling is associated with either suggested 

or confirmed tacit or explicit collusion. Erutku & Hildebrand (2010) examine cartel behavior in 

Quebec. The gasoline pricing pattern observed in these multiple cities and towns in Quebec had 

large increases followed by slow price declines. The collusion was explicit (phone calls to set 

price) during the price increase portion of the cycle but tacit (no communication) during the 

decreasing portion of the cycle. Similar to the Canadian episode(s), Wang (2008) describes 

similar cycling and collusion in Ballarat, Australia, in 1999-2000. Using pricing information 

along with evidence presented at trial, Wang finds that the price cycling pattern was a result of 

collusion by gas stations. Wang (2007, 2009) examines gasoline prices in Perth, Australia, and 

also detects price cycles. These cycles seem to be the outcome of a regulation that requires each 

station to report tomorrow’s price to the government today and not deviate from the reported 

price. Wang concludes that his results highlight the importance of price commitment in tacit 

collusion. 

Other authors have examined Canadian data and found price cycles in at least some of the 

cities examined, but have not linked cycling explicitly to a lack of competition. Noel (2007b) 

finds that cycling behavior is more prevalent in cities that have relatively more small firms. 
5

Eckert (2003) makes a similar observation. Noel (2007a) finds that in Toronto price increases 

tend to be led by the larger firms and price decreases tend to be led by smaller firms. Eckert 

(2002) shows that the cycles may be caused by asymmetric pass through of wholesale cost 

shocks. Atkinson (2009) examines prices in Guelph, Ontario, and finds very distinct, recurring 

price cycles. All these papers generally examine one or two cities, with the exception of Eckert 

(2003), who looks at 19 Canadian cities. 

 In terms of evidence of price cycling in U.S. cities, Allvine & Patterson (1974) describe a 

“yo-yo pattern” (p. 243) in prices for a number of mostly western U.S. cities at various intervals 

between 1971-1973. The cycles in each city end sometime in 1972 or 1973, which coincided with 

the lead up to the 1973 oil shortage. Castanias & Johnson (1993) present some summary statistics 

on price cycles in Los Angeles between 1968-1975 which show a similar pattern. Thus, cycling is 

not a recent phenomenon. 

 With more recent U.S. price data, Lewis (2009a) examines the price reaction of cycling 

and non-cycling cities to the 2005 hurricanes. Using 18 months of data from 2004-2005 covering 

85 cities in the Eastern half of the U.S., he finds that price cycling cities are concentrated in the 

Midwestern U.S. and tend to be associated with higher concentrations of independent gas 

stations. He also finds that cost changes are passed through more quickly in cities where retail 

gasoline prices follow an Edgeworth price cycle pattern and no difference in the average retail 

markup (based on unbranded rack prices) in cycling and non-cycling cities. 

Doyle et al. (2010) examine 115 U.S. cities for cycling for a one year period from 2000-

2001. Lewis (2009b) examines 280 U.S. cities for cycling between 2004-2008 using a three day 

moving average for prices. Both of these papers note that price cycling is generally concentrated 

in the Midwest. Doyle et al. focus on concentration of independent gas stations with convenience 

stores and the presence of brands as potential explanations for the prevalence of price cycling. 

Their main finding is the most concentrated and the least concentrated markets are less likely to 

cycle. They also find some evidence that cities with at least two major brands present are more 
6

likely to cycle. Doyle et al. also find no effect on average retail pricing, i.e., prices in cycling 

cities are not higher than in non-cycling cities. Lewis (2009b) suggests that price leadership and 

coordination by independent gas stations with centralized city-wide pricing, Speedway and Quik 

Trip, generates the cycling pattern in many Midwestern cities. He also examines Speedway data 

to show that in a number of cities Speedway tends to lead the price increases. Lewis & Noel 

(forthcoming) examine asymmetric pass through in 90 cities, some cycling and some not, and 

find that cycling cities have quicker pass through of cost changes from wholesale to retail than 

non-cycling cities, which is a similar conclusion to Lewis (2009a). 

3 Data

We have data on daily average regular grade retail gasoline prices for 355 cities from 

October 25, 2001, to December 31, 2007. For 20 select cities we also have daily wholesale (rack) 

prices for branded and unbranded gasoline and diesel fuel. These price data come from the Oil 

Price Information Service (OPIS). OPIS collects data on retail and wholesale prices in a large 

number of cities in the U.S. The retail data are generated from a sample of retail outlets that 

accept fleet/credit cards. In general more than 50 percent of stations in any city are observed on 

any given day. We subtract the gasoline taxes from the retail data. 

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

wholesale or “rack” prices for branded and unbranded gasoline, are observable to researchers.4

 

Variations in wholesale gasoline prices across areas and over time might play a role in explaining 

retail cycling. 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 

 

4

 The wholesale distribution point of gasoline is referred to as the “rack,” which is the point at a terminal 

where trucks obtain gasoline for retail stations. 
7

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 “lesseedealer” stations. These stations are owned by the refiner but are operated by separate entities. 

These stations pay a dealer tank wagon (DTW) price which is determined by the refiner and 

unobservable to the public. In addition, the wholesale price paid by different lessee-dealers 

operating in the same metropolitan area may vary.5

 Thus, at a given time, there may be a number 

of different wholesale prices across stations within the same region and the marginal cost may 

change from branded to unbranded over time. It is, therefore, difficult to control for the various 

types of wholesale prices with the limited observable wholesale prices but for a sample of cities 

where we have rack prices, we examine the possibility the wholesale prices cause retail price 

cycles. 

 In addition, these multiple ownership relationships make examining market structure in 

cycling cities and non-cycling cities more difficult. In order to examine the relationship between 

price cycling and the various market attributes of cycling and non-cycling cities, we purchased 

data from New Image Marketing, Ltd. on brand market shares and ownership structure within the 

brands. We purchased these data for 29 cities (16 cycling and 13 non-cycling) cities. This market 

share and ownership information was gathered by conducting a census of gasoline stations in 

these cities. 

4 Retail gasoline price cycles in U.S. cities 

4.1 Identifying price cycles 

The identification of Edgeworth price cycles begins with reference to the price pattern 

described in Maskin & Tirole (1988), which is a sharp price increase followed by smaller and 

 

5 See Meyer & Fischer (2004) for an extensive discussion of lessee-dealer pricing and zone pricing. 
8

more sustained price decreases, which together form a saw-tooth pattern. In our sample, some 

cities’ gasoline prices have a pattern very similar to the Edgeworth price cycle pattern and some 

do not. For example, in Figure 1, we plot the average daily retail price of gasoline in St. Louis, 

Missouri, and Newark, New Jersey, in 2007. While the two price series have a correlation 

coefficient of 0.95, St. Louis repeatedly exhibits a saw-tooth pattern while Newark has relatively 

smooth price trends. 

Castanias & Johnson (1993), Eckert (2002), Eckert & West (2004a, 2004b), Wang (2005, 

2007, 2008), Noel (2007a, 2007c), and Atkinson (2009), all rely on “casual empiricism”6

 to 

identify cycling cities, i.e., an eyeball test. While this identification method is not based on a 

formal statistical rule, these researchers have identified a number of traits in price patterns that 

suggest an Edgeworth price cycle. 

For instance, Castanias & Johnson (1993) make use of positive and negative “runs” (i.e., 

continuous price changes in the same direction) to describe how Los Angeles gas prices from 

1968-75 followed a saw-tooth pattern. Similarly, Eckert (2002) makes use of runs to describe 

how retail prices in Windsor, Ontario, from 1989-94 followed an asymmetric, cyclical pattern 

while wholesale prices did not. Eckert & West (2004a) make use of the fact that prices that have 

Edgeworth cycles will tend to have negative average first differences and less frequent first 

differences equal to zero. Similarly, Wang (2005) indexes for price rigidity at specific gas stations 

using the average number of days in which a station’s price does not change. Noel (2007a, 2007c) 

uses a Markov switching model to classify prices as either on the upswing portion (i.e., relenting 

phase) or downswing portion (i.e., undercutting phase) of an Edgeworth cycle. 

More recent research has identified cycling cities using either a statistical measure that 

parameterizes some portion of the Edgeworth pattern or estimating transition probabilities. Eckert 

(2003) counts the number of first differences in retail prices that are equal to zero. Cities with a 

relatively low count of zeros are considered price cycle cities. Lewis (2009a, 2009b) uses the 

 

6

 This is the term used by Eckert & West (2004a). 
9

median value of retail price changes to detect price cycles. Cities with a median less than -0.2 

cents (Lewis, 2009a) are considered price cycle cities. Doyle et al. (2010) also use the median 

value of retail price changes but use a more stringent cutoff of -0.5 cents. Finally, Noel (2007b) 

uses a Markov switching model based on transition probabilities to classify a city-period as 

cycling or non-cycling. 

In determining the best approach to identify cycling cities, we focus on two principal 

characteristics of Edgeworth cycles: (i) frequent price decreases relative to increases and (ii) 

smaller price decrease amounts relative to increase amounts. To that end, we use three statistical 

measures to encapsulate these characteristics. First, we average the ratio of days with a price 

decrease to days with a price increase across all the cycles within a city over the sample period, 

i.e., the ratio of down-to-up days, where higher values suggest an Edgeworth pattern.7 Second, we 

average the ratio of the average daily price increase amount to the average daily price decrease 

amount across all the cycles within a city over the sample period, i.e., the ratio of price increasesto-decreases, where a higher (absolute) value suggests an Edgeworth pattern. Third, like Doyle et 

al. (2010) and Lewis (2009a, 2009b), we calculate the median change in the daily price, where 

lower values suggest an Edgeworth pattern. 

In addition to the statistical measures, we use a Markov switching model based on Neftçi 

(1984) where we estimate two transition probabilities: (a) the probability of three continuous days 

of price increases and (b) the probability of three continuous days of price decreases. If (a) < (b) 

and the two probabilities are significantly different, then the city is considered a cycling city 

under the Markov approach.8

 

7

 We define a price cycle as a period when there is a price increase, or increases, followed by either a price 

decrease(s) or no change(s) in price. After observing at least one price decrease, whenever the next price 

increase occurs, then a new cycle begins. 

8 See the Appendix for details on the Markov switching model. 
10

4.2 The extent of retail gasoline price cycles in the U.S. 

In order to use information from all three statistical measures, we first calculated an 

overall rank for each of the 355 cities based on the average rank across the three measures, i.e., 

the ratio of down-to-up days, the ratio of price increases-to-decreases, and the median change in 

the daily price.9

 In Table 1, we list the top 10 percent of the cities in the sample that best conform 

to a price cycle pattern using the overall rank measure. Of these 35 cities, 10 are in Ohio (out of 

15 total Ohio cities in the sample); 8 in Indiana (out of 13); 8 in Michigan (out of 9); 3 in 

Kentucky (out of 7); 2 in Missouri (out of 6); 2 in Illinois (out of 10); 1 in Kansas (out of 4); and 

1 in Minnesota (out of 6). Overall, over a quarter of the cities in the top 10 percent are located in 

Ohio, and almost three-quarters of the cities in the top 10 percent are in Ohio, Indiana, or 

Michigan, all Midwest states. However, it is important to note that not all the cities in the states 

listed in Table 1 are classified as cycling cities. Specifically, the 35 cities in Table 1 represent 

exactly half of the total number of cities in our sample in the states listed in Table 1.10

 Second, we address a question that prior research has been unable to answer given data 

limitations (i.e., sample periods that are less than a year or two): do cities go in and out of price 

cycles? Table 2 takes the overall rank for the 35 cities in Table 1 and also presents the yearly rank 

for each city. This gives us six full years and a partial year (2001). Generally, the rank of the 

cities with regard to a cycling pattern stays relatively the same across the years. For instance, 

Indianapolis, Indiana, is the top cycling city in the overall sample and is in the top 5 each year. 

The other cities in the overall top 6 tend to remain in the yearly top 10 with some exceptions near 

the end of the sample. The overall top 7 through 15 cities tend to remain in the yearly top 25 with 

 

9

 It should be noted that the median price change measure, which is the most prevalent of the three 

measures in the prior literature, is the least correlated with the other measures in terms of city rank. It has a 

correlation coefficient with the ratio of down-to-up days and the ratio of price increases-to-decreases of 

0.73 and 0.49, respectively, for the 35 cities in Table 1. The correlation coefficient between the ratio of 

down-to-up days and the ratio of price increase-to-decrease is 0.86. 

10 Of the other 35 cities (not listed in Table 1) in the eight states, 25 are ranked in the top 25% while 30 are 

in the top 50%. The remaining 5 cities in the bottom 50% of the ranking are generally located on the border 

of non-cycling states or, in the case of Columbia, MO, right in the middle of the state given that Missouri 

borders Illinois and Kansas. The one exception is Topeka, KS, which is close to Kansas City, KS, which is 

ranked in the top 15%. 
11

only a few exceptions. The remaining 20 cities tend to have a slightly higher yearly variance, but 

only marginally so.11 Nonetheless, there are some notable movements in rank. Louisville, 

Kentucky, ranked as low as 28 in 2002 and as high as 2 in 2006. Similarly, Lexington, Kentucky, 

ranked as low as 30 in 2002 and as high as 1 in 2006. Wichita, Kansas, is ranked 27 overall but 

reached as high as 10 in 2006.12 Even given these exceptions, there is arguably a remarkable 

degree of stability in price cycling patterns in these cities. Over the sample period, the annual 

average price of regular gasoline increased from $1.42 to $2.80 per gallon, yet the cities that had 

price cycles in 2001/2002 generally continued to have price cycles in 2007. There are no 

instances where a city went permanently from cycling to non-cycling, and vice versa, in a 

meaningful way. 

 One shortcoming of the above statistical approach is that there is no natural test (beyond 

an arbitrary cutoff value) to classify a city as cycling versus non-cycling. While this fact reflects 

the reality that cycling patterns range from an almost perfect Edgeworth cycle shape to an almost 

completely flat shape, it does not make for tractable analyses. On the other hand, the Markov 

switching model does lend itself to a natural test to determine whether a city is cycling or not. We 

identify a city as cycling if the probability of a negative run is greater than a positive run at the 10 

percent level.13 Figure 2 shows the percentage of cycling cities, identified by the Markov model, 

in each state relative to non-cycling cities. As shown on the map, most cycling cites identified by 

the Markov model are also in the Midwest, with three quarters of the cities in Michigan, Ohio, 

Indiana, and Illinois classified as cycling cities. There are also a high percentage of cycling cities 

 

11 The average standard deviation for the top 15 cities (across all the full years, 2002-2007) is 5.0 while the 

remaining 20 cities have a standard deviation of 6.3. 

12 These three cities, Louisville, KY; Wichita, KS; and Lexington, KY, represent the cities with the most 

variability in year to year rank in Table 2. The explanation for the variability somewhat differs between the 

three cities. For Louisville, KY, all three rank criteria have similar yearly variance. For Wichita, KS, and 

Lexington, KY, the rank criterion based on the ratio of ratio of down-to-up days stands out as the most 

important source of variation. 

13 More conservative tests would be a requirement of statistical significance at the 5 percent or 1 percent 

levels. 
12

in West Virginia and Kentucky. With the exception of West Virginia, these are the same states 

which were identified in Table 1 using the more traditional, statistical approach.14

4.3 Cycling in select cities

In Table 3, we list the 20 cities for which we have wholesale and retail price data and 

characterize each city’s retail price change patterns. Specifically, the first column provides the 

city’s rank relative to the other cities in the larger 355 city data set. The table details the statistical 

characteristics of price cycles for each city over the entire sample period. We define a price cycle 

as a period when there is a price increase, or increases, followed by either a price decrease(s) or 

no change(s) in price. After observing at least one price decrease, whenever the next price 

increase occurs, then a new cycle begins. 

 For example, in Minneapolis(-St. Paul), Minnesota, the average price cycle lasted 8.6 

days where prices increased an average of 2.1 days while prices decreased an average of 6.6 days. 

Thus, days with a price decrease outnumbered days with a price increase by a factor of 3.2. In 

absolute value, the average daily price increase was 3.6 times greater than the average daily price 

decrease. The median price change in Minneapolis was -0.95 cents. The average price, excluding 

all taxes, over the sample period was 160 cents. 

 In contrast, the average price cycle in Seattle(-Bellevue-Everett), Washington, lasted 6.7 

days with approximately an equal number of days with an increase as with a decrease. In absolute 

value, the average price increase was only 1.1 times greater than the average price decrease. The 

median price change was -0.03 cents. The average price, excluding taxes, was 170 cents. 

 The results from Table 3 indicate that retail prices in Minneapolis(-St. Paul), St. Louis, 

Cleveland(-Lorain-Elyria), and Louisville have retail price patterns that are descriptively similar 

to Edgeworth price cycles. Each city has: (1) ratios of down to up days over 2.0; (2) ratios of 

 

14 Using the traditional approach, while outside of the top 10%, 3 of the 6 cities in West Virginia are ranked 

in the top 25%. 
13

average daily price increases to decreases over 3.0 in absolute value; and (3) median daily price 

changes below -0.60 cents. Consequently, all four cities would be considered Edgeworth price 

cycle cities based on the cut-off for median price changes used in previous studies, i.e., Doyle et 

al. (2010) and Lewis (2009b). The next two cities on the list in order of the cycling criteria are 

Detroit and Chicago. These two cities would not be cycle cities under the median first difference 

criteria used by Doyle et al. (2010) but would for Lewis (2009b). 

 We examined these twenty cities out of the 355 cities on which we have retail data 

because we were able to obtain detailed wholesale (rack) prices for these cities. We wanted to 

determine to what extent wholesale prices may be contributing to or causing retail price cycles. 

The last column of Table 3 presents the median unbranded rack price change for each city. In all 

cities the median unbranded rack price change was zero (rounded to two decimal points). The 

median price change for branded wholesale prices was zero as well.15

Using the Markov model to estimate transition probabilities, we see a similar ranking for 

the cycling cities. Table 4 shows the transition probabilities for the 20 select cities for regular and 

premium gasoline prices as well as diesel prices. The top four of the 20 cycling cities shown on 

Table 3, Minneapolis, St. Louis, Cleveland, and Louisville, have the lowest Wald p-values in 

Table 4, meaning the probability of cycling, greater runs of negative price changes, is the highest. 

The next two highest p-values are for Detroit and Chicago. Again, this mirrors the results in Table 

3. An advantage of using the Markov model is the test giving the level of confidence to reject that 

the transition probabilities are the same. 

 The transition probabilities for premium gasoline are very similar to regular gasoline. The 

same six cities show cycling behavior in premium prices. This may not be surprising since many 

 

15 We also investigated whether controlling for wholesale prices in the 20 select cities explained the 

heterogeneous price patterns across the cities. First, we examined margins for both branded and unbranded 

gasoline and found that cities with price cycles also had margins that looked like Edgeworth cycles, which 

suggests that wholesale prices could not explain retail price cycling. Second, we examined the cycling 

patterns of residuals from numerous regressions controlling for various measures of wholesale prices and 

lags of wholesale prices. Again, cities with price cycles also had residuals that looked like Edgeworth 

cycles, although in some cases slightly diminished. 
14

stations move the pricing of the three different octanes of gasoline in tandem. It is interesting, 

however, that retail diesel prices do not cycle in any of the twenty cities and, in general, the 

transition probabilities of three negative or three positives are very similar for these cities. The 

lack of retail diesel price cycles may be due to the fact that diesel sales are a small percentage of 

fuel sales at most gasoline stations and convenience stores.16

5 Explaining the presence of retail gasoline price cycles: station ownership 

characteristics 

 Several recent studies have examined the role that station characteristics (e.g., Doyle et 

al., 2010) or ownership structure (e.g., Noel, 2007b; Lewis, 2009a) play in explaining the 

presence of retail gasoline price cycling. The latter studies focus primarily on the influence that 

“independents,” i.e., gasoline stations (or networks thereof) that are not affiliated with a refiner’s 

brand. In general, these studies find that a larger number or proportion of independent stations in 

a local market correlates with the presence of price cycling and that these players tend to be the 

firms that initiate and “lead down” the market during the undercutting phase of the cycle. 

 While the presence or concentration of independent gasoline stations may be an 

important determinant of gasoline price cycling, it is possible that the concentration of branded 

(or vertically integrated) stations also plays a significant role. In particular, it may be the case that 

although independent stations tend to drive undercutting, integrated stations might largely explain 

the other side of the coin: namely, initiation of the relenting phase. The ability to lead market 

prices upwards after hitting the bottom of a cycle may be a function of being able to set prices 

simultaneously at a large number of stations. 

Refiners set the retail prices posted at their branded retail stations either directly (via their 

company owned and operated stations) or indirectly through their setting of the DTW to lessee-

 

16 The National Association of Convenience Stores (NACS) reports that in 2008 diesel sales were eight 

percent of fuel sales at convenience stores. See

<http://www.nacsonline.com/NACS/News/FactSheets/Motor%20Fuels/Pages/MotorFuelSales.aspx>. 
15

dealers. Higher concentrations (or a larger network) of these types of branded retail stations may 

also be required (i.e., in addition to independent stations) to drive any retail cycling behavior. 

Furthermore, failing to account for the role of branded stations may lead one to overestimate the 

true effect that independent stations exert on explaining the presence of retail price cycling across 

areas. This section explores the relative contributions that independent versus integrated gasoline 

stations play in determining the presence of city-level retail gasoline price cycling. 

 We obtained data on the proportion of city-level retail gasoline sales made through 

stations of various ownership structures from New Image Marketing, Ltd. for 29 metropolitan 

areas (16 cycling and 13 non-cycling).17 The following ownership structures/groups, indexed by 

O , are reflected in these data: (1) branded company owned and operated sites; (2) independent 

and branded jobber sites; and (3) lessee-dealer sites.18 Let f

i O s

( )

, Î (0,1] denote the share of total 

retail gasoline sales made in city i through stations of “flag” (or brand) f = 1,...,F that are 

operated under ownership structure O .

19 Define 

F

f

i O i O

f

HHI s( ) 2 , ,

1

( ) (0,1]

=

= Î å (1) 

as the Herfindahl-Hirschman Index (HHI) of “within-group” (i.e., stations of type O ) retail 

gasoline sales in city i . The possible values of HHIi O, range from a maximum of 1.0 to a 

 

17 It was not possible to obtain the New Image data for the same year for all 29 cities. For 25 of the cities 

the census is from 2000 or 2001 with the remainder in 1999. Since the cities were consistently cycling and 

the brand and ownership shares tend to be stable, we do not see this limitation as problematic. 

18 Separate data for independent and branded jobber sites are not available. 

19 For example, in a given city i we might observe the following combinations of flags and ownership 

structures: 

{; } f = = Shell O company-owned-and-operated (group 1), 

{ ;} f = = Chevron O jobber (group 2), 

{; } f = = Thrifty O independent (group 2), 

{; } f = = Chevron O lessee-dealer (group 3). 
16

minimum based on the specific distribution of the relevant flag shares. The HHIi O, increases 

(approaches one) as the as the number of flags decreases or the disparity in the size between flags 

(holding the number of flags constant) increases. 

 Using the above HHIs we estimate the following cross-sectional probit regression: 

Pr( 1) ( ) Cycle HHI X i O iO i = =F + +G a b åO , , (2) 

where Cyclei is an indicator taking a value of one if (based on the Markov switching model) city 

i is designated as a price cycling city and zero otherwise. The variable F denotes the standard 

normal distribution function, while a denotes the intercept term. By assumption, the regression 

error term under the above framework is , (0,1) ei O  N . The variable Xi denotes a vector of 

city-level Census demographic controls, which include median household income, population 

density, and total population measures, and G denotes a vector of coefficients. The bO are the 

primary coefficients of interest. If bO > 0 , then a higher concentration of within-group sales 

pertaining to ownership structure O is positively correlated with the probability that retail 

gasoline price cycling occurs in city i , all else equal (and vice versa). 

We also examine the natural log of the odds ratio (logistic transform) derived from the pvalues of the city-specific Wald statistics obtained from the Markov switching model (which are 

denoted pWald i, ) as an alternative dependent measure. The regression model in this framework is 

specified as: 

,

, , ,

ln

1

Wald i

O O iO i iO

Wald i

p HHI X

p

ab e

æ ö ç ÷

÷ = + +G + ¢ ç

ç - ÷÷ è ø å , (3) 

where 2 , (0, ) e s i O¢  N I denotes the error term. Equation (3) is estimated via Ordinary Least 

Squares (OLS). This model provides a rough approximation of the “strength” at which a city 

cycles. Specifically, a strongly cycling city is associated with a “small” pWald i, , and as such, if 
17

bO < 0 then a higher concentration of within-group sales pertaining to ownership structure O is 

correlated with a stronger cycling effect. 

 Table 5 presents the results of estimating both the cycling indicator and log odds models. 

Columns (1) and (5) control only for the HHIs pertaining to company-owned-and-operated and 

independent/jobber stations. Columns (2) and (6) then add the HHI corresponding to the lesseedealer stations. These latter results are presented separately since we lose seven observations for 

which data on lessee-dealer stations could not be obtained, and we only have 29 total potential 

observations to begin with. Columns (3) and (7) then add the covariates in Xi to the 

specifications in Columns (1) and (5), respectively, while Columns (4) and (8) do the same for 

Columns (2) and (6), respectively. 

 First consider the cycling indicator regressions in Columns (1)-(4). All of the reported 

Probit coefficient estimates are presented in terms of their marginal effects, with robust 

(heteroskedasticity-consistent) z-statistics in parentheses. The results consistently indicate that a 

an increase in the HHI of within-group sales of refiner company-owned-and-operated stations 

increases the probability of retail gasoline price cycling, and all of the coefficient estimates are 

statistically significant.20 In Columns (1)-(3), a 100-point increase in the HHI implies that an 

increase of approximately 1 to 2 percentage points in the probability that a city exhibits cycling 

behavior, all else equal.21 In Column (4), which represents the most fully specified model, the 

magnitude of the estimated marginal effect falls appreciably. Specifically, a 100-point increase in 

the HHI is predicted to result in a 0.04 percentage point increase in the probability that a city 

cycles. 

 The coefficient estimates pertaining to the HHI of independent and jobber sales are 

consistently and considerably larger in magnitude relative to those for the other ownership 

 

20 Note however, that we cannot reject the hypothesis that the slope coefficients are jointly equal to zero in 

Column (3). As such, due caution is warranted in interpreting those results. 

21 Note that the HHIs used in estimating the regressions presented in Table 5 are defined continuously on 

the unit interval (i.e., the HHIs are scaled by 10,000). 
18

groups; however, the coefficient estimates in Columns (1)-(3) are not statistically significant at 

conventional levels. The coefficient estimate in Column (4), however, is statistically significant at 

the 10 percent level and indicates that a 100-point increase in the independent/jobber HHI 

increases the probability of cycling by 0.3 percentage points. While small, the magnitude of this 

effect is substantially larger than that associated with company-owned-and-operated stations. 

Finally, most of the coefficient estimates on the demographic covariates are not statistically 

significant, the exception being median household income in Column (4). This latter result 

implies that cities with higher incomes will be more likely to exhibit cycling, which is consistent 

with Doyle et al. (2010). 

 The results obtained from estimating equation (3) in Columns (5)-(8) of Table 5 are 

seemingly consistent with those from the cycling indicator regressions. In each case the 

coefficient estimate on the company owned and operated HHI is negative (which, again, implies 

that a one unit increase in the variable is associated with a stronger cycling city) and statistically 

significant. Furthermore, the coefficient estimate on the lessee-dealer HHI is negative and 

statistically significant at the 10 percent level in Column (6) (whereas this variable is always 

insignificant in the cycling indicator regressions). In each individual specification the coefficient 

estimates on the jobber/independent HHIs are comparatively more negative, but never statistically 

significant. 

Treating the results obtained from Columns (4) and (8) as our “preferred” specifications, 

the results imply that the concentration of independents/jobbers within cities tends to explain the 

presence of cycling but not the strength of its effect. The concentration of refiner-affiliated 

company-owned-and-operated stations, which arguably are those for which the upstream refiner 

has greatest control over the downstream retail price, explain both the likelihood of cycling 

(although to a much smaller degree than the concentration of independents/jobbers) as well as the 

strength of the cycling behavior. Thus, unlike previous studies, we find that some vertically 
19

integrated (branded) retail gasoline stations are themselves potentially important drivers of the 

scale and scope of cycling in retail gasoline prices. 

6 Average retail gasoline price differences across cycling and non-cycling cities 

Many of the papers discussing price cycling in Australia and Canada have described or 

suggested either explicit or tacit collusion. The Maskin & Tirole (1998) model is one of dynamic 

oligopoly. Against this backdrop of less than perfect competition, there is the suggestion in Lewis 

(2009a) and Doyle et al. (2010) that prices may be no higher in cycle cities and pass through of 

cost changes may be more rapid in cities with price cycles than those without. We examine yearby-year whether retail prices are on average higher or lower in cycling than non-cycling cities. 

 Using the mean weekly retail prices––averaged over the course of a year––for all 

available OPIS cities, we examine by year whether higher or lower retail prices are associated 

with cycling. We identified a city as cycling using the aforementioned results and cutoff criteria 

of the Markov model. Letting i index cities, the cross-sectional regression model is given by 

P Cycle X i i ii = + +G + ab h , (4)

which is estimated using Feasible Generalized Least Squares (FGLS) and assuming 

heteroskedasticity in the error structure of cities located within the same state. The variables a

and hi are the constant and error terms, respectively; all other variables represent coefficients. 

The results of estimating two specifications are presented in Table 6 for each year from 

2002 to 2007. The first is a baseline specification that only controls for whether the city is 

identified as cycling (through the cycling indicator Cyclei ). The second specification adds 

several key demographic variables—represented by the vectorXi in equation (4)––which have 

been shown in the literature to be correlated with gasoline price levels (including those 

considered in Table 6). 
20

We find that without controlling for demographic variables cycle cities have lower prices 

relative to non-cycling cities in each of the six years in the data, with all of the cycle indicator 

coefficients being statistically significant at the 1 percent level. The magnitude of the cycling 

effect in the baseline specifications ranges from -1.1 to -8.1 cents per gallon. When controlling 

for the key demographic variables, we find negative and statistically significant price effects of 

being in a cycling city for four of the six years. In two other years the cycling indicator is 

negative and statistically insignificant. Only in 2002 is the cycling indicator coefficient positive, 

but it is not statistically significant in this case. And while there is some change on the 

coefficients on the demographic variables from year to year, they are generally of the same order 

of magnitude and significance across the six regressions. 

Controlling for the demographic variables tends to reduce the size of the cycling 

coefficients (i.e., move them in the positive direction). In the full specifications, the magnitude of 

the statistically significant cycling coefficients ranges from -1.0 to -5.1 cents per gallon, with an 

average effect of -2.9 cents per gallon. In order to gauge the economic significance of the latter 

estimate, consider the NACS report that: 

In 2006, a gasoline retailer’s average gross margin (before expenses) was 13.9 cents per 

gallon . . . . After expenses, typical net profits are per gallon are a few cents per gallon, at 

most . . . NACS estimates that the average retailer had a net pretax profit of between one 

and two cents [per gallon] in 2007.22 

Thus, a -2.9 cents a gallon retail price difference could translate into gross retail margins that 

were approximately 21 percent lower relative to non-cycling cities if wholesale costs and 

volumes are similar across cycling and non-cycling cities. 

 We conclude that the average price in a cycle city is not higher and, if anything, likely 

lower than in a non-cycling city. This result seems somewhat counterintuitive since Edgeworth 

price cycles are presumed to arise from an oligopolistic pricing game that others in the literature 

 

22 See 

<http://www.nacsonline.com/NACS/Resources/campaigns/GasPrices_2008/Pages/HowToGetGas.aspx>. 
21

have linked to tacit collusion.23 The results suggest that non-cycling markets may be relatively 

“less competitive” on average compared to cycling cities. The results also raise the question of 

why firms would continue to price in cycling patterns, or remain stuck in that equilibrium, given 

presumably higher prices in non-cycling cities. The answers to these questions are left for future 

research. 

7 Concluding remarks 

Our comprehensive analysis of retail price data from across the U.S. leads to the clear 

conclusion that retail price cycling is confined to the upper Midwest, mainly a five state region. 

While others in the literature have found gasoline price cycles in the Midwest, we examined a 

larger number of cities using multiple criteria to identify cycling. In addition we examined 

premium gasoline and diesel prices and found that premium prices cycled in the same cities as 

regular gasoline but diesel prices did not cycle. We also found, using 6 years of data that cities 

generally either cycle or they do not. We found no evidence in our data set of cities having 

periodic gasoline price cycles. 

We used a number of criteria for classifying a city has having cyclical retail pricing. All 

the criteria generally lead to the same conclusion, with a few notable caveats. The median price 

difference criteria can lead to meaningfully different conclusions with slightly different levels for 

the threshold value. The Markov model gives a clearer cut off for classifying cycling and noncycling cities. 

 With respect to the causes and consequences of gasoline price cycles, we find evidence 

that concentration of both independent/jobbers and branded refiner affiliated company-ownedand-operated stations are potentially important determinants of gasoline price cycles. More 

importantly, we find that cycling cites on average have no higher and in some cases lower retail 

prices. While additional research may lead to a more robust conclusion on this point, the current 

 

23 Erutku & Hildebrand(2010) and Wang(2008)
22

finding is disconnected from the dynamic model which is suggestive of tacit collusion and the 

literature examining tacit or explicit collusion in Canada and Australia. The puzzle of why price 

cycles exist if prices are no higher and seem to be lower in cycling cities is a topic for further 

research as well. 
23

References 

Allvine, Fred C. and James M. Patterson (1974), Highway Robbery, An Analysis of the Gasoline 

Crisis (Indiana University Press), Chapter 8 & Appendix. 

Atkinson, Benjamin (2009), “Retail Gasoline Price Cycles: Evidence from Guelph, Ontario Using 

Bi-Hourly, Station-Specific Retail Price Data,” Energy Journal 30: 85-109. 

Billingsley, Patrick (1961), Statistical Inference for Markov Processes (Chicago University 

Press). 

Castanias, Rick and Herb Johnson (1993), “Gas Wars: Retail Gasoline Price Fluctuations,” 

Review of Economics and Statistics 75: 171-74. 

Doyle, Joseph, Erich Muehlegger, and Krislert Samphantharak (2010), “Edgeworth Cycles 

Revisited,” Energy Economics 32: 651-60. 

Eckert, Andrew (2002), “Retail Price Cycles and Response Asymmetry,” Canadian Journal of 

Economics 35: 52-77. 

Eckert, Andrew (2003), “Retail Price Cycles and the Presence of Small Firms,” International 

Journal of Industrial Organization 21: 151-70. 

Eckert, Andrew and Douglas S. West (2004a), “A Tale of Two Cities: Price Uniformity and Price 

Volatility in Gasoline Retailing,” Annals of Regional Science 38: 25-46. 

Eckert, Andrew and Douglas S. West (2004b), “Retail Gasoline Price Cycles Across Spatially 

Dispersed Gasoline Stations,” Journal of Law and Economics 47: 245-73. 

Erutku, C. and V. A. Hildebrand (2010), “Conspiracy at the Pump,” Journal of Law and 

Economics 53, forthcoming. 

Falk, Barry (1986), “Further Evidence on the Asymmetric Behavior of Economic Time Series 

Over the Business Cycle,” Journal of Political Economy 5: 1096-1109. 

Fisher, R. A. (1935), Statistical Methods for Research Workers, 5th Edition, (Oliver and Boyd). 

Lewis, Matthew (2009a), “Temporary Wholesale Gasoline Price Spikes have Long-lasting Retail 

Effects: The Aftermath of Hurricane Rita,” Journal of Law and Economics 52: 581-605. 

Lewis, Matthew (2009b), “Price Leadership and Coordination in Retail Gasoline Markets with 

Price Cycles,” working paper. 

Lewis, Matthew and Michael Noel (forthcoming), “The Speed of Gasoline Price Response in 

Markets with and without Edgeworth Cycles,” Review of Economics and Statistics. 

Maskin, Eric and Jean Tirole (1988), “A Theory of Dynamic Oligopoly, II: Price Competition, 

Kinked Demand Curves, and Edgeworth Cycles,” Econometrica 56: 571-99. 
24

McQueen, Grant and Steven Thorley (1991), “Are Stock Returns Predictable? A Test Using 

Markov Chains,” Journal of Finance 46: 239-63. 

Meyer, David W. and Jeffrey H. Fischer (2004), “The Economics of Price Zones and Territorial 

Restrictions in Gasoline Marketing,” FTC Bureau of Economics Working Paper No. 271. 

Neftçi, Salih N. (1984), “Are Economic Time Series Asymmetric Over the Business Cycle?,” 

Journal of Political Economy 2: 307-28. 

Noel, Michael D. (2007a), “Edgeworth Price Cycles: Evidence from the Toronto Retail Gasoline 

Market,” Journal of Industrial Economics 55: 69-92. 

Noel, Michael D. (2007b), “Edgeworth Price Cycles, Cost-Based Pricing, and Sticky Pricing in 

Retail Gasoline Markets,” Review of Economics and Statistics 89: 324-34. 

Noel, Michael D. (2007c), “Do Gasoline Prices Respond Asymmetrically to Cost Shocks? The 

Confounding Effects of Edgeworth Cycles,” working paper. 

Sichel, Daniel E. (1989), “Are Business Cycles Asymmetric? A Correction,” Journal of Political 

Economy 5: 1255-1260. 

Rothman, Phillip (2003), “Reconsideration of the Markov Chain Evidence on Unemployment 

Rate Asymmetry,” Department of Economics, East Carolina University, working paper. 

Wang, Zhongmin (2007), “Station Level Gasoline Demand in a Market with Price Cycles,” 

working paper, July 2007. 

Wang, Zhongmin (2008), “Collusive Communication and Pricing Coordination in a Retail 

Gasoline Market,” Review of Industrial Organization 32: 35-52. 

Wang, Zhongmin (2009), “(Mixed) Strategy, Timing and Oligopoly Pricing: Evidence from a 

Repeated Game in a Timing-Controlled Gasoline Market,” Journal of Political Economy 117: 

987-1030. 
25

Appendix: A Markov-switching model for identifying Edgeworth price cycles 

We employ a Markov switching model based upon Neftçi (1984). Let ( ) pt

 denote the 

retail price in a given city during week t for  = { , ,} regular premium diesel , which over time 

is assumed to follow a mean-zero linearly regular stationary process. Define { }t I as a secondorder (“two-state”) Markov switching process such that 

( )

( )

1 if 0

1 if 0,

t t

t

t t

p

I

p

ìï

ï+ D>

= ï

í

ï

ï- D£ ïî



 (5) 

where Dt denotes the first-difference operator.24 The associated transition probabilities, denoted 

lij for i j , {0,1} = , are given by 

11 1 2

00 1 2

10 1 2

01 1 2

Pr( 1 | 1, 1)

Pr( 1 | 1, 1)

Pr( 1 | 1, 1)

Pr( 1 | 1, 1)

tt t

tt t

tt t

tt t

II I

II I

II I

II I

l

l

l

l

- -

- -

- -

- -

= =+ =+ =+ üï

ï

ï

ï

ï

ï

ï

ï = =- =- =- ï

ï

ï

ïï

ý

ï

ï

= =+ =+ =- ï

ï

ï

ï

ï

ï

ï

ï

= =- =- =+ ï

ïïþ

. (6) 

If a city’s retail or wholesale gasoline price series exhibits sharp increases and gradual decreases 

as suggested by the Maskin & Tirole (1988) model of Edgeworth cycles, then { }t I remains in 

state -1 longer than it remains in state +1. In this case, the retail price cycle is said to be 

asymmetric and would imply 00 11 l l > . If, on the other hand, the series is symmetric over the 

cycle then 00 11 l l = . 

 Our objective is to obtain estimates of the transition probabilities given in Eq. (6). Let sT

denote a realization of { }tI . The log-likelihood function is then given by 

( ) 11 00 10 01 0 0 11 11 11 11

00 00 00 00

10 10 10 10

01 01 01 01

, , , , , ln ln ln(1 )

ln ln(1 )

ln ln(1 )

ln ln(1 ).

L sT llllp p f l y l

fl y l

fl y l

fl y l

=+ + -

+ +-

+ +-

+ +-

 (7) 

The variable p0 denotes the initial condition (i.e., the probability of observing the initial two 

states), while the variables 11 01 f y , ,  represent the number of observed occurrences of the 

respective transitions throughout the sample period. 

 

24 As noted by Neftçi (1984, p. 314), an advantage of this procedure is that it can handle nonstationarity in 

the underlying data (i.e., pt ) given that the implied t I will often be plausibly stationary even when the 

former is not. 
26

Neftçi argues that it is necessary to estimate p0 when the number of observations 

contained in the relevant time series is small and when the initial state may contain useful 

information on the transition probabilities (e.g., when the process t I does not in fact start at 

t = 1 , which is usually the case). Neftçi’s paper develops a methodology for deriving the 

limiting probabilities of the initial conditions in terms of the transition probabilities.25 If, 

however, the number of observations available in the sample is relatively large (i.e., in an 

asymptotic sense) the initial state may be treated as a nuisance parameter (Billingsley, 1961). 

Since the number of daily city-specific price observations available in our dataset covers over a 

six year period (2001-2007), ignoring the influence of the initial condition is likely to be 

reasonable.26 With p0 = 0 , the maximum likelihood estimates (MLEs) of the four unknown 

parameters 00 11 10 01 L = [,,, ] llll ¢ are obtained by setting the four score equations of the loglikelihood function equal to zero and solving the parameters in terms of the transition counts.27

The general form of the score equations is given by 

0. 1

ij ij

ij ij ij

L f y

ll l

¶ =- = ¶ - (8) 

Solving Eq. (8) in terms of lij gives 

1

(1 )

( )

ˆ

ij ij

ij ij

ij ij ij ij

ij ij ij ij

ij

ij ij

ij ij

f y

l l

f l yl

lf y f

f l l f y

üï

ï = ï

ï - ïï

ï

ï

ï

ï

ï

 -= ï

ï

ï

ï

ý

ï

ï

 += ï

ï

ï

ï

ï

ï

ï

ï

ï

= = ï

ï

+ ï

ïþ

 (9) 

where ˆ

lij denotes the (approximate) MLE of lij . The asymptotic variance of ˆlij is given by28 

2 ˆ ˆ (1 ) ˆ( ) ij ij

ij

ij ij

l l s l f y- = + . (10) 

 

25 See Neftçi (1984, pp. 326-327). 26 Several studies that have relied upon a substantially smaller number of observations than are employed 

herein have demonstrated that estimating the initial condition along with the transition probabilities does 

not materially affect the magnitude of the latter when they are estimated alone. See, e.g., Falk (1986) and 

McQueen & Thorley (1991). Further, a particular advantage of treating 0 p as a nuisance parameter comes 

from the considerable reduction in the computation burden of estimating the transition probabilities 

(Rothman, 2003). Specifically, ignoring the initial state variables does not require using nonlinear 

numerical methods to approximate the maximum of the log-likelihood function. Rather, as demonstrated 

below, closed-form analytical solutions for the maximum likelihood estimators are easily obtained. 

27 McQueen and Thorley (1991, p. 243). 

28 See id., note 5.
27

Testing for the presence of Edgeworth price cycles (asymmetry) in gasoline prices involves 

testing the null hypothesis 0 00 11 H : l l = against the (two-sided) alternative 1 00 11 H : l l 1 . 

Hypothesis Testing 

Neftçi demonstrates how the test for asymmetry can be evaluated by using the estimate of 

the transition probabilities to construct a confidence region (ellipsoid), the center of which 

corresponds to the MLEs of l11 and l00 . All points within the confidence ellipsoid represent the 

true value of the latter estimate for a given confidence level.29 However, Sichel (1989) 

demonstrates that this procedure “has low power and is sensitive to noise” (p. 1259). Specifically, 

he shows that Neftçi’s test may fail to identify asymmetry that is actually present, and instead 

applies an asymptotic t-test that appears to give higher power. 

McQueen & Thorley (1991) test the symmetry hypothesis in their data by considering 

asymptotic Lagrange Multiplier, Likelihood Ratio, and Wald tests (all of which are approximately 

equal for large sample sizes). They note that: “The choice of test statistics is normally a matter of 

computational convenience” (p. 256). Again, the length of our time series data suggests that we 

can rely upon the direct analytical solutions for the MLEs and (asymptotic) variances of the 

Markov transition probabilities. This fact motivates the use of the Wald test since it uses the 

MLEs and asymptotic variance estimates of the unconstrained log-likelihood function, which 

correspond to the “unrestricted” estimates obtained by appealing to Eqs. (9) and (10). The 

computed value the Wald test under H0 is given by: 

2

00 11 2

1

11 00

ˆ ˆ ( )

ˆ ˆ () () df

l l

c sl sl =

-

-  . (11) 

This test statistics is used to determine whether there is a statistically significant Edgeworth price 

cycling effect within a given city over the sample period. 

 

29 See Neftçi (1984, pp. 315-318) for the formula used to construct the confidence ellipsoid and further 

discussion of this test. 
Figure 1 

Regular Unleaded Retail Prices for St. Louis, MO, and Newark, NJ (1/2007 – 12/2007

140160180200220240260280300

1/1/2007 1/15/2007 1/29/2007 2/12/2007 2/26/2007 3/12/2007 3/26/2007 4/9/2007 4/23/2007 5/7/2007 5/21/2007 6/4/2007 6/18/2007 7/2/2007 7/16/2007 7/30/2007 8/13/2007 8/27/2007 9/10/2007 9/24/2007 10/8/2007 10/22/2007 11/5/2007 11/19/2007 12/3/

Day

Cents

St. Louis, MO Newark, NJ
TABLE 1

TOP 10 PERCENT OF THE 355 CITIES IN TERMS OF CONFORMITY TO EDGEWORTH PRICE CYCLE PATTERN

 Rank by Criteria 

 

City Syate

Overall 

Rank 

Avg. 

Rank 

Across 

Criteria 

Ratio of 

Down to 

Up Days 

Ratio of 

Avg. Price 

Increase to 

Decrease 

Median Price 

Change 

Indianapolis IN 1 3.0 1 2 6 

Dayton-Springfield OH 2 3.3 4 5 1 

Columbus OH 3 5.7 6 9 2 

Toledo OH 4 5.7 8 6 3 

Cincinnati OH 5 6.0 7 7 4 

Minneapolis-St. Paul MN 6 6.7 3 3 14 

Saginaw-Bay City-Midland MI 7 9.0 5 12 10 

St. Louis MO 8 9.7 2 1 26 

Akron OH 9 10.7 11 4 17 

Lansing-East Lansing MI 10 11.3 10 17 7 

Grand Rapids-Muskegon-Holland MI 11 11.3 12 10 12 

Flint MI 12 12.7 13 16 9 

Cleveland-Lorain-Elyria OH 13 13.3 16 11 13 

Louisville KY 14 13.3 9 13 18 

Canton-Massillon OH 15 13.7 14 19 8 

Lexington KY 16 15.3 15 20 11 

Hamilton-Middletown OH 17 17.0 23 23 5 

Kalamazoo-Battle Creek MI 18 18.0 18 14 22 

Gary IN 19 18.3 19 8 28 

Fort Wayne IN 20 19.3 20 15 23 

Muncie IN 21 20.7 21 25 16 

South Bend IN 22 21.0 17 21 25 

Springfield IL 23 23.3 24 26 20 

Mansfield OH 24 24.0 26 27 19 

Elkhart-Goshen IN 25 24.7 25 28 21 

Lima OH 26 25.7 30 32 15 

Wichita KS 27 27.3 22 18 42 

Jackson MI 28 28.7 27 35 24 

Cincinnati KY 29 29.7 29 33 27 

Lafayette IN 30 31.0 28 36 29 

Bloomington-Normal IL 31 34.0 33 39 30 

Kansas City MO 32 35.0 31 24 50 

Ann Arbor MI 33 35.3 34 34 38 

Kokomo IN 34 35.7 32 43 32 

Detroit MI 35 37.3 41 22 49 
Texas

Iowa

Kansas

New Mexico

Illinois

Ohio

Missouri

Minnesota

Indiana

Michigan

Kentucky

West

Virginia

0

4

125 250 500 Miles

No cycle cities

Fewer than 25%

26% - 33%

34% - 50%

51% - 75%

Greater than 75%

Figure 2: Percent of Cycle Cities by State
 

TABLE 2 

TOP 10 PERCENT OF THE CITIES IN TERMS OF CONFORMITY TO THE

EDGEWORTH PRICE CYCLE PATTERN BY YEAR

 Annual Rankings 

 

City State

Overall 

Rank 2001 2002 2003 2004 2005 2006 2007 

Indianapolis IN 1 2 1 3 3 1 5 1 

Dayton-Springfield OH 2 19 5 1 1 7 3 12 

Columbus OH 3 7 2 4 4 12 8 5 

Toledo OH 4 3 3 2 6 4 19 16 

Cincinnati OH 5 8 7 10 2 6 9 7 

Minneapolis-St. Paul MN 6 1 8 5 10 9 7 6 

Saginaw-Bay City-Midland MI 7 4 9 14 14 8 4 8 

St. Louis MO 8 11 13 8 21 3 12 11 

Akron OH 9 16 19 16 5 17 11 9 

Lansing-East Lansing MI 10 5 10 15 11 11 6 2 

Grand Rapids-Muskegon-Holland MI 11 18 22 7 7 2 14 3 

Flint MI 12 6 6 9 13 13 16 22 

Cleveland-Lorain-Elyria OH 13 25 11 11 9 15 20 17 

Louisville KY 14 13 28 6 26 5 2 4 

Canton-Massillon OH 15 23 12 12 8 18 22 15 

Lexington KY 16 15 30 13 18 16 1 13 

Hamilton-Middletown OH 17 21 26 20 17 19 13 14 

Kalamazoo-Battle Creek MI 18 10 18 17 20 10 21 20 

Gary IN 19 9 24 23 12 14 15 18 

Fort Wayne IN 20 14 4 19 22 23 24 21 

Muncie IN 21 37 29 26 16 27 17 19 

South Bend IN 22 20 15 27 23 20 18 10 

Springfield IL 23 17 17 21 27 31 25 24 

Mansfield OH 24 31 21 24 15 28 26 33 

Elkhart-Goshen IN 25 36 16 25 24 24 27 23 

Lima OH 26 40 27 18 28 36 28 30 

Wichita KS 27 29 41 31 19 29 10 25 

Jackson MI 28 22 14 28 25 30 41 32 

Cincinnati KY 29 129 36 22 29 21 29 40 

Lafayette IN 30 44 25 29 30 33 35 27 

Bloomington-Normal IL 31 30 31 35 32 43 37 34 

Kansas City MO 32 33 37 38 33 35 23 49 

Ann Arbor MI 33 41 35 32 34 37 31 45 

Kokomo IN 34 96 39 40 31 41 47 31 

Detroit MI 35 24 38 34 36 39 34 57 

 

 = Indicates a ranking of 10 or lower 
TABLE 3

RETAIL PRICE CYCLE STATISTICS – 20 SELECT CITIES

       Avg. Cycle Characteristics Price Change   Levels (cents) Wholesale

                            

355

Rank City State    

Cycle

Length

Up

Days

Down

Days

Ratio

Down

to Up

Days

Ratio Avg.

Price Incr.

to Decr. Median

St.

Dev    Mean

St.

Dev

Unbranded

Rack

Median

Price Ch.

6 Minneapolis‐St. Paul MN    8.6 2.1 6.6 3.2  ‐3.6  ‐0.95 3.15    160 56 0.00

8 St. Louis MO    10.4 2.4 8.0 3.3  ‐4.0  ‐0.68 2.99    157 56 0.00

13 Cleveland‐Lorain‐Elyria OH    7.8 2.0 5.8 2.9  ‐3.4  ‐0.96 3.07    156 55 0.00

14 Louisville KY    8.3 2.1 6.3 3.1  ‐3.3  ‐0.83 3.39    163 58 0.00

35 Detroit MI    8.2 2.9 5.3 1.8  ‐2.7  ‐0.29 1.79    155 56 0.00

42 Chicago IL    7.2 2.5 4.6 1.8  ‐2.4  ‐0.27 1.38    163 57 0.00

63 Denver CO    7.9 3.1 4.7 1.5  ‐1.5  ‐0.13 1.10    159 59 0.00

65 Atlanta GA    9.6 4.1 5.5 1.3  ‐1.8  ‐0.10 1.57    155 59 0.00

70 Los Angeles‐Long Beach CA    9.8 4.1 5.6 1.4  ‐1.5  ‐0.11 0.97    174 57 0.00

95 Houston TX    9.0 4.1 4.9 1.2  ‐1.6  ‐0.05 1.00    155 58 0.00

110 Phoenix‐Mesa AZ    8.7 3.9 4.7 1.2  ‐1.2  ‐0.07 1.04    170 56 0.00

115 Dallas TX    7.3 3.4 3.9 1.1  ‐1.4  ‐0.04 1.04    157 57 0.00

119 New Orleans LA    5.6 2.6 3.0 1.2  ‐1.3  ‐0.05 1.03    157 58 0.00

145 San Francisco CA    6.0 2.7 3.2 1.2  ‐1.1  ‐0.06 0.99    184 54 0.00

146 Boston MA    5.9 2.8 3.0 1.1  ‐1.4  ‐0.03 1.11    163 56 0.00

177 Salt Lake City‐Ogden UT    5.9 2.7 3.1 1.1  ‐1.1  ‐0.05 0.93    158 57 0.00

178 Fairfax VA    5.9 2.8 3.0 1.1  ‐1.2  ‐0.02 1.19    160 57 0.00

208 Newark NJ    5.3 2.6 2.7 1.0  ‐1.1  ‐0.01 1.08    165 57 0.00

219 Miami FL    5.8 2.8 3.0 1.1  ‐1.1  ‐0.02 0.88    159 58 0.00

250 Seattle‐Bellevue‐Everett WA    6.7 3.2 3.5 1.1  ‐1.0  ‐0.03 0.88    170 57 0.00

 Notes: All figures correspond to retail prices for regular-grade gasoline. 
TABLE 4 

ESTIMATED MARKOV TRANSITION PROBABILITIES – 20 SELECT CITIES

 Regular Gasoline Premium Gasoline Diesel 

MLE Wald test MLE Wald test MLE 

 

City l00 l11 p-value l00 l11 p-value l00 l11

 

Atlanta 0.8408 0.7997 0.5120 0.7407 0.6886 0.4129 0.6059 0.6490 

Boston 0.7097 0.7253 – 0.4887 0.5519 – 0.4632 0.5649 

Chicago 0.8010 0.6013 0.0557 0.7204 0.5242 0.0722 0.5157 0.5806 

Cleveland 0.8136 0.1966 0.0000 0.7712 0.2227 0.0000 0.4617 0.4974 

Dallas 0.7981 0.8090 – 0.5621 0.5963 – 0.5609 0.6535 

Denver 0.8432 0.7976 0.5441 0.5832 0.6020 – 0.5659 0.6172 

Detroit 0.8273 0.6245 0.0483 0.7598 0.4396 0.0162 0.5643 0.5811 

Fairfax 0.7093 0.7707 – 0.4386 0.5375 – 0.4135 0.4603 

Houston 0.8643 0.8314 0.5336 0.5568 0.6169 – 0.5676 0.6722 

Los Angeles 0.8758 0.8490 0.6593 0.6151 0.6776 – 0.5710 0.6003 

Louisville 0.8433 0.3066 0.0001 0.7779 0.3162 0.0002 0.4312 0.5063 

Miami 0.7260 0.7550 – 0.4583 0.5356 – 0.4414 0.4864 

Minneapolis 0.8416 0.1655 0.0000 0.8036 0.3043 0.0019 0.5897 0.5882 

New Orleans 0.7312 0.7206 0.8346 0.4161 0.4861 – 0.4751 0.5434 

Newark 0.7256 0.7444 – 0.3973 0.4375 – 0.4459 0.4589 

Phoenix 0.8544 0.8316 0.6480 0.6565 0.6705 – 0.5588 0.6292 

Salt Lake City 0.7497 0.7786 – 0.4573 0.5000 – 0.5439 0.6296 

San Francisco 0.7569 0.7670 – 0.4022 0.4960 – 0.3725 0.4534 

Seattle 0.7967 0.7826 0.6965 0.4664 0.5772 – 0.5087 0.6184 

St. Louis 0.8774 0.4076 0.0007 0.7297 0.4904 0.0334 0.5622 0.6443 

 

Notes: The data correspond to daily city-specific average retail price data from September 25, 2001 to December 

31, 2007. The variable l11 (l00 ) denotes the MLEs of the transition probabilities associated with observing a 

positive (negative) retail price change in the current day conditional on observing positive (negative) price changes 

in the previous two days (see the Appendix for further detail). All MLEs reported above are statistically significant 

at the 1 percent level (estimated standard errors available upon request). The p-values are not shown for diesel 

prices since the relative magnitudes of the MLEs in this case suggest that cycling is never present. 
TABLE 5 

THE EFFECTS OF RETAIL-STATION OWNERSHIP STRUCTURE ON THE PRESENCE OF EDGEWORTH PRICE-CYCLES IN RETAIL GASOL

Dependent variable: 

Cycle 

ln

Independent variable: (1) (2) (3) (4) (5) (6) HHI of within-group sales of refiner company owned & operated sites 1.511** 1.324* 1.550** 0.043** -16.529** -37.119*

(2.37) (1.81) (2.36) (2.53) (2.60) (3.74) 

HHI of within-group sales of independent and jobber sites 5.148 6.284 5.32 0.299* -21.917 -57.10

(1.06) (1.31) (1.07) (1.92) (0.52) (1.01) 

HHI of within-group sales of lessee-dealers 0.238 0.030 -7.243

 (0.64) (1.49) (1.85) 

Median household income -1.96E-05 1.300E-06* 

 (0.95) (1.81) 

Population density -3.685E-04 -1.420E-06 

 (1.19) (0.13) 

Total population 2.364E-04 2.110E-05 

 (0.26) (0.88) 

Constant 2.542 15.082

 (0.48) (1.91) 

Observations 29 22 29 22 29 22 Pseudo R2 0.20 0.24 0.27 0.56 

p(Wald 2 c - statistic) [H0: All coefficients = 0] 0.059 0.308 0.063 0.020 

R2 0.25 0.43 

p(F-statistic) [H0: All coefficients = 0] 0.044 0.000 

 Notes: The results in Columns (1)-(4) are from a Probit regression, while those in Columns (5)-(8) are from OLS. Probit coefficient estimates are expressed in terms of ma

 of robust z-statistics (Columns (1)-(4)) and t-statistics (Columns (5)-(8)) in parentheses. 

 “*” = statistical significance at the 10 percent level in a two-tailed test  “**” = statistical significance at the 5 percent level in a two-tailed test  “***” = statistical significance at the 1 percent level in a two-tailed test 
Cycle -1.130*** 0.312 -3.244*** -1.003* -3.575*** -1.944*** -5.107*** -3.584*** -8.056*** 

(3.73) (0.77) (6.95) (1.86) (8.51) (3.72) (12.07) (6.39) (17.65) 

Median household income 3.066E-04*** 0.001*** 4.319E-04*** 1.899E-04*** 3.

(5.67) (7.97) (6.12) (2.83) 

Population density 0.001 3.436E-04 -0.001 -0.001 

(0.55) (0.27) (0.82) (0.81) 

Total population 1.15E-07 2.15E-07 2.39E-07 1.42E-07 

(0.84) (1.28) (1.38) (0.93) 

Percent urban 0.005 0.018 0.038 0.018 

(0.27) (0.62) (1.46) (0.72) 

Percent white -0.334*** -0.533*** -0.431*** -0.409*** 

(17.21) (7.49) (7.31) (12.58) 

Percent black -0.416*** -0.739*** -0.592*** -0.475*** 

(18.79) (11.43) (10.79) (15.13) 

Percent hispanic -0.181*** -0.337*** -0.292*** -0.207*** 

(7.38) (8.13) (7.15) (5.74) 

Percent drive alone -0.909*** -1.509*** -1.465*** -1.018*** 

(11.05) (12.14) (11.88) (8.99) 

Percent using public transportation -1.433*** -2.194*** -2.030*** -1.761*** 

(4.63) (5.44) (4.95) (4.46) 

Percent commuters with travel time > 30 min -0.273*** -0.378*** -0.249*** 0.014 

(4.18) (4.36) (2.85) (0.16) 

Percent with less than high school education 0.007*** 0.006* 0.005 0.003 

(2.92) (1.91) (1.51) (1.28) 

Percent with high school diploma 0.042 -0.06 0.014 0.024 

(0.57) (0.59) (0.15) (0.25) 

Percent with some college education 0.757*** 0.603*** 0.679*** 0.719*** 

(5.84) (3.11) (3.82) (4.16) 

Constant 92.926*** 142.244*** 113.207*** 197.634*** 140.856*** 215.883*** 182.375*** 244.831*** 211.839*** 2

(466.61) (45.64) (451.77) (28.97) (527.18) (35.44) (725.74) (56.24) (945.39) 

Observations 355 355 355 355 355 355 355 355 355 p (F -statistic) [H0: All coefficients = 0] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

Notes: Notes: All estimates are obtained using Feasible Generalized Least Squares (FGLS) assuming heteroskedasticity across cities within states. Absolute values of z-statistics are scategory is "other." “*” = statistical significance at the 10 percent level in a two-tailed test“**” = statistical significance at the 5 percent level in a two-tailed test“***” = statistical significance at the 1 percent level in a two-tailed test 

200

Table 6

Estimated Price Effects of Edgeworth Price Cycles in Retail Gasoline by Year (2002-2007)

2002 2003 2004 2005