EDGEWORTH CYCLES REVISITED * Joseph Doyle 1 Erich Muehlegger 2 Krislert Samphantharak 3. August 2009

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1 EDGEWORTH CYCLES REVISITED * Joseph Doyle 1 Erch Muehlegger 2 Krslert Samphantharak 3 August 2009 (under revson for resubmsson to Energy Economcs) Abstract Some gasolne markets exhbt remarkable prce cycles, where prce spkes are followed by a seres of small prce declnes: a pattern consstent wth a model of Edgeworth cycles descrbed by Maskn and Trole. We extend the model and emprcally test ts predctons wth a new dataset of daly staton-level prces n 115 US ctes. Consstent wth the theory, and often n contrast wth prevous emprcal work, we fnd the least and most concentrated markets are much less lkely to exhbt cyclng behavor both wthn and across ctes; areas wth more ndependent convenence-store gas statons are also more lkely to cycle. * We would lke to thank Justne Hastngs, Mchael Noel, Matthew Lews, Tavneet Sur, and partcpants at the Amercan Economcs Assocaton Annual Meetngs and the Internatonal Industral Organzaton Conference for helpful comments and dscussons. 1 MIT Sloan School of Management, 50 Memoral Drve, E52-447, Cambrdge MA Emal: jjdoyle@mt.edu 2 John F. Kennedy School of Government, Harvard Unversty, Malbox 25, 79 JFK Street, Cambrdge, MA Emal: Erch_Muehlegger@ksg.harvard.edu 3 Graduate School of Internatonal Relatons and Pacfc Studes, Unversty of Calforna at San Dego, 9500 Glman Drve #1519, La Jolla, CA Emal: krslert@ucsd.edu

2 I. Introducton Tremendous varaton exsts n the prcng strateges chosen by dfferent busnesses and how market prces dynamcally evolve n dfferent ndustres. Although a long lterature n ndustral organzaton dentfes dfferent equlbrum prcng strateges, n many cases the models do not make clear predctons as to why frms mght choose one set of strateges n one compettve envronment and choose a dfferent set of strateges n another compettve envronment. Retal gasolne markets provde a settng to study how the compettve envronment can affect these strateges. Gasolne prces are unque n that they are partcularly vsble to both compettors and consumers. Further, compettors are often found wthn close proxmty of one another. In ths settng, t seems plausble that frms compete on prce n a dynamc Bertrand game. Ths s evdent n a remarkable pattern n prces over tme when prce spkes are followed by slow reductons untl the next spke: a pattern consstent wth an Edgeworth cycle. Maskn and Trole (1988) frst specfed a dynamc Bertrand game n whch frms played Edgeworth cycle strateges n equlbrum. The model consders two dentcal compettors that sequentally choose from a fnte grd of prces. In the Edgeworth-cycle equlbra, f the opponent's prce s greater than margnal cost, the frm selects the prce that just undercuts her opponent's prce. If the opponent was prcng at margnal cost, wth some probablty the frm relents, choosng a much hgher prce and allowng the cycle of undercuttng to begn agan. In such equlbrum, the market clearng prce slowly falls to margnal cost untl one frm stochastcally relents, whch results n a prce spke. 1

3 Ths paper ams to shed lght on why we see Edgeworth cycles arse n some local gasolne markets, but not n others. To examne ths queston, we adapt Maskn and Trole (1988) to account for two sources of heterogenety amongst retal statons. Frst, we allow for loyal consumers who, due to geographc dfferentaton, brand loyalty or unobservable preference, do not swtch to compettors offerng margnally lower prces. Second, we allow frms to earn profts from goods complementary to the prmary good upon whch frms compete, such as convenence store operatons. By comparng how profts of cyclng and non-cyclng strateges vary wth the two sources of heterogenety, we generate testable predctons of where we would expect to see cyclng behavor. We test our predctons usng daly, staton-level prces for 115 US metropoltan areas, a larger dataset than n prevous studes. We document that Edgeworth cycles are only found n a subset of US ctes, and a subset of neghborhoods wthn these ctes. Consstent wth the theory, we fnd that greater market penetraton by ndependent gasolne statons offerng convenence store servces s assocated wth cyclng behavor. In addton, evdence suggests a non-monotonc relatonshp between cyclng and market concentraton: the least and most concentrated markets are less lkely to cycle. It appears that ctes and neghborhoods wth ntermedate levels of competton can support the type of prcng strateges that lead to Edgeworth cycles. The remander of the paper s organzed as follows: secton 2 offers an extenson to the Maskn and Trole model of Edgeworth cycles; secton 3 descrbes the data; secton 4 reports the emprcal models and results; and secton 5 concludes. II. Model 2

4 Maskn and Trole (1988) frst specfed a dynamc Bertrand game n whch frms played Edgeworth cycle strateges n equlbrum. Eckert (2003) ntroduces heterogenety n the market partcpants by consderng the case n whch one frm obtans greater than half of the market when both frms choose dentcal prces. Eckert shows that although cycle equlbra exst for all splts of the market, the speed of the cycles are negatvely correlated to the degree of asymmetry between the market partcpants. 4 Noel (2008) further extends the theory by provng the exstence of cyclng equlbrum computatonally for markets n whch frms face unequal dscount rates, asymmetrc capacty constrants and n the case of a tropoly rather than the duopoly assumed n Maskn and Trole. 5 In contrast to these papers, whch show the exstence of Edgeworth equlbra under dfferent markets, we examne how profts assocated wth cyclng and non-cyclng strateges vary wth brand loyalty and convenence store operaton. 6 Followng Maskn and Trole, we consder a dynamc game n whch N frms sequentally choose from a dscrete set of possble prces. We defne p t as frm 's choce of prce at tme t, p -t as the vector of prces of frm 's compettors, and p t as the vector of all frm prces at tme t. Frm faces a margnal cost of c. All consumers choosng to purchase from frm, settng prce p t, consume q(p t ). We focus on Markov perfect 4 As one frm's share of demand when dentcal prces are chosen rses, the frm has a greater ncentve to match rather than undercut her compettor's prces. Consequently, and the length of the undercuttng phase are negatvely related to the asymmetry between the two partcpants. 5 Noel also consders an extenson n whch frms are dfferentated along the Hotellng lne and consumers ncur travel costs. In ths case, undercuttng leads to partal (rather than full) capture of the other frm s demand Noel fnds that f dfferentaton s suffcently great, Edgeworth cycles no longer exst n equlbrum. 6 For purposes of ths paper, we focus on comparng the relatve expected profts earned by frms playng cyclng and non-cyclng strateges. We do not explctly prove exstence of cyclng equlbra for the locally-proxmate groups of statons observed n our data. To our knowledge, only Noel (2008) proves exstence of cyclng equlbra beyond a duopoly, focusng on the case of three symmetrc frms. Provng the exstence of cyclng equlbrum more generally s a substantally more challengng theoretcally exercse, whch we reserve for later work. 3

5 equlbra to the game, gven by a set of N reacton functons, {R (p -t )}. For each vector of opponent's prces, R (p -t ) maxmzes frm 's expected current and future profts assumng all frms contnue to play ther reacton functons. We specfy frm 's profts n perod t as Π t = (p t c )[α + β ( p t )]q(p t ) + γ [α + β ( p t )] (1) In our model, we dstngush two types of consumers. We let α denote the proporton of consumers loyal to frm, who always purchase from frm regardless of the prce frm chooses to set. β (p t ) denotes the proporton of consumers who wll swtch frms n response to the relatve prces offered by the frms. 7 We assume, wthout loss of generalty, that all consumers are ether loyal to a sngle frm or swtch frms dependng on the relatve prces that s, for all vectors p t, α + β ( p t ) = 1. By defnton, we assume that f frm has the hghest prce of the N frms, β (p t )=0. Furthermore, we defne β as the value of β (p t ) when frm has the lowest prce of the N frms: the hghest value β (p t ) can take. We let p * denote the prce that maxmzes profts from loyal consumers. 8 The frst term n the proft functon corresponds to sales of the prmary good for whch frm sets prce p t. The second term corresponds to addtonal profts accrued from the proporton of consumers who purchase from frm through sales of secondary goods. We use γ to denote the margnal proft earned by sellng the secondary good to 7 Although we do not further dstngush the preferences of consumers, consumers may have addtonal preferences that cause them to act loyally n some stuatons and prce shop n other stuatons. For example, a consumer wth a strong preference for purchasng from staton wth strong brand presence may act as a loyal consumer n a locaton where only one branded frm s present. In a locaton wth more than one branded staton, the consumer may swtch between branded statons n response to the prces each set. 8 Maskn and Trole consder a duopoly n whch α =0, γ =0, β (p,p j ) s equal to ether zero, one-half or one dependng on whether p s greater than, equal to or less than p j. Eckert allows an asymmetrc splt of the market when frms choose dentcal prces. 4

6 the proporton of consumers who choose to purchase from frm. In the context of retal gasolne statons, the frst term corresponds to purchases of gasolne, and the second term corresponds to purchases of other goods and servces offered by an afflated convenence store or servce staton. Implctly, we assume that frms attract customers on the bass of the posted prce of the prmary good (gasolne), and n some cases, may accrue addtonal profts from the secondary good (c-store sales). Followng Maskn and Trole, we use V t (p -t ) to denote frm 's expected profts when t s about to choose prces and frms play Markov perfect equlbrum strateges {R 1 (p -1t ), R 2 (p -2t ),, R N (p -Nt )} thereafter. 9 For notatonal convenence, let V α (p t ) and t V t β (p t ) denote the expected profts from gasolne sold to loyal customers and to frmswtchng customers when the frm plays R(p -t ). Let W tα (p t ) and W β t (p t ) denote the expected c-store or servce staton profts when the frm plays R(p -t ). We begn by characterzng the relatonshp between parameters α, β, and γ, and the expected profts earned by frms playng cyclng and non-cyclng strateges. We prove that as the share of loyal customers ncreases, the expected profts from playng a constant prce strategy rse more quckly than the expected profts from playng a cyclng * strategy. Furthermore, f α s suffcently hgh relatve to β, we prove that playng p strctly domnates all strateges exhbtng cyclng behavor. Second, we show that as γ ncreases, the relatve expected profts assocated wth cyclng rse relatve to noncyclng Multple Markov perfect equlbra (MPE) may exst - the value functon depends on the partcular MPE. 10 For brevty, we nclude proposton proofs n the appendx. 5

7 Proposton 1: Let {R 1 (p -1t ), R 2 (p -2t ),, R N (p -Nt )} be a set of reacton functons exhbtng cyclng behavor. As α ncreases, the expected profts earned by frm by playng strategy R (p -t ) ncrease less quckly than the expected profts assocated wth always playng p *. Corollary 2: There exst values of α and β such that frm would prefer to always play p * rather than play R (p -t ). As the share of loyal customers rses, the profts assocated wth playng the constant prce strategy, p *, rse more quckly than the profts assocated wth playng any cyclng strategy. Corollary 2 proves that f a frm has a suffcently hgh proporton of loyal customers, choosng the optmal statc prce for the loyal customers wll domnate any cyclng strategy. Thus, f a domnant frm n a market enjoys a suffcently great geographc or brand advantage over a smaller, ndependent rval, the larger frm may fnd that prcng to maxmze profts from loyal customers strctly domnates any strategy nvolvng cyclng, and the smaller frm would then capture the majorty of the frmswtchng customers. Our fndng, that a domnant frm wth a substantal number of loyal customers may be reluctant to partcpate n cycles, s consstent wth the computatonal fndng n Noel (2008), that f dfferentaton s suffcently hgh, prces cannot cycle n equlbrum. Proposton 3: Let {R 1 (p -1t ), R 2 (p -2t ),, R N (p -Nt )} be a set of reacton functons exhbtng cyclng behavor. As γ ncreases, the expected profts assocated wth playng 6

8 a strategy exhbtng cyclng behavor ncrease more quckly than the expected profts assocated wth playng p *. * Frm wllngness to play a cyclng strategy rather than p depends on whether the profts ganed by attractng frm-swtchng customers exceed the profts lost from suboptmally prcng the prmary good to loyal customers. As γ ncreases, the profts ganed from sellng both the prmary and secondary goods to frm swtchng customers ncrease relatve to the lost profts from settng a suboptmal prce for the prmary good. Emprcal Predctons Adaptng Maskn and Trole to allow for frm heterogenety provde several predctons about the characterstcs of cyclng and non-cyclng frms. 11 Proposton 1 suggests that potental benefts to cyclng are less pronounced for frms enjoyng geographc dfferentaton or brand loyalty. 12 Furthermore, proposton 3 suggests that the lkelhood of cyclng should also be correlated wth the presence of retal statons wth convenence stores. Based on our model predctons, we postulate that the geographc areas wth ndependent statons and, especally ndependent statons wth convenence stores, would be most lkely to exhbt cyclng behavor. We test these predctons at both the MSA and ZIP-code levels. III. Data Descrpton 11 Although, n ths paper we focus on cyclng behavor, the proposton holds for any alternatve reacton functon chosen by frm. 12 Noel (2007) ntuts ths relatonshp and fnds evdence consstent wth staton densty ncreasng the lkelhood of behavor consstent wth Edgeworth cycles. 7

9 The emprcal analyss uses a dataset of daly gasolne prces across 115 metropoltan statstcal areas (MSAs) n the Mdwest and Northeast U.S. from Aprl 1, 2000 to March 31, These data were collected at the staton level by the Wrght Express Fnancal Servces Corporaton, a leadng provder of payment processng and fnancal servces to commercal and government car, van and truck fleets n the Unted States. Ther Ol Prce Informaton Servce (OPIS) provdes prcng nformaton to the ndustry and transportaton companes. In addton to the retal prce, OPIS data nclude a measure of each staton s wholesale prce. Ths s a rack prce the prce at the termnal from the nearest refnery that produces the regulatory formulaton of gasolne used by the staton. These regonal prces also vary by brand of gasolne, and the data nclude these brand-specfc wholesale prces. Ths wholesale prce may dffer from the nternal transfer prce pad by refner-owned statons. It may also dffer from the staton s actual wholesale prce n that t does not nclude volume dscounts or delvery charges. 14 The OPIS data also nclude the street address of the staton. US Census of Populaton data at the ZIP code level n 2000 were matched to the statons, ncludng medan household ncome, populaton, and commutng behavor. Race and educatonal attanment measures were also collected. In addton, the 2000 US Census ZIP Code Busness Patterns database records the number of gasolne statons n each ZIP code. 13 Metropoltan areas nclude an urban core wth a populaton of at least 50,000, as well as surroundng countes ted economcally through drvng patterns a defnton well suted to studyng gasolne markets. The data nclude statons n the Mdwest, where there was a large prce spke n the sprng of 2000, as well as eastern states as a comparson, ncludng Arkansas, Connectcut, Illnos, Indana, Iowa, Kansas, Kentucky, Maryland, Massachusetts, Mchgan, Mnnesota, Mssour, Nebraska, New York, Oho, Pennsylvana, Rhode Island, Tennessee, Vrgna, West Vrgna, Wsconsn and Washngton, DC. 14 There s a lterature that consders the relatonshp between refners and retalers n gasolne markets, ncludng Shepard (1993), Slade (1998), and Taylor (2000). Volume dscounts are common for branded gasolne at the wholesale level. Estmates wth and wthout controls for wholesale prce are dscussed below. 8

10 One advantage of the OPIS data s that measurement error should be mnmzed, as the prces are recorded electroncally from ther clents charge cards. 15 A cost of usng credt card transactons s that they are only avalable for statons vsted by a card holder, whch results n mssng data especally on weekends. Over 33,000 statons are found at least once over the year n our data, and theses statons provde a farly accurate measure of brand coverage n a cty. When comparng statons n the prcng survey and those n the Census Busness Patterns data at the MSA level, then average number of statons s 262 and 274, respectvely. At a smaller scale, the medan ZIP code had three quarters of the statons surveyed. 16 Edgeworth cycles are characterzed by gradual downward prce movements, as frms margnally undercut compettors prces, followed by a prce spke. To emprcally categorze geographc areas as cyclng versus non-cyclng, the medan daly change n the retal prce s consdered, as n Lews (2008). In partcular, the daly change n retal prce was calculated for each staton wth at least two consecutve days of data, and then the medan of ths daly prce change at the MSA or ZIP code level was calculated. In cyclng markets, we would expect the medan prce change to be negatve, reflectng the greater number of days of fallng prces as opposed to the sudden jump n prce n the relentng phase. To ensure that the changes represent movements of a common set of statons, only statons that were present for at least 200 days over the year were ncluded 15 Further nformaton on the methodology s avalable n Doyle and Samphantharak (2008) and at 16 To explore the types of ZIP codes that have better coverage n the prcng sample, the ZIP code count of the number of statons n the sample was regressed on the observable characterstcs n Table 1. The man result s that more populous ZIP codes are assocated wth more staton surveyed, controllng for the number of statons n the Census data. 9

11 n these calculatons, although the results were smlar when all of the nformaton was used. In practce, we found that OPIS data can characterze cyclng behavor at the MSA and ZIP code levels, but they are not precse enough to characterze cyclng at the staton level. Furthermore, even n locatons where cyclng exsts, t s dffcult to observe whch staton relents at the bottom of the cycle, as the change lkely happens at a hgher frequency than our daly data can capture. Rather than estmatng cyclng behavor at the staton-level, we aggregate up to the MSA and ZIP code levels. The two man measures of market structure are the fracton of statons that are ndependent and measures of the brand concentraton n the market. Independent statons are not afflated wth a partcular ol refner, and they were dentfed n our sample by nvestgatng the brand name. The Socety of Independent Gasolne Marketers of Amerca (SIGMA) publshes ts member lst, whch provdes one measure of whether the brand was ndependent, and the remanng brands were nvestgated ndvdually. We further categorzed ndependents based on the proporton of ther retal outlets wth an attached convenence store, as reported n trade press, webstes and regulatory flngs. 17 Of the 45 ndependent brands observed n our data, twenty-sx brands operate convenence stores at more than half of ther retal outlets. In terms of the brands, one feature of gasolne markets s that some statons may be owned by the refner, whle others are franchses. Unfortunately, the data do not allow us to separate these two groups. Further, when we characterze brand shares, no quantty data are avalable at the daly level. Instead, the fracton of statons n our sample of a 17 Unfortunately, characterstcs of the staton, such as the number of pumps or whether there s a convenence store attached s not avalable n our prcng data. 10

12 partcular brand s used n calculatng the 3-brand concentraton rato and the brand HHI. Agan, the staton concentraton of each brand appears farly accurately measured, as the number of statons ever surveyed n each area s smlar to Census measures. IV. Emprcal Models and Results A. Prevous Emprcal Evdence Several papers emprcally document Edgeworth cycles n cty-level retal gasolne prce seres. Eckert analyzes prces for 19 Canadan ctes and fnds that market penetraton of ndependent gasolne retalers s negatvely correlated wth prce rgdty, consstent wth the results from hs theoretcal model. Noel (2007a) apples a Markov swtchng regresson to estmate the length of the undercuttng and relentng phases as well as the transton probabltes. Usng ten years of weekly, cty-level data for 19 Canadan ctes, Noel fnds that as ndependent retal staton market share ncreases, more markets exhbt cyclng behavor, a result that supports the predctons of Eckert's model. Lews (2008) fnds that prces fell more quckly n Edgeworth cycle markets than n noncyclng markets followng the Hurrcane Rta prce spke. In addton, he fnds a smlar relatonshp between ndependent retaler penetraton and prce cyclng as Noel (2007a), usng cty-level data for 83 US ctes. A second set of papers examne the characterstcs of Edgeworth cycles usng staton-level data wthn partcular markets. Noel (2007b) estmates cycle attrbutes usng sem-daly data on 22 retal gasolne statons n Toronto, Canada and Atknson (2008) examnes hourly data for 27 retal gasolne statons n Guelph, Canada. Both Noel and Atknson study the behavor of partcpants n prce cycles and examne whch frms n 11

13 each market are most lkely to relent at the bottom of the cycle. They tend to fnd that larger frms are more lkely to ntate the relentng phase, whereas smaller frms are more lkely to undercut. B. Edgeworth Cycles across US Ctes As mentoned, we calculate the medan daly prce change for each of our geographc areas followng Lews (2008). For ease of nterpretaton, we apply a cutoff below whch an area s classfed as exhbtng cyclng behavor. As a frst look, we ranked the MSAs n our sample by ther medan daly changes of average retal prce. Fgure 1 shows the average retal and wholesale prce over tme n 4 ctes: the cty wth the smallest (.e. largest negatve) medan change n retal prce (Toledo, OH: medan change equal to $ ), a cty near the medan of the daly prce change dstrbuton (Detrot, MI: $ ), and two ctes cty near the top of the rankng (Lncoln, NE, and Johnstown, PA). In the top 3 graphs, a large prce spke n the sprng of 2001 common to statons n the Mdwest domnates the frst few months of the seres. Ths spke was partally due to a mandated reformulaton and subsequent shortages (for more detal, see Doyle and Samphantharak, 2008). Later n the summer and the rest of the year, some of the ctes n the Mdwest reveal small decreases n prce followed by sudden ncreases. For Toledo, Detrot, and Lncoln, the wholesale prce movements are nearly dentcal, but the Toledo market has what appear to be Edgeworth cycles and the other two do not. Johnstown does not have the spke n Aprl 2000, nor does t exhbt cyclng behavor. It appears that the medan prce change measure reveals whch ctes tend to cycle. In partcular, ctes wth a medan prce declne of or more appear to exhbt cyclng 12

14 behavor, and ths cutoff wll be used n the analyss to compare cyclng and non-cyclng ctes. 18 Table 1 compares the characterstcs of the 20 cyclng MSAs wth the 95 noncyclng MSAs n our sample. The frst row shows that ths prce change n the cyclng MSAs s negatve a medan declne of 0.8 cents per day whereas non-cyclng MSAs show medan prce change close to zero. The average retal and wholesale prces are smlar across the two groups, wth retal prces durng ths tme perod close to $1.50 per gallon. Much of the dfference between retal and wholesale prce s comprsed of the state and federal taxes on gasolne. In terms of the fracton ndependent and brand HHI, the cyclng and non-cyclng ctes feature smlar measures. Ths smlarty masks a nonlnearty n the data that the most (and least) concentrated markets are less lkely to feature cyclng. The fracton of statons that are ndependent wth convenence store operatons does appear postvely related to cyclng n the raw means, wth these types of statons makng up 15% of cyclng-cty statons and only 9% of statons n non-cyclng ctes. When US Census characterstcs are consdered, non-cyclng MSAs nclude the largest ctes and have hgher average populaton densty levels (1600 per square mle vs. 1400). Cyclng ctes also have more statons on average (271 vs. 255). The medan household ncome s slghtly hgher n the average cyclng cty as well ($41,400 vs. $40,600). Among the employed populaton, commutng patterns are smlar across the two groups. Most workers drve to work alone, wth slghtly hgher rates n cyclng ctes 18 Appendx Fgures A1A and A1B show retal and wholesale prces over tme for the cutoff cty at and a cty wth a medan change n retal prces of

15 (83% vs. 80%). Meanwhle, the ctes are smlar n terms of racal composton. Among adults over the age of 25, the hgh school dropout rates are the same on average across the two groups. The percent wth college educaton s hgher n the non-cyclng MSAs (23% vs. 21%). Overall, the cyclng and non-cyclng MSAs appear smlar, wth the noncyclng MSAs ncludng the largest ctes. Cyclng & Brand Concentraton In the model, the prce elastcty of customers vares by frm, wth some frms enjoyng more brand loyalty or geographc advantage than others. One way that we characterze the potental for brand loyalty s by comparng ndependent statons wth the refner-afflated brands such as Exxon or Ctgo that nvest more heavly n brand dentfcaton. Further, the model suggests that n markets that are hghly concentrated the top frms wll have less ncentve to enter the cycle, and n hghly compettve markets, the tact colluson necessary to support cyclng may break down. As a frst look at these mplcatons, Table 2 compares the cyclng behavor across MSAs that vary by ther fracton of statons that are ndependent or ther brand concentraton levels. Panel A groups MSAs nto quartles based on the fracton of ndependent statons. The bottom quartle has 4% of statons that are ndependent on average, whereas the top quartle averages 35% of statons that are not afflated wth an ol refner. The relatonshp between the fracton ndependent and cyclng behavor has a marked nvese- U shape: 31% of ctes n the mddle two quartles exhbtng cyclng, whereas few ctes n the bottom or top quartle are found to cycle. Ths result s n contrast wth the prevous evdence that found more ndependent statons were assocated wth a hgher 14

16 lkelhood of cyclng behavor (Noel, 2007a). A possble explanaton s that the prevous evdence compared 19 ctes n Canada, whch do not appear to have the amount of varaton n the types of ctes to fnd such a relatonshp. Panel B shows that a greater proporton of statons that are ndependent does appear to be related to cyclng when those ndependents are also convenence store operators. The bottom two quartles of ctes here do not exhbt cyclng at all. For the top two quartles of ctes based on the fracton of ndependent statons wth convenence store operatons, 41% and 29% are found to cycle, respectvely. As the fracton of ndependent statons grows, ths may represent a more compettve market. To nvestgate the relatonshp between concentraton and cyclng drectly, Fgure 2 consders the 1-brand concentraton rato and the 3-brand concentraton rato. Local-lnear regresson estmates of the cyclng ndcator on these concentraton measures are reported. As the largest brand gets larger, the lkelhood of cyclng n the cty decreases. Ths s consstent wth a reduced ncentve by a domnant frm to engage n an Edgeworth cycle. The 3-brand concentraton rato shows a dstnctve nverse-u shape wth regard to cyclng. It appears that cyclng s much less lkely n ctes wth ether a hgh or low level of concentraton. Panel C of Table 2 further explores ths relatonshp between concentraton levels and cyclng n terms of HHI measured usng the share of statons n the area (smlar results are found when the 3-brand concentraton rato s used nstead). 14% of the markets n the least concentrated MSAs and 11% of the most concentrated MSAs can be categorzed as cyclng, compared to 31% n the 3 rd quartle. 19 These measures could be 19 Smlarly, the 3 brand concentraton rato (not shown) ncreases from 0.27, 0.49, 0.57, and 0.70 from the bottom to the top quartle, and the fracton of ctes that cycle n each quartle s 13%, 18%, 29%, and 11%. 15

17 related to the fracton of ndependent statons to the extent that large ndependent brands are drvng both measures. In practce, more ndependent statons are assocated wth less concentrated markets. 20 These raw comparsons do not take nto account dfferences between the MSAs. Table 1 showed that cyclng and non-cyclng MSAs are smlar, but the relatonshp between cyclng and concentraton may be affected by the demand characterstcs n the area. To test the relatonshp between cyclng behavor and the fracton of ndependent statons or brand concentraton, controllng for the demographc characterstcs of the MSAs, the followng model s estmated for MSA m: Y m = γ 0 + γ 1 I m + γ 2 H m + γ 3 X m + ε m (2) where Y m s a measure of the cyclng behavor of the MSA, ether the cyclng ndcator or the medan daly change n the retal prce; I m measures the fracton of ndependent statons n the MSA; H m s a vector of ndcator varables equal to one f the MSA s n a partcular quartle of the HHI dstrbuton and zero otherwse; X m s a vector of the MSA s characterstcs descrbed n Table 1, ncludng the demographc controls and the medan change n the wholesale prce. The model s estmated wth OLS to compare condtonal means, although the results for are smlar when probt models are used to estmate the model when the dependent varable s the cycle ndcator. Panel A of Table 3 reports the results when the ndcator for cyclng s the dependent varable, and Panel B reports the results for the medan change n daly prces the measure used to defne the cyclng ndcator. Ths measure allows all of the 20 Par-wse correlatons between the fracton of ndependent statons vs. HHI and between the fracton of ndependent statons vs. the top 3 brand concentraton are and -0.27, respectvely. 16

18 nformaton n the daly change to be used n estmatng the relatonshps, although the relatonshps are smlar n both Tables. Column (1) shows a lack of a lnear relatonshp between the fracton of statons that are ndependent n a cty and cyclng behavor, whereas Column (2) shows that the greater the proporton of statons that are ndependent wth sgnfcant convenence store operatons ncreases, so does the lkelhood of cyclng. To consder the nonlnearty shown n Table 2, Column (3) reports estmates from a model that ncludes ndcators for the quartles of the fracton of statons that are ndependent. Here, the bottom quartle s less lkely to cycle compared to the top quartle, although the dfference s not statstcally sgnfcant. As n Table 2, the mddle two quartles are where cyclng behavor s found most lkely to occur. Column (4) shows that across ctes that vary by ther fracton of statons that are ndependent wth sgnfcant convenence store operatons, the top two quartles are much more lkely to cycle. 21 Column (5) shows that the areas most lkely to cycle are those where the concentraton measure s n the 3 rd quartle, confrmng the uncondtonal results shown n Table 2. Columns (6) and (7) nclude both the fracton ndependent measures and the HHI quartle ndcators, and both results are robust. In partcular, the 3 rd quartle n terms of brand HHI s assocated wth a percentage-pont hgher lkelhood of cyclng compared to the most concentrated MSAs (s.e. = 0.11). Wth 17% of ctes found to cycle, ths s a large dfference. In terms of the control varables, the demographc characterstcs of the ctes are largely unrelated to cyclng behavor (see Appendx). In partcular, medan daly changes 21 These results were robust to categorzng statons as ndependent f they were SIGMA members, as opposed to the measure n the man results whch nvolved nvestgatng each brand name. 17

19 n our wholesale prce measure are unrelated to cyclng behavor. The greater proporton of workers who drve to work alone s (weakly) postvely related to cyclng behavor. These results suggest that cyclng behavor s less lkely to occur n the most compettve markets wth the most ndependent statons a stuaton when coordnaton may be nfeasble. Further, n the most concentrated markets, t may not be n the nterest of the domnant frms to enter the cycle. Rather, t s n the markets where the top 3 brands represent 50-60% of the market where we are seeng the cyclng behavor most pronounced. Although our model predcts that the most concentrated markets may be the least lkely to cycle, the observed non-monotoncty s not a drect predcton. There are several factors whch may help to explan to the non-monotonc relatonshp between cty-level concentraton and cty-level prce cycles. Frst, the non-monotoncty s consstent wth the theoretcal lterature that fnds that cyclng equlbra are more dffcult to support as the number of players ncreases (Noel 2008). Wth more compettors, each player becomes less wllng to be the frm whch ntates a prce jump, sacrfcng ts own profts untl other players follow. Second, the observed non-monotoncty may arse f concentraton helps frms to coordnate the tmng of jumps across the cty. If prces at each street corner cycle wth dfferent frequences, local prce cyclng may be dffcult to detect n cty-level prces. Although we typcally observe that the prce jumps occur on the same day n cyclng ctes, ths coordnaton may be stronger n more concentrated markets where the major frms can act as prce leaders. Fnally, only a subset of brands (or partcular pars of competng brands) may be wllng to engage n prce cycles. As a result, we may be less 18

20 lkely to see cycles at the cty-level n unconcentrated markets where these frms have a smaller market share or are less lkely to compete drectly. Consequently, the non-monotoncty we observe may arse from forces whch operate n dfferent drectons. Our model predcts that large frms wth substantal brand presence and potentally loyal customers are less lkely to cycle than small market share ndependents consequently, as concentraton falls, we may tend to see more cyclng behavor. On the other hand, there are a number of reasons why, as markets become hghly unconcentrated we may also be less lkely to observe cyclng at the cty-level. In the least concentrated ctes, cycles may be more dffcult to sustan or coordnate across more localzed markets. Prce Effects One queston that arses s whether cycles result n lower or hgher average prces. A complcaton s that cyclng s related to the compettve nature of the market, whch s predcted to affect prces as well. To consder the relatonshp between cyclng and prces, controllng for market concentraton, the followng model s estmated for market m: P m = γ 0 + γ 1 C m + γ 2 I m + γ 3 H m + γ 4 X m + ε m (3) where P m s the average retal prce n the cty, C m s a cyclng ndcator, I m and H m are measures of the market structure as above, and X m s a vector of controls ncludng the average wholesale prce n the market. The results are reported n Table 4, and cyclng s weakly related to lower prces. A cyclng cty s found to have lower prces by 1 to 2 cents per gallon on average 19

21 (s.e.=0.01). It appears that the cyclng ctes have cycles that spend roughly equal tme above and below the prce levels n non-cyclng ctes. Controllng for cyclng behavor, the fracton of ndependent statons s assocated wth hgher prces n the area, whereas the fracton of ndependent statons wth convenent store operatons s assocated wth lower prces. Meanwhle, HHI n the area s assocated wth hgher prces: ctes n top quartle n terms of brand concentraton have prces that average approxmately 5 cents per gallon. Ths result s robust to controls, wth ncome level and wholesale prce postvely related to the retal prce (see Appendx). Wth markups generally on the order of 5 cents per gallon n the Mdwest (Brannon, 2003), such a dfference appears economcally sgnfcant. 22 C. Edgeworth Cycles Wthn Ctes Gven that MSAs are defned by commutng patterns, t s not surprsng that prcng pressure s lkely transmtted across the MSA. However, the orgnal Maskn and Trole model evokes mages of gasolne statons competng on a street corner, and we nvestgate whether cyclng can be characterzed at a smaller unt of analyss, namely, at the ZIP code level. An advantage of nvestgatng cyclng behavor wthn ctes s that we can control for fxed characterstcs of MSAs that are dffcult to control but may be related to both cyclng behavor and market concentraton, such as the regulatory envronment. The fxed effects also control for regonal factors, as cyclng s found n the Mdwest and not n the Northeast of the U.S. That sad, store locatons are chosen wth future competton 22 Snce there was a large gas prce spke n the summer of 2000, we also perform a robustness check of ths result by droppng all of the observatons before September 1, 2000, recalculatng all of the varables from ths smaller set of observatons, and re-dong regressons n Table 4. The man concluson does not change. 20

22 n mnd, and convenence store operators, for example, may select areas wthn ctes that are more prone to cyclng behavor for reasons other than ther prcng strateges. To consder the source of Edgeworth cycles wthn and across ctes, we compared 5,900 ZIP codes to descrbe the determnants of cyclng at a smaller unt of analyss. To dentfy ZIP codes that cycle there are two data ssues. Frst, the ZIP code data are more lkely to suffer from mssng data problems compared to measures of prces at the cty level. The man results nclude all of the ZIP codes n the data, but results are smlar when the data are restrcted to ZIP codes wth observatons n at least 200 days out of the year. Second, t s useful for ease of nterpretaton to categorze ZIP codes as cyclng or non-cyclng, and we vsually nspected the data to arrve at a medan change n retal prce cutoff of Agan, the results are smlar when we use the medan change n retal prce tself rather than the dchotomous ndcator for cyclng, as well as when the cutoff remaned The emprcal models for ZIP code z n MSA m take the followng form: Y z = γ 0 + γ 1 W z + γ 2 X z + δ m ( z ) + ε z (4) where Y z s an ndcator for cyclng behavor or average prce n the ZIP code z and W z s a characterstc of the ZIP code of nterest from the theoretcal model, such as the presence of an ndependent staton wth a convenence store or the presence of domnant frm. In terms of ZIP code control varables, the medan change n the wholesale prce s ncluded to control for nput prce dynamcs. We also am to separate the effect of havng an ndependent or popular brand n the ZIP code from the number of gasolne statons by ncludng 20 ndcators for the number of statons. Further, ZIP code characterstcs 23 The MSA analyss used a cutoff of Appendx Fgures A2A and A2B show the tme seres of retal and wholesale prces for all ZIP codes that are categorzed as cyclng vs. those that are categorzed as not cyclng usng the cutoff. 21

23 taken from the US Census of Populaton n 2000 are ncluded. Models are also reported wth and wthout MSA fxed effects, δ m(z). The models reported are estmated usng OLS, although nearly dentcal results are found wth probt models. For comparablty wth the earler results and the dependence of prcng wthn a larger MSA market, the standard errors are clustered at the MSA level. Table 5 reports the results for cyclng behavor at the ZIP code level. The frst two rows consder the presence of an ndependent staton (ether wth or wthout major convenence store operatons), wth the excluded category ZIP codes wth no ndependent statons. 38% of ZIP codes have an ndependent gasolne staton, and 21% have a convenence-store ndependent. Column (1) ncludes no control varables and the presence of an ndependent gasolne staton wth sgnfcant convenence store operatons s a large predctor of cyclng n the ZIP code. Compared to a mean of 13%, the presence of at least one such staton s assocated wth a 28 percentage pont ncrease n the lkelhood of cyclng (In the raw data, 38% of ZIP codes wth a convenence-store ndependent are found to cycle compared to 6.5% of ZIP codes wth no such staton). The postve relatonshp survves the ncluson of detaled ZIP code controls, as well as MSA fxed effects (coeffcent = 0.16, s.e. = 0.03). Meanwhle, the presence of an ndependent wthout convenence store operatons s negatvely related to cyclng. In a model wth MSA fxed effects, the estmates are dentfed from dfferences n the ndependent store locatons wthn an MSA, and the estmated coeffcent s (s.e.=0.01). When the sample s lmted to the 20 ctes, 43% of the statons n our cyclng ctes are n ZIP codes that are also found to cycle. Agan ndependents are assocated 22

24 wth cyclng only when they are a convenence-store operator as well. ZIP codes wth such statons are 11 percentage ponts more lkely to cycle. In terms of covarates, the medan change n wholesale prces s negatvely related to cyclng, consstent wth cyclng beng a retal market phenomenon (see Appendx). Fgure A3 also shows that another measure of competton n the ZIP code, the number of statons, s postvely assocated wth cyclng. The relatonshp s relatvely flat after 10 statons. One explanaton for such a phenomenon s that as the number of statons grows, t s more lkely that there wll be ntense competton at the (very) local level of a street corner. Taken together, t appears that convenence-store ndependents are assocated wth an ncreased lkelhood that a cty cycles. The next two rows of Table 5 consder whether havng only one top brand n the ZIP code reduces the lkelhood of cyclng compared to havng two top brands. Top brands are defned as the two brands wth the hghest staton shares n the cty. If only one top player s n the ZIP code, t may have a hgher fracton of loyal consumers who lve or work nearby and they may eschew the costs of engagng n Bertrand-style prce movements. Furthermore, f a subset of consumers has a preference for purchasng from a top brand, over a lesser known staton, a lone top brand may enjoy some degree of brand loyalty. If more than one major brand s n the ZIP code, these consumers may swtch between them dependng on the prces whch they set reducng the loyalty to any gven brand. The results show that havng both of the top 2 brands s more predctve of cyclng than havng just one, consstent wth the noton that t takes at least two to play the game. Ths result s robust to controls, ncludng MSA fxed effects. 24 These results 24 Other measures of brand overlap n a cty were consdered. Smlar results are found when more than the top 2 brands are consdered, wth the presence of only one of the top 3 or 5 brands beng assocated wth 23

25 provde addtonal evdence that the observed cycles are ndeed a product of compettve forces among large players, as opposed to some (unobserved) mechancal process that leads to prce spkes. The last set of results replcates the retal prce results and s shown n Table As n Table 4, cyclng s assocated wth modest reductons n prce (between 1 and 3 cents on average, compared to an average gas prce at the tme of $1.52). It appears that cyclng results n prces that are more volatle, but are smlar to non-cyclng ctes on average. Meanwhle, the presence of an ndependent gasolne staton wth a convenence store n the ZIP code s assocated wth somewhat lower prces (1-4 cents), whereas the evdence s mxed wth regard to the presence of an ndependent wthout a convenence store, or the presence of one of the top two cty brands. D. Lmtatons The MSA results are cross-sectonal relatonshps wth the usual caveats that areas wth cyclng behavor may smply dffer compared to areas wthout cyclng behavor. The observable characterstcs look smlar across the groups, however, wth the excepton that the largest ctes do not appear to cycle. Results are smlar when ctes of greater than 2 mllon populatons are excluded. Also, the results are smlar when MSA fxed effects are ncluded to control for tme-nvarant characterstcs of ctes that mght affect the compettve envronment and cyclng behavor. In the end, the goals of the sgnfcantly less cyclng behavor. Cyclng by brand was also consdered, although mssng data lmtatons make ths type of comparson less compellng. 25 The number of observatons s slghtly dfferent n Table 6 compared to Table 5 due to mssng data for the change n wholesale prce n the set of controls used n Table 5. Results are nearly dentcal when ths varable s excluded and the same sample s used for both Tables. 24

26 emprcal exercse are more descrptve n nature, although the fndngs appear reasonable gven the results descrbed n the Secton 2. Second, the data are lmted by the frequency of mssng observatons, especally for weekends. Aggregate cty level data should categorze ctes that cycle versus those that do not. In addton, the results are smlar when the sample s lmted to statons that are frequently seen n the data. 26 It appears that our sample has suffcent coverage over the course of the year to characterze brand concentraton. Another lmtaton s the lack of quantty data results n measures of concentraton at the staton-share level rather than the usual market share for each brand. To the extent that staton shares reflect some mnmum quantty before a franchse s allowed to open, t seems lkely that such staton shares are suffcently hghly correlated wth quantty shares to serve as a relable proxy for HHI. In any event, the staton shares provde slghtly dfferent measure of concentraton, but one that reflects geographc coverage of the brands. Last, the cyclng behavor s found n the Mdwest, largely n Oho, Mchgan, Indana, and Illnos. The shape of the relatonshps descrbed n the larger sample s robust to lmtng the sample to statons only n the Mdwest, and we fnd that the ctes n the eastern U.S. provde a useful comparson group. 27 V. Concluson 26 The results are generally robust to lmtng the sample to ZIP codes wth at least 2, 4, and 6 gasolne statons n our prcng sample. See Appendx Table A2. 27 In our sample, Mdwest states are Indana, Illnos, Iowa, Kansas, Mchgan, Mnnesota, Mssour, Nebraska, Oho, and Wsconsn. 25

27 Retal gasolne markets are unque n that the prce for the product s broadcast for all to see, ncludng compettors. Ths facltates prce competton, and a strkng feature of these markets s that some exhbt what appear to be Edgeworth cycles. A refnement to the Maskn-Trole model that allows frms to retan some customers even when they are underbd suggests that markets wth domnant frms may not have the ncentve to enter such a cycle. Further, a necessary condton for such tact colluson s that the frms have some market power, and the least concentrated markets may not be able to support such cycles ether. The emprcal results use a dataset of daly prces across 115 ctes to descrbe the types of ctes that exhbt cyclng behavor. 17% of ctes n our sample have prce cycles. In contrast to evdence presented n pror work, our results suggest that ctes wth more ndependent statons are found less lkely to cycle. When ndependent statons wth sgnfcant convenence store operatons are consdered, however, a greater proporton of such statons are related to cyclng. Ths correlaton wth convenencestore ndependents and cyclng behavor s found wthn ctes as well: ZIP codes wth such stores much more lkely to have cyclng. Gven the complementary goods and the prce salence of the gasolne prce, the results are consstent to the predcton that these statons may have an ncentve to engage n prce reductons that can lead to the cyclng behavor. Further, the results suggest that the least and most concentrated ctes are less lkely to cycle. Meanwhle, cyclng behavor s not found to result n hgher or lower retal prces. These results are found controllng for cty characterstcs such as ncome levels, commutng patterns, changes n wholesale prces, as well as models that use 26

28 wthn-cty varaton n concentraton and cyclng behavor. It appears that a man characterstc that descrbes whch ctes exhbt Edgeworth cycles s the extent to whch the market s concentrated. 27

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