Pass-Though and Consume Seach: An Empiical Analysis by Timothy J. Richads, Miguel I Gómez and Jun Lee Suggested citation fomat: Richads. T. J., M. Gómez and J. Lee. 2012. Pass-Though and Consume Seach: An Empiical Analysis. Poceedings of the NCCC-134 Confeence on Applied Commodity Pice Analysis, Foecasting, and Maket Risk Management. St. Louis, MO. [http://www.famdoc.illinois.edu/nccc134].
Pass-Though and Consume Seach: An Empiical Analysis Timothy J. Richads, Miguel I Gómez and Jun Lee* Pape pesented at the NCCC-134 Confeence on Applied Commodity Pice Analysis, Foecasting, and Maket Risk Management St. Louis, Missoui, Apil 16-17, 2012 Copyight 2012 by Timothy J. Richads, Miguel I. Gómez and Jun Lee. All ights eseved. Reades may make vebatim copies of this document fo non-commecial puposes by any means, povided that this copyight notice appeas on all such copies. * Timothy J. Richads (tichads@asu.edu) is the Moison Pofesso of Agibusiness in the Moison School of Agibusiness and Resouce Management at Aizona State Univesity; Miguel I. Gómez (mig7@conell.edu) is an assistant pofesso in the Chales H. Dyson School of Applied Economics and Management at Conell Univesity; and Jun Lee (jl653@conell.edu) is a Ph.D. student in the Chales H. Dyson School of Applied Economics and Management at Conell Univesity. 1
Pass-Though and Consume Seach: An Empiical Analysis Retail-pice pass-though is one of the most impotant issues facing manufactues of consumepackaged goods. While etailes tend to pass wholesale pices though to consumes quickly and completely, they often do not pass tade pomotions on. Cuently, asymmetic pass-though is commonly thought to esult fom etailes. execise of maket powe. Altenatively, it may be due to consume seach behavio, and etailes' competitive esponse. We test this theoy using a panel theshold asymmetic eo coection model (TAECM) applied to wholesale and etail scanne data fo eady-to-eat ceeal fo a numbe of etailes in the Los Angeles metopolitan maket. We find that consume seach behavio contibutes significantly to impefect passthough. By allowing pass-though to depend on maket powe and consume seach costs, we find esults that ae contay to the conventional wisdom. Namely, maket powe causes etail pices to fall quickly and ise slowly, while consume seach costs cause etail pices to ise quickly and fall slowly pecisely the "ockets and feathes" phenomenon. Keywods: ceeal; panel data; etail-pice pass-though; theshold eo coection models; pice tansmission asymmety. JEL Code: C32, Q17. Intoduction The impotance of deal pass-though to manufactues is well undestood - the efficiency of tade pomotion dollas is commonly cited as one of the most impotant issues facing supplies (Gómez, Rao and McLaughlin 2007; Nijs et al. 2010). While manufactues would pefe etailes to completely pass-though tade deals, somewhat paadoxically, they would athe etailes not pass though wholesale pice inceases (Boyle 2009). In the past, this issue was little moe than a cuiosity. With input pices ising apidly fo food manufactues in 2008 and again in 2010, howeve, the poblem became vey eal. Manufactues wee foced to incease wholesale pices to maintain magins and, at the same time, incease tade deals in ode to maintain maket shae in a ising-pice envionment. Most of the empiical liteatue on tade pomotion pass-though (Kim and Staelin 1999; Kuma, Rajiv and Jeuland 2001; Ailawadi and Halam 2009; Nijs et al. 2010) consides only etaile esponses to negative changes in wholesale pices - tade pomotions - and not upwad movements in wholesale pices as well. In this study, we offe a moe compehensive teatment of pass-though that is elevant to both wholesale pice discounts and pice inceases. Incomplete tade pomotion pass-though can esult fom many potential causes: (1) demand cuvatue (Tyagi 2009); (2) infomation asymmeties (Kuma, Rajiv and Jeuland 2001; Busse, Silva-Russo and Zettelmeye 2006); (3) maket powe (Moothy 2005); o (4) inventoy cost (Cui, Raju and Zhang 2008). While each of these is likely elevant, the notion that pass-though depends fundamentally on moe pimitive types of consume behavio and not institutional igidity o excessive use of maket powe is a compelling one. Indeed, fomal tests of the ole of maket powe in mediating pass-though ates invaiably fail to find much influence (Fey and Manea 2007). Instead, ecent theoetical eseach on the moe geneal pass-though 2
issue maintains that incomplete pass-though by etailes is lagely a function of consumes' ational seach stategy, and etailes' ational esponse (Tappata 2009; Yuan and Han 2011). 1 Consequently, we offe a panel-data time-seies based empiical test that contols fo as many causal factos as possible, including a moe accuate measue of maket powe than used in the extant liteatue, in testing the hypothesis that consume seach behavio is lagely esponsible fo incomplete pomotion pass-though, and the asymmety of pass-though between tade pomotions and wholesale pice inceases. Empiical models of pomotion pass-though estimate eithe educed fom (Besanko, Dube and Gupta 2005) o stuctual (Kuma, Rajiv and Jeuland 2001; Ailawadi and Halam 2009) specifications of the pass-though mechanism between pomotions at eithe the manufactue o wholesale level and etail pices. If wholesale and etail pices tend towad a long-un equilibium, howeve, as is geneally thought to be the case, then the pice seies ae likely to be cointegated so an eo-coection model (ECM, Gange and Lee 1989) is moe appopiate. Ignoing the fact that the seies ae cointegated invites the likelihood of spuious egession, o finding a significant elationship when none exists in fact (Engel and Gange 1987). Howeve, simple ECMs ae misspecified when the undelying equilibium elationship is not specifically linea, but athe non-linea due to theshold effects. When etail pice adjustment occus only afte consumes peceive sufficient incentive to seach, both when pices ae ising and when they ae falling, etail pice pass-though likely occus only afte an adjustment-theshold is eached. Moeove, thee is nothing that would lead us to believe that the pice-elationship is symmetic between ising and falling pices. Consequently, ou empiical model is a theshold asymmetic eo coection model (TAECM) applied in the context of panel data. Ou empiical model is not new as Tsay (1989) developed methods fo testing fo thesholds in autoegessive models, while Balke and Fomby (1997) intoduced eo-coection to the geneal theshold famewok developed by Tsay (1989). The TAECM appoach is not only appopiate fo the poblem at hand, but povides useful infomation fo both eseaches inteested in the pefomance of the consume-poduct supply chain and pactitiones designing tade pomotion pogams and pice adjustments in esponse to inceased poduction costs. By fomally testing a model of consume seach, we povide evidence that incomplete pass-though is not, in fact, a esult of maket powe, but athe fully consistent with competitive behavio by etailes and wholesales. Fo pactitiones, undestanding why pass-though is impefect, and finding ways of dealing with the undelying causes of incomplete pass-though can help alleviate some of the inefficiencies inheent in the cuent system. Ou pimay objective is to explain why the pass-though ate fo tade pomotions and inceased wholesale pices tend to be geneally less than complete, o instantaneous, and is fa lowe than the pass-though ate fo wholesale pice inceases. While the liteatue contains othe empiical explanations fo this obsevation, ous is the fist to test the typical explanations against othes ecently advanced in the theoetical liteatue, in paticula, the influence of consume seach costs on pass-though. A seconday objective, theefoe, is to apply a new appoach to studying 1 In the economics liteatue, pass-though efes to the ate at which poduction costs ae passed-though to the etail pice; the tansmission of pices fom wholesale to etail, o the ate at which exchange ate fluctuations ae passed-along to consumes. In maketing, pass-though often efes to how much of evey dolla in tade pomotion is eflected in lowe etail pices. In this study, we assume a geneal definition and investigate the easons why etail pices change with espect to any vaiation in wholesale pices. 3
tade pomotion behavio that may be useful in othe categoies, othe makets, time peiods o etail envionments. We find that both consume seach costs and maket powe ae impotant in detemining the ate of etail-pice pass-though, but that consume seach costs explain the patten of asymmetic adjustment most often obseved in the data (i.e., the "ockets and feathes" phenomenon (Bacon 1991)). Specifically, maket powe causes etail pices to fall quickly and ise slowly - opposite to ockets and feathes - while consume seach costs cause etail pices to ise quickly and fall slowly. Deal pass-though, theefoe, can be expected to be highe among moe poweful etailes, and those that offe a low seach-cost envionment. Empiically modeling pass-though is difficult due to the fact that wholesale pice data ae geneally not available. Recent studies make significant and impotant contibutions to the empiical liteatue by using unique, yet popietay datasets (Ailawadi and Halam 2009; Nijs et al. 2010) that include etail and wholesale pices fo a matched-set of poducts. Nakamua and Zeom (2010) match etail coffee sales data with wholesale pice data obtained fom PomoData, Inc. fo a boad sample of etailes in the Los Angeles metopolitan aea. In this study, we mege IRI Infoscan data on band-level beakfast ceeal pices with wholesale pice and tadepomotion data fom PomoData matched at the UPC-level. By doing so, we ae able to est the elevance of publicly-available wholesale pice data fo estimating pass-though, and ensue that ou wholesale pices ae as close as possible to those actually paid fo ou sample of bands. This pape contibutes to the liteatue on etail-pice pass-though in thee ways. Fist, we offe an empiical test of a ecent theoetical explanations fo incomplete pass-though, namely vaiation in the intensity of consume seach between egimes of ising and falling pices. Hee, we also test fo the influence of etaile maket powe on pass-though. Second, ou empiical model extends existing models of pass-though as we explain incomplete pass-though both when wholesale pices ae ising and when they ae falling. Thid, we intoduce a new model of etail-pice pass-though in the context of panel data that explicitly takes into account the undelying time-seies popeties of etail and wholesale pices, and the elationship between them. By intoducing an econometic appoach that is new to pass-though analysis, we hope to povide insights that pevious empiical models wee unable to find. In the next section, we develop an empiical model of tade pomotion pass-though, beginning with theoetical insights and empiical tests of the theoy, and leading to a new model of pomotion pass-though that accounts fo ecent developments in the consume seach liteatue. In Section 3, we explain ou empiical model, including the panel integation and cointegation tests, the estimation of thesholds, and the identification of consume seach and maket powe in the econometic model. Section 4 consists of a desciption of ou empiical data, and some stylized facts gained though a peliminay investigation of ou wholesale and etail pice data. Estimation esults and a discussion of thei implications fo consume seach theoy ae povided in section 5, while section 6 offes some conclusions, moe geneal implications, and suggestions fo futue eseach that may addess some of the weaknesses of ou study o some of the new questions we aise. Modeling Pass-Though 4
Backgound Liteatue on Pass-Though Pehaps because of its impotance to manufactues, thee ae many explanations in the liteatue fo why tade pomotion money is eithe not passed though to consumes completely, o passed though moe than 100%. Bulow and Pfleidee (1983) and Tyagi (1999) explain vaiation in pass-though ates simply as a function of the cuvatue of demand. If demand is concave, then a single-poduct monopolist etaile will pass-though tade deals at a ate less than 100%, but some convex demand envionments imply equilibium pass-though ates geate than 100%. Retailes ae geneally not monopolists, howeve, so othes seek to explain incomplete passthough in a competitive envionment. Kim and Staelin (1999), fo example, constuct a theoetical model with which they seek to explain the obsevation that etailes ae eceiving moe and moe side-payments fom manufactues, but do not seem to pofit fom doing so. If manufactues set side-payments as Stackelbeg leades, and then etailes compete in pices, the authos show that it is still optimal fo manufactues to offe pomotional allowances even though pass-though is not complete. Similaly, Moothy (2005) also uses the natue of competition in the industy to explain incomplete deal pass-though. Specifically, his theoetical model of etail pass-though assumes that etailes pactice categoy management (optimize pofit ove categoies of elated poducts) and compete with othe etailes. A categoy-wide focus highlights the ole of coss-band pass-though, which he shows can be eithe positive o negative depending on the stuctue of demand fo poducts in the same categoy. Namely, band-substitution effects lead to negative coss-band pass-though as lowe wholesale pices fo one good lead to highe pices fo othes due to band-switching. On the othe hand, tade pomotion with stategic complementaity leads to lowe pices fo bands that compete with the pomoted band because pomotion ceates a geneal pofit oppotunity due to the lage oveall categoy size. Retail competition also adds anothe laye of complementaity as pomotion can aise the sales of all fims. Competitive consideations ae only pat of the stoy. Kuma, Rajiv and Jeuland (2001) explain the "patial pass-though" poblem as aising out of a fundamental infomation asymmety between consumes and etailes, and investigate ways in which manufactues may amelioate the poblem. While etailes most cetainly know when manufactue pices have fallen, consumes do not. Retailes have an incentive to etain as much of the pomotion as possible, but if they neve pass on a pomotion, and consumes know the distibution of tade pomotions, they will lose customes to the outside option. Retailes esolve the essential tension between pofitability and volume by offeing peiodic pomotions that match the tade pomotion offeed, signaling to consumes that they do, on occasion, pass-though the discounts. Manufactues can ease pass-though by paing tade pomotions with advetising diected at consumes, o combining a push and pull stategies. Obseving that lage, chain etailes ae amenable to tade pomotions, but independent etailes ae geneally not, Cui, Raju and Zhang (2008) develop a model of pomotion pass-though in which tade deals allow manufactues to pice disciminate between etailes with low inventoy cost and high inventoy cost. Only etailes with elatively low inventoy costs will fowad-buy, while the othes will pefe to not be offeed tade pomotions. Thei model explains why manufactues continue to offe tade deals despite thei evident inefficiency, and also why some etailes like tade pomotions, while othes do not. While they explain many of the appaent 5
paadoxes in tade pomotion, they do not explain why pass-though ates vay once the money is taken. Among empiical studies, Deze and Bell (2003) conside scan-back tade deals, which ae essentially ex-post pomotions in which the etaile is ewaded fo passing-though tade pomotions. Manufactues often lose money on tade pomotions due to etaile fowad-buying, o puchasing futue equiements only when the deal is on, diveting o impefect pass-though. Point-of-sale scannes allowed the emegence of scan-back deals, which fundamentally change the pofitability of tade pomotions fo manufactues. Though both a theoetical model and empiical testing, Deze and Bell (2003) explain manufactues' pefeence fo scan-back deals and show that they can be designed to leave etailes weakly bette off and manufactues stictly bette off. Moeove, they show that, fo the beveage categoy, scan-back deals do not lead to excess odeing and incease etail sales though lowe etail pices. Besanko, Dube and Gupta (2005) study pass-though ates fo 78 poducts ove 11 categoies fo a single supemaket etaile. Estimating a educed-fom model, they find pass-though ates geneally geate than 60%, and highe own-pass-though ates fo poducts with eithe a lage maket shae, o highe contibution magin. Small bands ae also disadvantaged with espect to cossband pass-though as pomoting lage bands is less likely to induce a simila esponse in smalle bands (positive pass-though), while pomoting smalle bands is moe likely to cause a discount-esponse in lage bands. Based on thei esults, coss-band pass-though cannot be ignoed, the citicism of McAliste (2009) notwithstanding. 2 Pauwels (2007) estimates an impulse-esponse function in 75 bands acoss 25 categoies to detemine the elative effects of own- and competito pomotion pass-though. Pauwels (2007) epots a pass-though ate of 65% fom wholesale to etail pices, but also finds that competitos match 15% of the wholesale pice eduction, educing the pomotion elasticity fom 1.78 by 10%. Howeve, this esponse ate is an aveage ove all categoies and vaies widely by band and categoy, with lage-shae categoies having highe pass-though ates than smalle categoies. Smalle bands ae paticulaly disadvantaged with espect to pomotions: they have lowe etail pass-though, have lowe etail suppot, benefit less fom competitive pomotions, but povide geate benefit to competitos though thei own pomotions. Othes find that tade pomotion pass-though ates can indeed be geate than 100%. Ailawadi and Halam (2009) conduct an empiical analysis of etaile pomotion pass-though using a unique dataset coveing all manufactue pomotion and allowance activity fo a two-yea peiod fom a single etaile. They find that the etaile passes-though moe than 100% of manufactue allowances in aggegate, but the median is fa less fo any single manufactue. Moeove, some manufactues ae pomoted even without funding.pivate label and high-shae manufactues in high-lift and high-magin categoies in paticula. They find that the most impotant deteminants of pass-though ae whethe the manufactue sells pivate labels and its maket shae, both in focal and othe categoies. In geneal, howeve, pass-though is highe in categoies with high shae, high lift, low concentation and, supisingly, low magin categoies. These findings ae impotant as they cast some doubt on whethe incomplete pass-though is even an empiical 2 McAliste (2007) agues that the multiple-zone picing data used by Besanko, Dube and Gupta (2005) does not eflect tuly independent picing decisions among zones. Contolling fo this fact, the authos do not find evidence of coss-band pass-though in the data used by Besanko, Dube and Gupta (2005). 6
eality. Taking an entiely diffeent appoach, Nijs et al. (2010) estimate pass-though ates fo a single poduct categoy using data fom ove 1,000 etailes in 30 states. Thei goal is to model pass-though in the context of the entie supply chain fo the categoy, because pass-though necessaily involves dynamic consideations that must change ove time, and vay acoss categoies. Vaiation in pass-though occus not only due to changes in the economic envionment, but also due to measuement discepancies as the authos show that accounting measues bias estimates of pomotion effectiveness because the aveage cost measues misstate the actual cost of the pomotion. Using coect, economic measues of cost they find mean pass-though pecentages of 71.0%, 59.0%, and 41.0% fo etailes, wholesales and the entie supply chin, espectively. Contay to Ailawadi, they find pass-though ates still significantly below 1 and that poduct and maket attibutes (competitiveness) have vey little influence on thei magnitude - modeling the entie supply chain still does not induce ove-shifting among consumes. In the economics liteatue, the question of pass-though typically concens how changes in manufactuing input cost o exchange-ate fluctuations ae passed though to consumes in the fom of etail pices. Nakamua and Zeom (2010) conside a numbe of altenative explanations fo less-than-complete exchange ate pass-though, including demand cuvatue, local cost conditions and stategic picing behavio on the pat of intemediaies. Benabou and Getne (1993) offe an altenative explanation gounded not in stuctual attibutes of the industy at hand, but athe in the uncetainty geneated by pice inflation. Specifically, Benabou and Getne (1993) ecognize that the infomation content in changing pices is endogenous to the agent's incentive to seach. Thei model shows that inflation actually leads to moe competitive outcomes as it povides a geate incentive to seach. Unde elatively high seach costs, howeve, the opposite occus as thei model pedicts that maket powe ises in the geneal level of inflation because the infomational content of pices is diminished. Moe ecent theoetical studies follow Benabou and Getne (1993) by focusing on consumes' incentives to seach, and the infomation content of pices. In the auto industy, Busse, Silva-Risso and Zettelmeye (2006) investigate the "pass-though invaiance hypothesis," namely that the incidence of a pomotion offeed by a thid-paty to the auto puchase tansaction (the manufactue) should be the same whethe it is offeed to eithe the buye (custome) o eselle (deale). Contay to the hypothesis, they find that end-consumes eceive 70% - 90% of a pomotion diected at customes, but only 30% - 40% of a pomotion tageted to deales. While custome pomotions ae well-publicized, deale pomotions ae not. Paticulaly in an envionment whee the end pice esults fom diect negotiations between the buye and the deale, infomation asymmeties ae the pimay cause of incomplete pomotion pass-though. Although supemaket pices ae not negotiated, shoppes' expectations can nonetheless be similaly conditioned by communication diectly fom the manufactue. Offeing coupons is one way in which manufactues can addess the incomplete pass-though poblem. Gestne and Hess (1991) show that coupons ae less expensive than pomotional allowances fo manufactues because coupons ae less costly than tying to induce etailes to lowe thei pice to consumes' esevation pice. A combination of push and pull stategies allows etailes to pice disciminate, but they also show that it is in manufactues inteest to offe ebates (coupons) even when all consumes use them and etailes do not pice disciminate. Ultimately, they ague that the pimay function of a push stategy is to induce pass-though, o 7
to povide incentives fo the etaile to paticipate. Fo puposes of this study, howeve, we do not have infomation on whethe pull stategies ae used in conjunction with tade pomotions so we implicitly assume that coupon use is andomly distibuted among the bands in ou sample, and that consumes edeem them acoss bands with equal pobability. Empiically, the notion that cost inceases ae passed quickly and completely though to consumes, but deceases in cost tend to lead to etail pices that fall moe like feathes (Bacon 1991), is well-documented. Seveal empiical studies attibute asymmetical pass-though to maket powe on the pat of etailes, whethe in gasoline (Boenstein, Cameon and Gilbet 1997; Deltas 2008; Velinda 2008), beef (Goodwin and Piggott 2001) o fesh poduce (Wad 1982). Peltzman (2000), howeve, finds no suppot fo the maket powe hypothesis in a compehensive study of pass-though coveing hundeds of poduct categoies. Although it is tempting to conjectue that asymmetic pice adjustment is due to maket powe, the pevasiveness of this obsevation in othewise seemingly competitive makets - like etail gasoline sales in a satuated maket - suggests that thee must be an altenative explanation. Reflecting a boad skepticism that maket powe could explain such a pevasive phenomenon, Yang and Ye (2008), Tappata (2009) and Yuan and Han (2011) exploe theoetical explanations that assume pass-though is detemined as an equilibium between competitive fims and ational consumes. Tappata (2009) extends the explanation fo equilibium pice dispesion developed in Vaian (1980) to endogenize consume seach behavio. He shows that ational consumes will seach moe when pices ae ising elative to when they ae falling, so pices ae moe apid to adjust in an upwad diection. Said diffeently, the dispesion of pices shinks when fims' costs ae high elative to when they ae low, because active seach constains fims' pice-setting powes. Similaly, Yuan and Han (2011) also show that etail pices ise quickly when costs incease because consumes seach moe intensively, but fall moe slowly when costs fall again as selles educe pices only enough to cause consumes to not seach fo new pices. Although these models ae each developed to explain pass-though of wholesale costs athe than tade deals, the emphasis on infomation asymmeties and seach suggests a valuable line of easoning that may explain some of the anomalies obseved in pomotion pass-though. Moeove, ou empiical model of pomotion pass-though is able to identify unique featues of the consume seach model, so we ae able to test whethe impefect pass-though esults fom seach o the moe usual explanation, maket powe. Unlike in the cost pass-though case, studying pomotion pass-though povides a unique oppotunity to test the infomation asymmety hypothesis as manufactues have the ability to esolve some of this asymmety though pull stategies such as couponing and advetising. We exploit this oppotunity in the empiical model below. Implications of a Model of Consume Seach and Pass-Though In this section, we outline a theoetical model of consume seach and show how ational consume behavio, and fim esponse, leads natually to a theshold asymmetic eo-coection model of etail-pice pass-though. Lewis (2008), howeve, notes that the existent seach models in the liteatue all apply to the homogeneous poduct case. While this assumption is elatively benign in the etail gasoline industy, it most cetainly does not descibe the etail food maket. Consequently, we extend the seach model of Tappata (2009) to allow fo diffeentiated poducts and deive a set of compaative statics that allow us to test ou undelying hypothesis, namely that impefect pass-though of tade pomotion deals is not due to the execise of maket powe 8
on the pat of etailes, but is athe an atifact of consume seach, and consume heteogeneity. As demonstated by Chanda and Tappata (2010), the non-sequential seach model of Tappata (2009) is sufficiently simple to geneate compaative static esults that ae testable with the appopiate data. Tappata (2009) extends Vaian (1980) in a elatively simple way by endogenizing consume seach behavio. Only a faction of consumes choose to seach, and seach behavio is endogenous to the peceived benefits of seaching, and the cost of doing so. Fims ae ational, so set less dispese pices when wholesale pices ae high elative to when they ae low, because thei ability to set pices is limited by a fixed esevation pice. Consumes ae ational, so anticipate such behavio on the pat of etailes and seach less when wholesale pices ae high. Pice expectations ae fomed adaptively so non-iid wholesale pice shocks have an impotant effect on seach behavio. If consume seach is at least in pat esponsible fo incomplete pass-though, then vaiables that influence the cost of seach ae useful in empiically identifying the effect of seach on passthough. Compaative statics of the Tappata (2009) consume seach model show the following esults. Fist, pice dispesion ises with the numbe of fims, and shifts towad monopoly pices, because the pobability of offeing the lowest pice in the maket declines at an exponential ate. Howeve, when endogenous seach is included, a highe numbe of fims in the maket induces moe consumes to seach, thus focing pices down. Consequently, the net effect of an incease in the numbe of fims, o poducts, is ambiguous in a consume seach model and cannot be used to identify the seach effect (contay to Lewis (2008)). Second, when seach is endogenous, highe wholesale pices cause seach intensity to fall, and etail pices to ise, but become less dispese. Because the opposite occus when wholesale pices fall, such as duing a pomotion, pices become moe dispese when tade pomotions educe wholesale pices. Intuitively, demand becomes moe elastic when pices ise, and less elastic when they fall, so etail pices adjust faste upwad than downwad. This effect, howeve, is indistinguishable fom what we would expect if the etaile execises monopoly picing powe (Moothy 2005). A thid effect is unique to the consume seach model as it applies to a multi-poduct etail context. Highe consume seach costs lead to lowe seach intensity and, hence, highe etail pices. 3 Consume seach costs, in tun, can be thought of in tems of the numbe of poducts offeed by the etaile. Theefoe, we use the numbe of poducts sold duing a given peiod as a poxy fo seach costs to identify whethe consume seach is a deteminant of pass-though asymmety. An Empiical Model of Pass-Though Ou empiical model consists of thee stages, following the geneal panel theshold eocoection methodology intoduced by Hansen (1999). In the fist stage, we test each of ou panel data seies - etail pices and wholesale pices - fo stationaity and, afte establishing the natue of the time-seies popeties of ou data seies, we then estimate the panel cointegation elationships between the etail and wholesale pice seies, which include tade pomotions. In the second stage, we use Hansen's (1999) appoach to estimate etail-pice adjustment thesholds 3 This paadox is not unique to the Tappata (2009) model as Diamond (1971) shows that, in a maket with homogeneous goods, the unique Nash equilibium as the numbe of fims ises conveges on the monopoly pice. 9
in panel data. Fom the theoy descibed above, two thesholds ae necessay to captue the appaent inability of etail pices to adjust completely, in eithe an upwad o downwad diection, in esponse to wholesale pice changes. In the thid stage, we use these estimated thesholds to define thee pice-adjustment egimes. We estimate the asymmetic eo-coection model in each egime, and test fo the effect of maket powe and consume seach costs on the speed of etail pice adjustment. Testing fo Integation and Cointegation in Panel Data In this section, we descibe how we test fo integation in etail and wholesale pices and fo cointegation between etail and wholesale ceeal pices in a panel data set. Typically, augmented Dickey-Fulle (ADF) o Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests ae commonly used fo this pupose in time seies fo a single coss-sectional unit of obsevation. Howeve, heteogeneities between individuals in panel data equie anothe type of unit oot test that takes into account the infomation povided by coss-sectional vaiation at each point in time. A numbe of appoaches have been developed to incease the powe of panel cointegation tests by exploiting the infomation povided by coss-sectional pice vaiation. Thee ae two boad types of test: (1) an ADF-type test that assumes a null hypothesis of nonstationaity, and (2) a KPSS-type that assumes a null hypothesis of stationaity. Examples of ADF-type tests include Levin, Lin and Chu (LLC 2002) and Im, Pesaan and Shin (IPS 2003). LLC and IPS popose panel unit oot tests on the basis of the standad ADF test in individual seies. Howeve, a citical assumption undelying these tests is that the coss sectional obsevations ae independent. Because the LLC and IPS tests ae biased in the pesence of cosssectional dependence, and that is pecisely the case with the panel dataset consideed hee, we use a test developed by Hadi (2000). While LLC (2002) and IPS (2003) appoaches ae based on ADF type unit oot test whee the null hypothesis is that all individual seies ae stationay, Hadi (2000) poposes a esidual-based Lagange Multiplie test which is an extension of stationaity test fo time seies of Kwiatkowki et al. (1992). The advantage of using Hadi's test is that it is unbiased in the case of coss-section dependency in the panel data. Moe specifically, Hadi consides the following epesentation in panel context with fixed effects and individual tends fo a given pice seies p it : p it = ρ t + γ it + ε it, (1) whee i, and t denote the coss-section and time-seies component, espectively; γ it = γ it + u it implies that p it follows a andom walk. Hee ε it and u it ae assumed to be mutually independent and iid ove coss-section and time-seies t. Theefoe, equation (1) can be witten as: whee e it = T t=1 u it = ρ t + γ 0 + T t=1 + ε it = ρ t + γ 0 + e it, (2) p it u it + ε it and γ 0 epesents the initial values, assumed to be fixed and unknown. The null hypothesis fo tend-stationaity is established by testing whethe the vaiance of the andom walk σ u 2 equals zeo. If σ u 2 = 0, then e it is educed to ε it, which implies that the andom walk γ it conveges to a constant (i.e., γ it γ 0 ). On the contay, when σ u 2 0, then e t is non 10
stationay, given that γ it is still a andom walk. Fo testing puposes, Hadi (2000) poposes the following one-side LM statistic: LM Hadi = 1 RT 2 R =1 T t=1 (S it ) 2 σ ε 2, (3) 2 2 whee σ ε is a consistent estimato of σ ε unde the null hypothesis that all panels ae stationay and (S it ) 2 T = j=1 ε j is the patial sum of the esiduals fom the egession in equation (2). Two pice seies in a supply chain ae often cointegated and ignoing these long-un comovements between two seies may lead to spuious paamete estimates in any model of passthough. The test developed by Johansen (1988) is commonly used in a pue time-seies context. Howeve, in panel data, the Johansen test can be biased because of heteogeneous coss-sectional popeties. Theefoe, we use a battey of tests developed by Pedoni (1999) that ae moe appopiate fo panel data. Specifically, Pedoni (1999) develops two classes of panel cointegation tests fo panels with heteogeneous cointegation vectos, employing a esidualbased appoach, that include both "within dimension" and "between dimension" components. Conside the long-un elationship between pices chaged by etaile (p it ) fo band i and wholesale pices paid by the same etaile (w it ), including individual effects (λ it ) and a time tend (t), witten as follows: p it = λ it + θ t + β w it + ε it. (4) In this model, the estimated esiduals fom the egession in (4) ae: ε it = p it λ it θ t β w it, whee ε it epesents deviations fom the long-un equilibium between the two pice seies. The esidual-based appoach to test fo co-integation examines whethe the esiduals contain a unit-oot unde the null hypothesis of no cointegation using the following geneal augmented Dickey-Fulle (ADF)-type test: whee u it is an iid eo tem. ε it = φε it 1 J j=1 + η j Δε it 1 + u it, (5) To accommodate heteogeneous coss-sectional vecto, Pedoni (1999) extends equation (4) by allowing η j and J to vay acoss individual accoding to: whee the othe tems ae as defined peviously. J ε t = φε t 1 + η j=1 j Δε t j + u t, (6) We apply the two diffeent classes of cointegation test statistics developed by Pedoni (1999): Panel statistics and Goup Mean statistics. Panel statistics, often efeed to as the "within" dimension test, ae analogous to panel unit-oot statistics against homogeneous altenatives. The Panel statistics ae based on pooling the esiduals of the egession in (4) along the "within" dimension of the panel. Panel statistics test the null hypothesis of no cointegation (φ = 0) fo 11
all coss-section individuals (), against the altenative hypothesis of φ = φ, 2 < φ < 0 fo all. Thee ae fou Panel test statistics: panel-υ, panel-ρ, panel-pp and panel-adf. These ae analogous to the vaiance atio test statistic, the panel vesion of the Phillips and Peon ρ- and t- statistics, and the augmented DF test statistic, espectively, whee φ is the autoegessive coefficient of the esiduals in the -th individual in equation (6). The Goup Mean statistics ae commonly known as "between" dimension tests and they ae simila to a panel unit oot statistic against heteogeneous altenatives. The Goup Mean statistics allow fo heteogeneous coefficients unde the altenative hypothesis: H A : φ = φ, 2 < φ < 0 fo all. We apply thee "within" dimension tests: a panel ρ-statistic, a panel PP-statistic and a panel ADF-statistic. These statistics ae obtained by aveaging the autoegessive coefficients fom the unit oot tests of the esiduals fo each individual in the panel. All seven cointegation tests ae asymptotically standad nomal-distibuted. The panel υ-statistic is a one-sided test, wheeas the othe six statistics ae two-sided tests. As we explain in moe detail below, we eject the null hypothesis of no co-integation elationship in each case. We find a single cointegation vecto fo each elationship, so poceed to estimate the panel eo coection model descibed in the next section. A Panel Theshold Asymmetic Eo Coection Model Given ou finding that etail and wholesale ceeal pices ae indeed co-integated, estimating pass-though ates consistently equies a panel eo-coection appoach. Based on obsevations by othes who have estimated pass-though ates in etail food makets (Goodwin and Piggott 2001), howeve, ou model should also accommodate asymmetical pass-though to upwad and downwad wholesale pice changes as well as theshold-effects. Asymmetic pass-though is likely in the ceeal industy because of the natue of competition among food etailes in many makets o consume seach costs, to name the two explanations that ae the focus of ou study. Futhe, pass-though is also likely to be non-linea, o involve significant theshold effects, due to the elatively high fixed costs.menu costs.associated with etail pice adjustment (Levy et al. 1997). Theefoe, we follow Hansen (1999) and include both non-lineaity and asymmety in the etail-pice pass-though model fo beakfast ceeal. Ou empiical appoach involves two stages: (1) in the fist stage we estimate the theshold paametes (o paametes in a multiegime model) following Hansen (1999), and (2) in the second stage, we estimate asymmetic and long-un pice adjustment tems conditional on the pio theshold paametes. We explain each stage moe fomally next. Conside the co-integation elationship between wholesale pice paid by etaile fo band i (w it ) and etail pice (p it ) chaged by etaile fo band i at time t as follows: ECT it = ε it = p it λ w it, (7) whee = 1,,R indexes etailes and t = 1,, T time peiods. The eo tem ε it, which is also efeed to as the eo coection tem (ECT it ) measues the deviation fom the long-un equilibium between the pice seies. In a standad eo coection model, these eo tems ae linea and identical egadless of the magnitude of deviations. Howeve, the adjustment costs efeed to above ae likely to geneate thesholds that tigge adjustments towad the long-un 12
equilibium in esponse to exogenous shocks. 4 A theshold model is a natual way to test the consume seach hypothesis because seach only occus, and etailes will only adjust pices in esponse, once the gains fom seach exceed consumes' maginal cost of seaching fo potentially lowe pices. Empiically, howeve, identifying pice-thesholds is poblematic because they ae unobseved in the data, so must be infeed fom obseved pice behavio. To test fo these potential nonlineaities we follow Hansen (1999) and employ the following autoegessive (AR) epesentation with a two-egime theshold fo the eo tem ε it in a balanced panel: Δε it = μ i + β (1) ECT it 1 + p=1 δ p Δε it 1 + e it, ECT it d γ 1 μ i + β (2) ECT it 1 + p=1 δ p Δε it 1 + e, (8) it, γ 1 < ECT it d whee γ 1 is the theshold paamete, and d measues the duation of the delay. Pice adjustment in this specification is asymmetic in the sense that the coefficients β (1) and β (2) may diffe based on whethe the magnitude of the eo-coection tem (ECT it 1 ) is smalle o lage than the theshold value γ 1. Hansen(1999) poposes a two-step appoach based on odinay least squaes to estimate the value of γ 1. Fist, the individual effect μ i in equation (8) is eliminated by emoving individual specific means. Let the vecto of independent vaiables, dependent vaiable and esiduals with individual-specific means emoved be witten as X, ε and e, espectively. Using this notation, equation (8) is ewitten as: ε = X (γ 1 )β + e so the coefficients β (1) and β (2) ae estimated by OLS, conditional on the value of γ 1, using the estimato: β (γ 1 ) = (X (γ 1 ) X (γ 1 )) 1 X (γ 1 )ε, (9) and the egession esiduals ae calculated as: ε (γ 1 ) = ε X (γ 1 )β (γ 1 ). The theshold value is subsequently estimated by minimizing the sum of squaed eos as follows (Chan 1993; Hansen 1999): γ 1 = ag min S 1 (γ 1 ) = ε (γ 1 ) ε (γ 1 ). (10) Although this method povides point estimates of the theshold paamete, it emains to daw infeences egading γ 1. Theefoe, the next step is to test the statistical significance of the estimated theshold value, unde the null hypothesis of β (1) = β (2). A likelihood atio (LR) test is used fo this pupose. The LR test statistic is calculated as: F 1 = (S 0 S 1 (γ 1 ))/σ 1 2, whee σ 1 2 = S 1 (γ 1 )/n(t 1) and S 0 is obtained fom the model without thesholds as follows: Δε it = μ i + β ECT it 1 + p=1 δ p Δε it p + e it, (11) 4 This fixed cost can be eithe explicit as in Levy et al. (1997), o implicit as in Blinde et al. (1998). An example of an implicit adjustment cost would be losing a consume to a competito who did not aise his etail pice. Indeed, the existence of thesholds in etail pice adjustment eflects the concept of etail pice fixity that is widely studied by maco and micoeconomists alike (Blinde et al. 1998). Delayed-esponse in etail pice adjustment can be due to menu costs (Levy et al. 1998), a failue to coodinate pice changes (Ball and Rome 1991), inventoy adjustment costs (Slade 1999) o the peception of pehaps a kinked-demand cuve wheeby competitos espond to a pice incease, but not a pice eduction (Blinde et al. 1998). 13
This LR test is somewhat poblematic, howeve, in that the asymptotic distibution of F 1 is nonstandad. Consequently, Hansen (1999) offes a bootstapped pocedue to obtain the p-value fom the fist-ode asymptotic distibution. While the model descibed above is moe ealistic than the basic model that assumes smooth pice adjustment, thee may be moe than one theshold in the eo coection pocess in which case it is necessay to test fo additional thesholds. Fo example, if we conside a two-theshold case (i.e., thee egimes), equation (8) is modified as follows: μ i + β (1) ECT it 1 + p=1 δ p Δε it 1 + e it, ECT it d γ 1 Δε it = μ i + β (2) ECT it 1 + p=1 δ p Δε it 1 + e it, γ 1 < ECT it d γ 2, (12) μ i + β (3) ECT it 1 + p=1 δ p Δε it 1 + e it, γ 2 < ECT it d whee γ 2 is assumed to unique fom γ 1. We again use the Hansen (1999) estimato fo multiplebeak-points. 5 Let S 1 (γ 1 ) be the sum of squaed eos estimated fom the single theshold model above. If the estimated γ 1 fom equation (9) is smalle than γ 2, conditional on the fixed value γ 1, the second theshold γ 2 is estimated can be obtained by finding the value that minimizes the conditional sum of squaes given by: γ 2 = ag min S 2 (γ 2 ) = S (γ 1, γ 2 ). (13) If the F 1 test ejects the null hypothesis of no theshold in favo of the existence of a single theshold, it is also necessay to test the null hypothesis of the existence of one theshold against the altenative hypothesis of the existence of two thesholds, o moe. The LR test statistic fo this pupose is F 2 = (S 1 (γ 1 ) S 2 (γ 2 ))/σ 2, whee the estimated vaiance is σ 2 = S 2 (γ 2 )/n(t 1). As in single theshold model, statistical significance is tested though a bootstap pocedue. If F 2 is sufficiently lage, the null hypothesis of one-theshold model can be ejected, in favo of a two-theshold model specification. The same pocedue is epeated to test fo the existence of moe than two thesholds. Once the theshold value is estimated, we then estimate a panel theshold eo coection model (ECM) that allows fo both asymmetic and nonlinea long-un pass-though. The panel ECM is witten in tems obseved band-level etail and wholesale pices as: Δp it = α 0i + θ (1) ECT it 1 ECT it 1 γ 1 α 0i + θ (2) ECT it 1 γ 1 < ECT it 1 γ 2 α 0i + θ (3) ECT it 1 > γ 2 ECT it 1 + α 1 Δp it 1 + α 1 Δp it 1 + α 1 Δp it 1 + α 2 Δw it + α 3 Δw it 1 + e it, + α 2 Δw it + α 3 Δw it 1 + e it, + α 2 Δw it + α 3 Δw it 1 + e it, (14) 5 Hansen (1999) uses esults fom Chong (1995) and Bai (1997) to show that a sequential estimato estimates multiple-beak-points consistently. 14
whee p it and w it 1 ae the band-level analogs of the etail and wholesale pice vectos intoduced above. Because ou focus is on pass-though, it is impotant to be vey clea as to how maginal changes in wholesale pices effect etail pices in this model. Fotunately, the TAECM povides a vey diect measue of pass-though. Recall that the ECT it vaiable measues the extent to which etail and wholesale pices deviate fom thei long-un equilibium. Theefoe, the pass-though ate is measued as the extent to which etail pices move back towad the longun equilibium, o the θ (k) paametes in (14). These paametes also allow us to test whethe maket powe o consume seach costs influence pass-though ates. Conventional wisdom in much of the ealie liteatue held that apid upwad etail pice adjustment and elatively sluggish downwad adjustment ("ockets and feathes") is due to etailes' execise of maket powe. Moe ecently, howeve, Tappata (2009) and Yang and Ye (2008) explain this phenomenon as fully consistent with ational consume seach behavio. Using the TAECM famewok, we popose a simple method of testing maket powe and consume seach as empiical deteminants of etail pass-though. Intoducing vaiables designed to measue etail maket powe and consume seach allows us to examine the souce of any picing asymmeties that may exist in the data. In this egad, ou empiical appoach goes beyond measuing pass-though asymmeties to explain why pass-though ates may diffe between ising and falling wholesale pice egimes. Indeed, one weakness of the TAECM appoach is that it is agnostic as to the souce of vaiation in adjustment ates ove time, wheeas the theoetical liteatue is vey explicit in this egad. Theefoe, we allow the adjustment paametes θ (k) to depend on measues of maket powe and consume seach. In the latte case, we assume seach costs vay diectly with the numbe of poducts ove which consumes seach, o the numbe of poducts in a etail stoe, N t. Wheeas Peltzman (2000) uses weak poxies fo maket powe to test whethe picing powe was esponsible fo picing asymmeties, we develop a educed-fom appoach moe akin to a "new empiical industial oganization" (NEIO) appoach. Nakamua and Zeom (2010) show that pass-though depends not only the cuvatue of demand, but on competitive esponses by competing bands in the same maket. We follow the appoach taken by Richads, Hamilton and Allende (2011) and allow the adjustment paametes to depend on etaile and time-vaying estimates of the absolute value of the demand elasticity, η it. 6 When the vaiation in demand is diven by factos specific to the band in question, this method can identify changes in maket powe ove time (Besnahan 1989) and can test fo the impact of maket powe on the pass-though ate in a moe poweful way than Peltzman (2000). Extending the TAECM developed above to include vaiety and maket powe leads to estimated vesion of the panel theshold ECM witten as: 6 By defining this vaiable in tems of the absolute value of the pice-elasticity of demand, highe values imply less maket powe. The demand elasticity is estimated using standad discete-choice methods. Specifically, we use a mixed logit model estimated with the simulated maximum likelihood /contol function appoach of Tain (2003) and Petin and Tain (2010). Details ae available fom the authos. 15
Δp it = α 0i + θ (1) (N t, η it ) ECT it 1 ECT it 1 γ 1 α 0i + θ (2) (N t, η it ) ECT it 1 γ 1 < ECT it 1 γ 2 α 0i + θ (3) (N t, η it ) ECT it 1 > γ 2 ECT it 1 + α 1 Δp it 1 + α 1 Δp it 1 + α 1 Δp it 1 + α 2 Δw it + α 3 Δw it 1 + e it, + α 2 Δw it + α 3 Δw it 1 + e it, + α 2 Δw it + α 3 Δw it 1 + e it, (15) whee the adjustment paametes ae allowed to vay with vaiety and picing powe, by band, etaile and by week. Ou pimay hypotheses, theefoe, concen the θ (k) paametes in equation (15), which ae assumed to be linea functions of consume seach costs and maket powe: θ (1) = φ 11 N t + φ 12 η it, θ (2) = φ 21 N t + φ 22 η it, θ (3) = φ 31 N t + φ 32 η it, (16) whee N t is measued as the numbe of stock-keeping units (SKUs) of eady-to-eat beakfast ceeal each week t fo each etaile, and the elasticity, η it, is the absolute value of the own-pice elasticity of demand that vaies by week, band and etaile. To fom testable hypotheses egading the values of each of the φ ij paametes, it is impotant to diffeentiate between the natue of the disequilibium in each egime. Fist, when ECT it 1 γ 1, etail and wholesale pices ae elatively close, so etail pices ae expected to ise. Second, when γ 1 < ECT it 1 γ 2, the gap between etail and wholesale pices is of a moe nomal value and no expectations as to etail pice movements ae fomed. Thid, when ECT it 1 > γ 2, etail pices ae elatively high and ae expected to fall to estoe the long-un equilibium. Next, ecall that lowe value of the own-pice elasticity epesents geate picing powe fo the band in question. Theefoe, conventional theoy maintains φ 12 > 0 as maket powe allows etailes to pass along moe of a wholesale pice shock than would othewise be the case, while φ 32 < 0 as etailes with maket powe need not pass-along immediately the full value of any eduction in wholesale pices. Said diffeently, etailes with maket powe ae less concened with competitive esponses to highe etail pices so aise them quickly when etail pices ae expected to ise (i.e., when wholesale pices ise), and lowe them slowly when etail pices ae expected to fall (i.e., when wholesale pices fall). The theoy is silent on how maket powe influences adjustment in the middle egime. With espect to consume seach costs, ecall that N t seves as a poxy fo seach costs faced by consumes. Geate vaiety implies highe seach costs because consumes must evaluate a geate numbe of altenatives befoe finding the one that they pefe. Theefoe, geate vaiety is expected to lead to less-complete adjustment in the lowe egime (φ 11 < 0) as the gains to seach ae elatively low when etail and wholesale pices ae close. Pass-though ates ae expected to ise in vaiety in the uppe egime (φ 31 > 0) because etail pices ae elatively high so the expected gains fom seach ae high. If φ 11 < 0, then the ate of upwad etail-pice adjustment slows in vaiety as the etuns to seaching ae lowe, fewe consumes ae seaching, and fims have less of an incentive to aise pices. Ou hypothesis is that the cost of seach ises in the numbe of vaiants offeed by the stoe, so the pass-though ate should fall accodingly. Futhe, because etailes with moe maket powe need not pass the tade deal on, we expect the downwad adjustment ate in etail pices to fall with maket powe (diectly with the elasticity of demand). This is the "ockets and feathes" phenomenon. 16