Differentiated Product Competition and the Antitrust Logit Model: An Experimental Analysis *

Transcription

1 Dfferentated Product Competton and the Anttrust Logt Model: An Expermental Analyss * by Douglas D. Davs Department of Economcs Vrgna Commonwealth Unversty Rchmond, VA E-mal: dddavs@vcu.edu Phone: (804) Fax: (804) and Bart J. Wlson Interdscplnary Center for Economc Scence George Mason Unversty, MSN 1B2 Farfax VA E-mal: bwlson3@gmu.edu Phone: (703) Fax: (703) March, 2003 Abstract Ths paper reports a laboratory experment desgned to begn a behavoral examnaton of the Anttrust Logt Model (ALM), a merger smulaton devce that U.S. anttrust authortes use to help determne when antcompettve problems may arse from horzontal mergers n dfferentatedproduct markets. We fnd that the ALM screens out non-problematc mergers rather well, even though the ALM predcts performance n specfc markets mprecsely. Further examnaton of the data suggests that n ths context, adustments to pre-merger devatons from the underlyng Nash equlbrum, rather than the exercse of market power drve post-merger performance. JEL Classfcatons: C9, L1, L4 Keywords: dfferentated products, anttrust analyss, expermental economcs * We thank the Edtor and two anonymous referees for ther helpful comments. The usual dsclamer apples. Fnancal assstance from the Natonal Scence Foundaton and the VCU Faculty Excellence fund s gratefully acknowledged. The data, nstructons, and appendx are avalable at

2 1. Introducton Anttrust merger enforcement polcy has changed substantally n the last decade. In 1992 the Department of Justce (DOJ) and the Federal Trade Commsson (FTC) revsed ther Horzontal Merger Gudelnes (Gudelnes) and added an enforcement focus on unlateral actvty to exstng consderatons about the potental for cooperatve behavor. 1 Most horzontal merger nvestgatons now focus on potental unlateral effects and are evaluated n terms of specfc models of olgopoly performance (Froeb, 1994). Horzontal mergers n dfferentated product markets are an mportant example. DOJ analysts argue that n such contexts the standard concentraton measure (the Herfndahl-Hrschman Index) provdes lttle gudance as to when antcompettve problems mght arse (see e.g., Werden and Froeb, 1996). In such cases pettoners may reasonably argue ether that the mergng partes compete n a very broad market and that concentraton s thus very low, or that markets are very narrow and that the proposed consoldaton presents no problem, snce products of the mergng enttes are unrelated. As a substtute for standard concentraton measures DOJ staff have developed an Anttrust Logt Model (ALM) merger smulaton to help dentfy antcompettve problems n dfferentated-product markets. The ALM assumes a logt demand system and that sellers nteract as Bertrand compettors. 2 The logt demand assumpton s extremely useful n ths context, snce nvestgators need only prces, market shares, a measure of the rate of substtutablty between products, and a measure of demand elastcty to generate predctons. The convenence of the ALM s appealng, and the approach may be useful for anttrust work. As Werden and Froeb (1996, p. 65) observe, even f consdered unrealstcally smplstc, merger smulatons provde a lttle lght n a very dark place. Nevertheless, a number of questons crtcal to the usefulness of ths approach are unanswered. Frst, the model s underlyng assumptons may be frequently volated n natural markets. In partcular, demand may be msspecfed as a logt system. Second, the ncentves that drve unlateral effects are subtle and may fal to affect behavor as predcted. Thrd, demand parameter estmates from naturally occurrng data may not be suffcently precse to allow accurate predctons of post-merger behavor. The relevance of the ALM s predctons n these more general crcumstances bears scrutny. 3 Ths paper reports an experment desgned to shed lght on these ssues. The usefulness of expermental methods n ths context bears emphass. The laboratory provdes a unque medum for evaluatng the predctve power of the ALM under best shot crcumstances, where the nvestgator 1

3 constructs an envronment that conforms strctly to the underlyng assumptons of the model, and where seller choces are not clouded by the rch varety of consderatons extraneous to the equlbrum analyss that may affect decsons n natural crcumstances. Although observng predcted behavor n the laboratory would say lttle about the relevance of the model n rcher natural crcumstances, a falure to observe predcted outcomes n the laboratory should rase serous questons about the potental value of the model as a predctor of behavor n the more complex natural world. Further, provded that the ALM works acceptably well strctly on ts doman, the laboratory nvestgator can also examne the effects of specfc devatons from mantaned underlyng assumptons on the predctve value of the model. The related expermental research ncludes Davs and Holt (1994), Davs and Wlson (2000), and Wlson (1998), who fnd that sellers both recognze and explot market power n a smple homogeneous-product prce-settng envronment wth dscrete unts. In each of these experments, market power s carefully dstngushed from the number of sellers, and market power clearly affects prces more than market structure. On the other hand, Wellford (1990) fnds that sellers encounter dffcultes n explotng the comparatvely subtle strategc advantages conferred by mergers n more conventonal olgopoly markets. In a seres of homogeneous Cournot markets she fnds that prces never ncrease sgnfcantly post-merger, as predcted by a non-cooperatve model. The lmted expermental research on dfferentated product olgopoles focuses on the effects of nformaton on performance. Dolbear et al. (1968) report that common knowledge about cost and demand structures tends to generate margnally lower prces n a dfferentated product prce-settng game. They also fnd that prces move nversely wth the number of sellers. More recently, Huck, Normann and Oechssler (2000) report that nformaton about the actons of ndvdual rvals tends to ncrease compettveness n a seres of 40-perod dfferentated product quadropoles. However, the effects of the added nformaton were sgnfcant only n Cournot markets and not n comparable Bertrand markets. In ther Bertrand markets, aggregate average results followed Nash predctons closely n ether nformaton condton. In ths paper we fnd, as wth prevous work, that Nash predctons organze outcomes better than the obvous rval ont-proft maxmzng (JPM) and compettve predctons. However, as s also the case wth much of the prevous research, the correspondence between predcted and observed outcomes s unformly weak, suggestng that the ALM holds lttle promse as a means of 2

4 predctng the prce effects of a merger. Surprsngly, the ALM performs reasonably well n ths envronment as a screenng devce, n the sense that most of the large post-merger prce effects occurred n markets where a large prce ncrease was predcted. However, closer examnaton of expermental results suggests that devatons from the underlyng equlbrum rather than market power exercse drve the ALM s predctve power. The remander of the paper s organzed as follows. Secton 2 sketches out pre- and postmerger predctons for a non-cooperatve Bertrand olgopoly wth dfferentated products. We develop predctons for logt and lnear demand specfcatons. Secton 3 descrbes expermental desgn, parameters and procedures, whle secton 4 presents the results. Secton 5 concludes. 2. Non-Cooperatve Predctons n Bertrand Competton Consder a market wth n prce-settng sellers, each of whom produces wthout fxed costs, and wth a constant margnal cost, c. Defnng q (p) as seller s demand functon gven the vector p of own and other prce choces, each seller optmzes π = ( p c ) q ( p). Takng frst order condtons and rearrangng terms generates the standard result p c = p / η, (1) where own prce elastcty η s defned as a postve number. Suppose now that two frms and k merge to form frm m. The obectve functon for the consoldated partes becomes π m = ( p c ) q ( p) + ( p c ) q ( p) k k k Rearrangng the frst order condtons to solve for the prce-cost dfference yelds for frm, p η q k k c = p / η + ( pk ck ) (2) η q and smlarly for frm k. The rghtmost term n (2) ndcates that the dfference between the prcng decsons of a merged and unmerged frm s that the merged partes account for the effects of ther own prces on the proftablty of ther related products. We evaluate pre-merger and post-merger predctons n lght of standard reference outcomes. The compettve outcome, where prce equals margnal cost, represents one natural alternatve, snce ths outcome represents a lmt to non-strategc, non-cooperatve behavor. The 3

5 ont proft maxmzng (JPM) condton, a lmt to gans from cooperaton, s another. Actng n concert, frms optmze π JPM = ( p c ) q ( p) Rearrangng frst order condtons yelds the optmal condton for any frm, p c = p ηk qk / η + ( pk ck ). (3) η q k Lookng at the rght sde of (3) we note that n the JPM condton each frm accounts for nteracton effects on all frms when makng an optmal prcng decson. More specfc predctons requre specfcaton of a demand system. We consder two demand systems below, logt and lnear. 2.1 Logt Demand The logt demand system, developed by McFadden (1974), s based on a random utlty model of consumer choce. Here we develop a very smple verson, where consumers substtute equally among all nsde products. 4 Consder a market consstng of n 1 nsde compettors, and an outsde good n that represents the all other goods. For consumer l, the utlty of a choce = 1,, n, may be wrtten as u = α β p + v, where α s a qualty parameter, β s a common slope l l parameter reflectng senstvty of consumers to a prce change, and vl s a consumer-specfc preference for the product. If v l follows an extreme value dstrbuton e v l f ( v l ) = e, the probablty P that consumers collectvely select a partcular seller becomes P = n e m= 1 α βp e α βp m m. The logt demand system produces the followng own and cross-prce elastctes, η = β p ( 1 P ) = [ β p(1 s ) + η s ] p /( p) (4) and η k = β p P = ( β p η) s p /( p), (5) 4

6 where s s frm s market share condtonal on the choce of an nsde good (e.g., s = P /[1 P n ]) and p s the share-weghted market prce. The mpled (postve) aggregate elastcty for all nsde goods s PI ( λ p) λ η = β ppn, (6) λ P ( p) where λ s a scalar evaluated at I λ = 1, and PI = (1 P n ). Only relatve dfferences n α s matter, so estmates are generated by arbtrarly selectng an αn for the outsde good. Relatveα s are derved from logs of the rato of P to P n : ln( P / P ) = α α β p. (7) n n The pre-merger predcton s found by nsertng the expresson for η n equaton (4) nto equaton (1) to produce p c = p /[ β p(1 s ) + η s ]. (8) Smlarly, nsertng the expressons for η and η k n equatons (4) and (5) nto equaton (2) generates the post-merger predcton. Solvng ths yelds p c = pk ck = p /[ β p(1 sm ) + η sm ], (9) where s m =s + s k. Anderson, de Palma and Thsse (1992) establsh than a unque equlbrum exsts for the above system. However, snce prce appears on both sdes of equatons (8) and (9), the soluton must be computed numercally. In general, the ALM smulaton process proceeds as follows. Frst, assumng that a market s n equlbrum, s (vector of market shares), p, β, and η s nserted nto both sdes of equaton (8). Adustng an mpled cost vector c to balance both sdes of equaton (8) generates the pre-merger equlbrum condton. The post-merger predcton s found by nsertng s, β and η and the mpled costs nto equaton (9), and adustng the post-merger prce vector untl both sdes of equaton (9) balance for each frm. It s worth notng that both the pre-merger equlbrum condton n equaton (8) and the post-merger equlbrum n equaton (9) are developed entrely n terms of p, s, and sngle measures of β and η. Anttrust authortes typcally ether have these data or can reasonably estmate them n the very tght tmeframes of the merger revew process. 5 Fnally, we fnd the JPM condton for all nsde frms by nsertng equatons (4) and (5) nto equaton (3) and smplfyng for each frm : 5

7 p c = 1/((1 P ) β ) p /η. (10) k = k 2.2. Lnear Demand Demand, of course, need not be logt. Indeed, logt demand systems ncorporate the potentally troublng ndependence of rrelevant alternatves assumpton, whch may be volated frequently n practce. 6 Deneckere and Davdson (1985) llustrate wth a lnear demand system some general results for mergers wth dfferentated products and prce competton, that parallel those generated above for logt demand. 7 A full development of ther results s not warranted here. However, to obtan a flavor of ther results, consder the standard demand system used by Huck, Norman and Oechssler (2000) 8 q = V α p + θ p, (11) where α > θ > 0. In ths case, the (postve) own prce elastcty s η = α p / q (12) and the cross prce elastcty s k η = θ p / q. (13) k Insertng equaton (12) nto equaton (1) generates the pre-merger equlbrum condton q p c =. (14) α When frms and k consoldate, substtutng equatons (12) and (13) nto equaton (2) yelds p q θ c = + ( pk ck ), α α whch mples that the post-merger mark-up of prces over costs s nversely related to own prce senstvty (α), and drectly related to the consumers preferences for substtutng between products (θ). The relatve effects of a merger on prces are more easly seen n the specal case where the two mergng frms have dentcal costs: qm p c = pk ck =, (15) α θ where q m = q + q k. A comparson of equatons (14) and (15) reveals that the prce-cost mark-up for the consoldated partes exceeds that for ndependent frms, provded that q / > α /( α θ ), a m q 6

8 condton that Deneckere and Davdson (1985) show s certan to hold for a downward slopng symmetrc lnear demand system. To fnd the JPM predctons, equatons (12) and (13) are nserted nto equaton (3) to yeld p c q = α + k θ ( pk ck ). (16) α In the specal case where costs are symmetrc, equaton (16) smplfes to qjpm pjpm cjpm = (17) α ( N 1)θ Equaton (17) exceeds equaton (15) as long as q m / q JPM α ( N 1) <, whch agan s a condton α θ that Deneckere and Davdson show s certan to hold wth down-slopng, symmetrc lnear demand. Unlke the logt case, the lnear dfferentated product olgopoly may be solved explctly. However, even for the smple demand system used here, the explct solutons yeld complcated, rather unenlghtenng expressons. More mportant for the present purpose of developng an expermental desgn, we note that gven equlbrum parameters for the logt model, an dentcal equlbrum condton can be generated n the lnear model. In the logt model, one mputes c as an equlbrum condton for gven parameters p, s, and η. Presumably, the number of (lnear demand) sellers N and total market sales Q = are also known. These varables determne unque own and cross prce elastctes, whch by equatons (12) and (13) determne α and θ n the lnear demand system. Insertng α, θ and p, nto the equlbrum condton for the lnear system represented n equaton (11) yelds a unque V. β N q = 1 Unlke pre-merger condtons, post-merger equlbrum condtons vary across demand systems (see Crooke, Froeb, Tschantz and Werden, 1999). In ths experment, we focus on the effects of the demand system on the behavoral stablty of the system, so our parameter choces mnmze predcted dfferences across demand systems. 3. Expermental Desgn and Procedures A prmary goal of ths experment s to gve the ALM a best shot of generatng predcted behavor. Toward ths end, we nclude as much symmetry n the desgn as possble. Sellers have symmetrc costs, and products dffer so that all sellers have symmetrc prces, shares and profts n 7

9 the pre-merger equlbrum. The market structure conssts of four sellers pre-merger, whch decays to three sellers post-merger. Ths choce of market structure reflects a balance of desgn needs. On the one hand, the magntude of predcted prce effects moves nversely wth the number of sellers, suggestng that we mnmze the number of sellers. On the other hand, we need to leave enough sellers post-merger to mantan a reasonable expectaton of non-cooperatve behavor, because the ALM predcts prce adustments on the bass of changes n non-cooperatve crcumstances Desgn The experment conssts of a seres of 24 dfferentated-product quadropoles. Each market conssts of 60 tradng perods. For the frst 30 perods each of four symmetrc sellers makes a seres of smultaneous prce choces. After perod 30, a merger occurs, and one seller s gven control over the producton decsons of another seller. The market then contnues wth three sellers for an addtonal 30 perods. Comparng post-merger behavor wth pre-merger predctons allows an assessment of the model s predctve power. The experment ncludes two desgn condtons. Frst, to generate some nsght nto the ALM s capacty to dfferentate between problematc and non-problematc mergers, we nduce a Large Effects desgn, where predcted prces ncrease post-merger by an amount that anttrust authortes would easly consder troublesome, and a Small Effects desgn, where the predcted prce ncrease would typcally not be vewed as problematc. As a reference, we use the 5% prce ncrease dentfed as crtcal to defnng the scope of markets n the Gudelnes. 10 Second, to allow some nsght nto the consequences of changng the underlyng demand system (albet farly subtlely), we examne both lnear and logt demand systems n each desgn. The four columns n Table 1 summarze the expermental parameters for each of the desgn condtons. As s clear from the bolded entres lsted n the row labeled Nash: Pre-Merger predctons, all markets are calbrated to generate dentcal pre-merger equlbrum prces p = 55 and market shares s = 25% for all sellers. In the Large Effects desgn, logt parameters (η =.22449, β = , c=20) and lnear parameters (V = 100, α = 7/3, θ=2/3 and c=20) are calbrated so that post-merger prces ncreases easly exceed 5%. For example the overall share weghted average prce (SWAP), ncreases 8.0% and 9.3% n the Logt and Lnear specfcatons, respectvely. In the Small Effects desgn, logt parameters (η = 1.575, β = and c=36.2) and lnear parameters (V 8

10 = 209.8, α = 13/3, θ = 2/3 and c=36.2) are calbrated so that post-merger prce ncreases less than 5%. The SWAP ncreases 2.3% and 1.8% n the Logt and Lnear specfcatons, respectvely. Despte the smlarty of pre- and post-merger predctons across the lnear and logt demand systems, shftng demand systems may have behavoral consequences. Most partcularly, cooperatve predctons dffer substantally across demand systems, partcularly n the Large Effects treatments. As seen n the JPM predctons lsted at the bottom of Table 1, the share-weghted ont proft maxmzng prce, P JPM, ncreases from 95.8 dollars n the Logt Large Effects treatment to 160 dollars n the Lnear Large Effects treatment. Thus, the lattude for gans from cooperatve behavor s much hgher n the lnear model than n the logt model. In the Small Effects treatments, the change n the JPM prce across demand systems s much smaller, ncreasng only from 62.5 dollars n the Logt Small Effects treatment to 63.1 dollars n the Lnear Small Effects treatment Procedures Each sesson conssts of 60 posted-offer tradng perods. At the outset of each sesson, partcpants st n vsually solated booths wth personal computers, and a montor reads nstructons aloud as partcpants follow along on a copy of ther own. In addton to explanng tradng rules and record-keepng procedures, the nstructons ndcate (a) that sellers all have the same unt costs (b) that these costs reman unchanged throughout the sesson, and (c) that sellers are dfferentated n the eyes of the fully revealng buyer, but that buyer preferences vs-à-vs each seller are symmetrc. 12 The very complete cost and demand nformaton provded n the nstructons s ntended to facltate noncooperatve outcomes, as suggested by Huck, Normann and Oechssler (2000). Fnally, the nstructons ndcated that lab dollars were converted nto cash at the rate of 10,000 lab dollars for US$1. 13 A perod proceeds as follows. Frst, sellers smultaneously choose prces, whch a montor records. The montor then publcly announces the prce decsons as he enters the nformaton nto a spreadsheet that determnes ndvdual sales quanttes. The montor then prvately dscloses to sales quanttes to partcpants. Sellers record all prce decsons and ndvdual sales quanttes n ther spreadsheets. Spreadsheet formulas calculate ndvdual and cumulatve earnngs pror to elctng prce decsons for each subsequent perod. In addton to ndvdual earnngs nformaton, sellers may access the prcng hstory n both tabular and graphcal form. 14 9

11 Each perod repeats the above process exactly, wth one excepton. After perod 30 a merger occurs, and one seller (the acqurng seller ) assumes operaton of a second seller s computer (the acqured seller ) for the remander of the sesson. For 16 sessons (eght Small Effects sessons and eght Large Effects), the acqurng seller had the hghest earnngs for perods 1 to 30 and the acqured seller had wth lowest earnngs for those perods. Ths selecton procedure was not explaned to partcpants. As a desgn parameter, the acquston rule s not well establshed n the expermental lterature. 15 We selected ths hghest earner acqurer rule n an effort to maxmze the chances of observng market power post-merger. However, other acquston rules may better characterze the natural parallel crcumstances. As a check on the mportance of the acquston rule, on post-merger performance we conducted an addtonal eght Large Effects sessons (four Logt and four Lnear), wth a random acqurer rule. In the random acqurer markets, after perod 30 one seller s randomly selected to be acqured, then after excludng the hgh earner pre-merger, another seller was randomly selected to be the acqurer. 16 In all sessons, the acqured seller receves a $7 buyout fee, n addton to ther appearance fee and ther salent earnngs for the sesson. The nstructons dd not dsclose n advance ether the merger or the total number of perods n a sesson. The partcpants were 96 undergraduate students at Vrgna Commonwealth Unversty and the Unversty of Arzona. No one partcpated n more than a sngle sesson. In addton to ther salent earnngs, the partcpants were pad a $6 appearance fee. Earnngs for the 90 to 130 mnute sessons averaged about $22.50, and ranged from $14.75 to $ To summarze, the experment conssts of 24 sessons: four sessons n each cell of the 2 2 desgn, {Logt, Lnear} {Small Effects, Large Effects}, wth the hgh earner acquston rule. In addton, the experment ncludes eght addtonal Large Effects sessons (four Logt and four Lnear) usng the random seller acquston rule. 4. Expermental Results The share weghted average prce (SWAP) for four representatve markets n Fgure 1 provdes a qualtatve summary of the expermental results. In each panel of the fgure, the hollow and sold dots denote Logt and Lnear sessons, respectvely. Notce that the all four tme seres smlarly drft smoothly across perods. Further, markets are more nearly drawn to Nash predctons than to ether to P JPM or c. Nevertheless, the markets do not unformly converge to Nash predctons. 10

12 The SWAP falls wth a ±5% band about the pre-merger Nash predcton, P o and post-merger Nash predctons P m (hghlghted as bolded lnes) only n the Small Effects markets. Comparng across panels suggests a treatment effect assocated wth changng the sze of predcted prce effects. Consderably larger prce swngs are shown n the upper Large Effects panel. On the other hand, the representatve markets suggest no obvous effect of changng the underlyng demand form. The overall magntude of prce swngs wthn the Large Effects and Small Effects panels appear smlar. In what follows we more formally establsh the above observatons suggested by Fgure 1, and then drawn some conclusons regardng the predctve power of the ALM. 4.1 Outcomes Relatve to Nash Predctons The absence of a unform tendency for markets to converge to a partcular outcome toward the ends of sessons complcates our summary of market performance. On the one hand, absent general convergence, a summary based on a specfc subset of fnal perod market data would provde potentally msleadng nformaton regardng treatment effects. On the other hand, weghtng equally decsons made n the fnal perods of a market wth those made n the ntal early perods, where sellers are ust learnng about demand and the market process may also reflect naccurately seller responses to treatment effects. We address ths problem by evaluatng performance usng three dfferent market segments as the unt of analyss: the entre pre-merger and the entre post merger segments (perods 1-30 and perods 31-60, respectvely), the fnal half of premerger and post-merger segments (perods and perods 46-60) and for the fnal fve premerger and post-merger segments (perods and perods 56-60). Tables A1.1 to A1.3 n the appendx report the mean pre-merger and post-merger SWAP for each market for each of these three segments. For purposes of brevty, we present n the text only summary comparsons of these measures. Table 2 provdes summary evdence regardng the relatve convergence of markets to Nash predctons. Columns (1) and (2) of Table 2 reprot, respectvely, the number of nstances where the mean SWAP s closer to unt costs, c, or the ont proft maxmzng prce P JPM than to the Nash predcton for the pre-merger perod, P o. The Nash predctons overwhelmngly out-perform the standard rval reference predctons. Pre-merger only the 30-perod segment had more than 2 of the 24 markets closer to c than to P o. (The fve 30-perod segments where markets were closer to c than 11

13 to P o reflect some tendency for prces to start below P o.) Smlarly, notce n column (2) that the mean SWAP s closer to P JPM than to P o only once, ndependent of the segment choce. Postmerger, the relatve drawng power of the post-merger Nash predcton, P m, s even stronger. As summarzed n columns (3) and (4) the mean SWAP s closer to c or P JPM only once and only n the 30 perod segment. Despte the relatve drawng power of Nash predctons, convergence remans rather ncomplete, as summarzed n Table 3. Columns (1) and (3) report that the mean SWAP s are wthn 5% of the underlyng Nash predcton n no more than one thrd of the markets (8 of 24), regardless of the segment-length used as a bass of analyss. Turnng to columns (2) and (4) observe that no more than 14 of the 24 markets fall wth 10% of the Nash predcton, agan ndependent of the segment-length used as a bass of analyss. Further, scannng down the segment blocks n Table 3 suggests no obvous tendency for markets to converge to Nash predctons toward the end of sessons. For example, as seen at the bottom of column (2), usng the last-5 perod segment as the unt of analyss, only 10 of the 24 markets are wthn 10% of P o, and the same number are wthn 10% of P o of usng a 30 perod segment as the unt of analyss. Smlarly, as seen n column 4, usng the last-5 perod segment as the unt of analyss post-merger, 12 of the 24 markets are wthn 10% of P m, compared to a slghtly larger number of 14 are wthn 10% of P m usng a 30 perod segment as the unt of analyss. In summary, statc non-cooperatve predctons organze behavor better than rval compettve or ont proft maxmzng outcomes; however, markets generally do not converge fully to Nash predctons. Ths frst result was expected, and ndeed, the antcpaton of ths result was one of the motvatng factors for ths research. The expermental market lterature s replete wth examples of the relatve drawng power of non-cooperatve predctons, n Bertrand type (posted-offer) envronments (see e.g., ch. 4, Davs and Holt, 1993). Nevertheless, the convergence observed n laboratory markets typcally does not ental anythng approachng a precse achevement of statc Nash predctons. We suspected that the persstent varablty n such markets would confound the behavoral relevance of relatvely small changes n Nash predctons motvated by merger-nduced changes to market power. Our second result evaluates the effects of changng the underlyng demand form and ownand cross-effect parameters. Frst, holdng predcted prce ncreases fxed, changng the underlyng demand system does not appear to affect convergence. Consder, for example, post-merger 12

14 performance usng the 30-perod segment as the unt of analyss, summarzed n the upper rght block of Table 3. Three of the eght Logt Large Effects markets are wthn 10% of P m, compared to four of the eght Lnear Large Effects markets. Smlarly, all four of the Logt Small Effects markets are wthn 10% of P o, as are three of the four Lnear Small Effects markets. Second, changng underlyng parameters does affect convergence: seven of the eght Small Effects markets are wthn 10% of the post-merger Nash prce P m as compared to only seven of the sxteen Large Effects markets. The absence of a demand functon effect and the sgnfcance of a parameter effect s robust to the choce of perod segment used as a bass of analyss and to both pre-merger and post mergerbehavor. The three columns of Table 4 lst p values for Fsher Exact Probablty tests of the null hypothess that the number mean SWAP s are wthn 10% of the Nash Predcton does not dffer across groups. As seen n columns (1) and (2) one cannot reect ths null hypothess for demand system changes ether for Large Effects or Small Effects markets at anythng approachng conventonal sgnfcance levels, regardless of the perod-segment used as the bass of analyss and regardless of whether we consder pre-merger or post-merger behavor. On the other hand, as seen n column (3) Small Effects markets clearly converge more completely than Large Effects markets. For every comparson except the 30-perod segment pre-merger, Small Effects markets are closer to the relevant Nash predcton than the comparable Large Effects markets at a mnmum 95% confdence level. To summarze, changng underlyng parameters affects behavor. Convergence to underlyng non-cooperatve predctons s more complete n markets wth smaller predcted comparatve-statc effects. However, holdng the predcted comparatve statc effects constant, changng the demand form does not to affect convergence n these markets. Ths second result suggests that the ALM mght perform well as a screenng devce, despte the generally poor drawng power of non-cooperatve predctons. Even though Small Effects markets do not latch on to noncooperatve predctons, larger prce swngs and more szable devatons occur n Large Effects markets, where larger effects would be predcted by the ALM. Pror to consderng the predctve power of the ALM we comment brefly on the effect of changng the acqurng-seller rule on post-merger performance. The hgh varablty of market outcomes and the relatve subtlety of predcted prce ncreases confound our drawng conclusons regardng the propensty of sellers to exercse market power and the effects of acqurng-seller rule alteratons on exercse of market power. Consder percentage ncreases post-merger prces n the 13

15 eght sessons wth the random acqurer rule wth the eght sessons wth the hgh earner acqurer rule (all Large Effects sessons). As the upper porton of Table 5 llustrates, dfferences across the merger rules never approach sgnfcance, even though for the last-15 and last-5 perod segments, medan prce ncreases are 8 percentage ponts hgher n the markets usng the hgh earner acqurer rule than n the sessons usng random acqurer rule. The consderably large standard devatons ndcate the very hgh varablty n outcomes wthn cells. Usng observed post-merger prce ncreases as a measure of market power s confounded further by the varablty of pre-merger prces relatve to the underlyng equlbrum. Markets substantally below P o may ncrease post-merger purely out of a weak tendency to equlbrate. The medan prce devatons from P o, shown n the bottom half of Table 5, provde evdence suggestng that ths effect may drve some of the dfferences n medan prce ncreases observed across the random acqurer and hghest earner acqurer sessons. Notce that for the last-15 and last-5 perod segments, medan pre-merger prces are 5 to 6 percentage ponts lower n the markets usng the hghest earner acqurer rule than those usng the random acqurer rule, whch would lead us to antcpate the larger medan ncreases observed post-merger n ths treatment. Other measures of market power smlarly do not dffer sgnfcantly across changes n the acqurng seller rule. In fact, overall, these measures suggest that sellers exercsed market power rather nfrequently. For example, n ths symmetrcal game, the model predcts that the merged frm should post the same prce n each market, and ths prce should be the hghest prce posted. Usng the fnal 15-perod segment as the unt of analyss, the consoldated frms posted the same prce for each frm more than 7 tmes n only 3 of the 24 markets. The merged seller was a prce leader more than 7 tmes n only eght markets. 17 In sum, nothng strongly suggests that changng the rule for dentfyng the acqurng seller alters outcomes, and ndeed, there s lttle evdence to suggest that sellers n any treatment exercsed market power frequently The Predctve Power of the ALM We now turn our attenton to how well predctons based upon pre-merger outcomes dstngush problematc mergers from non-problematc ones. If the form of the underlyng demand functon s known a pror, the true demand parameters (V, α and θ for a lnear system, and β n a logt system) are perfectly recoverable from observed prce and quantty data. 18 These parameters, combned wth a measure of observed equlbrum prce and quantty choces, mply a cost vector 14

16 c, and a post-merger prce vector p. As n the prevous subsecton, we consder all 30, last-15 and last-5 perod segments as unts of analyss. For each segment, we use each seller s average prce choce and average quantty outcome for that segment as the relevant measure of prce and market share data. In natural contexts, the analyst doubtfully knows wth certanty the underlyng functonal form of the demand system. To obtan some feel for the potental effects of demand msspecfcaton, we also estmate lnear parameters V, α and θ wth data from the logt demand markets and logt parameter β wth data from the lnear demand markets. Regressons wth prce and share (quantty) data from the frst 30 perods of each market yeld estmates of V, α and θ, or β. 19 Gven estmates of the relevant demand parameters, an mpled equlbrum cost vector c, we can generate post-merger prces and market share predctons, as n the case of known demand. Brevty consderatons prevent a complete dsplay of the pre-merger cost estmates and postmerger prce predctons. (See Tables A2.1 to A2.3 n the Appendx). We confne our comments to two observatons. Frst, usng observed prce and quantty data to generate mpled costs results n a cost structure that devates dramatcally from the actual costs, as llustrated n Fgure 2 llustrates for the 15-perod pre-merger segment. 20 Each of the four horzontally algned panels n the fgure dsplays the dstrbuton of mpled equlbrum costs for the 16 sellers n each treatment cell. The black bars llustrate the dstrbuton of mpled costs wth correctly specfed demand, whle the whte bars dsplay the mpled cost dstrbuton wth msspecfed demand. As each of the panels llustrated, mpled costs vary wldly from actual costs. Consder frst the black bars when the demand system s correctly specfed. For example, n the Logt Large Effects markets, shown at the top of Fgure 2, mpled costs range from 3.90 cents to cents, dramatcally dfferent from the actual unt costs of 20 cents. Even n the Lnear Small Effects treatment, where the devaton of mpled costs from actual costs s the smallest, mpled costs range from cents to cents, consderably dfferent than the actual unt costs of 36.2 cents. 21 Wth the possble excepton of some of the Logt Large Effects sessons, the whte bars llustratng mpled costs for msspecfed demand are not substantally more scattered than the black bars, suggestng that dsequlbrum prcng, rather than ncorrectly estmated demand causes the bulk of the mpled cost dsperson. 22 To summarze, our data ndcate that the assumpton of equlbrum behavor pre-merger s an mportant one and notceably unobserved n ths experment. Dsequlbrum prcng behavor can 15

17 result n mpled cost vectors that devate very substantally from actual costs. On the other hand, demand msspecfcaton n ths envronment, does not mportantly affect mpled costs. Ths result s mportant for two reasons. Frst, mpled cost heterogenetes mply smlarly heterogeneous post-merger prce predctons. Markets wth generally below equlbrum prces premerger wll generate smaller own and cross prce elastctes, whch n turn result n larger predcted prce ncreases post-merger. Subsequently observed prce ncreases, may thus reflect, at least n part, some tendency for markets to equlbrate post-merger. Second demand msspecfcaton does not appear to be a prmary motvaton for errant predctons n ths context. For ths reason, n what follows we confne our attenton to predctons wth correctly specfed demand. 23 Our second observaton pertans to the relatonshp between predcted and observed prce ncreases. Despte the mprecson of mpled costs, we surprsngly fnd that the ALM serves some role as a screenng devce. The scatter plot n Fgure 3 llustrates ths usng last-15 perods segments. 24 In the fgure the bolded horzontal and vertcal sold lnes llustrate 5% predcted and 5% observed ncreases, respectvely. Notce frst that predctons sometmes err very badly. For example, the observed 108% ncrease shown as the hollow dot labeled (1) n the fgure very substantally exceeds the predcted 18% ncrease. Smlarly, the observed 22% post-merger prce drop, shown as a sold dot labeled (2) was poorly predcted as a 5.2% prce ncrease. Nevertheless, 17 of the 24 markets are correctly classfed by the ALM. Eleven dots fall n the upper rght quadrant of the fgure, ndcatng nstances where a 5% or greater ncrease s correctly predcted. Another sx markets fall n the lower left quadrant, ndcatng nstances where 5% or lower prce ncreases were both predcted and observed. The mddle panel of Table 6 summarzes the classfcaton of outcomes by a predcted 5% ncrease, usng last 15-perods segments as the unt of analyss. Usng a Fsher exact probablty test, the null hypothess that the classfcaton process s random may be reected at a 95% confdence level. The left and rght panels of Table 6 report a comparable classfcaton of predcted and observed prce ncrease for last-5 and all 30 perod segments. As s clear from the table, the selecton of a subset of perods as the unt of analyss does not affect the result that the ALM has some capacty to dentfy potentally problematc mergers. 25 Further and perhaps as noteworthy s the small number of false negatves (nstances where post-merger prce ncreases are not predcted). Regardless of the segment used as the bass of analyss, of the 24 markets, the ALM fals to antcpate ust 2 nstances where prces ncreased by more than 5% post-merger. Thus, even 16

18 though the ALM does not accurately predct post-merger performance, the ALM here serves some role as a screenng devce. Gven the extremely poor organzng power of Nash predctons, and the rather questonable evdence of market power exercse, ths last result s surprsng (at least to us). Why does t happen? A large part of the explanaton les n the relatonshp between the predcted ncreases and pre-merger prce levels. In partcular, large prce ncreases tend to occur n markets that are substantally below equlbrum pre-merger. Ths tendency s llustrated by the scatter plot n Fgure 4, whch graphs the relatonshp between the percentage devaton from P o pre-merger, and the percentage observed prce ncrease post-merger, usng a last-15 perod segment as a unt of analyss. The strong nverse relatonshp between pre-merger prce devatons and post-merger prce ncreases shown n Fgure 4 s strkng. In fact, comparng Fgures 3 and 4 suggests that the relatonshp between pre-merger equlbrum devatons and post merger prce ncreases s stronger than that between ALM predctons and post-merger performance. 26 To more formally evaluate the relatonshp between predcted and observed post-merger behavor we regress observed post-merger percentage prce ncreases on two competng explaners of post-merger performance: (a) the percentage prce ncrease predcted by the ALM, and (b) the devaton of pre-merger prces from P o. 27 Specfcally, we estmate 3 O = β o + β r Dr + β1 X + β 2 X + ε, (19) where the dependent varable O s the observed percentage ncrease n prces post merger and X s a measure from pre-merger outcomes, ether the percentage ncrease predcted by the ALM, %PD, or the percentage devaton from the pre-merger Nash equlbrum prce, %ND. A cubc term X 3 s ncluded to allow for the possblty of non-lnear effects between observed and observed behavor that may work n the negatve doman as well as n the postve doman. Fnally, D r s an ndcator varable that takes on a value of 1 f the sesson used the random acqurer rule. Columns (1) to (3) of Table 7 reports the estmates relatng ALM predctons to observed prce ncreases. Notce that ndependent of the segment used as the unt of analyss, the regresson 2 does a reasonable ob explanng observed prce ncreases ( R s at least 0.41). Further, as ndcated at the bottom of the table, β 1 and β 2 are ontly dfferent from zero n each equaton. Columns (4) to (6) of Table 7 report the estmates of post-merger prce ncreases as a functon of devatons from the underlyng pre-merger Nash equlbrum. Notce that prce 17

19 devatons do a better ob explanng post merger prce movements than ALM predctons 2 ( R ranges between.67 and.70). Further, the choce of the merger rule less clearly affects performance n equatons (4) to (6), than n (1) to (3). β NR dffers sgnfcantly from zero only at 90% confdence level, and only for the last-15 perod segment, reflectng the result that pre-merger prces were hgher n several of the sessons conducted wth the random rule. In summary then, although ALM predctons appear to explan a consderable porton of post-merger prce ncreases, the devaton of pre-merger prces from the underlyng equlbrum appears to explan even more of post-merger prce ncreases. 5. Dscusson and Concluson The ALM appears to screen out problematc mergers qute well here, n the sense that large prce ncreases tend to arse n markets where szable ncreases are predcted. However, the evdence reported here suggests that the ALM predcts the potental to exercse market power, only to the extent to whch markets devate from the pre-merger equlbrum. In our markets t appears that the pre-merger devatons from the underlyng pre-merger equlbrum s a far more powerful drver of behavor than the exercse of market power per se. In naturally occurrng markets sellers, experenced wth ther market and well aware of ther strategc crcumstances, may exercse market power more obvously than s observed here. But naturally occurrng markets also undoubtedly devate from ther underlyng equlbrum to due a plethora of uncontrolled factors that affect them regularly. Allowng for the possblty that markets are out of equlbrum means that ALM predctons necessarly represent a combnaton of a potental for ncreased market power, and the extent to whch markets devate from the equlbrum. To us, ths represents an extremely questonable bass for publc polcy. Large predcted effects may be merely a consequence of depressed pre-merger prces. Small predcted effects may mean that prces exceed the underlyng equlbrum suffcently to dwarf consequences of market power. Unless the ALM can be modfed to dstngush potental market power exercse from the effects of pre-merger devatons we are skeptcal of ts value. 18

20 References Anderson, Smon P., Andre de Palma, and Jacque F. Thsse (1992) Dscrete Choce Theory of Product Dfferentaton. MIT Press Cambrdge, Mass. Crooke, Phlp, Luke Froeb and Steven Tschantz and Gregory J. Werden (1999) Effects of Assumed Demand Form on Smulated Post-merger Equlbra, Revew of Industral Organzaton, 15(3), Davs, Douglas D. and Charles A. Holt (1993) Expermental Economcs Prnceton N.J.: Prnceton Unversty Press. Davs, Douglas D. and Charles A. Holt (1994) Market Power and Mergers n Laboratory Markets wth Posted Prces, RAND Journal of Economcs, 25, Davs, Douglas D. and Bart J. Wlson (2000) Frm-specfc Cost Savngs and Market Power, Economc Theory 16, Deneckere, Raymond and Carl Davdson (1985) Incentves to Form Coaltons wth Bertrand Competton, Rand Journal of Economcs, 16(4), Dolbear, F.T., L.B. Lave, G. Bowman, A Leberman, E. Prescott, F. Fueter, and R. Sherman (1968) Colluson n Olgopoly: An Experment on the Effect of Numbers and Informaton Quarterly Journal of Economcs, 82(2), Eaton, B. Curts and Rchard G. Lpsey (1989) Product Dfferentaton Chapter 12 n Handbook of Industral Organzaton, Volume I, Schmalensee, R and R.D.Wllg eds. Elsever Scence Publshers B.V., Farrell, Joseph, and Carl Shapro (1990) Horzontal Mergers: An Equlbrum Analyss, Amercan Economc Revew, 80, Froeb, Luke M. (1994) Anttrust Webste Froeb, Luke M., Tmothy J. Tardff and Gregory J. Werden (1998) The Demsetz Postulate and the Welfare Effects of Mergers n Dfferentated Products Industres, Economc Inputs, Legal Outputs: The Role of Economcs n Modern Anttrust, Fred McChesney (ed.) London: John Wley&Sons. Froeb, Luke M. and Gregory J. Werden (1996) Smulatng the Effects of Mergers Among Noncooperatve Olgopolsts Economc and Fnancal Modelng wth Mathematca vol. 2. Hal Varan, ed., Sprnger-Verlag/Telos. Hoffman, Elzabeth and Sptzer, Matthew L. The Coase Theorem: Some Expermental Tests, Journal of Law and Economcs, 25, Aprl 1982,

21 Huck Steffen, Hans-Theo Normann and Jörg Oechssler (2000) Does Informaton about Compettors Actons Increase or Decrease Competton n Expermental Olgopoly Markets? Internatonal Journal of Industral Organzaton, 18, McFadden, Danel (1974) Condtonal Logt Analyss of Qualtatve Choce Behavor, n P. Zarembka, ed., Fronters n Econometrcs. Academc Press, New York Shapro, Carl (1989) Theores of Olgopoly Behavor The Handbook of Industral Organzaton, vol. 1, Elsever Scence Publshers B.V., 1989 pp Shubk, Martn. (1980) Market Structure and Behavor. Cambrdge: Harvard Unversty Press, Unted States Department of Justce and Federal Trade Commsson, Horzontal Merger Gudelnes, revsed, Aprl Wellford, Charssa P. (1990) Takeovers and Horzontal Mergers: Polcy and Performance. Ph. D. dssertaton, Unversty of Arzona. Werden, Gregory J., and Luke M. Froeb (1996) Smulaton as an Alternatve to Structural Merger Polcy n Dfferentated Products Industres, n Malcolm Coate and Andrew Klet, eds., The Economcs of the Anttrust Process, New York: Topcs n Regulatory Economcs and Polcy Seres, Kluwer, Werden, Gregory J., and Luke M. Froeb (1994) The Effects of Mergers n Dfferentated Products Industres: Logt Demand and Merger Polcy, Journal of Law, Economcs, and Organzaton, 10, Wlson, Bart J. (1998) What Colluson? Unlateral Market Power as a Catalyst for Countercyclcal Markups, Expermental Economcs, 1(2),

22 Large Effects Sessons P JP M -L near Prce A LogtM arket Merger Approxmate + 5% Band about N on-cooperatve Prce P JP M -L ogt 60 P o = P m A LnearMarket Prce P o = A LnearMarket Sm aleffects Sessons Merger A LogtM arket Approxmate + 5% Band about Non-Cooperatve Prce P JP M P m c SWAP paths for some representatve Markets. Fgure 21

23 LogtL arge Effects ActualMargnalCost Perods Cents LogtSm alleffects ActualMargnalCost Perods Cents ActualMargnalCost Lnear L arge Effects Perods Cents Lnear Sm alleffects Perods ActualMargnalCost Cents Fgure 2. Impled Cost Dstrbutons, based on Prce Decsons for the Fnal Ffteen Perods Pre-Merger (perods 16-30). Key: Grey bars reflect dstrbuton of mpled costs for correctly specfed demand. Whte bars ndcate reflect mpled costs wth ms-specfed demand. 22

24 (1)18% Increase Predcted 108% Increase Observed, 50% Observed % Increase 5% (2)5.2% Predcted Increase 22% Observed Reducton 25% 5% Predcted % Increase Key: Large Effects wth hghest earner acqurer rule Large Effects wth random acqurer rule Small Effects Fgure 3. Predcted Prce Increases (Perods 16-30) vs. Observed Prce Increases (Perods 46-60). 23

25 Observed % Increase 5% -15% -5% 5% -15% % Pre-M ergerd evaton from Equlbrum Key: Large Effects wth hghest earner acqurer rule Large Effects wth random acqurer rule Small Effects Fgure 4. Mean SWAP Devaton from P o (Perods 16-30) vs. Observed Prce Increases (Perods 46-60). 24

26 Table 1. Parameters and Predctons Logt Demand Lnear Demand Desgn Large Effects Small Effects Large Effects Small Effects Parameters η = η = β = s = 25% p = 55 β = s = 25% p = 55 V = 100 α = 7/3 θ = 2/3 c = 20 V = α = 13/3 θ = 2/3 c = 36.2 Equlbrum Condtons c = 20 η =1.57 η =.45 (Q I = 367.5) c = 36.2 η =2.92 η =.45 (Q I = 611) η =1.57 η =.45 η =2.92 η t=.45 Predctons p s Proft p s Proft p s Proft p s Proft Compettve Nash: Pre-Merger Nash: Post-merger Merged frms Other frms % SWAP all Jont-Proft Maxmzng

27 Table 2. Proxmty of mean SWAP to c and to P JPM Pre Merger Post Merger Treatment (Markets) Segments (1) Instances where (SWAP c) < (P o SWAP) (2) Instances where (P JPM SWAP) < (SWAP P o ) (3) Instances where (SWAP c) < (P m SWAP) (4) Instances where (P JPM SWAP) < (SWAP P m ) All 30 Perods Perods 1-30 Perods logt -large effects (8) logt -small effects (4) lnear- large effects (8) lnear- small effects (4) Total (24) Last 15 Perods Perods Perods logt large effects (8) logt small effects (4) lnear- large effects (8) lnear- small effects (4) Total (24) Last 5 Perods Perods Perods logt large effects (8) logt -small effects (4) lnear- large effects (8) lnear- small effects (4) Total (24)