Measuring Market Power in a Dynamic Oligopoly Model: The Dallas-Forth Worth Milk Market Case

Transcription

1 GSIR WORKING PAPERS Economc Developmen & Polcy Seres EDP06-4 Measurng Marke Power n a Dynamc Olgopoly Model: The Dallas-Forh Worh Mlk Marke Case Donghun KIM Inernaonal Unversy of Japan January 006 Graduae School of Inernaonal Relaons Inernaonal Unversy of Japan hp://gsr.uj.ac.jp/

2 GSIR Workng Papers Economc Developmen & Polcy Seres EDP06-4 Measurng Marke Power n a Dynamc Olgopoly Model: The Dallas-Forh Worh Mlk Marke Case Donghun Km * Asssan Professor, Inernaonal Developmen Program, Graduae School of Inernaonal Relaons, Inernaonal Unversy of Japan ABSTRACT We derve a dynamc srucural model based on a dynamc supergame model and measure marke power for he Dallas-Forh Worh mlk marke n he U.S. In parcular, we analyze he cyclcal behavor of frm conduc and evaluae bas n sac marke-power measures n a unfed manner by dervng and esmang a dynamc frs-order condon for prof maxmzaon. We fnd ha frm conduc n he Dallas-Forh Worh mlk marke s counercyclcal agans demand shocks and expeced fuure cos shocks. We also demonsrae ha he conduc parameer n a sac model underesmaes rue marke power f frms behavors are posed by a dynamc supergame. Keywords: Dallas-For Worh Mlk Marke, Conduc Parameer, Dynamc Supergame, Marke Power, Colluson JEL classfcaon: D4, L0, Q0 GSIR workng papers are prelmnary research documens, publshed by he Graduae School of Inernaonal Relaons. To faclae promp dsrbuon, hey have no been formally revewed and eded. They are crculaed n order o smulae dscusson and crcal commen and may be revsed. The vews and nerpreaons expressed n hese papers are hose of he auhor(s). I s expeced ha mos workng papers wll be publshed n some oher form. * I hank Ronald W.Coerll, Drk Czarnzk and parcpans a varous conferences for helpful commens. The usual dsclamer apples. 1

3 Measurng Marke Power n a Dynamc Olgopoly Model: The Dallas-Forh Worh Mlk Marke Case Donghun Km Asssan Professor, Inernaonal Developmen Program, Graduae School of Inernaonal Relaons, Inernaonal Unversy of Japan I. Inroducon Measurng he degree of compeon n olgopolsc markes and fndng he underlyng deermnans of such compeon are key acves n emprcal ndusral organzaon. Earler sudes focused on esmang conduc parameers ha dsngush collusve behavors from non-collusve behavors, usng conemporary observaons of oupus, coss, and prces. The leraure on measurng olgopolsc conduc follows from orgnal research by Iwaa (1974), Gallop and Robers (1979), and Appelbaum (198). 1 The sac conemporaneous conduc parameer s desgned o esmae he level of marke compeon n a one-sho game ha s repeaed over me. As he problem of repeaed olgopoly neracon has receved greaer aenon, he esmaon of me-varyng conduc parameers ha are ruly dynamc has become an ssue. Green and Porer (1984) predc a procyclcal behavor paern for markups because of prce reverson durng a perod of low demand. Hence he conduc parameer changes from collusve value o compeve value when here s an unancpaed negave demand shock. Meanwhle, Roemberg and Saloner (1986) predc ha prces and markups are couner-cyclcal. The ncenve o devae from collusve agreemens s greaer when demand s hgh, so he opmal prce decreases durng a boom o preven a devaon from he colluson n hs model. Hence he conduc parameer wll decrease 1 Oher examples of sudes esmang sac conduc parameers nclude Brander and Zhang (1990), Graddy (1995), and Berg and Km (1994) analyzng he U.S. arlne ndusry, he Fulon fsh marke n he U.S., and he Norwegan bankng secor, respecvely. Oher mehods for esmang marke power are found n Hall (1988) and Panza-Ross (1987). See Hyde and Perloff (1995) for a comparson of varous mehods. Anoher approach n NEIO s o esmae he demand and prcng relaonshp under specfc assumpons of marke compeon (Bresnahan, 1987). Ths approach has been used for dfferenaed produc markes wh prce compeon. See, for example, BLP (1995) and Nevo (001).

4 when demand s hgh. Emprcal sudes ha esmae me-varyng conduc nclude Bresnahan (1987), Brandar and Zhang (1993), and Galle and Schroeer (1995). Bresnahan (1987) analyzes changes n frm conduc n he md-1950s for he U.S auomoble ndusry. He fnds ha, n he ndusry, he collusve soluon s susaned n 1954 and n 1956 whle he compeve soluon holds n Brandar and Zhang (1993) esmae a regme-swchng model ha s derved from Green and Porer (1984) for he U.S. arlne ndusry durng he perod. They fnd ha Berrand, Courno, or carel one-sho sac games are rejeced and he reverson from colluson o Courno behavor s srongly suppored. Galle and Schroeer (1995) esmae a counercyclcal regme-swchng model n favor of he Roemberg-Woodford model for he 1930 s U.S. rayon ndusry. Bresnahan (1987) esmaes for a dfferenaed produc marke wh prce compeon whle Brandar and Zhang (1993), and Galle and Schoreer (1995) esmae for homogeneous produc markes wh quany seng. Our goal n hs paper s o analyze he cyclcal behavor of frm conduc n he Dallas-Forh Worh mlk marke n he U.S. and evaluae bas n sac marke-power measures n a unfed manner by dervng and esmang a dynamc frs-order condon for prof maxmzaon. To accomplsh hs, we specfy a srucural model ha s based on a dynamc supergame model for frm-level conduc. In he model, frms sell dfferenaed producs and choose prces so as o maxmze her profs, comparng he benef of a devaon from colluson wh he expeced fuure loss from he devaon. As n Roemberg and Saloner (1986) and Green and Porer (1984), here are cyclcal paerns of prces or markups n our model as frm conduc changes over me. We assume, however, ha here remans a me-nvaran conduc parameer ha measures an average level of marke power n he dynamc model. We call hs a core conduc parameer. We hen model a dynamc conduc parameer as a funcon of he core conduc parameer, demand shocks, and cos shocks. The demand shocks and cos shocks cause he dynamc conduc parameer o devae from he core conduc parameer. Hence we combne he concep of esmang an average level of collusveness wh ha of esmang me-varyng frm behavor n a sngle model. For example, f frms behave 3

5 as posed by Roemberg and Saloner (1986), hey wll mpose carel prces when no ncenve compably condon s bndng and wll charge prces lower han carel prces when an ncenve compably condon bnds. Hence he conduc parameer wll be hgher when no ncenve compably condon s bndng han when such a condon s bndng. Bu here sll exss an average level of marke power, whch s conssenly susaned f frms follow a dynamc ac colluson game. We also specfy an emprcal model based on sac prof maxmzaon o compare he conduc parameer esmaes from a sac model wh he core conduc parameer and o llusrae bas n he marke-power measure n a sac model. Cors (1995) suggess ha he conduc parameer capures he margnal response of he margns o demand shocks and ha can msrepresen he level of marke power f frm behavor n a marke follows a dynamc olgopoly game. In hs paper, we relae he bas n he measuremen of he conduc parameer o coss and demand shocks whch affec he ncenve compably consran, and show ha he omsson of he coss and demand shock n he specfcaon of an economerc model can generae he bas. Our daa consss of supermarke-level prces, quanes, and cos daa n he Dallas-Forh Worh area of he U.S. The daa s monhly, for he perod of March 1996 o July 000. I conans fve supermarkes ha cover 73% of he oal mlk marke n he area. Supermarkes compee wh one anoher consanly and hs may provde an ncenve for ac colluson. We consruc a panel daa se by combnng he ndvdual supermarke daa. We fnd ha he emprcal resuls for he Dallas-Forh Worh mlk marke are conssen wh he predcon of a dynamc supergame ha he conduc parameer wll be greaer han would be under Nash-Berrand compeon and lower han carel level f frm conduc follows a dynamc olgopoly game. The curren demand shock relave o expeced fuure demand has a sgnfcan and negave effec on frm conduc. The dynamc conduc parameer s, herefore, less han he core conduc parameer durng he boom. And expeced fuure cos shock has a counercyclcal effec on frm conduc. Emprcal resuls also demonsrae ha he sac conduc parameer underesmaes he degree of colluson n he Dallas-Forh Worh mlk marke. 4

6 Economercally, he sac model s a resrced verson of he full model ha s derved from dynamc prof maxmzaon. Tess rejec he resrcon. The sac model underesmaes he average conduc parameer of he dynamc model by more han 33% and s prce-cos margns by 9%. Ths ndcaes ha specfyng and esmang sac olgopoly models can msrepresen he degree of marke power. We also specfy dfferen forms of margnal cos funcon o es he sensvy of he resul. The resuls of hese ess show ha he conduc parameer under a lnear specfcaon s slghly smaller han s under a sem-log specfcaon, bu ha s a b greaer han s under a quadrac specfcaon. Meanwhle, n each specfcaon, he conduc parameer of he sac model has a endency o underesmae he conduc parameer of he dynamc specfcaon. The paper s organzed as follows. Frs, n Par II, we descrbe he Dallas-Forh Worh mlk marke and he correspondng daa. In Par III, we specfy a dynamc supergame model. We analyze emprcal resuls n Par IV and presen concludng commens n Par V. II. Marke and Daa The scanner daa used n hs analyss was obaned from Informaon Resources Inc (IRI). IRI collecs real grocery produc sales and merchadsng daa from a naonal sample of 1,080 supermarkes wh annual sales greaer han mllon dollars. The daa s a census-enhanced daabase consruced from 100% of he represenave key accouns sores and a sample echnque o esmae he remanng sores n each regon ha do no repor full sales daa. Daa s hen grouped by marke area defned by local couny defnons. Our daa consss of supermarke-level prces, quanes, and cos daa n he Dallas-Forh Worh area of he U.S. The marke populaon s 4.7 mllon, wh 1.7 mllon households. The medan household ncome s 44 housand dollars. The medan age s 33 and household sze s.7 persons. The daa come from fve supermarkes ha cover 73% of he oal mlk marke n he area. The supermarkes nclude Albersons, Kroger, Mnyard, Wn Dxe and Tom Thumb. The daa s monhly, for he perod of 5

7 March 1996 o July 000. Table 1 shows he sample sascs. p s own prce and s oher frm s prce, whch s a volume-weghed sum of he oher frms prces. Income s medan ncome level n he marke. RawMlk, p j Elecrc y, Wage, and PackngCos are monhly prce ndexes for raw mlk, elecrcy, wages, and packng cos. IneresRa e s ncluded o capure he effec of capal cos. The proxy for capal cos s he monhly prme neres rae. III. Specfcaon of A Dynamc Supergame Model We assume ha mlk producs are dfferenaed across supermarke chans. Supermarkes charge dfferen prces and exhb dfferen merchandsng acvy for mlk. Frm s prof funcon n a dfferenaed produc marke s: π = p q p, p ) C( q ( p, p )) (1) ( j j Where π s a frm s prof, p s a frm s prce, and p j s a prce for frm j. C q ( p, p )) s a frm s cos funcon. We assume ha a frm s margnal cos s ( j consan bu ha vares across frms and over me. Fnally, we represens a frm s demand funcon, q q, as follows: = α ) + Hereε s an error erm and 0 + α1 p + α p j + f ( Demand Shfers ε () α s are parameers o be esmaed. We defne a rgger sraegy for a supergame such ha each frm begns by chargng carel prces and connues o do so as long as all oher players do he same. Oherwse frms rever o Nash-Berrand prces followng any defecon and connue o play he Nash-Berrand game forever. 3 We assume ha a frm observes prces for =1,,, -1 a me T. Each frm solves a dynamc prof maxmzaon problem by comparng he benef of a devaon from he colluson wh he fuure loss caused by realaon. 4 We can hen wre a frm s prof maxmzaon condon as follows: 3 See Fredman (1971). Ths s hs grm rgger sraegy. 4 See Rohschld (199) for he susanably of colluson n dfferenaed duopoles when prce s he sraegc varable and Rohschld (1995) for he susanably of colluson n dfferenaed produc 6

8 b s.. π ( p; x, w ) + b * p ( x, w, δ ) = arg maxπ ( p; x, w ) = 1 δ E [ π nb ( x +, w + + = 1 )] π ( p; x, w ) δ E [ π ( p *( x Here π ( p; x, w ) s a frm s bes response prof a me. x and + nb (, w +, δ ); x +, w + )] (3) w are a demand shock and a cos shock a me, respecvely. π p; x, w ) s he prof for he realaon perod. If all oher frms play her Nash-Berrand equlbrum sraegy n every perod, he bes ha a sngle frm can do s o play s Nash-Berrand equlbrum sraegy n each perod. We assume ha frms rever o Nash-Berrand compeon durng ha perod. π *; x, w ) s a frm s prof ha s obaned when colluson s ( p + + susaned and p * s he opmal collusve prce. δ s a dscoun rae. Then he fuure expeced loss from he devaon s: = 1 nb δ E[ π ( p *( x+, w +, δ ); x+, w + ) π ( x+, w + 1)]. Followng hs, he frs-order condon for prof maxmzaon s: b q q p j π ( p; x, w ) ( 1+ ψ ){ q + [ p mc ] ( + )} ψ = 0 j (4) Where ψ s a Lagrange mulpler. The dynamc frs-order condon can be wren as: q q q ψ π ( p; x, w ) + [ p mc ] ( + θ *) = 0 1+ ψ j b (5) In (5) he conduc wll change dependng on wheher he ncenve compably condon bnds. Bu here s an average level of hs me-varyng conduc parameer, markes when sraegc varables can be swched. Deneckere (1983) shows ha when producs are good subsues, colluson s beer suppored n prce-seng games. 7

9 θ *, and we call he core conduc parameer. Theorecally, j q θ * =, = α1 and q j = α. If θ * = 0, hen a frm s conduc s conssen wh Nash-Berrand compeon. If 0 < θ * < 1, a frm s behavor s parally collusve, and f θ * = 1, s fully collusve. Only when he consran does no bnd,.e. when ψ = 0, s he same as he sac conduc parameer ha solves he sac frs-order condon: q q q + [ p mc ] ( + θ ) = 0 (6) If he sac model s correc, he error erm n an economerc model for (6) s a pure sochasc erm and herefore should no affec a frm s prcng behavor. If oher dynamc facors nfluence he prces, omed varable bas n esmang a sac model and he sac conduc parameer s possble. Ths mples ha he sac conduc parameer θ can under- or overesmae he core conduc parameer, dependng on he j sgn of b π ( p; x, w ) when ψ s greaer han zero. We now specfy a dynamc conduc parameer, θ, o analyze he cyclcal behavor of frm conduc. We can model he dynamc conduc parameer as a funcon of ψ π ( p; x, w ) he core conduc parameer and a erm ha s a funcon of 1+ ψ prcng relaonshp (5). b n he b ψ π ( p; x, w ) θ = θ * + γ [ ] (7) 1+ ψ In he specfcaon n (7), he frs erm, he core conduc parameer, measures he average level of colluson over me whle he second nonlnear erm capures he devaon from he average level. We model b ψ π ( p; x, w ) 1+ ψ as a funcon of 8

10 π ( p; x, w ) demand shocks and cos shocks because consran bndng and affeced by hem. We hus represen he dynamc conduc parameer as follows: θ = θ +G( x, w ) (8) * Dynamc models predc ha a frm s dynamc behavor s nfluenced by conemporary demand levels, expeced fuure demand, and expeced fuure coss. See, for example, Borensen and Shephard (1996). We herefore specfy G x, w ) as a funcon of hese varables: Agan, = θ * + ϕ1 + ϕ ( θ x w + e (9) x and w represen demand shocks and cos shocks. The advanages of he specfcaon n (9) are wo-fold. Frs, we can es he relaonshp beween he frm s conduc and boh demand shocks and cos shocks by specfyng a b are me-varyng conduc parameer. 5 If x has a negave sgn, hs mples counercyclcal frm conduc and markup as n Roemberg and Saloner (1986). If x s posvely assocaed wh θ, hs mples procyclcal frm conduc and markups as n Green and Porer (1984). Second, we can shed lgh on he source of bas ha dsngushes he core conduc parameer θ * n (5) and he sac conduc parameer θ n (6). Suppose ha he rue game s a dynamc supergame and ha he conduc parameer s a consan. Then we mus esmae θ * n (5). Bu f we assume a sac game wrongly, we are hen gong o esmae θ n (6). Ths wll produce a bas n he esmaon of marke power. Wha θ measures s no θ * bu θ * plus a bas erm. The bas erm s a funcon of demand shock and cos shocks. In hs case, marke power wll be underesmaed or overesmaed. Hence specfcaon (9) s a way of esmang θ * wh a bas correcon. Thus he srucural model o be esmaed s: 5 See Bresnahan (1987), Brandar and Zhang (1993), and Galle and Schroeer (1995) for me-varyng conduc. 9

11 q 11 4 = α 0 + α1 p + α p j + α k+ Monk + k= 1 = 1 + α * Income + ε 18 q q 1 p = mc + + ] q + v j α + 13 Sup [ θ (11) (10) θ x w + e (1) = θ * + ϕ1 + ϕ mc = γ + γ IneresRae + γ + γ Wage + γ Packng Cos + Frm s demand, q, s a funcon of own prce, RawMlk 4 = 1 γ + γ Elecrcy 6+ 3 Sup + δ p, he oher frm s prce, (13) p j, a volume-weghed sum of he oher frms prces, Mon, a monhly dummy o conrol for seasonaly, Sup, frm-specfc dummes, and Income, he medan ncome level n he marke. 6 Equaon (11) represens frm s prcng relaonshp and he specfcaon n (1) s he dynamc conduc parameer embedded n Equaon (11). The dynamc conduc parameer s a funcon of θ *, he core conduc parameer, x, demand shock, and w, cos shocks. To serve as a demand shock, x, we nclude curren ndusry oupu dvded by expeced fuure oupu. As a proxy for fuure oupu, ndusry oupu a +1 s used. For he cos shock, w, we use expeced fuure cos raher han conemporary cos. The fuure cos shock s approxmaed by he raw mlk prce a +1. If only sac prof maxmzaon maers, he parameers ϕ 1 and ϕ should be equal o zero. Hence he sac model s a resrced verson of he full model (11). Therefore we can es o deermne wheher hese resrcons are vald. We specfy x and k w n a mean devaon form so ha he average of θ converges o θ *. We specfy a frm s margnal cos (13) as a funcon of he followng facor prces and frm-specfc dummes: RawMlk, Elecrc y, Wage, and PackngCos are monhly prce 6 Among varables, ncome s yearly and ohers are monhly. 10

12 ndexes for raw mlk, elecrcy, wages, and packng cos. IneresRa e s ncluded o capure he effec of capal cos. The proxy for capal cos s he monhly prme neres rae. These npu prces are marke level. To capure he frm-level cos, we nclude fxed-effecs dummes for each supermarke, SUP. The brand dummes represen he frm-specfc producon cos, whch exhbs lle varaon over me (Nevo, 001). ε, v, e, and δ are error erms. We also specfy dfferen funconal forms of margnal cos o es he sensvy of he esmaon of he conduc parameer. One s a sem-log lnear form and he oher s a quadrac form. Equaon (14) represens he sem-log lnear specfcaon. mc = κ + κ 0 + κ1 ln( IneresRae ) + κ ln( RawMlk ) + κ3 ln( Elecrcy ) 4 ln( pack ) + κ5 ln( Wage ) + κ6 ln( Packng Cos ) + δ In Equaon (14), he npu prces are specfed n log form. k 0 represens frm fxed effecs and k s are parameers on he npu prces. δ s an error erm. (14) mc = ϖ 0 + ϖ IneresRae + ϖ Elecrcy 5 + ϖ Wage ϖ ( Wage ) 10 + ϖ ( IneresRae ) + ϖ ( Elecrcy ) 6 + ς + ϖ RawMlk + ϖ PackngCos ϖ ( Rawmlk ) 4 + ϖ ( PackngCos ) Meanwhle, n Equaon (15), on he npu prces. (15) ϖ 0 represens frm fxed effecs and ϖ s are parameers ς s an error erm. IV. Resuls We esmae he srucural model usng he Generalzed Mehod of Momens. We frs esmae he demand sde parameers and, gven he esmaed demand surface, we hen esmae he prcng relaonshp. We esmae he demand and prcng relaonshps separaely prmarly o compare he core conducor parameer wh he sac conduc parameer gven he esmaed demand funcon. An example of wo-sep esmaon of a 11

13 srucural model s found n Nevo (001). Table shows he esmaed demand-sde parameers. We use cos varables such as raw mlk prce, packng cos, wages, and neres raes as well as exogenous varables n he demand equaon as nsrumenal varables o conrol for prce endogeney. The value of he GMM objecve funcon ndcaes ha we are unable o rejec he model specfcaon a 10%, 5%, and 1%, respecvely. Crcal values for χ (4) are 7.78, 9.49, and 13.8 for each sgnfcance level. The coeffcens on prces are sgnfcan and have he expeced sgns. The sze of he coeffcen on own prce s greaer han ha on oher frms prces. Ths verfes ha producs are subsues and sraegc complemens. The coeffcen on own prce mples ha own-prce elascy s and cross-prce elascy s The elasces are calculaed a he mean n prce and quany. Ths mples ha frm margn s around 66% under he assumpon of Nash-Berrand compeon, because margn s smply he nverse of own-prce elascy. Prce-cos margn can be defned as p 1 [ p mc]/ p = [ η θ ηj ] where η s own-prce elascy and η j s p j cross-prce elascy. θ represens he conduc parameer. Under Nash-Berrand compeon, prce-cos margn s equal o zero. Hence prce-cos margn s smply he nverse of own-prce elascy. Table 3 presens he esmaon resuls for he fully dynamc prcng relaonshp. The nsrumenal varables for hs esmaon nclude monhly dummes, ncome, lagged quany and he oher frm s prce, and exogenous varables. We are unable o rejec he full model a he 5% sgnfcance level usng he χ es. The crcal value for χ (13) s.36. In Table 3, raw mlk prce and wage are posve and sgnfcan among facor prces. On he oher hand, packng cos has an unexpeced sgn bu s nsgnfcan. The coeffcen on neres s posve and nsgnfcan. Roller and Sckles (000) demonsrae ha droppng capal cos resuled n bas n conduc parameer esmaon for he European arlne ndusry. The mlk marke mgh no, however, be as capal nensve as he arlne ndusry, as he nsgnfcan sascal resul ndcaes. Meanwhle, he coeffcens on he frm fxed effecs, whch capure he me-nvaran 1

14 frm-specfc margnal coss, are posve and sgnfcan. The esmaed core conduc parameer ndcaes ha s sze s and s sgnfcan a 1%. Hence he average level of marke power s greaer han he level of Nash-Berrand compeon and lower han he level of he carel soluon. Ths average level of marke power also s greaer han wha s capured n he sac model. In he sac model he conduc parameer s esmaed as n Table 4. Hence he sac model underesmaes he average conduc parameer of he dynamc model by more han 33% and s prce-cos margn by 9%. 7 Ths mples ha here can be a sgnfcan bas n measurng marke power n a sac model f acual frm behavor does no follow a one-sho sac game. The demand shocks and cos shocks have negave and sgnfcan effecs on frm conduc. They are sgnfcan a he 5% level. The null hypohess, ha he parameers are equal o zero jonly, s also rejeced. The es sasc, χ (), s and s crcal value s 9.1 a he 1% sgnfcance level. We can es he valdy of he resrcon usng he values of he GMM objecve funcon of he full model and he resrced sac model. χ (15) χ (13) = = Ths es s arbued o Newey and Wes (1987). 8 Ths demonsraes ha he dynamc game maers n he Dallas-Forh Worh mlk marke. Ths resul also ndcaes ha he dynamc conduc parameer, θ, s counercyclcal o curren demand shock and expeced fuure cos ncrease. Hence marke prces are lower han carel prces when curren demand s hgher han expeced fuure demand and when frms expec fuure cos o ncrease. If expeced fuure cos ncreases, hen he expeced loss from he devaon wll decrease. Ths provdes frms wh an ncenve o devae from full colluson. The collusve marke prce mus be lowered o preven he devaon. The role of fuure cos s smlar o ha of curren demand shock relave o fuure demand. The resuls also demonsrae ha he sac conduc parameer can underesmae marke power when curren demand relave o fuure demand ncreases and frms expec fuure cos o ncrease. 7 See Table 5. 8 Refer also o Greene (003, p 549). 13

15 Table 6 compares he conduc parameers esmaed under dfferen specfcaons of margnal cos funcon. The resuls show ha he conduc parameer under he lnear specfcaon s slghly smaller han s under he sem-log specfcaon, whle s a b greaer here han s under he quadrac specfcaon. Meanwhle, n each specfcaon, he conduc parameer of he sac model has a endency o underesmae he conduc parameer of he dynamc specfcaon. V. Concluson In hs paper we derve a srucural model based on a dynamc olgopoly game and esmae marke power for he Dallas-Forh Worh mlk marke n he U.S. In parcular, we analyze he cyclcal behavor of frm conduc and evaluae bas n sac marke-power measures n a unfed manner by dervng and esmang a dynamc frs-order condon for prof maxmzaon. For hese purposes, we collec supermarke-level prces, quanes, and cos daa for he sample perod of March 1996 o February Supermarkes compee wh one anoher consanly and hs may provde an ncenve for ac colluson. The emprcal resuls ndcae ha we are unable o rejec he demand and prcng relaonshp specfcaon. The coeffcens of he demand funcon verfy ha mlk producs are subsues and sraegc complemens. The esmaed own-prce elascy s abou 1.5. Ths suggess ha frms margn s around 66% under he assumpon of Nash-Berrand compeon. We also fnd ha he resuls for he Dallas-Forh Worh mlk marke are conssen wh wha dynamc olgopoly models predc. The esmaed conduc parameer s greaer han he Nash-Berrand level and less han he carel soluon. And demand shock and fuure cos shock have counercyclcal effecs on curren frm conduc. We also llumnae he source of bas n measurng marke power usng a sac model. The sac model s a resrced verson of he full model ha s derved from dynamc prof maxmzaon. Tess rejec he resrcon. The sac model underesmaes he average conduc parameer of he dynamc model by more han 33% and s prce-cos margns by 9%. Ths resul demonsraes ha fng daa no an 14

16 economerc model n an arbrary manner can cause a msnerpreaon of marke power. We also fnd ha he conduc parameer under a lnear specfcaon s slghly smaller han s under a sem-log specfcaon, bu ha s a b greaer han s under a quadrac specfcaon. Meanwhle, n each specfcaon, he conduc parameer of he sac model has a endency o underesmae he conduc parameer of he dynamc specfcaon. References Appelbaum, E., (198), The Esmaon of he Degree of Olgopoly Power, Journal of Economercs, 19, Borensen, Severn and Andrea Shepard, (1996), Dynamc Prcng n Real Gasolne Markes, Rand Journal of Economcs, Vol 7, Issue 3, Branda, A. James and Anmng Zhang, (1993), Dynamc Olgopoly Behavor n he Arlne Indusry, Inernaonal Journal of Indusral Organzaon, Vol. 11, Bresnahan, F. Tmohy, (1987), Compeon and Colluson n he Amercan Auomoble Indusry: The 1955 Prce War, Journal of Indusral Economcs, June, Cors, Kenneh, (1999), Conduc Parameers and he Measuremen of Marke Power, Journal of Economercs, 88, Deneckere, R., (1983), Duopoly Supergame wh Produc Dfferenaon, Economcs Leers, 11, Ellson, Glenn, (1994), Theores of Carel Sably and he Jon Execuve Commee, Rand Journal of Economcs, 5(1), Galle, A. Grang and John R. Schroeer, (1995), The Effecs of he Busness Cycle on Olgopoly Coordnaon: Evdence from he U.S. Rayon Indusry, Revew of Indusral Organzaon, Gallop,D., and Robers, M., (1979), Frm Inerdependence n Olgopolsc Markes, Journal of Economercs, 10, Green, Edward J., and Porer, Rober H, (1984), Noncooperave Colluson Under Imperfec Prce Informaon, Economerca, 5(1), Greene, H. Wllam, (003), Economerc Analyss, Ffh Edon, Prence Hall. Genesove, Davd and Mulln, Wallace, (1998), Tesng Sac Olgopoly Models: Conduc and Cos n he Sugar Indusry, , Rand Journal of Economcs, 9(),

17 Hall, Rober E., (1988), The Relaonshp Beween Prce and Margnal Cos n U.S ndusry, Journal of Polcal Economy, 96(5), Hyde, Charles E. and Perloff, Jeffrey M., (1995), Can Marke Power Be Esmaed? Revew of Indusral Organzaon, 10: Iwaa, G., (1974), Measuremen of Conjecural Varaons n Olgopoly, Economerca 4, MacDonald, James M., (000), Demand Informaon And Compeon: Why Do Food Prces Fall a Seasonal Demand Peaks? Journal of Indusral Economcs, March, Vol XLVIII. Nevo, Avv, 001, Measurng Make Power n he Ready-To-Ea Cereal Indusry, Economerca, 69, Newey, W., and K. Wes, (1987), Hypohess Tesng wh Effcen Mehod of Momens Esmaon, Inernaonal Economc Revew, 8, pp Panza, John C., and Rosse, James N, (1987), Tesng for Monopoly Equlbrum, Journal of Indusral Economcs, 35(4), Roller, Lars-Hendrk and Sckles, Robn C., (000), Capacy and Produc Marke Compeon: Measurng Marke Power In a Puppy-Dog Indusry, Inernaonal Journal of Indusral Organzaon, 18, Roemberg, Julo J., and Saloner, Garh, (1986), A Supergame-Theorec Model of Prce Wars Durng Booms, Amercan Economc Revew, 76(3), Rohschld, R., (199), On he Susanably of Colluson n Dfferenaed Duopoles, Economcs Leers, 40, Rohschld, R., (1995), Susanng Colluson When he Choce of Sraegc Varable Is Endogenous, Journal of Economcs Behavor and Organzaon, 8,

18 Table 1) Sample sascs Varable Mean Sd Dev Mn Max p ( $/gallon) p ($/gallon) j q ( mllon gallon) Ineres Rae (%) RawMlk ($/gallon) Elecrc y ($/hour) Wage ($/hour) PackngCos (prce ndex/100) Medan Income (en housand $)

19 Table ) Demand Sde parameers Varables Parameer Sandard error p * p j ** Mon *** Mon Mon ** Mon * Mon * Mon ** Mon ** Mon Mon Mon Mon Sup * Sup * Sup * Sup Sup * Medan Income * GMM Objecve: (4) χ Noe) *: Sgnfcan a 1%; **: Sgnfcan a 5%; ***: Sgnfcan a 10%. 18

20 Table 3) Parameers n he prcng relaonshp (full Model) Varables Parameer Sandard error Margnal Cos IneresRa e RawMlk * Wage *** Elecrc y PackngCos Sup *** Sup ** Sup * 3 Sup * 4 Sup * 5 Conduc Parameer ( θ ) * θ * x ** w ** GMM objecve: χ (13) Noe) *: Sgnfcan a 1%; **: Sgnfcan a 5%; ***: Sgnfcan a 10% 19

21 Table 4) Parameers n he prcng relaonshp (Sac Model) Varables Parameer Sandard error Margnal Cos IneresRa e RawMlk * Wage ** Elecrc y PackngCos Sup Sup ** Sup * 3 Sup * 4 Sup * 5 Conduc Parameer θ * GMM objecve: χ (15) Noe) *: Sgnfcan a 1%; **: Sgnfcan a 5%; ***: Sgnfcan a 10% 0

22 Table 5) Frm conduc and mpled margns Conduc Conduc parameer Margns Sac conduc Model % Dynamc conduc Model % Table 6) Margnal Cos Funcons and Conduc Parameer The shape of margnal cos funcon Dynamc Model Sac Model Lner Sem log lnear Quadrac funcon