Measuring Market Power in a Dynamic Oligopoly Model: An Empirical Analysis

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1 Aprl, 2005 Measurng Marke Power n a Dynamc Olgopoly Model: An Emprcal Analyss Donghun Km * Inernaonal Developmen Program, Inernaonal Unversy of Japan, Kokusa-cho, Mnam Uonuma-sh, Ngaa , Japan, Emal: dhkm@uj.ac.jp, Fax: , Tel: I am ndebed o Rober T. Masson, Kap-Young Jeong, George Jakubson, and Ted O Donoghue for her suppor and gudance. I hank Ronald W.Coerll for helpful commens on varous porons of early draf. The usual dsclamer apples.

2 ABSTRACT We derve a dynamc srucural model based on a dynamc supergame model and measure marke power for he Dallas 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 mlk marke s couner-cyclcal 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. JEL: D4, L0, Q0 Key Words: Conduc Parameer, Dynamc Supergame, Marke Power, Colluson

3 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), Gollop and Robers (1979), and Appelbaum (1982). 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. 2 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 1 Oher examples of esmang sac conduc parameers nclude Brander and Zhang (1990), Graddy (1995), and Berg and Km (1994). They analyzed he U.S. arlne ndusry, he Fulon fsh marke n he U.S., and he Norwegan bankng secor, respecvely. 2 Oher mehods of esmang marke power nclude 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 (2001). 1

4 devaon from he colluson n hs model. Hence he conduc parameer wll decrease 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 regmeswchng 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 couner-cyclcal regme-swchng model n favor of he Roemberg-Woodford model n he 1930 s U.S. rayon ndusry. Bresnahan (1987) s for a dfferenaed produc marke wh prce compeon whle Brandar and Zhang (1993), and Galle and Schoreer (1995) are for homogenous produc markes wh quany seng. Our goal n hs paper s o 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. 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 produc and choose prce 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 sll s a me-nvaran conduc parameer ha measures an average level of marke power n he dynamc model. We call a core conduc parameer. We hen model a dynamc conduc parameer as a funcon 2

5 of he core conduc parameer, demand shocks, and cos shocks. The demand shocks and cos shocks make he dynamc conduc parameer devae from he core conduc parameer. Hence we combne he concep of esmang an average level of collusveness and esmang me-varyng frm behavor n a sngle model. For example, f frms behave 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. 3 Our daa consss of supermarke-level prces, quanes, and cos daa n he Dallas area of he U.S. The daa s monhly and ranges from March 1996 o July 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 and esmae common prcng behavor, conrollng for ndvduals dosyncrac prcng. 3 Cors (1999) demonsraes ha he conduc parameer n an emprcal model esmaes a margnal response of margn o demand shock raher han esmang he level of margn, and could herefore msrepresen marke power when frms behavors are posed by he dynamc supergame raher han by conjecural varaon equlbra. 3

6 We fnd ha he emprcal resuls for he Dallas mlk marke demonsrae very well wha a dynamc supergame predcs. The heory predcs 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 esmaed core conduc parameer s hgh bu less han 1. 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 couner-cyclcal effec on frm conduc. Emprcal resuls also demonsrae ha he sac conduc parameer underesmaes he degree of colluson n he Dallas mlk marke. Economercally, he sac model s a resrced verson of he full model ha s derved from dynamc prof maxmzaon. Tess rejec he resrcon. Ths ndcaes ha specfyng and esmang sac olgopoly models can msrepresen he degree of marke power. The paper s organzed as follows. Frs, n Par II we specfy a dynamc supergame model. We analyze emprcal resuls n Par III and presen concludng commens n Par IV. II. Specfcaon of A Dynamc Supergame Model Followng Roemberg and Saloner (1986), we assume ha frms n he marke observe prces and marke demand ex pos. We also 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: 4

7 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 assume ha a frm s demand funcon, q, s represened as follows: q = α + α p + α p + f ( Demand Shfers) + ε j (2) Hereε s an error erm and 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. 4 We assume ha a frm observes prces for =1, 2,, -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. 5 We can hen wre a frm s prof maxmzaon condon as follows: * p ( x, w, δ ) = arg maxπ ( p; x, w ) 4 See Fredman (1971). Ths s hs grm rgger sraegy. 5 See Rohschld (1992) 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 markes when sraegc varables can be swched. Deneckere (1983) shows ha when producs are good subsues, colluson s beer suppored n prce-seng games. 5

8 b s.. π ( p; x, w ) + = 1 δ E [ π nb ( x +, w + + = 1 )] π ( p; x, w ) δ E [ π ( p * ( x +, w +, δ ); x +, w + )] (3) b Here π ( p; x, w ) s a frm s bes response prof a me. x and nb ( w are a demand shock and a cos shock a me, respecvely. π p; x, w ) s he prof for he realaon perod. 6 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 susaned and ( p + + p * s he opmal collusve prce. δ s a dscoun rae. Then he fuure expeced loss nb [ , + 1 from he devaon s: 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 (4) j 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 (5) 1+ ψ j b 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, θ *, j q and we call he core conduc parameer. Theorecally, θ * =, = α1 and 6 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. 6

9 q j = α 2. 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) j 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. 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 here are oher dynamc facors ha 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 b π ( p; x, w ) sgn of when ψ s greaer han zero. To esmae he core conduc parameer θ *, we specfy a dynamc conduc parameerθ as a funcon of θ *, demand shocks, and cos shocks, raher han esmang he prcng relaonshp (5) drecly. 7 Hence we can model he dynamc conduc parameer as a funcon of he core conduc parameer and a erm ha s a funcon b ψ π ( p; x, w ) of : 1+ ψ b ψ π ( p; x, w ) θ = θ * + γ [ ] (7) 1+ ψ 7 Esmang he core conduc parameer θ * n equaon (5) dd no change he parameer value or s sgnfcance sascally. 7

10 ψ π ( p; x, w ) We model 1+ ψ b as a funcon of demand shocks and cos shocks b π ( p; x, w ) because consran bndng and are 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. 8 Therefore we specfy G x, w ) as a funcon of hese varables: ( θ θ * ϕ x ϕ w + e (9) = Agan x and w represen demand shocks and cos shocks. The advanages of specfcaon (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 me-varyng conduc parameer. 9 If x has a negave sgn, hen hs mples counercyclcal frm conduc and markup as n Roemberg and Saloner (1986). If x s posvely assocaed wh θ, hen 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 8 See Borensen and Shephard (1996), for example. 9 See Bresnahan (1987), Brandar and Zhang (1993), and Galle and Schroeer (1995) for me-varyng conduc. 8

11 rue game s a dynamc supergame and ha he conduc parameer s a consan. Then wha we need o esmae s 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: q 11 4 = α 0 + α1 p + α 2 p j + α k+ 2 Monk + k= 1 = 1 + α 18 * Income + ε α + 13 Sup (11) p = mc q q 1 + [ + θ ] q + ν (12) j θ x w + e (13) = θ * + ϕ1 + ϕ 2 mc = γ + γ IneresRae + γ RawMlk 0 + γ Wage γ Packng Cos = 1 γ + γ Elecrcy 6+ 3 Sup + δ (14) Frm s demand, q, s a funcon of own prce, p, he oher frm s prce, p j, a volumeweghed sum of he oher frms prces, Mon, a monhly dummy o conrol for seasonaly, k Sup, frm-specfc dummes, and Income, medan ncome level n he marke. 10 Equaon (12) represens frm s prcng relaonshp and specfcaon (13) s he dynamc conduc parameer embedded n Equaon (12). 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 10 Among varables, ncome s yearly and ohers are monhly. 9

12 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 2 should be equal o zero. Hence he sac model s a resrced verson of he full model (12). Therefore we can es f hese resrcons are vald. We specfy x, w n a mean devaon form so ha he average of θ converges o θ *. We specfy a frm s margnal cos (14) as a funcon of he followng facor prces and frm-specfc dummes: RawMlk, 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. To conrol for oher omed varables and a frm s dosyncrac prcng, and o capure only common prcng behavor, we nclude fxed effecs dummes for each supermarke, SUP. ε, v, e, and δ are error erms. The descrpve sascs for he varables are summarzed n Table 1. 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. The man reason we esmae he demand and prcng relaonshps separaely s o compare he core conducor parameer wh he sac conduc parameer gven he esmaed demand funcon. Table 2 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 can rejec he model specfcaon a 10%, 5% and 1%, 10

13 respecvely. 11 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 he own prce mples ha own-prce elascy s and cross-prce elascy s Ths mples ha frms margn s around 66% under he assumpon of Nash-Berrand compeon, because margn s smply he nverse of own-prce elascy. 13 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 canno rejec he full 2 2 model a he 5 % sgnfcance level usng he χ es. The crcal value for χ (13) s In Table 3, raw mlk prce s posve and sgnfcan among facor prces. On he oher hand, packng cos has an unexpeced sgn. The coeffcen on neres s nsgnfcan. Roller and Sckles (2000) demonsrae ha droppng capal cos caused 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. 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 Crcal values for χ (4) are 7.78, 9.49, and for each sgnfcance level. 12 Elasces are calculaed a he mean n prce and quany. p 13 1 Prce-cos margn can be defned as [ p mc]/ p = [ η θ ηj ]. η s own-prce elascy p j and η j s cross-prce elascy. θ represens he conduc parameer. Under Nash-Berrand compeon, θ = 0. Hence prce-cos margn s smply he nverse of own-prce elascy. 11

14 Hence he sac model underesmaes he average conduc parameer of he dynamc model by more han 33% and s prce-cos margn by9 %. 14 Ths mples ha here can be a sgnfcan bas n measurng marke power n a sac model f frms acual 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% sgnfcance level. The null hypohess ha he parameers are equal o zero jonly s also rejeced. The es sasc, χ (2), s and s crcal value s 9.21 a he 1 % sgnfcance level. 15 Ths demonsraes ha he dynamc game maers n he Dallas mlk marke. Ths resul also ndcaes ha he dynamc conduc parameer, θ, s couner-cyclcal 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 needs o be lowered o preven he devaon. The role of fuure cos s smlar o ha of curren demand shock relave o fuure demand. 16 The resuls 2 14 See Table We can es he valdy of he resrcon usng he values of he GMM objecve funcon of he full 2 2 model and he resrced sac model. χ (15) χ (13) = = Ths es s arbued o Newey and Wes (1987). Refer also o Greene (2003, p 549). 16 MacDonald (2000) shows ha prces of seasonal producs fall durng demand peak and prce declnes are no drven by fallng agrculural npu prces. He argues ha seasonal demand ncreases reduce he effecve coss of nformave adversng, and ncreased nformave adversng by realers and manufacurers n urn may allow for ncreased marke nformaon and greaer prce sensvy on he par of he buyers. 12

15 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. V. Concluson. In hs paper we derve a srucural model based on a dynamc olgopoly game and esmae marke power for he Dallas 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 he daa for he Dallas mlk marke fs well no 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 couner-cyclcal 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. Ths resul demonsraes ha fng daa no an economerc model n an arbrary manner can cause a msnerpreaon of marke power. 13

16 References Appelbaum, E., (1982), 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 27, 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, 25(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, 52(1), Greene, H. Wllam, (2003), 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, 14

17 29(2), 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 42, MacDonald, James M., (2000), Demand Informaon And Compeon: Why Do Food Prces Fall A Seasonal Demand Peaks? Journal of Indusral Economcs, March, Vol XLVIII. Newey, W., and K. Wes, (1987), Hypohess Tesng wh Effcen Mehod of Momens Esmaon, Inernaonal Economc Revew, 28, 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., (2000), 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., (1992), 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, 28, Warner, Elzabeh J. and Barsky, Rober B., (1995), The Tmng and Magnude of Real Sore Markdowns: Evdence from Weekend and Holdays, Quarerly Journal of Economcs, May, 110(2), pp

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

19 Table 2) Demand Sde parameers Varables Parameer Sandard error Cons an p * p j ** Mon Mon ** Mon * Mon * Mon ** Mon ** Mon Mon Mon Mon Mon Sup * Sup * Sup * Sup * Medan Income * 2 GMM Objecve: χ (4) Noe) *: Sgnfcan a 1 %, **: Sgnfcan a 5 %, ***: Sgnfcan a 10 %. 17

20 Table 3) Parameers n he prcng relaonshp (full Model) Varables Parameer Sandard error Margnal Cos Cons an * IneresRa e RawMlk * Wage Elecrc y PackngCos * Sup * Sup * Sup Sup * Conduc Parameer ( θ ) * θ * x ** w ** 2 GMM objecve: χ (13) Noe) *: Sgnfcan a 1 %, **: Sgnfcan a 5 %, ***: Sgnfcan a 10 % 18

21 Table 4) Parameers n he prcng relaonshp (Sac Model) Varables Parameer Sandard error Margnal Cos Cons an * IneresRa e RawMlk ** Wage Elecrc y PackngCos * Sup * Sup * Sup Sup ** Conduc Parameer θ * 2 GMM objecve: χ (15) Noe) *: Sgnfcan a 1 %, **: Sgnfcan a 5 %, ***: Sgnfcan a 10 % 19

22 Table 5) Frm conduc and mpled margns Conduc θ Margns Sac conduc Model % Dynamc conduc Model % 20