Compettve Assessment of an Olgopolstc Market Open to Internatonal Trade wth Incomplete Data Marc Ivald Toulouse School of Economcs Chantal Latgé-Roucolle Ecole Natonale de l Avaton Cvle, Toulouse Marsh 2013 Very prelmnary draft Do not crculate wthout permsson Abstract: Ths paper s amed at detectng whether an olgopolstc ndustry facng an nternatonal competton can sustan colluson or whether nternatonal trade dscplnes t to competton. To do so we consder a dfferentated-products olgopoly model and we estmate both demand and supply sdes of the ndustry under nvestgaton. The emprcal analyss s performed n four steps. In the frst step, we buld a mathematcal representaton of the workng of the ndustry. The second step s devoted to the estmaton of the model under the assumpton that the market s compettve. The thrd step provdes an estmaton of the model when t s assumed that the man frms on the market are formng a cartel and, more specfcally, are behavng lke a monopoly. Fnally, the fourth step conssts n comparng the two estmatons n ther capacty to represent realty,.e., detectng whch of the conducts competton or colluson s the most statstcally adequate to represent the workng of the market. The man result s that, n the ndustry under consderaton and regardng the perod of nterest, the competton model statstcally performs better than the colluson model. The very nnovatve part of the analyss here les n the use of a lmted amount of nformaton. Indeed we perform the estmaton of the model based on data from only one frm of the olgopoly and some aggregated data, thanks to the specfcaton and the role of the nternatonal sde of the market. Keyword: JEL Classfcaton: Acknoledgement: We would lke to thank partcpants of the ZEW Conference on Economc Methods n Competton Law Enforcement held n June 24-25, 2011, for helpful comments. Ths paper was ntated when Chantal Latgé-Roucolle was a consultant at LECG. We are sole responsble for the remanng errors. Correspondence: Marc Ivald, Toulouse School of Economcs, Unversty of Toulouse, 21, Allée de Brenne, 31000 Toulouse, France - marc.vald@tse-fr.eu. Chantal Latgé-Roucolle, Ecole Natonale de l Avaton Cvle, 7 avenue E. Beln, BP54005, 31055 Toulouse, France - chantal.latge roucolle@enac.fr. 1
1. Introducton Snce the Porter s semnal artcle publshed n 1983, relatvely few emprcal studes related to the workngs of cartels are publcly avalable, manly because of cartels llegalty and confdentalty constrants mposed to competent authortes. Ths paper contrbutes to ths lterature by provdng a test whch s amed at detectng whether an olgopolstc ndustry facng an nternatonal competton can sustan colluson or whether nternatonal trade dscplnes t to competton. The compettve constrant exerted by the nternatonal trade also plays a crucal role n the Röller and Steen s analyss of the Norwegan cement ndustry that experenced a perod durng whch a cartel was legally organzed cartel. For ths reason, Röller and Steen (2006) have access to all relevant data to study the effectveness of the cartel defned as the ablty to acheve proft maxmzaton n lght of a partcular sharng rule. Takng nto account ths rule and usng an estmaton of demand, they recoverng the cartel s margnal costs, whch are then the bass for measurng the cartel s effectveness and ts mpact on consumers and welfare. Our approach dffers n that we consder a dfferentated-products olgopoly model and we estmate both demand and supply sdes of the ndustry under nvestgaton before testng for colluson aganst competton. The confdentalty of the stuaton under compettve assessments prevents us to name the ndustry and frms nvolved. For ths reason; we refer heren to Country 1 as the domestc country, Frms A, B and C as the three frms actng n Country 1, and Product X as the man product type of the olgopoly. The emprcal analyss s performed n four steps. In the frst step, we buld a mathematcal representaton of the workng of the ndustry. The model dffers dependng on the level of competton prevalng on the market. The crucal pont of the analyss s the assumpton related to the status of capactes: full or excess. The confrontaton between the level of producton and the avalable capactes does lead to conclude wth certanty about the real constrant exerted by capactes. We wll then consder the two cases of bndng and nonbndng capacty constrant and select the assumpton that better matches the realty of the ndustry. The second step s devoted to the estmaton of the model under the assumpton that the market s compettve. Under ths assumpton we estmate the model n the two capacty condtons. The thrd step provdes an estmaton of the model when t s assumed that the man frms on the market are formng a cartel and, more specfcally, are behavng lke a 2
monopoly. Agan, under the assumpton of colluson we estmate the model n the two cases of capactes constrant. The fnal stage of these two prevous steps conssts n comparng the estmatons under the two dfferent capacty condtons and determnng ther ablty to represent realty. That s whch of the assumpton, full or excess capacty, s the most statstcally adequate to represent the workng of the ndustry. Whatever the functonng of the market n terms of competton, the man concluson at ths stage of the analyss s that full capacty mght be preferred to excess capacty. On ths bass, the fnal step conssts n comparng whch of the conducts competton or colluson s the most statstcally adequate to represent the workng of the market. The man result s that, n the ndustry under consderaton, regardng the perod of nterest and gven full capacty condtons, the competton model statstcally performs better than the colluson model. We dffer n three ways from prevous studes on cartel economcs. Frst, the lterature manly focuses on the cartel partcpants ncentves to respect ther collusve agreement as n Röller and Steen. For nstance, Davdson and Deneckere (1990) show that, under the assumpton on tact colluson on prces and competton on capacty, there exst some equlbrum where frms nvest n excess capacty. Ths results n cartel neffcences. The reason for ths neffcency les n the cartel sharng rules by whch the shares are allocated on the bass of producton capacty. Second, several artcles nvestgate the stablty of cartels followng Porter (1983). (See Ellson, 1994, and Vasconcelos, 2000.) Our approach s statc whch avods us to deal wth the queston of separatng colluson s and competton s perods n the tme seres, a task whch s hardly endogenezed by the model. Thrd, we develop a structural model comprsng demand and prcng equatons. Focusng also on the cement ndustry, Steen and Lars Sörgard (1999) use a reduced form model to analyze the effectveness of the cartel, but t prevents them from explanng the workng of the cartel. Röller and Steen (2006) use a structural approach to estmate the margnal costs as a frst step to assess the welfare gans from the cartel. However they do not account for the horzontal or vertcal dfferentaton of products. Now the man nnovatve part of our analyss les n the use of a lmted amount of nformaton. Indeed we perform the estmaton of the model based on data from only one frm of the olgopoly, on the prce and quantty of mports, and on some aggregated data related to the market, thanks to the specfcaton and the role of the nternatonal sde of the market. In other words, t s a further example of a relatvely rch econometrc model that can be estmated wthout a complete data set and that allow mplementng a test on anttrust practces whch s crtcal n competton polcy. 3
In general, the analyst must pay the prce of a lmted amount of nformaton by ntroducng a set of more or less strong dentfyng restrctons. Our analyss s not mmune of such assumptons that are dscussed n the sequel. At ths pont, we can already ndcate that the data on mports somewhat facltates our task here. Indeed, by assumng that the mports play the role of the outsde alternatve for the domestc customers and are provded by an mporter wth no strategc capacty n terms of prce competton whch, we consder, are mld assumptons- we easly reach dentfcaton of a statc Nash equlbrum based on a logttype demand model. Ths adds to the orgnalty and the specfc nterest of the proposed model. Secton 2 descrbes the ndustry and Secton 3 provdes a descrptve analyss whch s amed at motvatng the hypotheses whch serves to buld the economc model presented and estmated n Secton 4. Here we present the results of tests of colluson versus competton. 2. Man features of the ndustry under nvestgaton On the demand sde, the Country 1 ndustry comprses three domestc producers havng no fnancal nterests between them, namely FIRM A, FIRM B, FIRM C, and some mporters. They all provde the market wth a number of products that are used for producng other consumer goods. We consder the market for one product only, namely Product X, as t accounts roughly for eghty-fve percent of ndustry total sales, because, the two other products are complementary products to Product X. 1 Consequently, n terms of proft, ths choce leads to the analyss of frm s proft restrcted to Product X producton. The strategc behavour of domestc frms s descrbed n the sequel. There s also an nternatonal market for Product X and the frms sell on ths market takng the nternatonal prce as gven. In other words, none of the Country 1 frms s able to act as a prce-maker on the nternatonal market. Country 1 also mports Product X. Wthout loss of generalty, all the mporters are aggregated n one frm, the Importer. 2 The latter has here no strategc behavour: t acts as a compettve frnge. 3 1 There s an addtonal constrant due to data avalablty: The costs of producton for the two other products are mssng as well as the level of ther mports. The level of exports s avalable for the full perod under consderaton for FIRM A and Product X only. 2 When t s not explctly mentoned, we always refer to the market or the ndustry of Country 1 n the sequel. 3 In the appendces, the dfferent producers are referred by the ndex 1 for FIRM A, 2 for FIRM C, 3 for FIRM B and 0 for the Importer. 4
On the demand sde, a representatve customer can buy from any of the producers. 4 Although Product X s a qute homogenous product whch must satsfy some standards, there could be some dfferentaton among frms n terms of ther commercal networks and marketng actvtes. So, knowng the quantty t wants to buy, the customer has manly to compare the dfferent offers t can receve from the producers n terms of qualty and prces. In these condtons, the market share of any frm corresponds to the probablty that the customer chooses one of the frms on the market to satsfy ts demand. 5 (See Appendces 1 and 2 for presentaton of the demand model.) On the supply sde, the equlbrum condtons are determned by the combnaton of two basc elements: The behavour of the frms playng on the market - compettve or collusve - and the capacty condtons excess or full capacty. Facng demands for Product X from domestc and overseas customers, how do the frms react? Ths s where the conduct of frms enters the pcture. In the frst place, we assume that the market s compettve; n the second place, we then consder that the three frms behave lke a monopoly. In each case, we derve the strategc behavour of each domestc frm. 6 Assume frst that the market s compettve. The revenues of the frm come from two sources: the domestc sales evaluated at the domestc prce and the exports evaluated at the nternatonal prce whch the frm takes as gven. The frm produces Product X for the domestc and overseas markets usng a producton technology for whch the man nput s the Raw Materal Y. The prce of ths nput s the man drver of producton costs. Our vew s that each frm maxmzes ts proft usng two nstruments: The prce of ts product and the amount of ts exports. Frms behave strategcally, whch means that they consder that each compettor also maxmzes ts proft usng the same avalable nstruments. In the case of full capacty, the level of exports s obtaned from the capacty constrant as soon as the level of domestc producton s determned and vce versa. The frm has to arbtrage between sellng on the domestc market and exportng overseas. To make ts decson, the frm must choose a domestc prce so that the margnal revenue from sellng on the domestc market s equal to the nternatonal prce. In other words, the nternatonal prce, whch represents the opportunty costs of not exportng, plays the role of margnal costs. Under full capacty and f the capactes are dfferent among frms, one should expect dfferences n market shares, whatever the dfferentaton level of the product. 4 Gven data avalablty, one cannot account for the heterogenety of Country 1 customers,.e. for the dfferences among customers n terms of preferences and wllngness-to-pay. 5 We followed Berry (1994) for the descrpton of the demand sde of the ndustry. 6 The mathematcal presentaton of the model s postponed n Appendx 3. (See Ivald and Verboven, 2005.) 5
In the case of excess capacty, the frm faces the same arbtrage as n the case of full capacty, and so, agan, chooses a domestc prce so that the margnal revenue from sellng on the domestc market s equal to the nternatonal prce. However, ths tme, the amount of exports s defned so that the margnal cost of producng one addtonal unt of Product X, whether t s for the domestc market or for overseas, s just equal to the nternatonal prce. Note that, under excess capacty, f there s not much dfferentaton among frms so that each frm s ndvdual demand s smlar to the demand of ts compettors, one should expect that the ndustry converges to a symmetrc stuaton where all the domestc frms have roughly the same market share and put the same prce, snce they all take the nternatonal prce as a benchmark. Now assume that the domestc frms coordnate ther strateges. They can do t n dfferent ways n practce. Here we are consderng the extreme case where they all together behave as a monopoly. In other words, the coordnaton among them s so strong that they defne one unque domestc prce and the overall level of exports. That s, there s only one frm n the ndustry whch has bascally the same choces to perform than the ndvdual frm n the compettve case, except now that quanttes are defned at the ndustry level rather than at the ndvdual frm level. The decsons are dfferent whether there s excess capacty or that the capacty constrant s bndng. In ths latter case, the monopoly must equalze ts domestc margnal revenue to the nternatonal prce to determne ts domestc prce, and so ts domestc sales (for the whole ndustry) and n turn, ts exports. In the frst case, the monopoly equalzes ts margnal revenue to ts domestc prce to determne ts domestc producton, whle the level of exports s defned thanks to the equalty between margnal cost and nternatonal prce level. 3. Descrptve analyss Avalable data, whch covers the perod 2002-2008, are farly complete for FIRM A and for the whole ndustry. They bear on the domestc prces of FIRM A, ts domestc producton levels and exports, ts producton capactes, the prces of Raw Materal Y, the nternatonal Product X prces, the producton capactes of compettors, and the level of Country 1 exports of Product X. Some approxmatons of the market sze are also avalable. However, we do not observe the prces of Product X sold by compettors, nether one s able to measure any dfferences n terms of qualty between the dfferent frms. Ths manly drves the choce of the jont-proft maxmzaton assumpton to approxmate the coordnated 6
soluton among the domestc frms. Below we ndeed assume that the FIRM A s observed prce corresponds to the cartel prce f the frms n the ndustry maxmze ther jont proft. On the one sde, ths hypothess (to whch we refer as the monopoly case heren) can be deemed too strong; on the other sde, t s convenent snce the prces of other frms n the ndustry than the FIRM A are not necessary for the quanttatve analyss. 7 3.1. Market fgures The domestc market shares on the perod under nvestgaton for the three man compettors are reported n Table 1. FIRM A s market share s the hghest durng the perod under consderaton, wavng between 35% n 2005 and 42% n 2008. The yearly dfference n terms of market share between Frm A and the second producer, namely Frm B, s about 10%, except for 2005. The thrd producer, FIRM C, experences a jump n ts producton level n 2004-2005 followng the ncrease n ts producton capactes. Up to 2004, FIRM C market share s lower than the market share of mporters. Snce 2005, ths trend s reversed. Fnally, observe a sharp drop n mports at the end of perod. The dfferences n market shares across compettors mght be ndcatve of dfferentaton among each other products. In the absence of dfferentaton, the demand faced by the compettors would be smlar and the ndustry would converge to a symmetrc equlbrum. Table 1. Product X market shares Undertakng 2002 2003 2004 2005 2006 2007 2008 FIRM A 40% 36% 37% 35% 37% 40% 42% FIRM B 31% 34% 33% 33% 27% 30% 25% FIRM C 8% 8% 13% 21% 18% 23% 28% IMPORTS 20% 22% 17% 11% 18% 7% 4% Source: Confdental data on the ndustry Two types of prces are avalable for FIRM A: the lst prce and the fnal prce. Ther evolutons over the perod nto consderaton are farly smlar, as shown n Fgure 1, but the lst prces are sgnfcantly hgher than the fnal prces. As the fnal prces are the prces 7 Nonetheless mssng nformaton lmts our capacty to test for the robustness of our estmatons. 7
Country 2 and Country 3 are the man Product X mporters and they compete wth domestc frms products. Although the fnal prces of FIRM A are often hgher than the prces of mporters, there remans a postve demand for the domestc products. The domestc frms mght take advantage of ther domestc poston, dfferentatng ther producton of Product X probably through commercal networks and marketng actvtes. In the sequel, we aggregate the mporters n one unque frm (whch we refer to the Representatve Importer n the sequel) and we use a weghted average of mporters prces for the prce of mportatons. 8 Fgure 1 compares the evoluton of the two relevant prces on Product X market, namely FIRM A domestc prce (.e. fnal prce) and the average mport prce, wth the export prce. The latest s the nternatonal prce and s gven for exporter frms. Over the whole perod, 2002 to 2008, the prce of domestc Product X charged by FIRM A s hgher than the export prce. When consderng the unt cost of Product X producton, the export prce s often lower than the unt cost of producton. In 2004, 2005 and end 2007, t can append that the unt cost of producton s hgher than the domestc prce charged by FIRM A, leadng to negatve margns. Ths phenomenon mght be explaned by the need to reduce nventores whle the year ends. Fgure 1 fnally hghlghts the sngularty of year 2008, correspondng to the begnnng of the nternatonal downturn. Ths latter year s characterzed by hgh ncrease n prces and costs. Ths has to be kept n mnd for the forthcomng econometrc analyss. 8 We could have used the lowest prce of mporters prces. As a matter ths does not affect the results. 8
Fgure 1. Fnal prces versus lst and mported prces 600 550 500 450 400 350 300 Frm A Product X lst prce Frm A Product X fnal prce Country 2 Product X mported prce Country 3 Product X mported prce Source: Confdental data on the ndustry. The unt s euro per ton. Fgure 2. Frm A Product X fnal and exported prces, Product X average mport prce, Frm A Product X unt cost of producton and Raw Materal Y prce ( /ton) 900 800 700 600 500 400 300 200 100 0 Frm A Product X fnal prce Frm A Product X exported prce Country 1 Raw Materal Y prce Product X average mport prce Source: Confdental data on the ndustry 9
Consder now the quanttes. Assumng that the market s compettve, the relevant quanttes are the FIRM A s productons, both for domestc and nternatonal markets. Under ths assumpton, we conclude that FIRM A s domestc producton decreases untl 2004, then ncreases untl 2007 (See Fgure 2). In year 2008 starts the prevously descrbed downturn. The level of mports and the total market sze show roughly the same evoluton on the perod under consderaton, whle the exports ncrease untl 2005 and reman stable snce then. FIRM A s producton capactes ncrease n 2006. Assumng now coordnated practces across frms, the relevant quanttes are the combned productons of the three frms, both for domestc and nternatonal markets. Fgure 3 draws the evoluton over the perod under consderaton of the relevant fgures related to producton, mportatons, capactes and market sze. The dfferences between the market sze of Product X and the combned domestc volumes decrease over the perod. The overall evoluton of domestc producton s qute smlar to the evoluton of FIRM A s domestc producton. The combned exportatons keep ncreasng over the perod. Fgure 3. Domestc market sze, level of productons and capactes 2000000 1800000 1600000 1400000 1200000 1000000 800000 600000 400000 200000 0 2002 2003 2004 2005 2006 2007 2008 Product X Frm A Product X Frm A exported volume Product X mported volume Product X market sze Frm A capacty Source: Confdental data on the ndustry. The volumes are expressed n tons. 10
Fgure 4. Domestc levels of producton and mportatons 3000000 2500000 2000000 1500000 1000000 500000 0 2002 2003 2004 2005 2006 2007 2008 Product X combned Domestc volume Product X combned exported volume Product X mported volume Combned producton capacty Product X market sze Source: Confdental data on the ndustry. The volumes are expressed n tons. 3.2. Dscusson on capacty constrant 9 A crucal ssue to dentfy the equlbrum of the market s to characterze the level of capacty utlzaton. If one looks at the stuaton of FIRM A as presented n Fgure 5, the level of capacty utlzaton s hgher than 75 percent, whch s consdered as the effcent level of producton, n all years except n 2003 and 2004; these latter years experence excess capacty. Now, Fgure 6 dsplays how the capacty utlzaton has evolved durng the perod under nvestgaton at the ndustry level. We observe only one year where there are excess capactes, specfcally 2004. Wth 76.09 percent capacty utlzed, the year 2008 s just at the threshold for full capacty utlzaton. These are two specfc years: 2004 follows a perod of economc boom and 2008 s the begnnng of the nternatonal downturn. Gven ths observaton of perods of excess and full capactes, one should use the adequate model for each dfferent perod, gven that we restrct attenton to statc equlbrums. However, t would rase dentfcaton ssues of tme effects. Hence we estmate the model under the assumpton that there s full or excess capacty over the whole perod. 9 Here we consder total capacty referrng to physcal capactes that can be drected to domestc sales or to exports. 11
Fgure 5. Capacty utlzaton and market share for FIRM A 100% 56% 95% 54% Capacty utlzaton 90% 85% 80% 75% 70% 52% 50% 48% 46% 44% Market share 65% 42% 60% 2002 2003 2004 2005 2006 2007 2008 40% Capacty utlzaton Market share Source: Confdental data on the ndustry. Fgure 6. Capacty utlzaton at the ndustry level 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 2002 2003 2004 2005 2006 2007 2008 Source: Confdental data on the ndustry 12
4. Model specfcaton Ths secton ntroduces the econometrc model based on the framework dscussed so far: ) An olgopoly facng an nternatonal competton; ) Data manly avalable for one of the frms, namely FIRM A. 4.1. Demand sde Let ndex be equal to A or to 0 when t refers to FIRM A or to the Representatve Importer. 10 Based on a logt-type specfcaton, the demand functon addressed to frm s expressed as follows: ln( ) ln( ) = +, (1) s s0 δ αp ζ where s the market share of frm on the Product X domestc market, s s the market s 0 share of the Product X Importer on ths market, p s the prce charged by frm for one unt of the product, δ measures the observed qualty of product X sold by frm, ζ measures the unobserved qualty of product X sold by frm, and α s the margnal utlty of ncome. The market share of frm s measured as: s q = q + q 0 d, (2) where q s the producton level of frm, q s the total domestc producton (.e., the sum of d producton levels of all domestc frms) on the market, and q 0 s the total amount of mports of Product X. Hence the demand for product X results from a trade-off between qualty and prce. The term denoted by δ allows for a dfferentaton across undertakngs, whch mght be nterpreted as reflectng any own frm s characterstcs, n partcular ts capacty to react to new economc condtons. In the case of an exogenous shock, the demand would shft due to change n ths term. As a matter of fact, ths term s expressed as a functon of a dummy varable whch accounts for the specfc aspects of year 2008 compared to the other years, as prevously ponted out. Specfcally, we wrte: ( δ δ ) δ = +, (3), cst,2008 *dummy2008 where δ cst, and dummy 2008 are parameter to be estmated. 10 The mathematcal specfcaton of the demand equaton s precsely descrbed n Appendx 2. 13
The parameter α related to the prce, defned as the margnal utlty of ncome, mght be nterpreted as an exchange rate between one unt of qualty and one monetary unt. Note that, by specfyng ths parameter as a functon of Country 1 s GDP, that s to say, ( α α GDP) α = +, (4) cst GDP * where α cst and α GDP are parameter to be estmated, we expect t to be postve and decreasng wth GDP, reflectng a wealth effect, namely that a rcher country s less senstve to any change n money value. Whatever the assumpton, competton or colluson, two demand functons are estmated jontly n the model, the frst one for frm, FIRM A or the monopoly respectvely, the second one for the Importer. 11 The supply sde of the economy s characterzed by the mark-up of the frm, ether FIRM A or the monopoly dependng on the assumpton related to the level of competton. One can show that the mark-up s a functon of the own prce elastcty of demand; thus the mark-up s n partcular a functon of the parameter α descrbed n the demand equaton. 12 In our case, each frm maxmzes ts proft defned as the dfference between revenues and cost, where the revenues come from domestc sales and exports and where the cost s a functon of the total producton. On the domestc market, we assume that the frms compete n prce. Ths choce s drven by the observaton of frms behavours and s meanngful gven the Product X homogenety gven frms characterstcs. On the nternatonal market, the frms take prces as gven and compete n quanttes. Dervng the maxmzaton program of the frm, one can show that the mark-up s expressed n terms of the Product X export prce rather than n terms of margnal costs of producton. The expresson of the mark-up s the followng: p W 1 =, (4) α (1 s ) where: p, s are respectvely the prce charged by frm and ts market share on Product X domestc market; 11 The ndex equals 1 n the frst case and 0 n the second. The estmated parameters are reported n Table 9 and Table 10 of Appendx 4. 12 Appendx 3 descrbes the supply equatons as well as the equatons resultng from the frms maxmsaton program. 14
α s the margnal utlty of ncome and ts expresson s dentcal to the one n the demand functon; W s the prce for exports, whch s gven for frm. Whatever the assumpton, competton or colluson, the mark-up related to frm s the only mark-up ncluded n the model to be estmated. Under the assumpton of bndng capacty constrant, the mark-up equaton perfectly descrbes the behavour of the frm and allows us determnng the optmal level of domestc producton, whle the level of exportaton s deduced from the full capacty condton. However under the assumpton of non bndng capacty constrant, an addtonal equaton s necessary to descrbe the strategc behavour of the frm, as both the level of domestc producton and the level of exports have to be determned. Ths addtonal equaton expresses that the margnal cost of producton equals the export prce. The margnal cost of producton s expressed as a lnear functon of the Raw Materal Y prce and the total level of producton (domestc producton and exports). From an econometrc perspectve, both the equaton related to the margnal cost of producton and the equaton related to the total cost of producton wll be ncluded n the system to be estmated. The specfcaton for the total cost functon s the followng: where 1 TC( y ) = βcst + βrm. prm + βrm, Y. prm. y + βy ( y ) ² (5) 2 y s the total producton from of Product X, that s the sum over domestc producton, q, and exports x ; TC( y ) s the total cost to produce the quantty y ; p RM s the Raw Materal (RM) Y prce. Gven the specfcaton of the total cost functon, the margnal cost functon s expressed: RM, Y RM Y MC( y) = β. p + β y (6) The equlbrum s characterzed by equalty between margnal cost and export prce. Thus, under the assumpton of non bndng capacty constrant the followng relatonshp holds for frm : 15
W = β p + y RM, Y. RM βy 7) As explaned prevously, both ths latter equaton and the total cost functon related to frm are ncluded n the model to be estmated. The equlbrum on the Product X market s characterzed by a system of equatons related to both demand and supply. Gven the dentfcaton constrants of the model, we can show that the model mght be perfectly dentfed thanks to the descrpton of demand and supply of a unque frm belongng to the domestc olgopoly and the demand of the Importers on the domestc market. Because we observe the producton, prce and cost of Frm A, we use Frm A s data for the descrpton and the estmaton of the model. 1.2. Emprcal results The man results of the estmatons are reported n the Table 10 and Table 11 n Appendx 4. Under the assumpton of bndng capacty constrant, the equlbrum s descrbed by three equatons: the demand addressed to FIRM A or to the monopoly, the demand addressed to the Importer, and the mark-up. Under the assumpton of non bndng capacty constrant the equlbrum s descrbed by four man equatons: the demand addressed to FIRM A or to the monopoly, the demand addressed to the Importer, the mark-up and the margnal cost equaton; plus the addtonal total cost equaton. We focus here on the man economc ndcators that allow us selectng between the dfferent models and assumptons,.e. whether the capacty constrant s or not bndng and whether frms behavour s compettve or collusve. The economc ndcators are the estmated own prce elastcty of demand, the level of the estmated margn and the estmated margnal cost n the case of non-bndng capacty constrant. Moreover, the sgn of some of the parameters has to be check for economc consstency, for nstance the margnal utlty of ncome has to be postve. Frst, we dscuss the estmated model under the assumpton of competton on the market. We compare the level of the relevant economc ndcators obtaned under the two capacty condtons: full and excess capacty. Second, we dscuss the results of the models estmated under the assumpton of coordnated practces and we compare the level of the 16
relevant economc ndcators obtaned under the two capacty condtons. Then, we present the results of a statstcal standard test, the Vuong test, whch s a specfcaton test allowng the evaluaton of the assumptons on conduct that better represents the observed data. The two tests mplemented at frst lead to the selecton of the most relevant capacty condton, gven the market observatons and the two possble market condtons, competton or colluson. The results of these two prelmnary tests drve the last step of the analyss nvolvng the comparson of behavoural strateges under the assumpton of bndng capacty constrant.. Compettve behavour Under the assumpton of compettve behavour, the estmated parameters of the full or excess capacty models are reported n Table 10 of appendx 4. All the parameters are statstcally sgnfcant at 1%, 5% or 10% level whatever the capacty condton, except the parameter β Scrap,Y n the cost functon. Ths parameter corresponds to the cross effect between the prce of raw materals and the level of total producton. The parameters δ, =0,1, are postve, and the parameter α GDP, related to the GDP, s negatve as expected. Moreover the margnal utlty of ncome, α, s postve. Table 2 reports ts values for the two models wth bndng or non-bndng capacty assumpton. The margnal utlty of ncome s decreasng over the perod nto consderaton n the full capacty model. Although margnal utlty of ncome s constant, due to structural assumptons, n the excess capacty model. The margnal utlty of ncome s lower n the model wth non-bndng capacty assumpton than n the model wth bndng capacty assumpton. The own prce elastctes of demand belong to the nterval [-9.6;-6.17] n the case of bndng capacty constrant (see Table 3). They are lower n absolute value n the case of excess capacty where they belong to the nterval [-4.8;-2.4]. The estmated margns are reported n Table 4. Under full capacty assumpton, the estmated margns belong to the nterval [11.40, 16.40]. The margns are the lowest n 2006. Under the assumpton of excess capacty, the estmated margns belong to the nterval [22.70, 40.90]. They exhbt a hgher yearly varablty than n the case of bndng capacty constrant. Fnally the estmated margnal costs belong to the nterval [24.45, 66.12]. The lowest value s taken n 2008. 17
At ths stage of our analyss, the relatve values of own prce elastcty of demand and the relatve values of the estmated margns do not favour the assumpton of bndng or nonbndng capacty assumpton as a better approxmaton of the data. Wth respect to the man ndcators, one can conclude that the two models estmated under competton and full or excess capactes are coherent wth the man constrants mposed by the economc theory.. Collusve behavour The collusve behavour s based on the assumpton that the frms act all together lke a monopoly. Ths assumpton s n some sense stronger than the assumpton of jont proft maxmzaton. Recall that the choce to descrbe the collusve behavour by usng a monopoly model has been dctated by the lack of data on Product X prces set by the two compettors of FIRM A. The estmated parameters of the compettve and coordnated models are reported n Table 11 of Appendx 4. All the parameters are statstcally sgnfcant at 1% level whatever the bndng or non-bndng assumpton consdered, except the constant, (sgnfcant at 10% level), n the total cost functon and the parameter related to the nteracton between β cst Raw Materal Y prce and Product X producton n the total cost functon, β RM, Y, whch s not sgnfcant. The parameters δ, =0,1, are postve, as well as the margnal utlty of ncome, α. As well as under competton, the margnal utlty o ncome s decreasng over tme n the case of full capacty and constant and lower, up to 2006, n the case of excess capacty. From 2007 the margnal utlty of ncome becomes hgher n the excess capacty model. The own prce elastctes of demand are reported n Table 7. They belong to the nterval [-38.7;-8.5] n the case of bndng capacty constrant and exhbt a hgh varablty for each year nto consderaton. The own prce elastctes of demand are lower n absolute value n the case of non-bndng capacty assumpton as they belong to the nterval [-3.2, -1.00]. The estmated margns are reported n Table 8. Under the assumpton of bndng capacty constrant, the estmated margns belong to the nterval [2.8, 26.7]. The margns ncrease durng the perod under consderaton, except n 2003 to 2006. Under the assumpton of non-bndng capacty constrant, the estmated margns are on average hgher: they belong to the nterval [34%, 217%]. They do not exhbt any regular trend durng the overall perod. 18
Fnally the estmated margnal costs are reported n Table 9. They are on average hgher than n the case of compettve behavour. The analyss of the economc ndcator estmated under the assumpton of coordnated practces shows that when consderng the own prce elastcty values the non-bndng capacty constrant seems to be more relevant. Although when consderng the margns, the bndng capacty constrant leads to more realstc results. These results do not favour the assumpton of bndng or non-bndng capacty assumpton as a better approxmaton of the data. 19
Table 2. Estmated values of the margnal utlty of ncome under the assumpton of compettve behavour Year 2002 2003 2004 2005 2006 2007 2008 Competton bngng 0.034 0.033 0.032 0.031 0.030 0.028 0.027 Competton non- bndng 0.014 0.014 0.014 0.014 0.014 0.014 0.014 Source: Confdental data on the ndustry Table 3. Own prce elastctes of demand under the assumpton of competton YEAR 2002 2003 2004 2005 2006 2007 2008 # Obs 12 12 12 12 12 12 12 Competton bndng Mean -6.170-7.112-8.045-7.799-8.855-8.241-9.536 Std 0.542 0.735 1.198 1.214 0.928 1.051 3.311 Mn -7.006-8.215-9.663-9.101-10.970-10.482-18.331 Max -5.359-5.590-5.661-5.196-7.552-6.483-5.841 Competton non bndng Mean -2.462-2.928-3.429-3.439-4.077-3.969-4.781 Std 0.216 0.302 0.510 0.535 0.427 0.506 1.660 Mn -2.796-3.382-4.118-4.013-5.051-5.048-9.191 Max -2.139-2.301-2.413-2.291-3.477-3.123-2.929 Source: Confdental data on the ndustry Table 4. Estmated margns (expressed as percentage) under the assumpton of competton YEAR 2002 2003 2004 2005 2006 2007 2008 # Obs 12 12 12 12 12 12 12/11 Competton bndng Mean 16.320% 14.209% 12.729% 13.174% 11.402% 12.313% 11.405% Std 1.404% 1.582% 2.217% 2.491% 1.149% 1.548% 3.108% Mn 14.274% 12.172% 10.349% 10.988% 9.115% 9.541% 5.455% Max 18.660% 17.889% 17.665% 19.247% 13.241% 15.424% 17.120% Competton non bndng Mean 40.896% 34.515% 29.868% 29.878% 24.764% 25.564% 22.747% Std 3.519% 3.842% 5.201% 5.649% 2.495% 3.213% 6.198% Mn 35.768% 29.568% 24.283% 24.921% 19.797% 19.808% 10.880% Max 46.760% 43.455% 41.449% 43.652% 28.757% 32.025% 34.146% Source: Confdental data on the ndustry 20
Table 5. Estmated margnal costs under the assumpton of non bndng capacty constrant and competton YEAR 2002 2003 2004 2005 2006 2007 2008 # Obs 12 12 12 12 12 12 12 Competton non bndng Mean 66.112 59.655 47.759 54.368 60.134 51.588 24.459 Std 14.672 17.059 19.818 22.651 16.018 15.304 28.636 Mn 31.646 38.652 29.919 14.843 30.167 31.675-49.119 Max 81.952 95.751 83.976 92.852 80.570 87.107 55.600 Source: Confdental data on the ndustry Table 6. Estmated values of the margnal utlty of ncome under the assumpton of collusve practces Year 2002 2003 2004 2005 2006 2007 2008 Monopoly bndng 0.562 0.524 0.483 0.445 0.397 0.350 0.310 Monopoly non-bndng 0.038 0.038 0.038 0.038 0.038 0.038 0.038 Source: Confdental data on the ndustry Table 7. Own prce elastctes of demand under the assumpton of collusve practces YEAR 2002 2003 2004 2005 2006 2007 2008 # Obs 12 12 12 12 12 12 12 Monopoly bndng Mean -35.012-38.624-32.238-19.202-33.328-12.569-8.512 Std 11.378 9.811 11.768 7.697 10.348 7.436 9.103 Mn -50.031-51.440-52.186-36.107-47.101-28.416-31.268 Max -12.468-19.862-11.199-7.969-16.118-1.246 0.000 Monopoly non bndng Mean -2.375-2.809-2.543-1.646-3.198-1.368-1.047 Std 0.772 0.714 0.928 0.660 0.993 0.809 1.120 Mn -3.394-3.742-4.116-3.095-4.519-3.093-3.846 Max -0.846-1.445-0.883-0.683-1.546-0.136 0.000 Source: Confdental data on the ndustry 21
Table 8. Margns (expressed n %) under the assumpton of collusve practces YEAR 2002 2003 2004 2005 2006 2007 2008 # Obs 12 12 12 12 12 12 12 Monopoly bndng Mean 3.315% 2.815% 3.653% 6.137% 3.354% 14.720% 26.628% Std 1.693% 1.000% 1.885% 2.819% 1.293% 20.873% 25.401% Mn 1.999% 1.944% 1.916% 2.770% 2.123% 3.519% 3.198% Max 8.021% 5.035% 8.930% 12.548% 6.204% 80.251% 76.351% Monopoly non bndng Mean 48.857% 38.703% 46.317% 71.590% 34.958% 135.233% 216.501% Std 24.958% 13.750% 23.896% 32.887% 13.474% 191.769% 206.526% Mn 29.461% 26.726% 24.295% 32.308% 22.128% 32.332% 26.003% Max 118.221 % 69.217% 113.216% 146.385% 64.664% 737.285% 620.788% Source: Confdental data on the ndustry Table 9. Estmated margnal costs under the assumpton of non bndng capacty constrant and collusve practces YEAR 2002 2003 2004 2005 2006 2007 2008 # Obs 12 12 12 12 12 12 12 Monopoly non bndng Mean 124.938 112.816 90.516 103.019 113.976 97.984 47.050 Std 27.651 32.152 37.368 42.688 30.202 28.855 53.833 Mn 60.043 73.224 56.831 28.515 57.522 60.474-91.447 Max 154.792 180.883 158.831 175.565 152.480 164.977 105.681 Source: Confdental data on the ndustry. Vuong test as a test of model selecton A standard statstcal test to determne whch of two models better ft the data s the Vuong test. (See Gasm, Laffont and Vuong, 1992.) Ths test s based on the comparsons of lkelhood values of the estmated models, takng nto account the varance-covarance matrx of the parameters and the estmated errors of the models. In our specfc case, the Vuong test allows us comparng the assumpton of bndng and non bndng capacty constrants and the assumpton of competton and coordnated practces across frms. When testng assumpton A aganst assumpton B, f the Vuong test statstcs s hgher than 2, then the assumpton A s a better approxmaton of the data. If the Vuong test statstcs s lower than -2, then the assumpton B s a better approxmaton of the data. Fnally, f the 22
Vuong test statstcs belongs to [-2; 2], none of the assumpton can be statstcally preferred to the other. Three Vuong tests have been mplemented to determne whch are the capacty condtons and type of competton that preval on the market. Frst, we have tested the assumpton of bndng capacty constrant aganst non bdng capacty constrant n the case of compettve market. The Vuong statstcs takes the value 9.70. As t s hgher than 2, under the assumpton of competton between frms, we accept the assumpton of bndng capacty constrant. Then we have tested the assumpton of bndng capacty constrant aganst non bdng capacty constrant n the case of coordnated practces. The Vuong statstcs takes the value 3.15. As t s hgher than 2, under the assumpton of colluson between frms, we accept the assumpton of bndng capacty constrant. Fnally we have tested under the assumpton of bndng capacty constrant we have tested the assumpton of competton aganst the assumpton of coordnated practces. The Vuong statstcs takes the value 2.20. As t s hgher than 2, we can conclude that the competton between frms s the market condton whch better fts the observatons over the perod nto consderaton. Under the assumpton of bndng capacty constrant, the competton prevals over coordnaton. 2. Concluson The crucal pont whle mplementng the econometrc model s the assumpton related to full or excess capactes. If the level of 75 percent n capacty utlzaton s accepted as beng the full capacty threshold, the observaton of the capacty utlzaton over the perod under consderaton leads to the concluson of full capacty. Ths s confrmed statstcally by the Vuong tests mplemented n the two possble market condtons, competton and coordnaton between frms. Ths concluson mght be vald both for FIRM A and at the ndustry level under the assumpton of coordnated practces across the frms. We decded to mplement the econometrc model ether for full capactes or for excess capactes. The Vuong test whch s a test of model valdaton leads to the concluson that the bndng capacty constrant better fts the realty of the market. 23
Under ths more realstc assumpton of full capactes, the queston of market functonng s answered agan through a Vuong test mplementaton. The Vuong test leads to prefer the competton rather than the colluson for a better ft of the workng of the observed market. To conclude, f the full capacty assumpton s recognsed as the most realstc, whch the observed level of producton seems to ndcate on Product X market, then the fndngs of our econometrc analyss leads to the acceptance of competton between the three man players on the market under consderaton. 24
References Berry S. (1994), Estmatng Dscrete Choce Models of Product Dfferentaton, RAND Journal of Economcs, 25, p. 242-262. Davdson C. and R. Deneckere (1990), Excess Capacty and Colluson, Internatonal Economc Revew, 31(3), pp. 521-41. Gasm F., J.J. Laffont and Q. Vuong (1992), Econometrc Analyss of Collusve Behavor n a Soft-Drnk Market, Journal of Economcs and Management Strategy vol.1(2), p. 277-311 Ivald, M. and F. Verboven (2005), Quantfyng the effects from horzontal mergers n European competton polcy. Internatonal Journal of Industral Organzaton, 23, p. 669-691. Porter, R.H. (1983), A Study of Cartel Stablty: The Jont Executve Commttee, 1880-1886, Bell Journal of Economcs, 14, p. 301-314. Röller, L.H. and F. Steen (2006), On the Workngs of a cartel: Evdence from the Norwegan Cement Industry, The Amercan Economc Revew, Vol. 96, No. 1 (Mar., 2006), p. 321-338. Steen F. and L. Sorgard (1999) Semcolluson n the Norvegan Cement Market, European Economc Revew, 43(9), pp. 1775-96. 25
Appendx 1: Dervaton of equlbrum condtons Notatons The Product X s produced by three frms noted by = 1, 2, I = 3 and by an mporter ndexed by the number 0. The man notatons are as follows. We defne Q as the total domestc producton capacty, q the domestc producton of frm for product X, p the domestc prce of product X, x the export of frm, x 0 the total volume of exports of all domestc frms, q d 3 = q, the total domestc producton, q the mports, the mport prce, W the 0 p = 1 nternatonal prce, Q the domestc market sze (.e., the sum of the domestc producton and the mports. Demand elastctes For the logt specfcaton of the demand ntroduced n the text the own-prce elastcty s gven by p q ε = = αp (1 s q p ), (A.1) where s s the market share as defned above, and the cross-prce elastcty s obtaned as: p q ε = = α p s. (A.2) j j j j q pj Equlbrum condtons under competton Assume that the ndustry s compettve. In ths case, each frm sets her prce and the quantty exported so as to maxmze her proft, knowng that the other compettors are dong the same. Then the proft maxmzaton s as follows: Max p, x ( ) pq + Wx C q + x st q + x Q. (A.3) That s to say, each frm maxmzes ts proft defned as the dfference between revenues and cost, where the revenues come from domestc sales and exports and where the cost s a functon of the total producton. The frst order condtons are: 26
C q q + p λ = 0, (A.4a) q p C W λ = 0, (A.4b) x ( Q q x) λ 0 where λ s the multpler assocated wth the capacty condton. =. (A.4c) When the capacty constrant s bndng, p s chosen so that: ( p W) 1 p = p q q p, (A.5) snce W C C = + λ = + λ, and x s chosen so as x = Q q. x q When the capacty constrant s not bndng, then λ = 0 and p and and ( p W) 1 1 = = p p s q p x are chosen so that, (A.6) p q α ( 1 ) C C C = = x q q + x ( ) = W. (A.7) Equlbrum condtons under coordnaton Assume now that the frms n the ndustry behave as a monopoly,.e., maxmze ther jont proft. In ths case, the monopoly sets ts prces and ts exports by solvng the followng programme: 3 3 Max d px, = 1 = 1 pq + Wx0 C( q + x) st q + x0 Q. (A.8) When the capacty constrant s not bndng, and usng a result presented n Appendx 2 below, the frst-order condtons yeld the followng equlbrum condtons: and ( p W) p C C C = = x q q + x 1 =, (A.9) α ps 0 ( ) = W. (A.10) 27
Structure of the econometrc model The typcal econometrc model comprses four equatons: The demand that frm A faces, the demand for mported product X, the prcng equaton (for nstance Equaton (A.6) or Equaton (A.9), the cost functon of frm A, as t s ntroduced n the text. 28
Appendx 2: Note on the jont-proft maxmzaton case n a generc example Consder a set of frms that maxmzes ther jont proft. Assume that the technology exhbts constant returns to scale. The frst-order condtons are: Rearrangng yelds: px, 3 ( p c ) q. = 1 Max q q j q + ( p c ) + ( p c ) = 0. p j j p j p q q p q j qj q + ( p c ) + ( p c ) = 0. j j q p p j qj p p Replacng by the expressons of the elastctes from the logt specfcaton of the demand, we obtan: q + ( p c) α( 1 s) q + ( pj cj) αsq j = 0. Rearrangng yelds: j q ( p c ) αq + αs ( p c ) q = 0. k k k k Dvdng by the market sze obtans: s ( p c ) αs + αs ( p c ) s = 0, whch can be smplfed by k k k k. After rearrangng agan we observe that: s 1 p c = + p c α ( ) s, k k k k whch means that all margns are equal. So we can wrte: Hence: 1 p c 1 s =. α ( ) snce s s. = 0 1 1 p c =, α s 0 29
Appendx 4 Estmated parameters of the models and man relevant test statstcs Table 10. Estmated parameters under the assumpton of compettve practces Parameter Competton bndng Approx. Std Estmate Err t Value Approx.Pr > t 1st Stage R- Square Competton non-bndng Approx. Std Estmate Err t Value Approx.Pr > t 1st Stage R-Square δ 0 12.143 0.711 17.08 <.0001 1.000 5.454 1.001 14.95 <.0001 1.000 δ 0,2008 5.274 1.566 3.37 0.0012 1.000 2.611 1.272 8.44 <.0001 1.000 δ 1 13.357 0.702 19.04 <.0001 1.000 6.477 1.041 15.35 <.0001 1.000 δ 1,2008 6.750 1.561 4.32 <.0001 1.000 3.886 1.368 7.23 <.0001 1.000 α cst 0.049 0.009 5.70 <.0001 0.893 0.014 0.002 16.67 <.0001 0.781 αgdp -7.1E-07 3.1E-07-2.29 0.0244 0.935 β cst 5742536 2386451 1.91 0.060 1.000 β scrap 124769 36872 3.54 0.001 1.000 β scrap,y -0.252 0.475-0.99 0.324 0.858 β Y 0.001 0.001 3.79 0.000 0.401 Number of Observatons Used 83 82 Mssng 1 2 Statstcs for System Objectve 1.508 3.414 Objectve*N 125.151 279.941 Notes: If Approx.Pr > t < 0.01 the correspondng parameter s statstcally sgnfcant at level 1%; f 0.001< Approx.Pr > t < 0.05 the correspondng parameter s statstcally sgnfcant at level 5%; If Approx.Pr > t > 0.1 the correspondng parameter s not statstcally sgnfcant. 30
Table 11. Estmated parameters under the assumpton of collusve practces Parameter Monopoly bndng Approx. Std Estmate Err t Value Approx. Pr > t 1st Stage R- Square Monopoly non-bndng Approx. Std Estmate Err t Value Approx.Pr > t 1st Stage R-Square δ 0 171.918 14.663 11.72 <.0001 1.000 14.964 1.001 14.95 <.0001 1.000 δ 0,2008 37.994 12.725 2.99 0.004 1.000 10.739 1.272 8.44 <.0001 1.000 δ 1 176.755 14.955 11.82 <.0001 1.000 15.981 1.041 15.35 <.0001 1.000 δ 1,2008 29.823 12.734 2.34 0.022 1.000 9.892 1.368 7.23 <.0001 1.000 α cst 1.097 0.140 7.85 <.0001 0.827 0.038 0.002 16.67 <.0001 0.781 αgdp 0.00003 4.266E 6 6.00 <.0001 0.867 β cst 4556365 2386451 1.91 0.060 1.000 β scrap 130427 36872 3.54 0.001 1.000 β scrap,y 0.471 0.475 0.99 0.324 0.858 β Y 0.003 0.001 3.79 0.000 0.401 Number of Observatons Used 83 82 Mssng 1 2 Statstcs for System Objectve 1.821 2.509 Objectve*N 151.140 205.727 Notes: If Approx.Pr > t < 0.01 the correspondng parameter s statstcally sgnfcant at level 1%; f 0.001< Approx.Pr > t < 0.05 the correspondng parameter s statstcally sgnfcant at level 5%; If Approx.Pr > t > 0.1 the correspondng parameter s not statstcally sgnfcant. 31