On Equi-Weyl Almost Periodic Selections of Multivalued Maps

Material SelectionDuring recent years the selection of engineering materials has assumed great importance.Moreover,the process should be one of continual reevaluation. New materials often become available and there may be a decreasing availability of others. Concerns regarding environmental pollution, recycling and worker health and safety often impose new constraints. The desire for weight reduction or energy savings may dictate the use of different materials. Pressures from domestic and foreign competition, increased serviceability requirements, and customer feedback may all promote materials reevaluation. The extent of product liability actions, often the result of improper material use, has had a marked impact. In addition, the interdependence between materials and their processing has become better recognized. The development of new processes often forces reevaluation of the materials being processed.Therefore,it is imperative that design and manufacturing engineers exercise considerable care in selecting,specifying,and utilizing materials if they are to achieve satisfactory results at reasonable cost and still assure quality.The first step in the manufacture of any product is design,which usually takes place in several distinct stages:a)conceptual;(b)functional;(c)production design.During the conceptual-design stage,the designer is concerned primarily with the functions the product is to fuilill. Usually several concepts are visualized and considered,and a decision is made either that the idea is not practical or that the idea is sound and one or more of the conceptual designs should be developed further.Here,the only concern for materials is that materials exist that can provide the desired properties.If no such materials are available,consideration is given as to whether there is a reasonable prospect that new one could be developed within cost and time limitations.At the functional or engineering-design stage,a practical,workable design is developed.Fairly complete drawing are made,and materials are selected and specified for the various components.Often a prototype or working model is made that can be tested to permit evaluation of the product as to function,reliability,appearance,serviceability,and so on.Although it is expected that such testing might show that some changes may have to be made in materials before the product is advanced to the production-design stage,this should not be taken as an excuse for not doing a thorough job of materials selection.Appearance,cost,and reliability factors should be considered in detail,together with the functional factors.There is much merit to the practice of one very successful company which requires that all prototypes be built with the same materials that will be used in production and,insofar as possible,with the same manufacturing techniques.It is of little value to have a perfectly functioning prototype that cannot be manufactured economically in the expected salesvolume,or one that is substantially different from what the production units will be in regard to quality and reliability.Also,it is much better for design engineers to do a complete job of material analysis,selection,and specification at the development stage of design rather than to leave it to the production-design stage,where changes may be made by others,possibly less knowledgeable about all of the functional aspects of the product.At the production-design stage,the primary concern relative to materials should be that they are specified fully,that they are compatible with,and can be processed economically by,existing equipment,and that they are readily available in the needed quantities.As manufacturing progresses,it is inevitable that situations will arise that may require modifications of the materials being used.Experience may reveal that substitution of cheaper materials can be made.In most cases,however,change are much more costly to make aftermanufacturing is in progress than before it starts.Good selection during the production-design phase will eliminate the necessity for most of this type of change.The more common type of change that occurs after manufacturing starts is the result of the availability of new materials.These,of course,present possibilities for cost reduction and improved performance.However,new materials must be evaluated very carefully to make sure that all their characteristics are well established.One should always remember that it is indeed rare that as much is know about the proportion of product failure and product liability cases have resulted from new materials being substituted before their long-term properties were really known.Product liability actions have made it imperative that designers and companies employ the very best procedures in selecting materials.The five most common faults in material selection have been : (a)failure to know and use the latest and best information available about the materials utilized;(b)failure to foresee,and take into account the reasonable uses for the product(where possible,the designer is further advise to foresee and account for misuse of the product,as there have been many product liability cases in recent years where the claimant,injured during misuse of the product ,has sued the manufacturer and won);(c)the use of materials about which there was insufficient or uncertain data,particularly as to its long-term properties;(d)inadequate,and unverified,quality control procedures;and(e) material selection made by people who are completely unqualified to do so.An examination of the faults above will lead one to conclude that there is no good reason why they should exist.Consideration of them provides guidance as to know they can be eliminated.While following the very best methods in material selection may not eliminate all product-liability claims,the use of proper procedures by designers and industries can greatly reduce their numbers.From the previous discussion,it is apparent that those who select materials should have a broad,basic understangding of the nature and properties of materials and their processing.。

Intermetallic phase selection in 1XXX Al alloysC.M.Allen a,*,K.A.Q.O'Reilly a ,B.Cantor a ,P.V.Evans b a Oxford Centre for Advanced Materials and Composites,Department of Materials,University of Oxford,Parks Road,Oxford,OX13PH,UK b Alcan International Limited,Banbury Laboratory,Southam Road,Banbury,Oxon,OX167SP,UKAccepted 1October 1998CONTENTS1.INTRODUCTION 902.BINARY Al±Fe PHASES 922.1.The equilibrium Al±Fe 4AL 13eutectic 922.2.Metastable Al±Fe eutectic phases 932.2.1.Metastable Al±FeAl 6eutectic 952.2.2.Metastable Al±FeAl m eutectic 962.2.3.Metastable Al±FeAl x eutectics 972.2.4.Metastable Al±Fe 2Al 9eutectic 1012.2.5.Metastable Al±FeAl p eutectic 1012.2.6.The e ect of Si addition on the formation of Al±Fe phases 1013.TERNARY Al±Fe±Si PHASES 1023.1.The equilibrium a -AlFeSi and b -AlFeSi phases 1023.2.Metastable a -AlFeSi and b -AlFeSi phases 1053.2.1.Metastable cubic a -AlFeSi phase 1053.2.2.Metastable a v -AlFeSi phase 1063.2.3.Metastable a 0or q 1-AlFeSi phase 1063.2.4.Metastable a T -AlFeSi phase 1063.2.5.Metastable q 2-AlFeSi phase 1093.2.6.Metastable b H -AlFeSi phase 1114.FACTORS GOVERNING PHASE SELECTION IN 1XXX ALLOYS petitive growth 1124.1.1.Transition from Fe 4Al 13to FeAl 61124.1.2.Transition from Fe 4Al 13to FeAl x 1184.1.3.Transition from FeAL 6to FeAl m 1184.1.4.Transitions in Al±Fe±Si alloys petitive nucleation 1204.2.1.The transition from Fe 4Al 13to FeAl 61204.2.2.Promotion of nucleation of other phases 1224.3.Suppression of equilibrium solidi®cation reactions 1234.4.Metastable phase diagrams and solidi®cation microstructure selection maps 124Progress in Materials Science 43(1998)89±1700079-6425/99/$-see front matter #1999Elsevier Science Ltd.All rights reserved.PII:S 0079-6425(98)00003-6PERGAMON *Corresponding author:Tel.:+44-1865-273774;fax:+44-1865-273764;e-mail:chris.allen@.5.FIR TREE FORMATION IN DC CASTS 1275.1.Fir tree zones 1275.2.Cooling rate 1285.3.Fir tree nucleation 1305.4.Fir tree nucleation and growth 1325.5.E ect of solid fraction 1356.FIR TREE PHASES IN DC CASTS 1377.TRANSFORMATION OF METASTABLE PHASES 1407.1.The FeAl 6À4Fe 4Al 13transformation 1417.1.1.Transformation mechanism and activation energy 1417.1.1.1.Dissolution±precipitation mechanism and net activation energy 1417.1.1.2.Formation of acicular Fe 4Al 13precipitates 1437.1.1.3.Continuous heating transformation 1437.1.1.4.Two step ageing 1457.1.1.5.Isothermal transformation 1487.1.2.Transformation rate 1517.1.2.1.Microstructural scale 1517.1.2.2.E ect of cold work 1547.1.2.3.Presence of pre-existing nuclei 1547.2.The FeAl m À4Fe 4Al 13transformation 1567.3.E ect of Si on transformations of metastable Al±Fe phases 1577.4.Transformations involving ternary Al±Fe±Si phases 1588.EFFECT OF IMPURITIES ON PHASE FORMATION IN Al±Fe AND Al±Fe±Si ALLOYS 1599.EFFECT OF GRAIN REFINER ADDITIONS ON Al±Fe AND Al±Fe±Si ALLOYS 1649.1.Proposed mechanisms of primary Al grain re®nement 1649.2.The ro Ãle of grain re®ners on secondary/ternary phase selection 16610.SUMMARY 167REFERENCES1681.IntroductionFlat rolled aluminium products account for approximately 40%of the 24million tonnes annual world production of aluminium.These products are commonly used for packaging and canning,in electrical applications (e.g.capacitor electrodes),architectural cladding,cable wrap,lithographic printing and automotive sheet.About 90%of ¯at rolled products are produced from the melt by the following manufacturing route:the melt is degassed,®ltered and grain re®ned,then direct chill (DC)cast into rectangular or cylindrical water cooled ring moulds with removable bases.Fig.1shows a schematic of the DC casting process.The removable bases are withdrawn at a controlled rate as the metal solidi®es,resulting in the semicontinuous casting of rectangular ingots or cylindrical billets,typically 0.5±1m in diameter and 5±10m in length.The cast surface is often uneven,and the outermost H 0.2m of the cast in from surface is often of a coarser grain structure than the interior and can contain higher levels of segregates.The cast surface is commonly scalped o therefore,as discussed in Section 5.1,and the remainder heat treated in the temperature range 450±6008C,in the form of a pre-heat in order to e ect microstructural homogenization prior to rolling.Homogenization reduces segregation,encourages the transformation of metastable secondary and ternary phases into equilibrium phases,and acts to equilibrate solidC.M.Allen et al./Progress in Materials Science 43(1998)89±17090solution levels of soluble elements,resulting in certain cases in the precipitation of dispersoids.A series of both hot and cold rolls with intermediate annealing treatments are then applied to produce a foil or sheet of the required ®nal gauge,typically in the range 6±150m m (foil)or 150±3000m m (sheet),which is then commonly subjected to a ®nal anneal.A range of di erent aluminium alloys are DC cast and processed by the above route.The exact compositions depend upon the ®nal application of the casting,but Cu,Zn,Mg,Mn,Si and Fe are common alloying additions.The alloys that are the subject of this review are those designated AA1xxx by the International Alloy Designation System (IADS).Commercial 1xxx series Al alloys contain typically 0.5wt%Fe and 0.2wt%Si,sometimes present as deliberate alloying additions,but also as impurities.Other common impurities are Cu,Cr,Mn,Mg,V and Zn.Al±Ti±B additions are frequently used to promote primary Al grainre®nement.Fig.1.Schematic of the vertical DC casting process (after Maggs).C.M.Allen et al./Progress in Materials Science 43(1998)89±17091The identity,size and distribution of the secondary and ternary inter-metallic phases are critical in¯uences on the material properties of the alloy [74],including strength,toughness,formability,fatigue resistance,corrosion resistance and anodizing response [58].Anodizing quality and etching response are especially important in surface critical products such as lithographic printing sheet,as well as in sheet used in architectural applications.The solid solution content is particularly important in controlling properties such as electrical conductivity and recrystallization characteristics.Thermodynamic consider-ations often fail to predict correctly the phase content and solid solution content of the as-cast microstructure because of the non-equilibrium nature of solidi®cation during DC casting.The key alloy properties are controlled by solid solution levels and secondary and ternary phase crystallography and morphology,which in turn are dependent on complex kinetic competitions for nucleation and growth.In Sections 2and 3the wide range of both equilibrium and metastable secondary Al±Fe and ternary Al±Fe±Si phases reported in 1xxx alloys are examined.2.Binary Al±Fe phasesThe maximum equilibrium solid solubility of Fe in Al is very low,at H 0.05wt%Fe,and Fe is usually present therefore in the form of secondary Fe aluminide phases [74].The maximum equilibrium solid solubility of Si in Al is higher at H 1.6wt%,and low levels (H 0.1±0.2wt%)of Si in the bulk are readily accommodated therefore by dissolution in the Al matrix and in the Fe aluminides.Consequently,the phase contents of DC cast Al±Fe and Al±Fe±Si alloys with 0.1wt%Si are similar,although in the latter case the so called `binary'Fe aluminides often contain dissolved Si.Ternary Al±Fe±Si phases,as reviewed in Section 3,only form at higher bulk concentrations of Si,typically >0.1wt%Si in 0.2wt%Fe containing alloys,and >0.2wt%Si in 0.3±0.4wt%Fe containing alloys.2.1.The equilibrium Al±Fe 4Al 13eutecticFig.2shows the equilibrium Al±Fe binary phase diagram.As shown in Fig.2,the ®rst secondary phase to form on solidi®cation of dilute Al±Fe alloys under equilibrium conditions is given by the eutectic reaction;Liquid À4a ÀAl Fe 4Al 13 also denoted as FeAl 3Y or the y phaseThe exact temperature and composition of the invariant point is of some debate,but Liang and Jones [65]have recently reported 655.120.18C at 1.8wt%Fe,respectively.The eutectic temperature of 655.18C has subsequently been con®rmedC.M.Allen et al./Progress in Materials Science 43(1998)89±17092by Allen [4]using calorimetric methods.At the eutectic temperature the a -Al matrix has the maximum equilibrium solid solubility of Fe,at H 0.05wt%[74].The equilibrium secondary phase exists over a range of compositions,and is often denoted as having the stoichiometry of either FeAl 3or Fe 4Al 13.Black [15]determined from X-ray di raction studies that Fe 4Al 13has a c-face centred monoclinic structure containing 100atoms per unit cell [74].Fig.3a and b shows a typical TEM micrograph of needle shaped Fe 4Al 13particles at the grain boundaries in a DC cast ingot and a typical [100]zone axis selected area di raction pattern (SADP)from a crystal of Fe 4Al 13extracted from the Al matrix,respectively.Fe 4Al 13commonly forms relatively large angular precipitates in as-cast microstructures (Fig.3a),which increase hardness but lead to embrittlement,reducing formability and fatigue resistance.As shown in Fig.3b,Fe 4Al 13exhibits spot streaking in certain zone axis di raction patterns parallel to the (00l)reciprocal lattice vector,although it is not clear whether this is due to stacking faults or microtwinning on (001)[96,97].Fe 4Al 13can also form pseudo 10-fold twins,resulting from alternate repetition of (100)and (201)twins [56,57].Fig.4shows a bright ®eld TEM micrograph of a 10-fold branched dendritic particle present in a melt-spun Al±20at%Fe alloy.2.2.Metastable Al±Fe eutectic phasesAs long ago as 1925Dix [2]noted that fully eutectic microstructures could be attained in rapidly cooled alloys of Fe content well in excess of that of the equilibrium eutectic,1.8wt%.This indicated that large undercoolings are required to nucleate and/or grow the Al±Fe 4Al 13eutectic under certainsolidi®cationFig.2.Al rich corner of the equilibrium Al±Fe binary phase diagram.C.M.Allen et al./Progress in Materials Science 43(1998)89±17093conditions.The nucleation and growth requirements of both the Al±Fe 4Al 13and metastable Al±Fe eutectics is discussed in further detail in Section 4.2and 4.1,respectively.Under non-equilibrium solidi®cation conditions a rangeofFig.3.(a)Fe 4Al 13at grain boundaries in cast ingot.After Skjerpe [97].Reproduced by kind permission of Blackwell Science Ltd.(b).Typical [110]di raction pattern of a faulted Fe 4Al 13crystal.Faults on {001}planes produce lines parallel to the {001}direction in reciprocal space.After Skjerpe [96].Reproduced from Metallurgical and Materials Transactions by kind permission of TMS and ASM international.C.M.Allen et al./Progress in Materials Science 43(1998)89±17094thermodynamically metastable Al±Fe eutectic phases that have smaller undercoolings for nucleation and growth than Al±Fe 4Al 13can form in addition to Al±Fe 4Al 13.These are summarized in Table 1.The composition ranges of some of the metastable Al±Fe eutectics are shown in Fig.5.2.2.1.Metastable Al±FeAl 6eutectic Hollingsworth et al.[42]were the ®rst to identify one of the metastable Al±Fe eutectics displacing Al±Fe 4Al 13.They observed the displacement of Al±Fe 4Al 13by Al±FeAl 6in continuously cast Al±2wt%Fe.The exact solidi®cation conditions (cooling rate and solidi®cation velocity)at which this displacement occurs have since been characterized by Ba ckerud [12],Adam et al.[1,2],Hughes and Jones [45],Liang and Jones [85],Gilgien et al.[35],Evans et al.[32]and Thomas et al.[105]and will be discussed further in Section4.Liang and Jones [65]report the eutectic temperature as 652.920.28C,with a eutectic composition of 3.0wt%Fe.The crystal structure is c-face centred orthorhombic [96],with 28atoms per unit cell [74].FeAl 6is a common constituent of DC cast ingots and billets [112].Fig.6a and b show a typical TEM micrograph of FeAl 6eutectic embedded in an Al matrix and the corresponding [110]zone axis SADP.FeAl 6is also an important phase in Mn-containing alloys.MnAl 6and FeAl 6are isomorphous,and consequently Mn can substitute freely for Fe in the FeAl 6lattice,lowering its free energy.This raises the thermodynamic stability of the FeAl 6phase in Mn containing Al alloys (see Section 8and Table6).Fig.4.TEM micrograph of 10-fold branched dendritic Fe 4Al 13particle.After Kim and Cantor [56,57].Reproduced from Phil.Mag.A by kind permission of Taylor and Francis Ltd.C.M.Allen et al./Progress in Materials Science 43(1998)89±170952.2.2.Metastable Al±FeAl m eutectic Kosuge and co-workers [58]report that a metastable Al±FeAl m eutectic appears at higher cooling rates (e.g.>10K s À1in wedge-shaped moulds of Al±0.6wt%Fe)than those at which Fe 4Al 13and FeAl 6form.This phase has also been observed in the more rapidly cooled zones of DC cast billets [96,112].Fig.7a and b shows a typical TEM micrograph of a dendritic like FeAl m particle extracted from the Al matrix and the corresponding [110]zone axis SADP,respectively.As shown in Fig.7b,FeAl m exhibits incommensurate re¯ections in certain zone axis di raction patterns parallel to the (hh0)reciprocal lattice vector,due to stacking faults on (110)planes [96,98].The eutectic temperature and composition for FeAl m in Al±Fe binary alloys have not been determined.Allen et al.[5]have determined a eutectic temperature of 649.58C for FeAl m in Al±0.3wt%Fe-0.1wt%Si±0.05wt%V,1.7K lower than the eutectic temperature of 651.28C for Fe 4Al 13measured in the same alloy.The FeAl m phase exists over a range of compositions,with the value of m quoted in the range from 4.0to 4.4.The crystal structure is body centred tetragonal [96],the unit cell containing in the region of 110to 118atoms [98].Table 1Al±Fe phases formed in dilute Al±Fe alloysPhaseBravais lattice Lattice parameters References Fe 4Al 13c-Centred monoclinic a =15.49A ,Skjerpe [96,97]b =8.08A ,c =12.48A ,b =107.758FeAl 6c-Centred orthorhombic a =6.49A ,b =7.44A c =8.79AHollingsworth et al.[42],Ba ckerud [12],Jones [51],Adam and Hogan [1],Hughes and Jones [45]FeAl x (I)c-Centred orthorhombic a I 6A ,b I 7A ,Westengen [112],Skjerpe [96](x I 5.7±5.8)c I 4.7AFeAl x ??Young and Clyne [113](x I 5),Evans et al.[31](x I 4.5),Wang et al.[111]FeAl m Body centred tetragonal a =8.84A ,b =c =31.6AYoung and Clyne [113],Westengen [112],Skjerpe [96],Skjerpe [98](m I 4.0±4.4)Fe 2Al 9Monoclinic a =8.90A ,b =6.35A ,Simensen and Vellasamy [94],Brobak and Brusethaug [16],Griger et al.[38]c =6.32A ,b =93.48FeAl p Body centred cubic a =b =c =10.3A Ping et al.[80]C.M.Allen et al./Progress in Materials Science 43(1998)89±170962.2.3.Metastable Al±FeAl x eutectics Westengen [112]discovered another Al±Fe eutectic in DC cast material,denoted Al±FeAl x ,determining from EDX a stoichiometry of x I 5.8,with traces (<1wt%)of Si and Ni also being detected.Westengen was unable to determine the crystal structure of FeAl x from the irregular nature of its di raction patterns,and suggested that it was heavily faulted.Skjerpe also detected this phase,with a similar stoichiometry of x I 5.7,and containing 1.9wt%Si and 0.3wt%Ni.Fig.8a and b show a typical TEM micrograph of an FeAl x particle and a typically irregular SADP,respectively [96,97].Skjerpe indexed the strongest intensity spots of his di raction patterns to ®t a c-face centred orthorhombic unit cell of cell parameters very similar to that of FeAl 6(Table 1).HREM lattice imaging of FeAl x revealed that the di raction patterns arise from a complex stacking sequence in real space.Given also the similarity in stoichiometries (Fig.5),Skjerpe suggested that FeAl x was a Si modi®ed version of FeAl 6.The eutectic temperature and composition of this phase have not been reported.Another phase also denoted FeAl x has been reported by Young and Clyne [113].Young and Clyne determined x I 5from EDX data,and tentatively proposed a monoclinic crystal structure to ®t the XRD data they obtained from this phase.If this structure is correct then this is not therefore the same FeAl x as observed by Westengen and Skjerpe.Young and Clyne's FeAl x displaced Fe 4Al 13at cooling rates below that of FeAl 6during unidirectional solidi®cation experiments.Evans et al.[31]have similarly observed produced FeAl x at cooling rates intermediate between Fe 4Al 13and FeAl 6during unidirectional solidi®cation,with a valueofpositions of the common binary and ternary compounds found in dilute Al±Fe±Si alloys.After Langsrud [61].C.M.Allen et al./Progress in Materials Science 43(1998)89±17097Fig.6.(a)FeAl 6.After Westengen [112].Reproduced by kind permission of Carl Hauser Verlag,Munich,Germany.(b)[110]zone axis selected area di raction pattern of FeAl 6.After Westengen [112].Reproduced by kind permission of Carl Hauser Verlag,Munich,Germany.C.M.Allen et al./Progress in Materials Science 43(1998)89±17098x I 4.5.The XRD trace from this phase could not be made to ®t the monoclinic structure proposed by Young and Clyne however.Wang et al.[111]have since produced a fully eutectic microstructure of Al±FeAl x in Al±3wt%Fe±0.1wt%V alloys directionally solidi®ed at velocities in the range 0.09±1.03mm s À1,with the same XRD trace as Evans's FeAl x ,and have shown that Young and Clyne's structure determination was incorrect [33].The FeAl x eutectics produced by Young and Clyne,Evans et al.and Wang et al.are the same phase therefore,with x I 4.5±5.0,and in turn are di erent to the FeAl x eutectics produced by Westengen and Skjerpe,with x I5.7±5.8.Fig.7.FeAl m and corresponding [110]di raction pattern.Stacking faults on {hh0}planes lead to incommensurate re¯ections along the {hh0}direction in reciprocal space.After Skjerpe [96].Reproduced from Metallurgical and Materials Transactions by kind permission of TMS and ASM International.C.M.Allen et al./Progress in Materials Science 43(1998)89±17099Fig.8.(a)FeAl x .After Skjerpe [96].Reproduced from Metallurgical and Materials Transactions by kind permission of TMS and ASM International.(b)Di raction pattern from FeAl x showing incommensurate nature of re¯ections.After Skjerpe [96].Reproduced from Metallurgical and Materials Transactions by kind permission of TMS and ASM International.C.M.Allen et al./Progress in Materials Science 43(1998)89±1701002.2.4.Metastable Al±Fe 2Al 9eutectic Fig.9shows a typical TEM micrograph of Fe 2Al 9eutectic embedded in an Al matrix,obtained in strip cast Al±0.5wt%Fe±0.2wt%Si alloy [94].The stoichiometry of this phase was determined by EDX.Analysis of electron di raction patterns indicated a monoclinic crystal structure.The solidi®cation conditions under which this phase form are unclear.Tezuka and Kamio [104]noted that in DC cast Al±0.5wt%Fe,additions of >0.075wt%Co promoted the formation of the (Fe,Co)2Al 9phase.Fe 2Al 9and Co 2Al 9are isomorphous,and consequently Co can substitute freely for Fe in the Fe 2Al 9lattice,lowering its free energy.This raises the thermodynamic stability of the Fe 2Al 9phase in Co containing Al alloys (see Section 8and Table 6).2.2.5.Metastable Al±FeAl p eutectic Ping et al.[80]reported the formation of a metastable body centred cubic phase FeAl p (where p I 4.5)in directionally chill cast Al±(0.25±0.50)wt%Fe±0.125wt%Si.This phase has yet to be observed independently.2.2.6.The e ect of Si addition on the formation of Al±Fe phases As stated in Section 2,small quantities of Si (typically <0.1wt%Si bulk composition in 0.2wt%Fe containing alloys,and 0.2wt%Si in 0.3±0.4wt%Fe containing alloys)can be dissolved into the `binary'Fe aluminides.However,these aluminides have di erent degrees of Si solubility (Fig.5).Consequently,the Fig.9.Fe 2Al 9.After Simensen and Vellesamy [94].Reproduced by kind permission of Carl Hauser Verlag,Munich,Germany.C.M.Allen et al./Progress in Materials Science 43(1998)89±170101occurrence of FeAl 6which can only dissolve up to 0.5wt%Si in its lattice is restricted in Al±Fe±Si alloys.FeAl 6is replaced by Fe aluminides that can incorporate Si,such as Fe 4Al 13or FeAl m [61].3.Ternary Al±Fe±Si phases3.1.The equilibrium a -AlFeSi and b -AlFeSi phasesThree ternary phases form under equilibrium solidi®cation conditions in dilute Al±Fe±Si alloys of su ciently high bulk Si content,>0.1wt%Si in 0.2wt%Fe containing alloys,and >0.2wt%Si in 0.3±0.4wt%Fe containing alloys,at temperatures below that of the liquid 4Al +Fe 4Al 13eutectic reaction.Fig.10shows the liquidus projection and associated equilibrium solidi®cation reactions in the Al corner of the Al±Fe±Si ternary phase diagram.The three equilibrium ternary phases produced by either of two ternary peritectic reactions followed by a ternary eutectic reaction are;i.Liquid +Fe 4Al 13À4Al +Fe 2SiAl 8(also denoted as the a phase);ii.Liquid +Fe 2SiAl 8À4Al +FeSiAl 5(also denoted as the b phase);and/or iii.Liquid À4Al +Si +FeSiAl 5.A range of temperatures have been measured for these three invariant points in the ternary phase diagram:620±6388C for the a peritectic,611±6158C for the b peritectic and 576±5778C for the ternary eutectic [14,74,85].These ranges may re¯ect a di culty in nucleating or growing one or more of these phases during solidi®cation.This point is discussed in Section 4.3.Both phases exist over a range of compositions,as shown in Fig.5.The accepted stoichiometries as given above are those of Mondolfo [74].Both the a and b phases can adopt a number of di erent crystal structures.Table 2summarizes the structural variants of these two phases.Munson [75]determined from X-ray di raction studies that a -AlFeSi has a hexagonal crystal structure (Table 2),in agreement with earlier single crystal studies performed by Robinson and Black [86],and this was con®rmed in the same year by Sun and Mondolfo [102].The hexagonal crystal structure of a is also known in the literature as a H [86]or a 2[9,10].Fig.11a and b show a typical TEM micrograph of an a H particle in DC cast 1050alloy and corresponding [100]zone axis SADP,respectively [112].Dons [29]observed that a H survived heat treating in >99.9wt%pure Al based DC cast commercial purity alloys,to progressively higher temperatures with increasing bulk Si content of the alloy,from 4508C in Al±0.6wt%Fe±0.15wt%Si,to 6008C in Al±0.6wt%Fe±0.6wt%Si.Phragmen [79]determined that b -AlFeSi has a monoclinic crystal structure (Table 2).b -AlFeSi is an important ternary phase in wrought aluminium alloys.Fig.12shows a typical SEM micrograph of b platelets on a deep etched surface of a DC cast alloy,showing their characteristic long thin curving morphology,which can dramatically reduce ductility.C.M.Allen et al./Progress in Materials Science 43(1998)89±170102Table 2Common structural variants of the ternary phases Fe 2SiAl 8(a )and FeSiAl 5(b )PhaseBravail lattice Lattice parameters References a (a 1)Cubic a =12.56A (Im3)a =12.52A (Pm3)Cooper [23],Munson [75],Sun and Mondolfo [102],Westengen [112],Griger et al.[37],Turmezey et al.[109]a H (a 2)Hexagonal a =b =12.3A c =26.2A Dons [29],Munson [75],sun and Mondolfo [102],Griger et al.[37],Thoresen et al.[106]a v Monoclinic a =8.90A ,Dons [29]b =6.35A ,c =6.32A ,b =93.48a 0(q 1)c-Centred orthorhombic a =12.7A ,b =26.2A Westengen [112],Skjerpe [96],Ping et al.[80],Ping [82]c =12.7A q 2Monoclinic a =12.50A ,Ping et al.[80]b =12.30A ,c =19.70A ,b =1118a T c-Centred monoclinic a =27.95A ,b =30.62A ,Dons [29],Skjerpe [96],Jensen and Wyss [50],Turmezey et al.[109],Ping [82]c =20.73A ,b =97.748b Monoclinic a =6.12A Skjerpe [96]b =6.12A ,c =41.5A ,b =918b H Monoclinic a =8.9A ,Westengen [112],Skjerpe [96]b =4.9A ,c =41.6A ,b =928Fig.10.Liquidus surface and associated equilibrium phase ®elds in the Al corner of the ternary Al±Fe±Si phase diagram.After Skjerpe [96].Reproduced from Metallurgical and Materials Transactions by kind permission of TMS and ASM International.C.M.Allen et al./Progress in Materials Science 43(1998)89±170103Fig.11.(a)Hexagonal a H Al±Fe±Si.After Westengen [112].Reproduced by kind permission of Carl Hauser Verlag,Munich,Germany.(b)[100]zone axis selected area di raction pattern from a H .After Westengen [112].Reproduced by kind permission of Carl Hauser Verlag,Munich,Germany.C.M.Allen et al./Progress in Materials Science 43(1998)89±1701043.2.Metastable a -AlFeSi and b -AlFeSi phasesUnder non-equilibrium solidi®cation conditions,the liquid becomes enriched in Si,due to partitioning of the Si to the interdendritic liquid,and hence there is a greater tendency for ternary phases to form [61].In addition,a number of metastable structural variants of both the a -and b -AlFeSi ternary phases are commonly observed in commercial DC cast alloys,and are summarized in Table 2.3.2.1.Metastable cubic a -AlFeSi phase Munson [75]and Sun and Mondolfo [102]determined that the equilibrium hexagonal form of a -AlFeSi was only thermodynamically stable in high purity Al±Fe±Si alloys.Additions of V,Cr,Mn,Cu,Mo and W all promote a body-centred cubic structure for the a -AlFeSi phase,also known in the literature as c [79],a 1[9,10]or simply a [78].Additions of Ti,Ni,Zn and Mg do not promote the cubic structure [102].The cubic structure had also been previously observed by Phragmen [79]and Cooper [23],but had incorrectly been assumed to represent the equilibrium crystal structure for the a -AlFeSi phase.The cubic structure is isostructural with a -AlMnSi.Only 0.1wt%Mn is required therefore to stabilize the cubic form during solidi®cation at a cooling rate of 0.75K min À1[75].The stabilization of the cubic form by trace elements common to commercial purity alloys results in the cubic form being the one which is most commonly observed in commercial alloys.Westengen [112]observed cubic a in DC cast AA1050alloy in the more rapidly cooled outer zone of the billet.Weak h +k +l =odd integer spots were observed in the di raction patterns,indicating that the structure may not have been body centred but primitive cubic.Dons [29]observed cubic a in both as-cast and heat-treated DC cast commercialpurity Fig.12.SEM micrograph of b Al±Fe±Si platelets,in surface etched DC cast alloy.After Griger et al.[37].Reproduced by kind permission of Aluminium .C.M.Allen et al./Progress in Materials Science 43(1998)89±170105aluminium of Fe/Si ratio <1,which survived to progressively higher heat treatment temperatures with increasing bulk Si content.Fig.13a and b shows a typical TEM micrograph of a cubic a particle extracted from a DC cast Al±0.25wt%Fe±0.13wt%Si alloy,with a partly dendritic morphology,and a corresponding [111]zone axis SADP,respectively [97].Skjerpe observed cubic a in the more rapidly cooled outer 50mm of the billet.Griger et al.[37]observed cubic a in semicontinuously cast Al±0.5wt%Fe±0.2wt%Si,across the entire cross-section of the billet.Turmezey et al.[109]observed that the Si content of the cubic a phase was directly proportional to the bulk Si content,suggesting that direct Al t Si substitution can take place in the cubic a lattice.Thoresen et al.[106]investigated Al±4wt%(Fe,Mn)±7.5wt%Si alloys,with varying Fe:Mn ratios,in which the primary phase was a -AlFeSi,either in its cubic or hexagonal form,depending upon the bulk Mn content of the alloy [75].The total transition metal content (Fe +Mn)of the cubic a phase in the Al±(Fe,Mn)±Si alloy was less than the cubic a phase in the Al±Mn±Si alloy,indicating that vacancies stabilise the cubic a structure when both Fe and Mn are present.3.2.2.Metastable a v -AlFeSi phase Dons [29]observed a monoclinic structural variant of a -AlFeSi in DC cast commercial purity Al±0.2wt%Fe±0.2wt%Si,denoted a v .Dons stated that a v was structurally related to the Fe 2Al 9phase [94],the a-axis being 2.6%shorter and the c-axis 3.6%shorter than the monoclinic structure of Fe 2Al 9.However,the Si content of a v was in the range4.5±10.5wt%(corresponding to the Si content range typically observed in a H and a ),signi®cantly higher than the maximum Si content of H 2wt%seen in Fe 2Al 9.3.2.3.Metastable a 0or q 1-AlFeSi phase Fig.14a and b show a typical TEM micrograph of a 0particles embedded in a DC cast AA1050alloy and a corresponding [100]zone axis SADP,respectively [112].Westengen observed that a 0was closely related to the cubic a form,indexing the a 0di raction patterns as originating from a tetragonal unit cell.EDX data showed that a 0had a lower Si content than cubic a .Westengen therefore suggested that a 0was a low Si modi®cation of cubic a ,as illustrated in Fig. 5.Fig.15summarizes the subsequent EDX measurements made by Skjerpe [96]on particles in DC cast Al±0.25wt%Fe±0.13wt%Si,which supported the idea that a 0was a low Si modi®cation of cubic a .Ping et al.[80]also observed the a 0phase in DC cast Al±0.28wt%Fe±0.13wt%Si,but denoted it q 1,which formed at a cooling rate of H 10K s À1.Detailed convergent beam electron di raction analysis by Ping and co-workers [80,81]of a 0revealed a c-face centred orthorhombic structure,which was also con®rmed by [96].3.2.4.Metastable a T -AlFeSi phase Dons [29]observed a further structural variant of a -AlFeSi in DC cast commercial purity Al±0.2wt%Fe±0.2wt%Si,denoted a T ,whose crystalC.M.Allen et al./Progress in Materials Science 43(1998)89±170106。

CONNECTIVITY IN THE COMMERCIAL INTERNET *Jacques Cremer {,Patrick Rey {and Jean Tirole }We study the `backbone market'in the Internet.After discussing the structure of the Internet,we use an extension of the Katz-Shapiro network model to analyze the strategies that would be used by dominant backbone.We show that a larger backbone prefers a lower quality interconnection than the smaller one.We then analyze a `targeted degradation'strategy where the larger backbone lowers the quality of interconnection to its smaller rivals in turn.Finally,we show that the qualitative results are robust to the possibility of `multihoming'by clients.i.introductionThe Internet has entered a critically important period of transition from government ownership to commercial exploitation.Until recently,the Internet community was largely one of engineers working cooperatively to take the Internet o¡the ground,and the largest part of the initial network,the NSFNET,was privatized as late as 1995.In the commercial era that is just beginning,¢nancial stakes are huge,and the Internet is turning into a fascinating commercial battleground.While players in the industry are trying to design business models and contractual arrangements for the new environment,economic analysis has yet to produce guidance for strategy and competition policy.In fact,little is known about the `industrial organization of the Internet'.The early work on the economics of the Internet focused on the use of smart market auctions and peak-load pricing to allocate scarce transmission capacity ßBlackwell Publishers Ltd.2000,108Cowley Road,Oxford OX41JF,UK,and 350Main Street,Malden,MA 02148,USA.433THE JOURNAL OF INDUSTRIAL ECONOMICS 0022-1821Volume XLVIII December 2000No.4*The authors have advised GTE on the Internet aspects of the WorldCom-MCI merger,and are grateful to GTE for letting them use work done on that case for academic purposes.We should stress however that the views presented in this paper are our own,and need not re£ect GTE's.We are grateful to Scott Flick,Scott Marcus and Jim Venit,for helpful discussions on the technology and economics of the Internet.This paper was presented at the conference on `Competition and Innovation in the Personal Computer Industry',San Diego,24April 1999.We thank the sponsors of this conference for support and the participants for comment.{Authors'a¤liation:IDEI and GREMAQ (CNRS UMR 5604),Toulouse,France.email:jacques@ {IDEI and GREMAQ (CNRS UMR 5604),Toulouse,France.email:prey@cict.fr }IDEI and GREMAQ (CNRS UMR 5604),Toulouse,France,CERAS (CNRS UMR 2036),and MIT.email:tirole@cict.fr Mailing address for all three authors:IDEI,Universite de Toulouse 1,31042Toulouse Cedex,France.434jacques cre mer,patrick rey and jean tiroleamong competitive end users.1While this work is clearly relevant,in this paper we turn our attention on the strategic behavior of¢rms and on the role of antitrust policy in the commercial Internet environment.We will address only a small subset of the myriad fascinating questions related to these issues,focusing on the issue of connectivity.The Internet is a system of interconnected computer networks.In this industry char-acterized by strong network externalities,end users,consumers and busi-nesses,seek ubiquitous connectivity and purchase connectivity from Internet service providers(ISPs).Internet backbone providers(IBPs) provide high bandwidth long-haul transmission,routing and interconnec-tion to these ISPs and to their own vertically integrated ISPs and Web-hosting services.But is there a proper`backbone market',or should one consider IBPs as Internet service providers like all others and thus part of a broader market?And,if an IBP market indeed exists,what strategies can a player with substantial market power employ to enhance dominance? These questions stood at the heart of the joint investigation in1998by the US Department of Justice and the European Commission of the proposed merger between WorldCom and MCI,which each owned one of the four largest Internet backbones.Antitrust authorities feared that the merged entity would have incentives to degrade the quality of its inter-connection with the rest of the Internet,to introduce proprietary standards,or to impose tough interconnection agreements on other back-bones.2As a result of the investigation,the parties were required to divest about half of their Internet assets before they were allowed to merge.3 The paper is organized as follows.Section II presents a brief overview of the industry,and explains the role of backbones.Section III performs a market de¢nition and concentration analysis,thereby providing further details about demand substitution,supply response and potential entry. Our formal analysis builds on Katz and Shapiro's classic1985`model of sponsorship'in industries with network externalities.Each backbone has an installed base and otherwise competes for unattached customers. The bene¢t derived by a customer from joining a backbone is an increasing function of the size of his or her backbone and,in a complementary fashion,of the size of the other backbones and of the quality of inter-connection with the other backbones.This quality of interconnection is a1See,e.g.,MacKie-Mason and Varian[1995a,1995b];Gupta,Stahl and Whinston[1994] and Shenker,Clark,Estrin and Herzog[1996].2The analysis of the antitrust bodies can be found in their decisions,Commission[1998] and Commission[1998].3MCI sold its Internet assets(connecting1,300ISPs,60,000business customers and 250,000consumers)to Cable&Wireless.It also agreed to transfer1,000employees to Cable &Wireless and agreed not to woo back any customer for a period of two years.In March 1999,Cable&Wireless sued MCI WorldCom,alleging violations of the agreement.The suit was settled in early2000.ßBlackwell Publishers Ltd.2000.connectivity in the commercial internet435 strategic variable,and because`it takes two to tango',the quality ofinterconnection is governed by the preferences of the backbone which values interconnection the least.The results obtained throughout the paper all rest on the comparison between two impacts,on the backbone contemplating degradation,of a change in the quality of interconnection with another backbone.First, when connectivity between the two networks is degraded,both backbones face a demand reduction,as their customers'access to each others deteriorates.Second,a degradation of connectivity creates a quality di¡erentiation between the two networks.The larger backbone,which relies relatively less on access to the other backbone's customers,gains a competitive advantage,and competition between the two backbones is softened.However,when other backbones are present,a similar quality di¡erentiation e¡ect also handicaps both backbones relative to the other ones.Section IV analyzes the competition between two backbones of di¡erent sizes,and shows that the larger backbone has suboptimal incentives to maintain connectivity.Thanks to its larger installed base, the dominant backbone also acquires dominance in the market for un-attached customers when connectivity is not perfect.The poorer the interconnection and the stronger the network externality,the more dominant is this backbone,which,not surprisingly,is less eager to interconnect than its rival.Degradation is more likely,the larger the di¡erence in installed bases.Section V discusses modeling assumptions and the robustness of the conclusions.Section VI extends the analysis to di¡erent backbones con¢gurations. First,it shows that if there are four equal-sized backbones,none has an incentive to degrade interconnection.Intuitively,a backbone that degrades the quality of its interconnection with an equal-size backbone does not gain a competitive advantage over this backbone,and its quality relative to that of the other two backbones deteriorates.Second,we assume that two of these backbones merge and show that the new backbone,with its50%market share,still has no incentives to degrade simultaneously its two connections with the smaller backbones. However,we show that it can be optimal for the dominant backbone to degrade interconnection with one of the smaller backbones,that is to employ a`targeted degradation strategy'.Section VII extends the analysis to allow for the possibility that customers connect to several backbones(multihome)and analyzes whether multihoming impairs a dominance-enhancing degradation strategy.It¢rst looks at the impact of pre-existing multihoming by a fraction of the installed base.Keeping the di¡erence in sizes of installed bases constant,it shows that pre-existing multihoming is conducive to degradation by a dominant backbone.Intuitively,pre-existing multihoming lowers the pain ßBlackwell Publishers Ltd.2000.436jacques cre mer,patrick rey and jean tiroleof degradation(the reduction of demand),as well as,in the case of targeted degradation,the reduction in the competitive advantage enjoyed by the dominant backbone over the nontargeted backbone;and it does not a¡ect quality di¡erentiation between the targeting and targeted backbones. Interestingly,in the targeted degradation scenario,the dominant backbone prefers to target the small backbone with whom it has the most extensive customer overlap.Second,we allow new customers and singlehoming installed-base customers to attempt to circumvent the degradation policy by connecting to several backbones.We show that the conclusions are for the most part unchanged.Intuitively,customers choose to multihome only if the price charged by the second backbone to which they connect is smaller than the value that they attach to the new connections that it provides.But in equilibrium,the price charged by each network re£ects the value of the customer pool it uniquely gives access to.Second-homing to the dominant network brings high connectivity bene¢ts but is expensive;second-homing to a smaller network is cheaper but brings low connectivity bene¢ts.Thus, multihoming may not occur despite a degraded interconnection.Finally, we show that if multihoming occurs in reaction to a degraded interface, the smaller backbone's installed base is more likely to second-home to the dominant backbone than the dominant backbones's installed base to second-home to the smaller backbone.ii.structure of the internetII(i).End Users and Network ExternalitiesEnd users include residential and business users,who have access to the Internet either through dial up(over the phone line using modems)or through dedicated access;and web sites,which provide a wide variety of free or fee-based content as well as o¡erings of services(E-commerce,...).As its name indicates,the Internet is de¢ned by the fact that it enables connectivity.From its inception,it has been developed to enable com-munications between networks,and in its present state its most important feature is the ability for dial-up customers,Web sites hosts and dedicated access customers to exchange tra¤c across the entire system of inter-connected networks.This connectivity has been achieved¢rst through the widespread adoption of the TCP and IP protocols,which support transmission of packets,irrespective of the type of data that they carry:text,video,voice, etc.The standardization of protocols would have been of no consequence without the build-up of interfaces between networks,¢rst at the Network Access Points,and subsequently at private interconnects.The use of these interfaces has in turn been made possible by the development of a variety ßBlackwell Publishers Ltd.2000.connectivity in the commercial internet437 of contractual agreements between end-users and suppliers of Internetservices,and between these suppliers.It is important to note that the Internet's basic architecture was chosen and implemented by the US government,and especially the Department of Defense and the NSF,with much technical assistance from the academic community.The NSF stopped managing the Internet and funding the NSFNET on30April1995,although it continues funding research designed to improve its functioning.4The Internet has become the largest example of a deregulated communications network.However,it largely functions thanks to the institutions,standards and protocols that were chosen when the NSF was managing it,which in the long term will probably progressively lose their importance as technology evolves.The bene¢ts of connectivity arise because there are very strong network work externalities exist when the value for a customer of belonging to a network increases with the number of customers in this network.5In the case of the Internet,each customer pro¢ts in many direct and indirect ways from the presence of other customers.For instance, individuals derive direct bene¢ts from the fact that friends and acquain-tances are able to receive and send E-mail.A¢rm derives direct bene¢ts from the fact that a government agency builds a Web site where it can¢nd the texts of regulations that a¡ect its business.A new customer who connects to the Internet yields indirect bene¢ts to existing customers,by increasing the incentives of government agencies,non-pro¢t organizations and businesses to open new Internet sites.Consumers,whether individuals or organizations,can bene¢t fully from these network externalities only if connectivity is assured.II(ii).Providers of ConnectivityBetween end users can be found a host of intermediaries.Some inter-mediaries(for instance,search engines,portals,`infomediaries')provide users with guidance as to where to connect,what to buy and so forth.Other intermediaries provide transmission services:Internet Service Providers (ISPs)and Internet Backbone Providers(IBPs)Internet backbone providers(IBPs)transmit data over large regions of the world using long-haul¢ber-optic cables.They pick up the tra¤c4The NSF funded the construction by MCI of the very high speed backbone Network Service(vBNS),which operates at OC-12(622Mbps)and interconnects through ATM switches a number of NSF-sponsored research institutions.More recently,it has provided impetus for Internet II(Abilene)for academia,and the NGI for government(for more on the Internet activities of the NSF since privatization,see Marcus[1999,chapter14]).5See,e.g.,Rohlfs[1974],Katz and Shapiro[1985],Farrell and Saloner[1985],Tirole [1988,chapter10]and the Journal of Industrial Economics Symposium on Compatibility [1992].ßBlackwell Publishers Ltd.2000.438jacques cre mer,patrick rey and jean tirole generated by ISPs as well as that of their own customers and carry it overlong distances,connecting to each other and exchanging data at multiple points under the so-called`peering agreements'(see below).The IBPs also have the most sophisticated routing tables6of all Internet players.As we already observed,the Internet is a network of interconnected networks.Indeed,one of the main appeals of the Internet is its current almost ubiquitous connectivity:From almost any point(URL address)in the network can be sent messages to almost any other point.One may wonder how a network of7,000ISPs(4,500in the US)and5to50IBPs (depending on the exact de¢nition of IBPs7)can o¡er such ubiquitous connectivity.The answer to this question stems from the fact that the Internet has a basically hierarchical structure.8As illustrated by Figure1,IBPs sit on top of the hierarchy,customers lie at the bottom,and ISPs(to which can be added regional networks)stand in between.This may seem surprising since the Internet has been built to allow for very£exible organization and routing where the path of packets is optimized in real time depending on the loci of congestion in the network.However,a hierarchical structure o¡ers several bene¢ts.It facilitates routing by reducing the complexity of routing tables and by limiting the opportunities of gaming the system.A hierarchical structure also facilitates interconnection agreements by limiting the number of interconnection facilities,by clarifying responsi-bilities for immediacy,and by making it more transparent what installed base one is getting access to through a bilateral contract.Furthermore, and as we discuss in Section III,the hierarchical structure can accom-modate certain types of non-hierarchical relationships while preserving its basic nature.IBPs`peer'with each other.In so doing,they accept to route all tra¤c that is destined to their own customers,the customers of their customers, and so on.9Peering used to occur at public peering points,NAPs (Network Access Points)or MAEs(Metropolitan Access Exchanges), where networks could exchange tra¤c.The slow expansion of the capacity at these points while Internet tra¤c grows at a tremendous rate has led6At each node of the Internet,the routing table stores the instructions that the`router'uses to forward incoming messages to another node.7The¢ve big IBPs are Cable&Wireless(who owns the Internet assets that belonged to MCI),Sprint,MCI WorldCom,GTE and AT&T.8This implies that tra¤c goes up and down the hierarchy.For instance,if on Figure1a client of ISP A wants to send an E-mail message to another client of ISP A,the message will be directly retransmitted by A,and will never go on the Internet at large.On the other hand, a message to a client of ISP B must go through the backbone.9Notice that peering arrangements are di¡erent from transit agreements where a party accepts to carry tra¤c for another one to a third party.Peering commits each provider to accept data destined to its customers,to the customers of its customers and so on,while transit commits the provider to also carry data destined for third parties.ßBlackwell Publishers Ltd.2000.IBPs to turn to private peering,that is to exchanging tra¤c pairwise at a number of bilateral interfaces.IBPs impose a number of conditions to accept each other as peers:number and location of points of interface,10 national high-speed network,24-hour-per-day network operation center, etc.Currently,peering arrangements are of the bill-and-keep type;that is, each peer terminates without charge the tra¤c originating with other peers.This feature is probably a leftover of the transition process,and one may wonder whether IBPs will keep running their two-way interconnec-tion arrangements through bill-and-keep.IBPs do not make money directly from their peering relationships.To recover their huge investments in infrastructure,they charge their customers, who in turn charge their own customers.Charges are related to the capacity of the link between the network and its customer,but can also depend on usage.Thus,the Internet can be seen as a pyramid,in which monies are collected at the bottom and passed through to the top of the hierarchy.To be certain,the organization of the Internet is not purely hierarchical. For example,it may make sense for two ISPs,such as ISPs A and B in Figure 1,who are in the same city,to exchange tra¤c directly(engage in`secondary440jacques cre mer,patrick rey and jean tirolepeering')rather than let their mutual tra¤c move up and then down the hierarchy.Such sideway interconnections,however,do not contradict the fact that the Internet has a fundamentally hierarchical nature.II(iii).Threats to ConnectivityConnectivity requires cooperation among¢rms that are otherwise com-petitors.They must reach bilateral agreements on the locations and capacities of interfaces,and on the¢nancial terms through which they exchange tra¤c.All the major¢rms that provide Internet services must reach multilateral agreements on the protocols and standards that enable the exchange of tra¤c.Two trends will jeopardize this cooperation in the near future.First,as the operation of the Internet has been turned over to the private sector,and as a growing part of Internet service is provided by pro¢t maximizing¢rms,con£icts of interest will become more pro-nounced;one cannot rely on the generalized goodwill that characterized the`Internet community'in the1980s and early1990s to ensure the future of the Internet.One of the goals of this paper is to analyze the incentives large Internet players have to interconnect.Second,`interconnection'involves di¡erent levels of quality.An obvious dimension of quality is delay.Ignoring delays occurring at the end user's location(e.g.,web site),delays in the network occur both in the basic transport function(through the speed of transmission)and at switches (routers).These delays are managed at di¡erent levels on the Internet.In particular,if congestion builds up,for instance because capacity is not su¤cient at the interface between two backbones,the TCP protocol allows the routers to ask the senders of messages to slow down the rate at which data is sent.This limits the sizes of the queues that build up at the routers.11Notice that these delays can occur both inside networks or at their interface.Current interconnection agreements are based on a`best e¡ort'model;parties make a vague promise that they will do their best to limit delays on their own part of the exchanged tra¤c.While current delays are perfectly acceptable for services such as E-mail or Internet fax that do not require`immediacy',a number of new services require bounded delay.The development of real-time services such as Internet telephony,12 interactive teaching or video-conferencing(a surgeon in a teaching11The tra¤c is sometimes very variable in the short run(it is said to be bursty);then it can increase rapidly enough that routers run out of bu¡er space to store queued packets before senders slow down.Then,some packets are discarded.12Internet telephony,as its name indicates,refers to telephony over the Internet;unlike for a traditional phone call,for which a circuit is opened and dedicated to a single conver-sation for the whole length of the call,messages,like for other Internet services,are de-composed into tiny data packets,that may or may not take the same route,and are reassembled at termination.ßBlackwell Publishers Ltd.2000.hospital giving real-time advice on an operation in a rural hospital)requires very low and very uniform delays between sender and receiver;new protocols will be needed to allow the development of these applications,and networks will need to cooperate in order to o¡er premium services at reasonable prices.The development of premium services thus calls for new protocols sitting on top of the existing protocols,that will enable prioritizing messages,verifying delays,billing,etc.,as well as for the design of innovative two-way access arrangements thatinduce players to o¡er these premium services.In contrast,`premium services connectivity'will be lost if some large Internet operators develop proprietary standards and o¡er such services on a limited basis (between their customers),hoping that the proprietary o¡ering will create a competitive advantage.Cooperation on bounded-delay services is only one of many of the challenging industrial organization issues in the Internet.Consider the development of multicast real-time services.A football game or a concert in a country may be simultaneously transmitted over the Internet to millions of viewers all over the world.In the current system,when a sender sends a packet to multiple receivers,the packet is replicated at the source and one copy is sent to each receiver.This obviously puts unnecessary strain on the Internet;for example a single copy could be forwarded to a router near a city and be replicated only at this router for the Internauts in that city who have signaled they wanted to join the group of viewers.The standardization of multicast routing requires cooperation among the players.13Connectivity can in general be achieved in three ways:regulation,private negotiation among networks,and alternative methods,such as the customer's a¤liation to multiple networks.These methods of achieving connectivity place the burden on di¡erent parties:the government in the case of regulation,the suppliers of service in the case of private negoti-ations,and the customers in the other cases.Regulation of access has been the traditional way of guaranteeing interconnection for voice telephony,and this policy has been rea¤rmed in the United States,by the Telecommunications Act of February 1996and by the FCC,in the European Union,and indeed almost everywhere 14in the world.There is,however,a pronounced global trend toward reducing regulation and introducing enhanced competition in the telecommunica-tions industry,and the 1996US Telecommunications Act rea¤rmed US 13For more details on multicast services,see Shenker et al.[1996].14One notable exception is New Zealand,which experimented with unregulated negoti-ations for interconnection between a dominant operator and smaller operators;this solution has not operated smoothly,however,even though it was scrutinized under articles 36and 27of the competition law and even though the threat of re-regulation may also have put some pressure on the dominant operator.connectivity in the commercial internet 441ßBlackwell Publishers Ltd.2000.442jacques cre mer,patrick rey and jean tirolepolicy that the Internet remain`unfettered by Federal or State regulation'. It is therefore the competition authorities who must ensure,for example, that the bene¢ts of connectivity not be jettisoned with the emergence of a dominant player who would take advantage of the network externalities to `balkanize'the Internet and enhance its dominance.II(iv).Customer LoyaltyBecause the commercial Internet is recent and still in£ux,we have limited knowledge of consumer behavior.Obviously,customers are highly hetero-genous.Dial-up users,web sites,dedicated access customers and ISPs(as customers of other ISPs or IBPs)have di¡erent assessments of the price-quality trade-o¡,and furthermore,each category of customers exhibits high heterogeneity.Some customers,such as banks,value quality highly and are not very price sensitive,since a loss of connectivity has dire consequences for them.On the other hand,Fortune500corporate head-quarters may not care so much about small delays experienced by visitors of their web sites who consult their annual report.Some customers(such as universities)may be very price sensitive.There is also a wide heterogeneity in switching costs.Like in any other industry,switching costs may be psychological(including a limited ability to rethink and alter at each point of time all contractual relationships one is engaged in),technical or contractual.One determinant of the ease with which a customer can switch suppliers is the portability of IP addresses.For example,most ISPs obtain their address space from their connectivity supplier as part of their service contract,while the largest ones usually have their own address spaces.This hierarchical structure makes much sense from a routing perspective,but it creates substantial switching costs for those who do not have their own address space;similarly,a dedicated access customer may need to recon-¢gure its computers and renumber workstations following a switch.Based on high observed churning rates,physical switching costs for dial-up customers(who lose their E-mail addresses when they change ISPs)seem less substantial,although a proper econometric study should be conducted toassess the impact of poaching o¡ers and customer dissatisfaction on churn.contracts with their supplier of connectivity(often a year to a couple of years for web-hosting and dedicated-access customers;similarly,AOL is under a¢ve-year long-term contract with WorldCom).There are several possible rationales for such long-term contracts:recovery of costs incurred by the supplier(connection,collocation,set-up service costs);of the supplier's network capacity and of the capacity and location of inter-ßBlackwell Publishers Ltd.2000.。

Adaptation and Survival in Natural Selection Adaptation and survival in natural selection is a fascinating and complex process that has been shaping the diversity of life on Earth for millions of years. From the smallest microorganisms to the largest mammals, every living organism has evolved through the mechanism of natural selection to better suit its environment and increase its chances of survival. This process has led to the incredible diversity of life that we see today, with each species uniquely adapted to its specific niche in the ecosystem.One of the key aspects of adaptation and survival in natural selection is the concept of genetic variation. Genetic variation refers to the diversity of genes within a population, which is essential for natural selection to occur. Without genetic variation, there would be no raw material for evolution to work with, and species would not be able to adapt to changing environmental conditions. Genetic variation can arise through a variety of mechanisms, including mutations, genetic recombination, and gene flow between different populations. These mechanisms create the diversity of traits within a population, some of which may confer a survival advantage in certain environments.Another important aspect of adaptation and survival in natural selection is the role of environmental pressures. The environment plays a crucial role in shaping the traits of a species, as individuals with traits that are better suited to their environment are more likely to survive and reproduce. For example, in a harsh desert environment, individuals with traits that allow them to conserve water and tolerate high temperatures are more likely to survive and pass on their genes to the next generation. Over time, this can lead to the evolution of specific adaptations that are well suited to the unique challenges of the desert environment.In addition to genetic variation and environmental pressures, the concept of fitness is central to understanding adaptation and survival in natural selection. Fitness refers to the ability of an individual to survive and reproduce in its environment, and is ultimately what drives the process of natural selection. Individuals with traits that increase their fitness are more likely to pass on their genes to the next generation, leading to the spread of thoseadvantageous traits within the population. As a result, the population as a whole becomes better adapted to its environment, increasing its chances of survival.It is important to note that adaptation and survival in natural selection is not a perfect or predetermined process. Evolution does not have a specific goal or endpoint, and the traits that increase an individual's fitness in one environment may be detrimental in another. Additionally, environmental conditions are constantly changing, which means that what is advantageous today may not be advantageous tomorrow. As a result, natural selection is an ongoing and dynamic process, with species constantly adapting to new challenges and opportunities in their environment.From a human perspective, the concept of adaptation and survival in natural selection can be both awe-inspiring and humbling. The incredible diversity of life on Earth, and the myriad ways in which species have adapted to their environments, is a testament to the power of natural selection. It is a reminder of the interconnectedness of all living things, and the delicate balance that exists within ecosystems. At the same time, it serves as a stark reminder of the fragility of life, and the constant struggle for survival that is inherent to all living organisms.In conclusion, adaptation and survival in natural selection is a fundamental process that has shaped the diversity of life on Earth. Through genetic variation, environmental pressures, and the concept of fitness, species have evolved and adapted to their environments over millions of years. From a human perspective, this process is both inspiring and humbling, serving as a reminder of the interconnectedness and fragility of life. As our understanding of natural selection continues to grow, so too does our appreciation for the incredible diversity and resilience of the natural world.。

IMPORT DEMAND ELASTICITIES AND TRADE DISTORTIONS Hiau Looi Kee,Alessandro Nicita,and Marcelo Olarreaga*Abstract—This paper provides a systematic estimation of import demand elasticities for a broad group of countries at a very disaggregated level of product detail.We use a semiflexible translog GDP function approach to formally derive import demands and their elasticities,which are estimated with data on prices and endowments.Within a theoretically consistent framework,we use the estimated elasticities to construct Feenstra’s(1995) simplification of Anderson and Neary’s trade restrictiveness index(TRI). The difference between TRIs and import-weighted tariffs is shown to depend on the tariff variance and the covariance between tariffs and import demand elasticities.I.IntroductionI MPORT demand elasticities are crucial inputs into many ex ante analyses of trade reform.To evaluate the impact of regional trade agreements on tradeflows or customs revenue,one needs tofirst answer the question of how trade volumes would adjust.To estimate ad valorem equivalents of quotas or other nontariff barriers one often needs to transform quantity impacts into their price equivalent,for which import elasticities are necessary.Moreover,trade policy is often determined at much higher levels of disag-gregation than existing import demand elasticities.1This mismatch can lead to serious aggregation biases when calculating the impact of trade policy interventions that have become surgical procedures.Finally,to evaluate trade restrictiveness and welfare loss across different countries and years,one would need to have a consistent set of trade elasticities,estimated using the same data and methodology. These do not exist.The closest substitute,and the one often used by trade economists,is the survey of the empirical literature put together by Stern,Francis,and Schmacher (1976).More recent attempts to provide disaggregate esti-mates of import elasticities have been country specific and have mainly focused on the United States.2The objective of this paper is threefold.First,tofill in the gap in the literature by providing a systematic estimation of import demand elasticities for a broad range of countries at a fairly disaggregated level of product detail.Second,using the estimated elasticities and within a theoretically consis-tent framework,we construct measures of trade restrictive-ness based on Feenstra’s(1995)simplification of Anderson and Neary’s trade restrictiveness index(TRI).3The TRI is the uniform tariff that would maintain welfare at its current level given the existing tariff structure.Finally,using TRIs the paper analyzes the size and composition of tariff-induced trade distortions.The basic theoretical setup for the estimation of import demand elasticities is the production-based GDP function approach as in Kohli(1991)and Harrigan(1997).This GDP function approach is consistent with neoclassical trade the-ories,and it takes into account general equilibrium effects associated with the reallocation of resources due to exoge-nous changes in prices and endowments.As in Sanyal and Jones(1982),imports are considered inputs into domestic production,for given exogenous world prices,productivity, and endowments.In a world where a significant share of growth in world trade is explained by vertical specialization (Yi,2003),the fact that imports are treated as inputs into the GDP function—rather than asfinal consumption goods as in most of the previous literature—seems an attractive feature of this approach.More importantly,even if an imported good is ready forfinal consumption,before being sold in the domestic market it will incorporate some domestic value added associated with domestic transport and logistics, marketing,and retailing(see Sanyal&Jones,1982).This implies that all imported goods should be treated as inputs into the GDP function.The estimated import demand elasticities are defined as the percentage change in the quantity of an imported good when the price of this good increases by1%,holding prices of all other goods,productivity,and endowments of the economy constant.This is in contrast to the more commonly used price elasticities of demand,which are derived from utility maximization or expenditure minimization holding GDP or national income constant.As argued by KohliReceived for publication February22,2005.Revision accepted for publication July19,2007.*The authors are affiliated with the Development Research Group of the World Bank.Nicita is also affiliated with UNCTAD in Geneva.Olarreaga is also affiliated with the University of Geneva,and CEPR in London. We are grateful to James Anderson,Erwin Diewert,Robert Feenstra, James Harrigan,Kala Krishna,Peter Neary,David Weinstein,and two anonymous referees for very helpful suggestions.We also thank Paul Brenton,Hadi Esfahani,Joe Francois,Kishore Gawande,Catherine Mann, William Martin,Christine McDaniel,Guido Porto,Dave Richardson, Claudio Sfreddo,Clinton Shiells,Dominique Van Der Mensbrugghe,Alan Winters,and seminar participants at the ITI program of the NBER Summer Institute2005,the Center of Global Development,the Econo-metric Society Meetings2004at Brown University,the Empirical TradeAnalysis Conference at the Woodrow Wilson International Center,PREM week,and the World Bank for their comments.The views expressed here are those of the authors and do not necessarily reflect those of the institutions to which they are affiliated.1Trade policy is(almost by definition)often determined at the tariff line level.To our knowledge the only set of estimates of import demand elasticities at the six-digit level of the Harmonized System that exist in the literature are the ones provided by Panagariya,Shah,and Mishra(2001), for the import demand elasticity faced by Bangladesh exporters of apparel, and the elasticities of substitution across exporters to the United States by Broda and Weinstein(2006).2These include Shiells,Stern,and Deardorff(1986),Shiells,Roland-Holst,and Reinert(1993),Marquez(1999),Broda and Weinstein(2006), and Gallaway,McDaniel,and Rivera(2003).Note that some of these studies focus on elasticities of substitution or income elasticities rather than price elasticities.As shown in Blackorby and Russell(1989),the elasticity of substitution equals the cross price elasticity minus the own price elasticity.Thus,only when the cross price elasticity is0,as in the case of a Cobb-Douglas utility function,the elasticity of substitution is equal to the price elasticity,which in this case is equal to1.3See Anderson and Neary(1994,1996,2007).The Review of Economics and Statistics,November2008,90(4):666–682©2008by the President and Fellows of Harvard College and the Massachusetts Institute of Technology(1991)it seems that the former approach is more consistent with neoclassical international trade theories,where income is generally considered endogenous,and endowments and productivity are most of the time exogenous.While Kohli(1991)focuses mainly on aggregate import demand and export supply functions and Harrigan(1997)on industry-level export supply functions,this paper modifies the GDP function approach to estimate import demand elasticities at the six-digit level of the Harmonized System (HS).When estimating elasticities of the4,900goods at tariff line level,dealing with cross price effects can become insurmountable.In order to avoid running out of degrees of freedom in the estimation of the structural parameters of the GDP function,we reparameterize the fullyflexible translog function to be semiflexible,orflexible of degree one,as in Diewert and Wales(1988).This reparameterization signifi-cantly reduces the number of price-related translog param-eters from N(NϪ1)/2ϩN(around ten million in our case),to only N(around4,900),and yet isflexible enough to approximate up to the second order any twice continu-ously differentiable function at any point.A similar simpli-fication is used in Neary(2004)for the estimation of the AIDS and QUAIDS systems.Another practical problem we are facing is that the HS classification was only introduced in the late1980s,so even if we solve the n-good problem,we may still run out of degrees of freedom if we were to estimate the different parameters using only the time variation in the data.Thus, assuming that the structural parameters of the GDP function are common across countries(up to a constant)as in Harrigan(1997),we take advantage of the panel dimension of the data set by applying within estimators.Finally,we address econometric issues associated with the potential endogeneity and measurement errors of unit values,selection bias due to zero imports,the sluggish adjustment of imports to changes in prices,and other ex-planatory variables.More than377,000import demand elasticities have been estimated across117countries for4,900HS six-digit prod-ucts.The simple average elasticity across all countries and goods is aboutϪ3.12.The overallfit of the import demand elasticities is good.The median of bootstrap t-statistics is 3.3,and more than70%of the estimates are statistically significant.Using the estimated import demand elasticities,we con-struct TRIs for88countries for which tariff schedules are available.We show that the difference between TRI and import-weighted tariff depends on the variance of tariffs and the covariance between tariffs and import demand elastici-ties.Results suggest that the contribution of the variance of tariffs and their covariance with import demand elasticities to the overall trade restrictiveness of the countries in our sample is high,as import-weighted average tariffs underes-timate the restrictiveness of a country’s tariff regime by 64%on average.In some countries,such as the United States,TRI is more than three times higher than the import-weighted average tariff.This indicates the presence of disproportionately large tariff variance and covariance with import demand elasticities.Finally,we study the roles of tariffs’variance and covari-ance with import demand elasticities in determining the size and composition of the deadweight loss associated with the existing tariff schedules of the88countries.The results show that omitting the variance of tariffs and their covari-ance with import elasticities leads to the underestimation of the size of the total deadweight loss by55%.In other words, the overall deadweight loss due to tariffs is two times higher than average tariffs would imply.Countries that have the largest share of deadweight loss due to tariff variance are Japan,the Philippines,and Egypt.Countries where the covariance between tariffs and import elasticities plays a large role in causing deadweight loss are Sudan,Canada, and the United States.In particular,64%of the Canadian deadweight loss of$912million per annum can be attrib-uted to higher tariffs on more elastic imports such as wheat. Given that a high import demand elasticity could be due to close substitution with domestic goods,this result highlights that those industries that lobby for tariff protection are those that face severe import competition—a result that can in-form lobbying models.The rest of the paper is organized as follows.Section II provides the theoretical framework to estimate import de-mand elasticities,whereas section III describes the empiri-cal strategy.Section IV discusses data sources.Section V presents the results of the estimation of import demand elasticities.Section VI applies the estimated import demand elasticities to construct TRIs,as well as deadweight losses associated with existing tariff structures and their determi-nants.Section VII concludes.II.Theoretical Model—GDP Function Approach The theoretical model follows Kohli’s(1991)GDP func-tion approach for the estimation of trade elasticities.We also draw on Harrigan’s(1997)treatment of productivity terms in GDP functions.We willfirst derive the GDP and import demand functions for one country.However,assuming that the GDP function is common across all countries up to a country-specific term—which controls for country produc-tivity differences—it is then easily generalized to a multi-country setting in the next section.Consider a small open economy in period t.4Let S tʚR NϩM be the strictly convex production set in t of its net output vector q tϭ(q1t,q2t,...,q N t)and factor endowment vector v tϭ(v1t,v2t,...,v M t)Ն0.For the elements in the net output vector q t,we adopt the convention that positive4For a discussion of the relevance of the small country assumption when estimating trade elasticities,see Riedel(1988)and Panagariya et al. (2001).IMPORT DEMAND ELASTICITIES AND TRADE DISTORTIONS667numbers denote outputs,which include exports,and nega-tive numbers denote inputs,which include imported goods. We consider imported goods and competing domestically produced goods as differentiated products.Similarly,do-mestic products sold in the domestic market are differenti-ated from products sold in foreign markets(that is,ex-ported).Given the exogenous world price vector p˜tϭ(p˜1t, p˜2t,...,p˜N t)Ͼ0,the country-specific endowments,v t,and N-dimensional diagonal Hicks-neutral productivity matrix A tϭdiag{A1t,A2t,...,A N t},perfect competition leads firms to choose a mix of goods that maximizes GDP in each period t:G t͑p˜t,A t,v t͒ϵmaxq t͕p˜t⅐A t q t:͑q t,v t͒ʦS t͖f(1)G t͑p˜t A t,v t͒ϵmaxq t͕p˜t A t⅐q t:͑q t,v t͒ʦS t͖,(2)where G t(p˜t A t,v t),is the maximum value of goods the economy can produce given prices,Hicks-neutral produc-tivity,and factor endowments in period t.It is equal to the total value of output for exports andfinal domestic con-sumption minus the total value of imports(q n tϽ0for imports).In other words,the optimal net output vector is chosen to maximize GDP,for given prices,productivity,and endowments.We shall refer to the optimal net output vector as the GDP-maximizing net output vector,which includes GDP-maximizing import demands.As shown in Harrigan(1997),equation(2)highlights that price and productivity enter multiplicatively in the GDP function,G t(p˜t A t,v t).This property allows us to reexpress the GDP function,by defining the productivity inclusive price vector,p tϭ(p1t,p2t,...,p N t)Ͼ0:G t͑p t,v t͒ϭmaxq t͕p t⅐q t:͑q t,v t͒ʦS t͖,with(3) p tϵp˜t A t,and p n tϵp˜n t A n t,@n.(4)Notice that the productivity inclusive price vector,p t,is no longer common across countries even though the world price vector,p˜t,is identical across countries.This allows the model to betterfit the data where different world prices are observed for the same good in different countries.In a recent study,Schott(2004)successfully explains variation in unit values within tariff lines with GDP per capita—the higher is GDP per capita,the higher the unit value.To the extent that GDP per capita is a proxy for labor productivity, Schott’sfinding provides support for our productivity inclu-sive price level,p t.For G t(p t,v t)to be a well-defined GDP function,it is assumed to be homogeneous of degree one with respect to prices.Moreover,strict convexity of S t also ensures that the second-order sufficient conditions are satisfied,such that G t(p t,v t)is twice differentiable and it is convex in p t and concave in v t.To derive the import demand function,we apply the Envelope Theorem,which shows that the gradient of G t(p t,v t)with respect to p t is the GDP-maximizing net output vector,q t(p t,v t):5ץG t͑p t,v t͒ץp n tϭq n t͑p t,v t͒,@nϭ1,...,N.(5) Thus if good n is an imported good,equation(5)is the GDP-maximizing import demand function of good n,which is a function of prices and endowments.It also implies that an increase in import prices would reduce GDP(that is,q n tϽ0if n is an imported good).Given that G t(p t,v t)is continuous and twice differentiable,and is convex and homogeneous of degree one with respect to prices,the Euler Theorem implies that q n t is homogeneous of degree zero in prices,has nonnegative own price effects,and has symmet-ric cross price effects:6ץ2G t͑p t,v t͒ץp n tץp k tϭΆץq n t͑p t,v t͒ץp n tՆ0,@nϭkץq n t͑p t,v t͒ץp k tϭץq k t͑p t,v t͒ץp n t,@n k.(6)In other words,for everyfinal good,including exports,a price increase raises output supply;for every input,includ-ing imports,an increase in prices decreases input demand. In addition,if an increase in the price of an imported input causes supply of an exported output to decrease,then an increase in the price of the exported output would increase the demand of the imported input in the same magnitude. Equation(5)shows that the GDP-maximizing import demand function of good n is a function of prices and factor endowments.Thus,the implied own price effects of im-ports,and the import demand elasticities,are therefore conditioned on prices of other goods and aggregate endow-ments beingfixed.In other words,the GDP-maximizing import demand functions do not depend on income or utility,unlike the expenditure-minimizing Hicksian import demand functions or the utility-maximizing Marshallian import demand functions.This is because aggregate factor income and welfare are in fact endogenous to prices and endowments.Such a setup is more relevant for general equilibrium trade models,but may not be relevant for partial equilibrium micro models which often take aggregate in-come as exogenous.As a result,comparing the GDP-maximizing import demand elasticities with the existing5To ensure that the GDP function is differentiable and the gradient of G t(p t,v t)with respect to p t is the net output vector,we assume that there are at least as many factors as goods,MՆN.If there are more goods than factors,then the output vector is not unique,and the gradients need to be reinterpreted as a set of subgradient vectors(see Harrigan,1997).In the empirical section,we have three aggregate factors,which are assumed to be composite factors consistently aggregated from as many disaggregate factors as necessary to satisfy the assumption that there exist more factors than goods.See Kohli(1991)for details.6The latter by Young’s Theorem.THE REVIEW OF ECONOMICS AND STATISTICS 668Hicksian or Marshallian import demand elasticities in the literature may not be appropriate.Note that we will not be able to derive income elasticities from the GDP-maximizing import demand functions,but instead,we would be able to estimate the Rybczynski elasticities from equation (5),which shows how import demand reacts to changes in factor endowments.7To implement the above GDP function empirically,we first assume that G t (p t ,v t )follows a flexible translog functional form with respect to good prices and factor endowments,with n and k index goods,and m and l index factors:ln G t͑p t,v t͒ϭa 00t ϩ͸n ϭ1Na0n t ln p nt ϩ12͸n ϭ1N ͸k ϭ1N a nk tln p n t ln p k t ϩ͸m ϭ1Mb 0m t ln v mt(7)ϩ12͸m ϭ1M ͸l ϭ1M b ml tln v m t ln v l t ϩ͸n ϭ1N ͸m ϭ1Mc nm t ln p n t ln v m t,where all the translog parameters a ,b ,and c are indexed by t to allow for changes over time.As shown in Kohli (1991)and Harrigan (1997),such a fully flexible translog function can approximate any functional form up to second order without loss of generality.In addition,there are some nice features of the above specification that are absent in the more commonly used CES specification.First,we do not need to assume that the elasticity of substitution between goods is constant.Second,the elasticity of substitution of good i with respect to good j does not need to be equal to the elasticity of substitution of good j with respect to good i .Third,the underlying production function does not need to be weakly separable (Blackorby &Russell,1981).8To make sure that equation (7)satisfies the homogeneity and symmetry properties of a GDP function,we impose the following restrictions:͸n ϭ1Na0n tϭ1,͸k ϭ1Nank t ϭ͸n ϭ1Ncnmt tt ϭ0,a nkt ϭa knt ,@n ,k ϭ1,...,N ,(8)@m ϭ1,...,M .Furthermore,if we assume that the GDP function is homo-geneous of degree one in factor endowments,then we also need to impose the following restrictions:͸n ϭ1Nb0n t ϭ1,͸k ϭ1Nbnk t ϭ͸m ϭ1Mcnm t ϭ0,b nkt ϭb kn t ,@n ,k ϭ1,...,N ,(9)@m ϭ1,...,M .Given the translog functional form and the symmetry andhomogeneity restrictions,the derivative of ln G t (p t ,v t )with respect to ln p n t gives the equilibrium share of good n in GDP at period t :s nt͑p t ,v t ͒ϵp n t q n t ͑p t ,v t ͒G t ͑p t ,v t ͒ϭa 0n t ϩ͸k ϭ1Nank t ln p k t ϩ͸m ϭ1Mcnm t ln v mt ϭa 0n t ϩa nn t ln p n tϩ͸k nanktln p kt ϩ͸m ϭ1Mcnm t ln v m t ,@n ϭ1,...,N ,(10)where s n t is the share of good n in GDP (s n t Ͻ0if good nis an input,as in the case of imports).From equation (10)it can be shown that,if good n is an imported good,then the import demand elasticity of good n derived from its GDP-maximizing demand function is 9εnn tϵץq n t ͑p t ,v t ͒ץp n t p n t q n t ϭa nn t s nt ϩs n t Ϫ1Յ0,(11)@s n tϽ0.Thus we can infer the import demand elasticities once a nn is properly estimated based on equation (10).Note that the size of the import elasticity,εnn t ,depends on the sign of a nn t ,which captures the changes in the share of good n in GDP when the price of good n increases by 1%:εnnt ͭϽϪ1if a nn tϾ0,ϭϪ1if a nn tϭ0,ϾϪ1if a nntϽ0.The rationale is straightforward.If the share of imports inGDP does not vary with import prices (a nn t ϭ0),then the implied import demand is unitary elastic such that an7See section 5.3of Kohli (1991)for a thorough discussion on the various import demand specifications.8The only CES function that is compatible with a translog GDP function is a Cobb-Douglas function that has constant shares.The fact that we can estimate the share equations signals that good shares are not constant and do depend on relative prices and endowments that contradict the Cobb-Douglas production function.9Crosspriceelasticitiesof import demand are given byεnk t ϵץq nt ͑p t,v t͒ץpkt p kt qntϭankt s nt ϩs kt,@n k .IMPORT DEMAND ELASTICITIES AND TRADE DISTORTIONS 669increase in import price induces an equi-proportional de-crease in import quantities and leaves the value of importsunchanged.If the share of imports in GDP,which is nega-tive by construction,decreases with import price(a nn tϽ0), then the implied import demand is inelastic,so that anincrease in import price induces a less than proportionatedecrease in import quantities.Finally,if the share of importin GDP increases with import prices(a nn tϾ0),then the implied import demand must be elastic such that an increase in import price induces a more than proportionate decrease in import quantity.10III.Empirical StrategyWith data on output shares,unit values,and factor en-dowments,equation(10)is the basis for the estimation of import elasticities.In principle,we couldfirst estimate the own price effects,a nn t,for every good according to equation (10),and apply equation(11)to derive the implied esti-mated elasticities,since the own price elasticity is a linear function of own price effects.There are,however,at least three problems with the estimation of the elasticities using equation(10).First,there are more than4,900HS six-digit goods traded among countries in any given year.Moreover, there is also a large number of nontraded commodities that compete for scarce factor endowments and contribute to GDP in each country.Thus the number of explanatory variables in equation(10)could easily exhaust our degrees of freedom or introduce serious collinearity problems.Sec-ond,even after solving thisfirst problem,we could also run out of degrees of freedom given the short timespan of trade data available at the six-digit HS classification,which was introduced in the late1980s.Third,there are several econo-metric issues that may bias our results if they are not addressed.These include the endogeneity and measurement error of unit values,selection bias,and the sluggish adjust-ment of imports to changes in prices or any of the other explanatory variables.We tackle all these problems in turn.A.Estimating the N-Good Share EquationsEstimating the own price and cross price effects,a nk t,for each of the4,900HS six-digit goods is equivalent to estimating the upper triangle of the N by N second-order substitution matrix.Thus in total there would be N(NϪ1)/2ϩN parameters to be estimated,which works out to represent more than ten million parameters for each time period t!This is obviously not feasible,even if we restrict all the translog parameters to be time invariant,and the normal system of share equation techniques used in Kohli (1991)or Harrigan(1997)would not have been sufficient. We need a way to legitimately reduce the number of parameters to be estimated and focus on only those that are of interest:in our case,the own price import demand elasticities,and therefore the4,900diagonal elements of the substitution matrix.We adopt a semiflexible functional form developed in Diewert and Wales(1988)specifically designed to handle translog models with a large number of goods.Wefirst restrict all the translog parameters to be time invariant. Next,rather than allowing the substitution matrix of[a nk t]to have full rank,we restrict it to be of rank one by imposing the following constraints:a nk tϭ␥a n a k,@n k,(12) a nn tϭϪ␥a n͸k n a k,(13) where␥,a n,and a k are constants.Such reparameterization effectively reduces the fullyflexible translog function in equation(7)to beflexible of degree one.Diewert and Wales (1988)show that such a semiflexible functional form can still approximate a twice continuously differentiable func-tion at any point up to the second order,even though the matrix of second order partial derivatives with respect to prices is restricted to have rank one instead of the maximum possible rank of NϪ1.11They further show that the cost of estimating a semiflexible function,instead of a fullyflexible functional form,is that one misses part of the effect of a nn associated with the smallest eigenvalues,but in many situ-ations this cost is small.12It could be easily verified that for any good n,the above reparameterization satisfies the homogeneity constraint: a nnϩ¥k n a nkϭ0,as well as the symmetry constraint: a nkϭa kn.In other words,we approximate the full ranksecond-order substitution matrix by the product of a column vector,aϭ[a1,...,a N]Ј,and its transpose,and adjust the diagonal elements to satisfy all homogeneity constraints (13):͓a nk͔NϫNϭ␥a Nϫ1aЈ1ϫNϪdiagͫ␥a n a nϩ␥a n͸k n a kͬNϫN. The resulting share equation for each good n is10Kohli(1991)found an inelastic demand for the aggregate U.S.imports with a nnϽ0,while highly elastic demand for durables and service imports,with the corresponding a nnϾ0,when aggregate imports are broken down into three groups.11Neary(2004)uses this approach to estimate the AIDS or QUAIDS systems from an expenditure function.He starts with rank one,then uses the maximum likelihood estimates as the starting values for the estimation of a rank two matrix.With each iteration,one more column is added,and so is the rank of the matrix.Because of the number of goods involved,we stop at rank one,in view of the enormous complexity of going to higher ranks.12Diewert and Wales(1988)use Canadian data for ten consumer expenditure categories to illustrate that when the rank is small,semiflex-ible functional forms may lead to inelastic demand estimates.In our sample,as shown in the result section,the average estimated import elasticity isϪ2.46,and more than80%of the elasticity estimates are significant at the10%level.Thus the issue of inelastic demand may not be a severe problem in our sample.THE REVIEW OF ECONOMICS AND STATISTICS 670。

THE ACCOUNTING REVIEW American Accounting Association Vol.87,No.2DOI:10.2308/accr-10195 2012pp.589–616Selection Models in Accounting ResearchClive S.LennoxNanyang Technological UniversityJere R.FrancisUniversity of Missouri–ColumbiaZitian WangNanyang Technological UniversityABSTRACT:This study explains the challenges associated with the Heckman(1979)procedure to control for selection bias,assesses the quality of its application inaccounting research,and offers guidance for better implementation of selection models.A survey of75recent accounting articles in leading journals reveals that manyresearchers implement the technique in a mechanical way with relatively littleappreciation of important econometric issues and problems surrounding its ingempirical examples motivated by prior research,we illustrate that selection models arefragile and can yield quite literally any possible outcome in response to fairly minorchanges in model specification.We conclude with guidance on how researchers canbetter implement selection models that will provide more convincing evidence onpotential selection bias,including the need to justify model specifications and carefulsensitivity analyses with respect to robustness and multicollinearity.Keywords:selection model;Heckman;selection bias;endogeneity;treatment effect model.Data Availability:Data used are available from public sources identified in the study.I.INTRODUCTIONT his study evaluates the implementation of selection models in the accounting literature, provides guidance to accounting researchers on potential problems with selection models, and recommends some steps that can be taken to improve their implementation.Such guidance is especially important given the increased use of selection models and the frequent comments by editors and reviewers of the need to control for endogeneity and selection bias.OverWe thank Steven Kachelmeier(editor)and the two reviewers for their helpful comments throughout the review process. We also appreciate the comments of Mark Clatworthy,Bill Griffiths,Gilles Hilary,David Larcker,Christian Leuz,Siu Fai Leung,Ping-Sheng Koh,David Maber,Chul Park,Mike Peel,Jeff Pittman,and Terry Shevlin,and the research assistance of Rui Ge and Scott Seavey.Editor’s note:Accepted by Steven Kachelmeier.Submitted:April2010Accepted:July2011Published Online:November2011589the period 2000through 2009,we identify 75articles from The Accounting Review ,Journal of Accounting and Economics ,Journal of Accounting Research ,Contemporary Accounting Research ,and Review of Accounting Studies that use selection models out of 1,016empirical articles published in these journals over the same period.The recent trend is even stronger with 11percent of empirical articles employing a selection model during 2008to 2009.Selection occurs when observations are non-randomly sorted into discrete groups,resulting in the potential for coefficient bias in estimation procedures such as ordinary least squares (OLS)(Maddala 1991).The standard approach to controlling for selection bias is the procedure developed by Heckman (1979),hereafter referred to as the selection model.A convincing implementation requires the researcher to identify exogenous independent variables from the first stage choice model that can be validly excluded from the set of independent variables in the second stage regression (Little 1985).However,the importance of exclusion restrictions appears to have fallen under the radar of the accounting literature.A surprising number of studies (14of 75)fail to have any exclusions,and other studies (7out of 75)do not report the first stage model,making it impossible to determine if they imposed exclusion restrictions.Moreover,very few studies provide any theoretical or economic justification for their chosen restrictions.We demonstrate empirically that the selection model is fragile and that results can be non-robust and therefore unreliable when researchers choose exclusion restrictions in an ad hoc fashion or choose none at all.To improve the implementation of selection models in accounting research,we recommend careful reporting of sensitivity analyses and robustness tests,which,surprisingly,are uncommon in accounting studies that use selection models.The majority of the 75studies in our review do not report whether their inferences are sensitive to alternative exclusion restrictions,nor do they discuss the problems that can arise when using the selection model,such as high multicollinearity.Our central conclusion is that,as accounting researchers,we need to be more careful and rigorous in our implementation of selection models,particularly in the choice of exclusion restrictions.Further,because of the inherent limitations and fragility of selection models,we should also be much more circumspect with respect to claims about ‘‘controlling for selection bias.’’Last,it may not be feasible to implement a convincing selection model in some research settings and,in this case,our advice is that studies acknowledge this limitation and provide a caveat that the reported results could be affected by selection bias.The remainder of our article proceeds as follows.The next section discusses the selection model and implementation issues.Section III reviews how selection models have been used in the accounting literature and compares this with best practice.We also highlight the differences between our critique of selection models and those of Larcker and Rusticus (2010)and Tucker (2010),who survey the accounting literature’s implementation of regular instrumental variable (IV)estimation and Heckman models.Section IV provides three empirical examples based on past accounting studies and shows that inferences are extremely sensitive to fairly minor changes in the selection model’s specification.1Section V replicates and extends a study that was recently published in one of the top-tier accounting journals,demonstrating that its inferences are sensitive to minor changes in model specification.Section VI offers guidance on improving the implementation of selection models.These recommendations have important implications for editors and reviewers,as well as authors.Section VII concludes.1By ‘‘fairly minor ’’we mean the chosen research design would not necessarily arouse the suspicions of an editor or reviewer.590Lennox,Francis,andWang The Accounting ReviewMarch 2012II.CORRECTING FOR SELECTIVITY BIASThe Selection ModelThere are two distinct applications of the selection model.Thefirst—commonly known as a treatment effect model—is where an endogenous indicator variable(D)is included as an independent regressor.For example,a researcher might be interested in testing whether management earnings forecasts affect the cost of capital.In this case,the endogenous indicator variable(D)indicates whether the company issues an earnings forecast and the dependent variable is the cost of capital.The second application—sometimes known as a sample selection model—occurs when a regression is estimated on a subsample of observations.For example,a researcher might be interested in testing the determinants of management forecast accuracy.In this case,the dependent variable measures forecast accuracy and the regression is estimated on a subsample of companies that issue earnings forecasts.In both applications D is endogenous,raising potential concerns about bias.The treatment effect model can be written as follows:Y¼b0Xþh Dþu;ð1Þwhere X is a vector of exogenous variables(including an intercept)that affect the dependent variable,Y.The choice of D is estimated using a binary choice model:Düa00Zþa01Xþt;ð2Þwhere D¼1if D*!0and D¼0if D*,0.Equation(2)is usually estimated using probit,which assumes a normally distributed error term.The error terms in Equations(1)and(2),u and t,are assumed to have a bivariate normal distribution with mean zero and covariance matrix:r2qrqr1!If the error terms u and t are correlated(i.e.:q¼0),then E(u j D)¼0and the OLS estimate of h in Equation(1)will be biased.The intuition underlying the Heckman procedure is to control for this bias by estimating the inverse Mills’ratio(MILLS)from Equation(2):MILLS¼Eðu j DÞ¼uð^a0Zþ^a01XÞ=Uð^a00Zþ^a01XÞÀuð^a00Zþ^a01XÞ=ð1ÀUð^a00Zþ^a01XÞÞif D¼1if D¼0; (where u(.)and U(.)are the normal density and cumulative distribution functions,respectively.The researcher then controls for selection bias by adding MILLS to Equation(1),which becomes: Y¼b0Xþh Dþqr MILLSþe:ð3ÞThe error term e in Equation(3)is uncorrelated with D,which means that h is estimated without bias.The presence and direction of selection bias is inferred from the statistical significance and sign of the MILLS coefficient in Equation(3).2Note that the MILLS and D variables are correlated by construction,due to the fact that MILLS is a function of D,as defined above.Moreover,the2Equations(2)and(3)can be estimated using the traditional two-step approach or maximum likelihood(ML). Selection Models in Accounting Research591The Accounting Review March2012MILLS variable is also correlated by construction with the X variables in Equation (3).As we illustrate later,these correlations can result in high levels of multicollinearity.The sample selection model is conceptually the same as the treatment effect model except that Equation (3)is estimated for a subsample of observations rather than the full sample.For example,an accounting researcher may wish to estimate a model of forecast accuracy (Y )on a subsample of companies that issue forecasts (D ¼1).In this case,Equation (3)becomes Y ¼b 0X þh þqr MILLS 1þe ,where:MILLS 1¼u ð^a 00Z þ^a 01X Þ=U ð^a 00Z þ^a 01X Þ:Alternatively,accounting researchers may estimate separate Y models for the subsamples where D ¼1and D ¼0.For example,Chaney et al.(2004)estimate separate audit fee models for companies that hire Big N auditors (D ¼1)and companies that hire non-Big N auditors (D ¼0).When Equation (3)is estimated on the D ¼0subsample,the Y model becomes Y ¼b 0X þqr MILLS 0þe ,where:MILLS 0¼Àu ð^a 00Z þ^a 01X Þ=ð1ÀU ð^a 00Z þ^a 01X ÞÞ:Implementation IssuesThe difference between the OLS model in Equation (1)and the selection model in Equation (3)is that the latter includes MILLS as an additional independent variable.Identification of selection bias comes from two sources:(1)MILLS is nonlinear in its arguments (the X and Z variables),and(2)the Z variables are excluded from Equation (3).The Z variables are also known as ‘‘exclusion restrictions ’’because the researcher assumes they have no direct impact on Y ,such that any association between Y and Z is indirect through the MILLS variable.It is well known in econometrics that the researcher’s choice of exclusion restrictions is vital for implementing the selection model in a way that convincingly controls for endogeneity in D (Little 1985;Little and Rubin 1987;Manning et al.1987).First,the Z variables must be exogenous,otherwise the first stage coefficient estimates (and therefore MILLS )will be biased.Second,the Z variables need to be important determinants of D in Equation (2)in order for the MILLS variable to yield a powerful test for selection bias in Equation (3).Finally,it must be valid to exclude the Z variables from Equation (3).If a Z variable is incorrectly omitted from the Y model,then there is a classical correlated omitted variable problem.That is,a relevant Z variable is omitted from the second stage Y model and is correlated with the MILLS —which is a function of Z ,X ,and D —causing the MILLS coefficient to be biased.In turn,this means that MILLS will not properly control for the endogenous component of the D variable,such that the exogenous effect of D in Equation(3)will be estimated with bias.In many applications,the difficulty lies in finding good Z variables.While not good practice,it is possible to estimate selection models with no exclusion restrictions (i.e.,no Z ’s).The MILLS coefficients are technically identifiable even if the researcher imposes no exclusion restrictions because MILLS is nonlinear in its arguments.However,econometricians recommend against using nonlinearities to identify selection bias for two reasons (Little 1985).First,without Z variables,identification of the selection bias comes solely from the (untested)functional form assumptions.To illustrate,if Y is actually a nonlinear function of the X variables but the researcher incorrectly assumes that the relation is linear,then the MILLS variable will capture this functional form misspecification.The problem is that the researcher typically does not know whether the592Lennox,Francis,andWang The Accounting ReviewMarch 2012independent variables affect Y in a linear or nonlinear way and functional form assumptions typically have nofirm basis in theory.Second,the selection model is more likely to suffer from multicollinearity problems when there are no exclusion restrictions.Multicollinearity can arise in the selection model because,by construction,MILLS is correlated with the independent variables in the second stage(i.e.,X and D in Equation(3)).Multicollinearity is more likely to be problematic when there are no exclusion restrictions(i.e.,no Z variables)because MILLS is close to being linear over a wide range of its values(Manning et al.1987;Puhani2000;Li and Prabhala2007).There are two issues raised by having high multicollinearity.First,the coefficient standard errors are inflated,making it less likely that the coefficient estimates are statistically significant.We demonstrate in Section IV that inflated standard errors are important because they can result in the MILLS coefficient becoming statistically insignificant in the second stage estimation,which can lead to an incorrect inference with respect to the need to control for selection bias.In particular,we show that—even when the MILLS coefficient is statistically insignificant—inferences from the selection model can be different from those obtained without including MILLS.In this situation,the selection model indicates that it is legitimate to omit the insignificant MILLS variable,and yet,omitting MILLS gives different inferences for the treatment variable(D)because multicollinearity is then much lower.A second problem arises in a model that is not correctly specified.It is well known that when the model is correctly specified,the coefficients are estimated without bias even when multicollinearity is high.However,a less well-known problem arises when the model is misspecified,because in that situation multicollinearity can exacerbate the bias(Thursby1988). The risk of misspecification is particularly high in the selection model because the statistical identification of selectivity is through the assumed exclusion restrictions and the assumed functional form.If the researcher’s assumptions are incorrect,then the model is misspecified and,together with high multicollinearity,this can result in large biases.This is illustrated by our empirical examples in Section IV,where we show that relatively minor changes to the model specification can reverse the signs on the coefficients of interest and these opposing coefficients can attain high levels of statistical significance even when multicollinearity is high.III.SURVEY OF SELECTION MODELS IN ACCOUNTING RESEARCH This section evaluates whether the implementation issues discussed in Section II are relevant to the accounting literature.We begin by searching The Accounting Review,Journal of Accounting and Economics,Journal of Accounting Research,Review of Accounting Studies,and Contemporary Accounting Research for articles that use selection models.The search is undertaken electronically using the keywords‘‘endogeneity,’’‘‘Heckman,’’‘‘selection,’’and‘‘treatment effect,’’and results in75 articles in the ten-year period from2000–2009.Topic areas are shown in Table1,with16articles in auditing,16in disclosure,13in earnings management/quality,11in contracting/corporate governance, 2in tax,16in otherfinancial accounting topics,and1in management accounting.Panel A of Table2shows a sharp increase in selection models,with50of the75articles(67 percent)published in the most recent four-year period2006–2009,compared with just25(33 percent)in the earlierfive-year period(2000–2005).Panel B shows that52studies(69percent) estimate treatment effect models,while23studies(31percent)use the selection model to control for the fact that they are estimating the model on a non-random subsample.There are32studies(43 percent)that use selection models for their primary analysis.The remaining43studies(57percent) use selection models as a secondary analysis to corroborate inferences that are obtained without controlling for selection.Table2,Panel C reports that54studies(72percent)follow the recommended econometric practice of imposing one or more exclusion restrictions in the second stage model.However,a Selection Models in Accounting Research593The Accounting Review March2012surprising number of studies report selection models without exclusion restrictions.Eight studies have no Z variables whatsoever,while six report selection models both with and without exclusion restrictions.In another seven studies,the authors do not report the independent variables in the first stage models,so we are unable to determine whether they impose exclusion restrictions and it is impossible to evaluate the suitability of such restrictions.In summary,between 19and 28percent of accounting studies report selection models without exclusion restrictions.Of the 60articles that do impose exclusion restrictions,only three report whether their results are robust to alternative restrictions.Moreover,only three of the 60articles that employ Z variables attempt to provide an economic or theoretical rationale for the exclusions.This is important because,as shown later,ad hoc exclusion restrictions can yield non-robust inferences.TABLE 1Accounting Studies that Use Selection Models(2000–2009)DisclosureAuditing Other Financial Accounting Leuz and Verrecchia (2000)Kim et al.(2003)Beatty et al.(2002)Bushee et al.(2003)Weber and Willenborg (2003)Lang et al.(2003)Leuz (2003)Chaney et al.(2004)Ball and Shivakumar (2005)Baginski et al.(2004)Johnstone et al.(2004)Cowen et al.(2006)Atiase et al.(2005)Khurana and Raman (2004)Garfinkel and Sokobin (2006)Ahmed et al.(2006)Mansi et al.(2004)Ke and Yu (2006)Baber et al.(2006)Pittman and Fortin (2004)Bens and Johnston (2009)Marques (2006)Louis (2005)Butler et al.(2007)Verrecchia and Weber (2006)Guedhami and Pittman (2006)DeFond and Hung (2007)Engel et al.(2007)Fortin and Pittman (2007)Eberhart et al.(2008)Tucker (2007)Ruddock et al.(2007)Blouin and Krull (2009)Baber and Gore (2008)Behn et al.(2008)Feng et al.(2009)Rogers (2008)Choi et al.(2008)Jackson et al.(2009)Christensen et al.(2009)Chang et al.(2009)Kini et al.(2009)Collins et al.(2009)Choi et al.(2009)Wier (2009)Hui et al.(2009)Li (2009)Zhang (2009)Earnings Management/QualityContracting/Corporate Governance Tax Barton (2001)Roulstone (2003)Phillips (2003)Pincus and Rajgopal (2002)Fee and Hadlock (2004)Omer et al.(2006)Schrand and Wong (2003)Asquith et al.(2005)Haw et al.(2004)Davila and Penalva (2006)Management Accounting Kim and Yi (2006)Blacconiere et al.(2008)Muller and Riedl (2002)Morsfield and Tan (2006)Cheng and Farber (2008)Doyle et al.(2007)Frankel et al.(2008)Chung and Wynn (2008)Carter et al.(2009)Jiang (2008)Hoitash et al.(2009)Louis et al.(2008)Lara et al.(2009)Files et al.(2009)Nichols et al.(2009)Gong et al.(2009)Katz (2009)The sample is based on a search for the terms ‘‘endogeneity,’’‘‘Heckman,’’‘‘selection,’’and ‘‘treatment effect ’’for articles in The Accounting Review ,Journal of Accounting and Economics ,Journal of Accounting Research ,Review of Accounting Studies ,and Contemporary Accounting Research .594Lennox,Francis,andWangThe Accounting ReviewMarch 2012Studies typically rely on the existing literature to justify their choice of independent variables in the first and second stage model specifications.However,the critical issue for the selection model is the researcher’s choice of exclusion restrictions,that is,which of the independent variable(s)in the first stage model should be excluded from the second stage model.In this respect,many accounting studies fail to justify their exclusion of Z variables from the second stage.Some studies do explicitly point out that exclusion restrictions are desirable from an econometric point of view,but they nevertheless fail to explain why their chosen exclusion restrictions are valid.In most cases,the exclusion restrictions appear to be chosen in an ad hoc way without obvious justification.Likewise,Larcker and Rusticus (2010)(hereafter,LR)report that accounting studies using regular TABLE 2Descriptive Statistics for 75Accounting Studies that Use Selection Models(2000–2009)Panel A:The Increasing Use of Selection Models in the Accounting Literature2000200120022003200420052006200720082009TotalNumber of studies per year 113884127112075Panel B:Purpose of the Selection ModelDo studies estimate a treatment effects model or asample selection model?Treatment Effects Sample Selection Total 522375(69%)(31%)(100%)Do studies use the selection model for their primaryanalysis or as a secondary robustness test?Primary Secondary Total 324375(43%)(57%)(100%)Panel C:Implementation IssuesDo studies impose one or more exclusionrestrictions in the second stage model?Yes Yes/No a No Unclear b Total 5468775(72%)(8%)(11%)(9%)(100%)Of the 60studies that impose exclusion restrictions,do the studies report robustness results usingdifferent restrictions?Yes No Total 35760(5%)(95%)(100%)Of the 60studies that impose exclusion restrictions,do the studies attempt to justify them oneconomic grounds?Yes No Total 35760(5%)(95%)(100%)Do studies report multicollinearity diagnostics forthe endogenized regressor and the inverse Mills’ratio?Yes No Total 37275(4%)(96%)(100%)a The ‘‘Yes/No ’’group refers to studies that report alternate specifications both with and without an exclusion restriction.bThe ‘‘Unclear ’’group refers to studies where it is not disclosed whether any exclusion restrictions are imposed in the second stage.This situation arises when studies do not report the set of independent variables in the first stage model.The sample is based on a search for the terms ‘‘endogeneity,’’‘‘Heckman,’’‘‘selection,’’‘‘treatment effects ’’for articles in The Accounting Review ,Journal of Accounting and Economics ,Journal of Accounting Research ,Review of Accounting Studies ,and Contemporary Accounting Research .Selection Models in Accounting Research 595The Accounting ReviewMarch2012instrumental variables (IV)typically fail to justify their exclusion restrictions.3Finally,although selection models can suffer from high levels of multicollinearity (Manning et al.1987;Puhani 2000),only three of the 75studies report formal tests of multicollinearity.We conclude that many accounting studies implement the selection model in a mechanical way with limited appreciation of the econometric issues surrounding its implementation.This appraisal is similar to LR’s survey,but there are important differences between their critique and ours.The endogenous variables are continuous in the regular IV procedures examined by LR,whereas there is an endogenous indicator variable (i.e.,D )in the selection model.This means that the correction for endogeneity is different in the selection model compared with regular IV.In particular,the selection model uses the MILLS variable to control for the correlation between error terms,but there is no equivalent of MILLS in regular IV.This makes our critique different from LR in two important ways.First,MILLS is nonlinear in its arguments,which means that the selection model can technically be estimated even in the absence of any exclusion restrictions.In contrast,at least one exclusion restriction is required for identification in the regular IV approach.In the following section,we demonstrate that the selection model can yield non-robust inferences and multicollinearity is often high when the researcher chooses no exclusion restrictions.The second difference between regular IV and selection models is that researchers can use the statistical significance of the MILLS coefficient to assess the presence or absence of selection bias.However,as discussed in Section II,multicollinearity can complicate these inferences.In the following section,we shall demonstrate that—even when the MILLS coefficient is statistically insignificant,suggesting no selection bias—key conclusions reached from the selection model can still be very different from OLS.A lack of statistical significance can be caused by high multicollinearity,so a statistically insignificant MILLS coefficient does not necessarily mean there is no selection problem.Further,even when the MILLS coefficient is statistically significant,we demonstrate that inferences from the selection model are likely to be unreliable if exclusion restrictions are absent or are chosen in an ad hoc manner.A final difference between our study and LR is that we apply our critique to a study that has been published in a top-tier accounting journal (Section V).This is important because the empirical examples in Section IV and in LR are homemade in the sense that they do not directly replicate a published study.A skeptic might argue that our examples,as well as the example in LR,are extreme and not representative of the implementation of the selection model in published studies that pass the scrutiny of experienced editors and reviewers in top-tier journals.We show that this is not the case by illustrating implementation problems and non-robustness using a published study.Our study is also related to a discussion by Tucker (2010)about the relative merits of propensity score matching (PSM)versus the inverse Mills’ratio (IMR)approach.Tucker (2010)points out that these two approaches are not substitutes for each other because they are designed to address different problems.In particular,the PSM methodology controls for selection on ‘‘observables ’’i.e.,it controls for the correlation between the error term in the first stage model (u )and the independent variables in the second stage (i.e.,X and Z ).In contrast,the IMR approach controls for selection on ‘‘unobservables ’’(i.e.,it controls for the correlation between u and t ).4Our 3Our study is also related to Li and Prabhala (2007)who survey various applications of the selection model in the corporate finance literature.However,unlike our study,they do not offer a viewpoint as to whether researchers have applied the techniques correctly and they do not illustrate the fragility of the selection model using empirical examples.4Tucker (2010)makes two other points about Heckman models in the accounting literature.First,she points out that many studies fail to report which formulas they use to calculate the IMR variables and this lack of disclosure makes it difficult for the reader to interpret the signs of the coefficients on the IMR variables.Second,she notes that the two-step procedure is less efficient than maximum likelihood (ML)estimation.On this second point,we caution the reader that ML is not necessarily preferable despite its greater efficiency,as ML can yield inferences that are less robust than the two-step procedure (Puhani 2000).596Lennox,Francis,andWang The Accounting ReviewMarch 2012。

研究样本的选择原则英文回答：Principles of Sample Selection.1. Probability Sampling:Simple random sampling: Every subject has an equal chance of being selected.Stratified sampling: The population is divided into subgroups (strata) based on shared characteristics, and subjects are randomly selected from each stratum.Cluster sampling: The population is divided into clusters, and a random sample of clusters is chosen.2. Non-probability Sampling:Convenience sampling: Subjects are selected becausethey are easily accessible.Snowball sampling: Subjects are recruited through referrals from other participants.Quota sampling: Subjects are selected to match the demographic characteristics of the population.Purposive sampling: Subjects are selected based on their specific characteristics or knowledge of the research topic.3. Additional Considerations:Sample size: The number of subjects needed for statistical significance.Response rate: The proportion of subjects who participate in the research.Representativeness: The degree to which the sample reflects the target population.Bias: Any systematic error that influences the results.中文回答：研究样本选择原则。