On the Size-Dependence of the Inclination Distribution of the Main Kuiper Belt

Toward Loop Level Study of Supersymmetric Model at Futuree+e−Linear ColliderMihoko M.Nojiri1KEK Theory Group,Oho1-1,Tsukuba,Ibaraki,305,JapanAbstract.In the case with a large splitting between the squark and slepton masses,thesupersymmetric identities which enforce the equality of the gauge and gaugino couplingsare violated in the effective theory below the squark mass threshold.We compute the fullone-loop(s)quark corrected slepton production cross-sections.Wefind that the one-loopcorrected slepton production cross-sections can depend on the squark mass strongly,upto9%×log10(M˜Q /m˜).We investigate the squark mass sensitivity of the slepton cross-section measurements at a future linear collider.For sneutrino production accessible at√s=500GeV there can be sensitivity to squark masses at or larger than1TeV.1.IntroductionSupersymmetry is an attractive possibility beyond the standard model.Because of the relations super-symmetry imposes among the dimensionless couplings,the quadratic divergences in the Higgs sector are cut-offby the superpartner mass scale.The cancellations stabilize the hierarchy between the Planck scale and the weak scale.The minimal supersymmetric standard model(MSSM)is consistent with gauge coupling unification suggested by grand unified theories.Also,it is interesting that one of the hallmarks of supersymmetry,a light Higgs boson(m h<∼130GeV),is favored by globalfits to precision electroweak dataIn this contribution we examine the prospect of testing supersymmetry via a precise measurement of the lepton-slepton-gaugino vertex.The linear collider provides a suitably clean experimental environ-ment[1,2,3,4,5].Among the relations which account for the cancellations of quadratic divergences, supersymmetry relates the lepton-slepton-gaugino coupling to the usual gauge coupling.Although bare(or)couplings enjoy the relations imposed by supersymmetry,the effective gauge and gaugino couplings are not equal because supersymmetry is broken.In particular,all non-singlet nondegenerate supermultiplets such as the quark-squark supermultiplets contribute to the split-ting.Hence,measurements of the type we consider here not only provide for detailed tests of supersym-metry,but can also elucidate important features of the scale and pattern of supersymmetry breaking [6,7,8,9,10].For example,the(s)quark contribution to the splitting of the U(1)and SU(2)gaugino/gauge (s)lepton couplings grows logarithmically with the squark mass,asδg Y g Y 11g2Y48π2lnM˜Qm˜,δg2g23g2216π2lnM˜Qm˜.(1)This correction is obtained by evolving the couplings according to the renormalization group equations(RGE’s)of the effective theory[11]below the squark mass threshold.When M˜Q /m˜10the correction1Address after Oct.1st.Yukawa Institute,Kyoto University,Kyoto,Japan.E-mail:nojirim@theory.kek.jp.This work is supported in part by Grant in aid for Science and Culture of Japan(07640428,09246232)e −e +˜ ˜∗(a)e −e +˜ ˜∗(b)Figure 1.Feynman graphs of the one-loop quarks-squark corrections to the processes e −e +→˜˜ ∗,for (a)s -channel and (b)t -channel amplitudes.to the SU(2)(U(1))coupling is about 2%(0.7%).This gives rise to an enhancement of the t -channel slepton or gaugino production cross-section of about 8%(2.8%).If large statistics are available and systematic errors can be controlled,we can (assuming the MSSM)constrain the squark mass scale by this measurement.We restrict our attention to the measurement of the first generation lepton-slepton-gaugino cou-pling at an e −e +linear collider.Much study has been undertaken to determine how accurately we can expect to measure these couplings[3,5,7,10].In Ref.[10],we perform a full one-loop calculation of the slepton production cross-section within the MSSM.We include only (s)quark loops in the calculation,because the correction is enhanced by a color factor and the number of generations.The remaining corrections are small,and if we did include them we expect our conclusions would not change.In this contribution,we only discuss our calculation only briefly in section 2.We point out that,to a good approximation,the one-loop t -channel amplitudes can be rewritten in the same form as the tree-level amplitudes,with the replacement of the tree-level parameters with renormalized effective parameters.Hence we introduce the effective coupling,the effective masses,and the effective mixing matrix.In section 3we discuss our numerical results,and show how well we can measure the squark loop correction to the coupling,and thereby constrain the squark mass,assuming both slepton and chargino production are possible.We show the statistical significance of the results by combining our knowledge of the superpartner masses and cross-sections.The uncertainty in the slepton mass measurement is quite important in this analysis.In the last section,section 4,we give our conclusions.2.calculationIn this section we discuss the calculation of the cross-section of e +e −→˜ i ˜ ∗j ,where ˜ i =(˜e −L ,˜e −R ,˜νe ),including one-loop (s)quark corrections.The full result is explicitly given in Ref.[10];here we restrict ourselves to outline the general features of the calculation.The tree level slepton productions proceed through s-channel exchange of Z and γ,and t-channel exchange of neutralinos or charginos (˜χi ).To evaluate the one-loop amplitude,we treat all the param-eters appearing in this tree-level expression as running DR quantities,and add the contributions from the one-loop diagrams (see Fig.1).Note that the (s)quark loop corrections do not give rise to external wave-function renormalization.To avoid a complexities of several gauge interactions,let us consider e +e −→˜e +R ˜e −R production.If the √s m Z ,the process approximately proceeds through s-channel exchange of B boson which couples to hypercharge,and t-channel exchange of ˜B ,superpartner of B boson.The s-channel amplitude below squark mass threshold is very well approximated by effective coupling g effY (Q =√s ).g Y(Q )in MSSM is related to g effY as αeffY =αDR (1+Σq (Q )+Σ˜q (Q ))where Σq (Q )and Σ˜q (Q )is the gauge two point function from quark and squark loops respectively and Q is renormalization scale.The g DR Y (Q )is equivalent to the t-channel coupling g ˜B (Q ),but we do not directly measure the coupling.The t-channel amplitude is the sum of tree level contribution and 1-loop contribution shown in Fig1.(b).TheΣq (Q ),Σ˜q (Q )Σq˜q (Q )αeffi αeff˜G i αi (Q )α˜G i (Q )≡(↔m Z ,m W ,e SM ,sin θeffW ...)gauge sector SUSY gaugino sectorFigure 2.Schematic figure of the correction to SUSY relationdifference S /Y ≡(g eff˜B −g effY )/g effY ≡(Σq ˜q −Σq −Σ˜q )(Q )/2is the correction to the SUSY relation(Fig.2).The leading logarithms of the corrections S /at Q =m ˜ are exactly those of Eq.(1),showing that the RGE approach of Ref.[11]gives the proper results.Although both s-channel and t-channel diagrams receive one loop corrections from squark and quark loops,only t-channel amplitude receive physically interesting correction.Notice in our approxi-mation,s-channel amplitude receives oblique correction of the gauge two point function only,which is common to the e +e −collision at Z pole.The measurement at Z pole fixes the s-channel amplitude of slepton production,thanks to the gauge symmetry.In Ref[10],we also how the one-loop corrected t -channel amplitude can be well approximated bya tree-level form.For e +e −→˜eR ˜e R ,we find M t RR =2¯v p / −4 i =1¯g 2e ˜e R ˜B N ∗i 1N i 1(p 2)p 2m 2i (p 2)P R u ,(2)where p is t-channel momentum and ¯g e ˜e R ˜B (p 2)is the effective bino coupling defined as ¯g e ˜e R ˜B (p 2)=ˆg Y (Q ) 1−12˜ΣL 11(Q,p 2) ,(3)and ˜ΣL 11(p 2)is the bino-bino component of the neutralino two-point function,and ˆgY (Q )is coupling.The N ij and m i are the effective neutralino mixing matrix and neutralino masses obtained by diagonal-izing the effective neutralino mass matrix Y ij .¯g i ,N ij ,and m i are physical scale independent quantities to O (α).¯m i (¯m i )is the pole mass of neutralinos.We also checked numerically the expression Eq.(2)reproduce the full result very well.3.Numerical results3.1.m ˜Q Dependence of Various Cross SectionsWe next show the numerical dependence of the one-loop corrected cross-sections of e −e +→˜ i ˜ ∗j (˜ i =(˜e −L ,˜e −R ,˜νe ))on the squark mass.We consider the case where the initial electron is completelylongitudinally polarized.We therefore treat the following eight modes,e −L e+→˜e −L ˜e +L ,˜e −R ˜e +R ,˜e −L ˜e +R ,˜νe ˜ν∗e ,e −R e +→˜e −L ˜e +L ,˜e −R ˜e +R ,˜e −R ˜e +L ,˜νe ˜ν∗e .(4)The production involves the t channel exchange of chargino and neutralino,which depends of gaugino mass parameter M 1,M 2,higgsino mass parameter µ,and tan β.We take the three pole masses (m ˜χ01,m ˜χ+1,m ˜χ03),and tan β(M Z )as inputs.We assume |µ| M Z ,in which case M eff1 m ˜χ01,M eff2 m ˜χ+1,and |µeff| m ˜χ03hold,where M eff1,M eff2,and −µeffare the (1,1),(2,2),and (3,4)elements of the effective neutralino mass matrix Y ij ,defined in [10].We show in Fig.3the M ˜Q dependence of the cross-sections for left handed electron beam.Here we normalize the cross-sections to the tree-level values defined in Ref.[10].The one-loop cor-rected cross-sections of the modes which have a t -channel contribution are similar to tree-level ones at1000M Q (GeV)0.951.001.051.10σ(c o r r )/σ(t r e e )(a)e −Le −L e +L~ ~νν*~~e −L e +R~ ~e −R e +R~ ~5000500~Figure 3.The M ˜Q dependence of the slepton production cross-sections.Input parametersare m ˜χ01=100GeV,m ˜χ+1=200GeV,m ˜χ03=300GeV,tan β(M Z )=4,m ˜ =200GeV,A =0,µ<0,and √s =500GeV.The corrected cross-sections are normalized by thetree-level cross-sections[10].M ˜Q <∼300GeV,but increase linearly with log M ˜Q .Because the effective masses are equal to the input pole masses,the squark mass dependence of the one-loop corrected cross-sections is primarily due to the difference between the effective theory gauge and gaugino couplings.See Eq.(2)The two channels which have ˜W contributions (e −L e +→˜e −L ˜e +L ,˜νe ˜ν∗e )show the largest M ˜Q depen-dence.The channel e −L e +→˜e −L ˜e +R ,show smaller M ˜Q dependence from ˜B contributions.Nevertheless,we found these M ˜Q dependences are significantly larger than the renormalization scale dependence ofthe corrected cross-sections (see Fig.2).In contrast,the remaining channels,which have only s -channel contributions,show very little M ˜Q dependence,as explained in Section 2.3.2.Determination of M ˜Q The sfermion and chargino/neutralino production cross-sections depend on M 1,M 2,µ,tan β,and the sfermion mass m ˜ .The cross-sections also depend on the effective fermion-sfermion-gaugino coupling ¯g f ˜f ˜χ,which is nicely parameterized by log M ˜Q .By constraining ¯g f ˜f ˜χwe can determine M ˜Q ,if the rest of the parameters are known accurately enough.It has been demonstrated that an accurate determination of m ˜χand m ˜ is indeed possible if sfermions ˜are produced and dominantly decay into a charged lepton and a chargino or neutralino ˜χ[1,2].The measurement of the end point energies determine the masses.Recently,Baer et al.[4]performed a MC study for the case that left-handed sfermions are produced and decay into a gaugino-like chargino or neutralinos.In their example called point 3,˜νe ˜ν∗e production is followed by ˜ν(∗)e →e ∓˜χ±1.The decay mode ˜νe ˜νe ∗→e −e +˜χ+1˜χ−1→e −e +µ2j (νµ2˜χ01)is background free and the measured electron endpoint energies allow for a 1%measurement of m ˜χ±1and m ˜ν.The results of Ref.[4]encourage us to consider their example point 3.The chosen parameter set corresponds to m ˜νe =207GeV,m ˜χ+1=96GeV,m ˜χ01=45GeV and m ˜χ03=270GeV,and the lightest chargino and neutralinos are gaugino-like.Their study suggests that we can take m ˜χ+1,m ˜χ01,and m ˜νe as well constrained input parameters.For 20fb −1of luminosity,their MC simulations show that at 68%CL,(δm ˜χ+1,δm ˜νe )=(1.5GeV,2.5GeV).In the following we estimate the statistical significance of the radiative correction to the production cross-section.We focus solely on the ˜νe production cross-section,because it is larger than 1pb for a left-handed electron beam,and larger than the other sparticle production cross-sections at √s =500GeV.We would first like to provide a feel for the sensitivity to the squark mass scale and tan βin the ideal case where we ignore the slepton and gaugino mass uncertainties.In Fig.4(left)we show the statistical significance of the loop correction by plotting contours of constant cross-section.Here we fix the sneutrino mass and determine µ,M 1and M 2by fixing the one-loop corrected masses m ˜χ01,m ˜χ03,and m ˜χ+1.We plot the contours corresponding to the number of standard deviations of the fluctuation of the accepted number of events.The 1-σfluctuation corresponds to N input ,where N input is ournominal value of the number of events at M ˜Q =1000GeV and tan β(M Z )=4.The accepted number of events N is given byN =A ·σ(e −Le +→˜νe ˜νe )× BR(˜νe →e ˜χ+1) 2×100fb −1.(5)Here we took BR(˜νe →e ˜χ+1)=0.6and overall acceptance A =0.28.The number of accepted eventsat our nominal point N input is about 12800for µ<0.Figure 4.(left):The constraint on M ˜Q and tan βcoming from σ(e −e +→˜νe ˜ν∗e →e −e +˜χ+1˜χ−1),withdtL =100fb −1.The central value is taken as M ˜Q =1000GeV and tan β(M Z )=4.m ˜χ03=270GeV,µ<0(right):∆χ2min vs.M ˜Q with µ<0and fixed tan β,m ˜χ01and m ˜χ03,but allowing m ˜χ+1and m ˜νe to vary freely.We show the contours for µ<0in Fig.4(left).If tan βis well measured,M ˜Q is constrained toM ˜Q =1000+370−280GeV at 1-σsignificance.If instead we assume the constraint 2<tan β<8,the mildtan βdependence yields 700<M ˜Q <1900GeV.In the case µ>0,the mixing of chargino gives rise to significant tan βdependence.Increasing the squark mass can be compensated for by decreasing tan β,and measuring sneutrino production then determines a region of the (M ˜Q ,tan β)plane.We now turn to the effect of the mass uncertainties.The sneutrino production cross-section depends on the masses m ˜νe ,m ˜χ01,m ˜χ03and m ˜χ+1.Of these masses the cross-section is most sensitive to the sneutrino mass.All of the same chirality scalar production cross-sections suffer from the strong β3˜ kinematic dependence.Near threshold this results in an especially large sensitivity to the final-state mass.Although a simple statistical scale-up of the results of Ref.[4]implies a sneutrino mass uncertainty of only 0.3%,this nevertheless leads to a significant degradation in our ability to constrain the squark mass scale.(Systematic errors might be the limiting factor here.)Note,however,that the measurement of the sneutrino mass in Ref.[4]was obtained by studying a small fraction of the total sneutrino decay modes.The mode they studied amounts to only about 4%of the total sneutrino ing other modes,such as e −e +4j (2˜χ01),might reduce the mass error even further.Because the ˜νe production cross-section is significantly larger than the other slepton cross-sections,isolating the various sneutrino signatures is less affected by SUSY backgrounds such as e −e +→˜e −L ˜e +L →e −e +4j (2˜χ01).Now we show the constraint on the squark mass M ˜Q after taking into account the uncertainty of the masses δm ˜νe and δm ˜χ+1for µ<0case.The effect of δm ˜χ03turns out to be negligible for the case,and we assume it is possible to distinguishsign of µby measuring heavier ino mass differences at √s >2m ˜χ03.[10].In Fig.4(right)we plot ∆χ2min against M ˜Q ,where ∆χ2min is a minimum of ∆χ2with respect to variations in m ˜χ+1and m ˜νe .The region of M ˜Q where 2min <1,2,...corresponds to 1,2,...-σerror of the squark mass when the chargino and sneutrino mass uncertainties are taken intoaccount.The sneutrino mass uncertainty reduces the sensitivity of the production cross-section to M ˜Q considerably,because the effect of increasing M ˜Q can be compensated for by a small increase in m ˜νe .On the other hand,we do not find any significant effect due to non-zero δm ˜χ+1.From Fig.4(right)we see that in this case,even with the sneutrino mass uncertainty,we canreasonably constrain the squark mass scale.For example,at the 1-σlevel with M ˜Q =1TeV,weconstrain M˜Q to1+1.2−0.5TeV,using the naive scale up(from20fb−1to100fb−1)of the statisticalerrors of Ref.[4].This corresponds to the difference between the gauge and gaugino effective couplings,δg2/g2=0.011±0.006.This can be compared to the estimate of the constraintδg2/g2=±0.02from the chargino production measurement[7].Such comparisons are sensitive to different choices of parameter space and other assumptions.If we reduce the mass uncertainties by a factor of2,wefind the interesting constraint600<M˜Q<1500GeV.4.conclusionsSupersymmetry is a beautiful symmetry which relates bosons and fermions.If we wish to determine whether this symmetry is realized in nature,the relations imposed between particles and their super-partners must be confirmed by experiment.Of course,discovering a particle with the quantum numbers of a superpartner is thefirst very important step in this procedure.An equally important test,though, is the confirmation of the hard relations imposed by supersymmetry,for example,the equivalence of the gauge and gaugino couplings.It has been argued that a next generation linear collider would be an excellent tool to verify supersymmetry in this respect.Production cross-sections such asσ(e−e+→˜ ˜ ∗)andσ(e−e+→˜χ−i˜χ+i) involve the t-channel exchange of gauginos or sleptons,so they depend on gaugino couplings.[5,3] In this paper,we approached this problem from a somewhat different direction.Because super-symmetry must be badly broken by soft breaking terms,the tree-level relations of the couplings are also broken,by radiative corrections.The corrections are logarithmically sensitive to the splitting of the supersymmetry multiplets.To quantify this,we have calculated the full one-loop correction due to(s)quark loops of the slepton production cross-sections.The difference between the effective lepton-slepton-gaugino couplings g eff˜G i and the effective gauge couplings g effi is given by a coupling factor timeslog M˜Q /m˜.We gave an explicit example which illustrates that the statistics at the future linear collider may be enough to constrain the squark mass scale through the measurement of the slepton production cross-section.We found,with1-σsignificance,M˜Q could be constrained to1+1.2−0.5TeV by the measurement ofthe sneutrino production cross-section.We found this constraint in theµ<0case where we took into account the errors(based on existing MC simulation)of the sneutrino and light chargino masses,but assumed tanβwas well constrained by other measurements.The mass of the sleptons and gauginos must be measured very precisely in order to successfully constrain the squark mass scale via production cross-section measurements.In order to determine the ultimate sensitivity of this procedure,a thorough study of the systematic uncertainties in the slepton mass measurements is necessary.It is important to note that the constraint on the squark mass scale can be stronger than the one presented in this paper.Here,we estimated the sensitively to squark mass scale by utilizing sneutrino production followed by its decay into a chargino and an electron.Depending on the spectrum and center-of-mass energy,there will typically be many other production processes which involve t-channel exchange of gauginos or sleptons,and all those amplitudes have log M˜Qcorrections.The constraint on the squark mass we have realized here could be unique in the sense that this information may not be available at the LHC.Even if the LHC squark production rate is large,the gluino could be produced in even larger numbers,creating a large irreducible background to the squark signal.A large gluino background could make the extraction of the squark mass from kinematical variables difficult.On the other hand,if information on the squark masses is obtained at the LHC,we would have rather accurate predictions for the gaugino couplings.In this case,the measurement of the production cross-sections we considered here would constrain new supersymmetry-breaking physics with standard model gauge quantum numbers.In a sense,the study proposed here is similar in nature to studies performed at LEP and SLC.The physics of gauge boson two-point functions has been studied extensively at LEP and SLC,and it has provided strong constraints on new physics.Similarly,a future LC and the LHC might provide precision studies of the gaugino two-point functions,to realize a supersymmetric version of new precision tests.References[1]JLC Group,JLC-1,KEK Report No.92–16(1992).[2]T.Tsukamoto et al.,Phys.Rev.D51,3153(1995).[3]J.L.Feng,M.E.Peskin,H.Murayama,X.Tata,Phys.Rev.D52,1418(1995).[4]H.Baer,R.Munroe,X.Tata,Phys.Rev.D54,6735(1996).[5]M.M.Nojiri,K.Fujii,T.Tsukamoto,Phys.Rev.D54,6756(1996).[6]H.-C.Cheng,J.L.Feng,N.Polonsky,hep-ph/9706438.[7]H.-C.Cheng,J.L.Feng,N.Polonsky,hep-ph/9706476.[8]L.Randall,E.Katz,S.Su,hep-ph/9706478and MIT–CTP–2646,inpreparation.[9] D.M.Pierce,S.Thomas,SLAC–PUB–7474,in preparation.[10]M.M.Nojiri,Damien M.Pierce and Youichi Yamada,Slepton Production as a Probe of the Squark MassScale,KEK-TH520,hep-ph/9707244.[11]P.H.Chankowski,Phys.Rev.D41,2877(1990).。

剑桥雅思阅读5原文翻译及答案(test1)雅思阅读是块难啃的硬骨头，需要我们做更多的题目才能得心应手。

下面小编给大家分享一下剑桥雅思阅读5test1原文翻译及答案解析，希望可以帮助到大家。

剑桥雅思阅读5原文(test1)剑桥雅思系列真题是剑桥大学考试委员会外语考试部出版各类考试真题的唯一官方出版社出版的权威教材，书中包含最新的雅思全真试题资料，是各类雅思考生备考过程中必不可少的参考书。

非常适合学生自学的习题解答和听力录音文本。

READING PASSAGE 1You should spend about 20 minutes on Questions 1-13, which are based on Reading Passage 1 below.Johnson’s DictionaryFor the centur y before Johnson’s Dictionary was published in 1775, there had been concern about the state of the English language. There was no standard way of speaking or writing and no agreement as to the best way of bringing some order to the chaos of English spelling. Dr Johnson provided the solution.There had, of course, been dictionaries in the past, the first of these being a little book of some 120 pages, compiled by a certain Robert Cawdray, published in 1604 under the title A Table Alphabeticall ‘of hard usuall English wordes’. Like the various dictionaries that came after it during the seventeenth century, Cawdray’s tended to concentrate on ‘scholarly’ words; one function of the dictionary was to enable its student to convey an impression of fine learning.Beyond the practical need to make order out of chaos, the rise of dictionaries is associated with the rise of the English middle class, who were anxious to define and circumscribe thevarious worlds to conquer —lexical as well as social and commercial. it is highly appropriate that Dr Samuel Johnson, the very model of an eighteenth-century literary man, as famous in his own time as in ours, should have published his Dictionary at the very beginning of the heyday of the middle class.Johnson was a poet and critic who raised common sense to the heights of genius. His approach to the problems that had worried writers throughout the late seventeenth and early eighteenth centuries was intensely practical. Up until his time, the task of producing a dictionary on such a large scale had seemed impossible without the establishment of an academy to make decisions about right and wrong usage. Johnson decided he did not need an academy to settle arguments about language; he would write a dictionary himself and he would do it single-handed. Johnson signed the contract for the Dictionary with the bookseller Robert Dosley at a breakfast held at the Golden Anchor Inn near Holbom Bar on 18 June 1764.He was to be paid ￡1.575 in instalments, and from this he took money to rent Gou gh Square, in which he set up his ‘dictionary workshop’.James Boswell, his biographer, described the garret where Johnson worked as ‘fitted up like a counting house’ with a long desk running down the middle at which the copying clerks would work standing up. Johnson himself was stationed on a rickety chair at an ‘old crazy deal table’ surrounded by a chaos of borrowed books. He was also helped by six assistants, two of whom died whilst the Dictionary was still in preparation.The work was immense; filling about eighty large notebooks (and without a library to hand), Johnson wrote the definitions of over 40,000 words, and illustrated their many meanings with some 114,000 quotations drawn from English writing on everysubject, from the Elizabethans to his own time. He did not expect to achieve complete originality. Working to a deadline, he had to draw on the best of all previous dictionaries, and to make his work one of heroic synthesis. In fact, it was very much more. Unlike his predecessors, Johnson treated English very practically, as a living language, with many different shades of meaning. He adopted his definitions on the principle of English common law —according to precedent. After its publication, his Dictionary was not seriously rivalled for over a century.After many vicissitudes the Dictionary was finally published on 15 April 1775. It was instantly recognised as a landmark throughout Europe. ‘This very noble work,’ wrote the leading Italian lexicographer, ‘will be a perpetual monument of Fame to the Author, an Honour to his own Country in particular, and a general Benefit to the republic of Letters throughout Europe" The fact that Johnson had taken on the Academies of Europe and matched them (everyone knew that forty French academics had taken forty years to produce the first French national dictionary) was cause for much English celebration.Johnson had worked for nine years, ‘with little assistance of the learned, and without any patronage of the great; not in the soft obscurities of retirement, or under the shelter of academic bowers, but amidst inconvenience and distraction, in sickness and in sorrow’. For all its faults and eccentricities his two-volume work is a masterpiece and a landmark, in his own words, ‘setting the orthography, displaying the analogy, regulating the structures, and ascertaining the significations of English words’. It is the cornerstone of Standard English an achievement which, in James Boswell’s words ‘conferred stability on the language of his country.’The Dictionary, together with his other writing, made Johnson famous and so well esteemed that his friends were able to prevail upon King George Ⅲ to offer him a pension. From then on, he was to become the Johnson of folklore.Questions 1-3Choose THREE letters A-H.Write your answers in boxes 1-3 on your answer sheet.NB Your answers may be given in any order.Which THREE of the following statements are true of Johnson’s Dictionary?A It avoided all scholarly words.B It was the only English dictionary in general use for 200 years.C It was famous because of the large number of people involved.D It focused mainly on language from contemporary texts.E There was a time limit for its completion.F It ignored work done by previous dictionary writers.G It took into account subtleties of meaning.H Its definitions were famous for their originality.Questions 4-7Complete the summary.Choose NO MORE THAN TWO WORDS from the passage for each answer.Write your answers in boxes 4-7 on your answer sheet.In 1764 Dr Johnson accepted the contract to produce a dictionary. Having rented a garret, he took on a number of 4…………, who stood at a long central desk. Johnson did not have a 5………… available to him, but eventually produced definitions of in excess of 40,000 words written down in 80 large notebooks.On publications, the Dictionary was immediately hailed in many European countries as a landmark. According to his biographer, James Boswell, Johnson’s principal achievement was to bring 6……… to the English language. As a reward for his ha rd work, he was granted a 7………by the king.Questions 8-13Do the following statements agree with the information given in Reading Passage 1?In boxes 8-13 on your answer sheet, writeTRUE if the statement agrees with the informationFALSE if the statement contradicts the informationNOT GIVEN if there is no information on this8 The growing importance of the middle classes led to an increased demand for dictionaries.9 Johnson has become more well known since his death.10 Johnson had been planning to write a dictionary for several years.11 Johnson set up an academy to help with the writing of his Dictionary.12 Johnson only received payment for his Dictionary on its completion.13 Not all of the assistants survived to see the publication of the Dictionary.READING PASSAGE 2You should spend about 20 minutes on Questions 14-26, which are based on Reading Passage 2 below.Nature or Nurture?A A few years ago, in one of the most fascinating and disturbing experiments in behavioural psychology, Stanley Milgram of Yale University tested 40 subjects from all walks of lifefor their willingness to obey instructions given by a ‘leader’ in a situation in which the subjects might feel a personal distaste for the actions they were called upon to perform. Specifically M ilgram told each volunteer ‘teacher-subject’ that the experiment was in the noble cause of education, and was designed to test whether or not punishing pupils for their mistakes would have a positive effect on the pupils’ ability to learn.B Milgram’s expe rimental set-up involved placing the teacher-subject before a panel of thirty switches with labels ranging from ‘15 volts of electricity (slight shock)’ to ‘450 volts (danger —severe shock)’ in steps of 15 volts each. The teacher-subject was told that whenever the pupil gave the wrong answer to a question, a shock was to be administered, beginning at the lowest level and increasing in severity with each successive wrong answer. The supposed ‘pupil’ was in reality an actor hired by Milgram to simulate receiving the shocks by emitting a spectrum of groans, screams and writings together with an assortment of statements and expletives denouncing both the experiment and the experimenter. Milgram told the teacher-subject to ignore the reactions of the pupil, and to administer whatever level of shock was called for, as per the rule governing the experimental situation of the moment.C As the experiment unfolded, the pupil would deliberately give the wrong answers to questions posed by the teacher, thereby bringing on various electrical punishments, even up to the danger level of 300 volts and beyond. Many of the teacher-subjects balked at administering the higher levels of punishment, and turned to Milgram with questioning looks and/or complaints about continuing the experiment. In these situations, Milgramcalmly explained that the teacher-subject was to ignore the pupil’s cries for mercy and carry on with the experiment. If the subject was still reluctant to proceed, Milgram said that it was important for the sake of the experiment that the procedure be followed through to the end. His final argument was ‘you have no other choice. You must go on’. What Milgram was trying to discover was the number of teacher-subjects who would be willing to administer the highest levels of shock, even in the face of strong personal and moral revulsion against the rules and conditions of the experiment.D Prior to carrying out the experiment, Milgram explained his idea to a group of 39 psychiatrists and asked them to predict the average percentage of people in an ordinary population who would be willing to administer the highest shock level of 450 volts. The overwhelming consensus was that virtually all the teacher-subjects would refuse to obey the experimenter. The psychiatrists felt that ‘most subjects would not go beyond 150 volts’ and they further anticipated that only four per cent would go up to 300 volts. Furthermore, they thought that only a lunatic fringe of about one in 1,000 would give the highest shock of 450 volts.E What were the actual results? Well, over 60 per cent of the teacher-subjects continued to obey Milgram up to the 450-volt limit in repetitions of the experiment in other countries, the percentage of obedient teacher-subjects was even higher, reaching 85 per cent in one country. How can we possibly account for this vast discrepancy between what calm, rational, knowledgeable people predict in the comfort of their study and what pressured, flustered, but cooperative ‘teachers’ actually do in the laboratory of real life?F One’s first inclination might be to argue that there must be some sort of built-in animal aggression instinct that was activated by the experiment, and that Milgram’s teache-subjects were just following a genetic need to discharge this pent-up primal urge onto the pupil by administering the electrical shock. A modern hard-core sociobiologist might even go so far as to claim that this aggressive instinct evolved as an advantageous trait, having been of survival value to our ancestors in their struggle against the hardships of life on the plains and in the caves, ultimately finding its way into our genetic make-up as a remnant of our ancient animal ways.G An alternative to this notion of genetic programming is to see the teacher-subjects’ actions as a result of the social environment under which the experiment was carried out. As Milgram himself pointed out, ‘Most subjects in the experiment see their behaviour in a larger context that is benevolent and useful to society —the pursuit of scientific truth. The psychological laboratory has a strong claim to legitimacy and evokes trust and confidence in those who perform there. An action such as shocking a victim, which in isolation appears evil, acquires a completely different meaning when placed in this se tting.’H Thus, in this explanation the subject merges his unique personality and personal and moral code with that of larger institutional structures, surrendering individual properties like loyalty, self-sacrifice and discipline to the service of malevolent systems of authority.I Here we have two radically different explanations for why so many teacher-subjects were willing to forgo their sense of personal responsibility for the sake of an institutional authorityfigure. The problem for biologists, psychologists and anthropologists is to sort out which of these two polar explanations is more plausible. This, in essence, is the problem of modern sociobiology — to discover the degree to which hard-wired genetic programming dictates, or at least strongly biases, the interaction of animals and humans with their environment, that is, their behaviour. Put another way, sociobiology is concerned with elucidating the biological basis of all behaviour.Questions 14-19Reading Passage 2 has nine paragraphs, A-I.Which paragraph contains the following information?Write the correct letter A-I in boxes 14-19 on your answer sheet.14 a biological explanation of the teacher-subjects’ behaviour15 the explanation Milgram gave the teacher-subjects for the experiment16 the identity of the pupils17 the expected statistical outcome18 the general aim of sociobiological study19 the way Milgram persuaded the teacher-subjects to continueQuestions 20-22Choose the correct letter, A, B, C or D.Write your answers in boxes 20-22 on your answer sheet.20 The teacher-subjects were told that were testing whetherA a 450-volt shock was dangerous.B punishment helps learning.C the pupils were honest.D they were suited to teaching.21 The teacher-subjects were instructed toA stop when a pupil asked them to.B denounce pupils who made mistakes.C reduce the shock level after a correct answer.D give punishment according to a rule.22 Before the experiment took place the psychiatristsA believed that a shock of 150 volts was too dangerous.B failed to agree on how the teacher-subjects would respond to instructions.C underestimated the teacher-subjects’ willingness to comply with experimental procedure.D thought that many of the teacher-subjects would administer a shock of 450 volts.Questions 23-26Do the following statements agree with the information given in Reading Passage 2?In boxes 23-26 on your answer sheet, writeTRUE if the statement agrees with the informationFALSE if the statement contradicts the informationNOT GIVEN if there is no information on this23 Several of the subjects were psychology students at Yale University.24 Some people may believe that the teacher-subjects’ behaviour could be explained as a positive survival mechanism.25 In a sociological explanation, personal values are more powerful than authority.26 Milgram’s experiment solves an important question in sociobiology.READING PASSAGE 3You should spend about 20 minutes on Questions 27-40,which are based on Reading Passage 3 below.The Truth about the EnvironmentFor many environmentalists, the world seems to be getting worse. They have developed a hit-list of our main fears: that natural resources are running out; that the population is ever growing, leaving less and less to eat; that species are becoming extinct in vast numbers, and that the planet’s air and water are becoming ever more polluted.But a quick look at the facts shows a different picture. First, energy and other natural resources have become more abundant, not less so, since the book ‘The Limits to Growth’ was published in 1972 by a group of scientists. Second, more food is now produced per head of the world’s population than at any time in history. Fewer people are starving. Third, although species are indeed becoming extinct, only about 0.7% of them are expected to disappear in the next 50 years, not 25-50%, as has so often been predicted. And finally, most forms of environmental pollution either appear to have been exaggerated, or are transient —associated with the early phases of industrialisation and therefore best cured not by restricting economic growth, but by accelerating it. One form of pollution — the release of greenhouse gases that causes global warming — does appear to be a phenomenon that is going to extend well into our future, but its total impact is unlikely to pose a devastating problem. A bigger problem may well turn out to be an inappropriate response to it.Yet opinion polls suggest that many people nurture the belief that environmental standards are declining and four factors seem to cause this disjunction between perception and reality.One is the lopsidedness built into scientific research. Scientific funding goes mainly to areas with many problems. That may be wise policy, but it will also create an impression that many more potential problems exist than is the case.Secondly, environmental groups need to be noticed by the mass media. They also need to keep the money rolling in. Understandably, perhaps, they sometimes overstate their arguments. In 1997, for example, the World Wide Fund for Nature issued a press release entitled: ‘Two thirds of the world’s forests lost forever.’ The truth turns out to be nearer 20%.Though these groups are run overwhelmingly by selfless folk, they nevertheless share many of the characteristics of other lobby groups. That would matter less if people applied the same degree of scepticism to environmental lobbying as they do to lobby groups in other fields. A trade organisation arguing for, say, weaker pollution controls is instantly seen as self-interested. Yet a green organisation opposing such a weakening is seen as altruistic, even if an impartial view of the controls in question might suggest they are doing more harm than good.A third source of confusion is the attitude of the media. People are clearly more curious about bad news than good. Newspapers and broadcasters are there to provide what the public wants. That, however, can lead to significant distortions of perception. An example was America’s encounter with El Nino in 1997 and 1998. This climatic phenomenon was accused of wrecking tourism, causing allergies, melting the ski-slopes and causing 22 deaths. However, according to an article in the Bulletin of the American Meteorological Society, the damage it did was estimated at US$4 billion but the benefits amounted to some US$19 billion. These came from higher winter temperatures(which saved an estimated 850 lives, reduced heating costs and diminished spring floods caused by meltwaters).The fourth factor is poor individual perception. People worry that the endless rise in the amount of stuff everyone throws away will cause the world to run out of places to dispose of waste. Yet, even if America’s trash output continues to rise as it has done in the past, and even if the American population doubles by 2100, all the rubbish America produces through the entire 21st century will still take up only one-12,000th of the area of the entire United States.So what of global warming? As we know, carbon dioxide emissions are causing the planet to warm. The best estimates are that the temperatures will rise by 2-3℃ in this century, causing considerable problems, at a total cost of US$5,000 billion.Despite the intuition that something drastic needs to be done about such a costly problem, economic analyses clearly show it will be far more expensive to cut carbon dioxide emissions radically than to pay the costs of adaptation to the increased temperatures. A model by one of the main authors of the United Nations Climate Change Panel shows how an expected temperature increase of 2.1 degrees in 2100 would only be diminished to an increase of 1.9 degrees. Or to put it another way, the temperature increase that the planet would have experienced in 2094 would be postponed to 2100.So this does not prevent global warming, but merely buys the world six years. Yet the cost of reducing carbon dioxide emissions, for the United States alone, will be higher than the cost of solving the world’s single, most pressing health problem: providing universal access to clean drinking water and sanitation. Such measures would avoid 2 million deaths every year, andprevent half a billion people from becoming seriously ill.It is crucial that we look at the facts if we want to make the best possible decisions for the future. It may be costly to be overly optimistic — but more costly still to be too pessimistic.Questions 27-32Do the following statements agree with the claims of the writer in Reading Passage 3?In boxes 27-32 on your answer sheet, writeYES if the statement ag rees with the writer’s claimsNO if the statement contradicts the writer’s clamsNOT GIVEN if it is impossible to say what the writer thinks about this27 Environmentalists take a pessimistic view of the world fora number of reasons28 Data on the Earth’s natural resources has only been collected since 1972.29 The number of starving people in the world has increased in recent years.30 Extinct species are being replaced by new species.31 Some pollution problems have been correctly linked to industrialisation.32 It would be best to attempt to slow down economic growth.Questions 33-37Choose the correct letter, A, B, C or D.Write your answers in boxes 33-37 on your answer sheet.33 What aspect of scientific research does the writer express concern about in paragraph 4?A the need to produce resultsB the lack of financial supportC the selection of areas to researchD the desire to solve every research problem34 The writer quotes from the Worldwide Fund for Nature to illustrate howA influential the mass media can be.B effective environmental groups can be.C the mass media can help groups raise funds.D environmental groups can exaggerate their claims.34 What is the writer’s main point about lobby groups in paragraph 6?A Some are more active than others.B Some are better organised than others.C Some receive more criticism than others.D Some support more important issues than others.35 The writer suggests that newspapers print items that are intended toA educate readers.B meet their readers’ expec tations.C encourage feedback from readers.D mislead readers.36 What does the writer say about America’s waste problem?A It will increase in line with population growth.B It is not as important as we have been led to believe.C It has been reduced through public awareness of the issues.D It is only significant in certain areas of the country.Questions 38-40Complete the summary with the list of words A-I below.Write the correct letter A-I in boxes 38-40 on your answer sheet.GLOBAL WARMINGThe writer admits that global warming is a 38…………….challenge, but says that it will not have a catastrophic impact on our future, if we deal with it in the 39…………… way. If we try to reduce the levels of greenhouse gases, he believes that it would only have a minimal impact on rising temperatures. He feels it would be better to spend money on the more 40………… health problem of providing the world’s population with clean drinking water.A unrealisticB agreedC expensiveD rightE long-termF usualG surprisingH personalI urgent剑桥雅思阅读5原文参考译文(test1)TEST 1 PASSAGE 1参考译文：Johnson’s Dictionary约翰逊博士的字典For the century before Johnson’s Dictionary was published in 1775, there had been concern about the state of the English language. There was no standard way of speaking or writing and no agreement as to the best way of bringing some order to the chaos of English spelling. Dr Johnson provided the solution.约翰逊博士的《字典》于1775年出版，在此之前的一个世纪，人们一直对英语的发展状况担忧。

遗传学英语文献Genetics has been a field of study that has captivated the minds of scientists and laypeople alike for centuries. The intricacies of the genetic code and its influence on the development and behavior of living organisms have been the subject of extensive research and literature. In the realm of English literature, the topic of genetics has been explored in various forms, from scientific treatises to fictional narratives.One of the seminal works in the field of genetics is Charles Darwin's "On the Origin of Species," published in 1859. This groundbreaking publication laid the foundation for the theory of evolution through natural selection, which has had a profound impact on our understanding of genetics and the diversity of life on Earth. Darwin's work not only presented his scientific findings but also engaged in a broader philosophical discourse on the implications of his theory, sparking debates and conversations that continue to this day.Another notable contribution to the literature on genetics is the work of Gregor Mendel, an Augustinian friar whose experiments with peaplants in the mid-19th century laid the groundwork for our understanding of heredity. Mendel's laws of inheritance, which describe the patterns of genetic inheritance, have become a cornerstone of modern genetics. While Mendel's work was not widely recognized during his lifetime, it has since been celebrated as a pivotal moment in the history of science.In the realm of fiction, genetics has been a recurring theme, often used as a tool to explore the ethical and social implications of scientific advancements. One such example is Aldous Huxley's "Brave New World," published in 1932, which presents a dystopian future where human beings are genetically engineered and society is strictly controlled. Huxley's novel raises questions about the potential consequences of genetic manipulation and the impact it could have on individual autonomy and societal structures.Similarly, Mary Shelley's "Frankenstein," published in 1818, can be interpreted as an exploration of the ethical boundaries of scientific experimentation, particularly in the realm of creating life. The story of Victor Frankenstein's creation of a sentient being, and the subsequent consequences of his actions, has become a classic in the science fiction genre and continues to be analyzed and discussed in the context of genetics and the limits of scientific inquiry.In more recent years, the field of genetics has been further exploredin popular fiction, such as Michael Crichton's "Jurassic Park," which explores the potential of genetic engineering to resurrect extinct species. This novel, and the subsequent film adaptations, have captured the public's imagination and sparked discussions about the ethical and practical implications of such advancements.Beyond fiction, the field of genetics has also been the subject of various scientific texts and scholarly works, which have helped to advance our understanding of the genetic mechanisms that govern the development and function of living organisms. These works range from textbooks and research papers to more accessible popular science books, which aim to bridge the gap between the scientific community and the general public.One such example is James Watson and Francis Crick's "The Double Helix," a firsthand account of their groundbreaking discovery of the structure of DNA, which revolutionized our understanding of the genetic code. This book not only presents the scientific findings but also provides insights into the personalities and dynamics of the scientists involved in the research, offering a glimpse into the human side of scientific discovery.Another notable work in the field of genetics literature is "The Selfish Gene" by Richard Dawkins, published in 1976. This book presents a gene-centric view of evolution, which has had a significant impact onour understanding of the mechanisms of natural selection and the role of genetics in shaping the natural world. Dawkins' engaging writing style and thought-provoking ideas have made this book a classic in the field of evolutionary biology and genetics.In conclusion, the field of genetics has been the subject of a rich and diverse body of English literature, spanning from scientific treatisesto imaginative works of fiction. These literary contributions have not only advanced our understanding of the genetic mechanisms that govern living organisms but have also explored the ethical, social, and philosophical implications of our growing knowledge in this field. As the field of genetics continues to evolve, it is likely that we will see new and innovative perspectives emerge in the literature, further enriching our understanding of this captivating and ever-expanding area of study.。

ESCAPING NASH INFLATIONIN-KOO CHO,NOAH WILLIAMS,AND THOMAS J.SARGENTA BSTRACT.Mean dynamics describe the convergence to self-confirming equilibria of self-referential systems under discounted least squares learning.Escape dynamics recurrentlypropel away from a self-confirming equilibrium.In a model with a unique self-confirmingequilibrium,the escape dynamics make the government discover too strong a version ofthe natural rate hypothesis.The escape route dynamics cause recurrent outcomes close tothe Ramsey(commitment)inflation rate in a model with an adaptive government.Key Words:Self-confirming equilibrium,mean dynamics,escape route,large deviation,natural rate of unemployment,adaptation,experimenta-tion trap.‘If an unlikely event occurs,it is very likely to occur in the most likely way.’Michael Harrison1.I NTRODUCTIONBuilding on work by Sims(1988)and Chung(1990),Sargent(1999)showed how a government adaptivelyfitting an approximating Phillips curve model recurrently sets inflation near the optimal time-inconsistent ouctome,although later inflation creeps back to the time-consistent suboptimal outcome of Kydland and Prescott(1977).The good outcomes emerge when the government temporarily learns the natural rate hypothe-sis.The temporary escapes from the time-consistent outcome symptomize a remarkable type of escape dynamics that promote experimentation and that are induced by unusual shock patterns that interact with the government’s adaptive algorithm and its imperfect model.The escapes lead to dramatic changes in the government’s inflation policy as it temporarily overcomes its inflationary bias.Some simulated time paths of inflation for different specifications of the model are shown in Figure1.Inflation starts and remains near the high time-consistent value for a while,is rapidly cut to zero,but then gradually2IN-KOO CHO,NOAH WILLIAMS,AND THOMAS J.SARGENTF IGURE ofthe model.approaches the time-consistent high value again.This paper explains the dynamic forces that drive these outcomes.Escape dynamics from self-confirming equilibria can occur in a variety of models with large agents who use adaptive algorithms to estimate approximating models.1For con-creteness,this paper focuses on the Phillips curve model studied by Sargent(1999).The model has the following features:(1)the monetary authority controls the inflation rate, apart from a random disturbance;(2)the true data generating mechanism embodies a version of the natural rate hypothesis in an expectational Phillips curve;(3)as in Kydland and Prescott(1977),a purposeful government dislikes inflation and unemployment and a private sector forecasts inflation optimally;but(4)the monetary policy makers don’t know the true data generating mechanism and instead use a goodfitting approximating model.The fundamentals in the economy arefixed,including the true data generating mechanism,preferences,and agents’methods for constructing behavior rules.Changes in the government’s beliefs about the Phillips curve,and how it approximates the natural rate hypothesis,drive the inflation rate.Inspired by econometric work about approximat-ing models by Sims(1972)and White(1982),we endow the monetary authority,not with the correct model,but with an approximating model that it nevertheless estimates with good econometric procedures.We use the concept of a self-confirming equilibrium,a natural equilibrium concept for behavior induced by an approximating model.2In a self-confirming equilibrium,beliefs are correct about events that occur with positive probability in equilibrium.The approxi-mating model is‘wrong’only in its description of events that occur with zero probability in equilibrium.Among the objects determined by a self-confirming equilibrium are theESCAPING NASH INFLATION3 parameters of the government’s approximating model.While the self-confirming equi-librium concept differs formally from a Nash(or time consistent)equilibrium,3it turns out that the self-confirming equilibrium outcomes are the time-consistent ones.Thus,the suboptimal time consistent outcome continues to be our benchmark.Like a Nash equilibrium,a self-confirming equilibrium restricts population objects (mathematical expectations,not sample means).We add adaptation by requiring the government to estimate its model from historical data in real time.We form an adap-tive model by having the monetary authority adjust its behavior rule in light of the latest model estimates.Thus,we attribute‘anticipated utility’behavior(see Kreps(1998))to the monetary authority.Following Sims(1988),we study a‘constant gain’estimation al-gorithm that discounts past observations.Called a‘tracking algorithm’,it is useful when parameter drift is suspected(see e.g.Marcet and Nicolini(1997)).Results from the literature on least squares learning(e.g.,Marcet and Sargent(1989a), Woodford(1990),Evans and Honkapohja(1998))apply and take us part way,but only part way,to our goal of characterizing the dynamics of the adaptive system.That litera-ture shows how the limiting behavior of systems with least squares learning is described by an ordinary differential equation called the‘mean dynamics’.They describe the(un-conditionally)average path of the government’s beliefs,in a sense that we shall describe precisely.For our model,the mean dynamics converge to the self-confirming equilibrium and the time consistent outcome.Thus,the mean dynamics do not account for the recur-rent stabilizations in the simulations of Sims(1988),Chung(1990),and Sargent(1999). We show that these stabilizations are governed by another deterministic component of the dynamics,described by another ODE,the‘escape’dynamics.They point away from the self-confirming equilibrium and toward the Ramsey(or optimal-under-commitment) equilibrium outcome.So two sorts of dynamics dominate the behavior of the adaptive system.(1)The mean dynamics come from an unconditional moment condition,the least squaresnormal equations.These dynamics drive the system toward a self-confirmingequilibrium.4(2)The escape route dynamics propel the system away from a self-confirming equilib-rium.They emerge from the same least squares moment conditions,but they areconditioned on a particular“most likely”unusual event,defined in terms of the disturbance sequence.This most likely unusual event is endogenous.The escape route dynamics have a compelling behavioral interpretation.Within the confines of its approximate model,learning the natural rate hypothesis requires that the government generate a sufficiently wide range of inflation experiments.To learn even an imperfect version of the natural rate hypothesis,the government must experiment more than it does within a self-confirming equilibrium.The government is caught in an experimentation trap.The adaptive algorithm occasionally puts enough movement into the government’s beliefs to produce informative experiments.4IN-KOO CHO,NOAH WILLIAMS,AND THOMAS J.SARGENT1.1.Related literature.Evans and Honkapohja(1993)investigated a model with mul-tiple self-confirming equilibria having different rates of inflation.When agents learn through a recursive least squares algorithm,outcomes converge to a self-confirming equi-librium that is stable under the learning algorithm.When agents use afixed gain algo-rithm,Evans and Honkapohja(1993)demonstrated that the outcome oscillates among different locally stable self-confirming equilibria.They suggested that such a model can explain widefluctuations of market outcomes in response to small shocks.In models like Evans and Honkapohja(1993)and Kasa(1999),the time spent in a neighborhood of a locally stable equilibrium and the escape path from its basin of at-traction are determined by a large deviation property of the recursive algorithm.As the stochastic perturbation disappears,the outcome stays in a neighborhood of a particular locally stable self-confirming equilibrium(exponentially)longer than the others.This observation provided Kandori,Mailath,and Rob(1993)and Young(1993)with a wayto select a unique equilibrium in evolutionary models with multiple locally stable Nash equilibria.An important difference from the preceding literature is that our model has a unique self-confirming equilibrium.Despite that,the dynamics of the model resemble those for models with multiple equilibria such as Evans and Honkapohja(1993).With multiple locally stable equilibria,outcomes escape from the basin of attraction of a locally stable outcome to the neighborhood of another locally stable equilibrium.The fact that our model has a globally unique stable equilibrium creates an additional challenge for us, namely,to characterize the most likely direction of the escape from a neighborhood of the unique self-confirming equilibrium.As we shall see,the most likely direction entails the government’s learning a good,but not self-confirming,approximation to the natural rate hypothesis.anization.Section2describes the model in detail.Section3defines a self-confirming equilibrium.Section4describes a minimal modification of a self-confirming equilibrium formed by giving the government an adaptive algorithm for its beliefs.Section5uses re-sults from the theory of large deviations to characterize convergence to and escape froma self-confirming equilibrium.Section6shows that numerical simulations of escape dy-namics,like those in Sargent(1999),are well described by the numerically calculated theoretical escape paths.For the purpose of giving intuition about the escape dynamics, Section7specializes the shocks to be binomial,then adduces a transformed measure of the shocks that tells how particular endogenously determined unusual shock sequences drive the escape dynamics.Section8concludes.The remainder of this introduction de-scribes the formal structure of the model andfindings of the paper.1.3.Overview.The government’s beliefs about the economy are described by a vector of regression coefficients.It chooses a decision rule that makes the stochastic process for the economy be.But for the stochastic process,the bestfitting model ofthe economy has coefficients.A self-confirming equilibrium is afixed point of .The orthogonality conditions pinning down the bestfitting model can be expressed (1.1)ESCAPING NASH INFLATION5 We shall show thatwhereA self-confirming equilibrium is a set of population regression coefficients.We form an adaptive model by slightly modifying a self-confirming equilibrium.Rather than usingpopulation moments tofit its regression model,the government uses discounted leastsquares estimates from historical samples.We study how the resulting adaptive systemconverges to or diverges from a self-confirming equilibrium.Each period the govern-ment uses the most recent data to update a least squares estimate of its model co-efficients,then sets its policy according to.This is what Kreps(1998)calls an anticipated utility model.The literature on least squares learning in self-referential sys-tems(see Marcet and Sargent(1989a),Marcet and Sargent(1989b),Woodford(1990),andEvans and Honkapohja(2000))give conditions under which the limiting behavior of thegovernment’s beliefs are nearly deterministic and approximated by the following ordi-nary differential equation(ODE)is governed by the uniqueness and stability of the stationary points of the ODE.Our model has a unique self-confirming equilibrium.It supports the high inflationtime-consistent outcome of Kydland and Prescott(1977).The ODE(1.3),(1.4),is veryinformative about the behavior of our adaptive model.It is globally stable about theself-confirming equilibrium,and describes how the adaptive system is gradually drawnto the self-confirming equilibrium.But to understand how the sample paths recurrentlyvisit the better low-inflation outcome,we need more than the ODE(1.3,1.4).Until our work,such‘escape dynamics’had not been characterized analytically.Thispaper shows that they are governed by the ODE6IN-KOO CHO,NOAH WILLIAMS,AND THOMAS J.SARGENTrate hypothesis.Thus,like the mean dynamics,the escape dynamics are deterministic. We verify that these deterministic dynamics do a good job of describing the simulations. As Sims(1988)and Sargent(1999)emphasize,the evolution of beliefs during an es-cape is economically interesting because then the government discovers a good enough approximate version of the natural rate hypothesis to cause it to pursue superior policy that is supported by beliefs that are‘wrong’in the sense that they are not a self-confirming equilibrium.Nevertheless,in another sense those beliefs are more‘correct’than those in a self-confirming equilibrium because they inspire the government to leave the‘experi-mentation trap’that confines it within a self-confirming equilibrium.2.S ETUPTime is discrete and indexed by.Let be an i.i.d.sequence of random vectors with mean zero and covariance matrix.Let,respectively,be the unemployment rate,the rate of inflation,the public’s expected rate of inflation,and the systematic part of inflation determined by government policy.The government sets ,the public sets,then nature chooses shocks that determine and.The economy is described by the following version of a model of Kydland and Prescott(1977):(2.8)(2.9)(2.10)(2.11)where(2.12)Equation(2.8)is a natural rate Phillips curve;(2.9)says that the government sets infla-tion up to a random term;(2.10)imposes rational expectations for the public;(2.11)is the government’s decision rule for setting the systematic part of inflation.The de-cision rule is a function of the government’s beliefs about the economy,which are parameterized by a vector.For some purposes below we consider the simpler model in which the government only estimates a static regression of unemployment on inflation and a constant(i.e. ).We call this the static model.Since there is no temporal dependence in(2.8),(2.9),all of the temporal dependence in the model comes through the government’s beliefs.Under the static model specification,the government’s control rule can be calculated explicitly, allowing some of our characterizations to be sharper.2.1.The government’s beliefs and control problem.The government’s model of the economy is a linear Phillips curve(2.13)where the government treats as a mean zero,serially uncorrelated random term beyond its control.We shall eventually restrict,but temporarily regard it as arbitrary.TheESCAPING NASH INFLATION7 government’s decision rule(2.11)solves the problem:(2.14)where denotes the expectations operator induced by(2.13)and the minimization is subject to(2.13)and(2.9).We call problem(2.14)the Phelps problem.Versions of it were studied by Phelps(1967), Kydland and Prescott(1977),Barro and Gordon(1983),and Sargent(1999).We identify three salient outcomes associated with different hypothetical government’s beliefs: Belief1.If,then the Phelps problem tells the government to set for all.This is the Nash outcome of Sargent(1999),i.e.,the time-consistent outcome of Kydland and Prescott(1977).Belief2.If,for any,the government setsfor all.This is the Ramsey outcome,i.e.,the optimal time-inconsistent outcome of Kydland and Prescott(1977).Belief3.If the coefficients on current and lagged’s sum to zero,then asfrom below,the Phelps problem eventually sends arbitrarily close to.Under the actual probability distribution generated by(2.8),(2.9),(2.10),the value of the government’s objective function(2.14)is larger under the outcome than under outcome.Under Belief1,the government perceives a trade-off between in-flation and unemployment and sets inflation above zero to exploit that trade-off.Under Belief2,the government perceives no trade-off,sets inflation at zero,and accepts what-ever unemployment emerges.Under Belief3,the government thinks that although there is a short-term trade-off between inflation and unemployment when,there is no ‘long-term’trade-off.Through the workings of an‘induction hypothesis’that opens an apparent avenue by which the government can manipulate the current position of the Phillips curve(see Cho and Matsui(1995)and Sargent(1999)),the Phelps problem tells the government eventually to set inflation close to zero when is close to.In a common-knowledge model in which(2.13)is dropped and replaced by the as-sumption that the government knows the model,the outcome emerges as what Stokey(1989)and Sargent(1999)call the Nash outcome,and emerges as the Ram-sey outcome.In the common-knowledge model,these varying outcomes reflect different timing protocols and characterize a time-consistency problem analyzed by Kydland and Prescott.The mapping from government beliefs to outcomes is interesting only when the gov-ernment’s beliefs might be free.Our equilibrium concept,a self-confirming equilibrium, restricts those beliefs,and thereby narrows the outcomes relative to those enumerated above.However,the mapping from beliefs to outcomes play a role during escapes from self-confirming equilibria.8IN-KOO CHO,NOAH WILLIAMS,AND THOMAS J.SARGENT3.S ELF-CONFIRMING EQUILIBRIUM3.1.Restrictions on government’s beliefs.Define and(3.15)Let denote the history of the joint shock process up to.Evidently,from(2.8),(2.9),(2.10),(2.11),and therefore the process are both functions of:(3.16)Definition3.1.A self-confirming equilibrium is a that satisfies(3.17)The expectation in(3.17)is taken with respect to the probability distribution generated by(2.8),(2.9),(2.10),(2.11).Notice that is the time value of the object set to zero by the following least squares orthogonality condition:(3.18)Equations(3.18)are the orthogonality conditions that make in(2.13)a least-squares regression.Condition(3.17)thus renders the government’s beliefs consistent with the data.Condition(3.17)can be interpreted as asserting that is afixed point in a mapping from the government’s beliefs about the Phillips curve to the actual Phillips curve.Thus, let(3.19)and.Then notice that(3.20)(3.22)Given a government model in the form of a perceived regression coefficient vector and the associated government best response function,is the actual least squares regression coefficient induced by.Thus,maps government model to a bestfitting model.Equation(3.22)shows that(3.17)asserts that,so thatESCAPING NASH INFLATION9 the government’s model is the bestfitting model.See Marcet and Sargent(1989a)for a discussion of the operator in a related class of models.Elementary calculations show that there is a unique self-confirming equilibrium.It cor-responds to the beliefs(1)mentioned above.These beliefs support the Nash equilibrium outcome in the sense of Stokey(1989)and Sargent(1999).4.A DAPTATION4.1.Discounted least squares updating of.We modify the model now to consist of (2.8),(2.9),(2.10)as before,but replace(2.11)with(4.23)where remains the best-response function generated by the Phelps problem,and is the government’s time estimate of the empirical Phillips curve.The government estimates by the following recursive least squares algorithm:(4.24)(4.25)where is a gain parameter that determines the weight placed on current observations relative to the past.In this paper we consider the case in which the gain is constant.We want to study the behavior of system formed by(2.8),(2.9),(2.10),(4.23),(4.24)and(4.25).4.2.Mean dynamics.Wefind thefirst important component of dynamics by adapting the stochastic approximation methods used by Woodford(1990),Marcet and Sargent (1989a),and Evans and Honkapohja(2000).We call this component the mean dynamics because it governs the(unconditionally)expected evolution of the government’s beliefs. While previous applications of stochastic approximation results in economics have gener-ally considered recursive least squares with decreasing gain,we consider the case where the gain is constant.5Broadly similar results obtain in the constant and decreasing gain cases,but there are important differences in the asymptotics and the sense of convergence that we discuss below.To present convergence proofs,it helps to group together the components of the gov-ernment’s beliefs into a single vector.Define(4.26)Then the updating equations(4.24),(4.25)can be written(4.27)Now break the“update part”into its expected and random components.Defineis the mean of defined as(4.28)5See Evans and Honkapohja(2000)for extensive discussion of constant gain algorithms.10IN-KOO CHO,NOAH WILLIAMS,AND THOMAS J.SARGENTwhere(4.29)Then we can write the composite dynamics as(4.30))over time.As in the decreasing gain case,we can show that the asymptotic behavior of(4.30)is governed by an ODE,but the estimates converge in a weaker sense.Specifically,decreas-ing gain algorithms typically converge with probability one along a sequence of iterations as,but constant gain algorithms converge weakly(or in distribution)as across sequences of iterations,each of which is indexed by the gain.Note that we can rewrite(4.30)as(4.31)This equation resembles afinite-difference approximation of a derivative with time step ,but is perturbed by a noise term.The convergence argument defines a continuous time scale as,and interpolates between the discrete iterations to get a continuous process.Then by letting,the approximation error in thefinite difference goes to zero,and a weak law of large numbers insures that the noise term becomes negligible. We are left with the ODE:(4.33)We need the following set of assumptions.For reference,we also list the original num-ber in Kushner and Yin(1997).To emphasize the asymptotics,we include the superscript on the parameters denoting the gain setting.Assumptions A.A8.5.0:The random sequence is tight.6A8.5.1:For each compact set is uniformly integrable.7A8.5.3:For each compact set the sequence6A random sequence is tight if7A random sequence is uniformly integrable ifA8.5.4a:The ODE that is asymptotically stable.8A8.1.6:The functionthat is the self-confirming equilibrium,the estimate sequence converges weakly to the self-confirming equilibrium.Therefore,with high probability,as and we would expect the government’s beliefs to be near their self-confirming values,and the economy to be near the Nash outcome.However,in the next section we shall see that the beliefs can recur-rently escape the self-confirming equilibrium.Although the impact of noise terms goes to zero with the gain,for a given,“rare”sequences of shocks can have a large impact on the estimates and the economy.5.E SCAPEIn this section we determine the most likely rare events and how they push the gov-ernment’s beliefs away from a self-confirming equilibrium.To this end,wefirst present some general results from the theory of large deviations,a general method for analyzing small probability events.We then present results from Williams(2000),who applies these general results analytically to characterize the escape dynamics.5.1.Escape dynamics as a control problem.Throughout,we will only be interested in characterizing the escape problem for the Phillips curve coefficients.This motivates the following definition.Definition5.1.An escape path is a sequence of estimates that leave a set containing the limit pointfor someFollowing a convention in the large deviation literature,we set the initial point of an escape path to be the stable point,let be the set of all escape paths.For each,define8A point as and for each there exists an such that if for allDefinition5.2.Let be the(first)exit time associated with escape path. An absolutely continuous trajectory is a dominant escape path ifwill occur along with very high probability,if an escape ever occurs.To analyze the escape dynamics,we adapt the general results of Dupuis and Kushner (1989),which are themselves extensions of the theory of Freidlin and Wentzell(1984) for stochastic approximation models.After presenting some general results,we apply results of Williams(2000),who obtains explicit solutions of the escape dynamics that can be used to interpret the simulations calculated earlier by Sims(1988),Chung(1990),and Sargent(1999).Given the recursive formula(4.30),define the-functional as(5.35),and with the evolution of following the mean dynamics conditional on .(We let for trajectories that are not absolutely continuous.)In the context of continuous time diffusions,Freidlin and Wentzell(1984)characterized the dominant escape path as a solution of a variational problem.Their results have been extended to discrete time stochastic approximation models by Dupuis and Kushner(1985)and Dupuis and Kushner(1989).We adapt these results in the following theorem,whose main object is the solution of the following variational problem:(5.38)for someThe minimized value(1)Suppose that the shocks are i.i.d.and unbounded but that there exists a algebraand constants such that for all anda.s.Then we have:for some(2)If the shocks are i.i.d.and bounded,andbe the terminal point of the dominant escape path.Then for any and:.The next three parts establish stronger results under the assumption that the errors are bounded.Part(2)shows that under bounded errors,the asymptotic inequality in part(1)becomes an asymptotic equality. Part(3)shows that for small the time it takes beliefs to escape the self-confirming equi-librium becomes close to.It is known(see Benveniste,Metivier,and Priouret(1990)for example)that the asymptotic distribution of Markov processes can be characterized by the Poisson equa-tion,so it is natural that it appears here.This analysis then leads to a representation of the-functional as a quadratic form in,with a normalizing matrix that depends on the solution of the Poisson equation associated with.In general the solution of the Poisson equation can itself be a difficult problem,as it involves solving a functional equation.However in the important linear-quadratic-Gaussian case(which includes our model),the problem can be solved in the space of quadratic functions,and therefore the Poisson equation reduces to a matrix Lyapunov equation.This provides a tremendous simplification,as there are efficient numerical methods for solving Lyapunov equations. We summarize these arguments in the following theorem and remark.Theorem5.4.Suppose that Assumptions A hold,that follows a stationary functional au-toregression with a unique stationary distribution and Lipschitz continuous mean and variance functions,and that the function is Lipschitz continuous in.Then there is a matrix-valued function such that the dominant escape path and rate function can be determined by solving the following variational problem:(5.39)subject to(5.41)(5.42)for someProof.See Williams(2000).Remark5.5.In our model,follows a linear autoregression,the are i.i.d.normal,and is a quadratic function of.Then is a fourth moment matrix that can be calculated explicitly by solving matrix Lyapunov equations described in Appendix C.This theorem provides a clearer interpretation and analysis of the variational problem. The escape dynamics perturb the mean dynamics by a forcing sequence.Then is a quadratic cost function that measures the magnitude of the perturbations during the episode of an escape.In particular,we can think of(5.39)as a least squares problem, where plays the role of a covariance matrix.If we had then the beliefs adhere to the mean dynamics,and the cost would be zero.For the beliefs to escape from.Tofind the dominant escape path,we solve the control problem in(5.39).We form the Hamiltonian with co-states for the evolution of:It is easy to verify that the Hamiltonian is convex,so thefirst order conditions are nec-essary and sufficient.Taking thefirst order conditions,we see that the dominant escape path is characterized by the following set of differential equations:The path that achieves the minimum is the dominant escape path.This path characterizes the evolution of the parameters on the most likely path away from the stable point.The minimized value.There is a unique self-confirming equilibrium,depicted in Figure2.It has.To solve the problem numerically,it helps to recast the boundary value problem as an initial value problem.In the ODE system(5.43)and boundaries(5.42),the only com-ponents left undetermined are the initial conditions for the co-states.We can solve the problem by minimizing over these initial conditions,and determine the escape times and。

Agar and broth dilution methods to determine the minimal inhibitory concentration (MIC)of antimicrobial substancesIrith Wiegand,Kai Hilpert &Robert E W HancockCentre for Microbial Diseases and Immunity Research,University of British Columbia,2259Lower Mall Research Station,Vancouver,British Columbia,V6T 1Z4,Canada.Correspondence should be addressed to R.E.W.H.(bob@cmdr.ubc.ca).Published online 17January 2008;doi:10.1038/nprot.2007.521The aim of broth and agar dilution methods is to determine the lowest concentration of the assayed antimicrobial agent (minimal inhibitory concentration,MIC)that,under defined test conditions,inhibits the visible growth of the bacterium being investigated.MIC values are used to determine susceptibilities of bacteria to drugs and also to evaluate the activity of new antimicrobial agents.Agar dilution involves the incorporation of different concentrations of the antimicrobial substance into a nutrient agar medium followed by the application of a standardized number of cells to the surface of the agar plate.For broth dilution,often determined in 96-well microtiter plate format,bacteria are inoculated into a liquid growth medium in the presence of different concentrations of an antimicrobial agent.Growth is assessed after incubation for a defined period of time (16–20h)and the MIC value is read.This protocol applies only to aerobic bacteria and can be completed in 3d.INTRODUCTIONAgar dilution and broth dilution are the most commonly used techniques to determine the minimal inhibitory concentration (MIC)of antimicrobial agents,including antibiotics and other substances that kill (bactericidal activity)or inhibit the growth (bacteriostatic activity)of bacteria.The methods described here are targeted for testing susceptibility to antibiotic agents as opposed to other antimicrobial biocides such as preservatives and disinfectants.However,there are no major reasons why they cannot be used for these other antimicrobials.For agar dilution,solutions with defined numbers of bacterial cells are spotted directly onto the nutrient agar plates that have incorporated different antibiotic concentrations.After incubation,the presence of bacterial colonies on the plates indicates growth of the organism.Broth dilution uses liquid growth medium containing geometrically increasing concentrations (typi-cally a twofold dilution series)of the antimicrobial agent,which is inoculated with a defined number of bacterial cells.The final volume of the test defines whether the method is termed macro-dilution,when using a total volume of 2ml,or microdilution,if performed in microtiter plates using r 500m l per well.After incubation,the presence of turbidity or a sediment indicates growth of the organism.In both the agar and the broth dilution approaches,the MIC is defined as the lowest concentration (in mg l À1)of the antimicrobial agent that prevents visible growth of a microorganism under defined conditions.In clinical practice,this in vitro parameter is used to classify the tested microorganism as either clinically susceptible,intermediate or resistant to the tested drug.The interpretative standards for these classifications are published by different national organi-zations such as the Clinical and Laboratory Standards Institute (CLSI)1in the USA and the European Committee on Antimicrobial Susceptibility T esting (EUCAST)2.Breakpoints (the particular MIC that differentiates susceptible,and assumingly treatable,from resistant and assumingly untreatable organisms)are derived from microbiological and clinical experience,and can vary according to the particular species being examined and the particularantimicrobial agent.Features that define these breakpoints are MIC distributions of relevant species,pharmacodynamics and pharmacokinetics of the antimicrobial agent,and clinical outcome data.Resistance (above the breakpoint)is associated with a high likelihood of therapeutic failure,whereas susceptibility is associated with a greater probability of therapeutic success.For isolates classified as intermediate,the therapeutic effect is uncertain 3.MIC determinations can be used for monitoring the develop-ment of antibiotic drug resistance.MIC wild-type distribution databases are available for relevant species–drug combinations ().The highest MIC of the wild-type popu-lation is defined as the ‘epidemiological cut-off value’or wild-type (WT)cut-off value 3(Fig.1).Organisms with acquired resistance can be easily identified by showing higher MIC values than the epidemiological cut-off value.As even slight changes may become clinically relevant,the determination of MIC is a valuable means for resistance surveillance,as well as providing a valuable comparatorp u o r G g n i h s i l b u P e r u t a N 8002©n a t u r e p r o t o c o l s/m o c .e r u t a n .w w w //:p t thN u m b e r o f t e s t e d i s o l a t e sFigure 1|Distribution of MIC values for different isolates for given species (modified from Wiegand and Wiedemann 27).NATURE PROTOCOLS |VOL.3NO.2|2008|163for variants of a given antimicrobial agent and/or species with differential susceptibility.Indeed for new drug candidates,the MIC determination is one of the first steps to evaluate the antimicrobial potential.Specialized protocols can also allow inferences to be drawn regarding resistance mechanisms.For example,results from broth dilution MIC determination with certain b -lactam antibiotics (cefotaxime,cefpodoxime and/or ceftazidime)in the presence or absence of an inhibitor (clavulanic acid)can indicate the produc-tion of extended-spectrum b -lactamases when MICs are at least three twofold concentration steps lower in the presence of the b -lactamase inhibitor 1.Epidemiological resistance data further-more provide the basis for appropriate first-line therapy recom-mendations for empirical treatment.Dilution methods are considered as reference methods for in vitro susceptibility testing and are also used to evaluate the performance of other methods of susceptibility testing.Crucial parametersAs the test results vary widely under different test conditions,the procedures have to be standardized for intra-and inter-laboratory reproducibility.The protocols described here are adjusted to a step-by-step format and follow the guidelines of the two established organizations and committees,the CLSI 1and EUCAST 2.Modifica-tions are introduced for testing the susceptibility to cationic antimicrobial peptides and other cationic agents that tend to bind to surfaces.If implemented rigorously according to the procedures described herein,these modifications allow the generation of reliable data that will be comparable between different laboratories.The use of all methods of this protocol is limited to aerobic bacteria that grow well within 24h in the CLSI and EUCAST recommended test Mueller–Hinton growth medium.Mueller–Hinton broth (MHB)is a general purpose medium that can be used for cultivation of a wide variety of nonfastidious microorgan-isms.For growth of fastidious organisms,such as Streptococcus spp.,Haemophilus influenzae ,Neisseria gonorrheae ,Helicobacter pylori and Campylobacter spp.,the broth needs to be supplemented;furthermore,enrichment of the incubation atmosphere with CO 2and an extension of the incubation time may be necessary for growth.For these species,specific recommendations for medium composition and for test conditions can be found in the CLSI guidelines 1.MediumT o produce accurate and reproducible results,a number of addi-tional requirements must be fulfilled by the test medium for certain antibiotics or antibiotic/species combinations:Correct susceptibility testing of tetracyclines 4,5,daptomycin for gram-positive bacteria 6and aminoglycosides for Pseudomonas aeruginosa 5in broth medium is dependent on the content of Ca 2+and Mg 2+ions.Non-cation-adjusted (unsupplemented)MHB contains in general inadequate amounts of Ca 2+and Mg 2+ions (information given by manufacturer).The broth,therefore,needs to be supplemented with divalent cations when testing the abovementioned antibiotics and/or antibiotic-species combina-tions.The final concentration should be 20–25mg Ca 2+and 10–12.5mg Mg 2+per liter 1,which reflects the divalent cation concentration in blood.Cation-adjusted MHB is commerciallyavailable and only needs to be further supplemented with Ca 2+in case of daptomycin susceptibility testing,as the recommended calcium concentration for testing this antibiotic is 50mg l À1(ref.1).Please note however that cation-adjusted MHB should not be used when testing the activity of cationic antimicrobial peptides,as the presence of Ca 2+and Mg 2+ions causes a substantial inhibition of the cationic peptides’activity 7,8.Mueller–Hinton agar (MHA)needs to be supplemented with 2%(wt/vol)sodium chloride for testing susceptibility of Staphylococcus aureus to methicillin,oxacillin and nafcillin 1.Methicillin-resistant S.aureus (MRSA)are often heteroresistant with resistant and susceptible cells in the same culture and supplementation with NaCl enhances the expression of hetero-geneous resistance 9.T o avoid the adsorption of dalbavancin to plastic surfaces,the addition of polysorbate 80to broth at a final concentration of 0.002%(vol/vol)is recommended.Refer to the CLSI guidelines 1when testing this antibiotic.High levels of thymidine and thymine interfere with suscept-ibility testing of sulfonamides and trimethoprim 10.Contrary to the Difco MHB (not cation-adjusted),the BBL MHB (not cation-adjusted)is not explicitly formulated to have a low thymine and thymidine content.So,according to the manufac-turer,only the former may be used for broth dilution antimi-crobial susceptibility testing.Tigecycline is prone to oxidation,and it seems that its activity is affected by the amount of dissolved oxygen in the medium,which increases with the age of the broth.So,for broth dilution MIC tests with tigecycline,it is necessary to use fresh cation-adjusted MHB (o 12h after autoclaving)11.BacteriaThe bacteria subjected to antimicrobial susceptibility testing must be isolated in pure culture and should have been identified at the genus and species level.Most organisms are available from hospital laboratories,the American Type Culture Collection or other national collections (see Table 1).InoculumThe standardization of the bacterial cell number used for suscept-ibility testing is of critical importance for obtaining accurate and reproducible results.The recommended final inoculum size for broth dilution is 5Â105colony-forming units (cfu)ml À1;thep u o r G g n i h s i l b u P e r u t a N 8002©n a t u r e p r o t o c o l s/m o c .e r u t a n .w w w //:p t t h TABLE 1|Control organisms for antimicrobial susceptibility testing.Identical to ATCC strain Escherichia coli ATCC 25922NCTC 12241,CIP 76.24,DSM 1103Pseudomonas aeruginosa ATCC 27853NCTC 12934,CIP 76.110,DSM 1117Staphylococcus aureus ATCC 29213NCTC 12973,CIP 103429,DSM 2569Enterococcus faecalis ATCC 29212NCTC 12697,CIP 103214,DSM 2570ATCC,American Type Culture Collection,P.O.Box 1549,Manassas,VA 20108,USA;NTCT,NationalCollection of Type Cultures,Health Protection Agency,61Colindale Avenue,London NW95EQ,UK;CIP,Collection de l’Institut Pasteur,25–28Rue de Docteur Roux,75724Paris Cedex 15,France;DSMZ,Deutsche Sammlung von Mikroorganismen und Zellkulturen,Inhoffenstra e 7B,38124Braunschweig,Germany.164|VOL.3NO.2|2008|NATURE PROTOCOLSappropriate cell number in agar dilution experiments is set at 104cfu per spot.Higher inocula can lead to an increase in the MIC particularly if the tested bacterium produces an enzyme capable of destroying the antibiotic.An inoculum effect (e.g.,an eightfold or greater MIC increase upon testing with a 100-fold higher inoculum than recommended)is frequently seen when testing b -lactam suscept-ibility for isolates that produce b -lactamases that are able to inactivate b -lactam antibiotics 12.Lighter inocula than recom-mended may give artificially lower e of inocula with o 5Â105cfu ml À1in broth microdilution can lead to false-susceptible results as described for the detection of methicillin resistance in S.aureus 13and for resistance to certain b -lactams in b -lactamase overproducing Klebsiella oxytoca isolates 14.A fresh pure culture should be used for the preparation of the inoculum.T o avoid the selection of an atypical variant clone,bacteria from four to five normal-appearing colonies are taken to prepare a bacterial suspension with a density equivalent to 108cfu ml À1,which is later used for inoculation.Several options are available for the generation of the bacterial suspension (direct colony suspension into liquid and growth methods using either fresh or overnight cultures).The density of the cell suspension can be assessed spectrophotometri-cally for testing a small number of different bacterial isolates (n o 5).For a larger number of different bacterial isolates,to save time,a turbidity standard can be used as a visual parison between the standards and the turbidity of the bacterial suspensions will in fact point the researcher toward the appropriate dilution for the suspension.The turbidity of a so-called McFarland 0.5standard is equal to 1–2Â108cfu ml À1.McFarland 0.5turbidity standards are commercially available from several manufacturers (e.g.,bioMerieux,cat.no.70900or Scientific Device Laboratory).Alternatively,a BaSO 4turbidity standard equaling the McFarland 0.5standard can be prepared as described below.Once the bacterial suspension is adjusted,it must be used within 30min to avoid changes in the cell number 2.All protocols described here contain a paragraph on how to determine whether the correct inoculum density was used for the susceptibility testing.If the MIC tests are carried out in a laboratory on a routine basis,the cell counts of the inoculum need to be determined only periodically.For all other users,we recommend validating the accuracy of procedures for every test.Quality controlT o verify that the susceptibility results are accurate,it is necessary to include at least one control organism with every batch of MIC determinations.Control organisms are available from different strain collections (Table 1).The MICs for routinely used antibiotics for the quality control organisms are published 1,2and the test values for the control strains should be within the published range to be considered acceptable.LimitationsThe MIC value does not give an indication of the mode of action (cidal or static)of the antimicrobial agent.Within the MIC well or tube or on the agar plate with no visible growth,there may still be viable cells if the drug had a bacteriostatic effect on the bacterial species tested.Growth may resume after the removal of the drug.Alternatively,there may be partial inhibition resulting in impaired and reduced growth rates and consequently no visible growth within the time given.Both phenomena are different from the action of a bactericidal drug,which causes irreversible damage leading to cell death.Furthermore,even with the knowledge of the mode of action of an antimicrobial agent,the MIC value alone is a poor predictor of the efficacy of the drug in vivo .Factors that affect the response to therapy are far more complex and include host defense mechan-isms,underlying diseases of the patient,the site of infection,and the pharmacokinetic and pharmacodynamic properties of the drugs 15.Alternative method for determining MIC valuesMICs for commonly used antibiotics can be obtained using an agar diffusion method with commercially available strips containing an exponential gradient of antibiotic (Etest;AB Biodisk).The antibiotic diffuses into the agar medium inoculated with a lawn culture of the test organism.After overnight incubation,the MIC is read at the point of intersection of an elliptical growth inhibition zone with the strip that has an MIC scale printed on it.This test has been evaluated for a variety of bacteria/antibiotic combinations 16–21and is rapid and easy to use;however,it is limited to the antibiotic range supplied by the manufacturer and is an expensive test to use for screening.Several automated systems for antimicrobial susceptibility test-ing and identification of clinically relevant bacteria are now commercially available,e.g.,Phoenix Automated MicrobiologySystem (BD Diagnostic Systems),the VITEK 2System (bioMe ´r-ieux)and the MicroScan WalkAway-96System (Dade Behring).These systems are cost effective for clinical laboratories with a high throughput of clinical specimens.Fully automated systems reduce the time for setup and,depending on the system,also reduce the time to produce results compared to conventional tests.Moreover,they offer convenient interfaces with laboratory and hospital information systems.However,when testing certain organism-antimicrobial combinations limitations on the accuracy of the assessment of MIC values by these systems are known 22,23.Experimental designAs there are alternative routes for generating the bacterial suspen-sion with different time requirements and alternative methods to determine MIC values with potential pause point options that require advance planning of the workflow,the experiment should be carefully designed by the user before starting the protocol.The flowchart in Figure 2illustrates how the different stages are coordinated.Please examine this figure carefully to make an informed choice as to which experimental approach to embark on.MATERIALSREAGENTS.MHB (Difco;BD Diagnostics,cat.no.275730)sterilized by autoclaving .Mueller–Hinton II broth (cation-adjusted (CAMHB);BBL,BD Diagnostics,cat.no.212322)sterilized by autoclaving.MHA (Difco;BD Diagnostics).Agar,T echnical (Difco;BD Diagnostics,cat.no.281230).Solution A:0.02%acetic acid (Fisher)containing 0.4%BSA (BoehringerMannheim)p u o r G g n i h s i l b u P e r u t a N 8002©n a t u r e p r o t o c o l s/m o c .e r u t a n .w w w //:p t t h NATURE PROTOCOLS |VOL.3NO.2|2008|165.Solution B:0.01%acetic acid containing 0.2%BSA.Preparation of McFarland Standard 0.5:BaCl 2Á2H 2O (Sigma-Aldrich,cat.no.B0750),H 2SO 4(Fluka,cat.no.84721)!CAUTION H 2SO 4is very corrosive/toxic;handling must be performed under the hood;wear acid-resistant gloves and protective clothing (see REAGENT SETUP)..Cation adjustment:MgCl 2Á6H 2O (Fluka,cat.no.63072),CaCl 2Á2H 2O (Fluka,cat.no.21101).Physiological saline [0.9%(wt/vol)NaCl]sterilized by autoclaving EQUIPMENT.Spectrophotometer suitable for measuring at wave lengths of 600and 625nm.For antibiotics:sterile 96-well microtiter plates.We recommend polystyrene plates (BD Falcon;Fisher Scientific,cat.no.351177)for most antimicrobials as these are easier to read at the end of the experiment.For cationic antimicrobial agents such as peptides:96-well polypropylene microtiter plates (Costar,cat.no.3790)!CAUTION Avoid tissue culture treated or polystyrene plates as these are strongly negatively charged and will nonspecifically bind peptides..Eppendorf polypropylene microcentrifuge tubes,1.5ml (Fisher Scientific,cat.no.05-402-24B),sterilized.Screw-capped glass tubes,13Â100mm (Fisher Scientific,cat.no.14-930-10A).48-Pin replicator (Boekel Scientific,cat.no.140501)for inoculating agar dilution plates.Shaker,suitable for test tubes 13Â100mm.Parafilm (Pechiney Plastic Packaging;Fisher Scientific,cat.no.13-374-10).Glass tubes,13Â100mm (VWR International,cat.no.47729-572)with cap (Utech Products,cat.no.1017622),sterilized .Erlenmeyer flasks.Sterile petri dishes,15Â100mm (Fisherbrand;Fisher Scientific,cat.no.08-75-712).0.2-m m pore size cellulose acetate filters (Nalgene;Fisher Scientific,cat.no.190-2520).Cell spreader (Fisherbrand;Fisher Scientific,cat.no.08-100-11).Inoculation loop or cotton swabs (sterilized by autoclaving).Vortex mixerREAGENT SETUPPreparation of McFarland 0.5BaSO 4turbidity standard Prepare a 1.175%(wt/vol)barium chloride dihydrate (BaCl 2Á2H 2O)solution (0.048mol l À1BaCl 2)and a 1%(vol/vol)sulfuric acid (H 2SO 4)solution (0.18mol l À1,0.36N).Add 0.5ml of the 1.175%BaCl 2solution to 99.5ml of the 1%H 2SO 4solution with constant stirring to get a suspension.Measure the optical density of the turbidity standard using a spectrophotometer with a 1cm light path length.The correct absorbance at 625nm should be 0.08–0.13.Aliquot 4–6ml into screw-capped glass tubes.The tubes should have the same size as those for preparing the bacterial suspension for inoculation.Seal tubes tightly withParafilm and store in the dark at room temperature (20–23.51C).Standards are p u o r G g n i h s i l b u P e r u t a N 8002©n a t u r e p r o t o c o l s/m o c .e r u t a n .w w w //:p t t h Pure cultures of bacterial isolates (test and control)Day 1Day 2orPrior to testing (2 d required)Prepare overnight culturesPrepare media (store at 4 °C) and antibioticstock solutions (freeze)Antimicrobial susceptibility testing— part I Determine the cell count inovernight culturesPreparation of bacterial suspensionIncubate on nonselectiveagar overnightoror orSuspension with 1–2 × 108cfu/mlTake sample for cell count (ifused for agar dilution)Colony suspensionAdjust turbidity using a McFarland Standard 0.54–6 h growth methodPrepare overnight cultures inliquidGrowth method using overnight culturesAdjust turbidity using a spectrophotometerPrepare agar plates with antibiotics[Day 1 may be possibledepending on the antibiotic (store at 4 °C)]orororPreparebroth macro dilutions of antibioticPrepare broth micro dilutions of antibioticPrepare broth micro dilutions of peptideAntimicrobial susceptibility testing— part ll[Day 1 may be possible (freeze)]Inoculate agarplatesorInoculate broth macro dilutions of antibioticororTake sample for cell countRead MICsInoculate broth micro dilutions of peptideInoculate broth micro dilutions of antibioticDetermine cell countDay 3Figure 2|Flowchart for antimicrobial susceptibility testing.166|VOL.3NO.2|2008|NATURE PROTOCOLSstable for at least a month.!CAUTION H 2SO 4is corrosive/toxic;wear appro-priate safety clothing when handling concentrated H 2SO 4.Preparation of antibiotic-free nutrient-rich agar plates Prepare agar med-ium according to the manufacturer’s instructions.Alternatively,use nutrient-rich broth according to the manufacturer’s instructions and add 1.7%agar (17g agar per liter)before autoclaving.Approximately 20–25ml is necessary to pour one 15Â100mm petri dish.After autoclaving (e.g.,1211C,15min,1bar),cool the medium to 50–601C.Pour agar into the petri dishes and allow to set.Dry the surface of the agar plates either in an incubator or in a laminar air flow hood for 30min with the lid ajar.Store agar plates in plastic bags in inverted position (bottom facing up)at 41C.Adjustment of cation content of MHB medium (20–25mg Ca 2+and 10–12.5mg Mg 2+per liter)Prepare a 10mg ml À1Mg 2+stock solution by dissolving 8.36g of MgCl 2Á6H 2O in 100ml deionized water.Prepare a 10mg ml À1Ca 2+stock solution by dissolving 3.68g of CaCl 2Á2H 2O in 100ml deionized water.Filter-sterilize both stock solutions using 0.2-m m pore size cellulose-acetate filters.Prepare MHB according to the manufacturer’s instructions,autoclave and cool the medium to 2–81C before the addition of the cation solutions.Add 100m l of stock solution per 1mg l À1needed for 1l of medium.For example,add 2ml of Ca 2+stock solution if 20mg needs to be added to 1l MHB.Stock solution of the antimicrobial agent Antimicrobial agents should be stored in the dark at 41C in sealed containers containing a desiccant unless recommended otherwise by the manufacturer.We advise the storage ofantimicrobial peptides at 201C.Before weighing the antimicrobial agent,let the container warm at room temperature for B 2h to avoid condensation of water on the powder.Antibiotics are generally supplied by the manufacturer with the information about the potency (m g per mg powder)that needs to be taken into consideration when weighing the agent.For antibiotics,prepare a stock solution at 10mg ml À1when planning to use it for agar dilution (Step 4A).For broth dilution tests (Steps 4B and 4C)set up a stock solution with a concentration atleast ten times higher than the highest concentration to be tested.For testing antimicrobial peptides (Steps 4D and 4E),prepare a 20-fold concentrated stock e the following formula for calculating the right amount of antibiotic to be weighed (this does not apply to antimicrobial peptides):W ¼ðC ÂV ÞPwhere,W ¼weight of antimicrobial agent in milligram to be dissolved;V ¼desired volume (ml);C ¼final concentration of stock solution (m g ml À1);P ¼potency given by the manufacturer (m g mg À1).Use sterile containers and spatula for weighing the antimicrobial agent and dissolve in sterile distilled water or in the recommended solvent.A list ofsolvents for frequently used antibiotics is found in ref.24.Antibiotic solutions can be filter-sterilized using a 0.2-m m pore size cellulose-acetate filter.However,it has to be ascertained that the antibiotic does not bind to cellulose acetate (information that is sometimes given by the manufacturer).Do not filter-sterilize antimicrobial peptides,which tend to bind to anionic surfaces like cellulose acetate.Always use the fresh antibiotic stock solution for broth microdilution if it is planned to freeze the antibiotic containing microtiter plates at 701C for later usage.For other applications,aliquot the stocksolution.The volume of the aliquots depends on the downstream applications and in general one aliquot should contain the volume needed for one test.Containers need to be sterile,cold resistant and should seal tightly (e.g.,for smaller volumes sterile Eppendorf tubes can be used).Store the aliquots at 201C or below unless it is instructed otherwise by the manufacturer.Most antimicrobial agents are stable at À601C for at least 6months.Stability and storage information for frequently used antibiotics can be found in ref.24.Do not refreeze thawed stock solutions.Some antimicrobials,particularly b -lactams antibiotics,can degrade when thawed and refrozen repeatedly 1.PROCEDUREPreparation of the bacterial suspensionTIMING B 5min per isolate/overnight pause point1|Streak the bacterial isolates to be tested (including a control organism)onto nutrient-rich (e.g.,Mueller–Hinton)agar plates without inhibitor to obtain single colonies.2|Incubate plates for 18–24h at 371C.3|Different methods for the preparation of the inoculum can be used.Direct suspension of overnight colonies into broth or sterile saline solution (option A)is a very convenient method that can be used for most bacterial species.It is particularlyrecommended for fastidious organisms such as Streptococcus spp.,Haemophilus spp.and Neisseria spp.For some strains within a species,unpredictable clumping can occur with option A.Consequently,when colonies are difficult to suspend and an even suspension is difficult to achieve,freshly grown broth cultures can be diluted (option B).As an alternative to a freshly grown culture,an overnight broth culture can also be used (option C)according to the user’s preference.This method is not part of CLSI or EUCAST recommendations;however,the option to use overnight cultures is given in the guide to antimicrobial susceptibility testing of the British Society of Antimicrobial Chemotherapy 24.(A)Colony suspension methodTIMING B 5min per isolate (i)Prepare the antibiotic or peptide dilutions.(ii)For each isolate,select three to five morphologically similar colonies from the fresh agar plate from Step 2and touchthe top of each selected colony using a sterile loop or cotton swab.Transfer the growth into a sterile capped glass tube containing sterile broth or saline solution.Mix using a vortex mixer.(iii)Turbidity can be assessed visually by comparing the test and the McFarland Standard.Mix the McFarland 0.5BaSO 4stan-dard vigorously using a vortex mixer.Please note that commercially available standards containing latex particles should not be vortexed,but gently inverted several parison against a white background with contrasting black lines and good lighting are helpful.Alternatively,the turbidity can be verified measuring the absorbance of the suspension spectrophotometrically.The absorbance should be in the same range as that of the McFarland standard 0.5(OD625nm should be at 0.08–0.13).(iv)Adjust the suspension’s turbidity to that of a McFarland Standard 0.5by adding sterile distilled water,saline or broth,ifthe turbidity is too high,or by adding more bacterial material if is too low.m CRITICAL STEP After turbidity adjustment,the bacterial suspension should be used within 30min,as the cell number might otherwise change.p u o r G g n i h s i l b u P e r u t a N 8002©n a t u r e p r o t o c o l s/m o c .e r u t a n .w w w //:p t t h NATURE PROTOCOLS |VOL.3NO.2|2008|167。

6SCIENTIFIC HIGHLIGHT OF THE MONTH:DilutedMagnetic SemiconductorsMn atoms,or in general of transition metal atoms(TM),with typical concentrations of3-8%, are randomly distributed on the cation sites.Due to the small concentrations the systems behave structurally as semiconductors and can be easily grown on the corresponding parent substrate, i.e.,(Ga,Mn)As on GaAs.Moreover they can be doped and manipulated as semiconductors, which offers a large prospect for applications.However a problem of these DMS-systems is, that the Curie temperatures are well below room temperature,e.g.,170K for(Ga,Mn)As, representing the best investigated system.This is the major obstacle for applications[1,2,8].In this paper,we will discuss the basic electronic structure of dilute magnetic semiconductors. We will concentrate on the magnetic properties,in particular the exchange mechanism which control the ferromagnetism in these systems.Moreover we present calculations of the Curie temperatures based(i)on the most simple mean-field approximation and(ii)on sophisticated Monte Carlo methods.The ab-initio calculations are performed within the density functional formalism by using the Korringa-Kohn-Rostoker(KKR)method together with the coherent potential approximation(CPA)to describe the disorder in these systems.As a result we will show that there are two classes of DMS,one,in which the majority d-states are well localised below the valence band,and a second one,where impurity d-bands in the gap exist.In the former class the interaction is dominated by Zener’s p-d exchange being relatively weak,but longer ranged,while in the latter one Zener’s double exchange prevails,being strong but short ranged.Both have important consequences for the Curie temperatures.2Ab-initio Calculations for Dilute Magnetic SemiconductorsThe results presented in this review are obtained by ab-initio calculations based on density functional theory(DFT).Exchange and electronic correlation effects are described by the local density approximation,the standard working horse in thefield.As calculational method we use the KKR-Green function method.Green function methods avoid the calculation of eigenfunction φαand eigenvalues Eαof the Kohn-Sham equations of DFT.The Green function G(r,r ;E), defined as the causal solution of the Kohn-Sham equation with a unit source term at the position r¯h2(−E F dE Im G(r,r;E)(2)πand the density of states(DOS)in a certain volume V by a volume integral2n(E)=−randomly distributed on the cation sites,i.e.,on the Ga sites in GaAs.Therefore this disorder corresponds to the disorder in a random A c B1−c alloy where c=c A denotes the concentration of A atoms and c B=1−c A the one of B atoms.This disorder problem can be well described by the coherent potential approximation(CPA)[9],in which the atoms A and B are embedded in an effective‘CPA’-medium which is determined selfconsistently.If we denote the atomic t-matrices of the A-and B-atoms and of the CPA medium by t A,t B and t CPA,then the CPA selfconsistency condition,which determine t CPA,leads in the multiple scattering KKR description toc A T A+c B T B=0(4)where T A,B describes the total single-site T-matrix of an atom A or B embedded in the CPA medium on site0T A=(t A−t CPA)1V BZBZd k g(k)12 i=j J ij M i· M j(7)where M i and M j denote the local moments,in particular their directions,of the magnetic impurities i and j and J ij the exchange integral between these atoms.This we calculated by the formula of Liechtenstein[11],which describes the energy change due to a small change of the angle between both moments within the frozen potential approximation.1J ij=cM2 j(=i)J ij(10)3Note that in MFA only the sum of all J ij enters,but not the spatial extent.Therefore thecan also be calculated directly from the CPA total energies for the mean-field value T MF ACferromagnetic ground state E FM and from the disordered local moment state E DLM.In the mean-field approximation of the Heisenberg model the ground state energy H DLM vanishes for the DLM states1H DLM=−c2M2 i=j J ij(12)2Since orientational degrees of freedom should be described well by the Heisenberg model,we can identify the differenceH DLM−H FM=E CPA DLM−E CPA FM(13)Energy relative to the Fermi energy (eV)D O S (1/e V /U n i t C e l l , A t o m )Figure 1:Density of states of dilute magnetic semiconductors with 5%Mn impurities:(a)(Ga,Mn)N,(b)(Ga,Mn)P,(c)(Ga,Mn)As and (d)(Ga,Mn)Sb.The full curve gives the average DOS of the whole system,the dotted curve the local DOS of the Mn atoms.by the total energy difference for the ferromagnetic system,e.g.,Ga 1−c Mn ↑c As,and the DLMsystem with 50%Mn moments up and 50%down,i.e.,Ga 1−c Mn ↑c/2Mn ↓c/2As.By comparisonwith the above result for T MF A Cwe obtain then k B T MF A C =2c (14)Thus in MFA the Curie temperature is determined by the total energy difference per Mn atom between the DLM and FM state [12].Often the MFA does not give reliable results.In this case Monte Carlo simulations offer an (numerically)exact method to calculate the thermodynamic properties.For details see Sect.5.3Local Density of States and Curie Temperatures in MF AHere we present results of ab-initio calculations for a series of III-V DMS with 5%Mn impurities.We have chosen the sequence (Ga,Mn)N,(Ga,Mn)P,(Ga,Mn)As and (Ga,Mn)Sb,where only the anions N,P,As and Sb are different.For the results it is most important that the majority d -level of Mn has a lower energy than the atomic p -level of Sb,but a higher energy than the p -level of N,while the p -levels of P and As are intermediate.Fig.1shows the density of states (DOS)for the considered systems with 5%Mn on the Ga sites.The upper curves refers to the majority DOS,the lower inverted ones to the minority DOS,both for the ferromagnetic configuration.The full curves show the average total density of states of the DMS with 5%Mn.Due to the small concentration of Mn this is roughly the DOS of the pure semiconductors,consisting of the occupied valence band,dominated by the anion p -states and the empty conduction band,formed mostly by the Ga s -states.The dotted lines show the local DOS of the Mn atoms.We consider only the neutral charge state without additional dopants.Since Mn has 7valence electrons and substitutes for a Ga atom,3of the 7electrons can replace the 3Ga electrons in the valence band.The remaining 4electrons have to be put in new localised d -states in the band gap.Therefore the electronic structure of transition metal impurities in semiconductors is dominated by d -states in the gap,which for finite concentrations develop into impurity bands.Since Mn has a large moment,only the majority states are occupied leadingt --t +e +t --t +e CBCB +Figure 2:Impurity levels of magnetic transition metal impurities in semiconductors:For Mn on the III-site in III-V semiconductors the double degenerate e +state and two of the three degenerate t +states are occupied (left figure);the same states are occupied for Cr impurities on II-sites in II-VI semiconductors.On the other hand for Mn impurities in II-VI and Fe impurities in III-V semiconductors all five majority states (right figure)are occupied.to a so-called ‘high-spin state’.The impurity levels are schematically indicated in Fig.2.Two different impurity levels have to be distinguished:A twofold degenerate e -state (d z 2,d x 2−y 2),the wave functions of which for symmetry reasons hybridize very little with the valence band p -states,and a threefold degenerate t -state (d xy ,d yz ,d zx )which strongly hybridizes with the p -states,resulting in bonding-and antibonding hybrides.While the bonding hybrides are located in the valence band,the antibonding hybrides form the impurity t -states in the gap,which are due to the hybridization shifted to higher energies than the e -states.In the neutral configuration only the two e -states and two of the three t -states in the majority band are occupied,while the minority gap states are empty.In Fig.1both the e -and t -states can be very well seen for the GaN compound with 5%Mn.Since the d -states around the individual Mn atoms overlap and form an impurity band,the higher and broader band corresponds to the more extended t -states,and the lower narrow one to the more localised e -states.Within the valence band there is also some hybridised-in Mn DOS from the bonding t -hybrides.The Fermi level falls into the majority t -impurity band,such that per Mn atom exactly two e -states and two t -states are occupied,leaving one majority t -state and all minority d -states empty.Therefore the considered system is a half-metallic ferromagnet,with a moment of 4µB per Mn atom.When we move from Mn in GaN to Mn in GaP and GaAs we notice that the Mn d -level is shifted to lower energies.For (Ga,Mn)P the e -state has fully moved in the valence band,while the t -state forms with the valence p -states of the P atom a resonance at E F .Most of the local d -intensity of the Mn atom is now located at the bonding t -states within the valence band.For (Ga,Mn)As these trends are even somewhat stronger.Finally for (Ga,Mn)Sb,the resonance at the Fermi level has more or less disappeared,such that at E F the local Mn DOS agrees well with the DOS of the Sb atoms.Since the minority d -like gap states are in all cases unoccupied,the total moment is fixed to 4µB per Mn.However in the case of (Ga,Mn)Sb the situation is very different from (Ga,Mn)N,since in GaSb all 5majority d -states are occupied,while a hole exist in the Sb majority p -states at the Fermi level.Therefore the filling of the five d -resonances leads to a total moment of 5µB ,which is,however,reduced to 4µB per Mn atom by the empty states inC u r i e t e m p e r a t u r e (K )Mn concentration (%)Figure 3:Curie temperatures of Mn doped III-V semiconductors,as calculated in the mean field approximation as a function of the Mn concentration.the majority p -band.Thus in the CPA description the Sb atoms are weakly and homogeneously polarised,with an average moment of -1µB per Mn atom,being antiferromagnetically coupled to the Mn moments,such that the total moment per Mn atom is still 4µB .In summary the behaviour of Mn in GaN and GaSb is completely different.In fact,both systems represent two extremes:in (Ga,Mn)N the d -states are in the gap and form impurity bands at E F ,while in (Ga,Mn)Sb the d -states are at the lower end of the valence band and fully occupied,while a hole exist in the majority valence band.The behaviour of Mn in GaP and GaAs lies between these two extremes.In all cases the minority d -states are unoccupied.The Curie temperatures T C ,calculated in MFA for these systems,reflect this strongly differentbehaviour.Fig.3shows the calculated T MF A Cvalues for the four systems as a function of the concentration c of Mn impurities.For (Ga,Mn)Sb we find a linear dependence on the concen-tration,but in the other cases a strong non-linear dependence is obtained,which is particularpronounced for (Ga,Mn)N.As we will demonstrate below,in this case T MF A Cscales as the square root of the concentration c ,leading to very large T C values already for small concentra-tions of Mn.The behaviour of (Ga,Mn)As is intermediate between these extremes:a weaker √EFigure4:Double exchange:Due to the broadening of the impurity t-band with increasing Mn concentration c,states are transferred to lower energies,leading to an energy gain,if the Fermi√energy lies in the band.As explained in the text,the band width increases asc of the concentration.The energy gain due to band broadening is known as Zener’s double exchange[14].This can be proven by a theorem for tight-binding model.The square of the band width is given by the energy varianceW2=√c.ThisW (e V )Mn concentration (%)W (eV )22Figure 5:Impurity band width W and its square W 2for the impurity t -band in (Ga,Mn)N as a function of Mn concentration.The inset shows the local density of Mn gap states.seen in calculated DOS as is shown in Fig. 5.In the figure W and its square are plotted as a function of Mn concentration.The linear dependence of W 2on Mn concentration indicates a√c ,which explains the strong increase of the Curie temperature in MFA as shown inFig.3for (Ga,Mn)N.The double exchange mechanism is only important,if the Fermi energy lies in the band.If the band is completely occupied or empty,no energy can be gained by band broadening.Let us now consider the stability of the disordered local moment (DLM)(or spin-glass)state as compared to the ferromagnetic one.In the CPA-description of the DLM state,for a given Mn atom 50%of the neighboring Mn atoms have a moment being parallel aligned to the central moment,and 50%are antiferromagnetically aligned.The parallel aligned pairs lead,as in the ferromagnetic case,to a broadened impurity band,but with a reduced band width scaling asIM ,where t is the effective hopping matrix elementand IM is the exchange splitting,given by the exchange integral I times the local moment M .It is linear in c ,since the effects of several antiparallel aligned neighbours on the central atom superimpose on each other.Thus in the case of impurity bands in the gap,double exchange favors the ferromagnetic config-EnergyEnergyFigure6:Super exchange:Shown are the local densities of states for two impurities with moments S i=‘up’and S j=‘down’.Due to hybridisation of the majority and the minority d-wavefunctions the lower energy levels are shifted to lower and the higher levels to higher energies as indicated by the dashed lines.Due to hybridisation also small peaks occur locally for the ‘wrong’spin direction.The downward shift stabilises the antiferromagnetic alignment of the two local moments,provided the Fermi level falls between the two peaks,but not below or above.uration and always wins,if the Fermi energy lies(well)in the band.Then the energy gain due to double exchange,scaling as√Figure 7:Kinetic p -d exchange:The low-lying ‘localised’majority d -states hybridise with the majority valence p -band,pushing it up to higher energies as indicated by the dashed line.Anal-ogously the empty minority d -level pushes the minority valence p -states to lower energies.Since due to charge neutrality the valence band must have one hole per Mn atom,this hole is confined to the majority band,leading to an Sb moment of −1µB per Mn being antiferromagnetically aligned to the Mn-moments.T (K )c Mn-concentration (%)Figure 8:Meanfield Curie temperature of (Ga,Mn)As evaluated in the LDA and in the LDA+U approximation (with U =4eV).The inset shows the local density of states of the Mn atoms.Due to the Hubbard U of 4eV,the Mn majority d -states are shifted to lower energies,while the resonance at the Fermi level is diminished.This increases the importance of p -d kinetic exchange and reduces the double exchange,so that T C varies linear with concentration.proximation(LDA).This approximation works in most cases very well,but has its limit for correlated systems.One typical error is,that the spin splitting is usually too small.The error can be partially removed by the LDA+U method,where U stands for the Hubbard U param-eter of the Hubbard model.Fig.8shows the results of an LDA and LDA+U calculations for (Ga,Mn)As system with5%Mn.The inset shows the local Mn DOS in LDA and LDA+U, using a U parameter of U=4eV.As one sees,the U parameter of4eV shifts the majority peak by about1.3eV to lower energies,such that it is in good agreement with photoemission measurements[15,16].Since the d-states are now located in the lower region of the valence band,one expects that the p-d exchange becomes more dominant.The calculated Curie tem-peratures T MF AC indeed show this effect.The LDA results show a√3c i=0J0i is veryproblematic for dilute systems with low concentrations,since it does not require any information on the interaction range.This simplification leads to significant errors in the calculations of T C for low concentrations[17,18].It can be easily understood and is known as the percolation problem[19].Let us consider a Heisenberg model with a ferromagnetic exchange interaction only between nearest neighbors(nearest neighbor Heisenberg model),and see what happens when the system is diluted with non-magnetic sites as schematically shown in Fig.10-(a).024*********123451%5%15%(Ga, Mn)NE x c h a n g e i n t e r a c t i o n s (m R y )Distance (lattice constant)-0.4-0.200.20.40.60.80123453%15%(Ga, Mn)SbE x c h a n g e i n t e r a c t i o n s (m R y )Distance (lattice constant)5%00.20.40.60.811.21.4123451%15%(Ga, Mn)AsE x c h a n g e i n t e r a c t i o n s (m R y )Distance (lattice constant)5%01234123451%15%(Ga, Mn)PE x c h a n g e i n t e r a c t i o n s (m R y )Distance (lattice constant)5%Figure 9:Exchange coupling constants J ij between two Mn atoms as a function of the distance for three different concentrations.The concentration dependence arises from the screening effects of the other impurities,being described by the embedding of the two impurities in the CPA medium.When the concentration of magnetic sites is 100%,we have a perfect ferromagnetic network.Due to the dilution,the network is weakened,and for a concentration below a percolation threshold the ferromagnetism cannot spread all over the system leading to paramagnetic state since due to missing longer ranged interactions the moments can no longer align.Obviously this effect is not counted in the mean field equation for T C ,because the dilution effect is included only as a concentration factor c in the equation.In case of the nearest neighbor Heisenberg model,the percolation threshold c p for the fcc structure is 20%(note that the impurities sit on the fcc Ga sublattice of the zinc blende structure).In real systems such as (Ga,Mn)N the interaction reaches beyond the nearest neighbors and the real percolation threshold should be lower.However,below 20%the strong nn coupling is not so important anymore,since only the much weaker longer ranged interaction induces the ferromagnetism,so that the Curie temperature is expected to drop considerably and to be much smaller than the mean field value,being determined to a large extent by the strong nn coupling J 01.In order to take the percolation effect into account,we perform Monte Carlo simulation (MCS)for the classical Heisenberg model.The thermal average of magnetization M and its powers are calculated by means of the Metropolis algorithm [20].Due to the finite size of super cells used in the simulation,it is difficult to determine T C from the temperature dependence of M (T ) .In particular,when considering dilute systems,finite size effects and appropriate finite size scaling are of particular importance for a correct and efficient evaluation of T C by Monte Carlo simulations.To avoid this difficulty,we use the cumulant crossing method proposed by Binder [20].This method uses the finite size scaling in the forth order cumulant U 4which is defined as U 4=1− M 4 /( M 2 )2.U 4is calculated for various cell sizes and plotted as a function of(b) fcc nearest neighbor Heisenberg modelk T /J B C 01concentration c(a) 2D-square lattice (c = 0.59)pc = 1c = 0.7c = 0.3magnetic sitenon-magnetic siteFigure 10:(a)Schematic picture of dilute 2-dimensional nearest neighgor Ising model in square lattice.The percolation thereshold is 0.59in this case.(b)Curie temperatures of the classical nearest neighbour Heisenberg model for the fcc lattice as a function of the concentration.The full line gives the mean field results,being linear in c .The crosses connected by the dashed line give the exact values as obtained by Monte Carlo simulations (MCS),which vanish below the percolation threshold of c p =20%.The nn coupling constant J 01has been fixed at a constant value.temperature.If the cell size is larger than the correlation length,it can be shown that the U 4(T )curves for different sizes cross each other at three characteristic temperatures.Two of them are T =0and T =∞,and the other is T =T C .We use 3cell sizes (6×6×6,10×10×10and 14×14×14conventional fcc cells)to carry out the cumulant crossing method for T C calculations.First,as a pedagogical example we show the calculated T C for the dilute fcc nearest neighbour Heisenberg model as calculated by MFA and MCS in Fig.10-(b).For MCSs for dilute systems,we take 30different random configurations of magnetic sites for the ensemble average.As shown in Fig.10-(b),it is found that the MFA gives a reasonable,but too high estimation of T C for c =1.However,with decreasing c both curves decline with nearly the same slope and below the percolation threshold,c p =0.20,the Curie temperature vanishes.Thus in the dilute concentration range below 20%,which is most relevant for DMS systems,the failure of the MFA is evident [17,18].Next,we show the calculated T C values of (Ga,Mn)N (Fig.11-(a))and (Ga,Mn)As (Fig.11-(b))as obtained by the MCS from the J ij values in Fig.9.Thirty configurations of Mn atoms are considered for averaging and J ij interactions up to 15shells are included.As shown in Fig.11-(a),very small T C values are predicted for low concentrations in (Ga,Mn)N.The MFA values are almost 2orders of magnitude too large.Thus we find that the magnetism isC u r i e t e m p e r a t u r e (K )C u r i e t e m p e r a t u r e (K )C u r i e t e m p e r a t u r e (K )Cr concentration (%)C u r i e t e m p e r a t u r e (K )Cr concentration (%)Figure 11:Curie temperatures of (a)(Ga,Mn)N,(b)(Ga,Mn)As,(c)(Zn,Cr)S and (d)(Zn,Cr)Te as evaluated in the mean field approximation (MFA)and by Monte Carlo simulations (MCS)from the J ij values obtained in the LDA (see Fig.9).Due to the percolation problem the Curie temperature of (Ga,Mn)N is strongly reduced for small concentrations.This effect can also be seen in (Zn,Cr)S and (Zn,Cr)Te.Due to the longer interaction range the reduction of Curie temperatures effect is more moderate in (Ga,Mn)As.strongly suppressed due to the missing percolation of the strong nearest neighbour interactions.Only the weak,longer ranged interactions satisfy the percolation requirement,leading to small but finite Curie temperatures for 5,10and 15%of Mn.As shown in Fig.11-(b),due to the longer ranged interaction in (Ga,Mn)As,the reductions from the MFA are not very large,but still significant.Naturally these changes are larger for smaller concentrations.The T C values of 103K obtained for 5%Mn is in good agreement with the experimental values of 118K reported by Edmonds et al.[21].This values refers to measurements in thin films which are free of Mn-interstitials representing double donors.Including interactions beyond 15th shell,MCS could give slightly higher T C values for low concentrations.At very high concentrations we expect our results to increase towards the MFA values.The experimental situation for T C in (Ga,Mn)N is very controversial.There are many reports,where very high Curie temperatures,well above room temperature,have been observed,but also many observations of no ferromagnetism or only very low Curie temperatures.The above calcu-lations suggest,that a homogeneously ferromagnetic phase with a Curie temperature around or above room temperature can be excluded.Therefore the experimentally observed very high T C values have to be attributed to small ferromagnetic MnN clusters and segregated MnN phases,where the strong ferromagnetic nn interaction becomes fully effective.The same method for calculating T C is applied to (Zn,Cr)S and (Zn,Cr)Te as typical examples of II-VI DMS systems [22].Results are shown in Fig.11-(c)and -(d).In these compounds,impurity t -bands appear in the gap and 2/3of the impurity bands are occupied (namely,theyare equivalent to Mn-doped III-V DMS such as(Ga,Mn)N from electron occupation point of view),therefore the double exchange is dominant mechanism.As a result,MFA values of T C √show[4]R.J.Soulen Jr.,J.M.Byers,M.S.Osofsky,B.Nadgorny,T.Ambrose,S.F.Cheng,P.R.Broussard,C.T.Tanaka,J.Nowak,J.S.Moodera,A.Barry and J.M.D.Coey,Science 28285(1988).[5]H.Kato,T.Okuda,Y.Okimoto,Y.Tomioka,K.Oikawa,T.Kamiyama and Y.Tokura,Phys.Rev.B69184412(2004).[6]H.Ohno,H.Munekata,T.Penney,S.von Molnar,L.L.Chang,Phys.Rev.Lett.682664(1992).[7]H.Ohno,A.Shen,F.Matsukura,A.Oiwa,A.Endo,S.Katsumoto and Y.Iye,Appl.Phys.Lett.69363(1996).[8]S.A.Wolf,D.D.Awschalom,R.A.Buhrman,J.M.Daughton,S.von Molnar,M.L.Roukes,A.Y.Chtchelkanova and D.M.Treger,Science2941488(2001).[9]H.Akai and P.H.Dederichs,Phys.Rev.B478739(1993).[10]H.Akai,Department of Physics,Graduate School of Science,Osaka University,Machikaneyama1-1,Toyonaka560-0043,Japan,akai@phys.sci.osaka-u.ac.jp(2000)[11]A.I.Liechtenstein et al.,J.Magn.Magn.Matter6765(1987).[12]K.Sato,P.H.Dederichs and H.Katayama-Yoshida,Europhys.Lett.61403(2003).[13]K.Sato,P.H.Dederichs,H.Katayama-Yoshida and J.Kudrnovsky,J.Phys.Condens.Matt.16S5491(2004).[14]H.Akai,Phys.Rev.Lett.813002(1998).[15]J.Okabayashi et al.,Phys.Rev.B59R2486(1999).[16]O.Rader et al.,Phys.Rev.B69075202(2004).[17]K.Sato,W.Schweika,P.H.Dederichs and H.Katayama-Yoshida,Phys.Rev.B70201202(2004).[18]L.Bergqvist,O.Eriksson,J.Kudrnovsky,V.Drchal,P.Korzhavyi and I.Turek,Phys.Rev.Lett.93137202(2004).[19]D.Stauffer and.Aharony,Introduction to Percolation Theory(Taylor and Francis,Philadel-phia,1994).[20]K.Binder and D.W.Heerman,Monte Carlo Simulations in Statistical Physics(Springer,Berlin,2002).[21]K.W.Edmonds et al.,Appl.Phys.Lett.814991(2002).[22]T.Fukushima,K.Sato,H.Katayama-Yoshida and P.H.Dederichs,Jpn.J.Appl.Phys.43L1416(2004).[23]H.Saito,V.Zayets,S.Yamagata and K.Ando,J.Appl.Phys.957175(2004).[24]N.Ozaki,N.Nishizawa,K.-T.Nam,S.Kuroda and K.Takita,Phys.Status Solidi C1957(2004).。

Unit 8 Section A Animals or children?—A scientist's choice动物还是孩子？——一位科学家的选择1 I am the enemy! I am one of those cursed, cruel physician scientists involved in animal research. These rumors sting, for I have never thought of myself as an evil person. I became a children's doctor because of my love for children and my supreme desire to keep them healthy. During medical school and residency, I saw many children die of cancer and bloodshed from injury —circumstances against which medicine has made great progress but still has a long way to go. More importantly, I also saw children healthy thanks to advances in medical science such as infant breathing support, powerful new medicines and surgical techniques and the entire field of organ transplantation. My desire to tip the scales in favor of healthy, happy children drew me to medical research.1 我就是那个敌人！我就是那些被人诅咒的、残忍的、搞动物实验的医生科学家之一。

Chaotic Interest Rate Rules∗Jess Benhabib†New York UniversityStephanie Schmitt-Groh´e‡Rutgers University and CEPRMart´ın Uribe§University of PennsylvaniaAugust15,2001AbstractA growing empirical and theoretical literature argues in favor of specifying monetarypolicy in the form of Taylor-type interest rate feedback rules.That is,rules wherebythe nominal interest rate is set as an increasing function of inflation with a slope greaterthan one around an intended inflation target.This paper shows that such rules caneasily lead to chaotic dynamics.The result is obtained for feedback rules that dependon contemporaneous or expected future inflation.The existence of chaotic dynamicsis established analytically and numerically in the context of calibrated economies.Thebattery offiscal policies that has recently been advocated for avoiding global indeter-minacy induced by Taylor-type interest-rate rules(such as liquidity traps)are shown tobe unlikely to provide a remedy for the complex dynamics characterized in this paper.JEL Classification Numbers:E52,E31,E63.Keywords:Taylor rules,chaos,periodic equilibria.∗We thank for comments seminar participants at the2001NBER Summer Institute and for technical assistance the C.V.Starr Center of Applied Economics at New York University.†Phone:212998-8066.Email:jess.benhabib@.‡Phone:7329322960.Email:grohe@.§Phone:2158986260.Email:uribe@.1IntroductionIn much of the recent literature on monetary economics it is assumed that monetary policy takes the form of an interest-rate feedback rule whereby the central bank sets the nominal interest rate as a function of some measure of inflation and the level of aggregate activity. One justification for this modeling strategy is empirical.Several authors,beginning with Taylor(1993)have documented that the central banks of major industrialized countries im-plement monetary policy through interest-rate feedback rules of this type.1These empirical studies have further shown that since the early1980s interest-rate feedback rules in devel-oped countries have been active in the sense that the nominal interest rate responds more than one for one to changes in the inflation measure.For example,Taylor(1993)finds that for the U.S.during the post-Volker era,the inflation coefficient of the interest-rate feedback rule is about1.5.In his seminal paper,Taylor(1993)also argues on theoretical grounds that active interest-rate feedback rules—which have become known as Taylor rules—are desirable for aggregate stability.The essence of his argument is that if in response to an increase in inflation the central bank raises nominal interest rates by more than the increase in inflation,the resulting increase in real interest rates will tend to slowdown aggregate demand thereby curbing inflationary pressures.Following Taylor’s influential work,a large body of theoretical research has argued in favor of active interest rate rules.One argument in favor of Taylor-type rules is that they guarantee local uniqueness of the rational expectations equilibrium.2 The validity of the view that Taylor rules induce determinacy of the rational expectations equilibrium has been challenged in two ways.First,it has been shown that local determinacy of equilibrium under active interest-rate rules depends crucially on the assumed preference and technology specification and as well as on the nature of the accompanyingfiscal regime (Leeper,1991;Benhabib,Schmitt-Groh´e and Uribe,2001b,Carlstrom and Fuerst,2000and 2001a,and Dupor,1999).Second,even in cases in which active interest-rate rules guarantee uniqueness of the rational expectations equilibrium locally,they may fail to do so globally. Specifically,Benhabib,Schmitt-Groh´e,and Uribe(2001a)and Schmitt-Groh´e and Uribe (2000a,b)show that interest-rate rules that are active around some inflation target give rise to liquidity traps.That is,to unintended equilibrium dynamics in which inflation falls to a low and possibly negative long-run level and the nominal rate falls to a low and possibly zero level.In this paper,we identify a third form of instability that may arise under Taylor-type policy rules.Specifically,we show that active interest-rate rules may open the door to equilibrium cycles of any periodicity and even chaos.These equilibria feature trajectories that converge neither to the intended steady state nor to an unintended liquidity trap. Rather the economy cycles forever around the intended steady state in a periodic or aperiodic fashion.Interestingly,such equilibrium dynamics exist precisely when the target equilibrium is unique from a local point of view.That is,when the inflation target is the only equilibrium level of inflation within a sufficiently small neighborhood around the target itself.We establish the existence of periodic and chaotic equilibria analytically in the context 1See for instance Clarida,Gal´ı,and Gertler(1998),Clarida and Gertler(1997),and Taylor(1999).2See,for example,Leeper(1991),Rotemberg and Woodford(1999),and Clarida,Gal´ı,and Gertler(2000).of a simple,discrete-time,flexible-price,money-in-the-production-function economy.For analytical convenience,we restrict attention to a simplified Taylor rule in which the nominal interest rate depends only on inflation.We consider two types of interest rate feedback rules. In one the argument of the feedback rule is a contemporaneous measure of inflation and in the other the central bank responds to expected future inflation.We show that the theoretical possibility of complex dynamics exists under both specifications of the interest rate feedback rule.To address the empirical plausibility of periodic and chaotic equilibria,we show that these complex dynamics arise in a model that is calibrated to the U.S.economy.The remainder of the paper is organized in four sections.Section2presents the basic theoretical framework and characterizes steady-state equilibria.Section3demonstrates the existence of periodic and chaotic equilibria under a forward-looking interest-rate rule.Sec-tion4extends the results to the case of Taylor-type rules whereby the nominal interest rate depends upon a contemporaneous measure of inflation.Finally,section5discusses the ro-bustness of the results to a number of variations in the economic environment.It shows that periodic equilibria also exist when the Taylor rule is globally linear and does not respect the zero bound on nominal rates.In addition it considers the consequences of assuming that money affects output with lags.The section closes with a brief discussion about learn-ability of the equilibria studied in the paper and the design of policies geared at restoring uniqueness.2The economic environment2.1HouseholdsConsider an economy populated by a large number of infinitely lived agents with preferences described by the following utility function:∞t=0βtc t1−σ1−σ;σ>0,β∈(0,1)(1)where c t denotes consumption in period t.Agents have access to two types offinancial asset:fiat money,M t,and government bonds,B ernment bonds held between periods t and t+1pay the gross nominal interest rate R t.In addition,agents receive a stream of real income y t and pay real lump-sum taxesτt.The budget constraint of the representative household is then given byM t+B t+P t c t+P tτt=M t−1+R t−1B t−1+P t y t,where P t denotes the price level in period t.Letting a t≡(M t+B t)/P t denote realfinancial wealth in period t,m t≡M t/P t denote real money balances,andπt≡P t/P t−1the gross rate of inflation,the above budget constraint can be written asa t+c t+τt=(1−R t−1)πt m t−1+R t−1πta t−1+y t.(2)To prevent Ponzi games,households are subject to a borrowing constraint of the formlim t→∞a tt−1j=0(R j/πj+1)≥0.(3)We motivate a demand for money by assuming that real balances facilitatefirms trans-actions as in Calvo(1979),Fischer(1974),and Taylor(1977).Specifically,we assume that output is an increasing and concave function of real balances.Formally,y t=f(m t).(4) Households choose sequences{c t,m t,y t,a t}∞t=0so as to maximize the utility function(1) subject to(2)-(4),given a−1.Thefirst-order optimality conditions are constraints(2)-(4) holding with equality andc−σt=βc−σt+1R tπt+1(5)f (m t)=R t−1R t.(6)Thefirst optimality condition is a standard Euler equation requiring that in the margin a dollar spent on consumption today provides as much utility as that dollar saved and spent tomorrow.The second condition says that the marginal productivity of money at the optimum is equal to the opportunity cost of holding money,(R t−1)/R t.2.2The monetary/fiscal policy regimeFollowing a growing recent empirical literature that has attempted to identify systematic components in monetary policy,we postulate that the government conducts monetary policy in terms of an interest rate feedback rule of the formR t=ρ(πt+j);j=0or1.(7) We consider two cases:forward-looking interest rate feedback rules(j=1)and contem-poraneous interest rate feedback rules(j=0).Under contemporaneous feedback rules the central bank sets the current nominal interest rate as a function of the inflation rate between periods t−1and t.We also analyze the case of forward-looking rules because a number of authors have argued that in the post-Volker era,U.S.monetary policy is better described as incorporating a forward-looking component(see Clarida et al.,1998;Orphanides,1997).We impose four conditions on the functional form of the interest-rate feedback rule:First, in the spirit of Taylor(1993)we assume that monetary policy is active around a target rate of inflationπ∗>β;that is,the interest elasticity of the feedback rule atπ∗is greater than unity,orρ (π∗)π∗/ρ(π∗)>1.Second,we impose the restrictionρ(π∗)=π∗/β,which ensuresthe existence of a steady-state consistent with the target rate of inflation.Third,we assume that the feedback rule satisfy(strictly)the zero bound on nominal interest rates,ρ(π)>1 for allπ.Finally,we assume that the feedback rule is nondecreasing,ρ (π)≥0for allπ.Government consumption is assumed to be zero.Thus,each period the government faces the budget constraint M t+B t=M t−1+R t−1B t−1−P tτt.This constraint can be written in real terms in the following form:a t=R t−1πta t−1−R t−1−1πtm t−1+τt.(8)This expression states that total government liabilities in period t,a t,are given by liabilities carried over from the previous period,including interest,R t−1/πt a t−1,minus total consol-idated government revenues,given by the expression in square brackets on the right-hand side.Consolidated government revenues,in turn,have two components:seignorage revenue, [(R t−1−1)/πt]m t−1,and regular taxes,τt.We assume that thefiscal regime consists of setting consolidated government revenues as a fraction of total government liabilities.Formally,R t−1−1πtm t−1+τt=ωa t−1;ω>0.(9) Combining the above two expressions,(8)and(9),we obtain:a t=R t−1πt−ωa t−1(10)Given our maintained assumption thatω>0,this expression implies thatlim t→∞a tt−1j=0(R j/πj+1)=0.(11)Therefore,the assumedfiscal policy ensures that the household’s borrowing limit holds with equality under all circumstances.2.3EquilibriumCombining equations(2)and(8)implies that the goods market clears at all times:y t=c t.(12) We are now ready to define an equilibrium real allocation.Definition1An equilibrium real allocation is a set of sequences{m t,R t,c t,πt,y t}∞t=0satis-fying R t>1,(4)-(7)and(12).Given a−1and any pair of equilibrium sequences{R t,πt}∞t=0,equation(10)gives rise to a sequence{a t}∞t=0that,as shown above,satisfies the transversality condition(11).For analytical and computational purposes,we will focus on the following specific para-meterizations of the monetary policy rule and the production function:R t=ρ(πt+j)≡1+(R∗−1) πt+jπ∗A(R∗−1);R∗=π∗/β(13)andf(m t)=[amµt+(1−a)¯yµ]1µ;µ<1,a∈(0,1].(14) We assume that A/R∗>1,so that at the target rate of inflation the feedback rule satisfies the Taylor criterionρ (π∗)π∗/ρ(π∗)>1.In other words,at the target rate of inflation,the interest-rate feedback rule is active.The parameter¯y is meant to reflect the presence of a fixed factor of production.Under this production technology one may view real balances either as directly productive or as decreasing the transaction costs of exchange.3 With these particular functional forms,an equilibrium real allocation is defined as a set of sequences{m t,R t,c t,πt,y t}∞t=0satisfying R t>1,(5),(6),and(12)-(14).2.4Steady-state equilibriaConsider constant solutions to the set of equilibrium conditions(5),(6),(12),(13),and (14).Because none of the endogenous variables entering in the equilibrium conditions is predetermined in period t(i.e.,all variables are‘jump’variables),such solutions represent equilibrium real allocations.We refer to this type of equilibrium as steady-state equilibria. By equation(5),the steady-state nominal interest rate R is related to the steady-state inflation rate as R=β−1π.In addition,the interest-rate feedback rule(13)implies that R=ρ(π).Combining these two expressions,yields the steady-state conditionβ−1π=ρ(π).Figure1depicts the left-and right-hand sides of this condition for the particular functional form ofρ(π)given in equation(13).Clearly,one steady-state value of inflation is the target inflation rateπ∗.The slope ofρ(π)atπ∗isβ−1A/R∗which is greater than the slope of the left-hand side,β−1.This means that at this steady state monetary policy is active.We therefore refer to this steady-state equilibrium as the active steady state,and denote the associated real allocation by(y∗,c∗,m∗,R∗,π∗).The particular functional form assumed for the interest-rate feedback rule implies thatρ(π)is strictly convex,strictly increasing,and strictly greater than one.Consequently,there exists another steady state value of inflation,πp,which lies betweenβandπ∗.Thus,the steady-state interest rate associated withπp, R p=πp/βis strictly greater than one.Further,at this second steady state,the feedback rule is passive.To see this,note thatρ (πp)<β−1,which implies thatρ (πp)πp/ρ(πp)=ρ (πp)β<1.Thus,we refer to this steady-state equilibrium as the passive steady state and denote the implied real allocation by(y p,c p,m p,R p,πp).43It is also possible to replace thefixed factor¯y with a function increasing in labor,and add leisure to the utility function.The current formulation then would correspond to the case of an inelastic labor supply.4For the steady-state levels of output and real balances to be well defined(i.e.,positive real values),it is necessary that(R p−1)/R p>a1/µwhenµ>0and that(R∗−1)/R∗<a1/µwhenµ<0.Given all other parameter values,these restrictions are satisfied for a sufficiently small.3Equilibrium Dynamics Under Forward-Looking Interest-Rate Feedback RulesConsider the case in which the central bank sets the short-term nominal interest rate as a function of expected future inflation,that is,j =1in equation (13).Combining 6)and (14)yields the following negative relation between output and the nominal interest rateR t =R (y t );R <0.(15)This expression together with (5),(12),and (13),implies a first-order,non-linear difference equation in output of the form:y t +1=F (y t )≡β1/σy tR (y t )ρ−1(R (y t )) 1/σ,(16)where ρ−1(·)denotes the inverse of the function ρ(·).Finding an equilibrium real allocationthen reduces to finding a real positive sequence {y t }∞t =0satisfying (16).53.1Local EquilibriaConsider perfect-foresight equilibrium real allocations in which output remains forever in an arbitrarily small neighborhood around a steady state and converges to it.To this end,we log-linearize (16)around y ∗and y p .This yieldsy t +1= 1+ R σ 1−1 ρy t ,(17)where y t denotes the log-deviation of y t from its steady-state value.The parameter R <0denotes the elasticity of the function R (·),defined by equation (15),with respect to y t evaluated at the steady-state value of output.Finally, ρ>0denotes the elasticity of the interest-rate feedback rule with respect to inflation at the steady state.Consider first the passive steady state.As shown above,in this case the feedback-rule is passive,that is, ρ<1.It follows that the coefficient of the linear difference equation (17)is greater than one.With y t being a non-predetermined variable,this implies that the passive steady state is locally the unique perfect-foresight equilibrium.Now consider the local equilibrium dynamics around the active steady state.By assump-tion,at the active steady state ρis greater than 1.This implies that the coefficient of the difference equation (17)is less than unity.For mildly active policy rules,that is, ρclose to one,the coefficient of (17)is less than one in absolute value.Consequently,in this case the rational expectations equilibrium is indeterminate.It follows from our analysis that the 5An additional restriction that solutions to (16)must satisfy in order to be able to be supported as equi-librium real allocation is that 1−a 1/(1−µ)1−a −1/µ¯y >y t >(1−a )1/µ¯y when µ>0and 1−a 1/(1−µ)1−a−1/µ¯y <y t <(1−a )1/µ¯y when µ<0.These constraints ensure that R t ≥1and that m t is a positive real number.parameter value ρ=1is a bifurcation point of the dynamical system(17),because at this value the stability properties of the system changes in fundamental ways.For sufficiently active policy rules,a second bifurcation point might emerge.In particu-lar,if R/σ<−2,then there exists an ρ>1at which the coefficient of the linear difference equation(17)equals minus1.Above this value of ρthe coefficient of the difference equa-tion is greater than one in absolute value and the equilibrium is locally unique,as in the neighborhood of the passive steady state.One might conclude from the above characterization of local equilibria that as long as the policymaker peruses a sufficiently active monetary policy,he can guarantee a unique equilibrium around the inflation targetπ∗.In this sense active monetary policy might be viewed as stabilizing.However,this view can be misleading.For the global picture can look very different.We turn to this issue in the next subsection.3.2ChaosConsider the case of a sufficiently active monetary policy stance that ensures that the inflation target of the central bank,π∗,is locally the unique equilibrium.Formally,assume that at the active steady state ρ>1/(1+2σ/ R).6Such a monetary policy,while stabilizing from a local perspective,may be quite destabilizing from a more global perspective.In particular, there may exist equilibria other than the active steady-state,with the property that the real allocationfluctuates forever in a bounded region around the target allocation.These equilibria include cycles of any periodicity and even chaos(i.e.,non-periodic deterministic cycles).To address the possibility of these disturbing equilibrium outcomes,wefirst establish theoretically the conditions under which periodic and chaotic dynamics exist.We then show that these conditions are satisfied under plausible parameterizations of our simple model economy.3.2.1ExistenceTo show the existence of chaoticfluctuations,we apply a theorem due to Yamaguti and Matano(1979)on chaotic dynamics in scalar systems.To this end,we introduce the following change of variable:q t=µlny ty p.E quation(16)can then be written asq t+1=H(q t;α)≡q t+αh(q t),(18) where the parameterαand the function h(·)are defined asα=1σ6We are implicitly assuming that the second bifurcation point exists,that is,that the condition R/σ<−2 is satisfied.andh(q t)=(−µ)ln(ρ−1(R(y p e q t/µ))−lnβ−ln R(y p e q t/µ).We restrict attention to negative values ofµ.As we discuss below,this is the case of greatest empirical interest.The function h is continuous and has two zeros,one at q=0and the other at q∗≡µln(y∗/y p)>0.Further h is positive for q t∈(0,q∗)and negative for q t/∈[0,q∗]. To see this,note that h(q)is simply the natural logarithm of[β−1π/ρ(π)](−µ)and thatπis a monotonically increasing function of q.As can be seen fromfigure1,β−1πis equal toρ(π)at the passive and active steady states(πp andπ∗),is greater thanρ(π)between the two steady states(π∈(πp,π∗)),and is smaller thanρ(π)outside this range(π/∈[πp,π∗]). It follows that the differential equation˙x=h(x)has two stationary(steady-state)points,0 and q∗.In addition,the stationary point q∗is asymptotically stable.We are now ready to state the Yamaguti and Matano(1979)theorem.Theorem1(Yamaguti and Matano(1979))Consider the difference equationq t+1=H(q t;α)≡q t+αh(q t).(19) Suppose that(a)h(0)=h(q∗)=0for some q∗>0;(b)h(q)>0for0<q<q∗;and(c) h(q)<0for q∗<q<κ,where the constantκis possibly+∞.Then there exists a positive constant c1such that for anyα>c1the difference equation(19)is chaotic in the sense of Li and Yorke(1975).Suppose in addition thatκ=+∞.Then there exists another constant c2,0<c1<c2, such that for any0≤α≤c2,the map H has an invariantfinite interval[0,γ(α)](i.e.,H maps[0,γ(α)]into itself)withγ(α)>q∗.Moreover,when c1<α≤c2,the above-mentioned chaotic phenomenon occurs in this invariant interval.The application of this theorem to our model economy is immediate.It follows that there ex-ist parameterization of the model for which the real allocation cycles perpetually in a chaotic fashion,that is,deterministically and aperiodically.According to the theorem,chaotic dy-namics are more likely the larger is the intertemporal elasticity of substitution,1/σ.We next study the empirical plausibility of the parameterizations consistent with chaos.3.2.2Empirical plausibilityTo shed light on the empirical plausibility of the existence of chaotic equilibria under active monetary policy,consider the following calibration of the model economy.The time unit is a quarter.Let the intended nominal interest rate be6percent per year(R∗=1.061/4),which corresponds to the average yield on3-month U.S.Treasury bills over the period1960:Q1 to1998:Q3.We set the target rate of inflation at4.2percent per year(π∗=1.0421/4). This number matches the average growth rate of the U.S.GDP deflator during the period 1960:Q1-1998:Q3.The assumed values for R∗andπ∗imply a subjective discount rate of1.8 percent per year.Following Taylor(1993),we set the elasticity of the interest-rate feedback rule evaluated atπ∗equal to1.5(i.e.,A/R∗=1.5).There is a great deal of uncertainty about the value of the intertemporal elasticity of substitution1/σ.In the real-business-cycle literature,authors have used values as low as1/3(e.g.,Rotemberg and Woodford,1992)and as high as1(e.g.,King,Plosser,and Rebelo, 1988).In the baseline calibration,we assign a value of1.5toσ.We will also report the sensitivity of the results to variations in the value assumed for this parameter.Equations(6)and(14)imply a money demand function of the formm t=y tR t−1aR t1/(µ−1).(20)Using U.S.quarterly data from1960:Q1to1999:Q3,we estimate the following money demandfunction by OLS:7ln m t=0.0446+0.0275ln y t−0.0127lnR t−1R t+1.5423ln m t−1−0.5918ln m t−2t-stat=(1.8,4.5,−4.7,24.9,−10.0)R2=0.998;DW=2.18.We obtain virtually the same results using instrumental variables.8The short-run log-log elasticity of real balances with respect to its opportunity cost(R t−1)/R t is-0.0127,while the long-run elasticity is-0.2566.The large discrepancy between the short-and long-run interest rate elasticities is due to the high persistence of real balances in U.S.data.This discrepancy has been reported in numerous studies on U.S.money demand(see,for example, Goldfeld,1973;and Duprey,1980).Our model economy does not distinguish between short-and long-run money demand elasticities.Thus,it does not provide a clear guidance as to which estimated elasticity to use to uncover the parameterµ.Were one to use the short-run elasticity,the implied value ofµwould be-77.The value ofµfalls to-3when one uses the long-run money demand elasticity.In the baseline calibration of the model,we will assign a value of−9,which implies a log-log interest elasticity of money demand of-0.1.We will also show results for a variety of other values within the estimated range.9 To calibrate the parameter a of the production function,we solve the money demand equation(20)for a and obtaina=R t−1R tm ty t1−µ.We set m t/y t=4/5.8to match the average quarterly U.S.M1to GDP ratio between1960:Q1 and1999:Q3.We also set R to1.061/4as explained above.Given the baseline value ofµ,the implied value of a is0.000352.10Finally,we set thefixed factor¯y at1.Table1summarizes the calibration of the model.7We measure m t as the ratio of M1to the implicit GDP deflator.The variable y t is real GDP in chained 1996dollars.The nominal interest rate R t is taken to be the gross quarterly yield on3-month Treasury bills.8As instruments we choose thefirst three lags of ln y t and ln(R t−1)/R t,and the third and fourth lags of ln m t.9An alternative strategy would be to build a model where lagged values of real balances emerge endoge-nously as arguments of the liquidity preference function.However,such exercise is beyond the scope of this paper.10In calibrating a,we do not use the estimated constant in our money demand regression.The reason is that the model features a unit income elasticity of money demand whereas the regression equation does not.Table1:Calibrationβσµa¯yπ∗R∗A0.996 1.5-90.0003521 1.0103 1.0147 1.522Note:The time unit is1quarter.Figure2shows thefirst three iterates of the difference equation(16),which describes theequilibrium dynamics of output,for the baseline calibration.In all of the three panels,thestraight line is the45o degree line and the range of values plotted for output starts at theactive steady state,y∗,and ends at the passive steady state,y p.Thefigure shows that thesecond-and third iterates of F havefixed points other than the steady-state values y∗and y p.This means that there exist two-and three-period cycles.The presence of three-period cycles is of particular importance.For,by Sarkovskii’s(1964)theorem,the existence ofperiod-three cycles implies that the map F has cycles of any periodicity.Moreover,as aconsequence of the result of Li and Yorke(1975),the existence of period-three cycles implieschaos.That is,for the baseline calibration there exist perfect-foresight equilibria in whichthe real allocationfluctuates perpetually in an aperiodic fashion.Indeed,three-period cycles emerge for any value ofσbelow1.75.Thisfinding is linewith theorem1,which states that there exists a value forσbelow which chaotic dynamicsnecessarily occur.On the other hand,for values ofσgreater than1.75,three-period cyclesdisappear.This does not mean,however,that for such values ofσthe equilibrium dynamicscannot be quite complex.For example,forσbetween1.75and1.88,we could detect six-period cycles.Sarkovskii’s theorem guarantees that if six-period cycles exist,then cycles of periodicities2n3for all n≥1also exist.Forσbetween1.88and2period-four and period-two cycles exist.11Wefind that for values ofµless than-7.5,the economy has three-period cycles when all other parameters take their baseline values.On the other hand,for values ofµgreater than -7.5three-period cycles cease to exist.Therefore,the more inelastic is the money demand function,the more likely it is that chaotic dynamics emerge.4Equilibrium dynamics under contemporaneous Tay-lor rulesConsider the case that the interest-rate feedback rule depends on a contemporaneous measure of inflation,that is,j=0in equation(13).For simplicity,in this section we focus on a special parameterization of the production function given in(14).Specifically,we assume that the elasticity of substitution between real balances and thefixed factor of production is one,1/(1−µ)=1and normalize thefixed factor to unity.Then the production function can be written as:y t=m a t.(21) An equilibrium real allocation is then defined as a set of sequences{m t,R t,c t,πt,y t}∞t=0 satisfying R t>1,(5),(6),(12),(13)(with j=0),and(21).Combining these equilib-rium conditions yields the followingfirst-order non-linear difference equation describing the equilibrium law of motion of the nominal interest rate:R∗R tR t−1R tσa1−a=R∗−1R t+1−1(R∗−1)/AR t+1−1R t+1σa1−a.(22)4.1Local equilibriaTo characterize local equilibrium dynamics,we log-linearize(22)around the steady state R ss,where R ss takes the values R∗or R p.This yields:Rt+1=θ R t ,whereθ≡δ(R ss)−1δ(R ss)−R∗−1R ss−1R ssA,11Forσ>1.71,the aforementioned cycles occur in a feasible invariant interval.That is,in a feasible interval A such that F(A)∈A.The interval A contains both steady states.The upper end of the interval coincides with y p and the lower end is below y∗.In terms of the notation of the Yamaguti and Matano (1979)theorem,the values of1/σof1/1.75and1/1.71correspond to the constants c1and c2,respectively.。

CAPITAL ACCOUNT LIBERALIZATION AND WAGEINEQUALITY∗Mauricio Larrain†Columbia UniversityThis version:June2013AbstractThis paper analyzes the distributional consequences of capital account lib-eralization.Opening the capital account allowsfinancially constrainedfirms toborrow capital from abroad.I argue that since capital is more substitutablefor unskilled workers and more complementary to skilled workers,liberalizationincreases the relative demand for skilled labor,leading to higher wage inequal-ing aggregate data and exploiting the variation in the timing of capitalaccount reforms across23industrialized countries,Ifind strong evidence thatopening the capital account increases wage inequality.In order to identify themechanism driving this effect,I use sectoral data and exploit the variation in ex-ternalfinancial dependence and capital-skill complementarity across industries.Myfindings show that capital account liberalization increases wage inequalityparticularly in industries with both highfinancial needs and strong complemen-tarity.Overall,the results suggest that liberalization is a relevant driving forcebehind wage inequality.∗I am deeply indebted to Yuriy Gorodnichenko,Ted Miguel,and Atif Mian for their advice and en-couragement.I also thank Geert Bekaert,David Card,Fred Finan,Todd Gormley,Ross Levine,Ulrike Malmendier,Elias Papaioannou,Andres Rodriguez-Clare,David Romer,Emmanuel Saez,Shang-Jin Wei,and Daniel Wolfenzon for their helpful comments.This paper also benefited from the comments of seminar participants at the Boston Fed,Brown University,Columbia Business School,Federal Reserve Board,Notre Dame,Princeton,UBC Sauder,Chicago Booth,UC Berkeley,UC Riverside,Pac-Dev, Midwest Macro Meetings,WFA conference,LBS Summer Symposium,and several institutions in Chile.I am grateful for funding from the Kauffman Foundation and the Center for Equitable Growth at UC Berkeley.This paper was previously circulated under the title“Does Financial Liberalization Contribute to Wage Inequality?The Role of Capital-Skill Complementarity.”†Columbia Business School.Mailing address:3022Broadway,Uris Hall813.New York,NY, 10027.E-mail address:mlarrain@.1IntroductionIn the last four decades,many developed and developing countries have opened their capital accounts,lifting legal restrictions imposed on international capital transac-tions.1Although there is a growing consensus that capital account liberalization leads to higher economic growth(Quinn and Toyoda,2008),it is still unclear whether liberal-ization benefits the whole population equally,or whether it disproportionately benefits the rich or the poor.This paper attempts tofill this gap by analyzing the effect of liberalization on the relative wage between skilled and unskilled workers.Opening the capital account allowsfinancially constrainedfirms to access the in-ternationalfinancial market and borrow capital from more capital-abundant countries.I argue that since capital and skilled labor are more complementary as inputs than are capital and unskilled labor,liberalization increases the relative demand for skilled labor.In equilibrium,this enlarges the wage gap between skilled and unskilled workers, leading to higher inequality.Figure1plots the cumulative change in capital account openness against the cu-mulative change in wage inequality for23industrialized economies from1975-2005. Capital openness is measured with the Chinn and Ito(2006)index.Wage inequality is measured as the wage gap between workers with college and high-school education. The Figure shows a positive correlation between the change in capital openness and in-equality.In this paper,I argue that the relationship is causal and that capital account liberalization leads to higher wage inequality.[Include Figure1here]This paper makes two contributions.First,it provides thefirst piece of empirical evidence on the effects of capital account liberalization on wage inequality.From a policy perspective,it is very important to understand both the efficiency and distri-butional consequences of opening the capital account.Second,wage inequality has increased in several countries in recent decades.The most common explanations for 1This includes,for example,allowing domestic businesses to obtain loans from foreign banks, allowing foreigners to purchase domestic debt,and allowing foreigners to invest in the domestic stock market.1this phenomenon are skill-biased technological change,trade liberalization,and changes in labor market institutions.This paper highlights the importance of capital account liberalization as an additional factor contributing to rising inequality.I follow a two-fold empirical strategy.First,I use aggregate data and exploit the variation in the timing of capital account reforms across countries and conduct a gener-alized difference-in-differences test.I calculate the difference in wage inequality before and after a country opens its capital account and compare it to the same change in countries not implementing reform during that period.Ifind strong evidence that capital account liberalization increases wage inequality.2Opening the capital account increases wage inequality by4%.In estimating this effect,I include country and year fixed effects and control for a series of time-varying determinants of wage inequality.Second,I use sectoral data to identify the mechanism by which capital market in-tegration leads to higher inequality.According to the mechanism,liberalization allows financially constrainedfirms to demand more capital,which in turn increases the rel-ative demand for skilled labor.Both effects vary across industries.The capital stock should increase more infirms producing in industries that are typically dependent on externalfinance for growth.Likewise,the relative demand for skilled labor should increase more infirms producing in industries with strong complementarity between capital and skills.If labor mobility across sectors is limited,then capital account liberalization should increase wage inequality particularly in industries with high ex-ternalfinancial dependence and strong capital-skill complementarity.3To identify the channel,I exploit the variation in external dependence and complementarity across sectors.To conduct the cross-sectional analysis,I rank industries regarding the two cross-sectoral characteristics.I use the Rajan and Zingales(1998)externalfinancial depen-dence index to identify an industry’s need for externalfinance.Financial dependence is the fraction of capital expenditures notfinanced with internal cashflows.To obtain a measure of capital-skill complementarity,I estimate a skilled labor share equation2I define liberalization as a one standard deviation increase in the Chinn and Ito(2006)index.3If workers accumulate sector-specific human capital,labor will not be fully mobile across industries and wages will not be equalized across sectors.See Dickens and Katz(1987)and Krueger and Summers (1987)for evidence on large inter-industry wage differentials.2for each industry.I define complementarity as the elasticity of the share of wages paid to skilled labor with respect to capital intensity.I start by exploiting the variation in externalfinancial dependence across sectors and analyze the effect on the sectoral capital stock per unit of skilled labor.I calculate the before-after change in the capital stock in industries with high external depen-dence in a country opening its capital account and compare it to the same change in industries with low dependence within the same country.The difference-in-differences specification includes a full set of country-year,country-industry,and industry-year fixed effects.Ifind that capital liberalization increases the capital stock in industries that are highly dependent on externalfinance(75th percentile in the index)by10% more than in industries with low dependence(25th percentile).Next,I exploit the cross-sectoral variation in both externalfinancial dependence and capital-skill complementarity and analyze the effect on sectoral wage inequality. Ifind that within above-median dependence industries,capital account liberalization increases wage inequality in industries with strong complementarity(75th percentile in the index)by3.5%more than in industries with weak complementarity(25th per-centile).Within below-median dependence industries,the effect does not vary with capital-skill complementarity.I also pool all industries together and conduct a triple difference-in-differences test.Ifind that liberalization increases wage inequality in in-dustries with high external dependence and strong complementarity by2.5%more than in the remaining industries.Finally,I show that the results are not driven by either skill-biased technological change or trade liberalization.I also provide preliminaryfirm-level evidence,from an emerging market,suggesting that the transmission mechanism highlighted in this pa-per works at thefirm level as well.I conduct a series of additional tests that further strengthen the paper’s results.First,I document that the differential effect on in-equality is larger for older workers,who are less mobile across industries than younger workers.Second,Ifind that the differential effect is larger for female workers than for male workers.Third,I document that the effect is larger in countries with strong investor stly,I provide suggestive evidence that the effect on inequality also extends to emerging markets.3Related literature.This paper contributes to a growing literature that analyzes the real effects of capital account liberalization.The primary focus has been on economic growth.4There is only one paper that analyzes the effects on inequality:Das and Mohapatra(2003).The authors use aggregate data andfind a positive effect of stock market liberalization on the share of income held by the top quintile.I go one step further and use sectoral data to pin down the channel by which capital liberalization affects inequality.By providing evidence of a specific mechanism,I provide a stronger test of causality.Other papers have studied the broader link betweenfinancial development and in-come inequality.The evidence on this relationship is mixed.At the aggregate level, Beck et al.(2007)find a negative link,while Bumann and Lensink(2012)find a posi-tive one.At the micro level,Beck et al.(2010)document a negative link,while Jerz-manowski and Nabar(2011)document a positive one.By tracing down a particular mechanism,I provide a better understanding on howfinance affects inequality.My work also relates to a recent literature linkingfinance and labor.Benmelech et al.(2011)show that the availability of credit plays an important role infirm-level employment decisions.Pagano and Pica(2012)find thatfinancial development is asso-ciated with greater employment growth.Chari et al.(2012)show that capital market integration increases the level of wages.I contribute to this literature by analyzing the relationship betweenfinance and the wages of workers with different levels of skills.This paper also relates to a large literature analyzing the determinants of rising wage inequality.5Starting with Katz and Murphy(1992),several papers have documented that the wage gap between skilled and unskilled workers has widened in many countries during the last decades.The standard explanations include skill-biased technological progress,trade openness,and labor institution changes.The role of capital market integration,however,has been absent in this discussion.I contribute to this literature by stressing that capital account liberalization is a relevant driving force behind wage inequality.The channel of transmission of this paper relies on the capital-skill complemen-4See,among others,Henry(2000)and Bekaert et al.(2005).5See Katz and Autor(1999)for a review of this literature.4tarity hypotheses.Griliches (1969)was the first to provide evidence that capital is more substitutable for unskilled workers and more complementary to skilled workers.6Starting with Krusell et al.(2000),several papers have linked capital accumulation to wage inequality through capital-skill complementarity.More recently,Parro (2013)and Burstein et al.(2013)show that international trade has important effects on wage inequality through its impact on the import of capital equipment.I argue that capi-tal market integration also has important effects on inequality through the inflows of foreign capital.Finally,the strategy of exploiting cross-sectoral heterogeneity to pin down the trans-mission mechanism comes from Rajan and Zingales (1998).Gupta and Yuan (2009)use cross-country,cross-industry data to analyze the relationship between capital account liberalization and growth.They find that liberalization increases growth particularly in industries heavily dependent on external finance.I also use cross-country,cross-industry data.However,I focus on inequality instead of growth.In addition,I exploit cross-sectoral variation in both external financial dependence and capital-skill comple-mentarity to identify the effect.2Analytical frameworkIn this Section,I present a very simple framework to understand the relationship be-tween capital account liberalization,capital-skill complementarity,and wage inequality.2.1Capital-skill complementarityConsider an economy in which firms produce with a three-factor production function:y =f (k,s,u ),where y denotes output,k physical capital,s skilled labor,and u unskilled labor.Denote by σi,j the elasticity of substitution between factors i and j .7The “capital-skill complementarity hypothesis”states that physical capital is more complementary to skilled labor than to unskilled labor,i.e.,σk,u >σk,s .In other words,capital and skilled labor are relative complements while capital and unskilled labor are 6See Hamermesh (1993)for a more recent review of this literature.7The Allen-Uzawa partial elasticity of substitution is defined as σi,j ≡∆%(i/j )∆%(∂f∂j /∂f ∂i )for i,j ∈{k,s,u }.5relative substitutes.If labor markets are competitive,firms demand labor until the point where the marginal product of labor equals the wage:∂f/∂s=w s and∂f/∂u=w u,where w s denotes the skilled wage and w u the unskilled wage.I define wage inequality as the relative wage between skilled and unskilled workers,i.e.,(w s/w u).The capital-skill complementarity hypothesis implies that∂(w s/w u)∂k>0.Intuitively,if capital and skilled labor are relative complements,an increase in the capital stock increases the relative demand for skilled labor.Since labor is paid its marginal product,this leads to higher wage inequality.As an example,consider the following standard,two-level CES production function:y=uσ+(λkρ+(1−λ)sρ)σρ1σ,(1)whereλis a parameter that governs income shares andσ,ρ<1are parameters thatgovern the elasticities of substitution.The elasticity of substitution between capital and unskilled labor is11−σand the elasticity of substitution between capital and skilledlabor is11−ρ.Capital-skill complementary requires thatσ>ρ.With this specification, I can log-linearize the ratio between the skilled and unskilled wage and obtain the following expression for wage inequality(Krusell et al.,2000):logw sw uσ−ρρksρ+(1−σ)logus(2)From equation(2),I can calculate the effect of an increase in capital on wage inequality as follows:∂log(w s/w u)∂(k/s)=(σ−ρ)kρ−1sρUnder capital-skill complementarity(σ>ρ),an increase in the capital stock perunit of skilled labor increases wage inequality,∂log(w s/w u)∂(k/s)>0.In the empirical analysis, I use the capital stock per unit of skilled labor as the relevant measure of capital. Equation(2)also highlights that,sinceσ<1,a decrease in the relative supply ofskilled labor also increases wage inequality,∂log(w s/w u)∂log(u/s)>0.62.2Capital account liberalization and wage inequalityIn the economy,there are legal restrictions imposed on international capital transac-tions.Letθdenote the parameter that summarizes the degree of international capital mobility.Capital account liberalization is a policy that increasesθ.This policy allows financially constrainedfirms to borrow from abroad.I model capital market reform through the function k=k(θ),where∂k/∂θ>0.I also assume that both types of labor are supplied inelastically.This simple framework delivers a series of testable implications.Prediction1.Capital account liberalization increases wage inequality.Intuitively,the policy leads to capital accumulation.Since capital and skilled labor are relative complements,this increases the relative demand for skilled labor.In equi-librium,this increases the relative wage between skilled and unskilled workers.I can decompose the effect of capital liberalization on wage inequality into a“capital effect”and a“complementarity effect”:∂(w s/w u)∂θ=∂(w s/w u)∂kComplementarity-effect·∂k∂θCapital-effectThe capital effect measures capital deepening,while the complementarity effect measures the extent to which capital deepening increases the relative demand for skilled labor.For a given complementarity effect,the effect on wage inequality is increasing in the capital effect.Likewise,for a given capital effect,the effect on inequality is increasing in the complementarity effect.In fact,if the capital effect is absent,there will be no complementarity effect.Within an economy,the strength of both effects varies acrossfirms and industries.Prediction2.Capital account liberalization increases the capital stock particularly in industries with high externalfinancial dependence.For technological reasons,firms in some industries require more externalfinance to produce than in other industries.For example,firms in some industries face higher7fixed costs,and thus operate at larger scales,than in other industries.It follows that firms in these industries depend more on externalfinancing and will be morefinan-cially constrained.Since capital account liberalization allowsfirms to tap international financial markets,firms in industries with high externalfinancial needs will benefit the most.Therefore,the“capital effect”will be stronger in industries with high needs for externalfinance.Prediction3.Capital account liberalization increases wage inequality particularly in industries with high externalfinancial dependence and strong capital-skill complemen-tarity.Again for technological reasons,the production functions in some industries exhibit stronger complementarity between capital and skills than in other industries.For example,in some industries workers carry out a limited set of activities,which can be accomplished by following explicit rules.Since capital can more easily substitute unskilled labor when unskilled workers conduct routine tasks,the production functions in these industries will exhibit strong capital-skill complementarity.8As a result,the relative demand for skilled labor responds strongly to an increase in the capital stock. Therefore,for a given“capital effect,”the“complementarity effect”will be stronger in industries with strong complementarity between capital and skills.If labor is fully mobile across industries,then skilled labor willflow towards the industry with strong complementarity until the relative wage is equalized across sectors. However,although all workers have the opportunity to switch sectors,not all do so and wages do not equilibrate across sectors.Workers with sufficient accumulated sector-specific human capital will notfind the higher relative wage attractive enough to switch. As a result,capital account liberalization will increase wage inequality particularly in industries in which the“capital effect”and the“complementarity effect”are strong. In the long run,new generations of workers enter the labor force and wage inequality is equalized across sectors.98Under specification(1),a higher degree of capital-skill complementarity corresponds to a larger value of(σ−ρ).9Several studies show that trade liberalization adjustment occurs through relative wage changes rather than labor reallocation across sectors.See Goldberg and Pavcnik(2007)for a review of this literature.83Empirical strategyTo estimate the effect of capital account liberalization on wage inequality,I follow a two-fold empirical strategy.First,I use aggregate data and exploit the variation in the timing of capital account reforms across countries.Second,in order to pin down the transmission mechanism,I use sectoral data and exploit the variation in external financial dependence and capital-skill complementarity across sectors.For the aggregate analysis,I exploit the cross-country,cross-time variation in the timing of capital account reforms.This allows me to identify the effect in a difference-in-differences setup.To understand the intuition,consider a country opening its capital account(“treatment group”).First,I compute the difference in inequality before and after the capital account change.However,this estimate could be affected by other global factors taking place at the same time.To control for such factors,I also estimate the before-after difference in inequality for countries that did not implement changes to the capital account during the time period(“control group”).The difference between these two differences captures the effect of capital account liberalization on aggregate inequality.In particular,I estimate a difference-in-differences test in multiple treatment groups and multiple time periods setting(Imbens and Wooldridge,2009).The specification includes countryfixed effects,which allow me to exploit the within-country variation across time.It also includes yearfixed effects to exploit the cross-country variation within a moment in time.The difference-in-differences cancels out any global factors that are common to the treatment and control groups.However,there might be other factors affecting inequality that are specific to the treatment group.I address this issue in the estimation by controlling for a series of time-varying factors that affect inequality.10To provide a stronger test of causality,in the second part of the analysis I pro-vide evidence of a specific mechanism by which capital account liberalization affects inequality.According to the analytical framework,the effect of capital account reform varies across industries.I use sectoral data and exploit the cross-sectoral variation in 10I control for the relative supply of skilled labor,trade openness,inflation,government expenditure to GDP,GDP per capita,and private credit to GDP.Beck et al.(2007)use a similar set of controls.9order to identify the channel.Thefirst part of the mechanism works though capital accumulation,so I start by exploiting the variation in externalfinancial dependence across industries.Consider a country opening its capital account.First,I calculate the difference in the capital stock before and after openness in industries with high external dependence(“treatment group”).Next,I estimate the before-after difference in industries with low dependence(“control group”).The difference between these two differences estimates the differential effect of liberalization across sectors within a country implementing reform.The generalized difference-in-differences specification includes country-yearfixed effects,which allow me to exploit the variation across industries within a country at a moment in time.It also includes country-industryfixed effects to exploit the within country-industry variation across time.Finally,the specification includes sector-year fixed effects to ensure that the estimates are not driven by global shocks affecting inequality within a certain subset of industries.Thefinal part of the mechanism works through capital-skill complementarity.Within industries with high external dependence,capital account liberalization should increase wage inequality particularly in industries with strong complementarity.Therefore,I exploit the cross-sectoral variation in both external dependence and capital-skill com-plementarity.I conduct a triple difference-in-differences estimation in which I compare inequality before and after capital account reform,between industries with high and low financing needs,and between industries with strong and weak complementarity.The identification assumption is that there are not other concurrent factors that increase inequality particularly in the subset of industries with both highfinancial dependence and strong complementarity.Throughout the paper,I argue that this is a highly plausible assumption.4Data4.1Capital account liberalizationThe traditional approach to measuringfinancial openness is to use the information provided by the IMF’s“Annual Report on Exchange Arrangements and Exchange10Restrictions”(AREAER),which reports the extent of rules and regulations affecting cross-borderfinancial transactions.In this paper,I use the index of capital account openness developed by Chinn and Ito(2006),which captures both the extent and intensity of restrictions to capital mobility.The Chinn and Ito data allows me to maximize the number of countries in the sample.In Section7,I show that the results are robust to using alternative de jure and de facto capital openness measures.The Chinn and Ito measure is based on a set of four AREAER measures for re-strictions on capital mobility:(1)openness of the capital account,(2)openness of the current account,(3)stringency of requirements for repatriation of export proceeds,and (4)existence of multiple exchange rates.These binary variables are set equal to one when restrictions are non-existent and zero otherwise.This index is thefirst principle component of the four binary variables.The index has a higher value for countries that are more open to cross-borderfinancial transactions.It is constructed such that the series has a mean of zero.11The sample consists of23industrialized countries from1975-2005.The composition of the sample is the result of intersecting the wage dataset described below with the Chinn and Ito data.Table1reports the evolution of capital account openness across countries and time.There is substantial variation of capital market openness across countries and across time.Some countries(e.g.,Germany and United States)have open capital accounts during the entire sample period.Eastern European countries, on the other hand,opened very quickly towards the end of the sample.The sample includes countries that opened in the1980s(e.g.,Denmark and Italy)and others that opened in the1990s(e.g.,Portugal and Spain).[Include Table1here]Capital account liberalization should decrease the cost of capital through the inflow of foreign funds from countries with more abundant capital.In Figure2,I plot the cumulative change in capital account openness against the cumulative change in the lending interest rate of domestic banks,from1975-2005.The Figure shows a strong negative correlation between the change in capital account openness and the interest 11The minimum attainable value is-1.85and the maximum attainable is2.45.11rate.The lower cost of capital should encouragefirms to increase their capital stock.I construct a measure of aggregate capital stock from investment through the perpetual inventory method using data from the Penn World Tables(Caselli,2005)12.Figure3 plots the cumulative change in capital account openness against the cumulative per-centage change in the capital stock per unit of skilled labor.According to the Figure, there is a strong positive correlation between the change in capital openness and the capital stock.[Include Figures2and3here]4.2Wage inequalityThe data on wage inequality comes from the EU-KLEMS dataset,a statistical and analytical research projectfinanced by the European Commission.13EU-KLEMS pro-vides sectoral data on capital stock,hours worked,and wages by skill level.I define skilled labor as the labor force with some college education and unskilled labor as the labor force with high-school education.Wage inequality is the ratio between the wage of workers with college and high-school education.The wage data is available for23 industrialized countries over1975-2005.There is information for15industries at the two-digit level of aggregation.Six industries are manufacturing,ranging from wood to machinery.The remaining nine industries are non-manufacturing,ranging from retail to construction.The physical capital data is available for a subset of only14countries.Table2reports the evolution of wage inequality across countries and time.For any given time period,there is abundant variation in inequality across countries.Wage inequality is highest in Eastern European countries,where the wage of skilled work-ers is more than double the wage of unskilled workers.Wage inequality is lowest in Scandinavian countries.There is a lot of variation in inequality across time.Wage inequality between1975and2005increased in more than half of the countries in the 12For some countries,there are relatively few observations for investment,so it is likely that the capital stock is measured with error.I prefer to construct the aggregate capital stock myself since the wage dataset provides capital information for only14countries.13EU-KLEMS stands for European Union level analysis of capital(K),labour(L),energy(E), materials(M),and service(S)inputs.12。