Department of Economics Working Paper Series

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1 Depatment of Economcs Wokng Pape Sees Reputaton and Effcency: A Nonpaametc Assessment of Ameca s Top-Rated MBA Pogams Subhash C. Ray Unvesty of Connectcut Yongl Jeon Cental Mchgan Unvest Wokng Pape 23-3 Mach Mansfeld Road, Unt 63 Stos, CT Phone: (86) Fax: (86)

2 Abstact Wdely publczed epots of fesh MBAs gettng multple ob offes wth sx-fgue annual salaes leave a long-lastng geneal mpesson about the hgh qualty of selected busness schools. Whle such spectacula achevement n ob placement ghtly deseves ecognton, one should not lose sght of the esouces expended n ode to accomplsh ths esult. In ths study, we employ a measue of Paeto-Koopmans global effcency to evaluate the effcency levels of the MBA pogams n Busness Week s top-ated lst. We compute nput- and outputoented adal and non-adal effcency measues fo compason. Among thee te goups, the schools fom a hghe te goup on aveage ae moe effcent than those fom lowe tes, although vaatons n effcency levels do occu wthn the same te, whch exst ove dffeent measues of effcency. Jounal of Economc Lteatue Classfcaton: I2, D6, N3 Keywods: Data Envelopment Analyss, Paeto-Koopmans global effcency, Reputaton Ou thanks to Stephen M. Mlle fo useful comments.

3 . Intoducton Snce 988, Busness Week magazne egulaly publshes bennally a lst of the top-anked busness schools n the U.S. Ths ankng eflects suvey questonnae esponses fom copoate ecutes, on the one hand, and cuent and ecent gaduates, on the othe. Apat fom enhancng the pestge of ndvdual schools, ths ankng can sgnfcantly nfluence popula pecepton about the qualty of the MBAs fom dffeent schools and, thus, affect the statng salaes. Conceptually, a pofessonal educaton poduces the stock of maketable human captal of the ndvduals gaduatng fom the pogam. Although fa fom pefect, the salay offe eceved on gaduaton povdes a easonable ndex of the maket value of the human captal. It s also tue, howeve, that the students ente the pogam wth vayng ntal stocks of human captal. Pe- MBA eanngs povde an ndex of the human captal acqued po to enteng the pogam. Thus, the ncemental contbuton of the pogam s the dffeental between the pe- and post- MBA annual eanngs. Reputatonal ankng of a busness school pmaly eflects popula pecepton of ts gaduates n the post-mba caees. But one should not neglect the esouces expended to accomplsh the bette achevements n ob placement. Havad MBAs epoted aveage statng base salay of $9,675 and a total compensaton package woth $63,792 (ncludng othe compensaton of $5,97 and a one tme sgnng bonus of $2,2) fo the gaduatng class of 998. Fo the gaduates of Maott School of Busness at Bgham Young Unvesty (BYU), the coespondng aveage base salay and total compensaton package wee $66,789 and $99,8, espectvely. What s seldom mentoned s that the aveage pe-mba salay of Havad s gaduatng class was aleady as hgh as $68, and a much moe modest $27,684 at BYU. In fact, when accountng fo dffeences n tuton and othe expenses, the annutzed value 3

4 of the gan n eanngs fo BYU gaduates exceeds that fo the Havad gaduates. The statng pay package by tself does not accuately eflect the success level of a school. Smlaly, most top-ated schools admt only students wth hgh GMAT scoes. Thus, the gaduates ae peselected fo a successful post-mba caee. In sum, the extent of "value added" s often ovestated. The obectve of management educaton s to poduce effcent manages. Effcent management of poducton eques optmal utlzaton of esouces. Effcency s nconsstent wth ethe unealzed potental ncease n output o avodable waste of nputs. To what extent do these top ated schools pactce what they peach? Moe specfcally, do these schools themselves, when vewed as poducton unts, make effcent use of the esouces? Decson makng poblems paallel poducton pocesses, whee desable outcomes of the decson play the ole of outputs whle actons o condtons facltatng these outcomes play the ole of nputs. The most mpotant achevement of busness school wdens the dffeence between the post-mba and pe-mba salaes of ts gaduates. Also, the numbe of ob offes povdes anothe output dmenson. Inputs, on the othe hand, nclude faculty and othe esouces employed as well as the qualty of the enteng class. Othe factos, such as the gende ato and the popoton of ntenatonal students, can affect the outputs, and theefoe they may ente as nputs n an appopately specfed model. In ths study, we employ Data Envelopment Analyss (DEA) to evaluate the effcency of Busness Week's top-ated busness schools fo the yea Johnes and Johnes (993) use DEA to measue eseach effcency of a numbe of Economcs depatments fom Btsh 3 The method of DEA was ntoduced by Chanes, Coope, and Rhodes (978) to non-paametcally measue techncal effcency of poducton unts wth efeence to a technology exhbtng constant etuns to scale. Subsequently, Banke, 4

5 unvestes based on publcaton and pesonnel data collected by the Royal Economc Socety. Buton and Phmste (994) apply DEA to evaluate effcency of a set of "coe ounals" dentfed by Damond (989). Beu and Raab (994) analyze the data fom the Top-25 Natonal unvestes and Lbeal Ats colleges to measue the effcency levels usng DEA. They fnd that seveal of the best-ated unvestes lke Cal Tech (ated 5 th ) and Chcago (ated th ) opeate at less than 9% effcency. Colbet, Levay and Shane (999) detemne a moe accuate ankng of U.S. MBA pogams based on DEA and also compae the effcency levels wth thee foegn MBA pogams. No study, howeve, consdes a measue of Paeto-Koopmans non-adal effcency. Unlke most DEA studes, ths pape uses a global (athe than a adal) effcency measue poposed by Pasto, Ruz, and Svent (999) to evaluate the MBA pogams n the lst. Input- and output-oented adal and non-adal measues ae also computed fo compason. Effcency n the top te exceeds that n the lowe tes. Seveal of the schools n the top-25 lst, howeve, emege as neffcent, whle many schools n the lowe backets exhbt hgh effcency. 4 Ths pape s oganzed as follows. In secton 2, we povde the theoetcal backgound and a bef descpton of the DEA methodology. Secton 3 dscusses the mplcatons of the vaous effcency measues calculated. Secton 4 summazes the conclusons. 2. Non-Radal Measues of Techncal Effcency Chanes, and Coope (984) genealzed the model to accommodate vaable etuns to scale. 4 Ths pape extends and updates unpublshed Ray (998), whch evaluates the effcency of top-4 MBA schools n Busness Week s 994 lstng. 5

6 Consde the poducton possblty set: T ={(x, y): y can be poduced fom x}, () whee x s an n-element nput bundle and y s an m-element output bundle. Unlke paametc models, the non-paametc appoach DEA does not specfy the poducton possblty set explctly. Instead, t only assumes that: (a) all obseved nput-output bundles ae feasble; (b) nputs ae feely dsposable; (c) outputs ae feely dsposable; and (d) the poducton possblty set s convex. If (x, y ) s a feasble poducton plan, then ( x, y ) T mples that y can be poduced fom x. The Debeu-Faell nput-oented measue of techncal effcency of the bundle (x, y ) s TE I (x, y ) = mn θ : (θx, y ) T. (2) Smlaly, the coespondng output-oented measue s TE O (x, y ) = * ϕ (3) whee ϕ * = max ϕ : (x,ϕ y ) T. To evaluate the nput-oented adal techncal effcency of a fm poducng output y fom nput x unde vaable etuns to scale n any empcal applcaton, one solves the followng DEA model due to Banke, Chanes, and Coope (BCC) usng a sample of obseved nput-output bundles (x, y ) ( =,2,,N): mn θ s.t. λ y y; ( =,2,,m); λ x θ x ; (=, 2,, n); (4) λ = ; λ ; ( =, 2,, N). Smlaly, fo the output-oented adal measue, one solves the followng poblem: 6

7 max φ s.t. λ y φy; ( =,2,,m); λ x x ; (I =, 2,, n); (5) λ = ; λ ; ( =, 2,, N). The output-oented measue s the nvese of the optmal value of the obectve functon. In geneal, many nput bundles exst othe than x, all of whch can also poduce y. Fo the specfc output bundle y, we can defne the nput (equement) set V(y ) = { x : y can be poduced fom x }. (6) Fo each specfc output bundle y, thee s a specfc nput set V(y). Thus, the same poducton possblty set T geneates a famly of nput sets. Evey obseved nput bundle x les n the nput set of the coespondng output bundle y. Futhe, f x V(y ) and x x, then x V(y ). Also, f x V(y ) and y y, then x V(y ). If the poducton possblty set T s convex, the nput sets ae also convex. Many nput bundles n the nput set of a specfc output bundle ae neffcent, because one can poduce the taget output fom a smalle nput bundle. These ae stctly nteo ponts of the nput set. By contast, the soquant of an output bundle y conssts only of bounday ponts of V(y ). The soquant of y s V ( y ) = { x : x V ( y ) and λx V ( y ) f λ < }. (7) Thus, f x V ( y ), then t s not possble to educe all nputs even by the smallest amount and stll poduce the output level y. The quantty of at least one nput n the x bundle must be stctly bndng. Fom the defnton of the soquant, f x V (y ), then the nput-oented techncal effcency of (x, y ) equals unty. Indeed, evey nput-oented adal poecton of 7

8 an neffcent nput-output bundle (x, y) les n the soquant of the output bundle y. The effcent subset of the soquant of any output bundle y s defned as V * ( y ) = { x : x V ( y ) and x' V ( y ) f x' x}. (8) Note that f x V * (y ), then educng any nput n the x bundle endes the output bundle y nfeasble. Thus, evey nput bundle n the effcent subset of the soquant of an output bundle s techncally effcent and no slack exsts n any ndvdual nput. The non-adal measue, poposed by Fäe and Lovell (978), measues the techncal effcency of a fm elatve to a pont n the effcent subset of the soquant. In an output-oented analyss of techncal effcency, the obectve s to poduce the maxmum output fom a gven quantty of nputs. Fo ths, we fst defne the (poducble) output set of any gven nput bundle. Fo the nput bundle x, the output set P(x ) = { y: (x, y) T} (9) conssts of all output bundles that x can poduce. Because dffeent output sets exst fo dffeent nput bundles, the poducton possblty set s equvalently chaactezed by a famly of output sets. If (x, y ) s an actually obseved nput-output combnaton, then y P( x ). Futhe, f y P(x ) and f x x, then y P(x ). Smlaly, f y P(x ) and f y y, then y P(x ). Fnally, convexty of T ensues that each output set P(x) s also convex. The output soquant of any nput bundle x s defned as P( x ) = { y : y P( x ) and λy P( x ) f λ > }. () Thus, f y P (x ), then the output-oented adal techncal effcency of the pa (x, y ) equals unty, because one cannot ncease all outputs holdng the nput bundle unchanged. Ths does not, of couse, ule out the possblty that one can ncease some ndvdual 8

9 components of the y output bundle. The effcent subset of the output soquant of x, on the othe hand, s * P ( x ) = { y : y P( x ) and y' P( x ) f y' y }. () Theefoe, an output-oented adal techncally effcent poecton of y poduced fom x onto P(x ) may nclude slacks n ndvdual outputs. But no such slacks may exst, f the poecton s onto P * (x ). The adal measue of output-oented techncal effcency does not eflect any unutlzed potental fo nceasng ndvdual outputs. Agan, as shown below, a non-adal, output-oented measue does nclude all potental nceases n any component of the output bundle. The poblem of slacks n any optmal soluton of a adal DEA model ases because we seek to expand all outputs o contact all nputs by the same popoton. In non-adal models, one allows the ndvdual outputs to ncease o the nputs to decease at dffeent ates. Fäe and Lovell (978) ntoduced the followng output-oented, non-adal measue of techncal effcency, whch they called the Russell measue: 5 whee RM y ( x, y ) =, (2a) ρ y ρ = max y m s.t. λ y φ y; ( =,2,,m); φ 5 Fäe and Lovell allow ndvdual components of the nput o output bundle to take zeo values. They defne the ndcato vaables δ that take the value, f output s, and othewse. The obectve functon s φ ρ y =. δ Thoughout the pesent analyss, we assume that all nputs and outputs ae stctly postve. The Range Adusted Measue (RAM) ntoduced by Coope, Pak, and Pasto (999) can accommodate zeo nputs o outputs unless the elevant nput/output s constant acoss obsevatons. 9

10 λ x x ; (I =, 2,, n); (2b) λ = ; φ ; ( =, 2,,m); λ ; ( =, 2,, N). When output slacks do exst at the optmal soluton of a adal DEA model, the non-adal Russell measue falls below the conventonal measue obtaned fom an output-oented BCC model. That s, because the adal poecton s always a feasble pont fo ths poblem, * ρ y φ. Hence, the non-adal Russell measue of techncal effcency neve exceeds the coespondng adal measue. The analogous nput-oented non-adal measue of techncal effcency s: 6 whee RM x ( x, y ) = ρ, (3a) x ρ = mn x n s.t. λ y y; ( =,2,,m); θ λ x θ x ; (=, 2,, n); (3b) λ = ; θ ; (=, 2,, n); λ ; ( =, 2,, N). The optmal soluton poects the obseved nput bundle x onto the bundle x * = (θ * x, θ2*x 2,, θn * x n ) n the effcent subset of the soquant of the output y. 7 6 See Russell (985) fo a numbe of lmtatons of ths non-adal measue. Zeschang (984) poposes a two-step Russell extended-faell measue that syntheszes the best featues of the conventonal adal Debeu-Faell measue and the non-adal Russell measue. In the nput-oented case, ths extended measue emeges by fst poectng an obseved nput bundle x adally onto the soquant of the coespondng output bundle. Once one acheves ths popotonal scalng (by the facto θ), one poects any nput slack pesent n ths bundle θx futhe onto the effcent subset of the soquant by solvng the non-adal poblem fo RM x (θx, y ). When no nput slack exsts n the adal poecton of the obseved nput bundle, no futhe adustment need occu so that the adal and non-adal measues concde. 7 In an altenatve appoach, Togesen, Fosund, and Kttelsen (996) adust the effcent adal poecton of the output bundle fo slacks n ndvdual outputs to obtan a non-adal poecton onto the effcent subset of the output soquant. Instead of a summay measue of effcency combnng the adal expanson facto wth the slacks, they epot the potental output quanttes ndvdually eflectng the output-specfc effcency levels.

11 No appoach focuses on output and nput slacks smultaneously, howeve. Because these ae ethe output-oented o nput-oented measues, ethe nput slacks o output slacks ae gnoed. Instead, we consde a non-adal measue that accommodates slacks n both outputs and nputs. An nput-output combnaton (x, y ) s not Paeto-Koopmans effcent f t volates ethe of the followng neffcency postulates: () It s possble to ncease at least one output n the bundle y wthout educng any othe output and wthout nceasng any nput n the bundle x ; o () It s possble to educe at least one nput n the bundle x wthout nceasng any othe nput and wthout educng any output n the bundle y. Clealy, unless RM x (x, y ) = RM y (x, y ) =, at least one of the two neffcency postulates s volated and (x, y ) s not Paeto-Koopmans effcent. Input-output bundle (x, y ) s Paeto-Koopmans effcent, when both of the followng condtons hold: * () x V ( y ) and () y P * ( x ). Consde the vectos θ = θ, θ,..., θ ) and φ = φ, φ,..., φ ). A non-adal Paeto- ( 2 n ( 2 m Koopmans measue of techncal effcency of the nput-output pa (x, y ) s computed as: Γ = mn n m θ φ s.t. N = λ y φ y ( =,2,..., m); ; N = λ x θ x ( =,2,..., n); (4) ; φ ; ( =,2,..., m); θ ; ( =,2,..., n); N = λ = ; λ ; ( =,2,..., N).

12 Note that the effcent nput-output poecton (x *, y * ) satsfes x * = N = * * * λ x x and y = λ y y. N = Thus, (x, y ) s Paeto-Koopmans effcent, f and only f φ * = fo each output and θ * = fo each nput, mplyng Γ =. We can vsualze the Paeto-Koopmans genealzed effcency measue (GEM) as the poduct of two factos. The fst s the nput-oented component (GEMIN) γ = and the second s an output-oented component (GEMOUT) n θ γ 2 = m φ. Thus, Γ = γ. γ 2. The obectve functon n ths mathematcal pogammng poblem s non-lnea. Coope, Pak, and Pasto (999) note that one can use a lnea appoxmaton. In the pesent context, howeve, the obectve functon n (4) lneazes as: Γ = f f f ( θ, φ) f ( θ, φ ) + ( θ θ ) + ( φ φ ). (5) θ φ Note that f = θ m n n θ f and =. 2 φ m φ φ (5a) (5b) Thus, usng θ = fo all and φ = fo all, at the pont of appoxmaton, Γ + n θ m φ. (6) We may, theefoe, solve the lnea pogammng poblem: 2

13 mn n θ m φ s.t. N = λ y φ y ( =,2,..., m); ; N = λ x θ x ( =,2,..., n); (7) ; φ ; ( =,2,..., m); θ ; ( =,2,..., n); N = λ = ; λ ; ( =,2,..., N). Once we obtan the optmal ( θ *, φ * ) fom ths poblem 8, we use Γ * = n m θ φ * * (8) as a measue of the Paeto-Koopmans effcency of (x, y ). Note that ths LP poblem s a specal case of the moe geneal optmzaton poblem wth the same constants, but the obectve functon mn Ω = α θ β φ s.t. N = λ y φ y ( =,2,..., m); ; N = λ x θ x ( =,2,..., n); (9) ; φ ; ( =,2,..., m); θ ; ( =,2,..., n); N = λ = ; λ ; ( =,2,..., N). Settng α = n fo all and = m β fo all, we get the Paeto-Koopmans poblem. If, 8 One may choose to use the optmal soluton (θ *,φ * ) as the new pont of appoxmaton and update (5a-b) to obtan new coeffcents fo the obectve functon fo the LP poblem n (7). The teatve pocess may be temnated 3

14 addtonally, we set β = fo all, we get the nput-oented Russell measue. Futhe, when all estct each α = α, we get the usual nput-oented adal DEA poblem. Smlaly, the estctons α = fo all lead to the output-oented Russell poblem. Futhe estctng β = β fo all, we get the usual output oented adal DEA poblem. 3. The Empcal Analyss Reputaton and Effcency In ths study, we consde a 2-output, 6-nput technology fo busness schools. The fst output GAIN measues the dffeence between the annutzed pe- and post-mba eanngs flow of a epesentatve gaduate of the school, whch can be teated as the value added. Management educaton helps the students acque and develop vaous management sklls, whch make them moe valuable to subsequent employes. Theefoe, n an effcent maket, a gaduate wth bette sklls elevant fo effectve management wll be ewaded wth a hghe salay. Anothe component of the output bundle s the adusted placement ate (PLACE). Moe wothy canddates usually geneate multple ob offes. Gven that the ob placement ate does not each %, howeve, the aveage numbe of offes eceved by the gaduates who actually get any offe s adusted by the pobablty that a gaduatng student has an offe n hand. The sx nputs nclude: () the faculty-student ato (FSRATIO), () the aveage GMAT scoe of the ncomng class (GMAT), () the degee of selectvty n the admsson pocess measued by the popoton of applcatons eected (REJECT), (v) the pecentage of male students n the class (MALE), (v) the pecentage of U.S. students n the class (US), and (v) the expendtue pe student (BUDGET). Faculty-student ato measues an mpotant school nput. when the optmal values of (θ, φ) change by less than some small value n two successve teatons. 4

15 An ncease n the FSRATIO should contbute postvely to the output bundle. The student's backgound s measued n two altenatve ways. One possble measue s the popoton of applcants accepted fo admsson by a school. The moe selectve the school s, the hghe s ts eecton ate and the bette s the qualty of ts gaduatng students. Self-selecton, howeve, may occu n the applcant pools acoss schools, whee bette applcants taget only the moe eputed schools (lke Havad o Stanfod). In that case, the second quatle of the pool of applcants fo one school may nclude bette applcants than the top quatle fo anothe. Hence, a eecton ate of 8% fo both schools does not mply the same qualty of the students admtted. An altenatve measues selectvty by the aveage GMAT scoes of the n-comng class acoss schools. In ths study, we nclude both measues of student qualty as nputs. The two demogaphc vaables, MALE and US, eflect chaactestcs of the students that may affect the salaes wthout affectng the manageal ablty. Due to famly constants, a female MBA exhbts less moblty than the male gaduates n he class, mplyng that he statng salay s lowe, on aveage. Also, a gende bas may exst aganst female gaduates n the maket. Fo both easons, a school wth a hghe popoton of female students may fnd that the expected salay ncease (pe- vs. post-mba) s lowe. Smla logc apples fo a school wth a hghe popoton of ntenatonal students. Often, due to vsa poblems, MBAs who ae not U.S. esdents accept obs that pay lowe than aveage. On the othe hand, outstandng MBAs who ae foegn natonals may etun to the own countes. As a esult, the aveage salaes of those who accept employment n the U.S. pobably ae lowe. By ncludng the nputs MALE and US, we contol fo these two "qualtatve dmensons" of the student nput. Fnally, BUDGET measues esouces spent pe student. The data fo the ndvdual schools used n ths study wee downloaded fom the Busness Week webste. The appendx povdes detals of constucton of 5

16 the vaous nput and output vaables. Table epots the nput-output data fo the ndvdual schools used n ths study and the goup-wse aveage values. The schools ae lsted accodng to the ankng n the Busness Week lst. They ae gouped nto 3 categoes te- conssts of the top-25 schools, te-2 ncludes the next 25 schools, and te-3 ncludes schools fom the next lowe categoy. On aveage, the schools fom a hghe categoy acheve hghe salay gan and a bette placement ecod than schools fom a lowe categoy. At the ndvdual school level, Canege Mellon Unvesty shows the hghest gan ($43,376), closely followed by New Yok Unvesty ($43,354). At the othe end, Unvesty of Floda shows a modest gan of $2,636. In tems of placement, Pudue Unvesty wth 4. ob offes pe gaduate poves most successful, whle SUNY Buffalo and Thundebd wth only.5 offes pe gaduate show the pooest pefomance. Examnng school esouces, the top-25 schools possess a substantally lowe faculty-student ato than the schools n the othe categoes whle the te-2 schools have a substantally lowe expendtue pe pupl compaed to the othe two categoes. Geoga Tech wth an expendtue level of $73,54 towes ove all othes. Tulane, Unvesty of Geoga, Havad, and Unvesty of Pennsylvana also spend n excess of $, pe student. Unvesty of Tennessee, Knoxvlle spends a mee $3,4 pe student. South Caolna spendng of $9,4 pe pupl was the second lowest. Schools n hghe categoes ae, as expected, moe selectve wth both hghe aveage GMAT scoes and hghe eecton ates. Stanfod accepts only 7% of the applcants and enolls a class wth an aveage GMAT scoe of 722. At the othe exteme, Clak Atlanta (anked 54 th ) wth a eecton ate nea 3% possesses an aveage GMAT scoe of 43. The popoton of US students does not move much (between 7.6% and 73.6%), on aveage, acoss all thee categoes. Compaed to the othe categoes, te-3 schools possess a hghe popoton of 6

17 female students (33.8%). Table 2 epots the goup-wse and ndvdual aveage levels of the global effcency measue (GEM), along wth ts vaous components. The aveage levels of Paeto-Koopmans global effcency measue equal 9.7% fo te-, 85.6% fo te-2, and 74.% fo te-3 schools. Because the oveall scoe, GEM, s the poduct of the two components, GEMIN and GEMOUT, we also examne them sepaately. The nput-oented facto, GEMIN, eflects the neffcency assocated wth possble educton n nputs, whle the output-oented facto, GEMOUT, shows the neffcency due to unealzed potental ncease n outputs. Fo the top-25 schools, both nput- and output-effcency levels (GEMIN and GEMOUT) equal about 95%. Te-2 schools show a lowe level of output effcency than nput effcency. The dffeence s moe ponounced fo the te-3 schools. Of the 25 schools n te-, ae neffcent. Two schools (Texas-Austn and Indana) opeate at effcency as low as 66%, sx othes (ncludng Datmouth, Vgna, UCLA, and UC Bekeley) opeate at effcency below 8% whle thee othes (ncludng 6 th anked Columba, and 9 th anked Stanfod) opeate below 9% effcency. In all cases, the output effcency component falls below the nput effcency component. Among the te-2 schools, 2 opeate at less than % Paeto-Koopmans effcency. Azona (53%), Geoga (46%), and Penn State (5%) exhbt the least effcency not only wthn ths goup, but also n the whole sample. Among the te-3 schools, only 2 (Boston and Clak Atlanta) of the ae effcent. The columns φ and φ2 show the potental ncease n the two outputs, f the school attans ts Paeto- Koopmans effcent poecton. Fo example, the optmal value of φ fo Datmouth s.24. Ths mples that the aveage salay gan acheved by ts gaduates could each nealy $37,75 (nstead of the actual $29,899). The nput contacton factos θ though θ5 do not show any 7

18 sgnfcant potental fo nput educton. Fo the pe student expendtue, the optmal value of θ6 s below.5 fo Indana (.3), Geoga (.2), Penn State (.4), Geoga Tech (.27), and Tulane (.37). Table 3 shows the ndvdual and goup-wse aveage values of the adal and non-adal nput- and output-oented effcency measues along wth the GEM and ts nput- and outputoented components. Note that the GEMIN (GEMOUT) measue often exceed the coespondng RUSSIN (RUSSOUT) measue. Ths occus because the nput-oented (outputoented) Russell measue gnoes slacks n the outputs (nputs) n the optmzaton. The aveage output-oented measues of effcency (RUSSOUT, GEMOUT, BCC) compae favoably wthn each categoy. But the nput-oented BCC adal measue exceeds the non-adal Russell measue (especally fo the te-3 schools) by lage amounts. Ths clealy eflects the pesence of vey hgh levels of slack n a patcula nput (BUDGET) n a numbe of schools n ths categoy. Whle the BCC adal measue gnoes ths slack, the nput-oented Russell measue captues the slack. At the ndvdual level, schools opeate at espectable levels of effcency, n geneal, when only adal nput- o output-oented BCC measues ae consdeed. But even by the output-oented BCC adal measue seveal schools (Azona (.67), Geoga (.66), Texas A&M (.66), UC-Davs (.66) and Washngton-Seattle (.63)) opeate at patculaly low levels of effcency. 4. Concluson In ths pape, we fomulate a DEA model to obtan Paeto-Koopmans measues of techncal effcency fo the top-6 busness schools fom the 998 ankng of Busness Week. We categoze the schools nto 3 goups -- the top 25 schools, the schools anked fom 26 th to 5 th 8

19 place, and the followng schools. Seveal top-ated schools exhbt techncal neffcency, snce t s possble to ncease the "outputs" whle educng some of the "nputs" at the same tme. On the othe hand, many lowe-ated schools exhbt hgh effcency. Ou esults show that eputatonal ankngs ae pncpally based on the outcomes measued by salay gans and placement ates wthout elatng these outcomes to the nputs used. A school wth less spectacula salay gans can exhbt moe effcent poducton when both nputs and outputs ae taken nto consdeaton. That s, many of the schools n the "unne up" lst ae fully effcent whle seveal fom the "top-25" lst ae not. Futhe, a adal measue of effcency -- whethe nput- o output- oented -- geneally pesents an unduly favoable pctue of the pefomance of a school when any knd of techncal neffcency exsts. Fnally, a note of cauton s n ode. The pesent study looks at the MBA pogams puely fom the standpont of techncal effcency n esouce utlzaton. Numeous othe factos sgnfcantly nfluence the mage of a busness school. A moe effcent pogam need not match an applcant s best choce. Pesonal cost-beneft atos may domnate the nput-output ato emboded n these techncal effcency measues. Also, ou study looks only at the statng salaes of busness school gaduates and fals to take account of how the ncomes gow ove tme once they ae employed. 9

20 APPENDIX Inputs and Outputs n DEA Output : GAIN = aveage post MBA salay + annuty value of fst yea compensaton - aveage pe MBA salay - 2 yeas tmes annuty value of tuton and fee ncludng oom & boad whee () annuty value of fst yea compensaton ncludes aveage sgnng bonus and aveage othe compensaton; nteest ate s equal to 5% fo the next 25 yeas (2) 2 yeas *annuty value of tuton and fee ncludes oom & boad (that s, Annual Out-of-State Tuton*pobablty(out-of-state)+ Annual In-State Tuton*[-Pobbablty(out of state)]+room & Boad) and also makng annuty values by usng 5% nteest ate fo the next 25 yeas Output 2: PLACE = ob offes by gaduaton =Aveage Job Offes pe student * the pecentage of gaduates wth ob offes Input : FSRATIO = faculty- student ato = (esdent faculty+.5 vstng faculty) / (full tme student +.5 pat tme student) Input 2: GMAT = aveage GMAT scoe Input 3: REJECT = selectvty (applcants accepted), unt: pecentage Input 4: MALE = female enollment pecentage, unt: pecentage Input 5: US = ntenatonal enollment pecentage, unt:pecentage Input 6: BUDGET = 998/99 school budget / enollment Whee enollment = full tme student +.5 * pat tme student 2

21 Refeences: Banke, R.D., A. Chanes, and W.W. Coope (984) "Some Models fo Estmatng Techncal and Scale Ineffcences n Data Envelopment Analyss", Management Scence, pp Beu, T.M. and R.L. Raab (994) "Effcency and Peceved Qualty of the Naton's "Top 25" Natonal Unvestes and natonal Lbeal Ats Colleges: An Applcaton of Data Envelopment Analyss to Hghe Educaton", Soco-Economc Plannng Scences, vol 28, pp Buton, M.P. and E. Phmste (995) "Coe Jounals: A Reappasal of the Damond Lst", The Economc Jounal, vol 5, pp Chanes, A., W.W. Coope, and E. Rhodes (978) "Measung the Effcency of Decson Makng Unts", Euopean Jounal of Opeatonal Reseach, vol 2, pp Colbet, A., R.A. Levay, and M.C. Shane (2) Detemnng the Relatve Effcency of MBA Pogams usng DEA, Euopean Jounal of Opeatonal Reseach, vol 25, pp Coope, W.W., Pak, K.S. and Pasto, J.T. (999) RAM: A ange adusted measue of effcency fo use wth addtve models, and elatons to othe models and measues n DEA, Jounal of Poductvty Analyss, vol, pp Damond, A.M. (989) "The Coe Jounals n Economcs", Cuent Contents, vol 2, pp 4-. Fäe, R. and C.A.K. Lovell (978) "Measung the Techncal Effcency of Poducton", Jounal of Economc Theoy; vol 9, pp Johnes, G. and J. Johnes (993) "Measung the Reseach Pefomance of U.K. Economcs Depatments: An Applcaton of Data Envelopment Analyss", Oxfod Economc Papes, vol 45, pp Pasto, J.T., J.L. Ruz, and I. Svent (997) "An Enhanced DEA Russell Gaph Effcency Measue", Euopean Jounal of Opeatonal Reseach, vol 5, pp Ray, S. C. (998), Paeto-Koopmans Measue of Effcency n Management Educaton: How Well managed ae Ameca s Top-4 Busness Schools?, Pesented at the 2 Noth Amecan Poductvty Wokshop. 2

22 Russell, R. R. (985) "Measues of Techncal Effcency", Jounal of Economc Theoy, vol 35, pp Togesen, A.M., F. Fosund, and S. C. Kttelsen (996) "Slack-adusted Effcency Measuement and Rankng of Effcent Unts", Jounal of Poductvty Analyss, vol 7, pp Vaan, H. (984) "The Nonpaametc Appoach to Poducton Analyss", Econometca, vol 54, pp Zeschang (984). An Extended Faell Effcency Measue, Jounal of Economc Theoy, 33,

23 Table : The Busness Schools Data and Summay Statstcs output output 2 nput nput 2 nput 3 nput 4 nput 5 nput 6 no Te school name Gan PLACE FSRATIO GMAT REJECT MALE US BUDGET Goup top 25 aveage Aveage next 25 aveage te-3 aveage top 25 Pennsylvana (Whaton) top 25 Nothwesten (Kellogg) top 25 Chcago top 25 Mchgan top 25 Havad top 25 Columba top 25 Duke (Fuqua) top 25 Conell (Johnson) top 25 Stanfod top 25 Datmouth (Tuck) top 25 UVA (Daden) top 25 UCLA (Andeson) top 25 NYU (Sten) top 25 Canege Mellon top 25 MIT (Sloan) top 25 UC Bekeley top 25 Washngton Unvesty (Oln) top 25 Texas at Austn top 25 UNC (Kenan-Flagle) top 25 Yale top 25 Indana (Kelley) top 25 Mayland (Smth) top 25 Wsconsn -- Madson top 25 Pudue (Kannet) top 25 USC (Mashall) next 25 Azona (Elle) next 25 Azona State next 25 Babson (Oln) next 25 BYU (Maott) next 25 Emoy (Gozueta) next 25 Geogetown next 25 Geoga (Tey) next 25 Illnos at Ubana-Champagn next 25 Iowa next 25 Mchgan State (Boad) next 25 Note Dame next 25 Oho State (Fshe) next 25 Penn State (Smeal) output output 2 nput nput 2 nput 3 nput 4 nput 5 nput 6 23

24 no Te school name Gan PLACE FSRATIO GMAT REJECT MALE US BUDGET 39next 25 Pttsbugh (Katz) next 25 Rce (Jones) next 25 Rocheste (Smon) next 25 SMU (Cox) next 25 South Caolna (Dala Mooe) next 25 Tennessee -- Knoxvlle next 25 Texas A&M next 25 Thundebd next 25 UC Ivne next 25 Vandeblt (Owen) next 25 Wake Foest (Babcock) next 25 Wllam & May te-3 Boston College te-3 Boston Unvesty te-3 Case Westen (Weathehead) te-3 Clak Atlanta te-3 Floda (Wangton) te-3 Geoga Tech (DuPee) te-3 Mnnesota (Calson) te-3 SUNY Buffalo te-3 Tulane (Feeman) te-3 UC Davs te-3 Washngton -- Seattle

25 Table 2: Paeto-Koopmans Measue of Effcency and ts Components no te school name φ φ2 θ θ2 θ3 θ4 θ5 θ6 GEMIN GEMOUT GEM Goup Top 25 aveage Aveage next 25 aveage te-3 aveage top 25 Pennsylvana (Whaton) top 25 Nothwesten (Kellogg) top 25 Chcago top 25 Mchgan top 25 Havad top 25 Columba top 25 Duke (Fuqua) top 25 Conell (Johnson) top 25 Stanfod top 25 Datmouth (Tuck) top 25 UVA (Daden) top 25 UCLA (Andeson) top 25 NYU (Sten) top 25 Canege Mellon top 25 MIT (Sloan) top 25 UC Bekeley top 25 Washngton Unvesty (Oln) top 25 Texas at Austn top 25 UNC (Kenan-Flagle) top 25 Yale top 25 Indana (Kelley) top 25 Mayland (Smth) top 25 Wsconsn -- Madson top 25 Pudue (Kannet) top 25 USC (Mashall) next 25 Azona (Elle) next 25 Azona State next 25 Babson (Oln) next 25 BYU (Maott) next 25 Emoy (Gozueta) next 25 Geogetown next 25 Geoga (Tey) next 25 Illnos at Ubana-Champagn next 25 Iowa next 25 Mchgan State (Boad) next 25 Note Dame next 25 Oho State (Fshe) next 25 Penn State (Smeal) no te school name φ φ2 θ θ2 θ3 θ4 θ5 θ6 GEMIN GEMOUT GEM 39next 25 Pttsbugh (Katz)

26 4next 25 Rce (Jones) next 25 Rocheste (Smon) next 25 SMU (Cox) next 25 South Caolna (Dala Mooe) next 25 Tennessee -- Knoxvlle next 25 Texas A&M next 25 Thundebd next 25 UC Ivne next 25 Vandeblt (Owen) next 25 Wake Foest (Babcock) next 25 Wllam & May te-3 Boston College te-3 Boston Unvesty te-3 Case Westen (Weathehead) te-3 Clak Atlanta te-3 Floda (Wangton) te-3 Geoga Tech (DuPee) te-3 Mnnesota (Calson) te-3 SUNY Buffalo te-3 Tulane (Feeman) te-3 UC Davs te-3 Washngton -- Seattle

27 Table 3: Radal and Non-adal Measues of Techncal Effcency nput-oented measues output-oented measues no te school name GEM CCR BCC RUSSIN GEMIN CCR BCC RUSSOUT GEMOUT Goup top 25 aveage Aveage next 25 aveage te-3 aveage top 25 Pennsylvana (Whaton) top 25 Nothwesten (Kellogg) top 25 Chcago top 25 Mchgan top 25 Havad top 25 Columba top 25 Duke (Fuqua) top 25 Conell (Johnson) top 25 Stanfod top 25 Datmouth (Tuck) top 25 UVA (Daden) top 25 UCLA (Andeson) top 25 NYU (Sten) top 25 Canege Mellon top 25 MIT (Sloan) top 25 UC Bekeley top 25 Washngton Unvesty (Oln) top 25 Texas at Austn top 25 UNC (Kenan-Flagle) top 25 Yale top 25 Indana (Kelley) top 25 Mayland (Smth) top 25 Wsconsn -- Madson top 25 Pudue (Kannet) top 25 USC (Mashall) next 25 Azona (Elle) next 25 Azona State next 25 Babson (Oln) next 25 BYU (Maott) next 25 Emoy (Gozueta) next 25 Geogetown next 25 Geoga (Tey) next 25 Illnos at Ubana-Champagn next 25 Iowa next 25 Mchgan State (Boad) next 25 Note Dame next 25 Oho State (Fshe) next 25 Penn State (Smeal) nput-oented measues output-oented measues 27

28 no te school name GEM CCR BCC RUSSIN GEMIN CCR BCC RUSSOUT GEMOUT 39next 25 Pttsbugh (Katz) next 25 Rce (Jones) next 25 Rocheste (Smon) next 25 SMU (Cox) next 25 South Caolna (Dala Mooe) next 25 Tennessee -- Knoxvlle next 25 Texas A&M next 25 Thundebd next 25 UC Ivne next 25 Vandeblt (Owen) next 25 Wake Foest (Babcock) next 25 Wllam & May te-3 Boston College te-3 Boston Unvesty te-3 Case Westen (Weathehead) te-3 Clak Atlanta te-3 Floda (Wangton) te-3 Geoga Tech (DuPee) te-3 Mnnesota (Calson) te-3 SUNY Buffalo te-3 Tulane (Feeman) te-3 UC Davs te-3 Washngton -- Seattle