MEASURING PRODUCTIVE EFFICIENCY AND COST OF PUBLIC EDUCATION

Transcription

1 Measuring Prducive Efficienc and Cs Of Public Educain MEASURING PRODUCTIVE EFFICIENCY AND COST OF PUBLIC EDUCATION Kalan Chakrabr Empria Sae Universi ABSTRACT This sud eamines he relainship beween schl disrics spending and varius schl and nn-schl facrs including prducive efficienc. An average cs funcin and a prducin funcin fr educain are esimaed. Empirical esimain uses hree ears panel daa frm unified schl disrics in Kansas. An efficienc inde is cnsruced and he al facr prducivi is measured. This sud fund eisence f significan ecnmies f scale fr Kansas schl disrics. Hwever inefficien disrics had spend mre achieve a given perfrmance sandard fr is sudens. The average schl disric is 89.6 percen efficien and here was n grwh in al facr prducivi ver he enire perid f sud. INTRODUCTION AND BACKGROUND Wih a view imprving he quali f public educain in he U.S. ver he pas few decades researchers have been invesigaing w fundamenal aspecs f he educain ssem: impac f class size n suden learning; and facrs direcl and indirecl influence suden perfrmance. The frmer caegr f sud mainl invesigaed he relainship beween class size and ependiure per suden and sudens academic achievemen. The secnd caegr f sud invesigaed hw effecive are he eacher schl and nn-schl inpus fr imprving sudens achievemen scres. The lieraure n public educain has mied respnses fr bh f hese grups. Sudies b Hanushek e al [ and 22] Riew [27] and Walberg and Fwler [30] fund n cnsisen relainship eiher beween schl inpus and suden perfrmance r class size and suden achievemen. Currenl he issue f ecnmies f scale and efficienc in public educain is under cninued scruin and plas a vial rle in he frmulain f a sund educain plic in Kansas. In he academic ear Kansas enrlled ne percen f he pupils in he nain bu had.62 percen f he nain s schls and 2.0 percen f he schl disrics in he Unied Saes Augenblick and Mers []. Beween and he number f schl disrics in Kansas drpped frm Cnslidain r merger fr lw perfrming and high cs schl/disric has been recmmended fr ecnmies f scale bu fen ne vial quesin remains unanswered: will reducin in cs imprve he perfrmance level f he sudens? In an aemp find a schl/disric pimal size pas sudies have esimaed an average cs funcin fr educain. Hwever recen sudies have fund ha in reali here is n pimum size ha can deliver a required perfrmance sandard wih minimum cs. Sme f he facrs ha influence sudens learning prcess are n capured in a cnveninal cs funcin. Befre frmulaing an plic fr rerganizing schls i is essenial ha he plicmakers and he schl 23

2 Suhwesern Ecnmic Review adminisrars undersand he cmpleiies underling educainal prducin and cs funcins. Building upn he sud b Duncmbe and Yinger [9] his sud esimaes an educainal cs funcin ha is cnrlled fr prducive inefficienc f he disric. The ependiure per suden in a disric depends n nl n he cs f inpus and he educainal envirnmen wihin which i peraes bu als n he efficien uilizain f is resurces b he disric adminisrars. The bjecives f he curren sud are w flds: measure he prducive efficienc and al facr prducivi fr he Kansas schl disrics; and 2 esimae an average cs funcin depicing he relainship beween he peraing cs per suden and varius schl and nn-schl facrs including he disrics inefficienc effec. This paper is rganized as fllws. The ne secin develps he cncepual framewrk fr an educainal prducin funcin and cs funcin fllwed b a secin n he daase and variables used in his sud. Furh secin analzes he empirical resuls fllwed b he summar and cnclusin secin. EDUCATIONAL PRODUCTIONAND COST FUNCTION Schl disrics are impaced b varius schl and nn-schl inpus prduce muliple upus ha are assumed be measurable b achievemen es scres. The purpse f educain is ransmi knwledge and develp he suden s basic cgniive skills. These abiliies fen are measured b he scres in sandardized ess such as reading wriing and mahemaics. Schl inpus ha are assciaed wih achievemen scres are generall measured b he suden-eacher rai he educainal qualificains f eachers eaching eperience and varius insrucinal and nn-insrucinal ependiures per suden Chakrabr e al [2]. Nn-schl inpus generall include sciecnmic saus f he sudens and her envirnmenal facrs ha influence sudens prducivi. Variables idenifing sciecnmic saus f he sudens are famil incme number f parens in he hme and parenal educain. Envirnmenal facrs are fen measured b gegraphic lcain e.g. rural vs. urban and ne prper assessed value per suden. Ms f he sudies in educainal prducin fund an insignifican relainship beween schl inpus and upus. In cnras Walberg e al [30] Hanushek [6 7] Deller and Rudnicki [5] Cper and Chn [4] and Faire e al [2] fund ha sciecnmic and envirnmenal facrs significanl affec achievemen scres. Using a var large and unique daase frm Teas public schls Rivkin e al [28] fund ha eacher quali raher han famil facr is mre impran fr raising he achievemen fr lw incme sudens. In he measure f echnical efficienc a schl disric is cnsidered echnicall efficien if i achieves he highes pssible upu i.e. achievemen scre frm a given amun f resurces used r cnversel uses minimum resurces prduce a given level f upu. In his sud upu f he educainal prducin funcin is measured as he disric level average es scres fr mahemaics and reading. A mahemaical prgramming echnique called daa envelpmen analsis DEA is used in his sud cnsrucs he bes pracice prducin frnier. Sme f he majr advanages f using DEA fr measuring efficienc are is abili handle muliple upus i is nnparameric and i des n require inpu prices. In DEA he perfrmance f a disric is evaluaed in erms f is abili eiher reduce an inpu vecr r epand an upu vecr subjec he resricins impsed b he 24

3 Measuring Prducive Efficienc and Cs Of Public Educain bes-bserved pracice. This measure f perfrmance is relaive in he sense ha efficienc in each schl disric is evaluaed agains he ms efficien disric and measured b he rai f acual bserved upu maimal penial upu. The rai can ake he values beween zer and ne and ne being perfecl efficien. Hwever if a schl/disric is fund efficien des n necessaril impl ha i prduces he maimum level f upu given he se f inpus. I implies ha i is a bes pracice disric in he sample Nulas and Kekar [24]. The cnsrucin f a simple upu riened DEA mdel and he al facr prducivi inde is prduced in he Appendi. Previus sudies have fund ha cs f achieving a perfrmance sandard varies acrss schl disrics Ruggier [29]. A pr schl disric generall needs a higher level f per-suden ependiure achieve a perfrmance sandard equal wih ha f a wealh disric. A disric is hugh f as prducive and efficien if i achieves he sandard level f perfrmance while uilizing he minimum f resurces when cmpared is peer disrics. The ependiure per suden fr a disric depends n he upu level i chses and n he price f inpus. Because f he unique naure f he educainal prducin prcess where upu is he amun f learning raher han amun f insrucin envirnmen is a vial inpu in achieving a sandard perfrmance fr an disric Hanushek [7]; Racliffe e al [26]; Dwnes and Pgue [6]; Duncmbe e al [7]; Chakrabr e al [3]. Brrwing frm he Duncmbe and Yinger [9 8] his sud esimaes a cs funcin epressed as: C = α β X β P β N β F β D ε where C is he ependiure per suden in he disric; X is he varius measures f sudens perfrmance mah and reading scres; P is he price f varius inpus he disric pas such as eachers salaries; N is he disric size; F is he sudens sciecnmic saus; D is he her suden characerisics; and ε is he unbserved disric characerisics. One f he crucial unbserved facrs in he abve equain is disric efficienc. Hlding her hings cnsan a mre efficien disric ms likel wuld spend less per suden achieve he same sandard. In rder capure he effec f unbserved facrs n disric spending Duncmbe and Yinger included a disric efficienc inde as ne f he independen variables in heir cs funcin using New Yrk daa. A similar apprach has been underaken in his sud. A echnical efficienc inde fr each schl disric is esimaed using DEA and his efficienc inde is included as ne f he independen variables in he cs funcin. Duncmbe and Yinger used dumm variables idenifing pes f disrics i.e. rural/urban in rder capure he effecs f unbserved disric characerisics in heir cs funcin. This sud uses linear fied and randm effec mdels designed fr panel daa analsis esimae he cs funcin. In he esimain f an educainal cs funcin i is ver impran ha prper variables are included and he regressin equain is crrecl specified. A prper specificain f a cs funcin shuld avid including an ependiure relaed variables as independen variable. Krueger [23] pined ha if ependiure per suden is used as an eplanar variable in a cs funcin ha wuld creae an inerpreaive prblem fr he effec f class size. 25

4 Suhwesern Ecnmic Review The specificain and esimain f he cs funcin in his sud is based n sund ecnmeric cnsiderain and is linked an educainal prducin funcin. Alhugh each schl disric in his sud is bserved ver a perid f hree ears a pled OLS regressin wih 92 bservains wuld n be an efficien esimar because i assumes ha bh inercep and slpe cefficiens are same fr all disrics. Iniiall he linear mdels fr panel daa bh fied effec and randm effec mdels were applied esimae he cs funcin. Based n he Hausman es we failed rejec he hphesis ha he disric specific effecs are fied. Furher in rder deermine wheher he ne-wa r he w-wa fied effec mdel represen he daa bes he r-squares and Hausman es saisics bained frm each mdel were cmpared. The w-wa fied effec mdel prduced he beer resuls fr his daa. Thereicall he ne-wa fied effec mdel assumes ha he inerceps var bu he slpe cefficiens are same; and he w-wa fied effec mdel has an verall cnsan as well as a grup effec fr each grup and a ime effec fr each ime. The mdified cs funcin esimaed in his sud is wrien as: C i = α α γ β Z ε 0 i k i i 2 where i is he number f disrics; is he number f perids; α i is he grup effec; γ is he ime effec; β k are he unknwn cefficiens be esimaed; vecr Z represens riginal variables X P N F and D frm equain. Z als includes an efficienc inde fr each disric fr each ear under sud. In he cs funcin esimain i is hphesized ha he cefficien f he measure f upu X wuld be psiive enrllmen wuld be negaive N enrllmen square wuld be psiive signifing U-shape average cs curve eachers salar P wuld be psiive and percen f sudens qualified fr free and reduced lunch F wuld be psiive. I is hphesized ha he disrics efficienc inde wuld be negaivel relaed ependiure per suden impling higher cs fr inefficien disrics. DATASET The disric level daa fr all educainal inpus and upus were prvided b he Kansas Sae Deparmen f Educain Tpeka. Infrmain n inpus and upus were bained fr he academic ears and The upus fr ur educainal prducin funcin are measured as he sandardized es scres fr mahemaics and reading. These ess are adminisered all disrics fr sudens a he 4h 7h and 0h; and 3rd 7h and 0h grade respecivel. Since he infrmain n ms f he variables are available a he disric level esimaing separae cs funcins fr each f hse grade levels are n pssible. Hence disric level average aggregaed scres fr mah and reading were generaed and used in his sud. I is recgnized ha b aggregain f es scres sme infrmain is ls which is ne f he limiains f his sud. Sandardized ess fr science and scial science were n inrduced fr Kansas public schls unil academic ear The rainale fr using nl mah and reading scres is ha he mah and reading skills are recgnized as he w ms pwerful deerminans fr fuure success and 26

5 Measuring Prducive Efficienc and Cs Of Public Educain earning penial in he public educain lieraure Murnane e al [24]. Krueger [23] fund ha ne sandard deviain increase in eiher mah r reading scres in elemenar schls was assciaed wih abu 8 percen higher earning in jbs. Schl and nn-schl inpus used in his sud are measured as peraing ependiure per suden; suden-eacher rai; average cnaced salar fr eachers; and percen f disric sudens receiving free r subsidized lunch. Operaing ependiure includes ependiure fr insrucin adminisrain and plan mainenance and perain. I is recgnized ha infrmain n sme f he majr insrucinal inpus such as eachers educainal qualificain and ears f eaching eperience are missing frm his sud. This is because infrmain n hese variables a he disric level is n readil available frm he Kansas sae deparmen f educain. Our educainal prducin funcin uses mah and reading scres as w upus; and peraing ependiure per suden eacher-suden rai eachers salar and percen f suden qualified fr free and reduced lunch AFDC as inpus. The inclusin f nn-cnrllable inpus fr measuring echnical efficienc using DEA is n ver cmmn in he lieraure; hwever his sud fllws Duncmbe and Yinger [8 9] wh have used egenus variables in measuring echnical efficienc f New Yrk schl disrics. The descripive saisics f he daa are presened in Table. Table Descripive Saisics f he Daa bs = 92 Variables Mean Minimum Maimum Mah Cmpsie 4 h 7 h and 0 h Reading Cmpsie 3 rd 7 h and 0 h Operaing ependiure per suden $ Suden-eacher rai Disric enrllmen Average cnaced eacher s salar $ Percen f sudens receiving Free and subsidized lunch AFDC ANALYSIS OF RESULTS The echnical efficienc scres frm DEA esimain fr all 304 disrics are n repred in his paper. Hwever a summar f he efficienc scres is prduced in Table 2. Onl 4 u f 304 disrics were fund full efficien. Technical efficienc fr 53 disrics is beween 99.9 and 95.0 percen. On average schl disrics in Kansas are 89.2 percen efficien impling disrics wuld be able prduce he same sandard f educainal upu using 89.2 percen f heir curren level f inpu usage. The leas efficien disric is Washingn which is 70. percen efficien. Mre han half f he disrics in Kansas 60 are peraing a an efficienc level 90 percen r belw. Clumn 3 5 and 7 f Table 2 presen he summar f he indices fr efficienc change echnlgical prgress and al facr prducivi change 2 deail resuls are n repred in he paper. Fr an f hese rais a value less han ne implies deerirain r decrease and graer han ne denes grwh r imprvemen. On he average annual decrease in al facr prducivi fr disrics in Kansas is.5 percen. The cause f decrease in al facr prducivi is 27

6 Suhwesern Ecnmic Review Mean Efficienc Table 2 Summar f Mean Technical Efficienc Efficienc Change Technlgical Change and Tal Facr Prducivi Change Indices Ns USD 2 Percen Grwh EFFCH 3 Ns USD 4 Percen Grwh TECHCH 5 Ns USD 6 Percen Grwh TFPCH 7 Ns USD Belw AVG = AVG = AVG = AVG = USD-unified schl disric EFFCH-efficienc change TECHCH-echnlgical prgress/change TFPCH-al facr prducivi change furher analzed b breaking i in indees f echnlgical change and efficienc change. The decrease in al facr prducivi.5 percen is he ne effec f echnlgical change -2. percen and grwh in efficienc change 0.6 percen. Negaive echnlgical change can ccur due ne u migrain f skilled and rained persnnel fr he Sae r regin causing inward shif f he prducin frnier. Anher eplanain culd be a measuremen errr fr inpu and upu variables used in he sud r due he presence f uliers in he daa. Table 3 Educainal Cs Funcin Esimaes Kansas Schl Disrics Dependen variable Ln peraing ependiure per suden Variables Cefficien -saisics Mah Cmpsie 4 h 7 h and 0 h * Reading Cmpsie 3 rd 7 h and 0 h * Lnenrllmen * Lnenrllmen * Lneacher s salar Percen f sudens receiving Free and subsidized lunch AFDC Efficienc percen * Cnsan * R-square Hausman es saisics 280 *-indicaes significan a 5 percen r belw level Table 3 presens he cefficien esimaes frm he cs funcin using a wwa fied effec mdel using disric and ime dumm variables. Large value f Hausman es saisics suggess fied effec mdel is mre apprpriae fr ur daa. Overall he regressin equain has a gd fi. The cefficiens n all eplanar variables have epeced sign. Ecep fr he cefficien n eachers salar and AFDC all cefficiens are significanl differen frm zer a he 5 percen r belw 28

7 Measuring Prducive Efficienc and Cs Of Public Educain level. The resuls bained frm his sud are ver similar he ne bained b Duncmbe and Yinger [8 9] fr he New Yrk daa. Psiive cefficiens n he variable mah and reading scre measure f upus sugges ha i css mre generae a higher level f upu. Highl significan and negaive cefficien n enrllmen and psiive and significan cefficien n enrllmen-squared suggess per suden ependiure decreases iniiall reaching a minimum as enrllmen increases and hen increases as enrllmen increases. This is pical fr a U-shaped average cs funcin. The elasici fr eachers salar is 0.3 which implies ha a ne percen increase in eachers salar wuld cause 0.3 percen increase in ependiure per suden. The effec f sciecnmic saus f he sudens did n appear be significan in his sud hugh psiive cefficien implies i css mre fr he pr schl disrics educae is sudens. The negaive and highl significan cefficien n he efficienc variable suggess an inverse relainship beween disrics efficienc and per suden ependiure. Fr eample ne percen increase in efficienc wuld cause w percen decease in ependiure per suden. This is ne f he ms impran findings frm his sud. SUMMARY AND CONCLUSION This sud measured echnical efficienc and al facr prducivi and esimaed an average cs funcin using hree-ear panel daa fr 304 schl disrics in Kansas. The efficienc measure used a muli-upu and muli-inpu mdel applied daa envelpmen analsis. The sud fund ha n average disrics are 89.2 percen efficien. Cmparisn f al facr prducivi TFP change acrss disric and ver ime shwed significan differences acrss disrics hwever n average ms f he disrics eperienced a decrease in TFP grwh. One f he ineresing resuls fund in his sud is ha disrics wih lw echnical efficienc a he beginning f he perid eperienced he highes grwh in TFP a he end. Fr eample Bazine ID-D0304 Jahawk ID-D0346 and Vermillin ID-D0380 had he lwes echnical efficienc scres in and respecivel 3 bu in 999 hese disrics achieved ne f he highes TFP grwhs. 2.7 and.8 percen respecivel 4. This cnfirms ne f he esablished facs in prducivi analsis acrss ime ha disrics wih lw prducivi r efficienc a he beginning wuld gain ms frm he diffusin f echnlgical knwledge available in he laer ears. As a resul hese disrics wuld be able push heir prducin frnier farher during he sud perid han hse wh were mre efficien a he beginning. The regressin resuls frm he cs funcin ha accuns fr efficienc differences indicae ha i css less per sudens fr efficien disrics achieve a se f sandards. The implicain f he resul is especiall impran fr Kansas plicmakers and schl adminisrars when frmulaing a plic fr rerganizing schl disrics and revising schl funding frmula. One her ineresing resul fund in his sud is he eisence f significan ecnmies f scale in he prducin f educain in he sae. Alhugh his sud des n idenif which disrics will achieve cs reducin frm cnslidain he resuls cnfirm verall ecnmies f scale in public educain in Kansas. A he curren sae f ur ecnm when ms f he saes are eperiencing budge cus in public educain cnslidain will 29

8 Suhwesern Ecnmic Review definiel save sme a dllars. Hwever in rder achieve maimum effeciveness frm disric cnslidain i is ver essenial ha a prin f he saved mne be spen n hiring reenin and raining and develpmen f he eaching persnnel and fr he imprvemen f echnlg in schls. This will evenuall imprve he verall sudens perfrmance bh fr he cnslidaed and he eising schl disrics. Oherwise i is mre likel ha hrugh cnslidain we will be sacrificing quali fr cs in ur public educain ssem. 30

9 Measuring Prducive Efficienc and Cs Of Public Educain APPENDIX In a simple upu-riened DEA mdel Le N n =... R M m =... R be a vecr f n inpus prducing a vecr f m upus in perid. If we define he prducin pssibili se fr as P hen i gives all pssible cmbinains f ha can be prduced frm inpu vecr. Hence he upu disance funcin is defined as: D = min θ subjec P θ A Given he echnlg in he abve specificain he Farrell s 957 upu riened measure f echnical efficienc fr acivi k is bained b maimizing he reciprcal f he disance funcin in equain. Ma D = θ θ z Subjec K A2 θ km z k km m = 2... M ; K k= z k kn kn n = 2... N; k= z k 0 k = 2... K k k D = Hence implies disric k is he ms efficien and lies n he prducin frnier and an value less han.0 implies he firm is peraing belw he prducin frnier. The resricive assumpin f cnsan reurns scale n he prducin echnlg is furher relaed and a variable reurns scale wih srng dispsabili is impsed b he fllwing resricin n he inensi vecr z k =. The Tal Facr Prducivi Malmquis Prducivi Inde Over ime an increase in efficienc ma cause an upward shif in he prducin frnier leading grwh in prducivi. Imprvemen in al facr 3

10 Suhwesern Ecnmic Review 32 prducivi als called Malmquis prducivi inde culd be due eiher imprvemen in echnical efficienc r imprvemens in echnlg. Fare e al. [3] decmpsed he Malmquis Prducivi Inde fr ih farm in perid as he prduc f an efficienc change inde and echnlgical prgress. A prducivi inde is cnsruced eamining he upus in perid and relaive echnlg available in perid and and using he gemeric mean. The epressin fr Malmquis prducivi inde is: = MALM D D * 2 * D D D D A3 * T E MALM = A4 Superscrip and represen he curren and he ne perid respecivel. The funcin E. represens he prducivi change arising frm changes in echnical efficienc which is measured b he rai f w disance funcins a w differen pins in ime. The funcin T. represens changes in prducivi due a echnlgical prgress. This is cmpsed f disance funcins which mi echnlg frm ne ime perid wih bservains frm anher ime perid which are hen averaged gemericall. Fr eample he mied perid disance funcin D cmpues he larges pssible cnracin f inpus bserved in ime perid s ha he level f upu in ha perid can be prduced using echnlg frm ime perid. The echnlg inde capures he shif in echnlg beween perid and evaluaed a w differen daa pins and. Fr a deailed discussin n Malmquis prducivi inde readers ma cnsul Dmazlick and Weber [ 0]. ENDNOTES. The deail resuls frm DEA mdel esimaing efficienc scres fr 304 USD are available frm he auhr upn reques. 2. The deail resuls frm Tal Facr Prducivi Inde and is cmpnens efficienc change echnlgical change and al facr prducivi grwh fr each schl disric are available frm he auhr upn reques. 3. See ne abve. 4. See ne 2 abve.

11 Measuring Prducive Efficienc and Cs Of Public Educain REFERENCES Augenblick Jhn Jhn Mers and Jusin Silversein. A cmprehensive sud n he rganizain f Kansas schl disrics. Prepared fr Kansas Sae Bard f Educain. Augenblick & Mers Inc. Jan Chakrabr Kalan. Basudeb Biswas and W. Cris Lewis. 200 Measuremen f echnical efficienc In public educain: A schasic and nnschasic prducin funcin apprach. Suhern Ecnmic Jurnal 674: Chakrabr Kalan. Basudeb Biswas and W. Cris Lewis Ecnmies f scale in public educain: An ecnmeric analsis. Cnemprar Ecnmic Plic Vl 82: Cper Samuel T. and Elchanan Chn. 997 Esimain f a frnier prducin funcin fr Suh Carlina educainal prcess. Ecnmics f Educain Review 6: Deller Seven C. and Edward Rudnicki. 993 Prducin efficienc in elemenar educain: The case fr Maine public schls. Ecnmics f Educain Review 2: Dmazlick B. R. and W. Weber. 998 Deerminans f Tal Facr Prducivi Technlgical Change and Efficienc Differencials Amng sae Review f Reginal Sudies 28: Dmazlick B. R. and W. Weber. 997 Tal Facr Prducivi in he Cniguus Unied Saes Jurnal f Reginal Science 37: Dwnes T. and T. Pgue 994 Adjusing Schl Aid Frmulas fr he Higher Cs f Educaing Disadvanaged Sudens. Nainal Ta Jurnal 47: Duncmbe W. J. Jr. Ruggier. and J. Yinger J. Alernaive Appraches Measuring Cs f Educain In H. F. Ladd Eds. Hlding Schls Accunable: Perfrmance Based Refrm in Educain Washingn DC. The Brkings Insiuin. Duncmbe William and Jhn Yinger. 997 Wh is i s hard help cenral ci schls? Jurnal f Plic Analsis and Managemen Vl 6 : Duncmbe William and Jhn Yinger Financing higher suden perfrmance sandards: he case f New Yrk Sae. Ecnmics f Educain Review 9: Fare Rlf. Shawna Grsskpf. and William Weber. 989 Measuring schl disric perfrmance. Public Finance Quarerl 7: Fare Rlf. Shawna Grsskpf. and C.A. Kn Lvell. Prducin frniers. Cambridge MA: Cambridge Universi Press 994. Hanushek Eric A. 997 Assessing he effecs f schl resurces n suden perfrmance: An updae. Educainal Evaluain and Plic Analsis 92: Hanushek Eric A. The evidence n class size. In Earning and Learning: Hw schls maers edied b Susan E. Maer and Paul Peersn Washingn DC: Brkings Insiuin 999. Hanushek Eric A. 97 Teacher characerisics and gains in suden achievemen: Esimain using micr daa. American Ecnmic Review 62: Hanushek Eric A. 986 The ecnmics f schling: Prducin and efficienc in public schls. Jurnal f Ecnmic Lieraure 24:

12 Suhwesern Ecnmic Review Hanushek Eric A. 989 Ependiure efficienc and equi in educain: The Federal Gvernmen s rle. American Ecnmic Review 792: Hanushek Eric A. 996a A mre cmplee picure f schl resurce plicies. Review f Educainal Research LXVI: Hanushek Eric A. Schl resurces and suden perfrmance. In Gar Burless edir Des Mne Maer? The Effec f Schl Resurces n Suden Achievemen and Adul Success Washingn DC 996b: Brkings Insiuin Hanushek Eric A. and Seven G. Rivkin. 997 Undersanding he weniehcenur grwh in U.S. schl spending. Jurnal f Human Resurces 32: Hanushek Eric A. The evidence n class size. Occasinal Paper Number 98- W. Allen Wallis Insiue f Pliical Ecnm Universi f Rcheser Rcheser NY Feb 998. Krueger Alan B. Ecnmic cnsiderains and class size. Wrking Paper #447 Princen Universi Murnane Richard J. Impac f schl resurces n he learning f inner ci children. Cambridge MA: Ballinger 975. Nulas Ahanasis G. and K.W. Kekar. 998 Efficien Uilizain f Resurces in Public Schls: A Case Sud f New Jerse. Applied Ecnmics 30: Pez Tm. Cerified persnnel repr prfile: Kansas Sae Bard f Educain June Racliffe K. B. Riddle. and J. Yinger. 990 The Fiscal Cndiin f Schl Disrics in Nebraska: Is Small Beauiful? Ecnmics f Educain Review 9: Riew J. 986 Scale Ecnmies Capaci Uilizain and Schl Css: A Cmparaive Analsis f Secndar and Elemenar Schls. Jurnal f Educain Finance : Rivkin Seven G. Eric A. Hanushek and Jhn F. Kain. Teachers schls and academic achievemen. April 200. Ruggier Jhn. 200 Deermining he base cs f educain: An analsis f Ohi schl disrics. Cnemprar Ecnmic Plic Vl 93: Walberg H. and W. Fwler. 987 Ependiure and size efficiencies f public schl disrics. Educainal Research 6: ACKNOWLEDGMENTS The auhr wuld like acknwledge Helwis Tjhai Graduae Assisance Deparmen f ACIS fr arranging he enire daase fr his sud; and Dr. Jhn Pggi a he Cener fr Educainal Tesing and Evaluain Universi f Kansas Lawrence fr prviding he infrmain n achievemen es scres fr schl disrics. The auhr is graeful Dr. Edward McNerne Edir and an annmus referee fr heir helpful cmmens. The auhr bears he sle respnsibili fr he views epressed in he paper and an errr. This prjec is pariall funded b he deparmen f ACIS Schl f Business Empria Sae Universi.