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1、StochasticFrontiers²Inthissectionwetakethemaximumlikelihoodapproachandapplyittoafairlyusefulandpowerfultool-stochasticfrontierestimation.²What'sthebasicidea?Howtoestimateeconomicrelationshipsthatoughttobemodeledasupperorlowerfrontiersratherthanaverages.²Forexample:Considerademandc
2、urve.Fromthetheoryofdemand,thedemandcurveisafrontierwhichtellsthe¯rmthemostitcanchargeforthemarginalunit.²EconometricsviatraditionalOLSwouldgatherPriceandQuantitydataandestimateanaveragedemandcurve.AtanyQ0themodelpredictsP0butthe¯rmcouldactuallychangePA.TheaverageOLSapproachmighto
3、verorunderpredictprice.²Themodeltheunderpredictscoststhe¯rmmoney.Themodeltheoverpredictsmightbecatastrophic.²Frontierestimationtriesto¯xthisproblem.However,notalldataareconducetoSFA.²Uses:Productionfunctions,costfunctions,demandmodels,testofunione®ectiveness,agencycosts,reservatio
4、nwages,schooloutcomes,pro¯tability,survivorship,mergerandacquisitionanalysis,e®ectofshadowinputssuchascorruption.²Considerthetraditionalproductionfunction:1²Thisisthesingleinputcasewhereq=f(X).Theslopeoftherayfromtheoriginisameasureofproductivityq=X.Notethatq=XatPointAislessthanat
5、PointBandPointC.²Wecanimaginetechnologicalchangeovertimewhichwouldbeashiftintheproductionfrontier²Usingmultipleinputs,thepicturechangesalittle:²PointPisine±cientrelativetoPointM.PointAisbothtechnicallyandallocativelye±ciency.²WecanmeasureTechnicalE±ciencyasTE=OM=OPandTechnicalIne±
6、ciencyas1¡TE=1¡OM=OP.²Allocativee±ciencyismeasuredasON=OM·1.²Overalle±ciencyismeasuredas(OM=OP)(ON=OM)=(ON=OP)2History²Farrell(1957,JournaloftheRoyalStatisticalSociety,SeriesA):Derivesaproductionfunctionapproachandidenti¯estwosourcesof¯rmine±ciency/e±ciency1.TechnicalE±ciency:Prod
7、ucethemostoutputwithagivenlevelofinputs2.AllocativeE±ciency:Produceagivenoutputascheaplyaspossible.²Mostofthetimewefocusontechnicale±ciencyintheexplanation²Todetermineifa¯rmise±cient,wehavetoknowtheproductionfunctionofthefullye±cient¯rm.²However,weneverknowthefullye±cientproductio
8、nfunction²Farrellsuggestedestimat
