STATA中SFA的实现过程.pdf

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1、StochasticFrontiers²Inthissectionwetakethemaximumlikelihoodapproachandapplyittoafairlyusefulandpowerfultool-stochasticfrontierestimation.²What'sthebasicidea?Howtoestimateeconomicrelationshipsthatoughttobemodeledasupperorlowerfrontiersratherthanaverages.²Forexample:Considerademandcurve.From

2、thetheoryofdemand,thedemandcurveisafrontierwhichtellsthe¯rmthemostitcanchargeforthemarginalunit.²EconometricsviatraditionalOLSwouldgatherPriceandQuantitydataandestimateanaveragedemandcurve.AtanyQ0themodelpredictsP0butthe¯rmcouldactuallychangePA.TheaverageOLSapproachmightoverorunderpredictp

3、rice.²Themodeltheunderpredictscoststhe¯rmmoney.Themodeltheoverpredictsmightbecatastrophic.²Frontierestimationtriesto¯xthisproblem.However,notalldataareconducetoSFA.²Uses:Productionfunctions,costfunctions,demandmodels,testofunione®ectiveness,agencycosts,reservationwages,schooloutcomes,pro¯t

4、ability,survivorship,mergerandacquisitionanalysis,e®ectofshadowinputssuchascorruption.²Considerthetraditionalproductionfunction:1²Thisisthesingleinputcasewhereq=f(X).Theslopeoftherayfromtheoriginisameasureofproductivityq=X.Notethatq=XatPointAislessthanatPointBandPointC.²Wecanimaginetechnol

5、ogicalchangeovertimewhichwouldbeashiftintheproductionfrontier²Usingmultipleinputs,thepicturechangesalittle:²PointPisine±cientrelativetoPointM.PointAisbothtechnicallyandallocativelye±ciency.²WecanmeasureTechnicalE±ciencyasTE=OM=OPandTechnicalIne±ciencyas1¡TE=1¡OM=OP.²Allocativee±ciencyismea

6、suredasON=OM·1.²Overalle±ciencyismeasuredas(OM=OP)(ON=OM)=(ON=OP)2History²Farrell(1957,JournaloftheRoyalStatisticalSociety,SeriesA):Derivesaproductionfunctionapproachandidenti¯estwosourcesof¯rmine±ciency/e±ciency1.TechnicalE±ciency:Producethemostoutputwithagivenlevelofinputs2.AllocativeE±c

7、iency:Produceagivenoutputascheaplyaspossible.²Mostofthetimewefocusontechnicale±ciencyintheexplanation²Todetermineifa¯rmise±cient,wehavetoknowtheproductionfunctionofthefullye±cient¯rm.²However,weneverknowthefullye±cientproductionfunction²Farrellsuggestedestimat